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Merge pull request #4479 from yotamfe/bosonic-pimd-langevin

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Adding support for bosonic path integral molecular dynamics simulations
This commit is contained in:
Axel Kohlmeyer
2025-03-12 15:28:51 -04:00
committed by GitHub
parent 4246fab500 3e62e660e5
commit f097e8d951
28 changed files with 3260 additions and 56 deletions
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2
doc/src/Commands_fix.rst
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@ -162,6 +162,8 @@ OPT.
* :doc:`phonon <fix_phonon>`
* :doc:`pimd/langevin <fix_pimd>`
* :doc:`pimd/nvt <fix_pimd>`
* :doc:`pimd/langevin/bosonic <fix_pimd_bosonic>`
* :doc:`pimd/nvt/bosonic <fix_pimd_bosonic>`
* :doc:`planeforce <fix_planeforce>`
* :doc:`plumed <fix_plumed>`
* :doc:`poems <fix_poems>`

2
doc/src/fix.rst
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@ -341,6 +341,8 @@ accelerated styles exist.
* :doc:`phonon <fix_phonon>` - calculate dynamical matrix from MD simulations
* :doc:`pimd/langevin <fix_pimd>` - Feynman path-integral molecular dynamics with stochastic thermostat
* :doc:`pimd/nvt <fix_pimd>` - Feynman path-integral molecular dynamics with Nose-Hoover thermostat
* :doc:`pimd/langevin/bosonic <fix_pimd_bosonic>` - Bosonic Feynman path-integral molecular dynamics for with stochastic thermostat
* :doc:`pimd/nvt/bosonic <fix_pimd_bosonic>` - Bosonic Feynman path-integral molecular dynamics with Nose-Hoover thermostat
* :doc:`planeforce <fix_planeforce>` - constrain atoms to move in a plane
* :doc:`plumed <fix_plumed>` - wrapper on PLUMED free energy library
* :doc:`poems <fix_poems>` - constrain clusters of atoms to move as coupled rigid bodies

76
doc/src/fix_pimd.rst
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@ -1,5 +1,7 @@
.. index:: fix pimd/langevin
.. index:: fix pimd/nvt
.. index:: fix pimd/langevin/bosonic
.. index:: fix pimd/nvt/bosonic
fix pimd/langevin command
=========================
@ -7,6 +9,12 @@ fix pimd/langevin command
fix pimd/nvt command
====================
:doc:`fix pimd/langevin/bosonic <fix_pimd_bosonic>` command
===========================================================
:doc:`fix pimd/nvt/bosonic <fix_pimd_bosonic>` command
======================================================
Syntax
""""""
@ -20,34 +28,37 @@ Syntax
* keywords for style *pimd/nvt*
.. parsed-literal::
*keywords* = *method* or *fmass* or *sp* or *temp* or *nhc*
*method* value = *pimd* or *nmpimd* or *cmd*
*fmass* value = scaling factor on mass
*sp* value = scaling factor on Planck constant
*temp* value = temperature (temperature units)
*nhc* value = Nc = number of chains in Nose-Hoover thermostat
*keywords* = *method* or *fmass* or *sp* or *temp* or *nhc*
*method* value = *pimd* or *nmpimd* or *cmd*
*fmass* value = scaling factor on mass
*sp* value = scaling factor on Planck constant
*temp* value = temperature (temperature units)
*nhc* value = Nc = number of chains in Nose-Hoover thermostat
* keywords for style *pimd/langevin*
.. parsed-literal::
*keywords* = *method* or *integrator* or *ensemble* or *fmmode* or *fmass* or *scale* or *temp* or *thermostat* or *tau* or *iso* or *aniso* or *barostat* or *taup* or *fixcom* or *lj*
*method* value = *nmpimd* (default) or *pimd*
*integrator* value = *obabo* or *baoab*
*fmmode* value = *physical* or *normal*
*fmass* value = scaling factor on mass
*temp* value = temperature (temperature unit)
*keywords* = *method* or *integrator* or *ensemble* or *fmmode* or *fmass* or *scale* or *temp* or *thermostat* or *tau* or *iso* or *aniso* or *barostat* or *taup* or *fixcom* or *lj*
*method* value = *nmpimd* (default) or *pimd*
*integrator* value = *obabo* or *baoab*
*ensemble* value = *nvt* or *nve* or *nph* or *npt*
*fmmode* value = *physical* or *normal*
*fmass* value = scaling factor on mass
*temp* value = temperature (temperature unit)
temperature = target temperature of the thermostat
*thermostat* values = style seed
*thermostat* values = style seed
style value = *PILE_L*
seed = random number generator seed
*tau* value = thermostat damping parameter (time unit)
*scale* value = scaling factor of the damping times of non-centroid modes of PILE_L thermostat
*iso* or *aniso* values = pressure (pressure unit)
*tau* value = thermostat damping parameter (time unit)
*scale* value = scaling factor of the damping times of non-centroid modes of PILE_L thermostat
*iso* or *aniso* values = pressure (pressure unit)
pressure = scalar external pressure of the barostat
*barostat* value = *BZP* or *MTTK*
*taup* value = barostat damping parameter (time unit)
*fixcom* value = *yes* or *no*
*lj* values = epsilon sigma mass planck mvv2e
*barostat* value = *BZP* or *MTTK*
*taup* value = barostat damping parameter (time unit)
*fixcom* value = *yes* or *no*
*lj* values = epsilon sigma mass planck mvv2e
epsilon = energy scale for reduced units (energy units)
sigma = length scale for reduced units (length units)
mass = mass scale for reduced units (mass units)
@ -62,6 +73,8 @@ Examples
fix 1 all pimd/nvt method nmpimd fmass 1.0 sp 2.0 temp 300.0 nhc 4
fix 1 all pimd/langevin ensemble npt integrator obabo temp 113.15 thermostat PILE_L 1234 tau 1.0 iso 1.0 barostat BZP taup 1.0
Example input files are provided in the examples/PACKAGES/pimd directory.
Description
"""""""""""
@ -76,7 +89,14 @@ partition function for the original system to a classical partition
function for a ring-polymer system is exploited, to efficiently sample
configurations from the canonical ensemble :ref:`(Feynman) <Feynman>`.
The classical partition function and its components are given
.. versionadded:: 11Mar2025
Fix *pimd/langevin/bosonic* and *pimd/nvt/bosonic* were added.
Fix *pimd/nvt* and fix *pimd/langevin* simulate *distinguishable* quantum particles.
Simulations of bosons, including exchange effects, are supported with the :doc:`fix pimd/langevin/bosonic <fix_pimd_bosonic>` and :doc:`fix pimd/nvt/bosonic <fix_pimd_bosonic>` commands.
For distinguishable particles, the isomorphic classical partition function and its components are given
by the following equations:
.. math::
@ -222,7 +242,7 @@ be *PILE_L* (path integral Langevin equation local thermostat, as described in :
The keyword *tau* specifies the thermostat damping time parameter for fix style *pimd/langevin*. It is in time unit. It only works on the centroid mode.
The keyword *scale* specifies a scaling parameter for the damping times of the non-centroid modes for fix style *pimd/langevin*. The default
damping time of the non-centroid mode :math:`i` is :math:`\frac{P}{\beta\hbar}\sqrt{\lambda_i\times\mathrm{fmass}}` (*fmmode* is *physical*) or :math:`\frac{P}{\beta\hbar}\sqrt{\mathrm{fmass}}` (*fmmode* is *normal*). The damping times of all non-centroid modes are the default values divided by *scale*.
damping time of the non-centroid mode :math:`i` is :math:`\frac{P}{\beta\hbar}\sqrt{\lambda_i\times\mathrm{fmass}}` (*fmmode* is *physical*) or :math:`\frac{P}{\beta\hbar}\sqrt{\mathrm{fmass}}` (*fmmode* is *normal*). The damping times of all non-centroid modes are the default values divided by *scale*. This keyword should be used only with *method*=*nmpimd*.
The barostat parameters for fix style *pimd/langevin* with *npt* or *nph* ensemble is specified using one of *iso* and *aniso*
keywords. A *pressure* value should be given with pressure unit. The keyword *iso* means couple all 3 diagonal components together when pressure is computed (hydrostatic pressure), and dilate/contract the dimensions together. The keyword *aniso* means x, y, and z dimensions are controlled independently using the Pxx, Pyy, and Pzz components of the stress tensor as the driving forces, and the specified scalar external pressure.
@ -334,8 +354,8 @@ it outputs multiple log files, and different log files contain information
about different beads or modes (see detailed explanations below). If *ensemble*
is *nve* or *nvt*, the vector has 10 values:
#. kinetic energy of the normal mode
#. spring elastic energy of the normal mode
#. kinetic energy of the bead (if *method*=*pimd*) or normal mode (if *method*=*nmpimd*)
#. spring elastic energy of the bead (if *method*=*pimd*) or normal mode (if *method*=*nmpimd*)
#. potential energy of the bead
#. total energy of all beads (conserved if *ensemble* is *nve*)
#. primitive kinetic energy estimator
@ -412,12 +432,20 @@ variable, e.g.
velocity all create 300.0 1234${ibead} rot yes dist gaussian
Related commands
""""""""""""""""
:doc:`pimd/nvt/bosonic <fix_pimd_bosonic>`, :doc:`pimd/langevin/bosonic <fix_pimd_bosonic>`
Default
"""""""
The keyword defaults for fix *pimd/nvt* are method = pimd, fmass = 1.0, sp
= 1.0, temp = 300.0, and nhc = 2.
The keyword defaults for fix *pimd/langevin* are integrator = obabo, method = nmpimd, ensemble = nvt, fmmode = physical, fmass = 1.0,
scale = 1, temp = 298.15, thermostat = PILE_L, tau = 1.0, iso = 1.0, taup = 1.0, barostat = BZP, fixcom = yes, and lj = 1 for all its arguments.
----------
.. _Feynman:

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doc/src/fix_pimd_bosonic.rst Normal file
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@ -0,0 +1,237 @@
.. index:: fix pimd/langevin/bosonic
.. index:: fix pimd/nvt/bosonic
fix pimd/langevin/bosonic command
=================================
fix pimd/nvt/bosonic command
============================
Syntax
""""""
.. code-block:: LAMMPS
fix ID group-ID style keyword value ...
* ID, group-ID are documented in :doc:`fix <fix>` command
* style = *pimd/langevin/bosonic* or *pimd/nvt/bosonic* = style name of this fix command
* zero or more keyword/value pairs may be appended
* keywords for style *pimd/nvt/bosonic*
.. parsed-literal::
*keywords* = *method* or *fmass* or *sp* or *temp* or *nhc*
*method* value = *pimd* or *nmpimd*
*fmass* value = scaling factor on mass
*sp* value = scaling factor on Planck constant
*temp* value = temperature (temperature units)
*nhc* value = Nc = number of chains in Nose-Hoover thermostat
* keywords for style *pimd/langevin/bosonic*
.. parsed-literal::
*keywords* = *integrator* or *ensemble* or *fmass* or *temp* or *thermostat* or *tau* or *fixcom* or *lj* or *esych*
*integrator* value = *obabo* or *baoab*
*ensemble* value = *nvt* or *nve*
*fmass* value = scaling factor on mass
*temp* value = temperature (temperature unit)
temperature = target temperature of the thermostat
*thermostat* values = style seed
style value = *PILE_L*
seed = random number generator seed
*tau* value = thermostat damping parameter (time unit)
*fixcom* value = *yes* or *no*
*lj* values = epsilon sigma mass planck mvv2e
epsilon = energy scale for reduced units (energy units)
sigma = length scale for reduced units (length units)
mass = mass scale for reduced units (mass units)
planck = Planck's constant for other unit style
mvv2e = mass * velocity^2 to energy conversion factor for other unit style
*esynch* value = *yes* or *no*
Examples
""""""""
.. code-block:: LAMMPS
fix 1 all pimd/nvt/bosonic method pimd fmass 1.0 sp 1.0 temp 2.0 nhc 4
fix 1 all pimd/langevin/bosonic integrator obabo temp 113.15 thermostat PILE_L 1234 tau 1.0
Example input files are provided in the examples/PACKAGES/pimd_bosonic directory.
Description
"""""""""""
These fix commands are based on the fixes :doc:`pimd/nvt and
pimd/langevin <fix_pimd>` for performing quantum molecular dynamics
simulations based on the Feynman path-integral formalism. The key
difference is that fix *pimd/nvt* and fix *pimd/langevin* simulate
*distinguishable* particles, while fix *pimd/nvt/bosonic* and fix
*pimd/langevin/bosonic* perform simulations of bosons, including exchange
effects. The *bosonic* commands share syntax with the equivalent commands for distinguishable particles.
The user is referred to the documentation of :doc:`these commands <fix_pimd>`
for a detailed syntax description and additional, general capabilities
of the commands. The major differences from fix *pimd/nvt* and fix *pimd/langevin* in terms of
capabilities are:
* Fix *pimd/nvt/bosonic* only supports the "pimd" and "nmpimd" methods. Fix
*pimd/langevin/bosonic* only supports the "pimd" method, which is the default
in this fix. These restrictions are related to the use of normal
modes, which change in bosons. For similar reasons, *fmmode* of
*pimd/langevin* should not be used, and would raise an error if set to
a value other than *physical*.
* Fix *pimd/langevin/bosonic* currently does not support *ensemble* other than
*nve*, *nvt*. The barostat related keywords *iso*, *aniso*,
*barostat*, *taup* are not supported.
* Fix *pimd/langevin/bosonic* also has a keyword not available in fix
*pimd/langevin*: *esynch*, with default *yes*. If set to *no*, some
time consuming synchronization of spring energies and the primitive
kinetic energy estimator between processors is avoided.
The isomorphism between the partition function of :math:`N` bosonic
quantum particles and that of a system of classical ring polymers at
inverse temperature :math:`\beta` is given by :ref:`(Tuckerman)
<book-Tuckerman>`:
.. math::
Z \propto \int d{\bf q} \cdot \frac{1}{N!} \sum_\sigma \textrm{exp} [ -\beta \left( E^\sigma + V \right) ].
Here, :math:`V` is the potential between different particles at the same
imaginary time slice, which is the same for bosons and distinguishable
particles. The sum is over all permutations :math:`\sigma`. Recall that
a permutation matches each element :math:`l` in :math:`1, ..., N` to an
element :math:`\sigma(l)` in :math:`1, ..., N` without repetitions. The
energies :math:`E^\sigma` correspond to the linking of ring polymers of
different particles according to the permutations:
.. math::
E^\sigma = \frac{mP}{2\beta^2 \hbar^2} \sum_{\ell=1}^N \sum_{j=1}^P \left(\mathbf{q}_\ell^j - \mathbf{q}_\ell^{j+1}\right)^2,
where :math:`P` is the number of beads and :math:`\mathbf{q}_\ell^{P+1}=\mathbf{q}_{\sigma(\ell)}^1.`
Hirshberg et. al. showed that the ring polymer potential
:math:`-\frac{1}{\beta}\textrm{ln}\left[ \frac{1}{N!} \sum_\sigma e ^ {
-\beta E^\sigma } \right]`, which scales exponentially with :math:`N`,
can be replaced by a potential :math:`V^{[1,N]}` defined through a
recurrence relation :ref:`(Hirshberg1) <Hirshberg>`:
.. math::
e ^ { -\beta V^{[1,N]} } = \frac{1}{N} \sum_{k=1}^N e ^ { -\beta \left( V^{[1,N-k]} + E^{[N-K+1,N]} \right)}.
Here, :math:`E^{[N-K+1,N]}` is the spring energy of the ring polymer
obtained by connecting the beads of particles :math:`N - k + 1, N - k +
2, ..., N` in a cycle. This potential does not include all :math:`N!`
permutations, but samples the same bosonic partition function. The
implemented algorithm in LAMMPS for calculating the potential is the one
developed by Feldman and Hirshberg, which scales like :math:`N^2+PN`
:ref:`(Feldman) <Feldman>`. The forces are calculated as weighted
averages over the representative permutations, through an algorithm that
scales the same as the one for the potential calculation, :math:`N^2+PN`
:ref:`(Feldman) <Feldman>`. The minimum-image convention is employed on
the springs to account for periodic boundary conditions; an elaborate
discussion of the validity of the approximation is available in
:ref:`(Higer) <HigerFeldman>`.
Restart, fix_modify, output, run start/stop, minimize info
"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""
The use of :doc:`binary restart files <restart>` and :doc:`fix_modify
<fix_modify>` is the same as in :doc:`fix pimd <fix_pimd>`.
Fix *pimd/nvt/bosonic* computes a global 4-vector, which can be accessed by
various :doc:`output commands <Howto_output>`. The quantities in
the global vector are:
#. the total spring energy of the quasi-beads,
#. the current temperature of the classical system of ring polymers,
#. the current value of the scalar virial estimator for the kinetic
energy of the quantum system :ref:`(Herman) <HermanBB>` (see the justification in the supporting information of :ref:`(Hirshberg2) <HirshbergInvernizzi>`),
#. the current value of the scalar primitive estimator for the kinetic
energy of the quantum system :ref:`(Hirshberg1) <Hirshberg>`.
The vector values calculated by fix *pimd/nvt/bosonic* are "extensive", except
for the temperature, which is "intensive".
Fix *pimd/langevin/bosonic* computes a global 6-vector, which can be accessed
by various :doc:`output commands <Howto_output>`. The quantities in the
global vector are:
#. kinetic energy of the beads,
#. spring elastic energy of the beads,
#. potential energy of the bead,
#. total energy of all beads (conserved if *ensemble* is *nve*) if *esynch* is *yes*
#. primitive kinetic energy estimator :ref:`(Hirshberg1) <Hirshberg>`
#. virial energy estimator :ref:`(Herman) <HermanBB>` (see the justification in the supporting information of :ref:`(Hirshberg2) <HirshbergInvernizzi>`).
The first three are different for different log files, and the others
are the same for different log files, except for the primitive kinetic
energy estimator when setting *esynch* to *no*. Then, the primitive
kinetic energy estimator is obtained by summing over all log files.
Also note that when *esynch* is set to *no*, the fourth output gives the
total energy of all beads excluding the spring elastic energy; the total
classical energy can then be obtained by adding the sum of second output
over all log files. All vector values calculated by fix
*pimd/langevin/bosonic* are "extensive".
For both *pimd/nvt/bosonic* and *pimd/langevin/bosonic*, the contribution of the
exterior spring to the primitive estimator is printed to the first log
file. The contribution of the :math:`P-1` interior springs is printed
to the other :math:`P-1` log files. The contribution of the constant
:math:`\frac{PdN}{2 \beta}` (with :math:`d` being the dimensionality) is
equally divided over log files.
Restrictions
""""""""""""
These fixes are part of the REPLICA package. They are only enabled if
LAMMPS was built with that package. See the :doc:`Build package
<Build_package>` page for more info.
The restrictions of :doc:`fix pimd <fix_pimd>` apply.
Related commands
""""""""""""""""
:doc:`pimd/nvt <fix_pimd>`, :doc:`pimd/langevin <fix_pimd>`
Default
"""""""
The keyword defaults for fix *pimd/nvt/bosonic* are method = pimd, fmass = 1.0,
sp = 1.0, temp = 300.0, and nhc = 2.
The keyword defaults for fix *pimd/langevin/bosonic* are integrator = obabo,
method = pimd, ensemble = nvt, fmass = 1.0, temp = 298.15, thermostat =
PILE_L, tau = 1.0, fixcom = yes, esynch = yes, and lj = 1 for all its
arguments.
----------
.. _book-Tuckerman:
**(Tuckerman)** M. Tuckerman, Statistical Mechanics: Theory and Molecular Simulation (Oxford University Press, 2010)
.. _Hirshberg:
**(Hirshberg1)** B. Hirshberg, V. Rizzi, and M. Parrinello, "Path integral molecular dynamics for bosons," Proc. Natl. Acad. Sci. U. S. A. 116, 21445 (2019)
.. _HirshbergInvernizzi:
**(Hirshberg2)** B. Hirshberg, M. Invernizzi, and M. Parrinello, "Path integral molecular dynamics for fermions: Alleviating the sign problem with the Bogoliubov inequality," J Chem Phys, 152, 171102 (2020)
.. _Feldman:
**(Feldman)** Y. M. Y. Feldman and B. Hirshberg, "Quadratic scaling bosonic path integral molecular dynamics," J. Chem. Phys. 159, 154107 (2023)
.. _HigerFeldman:
**(Higer)** J. Higer, Y. M. Y. Feldman, and B. Hirshberg, "Periodic Boundary Conditions for Bosonic Path Integral Molecular Dynamics," arXiv:2501.17618 (2025)
.. _HermanBB:
**(Herman)** M. F. Herman, E. J. Bruskin, B. J. Berne, J Chem Phys, 76, 5150 (1982).

16
doc/utils/sphinx-config/false_positives.txt
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@ -8,6 +8,7 @@ abi
abo
Abramyan
absTol
Acad
Acc
Accelerys
Accelrys
@ -338,6 +339,7 @@ bodyflag
bodyforce
bodystyle
Bogaerts
Bogoliubov
Bogusz
Bohrs
boltz
@ -357,6 +359,8 @@ boostostat
boostostatting
Boresch
borophene
bosonic
bosons
Botero
Botu
Bouguet
@ -1079,6 +1083,7 @@ estretch
esu
esub
esw
esynch
et
etag
etap
@ -1142,6 +1147,7 @@ fdotr
fdt
fe
Fehlberg
Feldman
Fellinger
femtosecond
femtoseconds
@ -1151,6 +1157,8 @@ Fennell
fep
FEP
fermi
fermion
fermions
Fermionic
Ferrand
fexternal
@ -1191,6 +1199,7 @@ Finnis
Fiorin
fitpod
fivebody
fixcom
fixID
fj
Fji
@ -1211,6 +1220,7 @@ fmag
fmass
fmatch
fmm
fmmode
fmt
fmtlib
fmx
@ -1484,6 +1494,7 @@ hgrid
hhmrr
Hibbs
Higdon
Higer
hiID
Hijazi
Hilger
@ -2609,6 +2620,7 @@ nn
nnodes
npits
npj
nmpimd
nO
Nocedal
nocite
@ -2737,6 +2749,7 @@ nylo
nz
Nz
nzlo
obabo
ochre
ocl
octahedral
@ -2937,6 +2950,7 @@ Pieniazek
Pieter
pIm
pimd
pimdb
Piola
pIp
pipelining
@ -3286,6 +3300,7 @@ RiRj
Risi
Rix
Riy
Rizzi
rj
Rj
Rjinner
@ -3719,6 +3734,7 @@ Tanmoy
Tartakovsky
taskset
taubi
taup
Tavenner
taylor
tb

11
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@ -0,0 +1,11 @@
This directory contains example input files for the pimd/nvt/bosonic and pimd/langevin/bosonic fix commands.
The demonstrated system is that of 3 non-interacting bosons in a harmonic trap.
The input files initiate a simulation of 100 steps using 4 beads. The expected output log files are included.
The input files can be edited to provide a physically meaningful output, by extending the simulations to a few nanoseconds
and increasing the number of beads (32 beads should be enough).
The total energy can be computed by summing the potential energy and either the virial or primitive kinetic energy estimator, and averaging over time.
Notice that for pimd/langevin/bosonic the summed value of either kinetic estimator is printed across all log files.
It should be taken from a single log file, with all files providing the same output.
For pimd/nvt/bosonic, one has to sum over the output of all log files. For the potential energy, summing over log files is required for both fix commands.
The obtained energy should be compared to the analytical value of 0.00058031 Hartree.

57
examples/PACKAGES/pimd_bosonic/harmonic_trap_langevin/in.lmp Normal file
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@ -0,0 +1,57 @@
# Units and dimensions
units electron
dimension 3
boundary p p p
atom_style atomic
atom_modify map yes
pair_style none
# Time step (in femtoseconds)
timestep 0.5
# Temperature (in Kelvin)
variable Temp equal 17.4
# Force constant (in Hartree energies per Bohr radius squared)
variable k equal 1.2154614120000001e-08
# Number of beads
variable Nbeads equal 4
variable ibead uloop ${Nbeads} pad
variable seed equal 18889
# Create box and atoms. All distances are in Bohr
region box block -1500 1500 -1500 1500 -1500 1500
create_box 1 box
variable a loop 3
label loop
variable x1 equal -15.0+0.5*v_a
variable y1 equal 10.0-0.5*v_a
variable z1 equal 1+0.5*v_a
create_atoms 1 single ${x1} ${y1} ${z1}
next a
jump SELF loop
# Electron mass (in amu)
mass 1 0.00054858
# Initialize velocities
velocity all create ${Temp} ${seed}${ibead} mom yes rot yes dist gaussian
# Add harmonic external force
fix harm all spring/self ${k}
# Add harmonic potential energy to total energy and potential energy
fix_modify harm energy yes
# PIMD command
fix pimdb all pimd/langevin/bosonic ensemble nvt temp ${Temp} thermostat PILE_L 12345 tau 50 fixcom no
# Outputs
variable prim_kinetic equal f_pimdb[5]
variable virial equal f_pimdb[6]
thermo_style custom step pe v_virial v_prim_kinetic
thermo 1
run 100

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examples/PACKAGES/pimd_bosonic/harmonic_trap_langevin/log.lammps.0 Normal file
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@ -0,0 +1,236 @@
LAMMPS (4 Feb 2025)
Processor partition = 0
# Units and dimensions
units electron
dimension 3
boundary p p p
atom_style atomic
atom_modify map yes
pair_style none
# Time step (in femtoseconds)
timestep 0.5
# Temperature (in Kelvin)
variable Temp equal 17.4
# Force constant (in Hartree energies per Bohr radius squared)
variable k equal 1.2154614120000001e-08
# Number of beads
variable Nbeads equal 4
variable ibead uloop ${Nbeads} pad
variable ibead uloop 4 pad
variable seed equal 18889
# Create box and atoms. All distances are in Bohr
region box block -1500 1500 -1500 1500 -1500 1500
create_box 1 box
Created orthogonal box = (-1500 -1500 -1500) to (1500 1500 1500)
1 by 1 by 1 MPI processor grid
variable a loop 3
label loop
variable x1 equal -15.0+0.5*v_a
variable y1 equal 10.0-0.5*v_a
variable z1 equal 1+0.5*v_a
create_atoms 1 single ${x1} ${y1} ${z1}
create_atoms 1 single -14.5 ${y1} ${z1}
create_atoms 1 single -14.5 9.5 ${z1}
create_atoms 1 single -14.5 9.5 1.5
Created 1 atoms
using lattice units in orthogonal box = (-1500 -1500 -1500) to (1500 1500 1500)
create_atoms CPU = 0.000 seconds
next a
jump SELF loop
variable x1 equal -15.0+0.5*v_a
variable y1 equal 10.0-0.5*v_a
variable z1 equal 1+0.5*v_a
create_atoms 1 single ${x1} ${y1} ${z1}
create_atoms 1 single -14 ${y1} ${z1}
create_atoms 1 single -14 9 ${z1}
create_atoms 1 single -14 9 2
Created 1 atoms
using lattice units in orthogonal box = (-1500 -1500 -1500) to (1500 1500 1500)
create_atoms CPU = 0.000 seconds
next a
jump SELF loop
variable x1 equal -15.0+0.5*v_a
variable y1 equal 10.0-0.5*v_a
variable z1 equal 1+0.5*v_a
create_atoms 1 single ${x1} ${y1} ${z1}
create_atoms 1 single -13.5 ${y1} ${z1}
create_atoms 1 single -13.5 8.5 ${z1}
create_atoms 1 single -13.5 8.5 2.5
Created 1 atoms
using lattice units in orthogonal box = (-1500 -1500 -1500) to (1500 1500 1500)
create_atoms CPU = 0.000 seconds
next a
jump SELF loop
# Electron mass (in amu)
mass 1 0.00054858
# Initialize velocities
velocity all create ${Temp} ${seed}${ibead} mom yes rot yes dist gaussian
velocity all create 17.4 ${seed}${ibead} mom yes rot yes dist gaussian
velocity all create 17.4 18889${ibead} mom yes rot yes dist gaussian
velocity all create 17.4 188891 mom yes rot yes dist gaussian
# Add harmonic external force
fix harm all spring/self ${k}
fix harm all spring/self 1.215461412e-08
# Add harmonic potential energy to total energy and potential energy
fix_modify harm energy yes
# PIMD command
fix pimdb all pimd/langevin/bosonic ensemble nvt temp ${Temp} thermostat PILE_L 12345 tau 50 fixcom no
fix pimdb all pimd/langevin/bosonic ensemble nvt temp 17.4 thermostat PILE_L 12345 tau 50 fixcom no
# Outputs
variable prim_kinetic equal f_pimdb[5]
variable virial equal f_pimdb[6]
thermo_style custom step pe v_virial v_prim_kinetic
thermo 1
run 100
Initializing PI Langevin equation thermostat...
Bead ID | omega | tau | c1 | c2
0 9.11206647e-03 5.00000000e+01 9.95012479e-01 9.97505201e-02
1 9.11206647e-03 5.00000000e+01 9.95012479e-01 9.97505201e-02
2 9.11206647e-03 5.00000000e+01 9.95012479e-01 9.97505201e-02
3 9.11206647e-03 5.00000000e+01 9.95012479e-01 9.97505201e-02
PILE_L thermostat successfully initialized!
WARNING: No pairwise cutoff or binsize set. Atom sorting therefore disabled. (../atom.cpp:2444)
WARNING: Communication cutoff is 0.0. No ghost atoms will be generated. Atoms may get lost. (../comm_brick.cpp:212)
Per MPI rank memory allocation (min/avg/max) = 2.801 | 2.801 | 2.801 Mbytes
Step PotEng v_virial v_prim_kinetic
0 0 1.3661449e-08 0.0009918329
1 1.3158398e-09 1.8742641e-09 0.00099182267
2 5.0818396e-09 7.1801177e-09 0.00099180053
3 1.2446727e-08 1.4372388e-08 0.00099176038
4 2.1754941e-08 3.1274072e-08 0.00099170266
5 3.2927703e-08 5.2470231e-08 0.00099162511
6 4.7293056e-08 7.2301291e-08 0.00099153
7 6.526455e-08 9.5440683e-08 0.00099141194
8 8.6974168e-08 1.1669162e-07 0.00099127168
9 1.1249595e-07 1.3551097e-07 0.00099109846
10 1.4190482e-07 1.6050328e-07 0.00099089759
11 1.7313555e-07 1.8645705e-07 0.0009906735
12 2.0672874e-07 2.1181418e-07 0.00099042271
13 2.4042615e-07 2.4218941e-07 0.00099012073
14 2.7524432e-07 2.7507982e-07 0.00098977876
15 3.1513375e-07 3.1771012e-07 0.00098940169
16 3.6161087e-07 3.6075963e-07 0.00098900826
17 4.0813191e-07 4.0059005e-07 0.00098859985
18 4.5194598e-07 4.3883585e-07 0.00098817535
19 4.9898075e-07 4.8036287e-07 0.00098770764
20 5.5458728e-07 5.2362451e-07 0.00098721266
21 6.1220768e-07 5.7705077e-07 0.00098670407
22 6.6573849e-07 6.3271105e-07 0.00098617081
23 7.2475089e-07 6.9382916e-07 0.00098557406
24 7.804837e-07 7.5979853e-07 0.0009849612
25 8.3194987e-07 8.232213e-07 0.00098434971
26 8.8723792e-07 8.9901705e-07 0.0009836645
27 9.3837241e-07 9.7033126e-07 0.0009830068
28 9.897077e-07 1.0444697e-06 0.00098229311
29 1.043431e-06 1.1208219e-06 0.00098150213
30 1.0900368e-06 1.1899315e-06 0.00098077686
31 1.1303314e-06 1.2560026e-06 0.00098003518
32 1.1725968e-06 1.3287355e-06 0.00097921099
33 1.2081344e-06 1.399856e-06 0.0009784037
34 1.2449387e-06 1.4769272e-06 0.00097754491
35 1.2852285e-06 1.5642459e-06 0.00097667479
36 1.3234189e-06 1.6571388e-06 0.00097572641
37 1.3666391e-06 1.7603492e-06 0.00097475881
38 1.4102743e-06 1.8666516e-06 0.00097373763
39 1.454172e-06 1.9696572e-06 0.0009727081
40 1.5031422e-06 2.0910539e-06 0.00097155807
41 1.5538491e-06 2.2198868e-06 0.00097030871
42 1.6079193e-06 2.3576614e-06 0.00096896762
43 1.6637051e-06 2.496284e-06 0.00096760456
44 1.7189714e-06 2.637657e-06 0.00096619083
45 1.7656688e-06 2.795845e-06 0.00096470693
46 1.8092153e-06 2.9727162e-06 0.00096303835
47 1.8415769e-06 3.1451673e-06 0.00096140406
48 1.8664597e-06 3.3241907e-06 0.00095971129
49 1.8940033e-06 3.5094834e-06 0.00095790964
50 1.9211844e-06 3.7049195e-06 0.00095603039
51 1.9533838e-06 3.9139587e-06 0.0009540918
52 1.9833776e-06 4.1289537e-06 0.0009520767
53 2.0106231e-06 4.3481079e-06 0.00095003676
54 2.0429292e-06 4.5702968e-06 0.00094802906
55 2.0747842e-06 4.7928135e-06 0.00094600351
56 2.1043981e-06 5.0253448e-06 0.0009438419
57 2.1474343e-06 5.2569331e-06 0.00094169256
58 2.2115003e-06 5.4997767e-06 0.00093948055
59 2.2773037e-06 5.7547729e-06 0.00093714003
60 2.3402972e-06 6.0074589e-06 0.00093480857
61 2.4107157e-06 6.2647899e-06 0.00093244785
62 2.4953095e-06 6.5384938e-06 0.00092998209
63 2.58923e-06 6.8124372e-06 0.00092751453
64 2.682021e-06 7.0913777e-06 0.00092505171
65 2.7538688e-06 7.3773956e-06 0.00092256944
66 2.8444661e-06 7.6811232e-06 0.00091984092
67 2.9532286e-06 7.9951107e-06 0.0009170037
68 3.0551339e-06 8.3096758e-06 0.00091414977
69 3.1625164e-06 8.6232285e-06 0.00091137219
70 3.2717759e-06 8.9388929e-06 0.00090857909
71 3.3924986e-06 9.2524846e-06 0.00090583473
72 3.5236727e-06 9.5688611e-06 0.00090308342
73 3.6440162e-06 9.8873586e-06 0.00090026584
74 3.7692169e-06 1.0203245e-05 0.00089755256
75 3.8946044e-06 1.0523755e-05 0.00089485804
76 4.0498738e-06 1.0848398e-05 0.00089217189
77 4.2099346e-06 1.1164286e-05 0.00088956967
78 4.3589564e-06 1.1466652e-05 0.00088700311
79 4.5069481e-06 1.177381e-05 0.00088439373
80 4.6635354e-06 1.2059606e-05 0.00088199635
81 4.8398269e-06 1.233837e-05 0.0008797438
82 5.0191539e-06 1.261531e-05 0.00087745162
83 5.205285e-06 1.2899972e-05 0.00087506863
84 5.3708116e-06 1.3160246e-05 0.00087288444
85 5.5534416e-06 1.3438712e-05 0.00087052617
86 5.7613e-06 1.372546e-05 0.00086818634
87 5.9645662e-06 1.4017631e-05 0.00086572407
88 6.1830289e-06 1.4328439e-05 0.000862992
89 6.423646e-06 1.4640964e-05 0.00086017364
90 6.688219e-06 1.4978644e-05 0.0008570595
91 6.9305603e-06 1.5307214e-05 0.00085411601
92 7.1857573e-06 1.5649328e-05 0.00085112325
93 7.4653538e-06 1.6015833e-05 0.0008479391
94 7.8132911e-06 1.6393131e-05 0.00084474237
95 8.1540941e-06 1.674573e-05 0.00084165639
96 8.4943231e-06 1.7094435e-05 0.00083858996
97 8.8504733e-06 1.7451741e-05 0.00083536142
98 9.2042324e-06 1.780703e-05 0.00083221292
99 9.5058078e-06 1.8141862e-05 0.00082913227
100 9.8087647e-06 1.8457846e-05 0.00082619877
Loop time of 0.122922 on 1 procs for 100 steps with 3 atoms
Performance: 35144210.362 fs/day, 0.000 hours/fs, 813.523 timesteps/s, 2.441 katom-step/s
70.1% CPU use with 1 MPI tasks x no OpenMP threads
MPI task timing breakdown:
Section | min time | avg time | max time |%varavg| %total
---------------------------------------------------------------
Pair | 0 | 0 | 0 | 0.0 | 0.00
Neigh | 1.1593e-05 | 1.1593e-05 | 1.1593e-05 | 0.0 | 0.01
Comm | 9.2183e-05 | 9.2183e-05 | 9.2183e-05 | 0.0 | 0.07
Output | 0.023243 | 0.023243 | 0.023243 | 0.0 | 18.91
Modify | 0.099386 | 0.099386 | 0.099386 | 0.0 | 80.85
Other | | 0.0001896 | | | 0.15
Nlocal: 3 ave 3 max 3 min
Histogram: 1 0 0 0 0 0 0 0 0 0
Nghost: 0 ave 0 max 0 min
Histogram: 1 0 0 0 0 0 0 0 0 0
Neighs: 0 ave 0 max 0 min
Histogram: 1 0 0 0 0 0 0 0 0 0
Total # of neighbors = 0
Ave neighs/atom = 0
Neighbor list builds = 33
Dangerous builds = 0

228
examples/PACKAGES/pimd_bosonic/harmonic_trap_langevin/log.lammps.1 Normal file
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@ -0,0 +1,228 @@
LAMMPS (4 Feb 2025)
Processor partition = 1
# Units and dimensions
units electron
dimension 3
boundary p p p
atom_style atomic
atom_modify map yes
pair_style none
# Time step (in femtoseconds)
timestep 0.5
# Temperature (in Kelvin)
variable Temp equal 17.4
# Force constant (in Hartree energies per Bohr radius squared)
variable k equal 1.2154614120000001e-08
# Number of beads
variable Nbeads equal 4
variable ibead uloop ${Nbeads} pad
variable ibead uloop 4 pad
variable seed equal 18889
# Create box and atoms. All distances are in Bohr
region box block -1500 1500 -1500 1500 -1500 1500
create_box 1 box
Created orthogonal box = (-1500 -1500 -1500) to (1500 1500 1500)
1 by 1 by 1 MPI processor grid
variable a loop 3
label loop
variable x1 equal -15.0+0.5*v_a
variable y1 equal 10.0-0.5*v_a
variable z1 equal 1+0.5*v_a
create_atoms 1 single ${x1} ${y1} ${z1}
create_atoms 1 single -14.5 ${y1} ${z1}
create_atoms 1 single -14.5 9.5 ${z1}
create_atoms 1 single -14.5 9.5 1.5
Created 1 atoms
using lattice units in orthogonal box = (-1500 -1500 -1500) to (1500 1500 1500)
create_atoms CPU = 0.000 seconds
next a
jump SELF loop
variable x1 equal -15.0+0.5*v_a
variable y1 equal 10.0-0.5*v_a
variable z1 equal 1+0.5*v_a
create_atoms 1 single ${x1} ${y1} ${z1}
create_atoms 1 single -14 ${y1} ${z1}
create_atoms 1 single -14 9 ${z1}
create_atoms 1 single -14 9 2
Created 1 atoms
using lattice units in orthogonal box = (-1500 -1500 -1500) to (1500 1500 1500)
create_atoms CPU = 0.000 seconds
next a
jump SELF loop
variable x1 equal -15.0+0.5*v_a
variable y1 equal 10.0-0.5*v_a
variable z1 equal 1+0.5*v_a
create_atoms 1 single ${x1} ${y1} ${z1}
create_atoms 1 single -13.5 ${y1} ${z1}
create_atoms 1 single -13.5 8.5 ${z1}
create_atoms 1 single -13.5 8.5 2.5
Created 1 atoms
using lattice units in orthogonal box = (-1500 -1500 -1500) to (1500 1500 1500)
create_atoms CPU = 0.000 seconds
next a
jump SELF loop
# Electron mass (in amu)
mass 1 0.00054858
# Initialize velocities
velocity all create ${Temp} ${seed}${ibead} mom yes rot yes dist gaussian
velocity all create 17.4 ${seed}${ibead} mom yes rot yes dist gaussian
velocity all create 17.4 18889${ibead} mom yes rot yes dist gaussian
velocity all create 17.4 188892 mom yes rot yes dist gaussian
# Add harmonic external force
fix harm all spring/self ${k}
fix harm all spring/self 1.215461412e-08
# Add harmonic potential energy to total energy and potential energy
fix_modify harm energy yes
# PIMD command
fix pimdb all pimd/langevin/bosonic ensemble nvt temp ${Temp} thermostat PILE_L 12345 tau 50 fixcom no
fix pimdb all pimd/langevin/bosonic ensemble nvt temp 17.4 thermostat PILE_L 12345 tau 50 fixcom no
# Outputs
variable prim_kinetic equal f_pimdb[5]
variable virial equal f_pimdb[6]
thermo_style custom step pe v_virial v_prim_kinetic
thermo 1
run 100
WARNING: No pairwise cutoff or binsize set. Atom sorting therefore disabled. (../atom.cpp:2444)
WARNING: Communication cutoff is 0.0. No ghost atoms will be generated. Atoms may get lost. (../comm_brick.cpp:212)
Per MPI rank memory allocation (min/avg/max) = 2.801 | 2.801 | 2.801 Mbytes
Step PotEng v_virial v_prim_kinetic
0 0 1.3661449e-08 0.0009918329
1 7.3810761e-10 1.8742641e-09 0.00099182267
2 3.0654593e-09 7.1801177e-09 0.00099180053
3 6.4534507e-09 1.4372388e-08 0.00099176038
4 1.1681892e-08 3.1274072e-08 0.00099170266
5 1.8404818e-08 5.2470231e-08 0.00099162511
6 2.6171374e-08 7.2301291e-08 0.00099153
7 3.5990441e-08 9.5440683e-08 0.00099141194
8 4.9770229e-08 1.1669162e-07 0.00099127168
9 6.6159035e-08 1.3551097e-07 0.00099109846
10 8.7281867e-08 1.6050328e-07 0.00099089759
11 1.1505206e-07 1.8645705e-07 0.0009906735
12 1.4564491e-07 2.1181418e-07 0.00099042271
13 1.8674942e-07 2.4218941e-07 0.00099012073
14 2.3275077e-07 2.7507982e-07 0.00098977876
15 2.833552e-07 3.1771012e-07 0.00098940169
16 3.3078875e-07 3.6075963e-07 0.00098900826
17 3.7783787e-07 4.0059005e-07 0.00098859985
18 4.3007763e-07 4.3883585e-07 0.00098817535
19 4.8592613e-07 4.8036287e-07 0.00098770764
20 5.4429898e-07 5.2362451e-07 0.00098721266
21 6.0140068e-07 5.7705077e-07 0.00098670407
22 6.6036274e-07 6.3271105e-07 0.00098617081
23 7.3748601e-07 6.9382916e-07 0.00098557406
24 8.1086859e-07 7.5979853e-07 0.0009849612
25 8.8638234e-07 8.232213e-07 0.00098434971
26 9.8252709e-07 8.9901705e-07 0.0009836645
27 1.0768657e-06 9.7033126e-07 0.0009830068
28 1.1810654e-06 1.0444697e-06 0.00098229311
29 1.2964318e-06 1.1208219e-06 0.00098150213
30 1.4097624e-06 1.1899315e-06 0.00098077686
31 1.5368367e-06 1.2560026e-06 0.00098003518
32 1.6777082e-06 1.3287355e-06 0.00097921099
33 1.8186759e-06 1.399856e-06 0.0009784037
34 1.9730383e-06 1.4769272e-06 0.00097754491
35 2.1285065e-06 1.5642459e-06 0.00097667479
36 2.2809575e-06 1.6571388e-06 0.00097572641
37 2.4393024e-06 1.7603492e-06 0.00097475881
38 2.6212592e-06 1.8666516e-06 0.00097373763
39 2.8115312e-06 1.9696572e-06 0.0009727081
40 3.0115212e-06 2.0910539e-06 0.00097155807
41 3.2325069e-06 2.2198868e-06 0.00097030871
42 3.4582526e-06 2.3576614e-06 0.00096896762
43 3.6838101e-06 2.496284e-06 0.00096760456
44 3.9267475e-06 2.637657e-06 0.00096619083
45 4.1942569e-06 2.795845e-06 0.00096470693
46 4.4694976e-06 2.9727162e-06 0.00096303835
47 4.7570486e-06 3.1451673e-06 0.00096140406
48 5.0917213e-06 3.3241907e-06 0.00095971129
49 5.4581889e-06 3.5094834e-06 0.00095790964
50 5.8607381e-06 3.7049195e-06 0.00095603039
51 6.2673583e-06 3.9139587e-06 0.0009540918
52 6.6764632e-06 4.1289537e-06 0.0009520767
53 7.0828028e-06 4.3481079e-06 0.00095003676
54 7.4858144e-06 4.5702968e-06 0.00094802906
55 7.8711706e-06 4.7928135e-06 0.00094600351
56 8.2756726e-06 5.0253448e-06 0.0009438419
57 8.6667628e-06 5.2569331e-06 0.00094169256
58 9.0585083e-06 5.4997767e-06 0.00093948055
59 9.4634766e-06 5.7547729e-06 0.00093714003
60 9.8696653e-06 6.0074589e-06 0.00093480857
61 1.0308345e-05 6.2647899e-06 0.00093244785
62 1.0757919e-05 6.5384938e-06 0.00092998209
63 1.1183568e-05 6.8124372e-06 0.00092751453
64 1.1585073e-05 7.0913777e-06 0.00092505171
65 1.1993605e-05 7.3773956e-06 0.00092256944
66 1.2382612e-05 7.6811232e-06 0.00091984092
67 1.2768116e-05 7.9951107e-06 0.0009170037
68 1.3181941e-05 8.3096758e-06 0.00091414977
69 1.3605472e-05 8.6232285e-06 0.00091137219
70 1.4027012e-05 8.9388929e-06 0.00090857909
71 1.4471706e-05 9.2524846e-06 0.00090583473
72 1.4896833e-05 9.5688611e-06 0.00090308342
73 1.5345003e-05 9.8873586e-06 0.00090026584
74 1.5779905e-05 1.0203245e-05 0.00089755256
75 1.6189898e-05 1.0523755e-05 0.00089485804
76 1.6654778e-05 1.0848398e-05 0.00089217189
77 1.7131363e-05 1.1164286e-05 0.00088956967
78 1.7572176e-05 1.1466652e-05 0.00088700311
79 1.8000817e-05 1.177381e-05 0.00088439373
80 1.838117e-05 1.2059606e-05 0.00088199635
81 1.8762432e-05 1.233837e-05 0.0008797438
82 1.9099052e-05 1.261531e-05 0.00087745162
83 1.9507863e-05 1.2899972e-05 0.00087506863
84 1.9885648e-05 1.3160246e-05 0.00087288444
85 2.0266439e-05 1.3438712e-05 0.00087052617
86 2.0612316e-05 1.372546e-05 0.00086818634
87 2.0959061e-05 1.4017631e-05 0.00086572407
88 2.13065e-05 1.4328439e-05 0.000862992
89 2.1634898e-05 1.4640964e-05 0.00086017364
90 2.2023174e-05 1.4978644e-05 0.0008570595
91 2.2431573e-05 1.5307214e-05 0.00085411601
92 2.2872283e-05 1.5649328e-05 0.00085112325
93 2.338476e-05 1.6015833e-05 0.0008479391
94 2.3912199e-05 1.6393131e-05 0.00084474237
95 2.437725e-05 1.674573e-05 0.00084165639
96 2.4828999e-05 1.7094435e-05 0.00083858996
97 2.5286762e-05 1.7451741e-05 0.00083536142
98 2.5769956e-05 1.780703e-05 0.00083221292
99 2.624134e-05 1.8141862e-05 0.00082913227
100 2.6731735e-05 1.8457846e-05 0.00082619877
Loop time of 0.122878 on 1 procs for 100 steps with 3 atoms
Performance: 35156789.883 fs/day, 0.000 hours/fs, 813.815 timesteps/s, 2.441 katom-step/s
46.7% CPU use with 1 MPI tasks x no OpenMP threads
MPI task timing breakdown:
Section | min time | avg time | max time |%varavg| %total
---------------------------------------------------------------
Pair | 0 | 0 | 0 | 0.0 | 0.00
Neigh | 1.9787e-05 | 1.9787e-05 | 1.9787e-05 | 0.0 | 0.02
Comm | 9.2033e-05 | 9.2033e-05 | 9.2033e-05 | 0.0 | 0.07
Output | 0.0022584 | 0.0022584 | 0.0022584 | 0.0 | 1.84
Modify | 0.12033 | 0.12033 | 0.12033 | 0.0 | 97.93
Other | | 0.0001755 | | | 0.14
Nlocal: 3 ave 3 max 3 min
Histogram: 1 0 0 0 0 0 0 0 0 0
Nghost: 0 ave 0 max 0 min
Histogram: 1 0 0 0 0 0 0 0 0 0
Neighs: 0 ave 0 max 0 min
Histogram: 1 0 0 0 0 0 0 0 0 0
Total # of neighbors = 0
Ave neighs/atom = 0
Neighbor list builds = 44
Dangerous builds = 0

228
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LAMMPS (4 Feb 2025)
Processor partition = 2
# Units and dimensions
units electron
dimension 3
boundary p p p
atom_style atomic
atom_modify map yes
pair_style none
# Time step (in femtoseconds)
timestep 0.5
# Temperature (in Kelvin)
variable Temp equal 17.4
# Force constant (in Hartree energies per Bohr radius squared)
variable k equal 1.2154614120000001e-08
# Number of beads
variable Nbeads equal 4
variable ibead uloop ${Nbeads} pad
variable ibead uloop 4 pad
variable seed equal 18889
# Create box and atoms. All distances are in Bohr
region box block -1500 1500 -1500 1500 -1500 1500
create_box 1 box
Created orthogonal box = (-1500 -1500 -1500) to (1500 1500 1500)
1 by 1 by 1 MPI processor grid
variable a loop 3
label loop
variable x1 equal -15.0+0.5*v_a
variable y1 equal 10.0-0.5*v_a
variable z1 equal 1+0.5*v_a
create_atoms 1 single ${x1} ${y1} ${z1}
create_atoms 1 single -14.5 ${y1} ${z1}
create_atoms 1 single -14.5 9.5 ${z1}
create_atoms 1 single -14.5 9.5 1.5
Created 1 atoms
using lattice units in orthogonal box = (-1500 -1500 -1500) to (1500 1500 1500)
create_atoms CPU = 0.000 seconds
next a
jump SELF loop
variable x1 equal -15.0+0.5*v_a
variable y1 equal 10.0-0.5*v_a
variable z1 equal 1+0.5*v_a
create_atoms 1 single ${x1} ${y1} ${z1}
create_atoms 1 single -14 ${y1} ${z1}
create_atoms 1 single -14 9 ${z1}
create_atoms 1 single -14 9 2
Created 1 atoms
using lattice units in orthogonal box = (-1500 -1500 -1500) to (1500 1500 1500)
create_atoms CPU = 0.000 seconds
next a
jump SELF loop
variable x1 equal -15.0+0.5*v_a
variable y1 equal 10.0-0.5*v_a
variable z1 equal 1+0.5*v_a
create_atoms 1 single ${x1} ${y1} ${z1}
create_atoms 1 single -13.5 ${y1} ${z1}
create_atoms 1 single -13.5 8.5 ${z1}
create_atoms 1 single -13.5 8.5 2.5
Created 1 atoms
using lattice units in orthogonal box = (-1500 -1500 -1500) to (1500 1500 1500)
create_atoms CPU = 0.000 seconds
next a
jump SELF loop
# Electron mass (in amu)
mass 1 0.00054858
# Initialize velocities
velocity all create ${Temp} ${seed}${ibead} mom yes rot yes dist gaussian
velocity all create 17.4 ${seed}${ibead} mom yes rot yes dist gaussian
velocity all create 17.4 18889${ibead} mom yes rot yes dist gaussian
velocity all create 17.4 188893 mom yes rot yes dist gaussian
# Add harmonic external force
fix harm all spring/self ${k}
fix harm all spring/self 1.215461412e-08
# Add harmonic potential energy to total energy and potential energy
fix_modify harm energy yes
# PIMD command
fix pimdb all pimd/langevin/bosonic ensemble nvt temp ${Temp} thermostat PILE_L 12345 tau 50 fixcom no
fix pimdb all pimd/langevin/bosonic ensemble nvt temp 17.4 thermostat PILE_L 12345 tau 50 fixcom no
# Outputs
variable prim_kinetic equal f_pimdb[5]
variable virial equal f_pimdb[6]
thermo_style custom step pe v_virial v_prim_kinetic
thermo 1
run 100
WARNING: No pairwise cutoff or binsize set. Atom sorting therefore disabled. (../atom.cpp:2444)
WARNING: Communication cutoff is 0.0. No ghost atoms will be generated. Atoms may get lost. (../comm_brick.cpp:212)
Per MPI rank memory allocation (min/avg/max) = 2.801 | 2.801 | 2.801 Mbytes
Step PotEng v_virial v_prim_kinetic
0 0 1.3661449e-08 0.0009918329
1 8.3480048e-10 1.8742641e-09 0.00099182267
2 2.8201389e-09 7.1801177e-09 0.00099180053
3 7.3605781e-09 1.4372388e-08 0.00099176038
4 1.4967393e-08 3.1274072e-08 0.00099170266
5 2.4978087e-08 5.2470231e-08 0.00099162511
6 3.5908849e-08 7.2301291e-08 0.00099153
7 4.8226614e-08 9.5440683e-08 0.00099141194
8 6.3621045e-08 1.1669162e-07 0.00099127168
9 8.0119736e-08 1.3551097e-07 0.00099109846
10 9.7965614e-08 1.6050328e-07 0.00099089759
11 1.1538858e-07 1.8645705e-07 0.0009906735
12 1.365443e-07 2.1181418e-07 0.00099042271
13 1.5920175e-07 2.4218941e-07 0.00099012073
14 1.8252589e-07 2.7507982e-07 0.00098977876
15 2.0858909e-07 3.1771012e-07 0.00098940169
16 2.3676046e-07 3.6075963e-07 0.00098900826
17 2.689757e-07 4.0059005e-07 0.00098859985
18 3.0022172e-07 4.3883585e-07 0.00098817535
19 3.3127637e-07 4.8036287e-07 0.00098770764
20 3.6044366e-07 5.2362451e-07 0.00098721266
21 3.8484646e-07 5.7705077e-07 0.00098670407
22 4.1435067e-07 6.3271105e-07 0.00098617081
23 4.4508994e-07 6.9382916e-07 0.00098557406
24 4.7879333e-07 7.5979853e-07 0.0009849612
25 5.0918223e-07 8.232213e-07 0.00098434971
26 5.4733661e-07 8.9901705e-07 0.0009836645
27 5.7932115e-07 9.7033126e-07 0.0009830068
28 6.1775401e-07 1.0444697e-06 0.00098229311
29 6.6883535e-07 1.1208219e-06 0.00098150213
30 7.0943445e-07 1.1899315e-06 0.00098077686
31 7.4477897e-07 1.2560026e-06 0.00098003518
32 7.8183156e-07 1.3287355e-06 0.00097921099
33 8.1987667e-07 1.399856e-06 0.0009784037
34 8.5514962e-07 1.4769272e-06 0.00097754491
35 8.9607784e-07 1.5642459e-06 0.00097667479
36 9.4986753e-07 1.6571388e-06 0.00097572641
37 1.0024729e-06 1.7603492e-06 0.00097475881
38 1.0526731e-06 1.8666516e-06 0.00097373763
39 1.103419e-06 1.9696572e-06 0.0009727081
40 1.1640352e-06 2.0910539e-06 0.00097155807
41 1.2292837e-06 2.2198868e-06 0.00097030871
42 1.3024454e-06 2.3576614e-06 0.00096896762
43 1.3788736e-06 2.496284e-06 0.00096760456
44 1.4503248e-06 2.637657e-06 0.00096619083
45 1.5334106e-06 2.795845e-06 0.00096470693
46 1.6246777e-06 2.9727162e-06 0.00096303835
47 1.715884e-06 3.1451673e-06 0.00096140406
48 1.8096683e-06 3.3241907e-06 0.00095971129
49 1.916714e-06 3.5094834e-06 0.00095790964
50 2.0374848e-06 3.7049195e-06 0.00095603039
51 2.1747488e-06 3.9139587e-06 0.0009540918
52 2.3236882e-06 4.1289537e-06 0.0009520767
53 2.4790586e-06 4.3481079e-06 0.00095003676
54 2.6478101e-06 4.5702968e-06 0.00094802906
55 2.8275135e-06 4.7928135e-06 0.00094600351
56 3.0338638e-06 5.0253448e-06 0.0009438419
57 3.2428318e-06 5.2569331e-06 0.00094169256
58 3.4414566e-06 5.4997767e-06 0.00093948055
59 3.6324968e-06 5.7547729e-06 0.00093714003
60 3.8269172e-06 6.0074589e-06 0.00093480857
61 4.0183315e-06 6.2647899e-06 0.00093244785
62 4.2263009e-06 6.5384938e-06 0.00092998209
63 4.4382735e-06 6.8124372e-06 0.00092751453
64 4.6488232e-06 7.0913777e-06 0.00092505171
65 4.8707403e-06 7.3773956e-06 0.00092256944
66 5.1178339e-06 7.6811232e-06 0.00091984092
67 5.377713e-06 7.9951107e-06 0.0009170037
68 5.63843e-06 8.3096758e-06 0.00091414977
69 5.8975743e-06 8.6232285e-06 0.00091137219
70 6.168921e-06 8.9388929e-06 0.00090857909
71 6.4488238e-06 9.2524846e-06 0.00090583473
72 6.7115203e-06 9.5688611e-06 0.00090308342
73 6.995134e-06 9.8873586e-06 0.00090026584
74 7.284199e-06 1.0203245e-05 0.00089755256
75 7.6029528e-06 1.0523755e-05 0.00089485804
76 7.9431391e-06 1.0848398e-05 0.00089217189
77 8.2768015e-06 1.1164286e-05 0.00088956967
78 8.6058917e-06 1.1466652e-05 0.00088700311
79 8.9683477e-06 1.177381e-05 0.00088439373
80 9.3324487e-06 1.2059606e-05 0.00088199635
81 9.6876036e-06 1.233837e-05 0.0008797438
82 1.0061754e-05 1.261531e-05 0.00087745162
83 1.0457019e-05 1.2899972e-05 0.00087506863
84 1.0866064e-05 1.3160246e-05 0.00087288444
85 1.1298832e-05 1.3438712e-05 0.00087052617
86 1.1762526e-05 1.372546e-05 0.00086818634
87 1.2264941e-05 1.4017631e-05 0.00086572407
88 1.2784125e-05 1.4328439e-05 0.000862992
89 1.332533e-05 1.4640964e-05 0.00086017364
90 1.3897966e-05 1.4978644e-05 0.0008570595
91 1.4473024e-05 1.5307214e-05 0.00085411601
92 1.5067033e-05 1.5649328e-05 0.00085112325
93 1.5677943e-05 1.6015833e-05 0.0008479391
94 1.6254294e-05 1.6393131e-05 0.00084474237
95 1.6791089e-05 1.674573e-05 0.00084165639
96 1.7362795e-05 1.7094435e-05 0.00083858996
97 1.7961498e-05 1.7451741e-05 0.00083536142
98 1.8568337e-05 1.780703e-05 0.00083221292
99 1.9188379e-05 1.8141862e-05 0.00082913227
100 1.9789011e-05 1.8457846e-05 0.00082619877
Loop time of 0.112003 on 1 procs for 100 steps with 3 atoms
Performance: 38570373.396 fs/day, 0.000 hours/fs, 892.833 timesteps/s, 2.678 katom-step/s
52.7% CPU use with 1 MPI tasks x no OpenMP threads
MPI task timing breakdown:
Section | min time | avg time | max time |%varavg| %total
---------------------------------------------------------------
Pair | 0 | 0 | 0 | 0.0 | 0.00
Neigh | 1.4356e-05 | 1.4356e-05 | 1.4356e-05 | 0.0 | 0.01
Comm | 9.7936e-05 | 9.7936e-05 | 9.7936e-05 | 0.0 | 0.09
Output | 0.0017373 | 0.0017373 | 0.0017373 | 0.0 | 1.55
Modify | 0.10997 | 0.10997 | 0.10997 | 0.0 | 98.19
Other | | 0.0001804 | | | 0.16
Nlocal: 3 ave 3 max 3 min
Histogram: 1 0 0 0 0 0 0 0 0 0
Nghost: 0 ave 0 max 0 min
Histogram: 1 0 0 0 0 0 0 0 0 0
Neighs: 0 ave 0 max 0 min
Histogram: 1 0 0 0 0 0 0 0 0 0
Total # of neighbors = 0
Ave neighs/atom = 0
Neighbor list builds = 41
Dangerous builds = 0

228
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LAMMPS (4 Feb 2025)
Processor partition = 3
# Units and dimensions
units electron
dimension 3
boundary p p p
atom_style atomic
atom_modify map yes
pair_style none
# Time step (in femtoseconds)
timestep 0.5
# Temperature (in Kelvin)
variable Temp equal 17.4
# Force constant (in Hartree energies per Bohr radius squared)
variable k equal 1.2154614120000001e-08
# Number of beads
variable Nbeads equal 4
variable ibead uloop ${Nbeads} pad
variable ibead uloop 4 pad
variable seed equal 18889
# Create box and atoms. All distances are in Bohr
region box block -1500 1500 -1500 1500 -1500 1500
create_box 1 box
Created orthogonal box = (-1500 -1500 -1500) to (1500 1500 1500)
1 by 1 by 1 MPI processor grid
variable a loop 3
label loop
variable x1 equal -15.0+0.5*v_a
variable y1 equal 10.0-0.5*v_a
variable z1 equal 1+0.5*v_a
create_atoms 1 single ${x1} ${y1} ${z1}
create_atoms 1 single -14.5 ${y1} ${z1}
create_atoms 1 single -14.5 9.5 ${z1}
create_atoms 1 single -14.5 9.5 1.5
Created 1 atoms
using lattice units in orthogonal box = (-1500 -1500 -1500) to (1500 1500 1500)
create_atoms CPU = 0.000 seconds
next a
jump SELF loop
variable x1 equal -15.0+0.5*v_a
variable y1 equal 10.0-0.5*v_a
variable z1 equal 1+0.5*v_a
create_atoms 1 single ${x1} ${y1} ${z1}
create_atoms 1 single -14 ${y1} ${z1}
create_atoms 1 single -14 9 ${z1}
create_atoms 1 single -14 9 2
Created 1 atoms
using lattice units in orthogonal box = (-1500 -1500 -1500) to (1500 1500 1500)
create_atoms CPU = 0.000 seconds
next a
jump SELF loop
variable x1 equal -15.0+0.5*v_a
variable y1 equal 10.0-0.5*v_a
variable z1 equal 1+0.5*v_a
create_atoms 1 single ${x1} ${y1} ${z1}
create_atoms 1 single -13.5 ${y1} ${z1}
create_atoms 1 single -13.5 8.5 ${z1}
create_atoms 1 single -13.5 8.5 2.5
Created 1 atoms
using lattice units in orthogonal box = (-1500 -1500 -1500) to (1500 1500 1500)
create_atoms CPU = 0.000 seconds
next a
jump SELF loop
# Electron mass (in amu)
mass 1 0.00054858
# Initialize velocities
velocity all create ${Temp} ${seed}${ibead} mom yes rot yes dist gaussian
velocity all create 17.4 ${seed}${ibead} mom yes rot yes dist gaussian
velocity all create 17.4 18889${ibead} mom yes rot yes dist gaussian
velocity all create 17.4 188894 mom yes rot yes dist gaussian
# Add harmonic external force
fix harm all spring/self ${k}
fix harm all spring/self 1.215461412e-08
# Add harmonic potential energy to total energy and potential energy
fix_modify harm energy yes
# PIMD command
fix pimdb all pimd/langevin/bosonic ensemble nvt temp ${Temp} thermostat PILE_L 12345 tau 50 fixcom no
fix pimdb all pimd/langevin/bosonic ensemble nvt temp 17.4 thermostat PILE_L 12345 tau 50 fixcom no
# Outputs
variable prim_kinetic equal f_pimdb[5]
variable virial equal f_pimdb[6]
thermo_style custom step pe v_virial v_prim_kinetic
thermo 1
run 100
WARNING: No pairwise cutoff or binsize set. Atom sorting therefore disabled. (../atom.cpp:2444)
WARNING: Communication cutoff is 0.0. No ghost atoms will be generated. Atoms may get lost. (../comm_brick.cpp:212)
Per MPI rank memory allocation (min/avg/max) = 2.801 | 2.801 | 2.801 Mbytes
Step PotEng v_virial v_prim_kinetic
0 0 1.3661449e-08 0.0009918329
1 8.448696e-10 1.8742641e-09 0.00099182267
2 3.5286528e-09 7.1801177e-09 0.00099180053
3 8.2936659e-09 1.4372388e-08 0.00099176038
4 1.4586045e-08 3.1274072e-08 0.00099170266
5 2.4161875e-08 5.2470231e-08 0.00099162511
6 3.8801085e-08 7.2301291e-08 0.00099153
7 5.9758384e-08 9.5440683e-08 0.00099141194
8 8.5838823e-08 1.1669162e-07 0.00099127168
9 1.1684437e-07 1.3551097e-07 0.00099109846
10 1.4954974e-07 1.6050328e-07 0.00099089759
11 1.8686687e-07 1.8645705e-07 0.0009906735
12 2.2747543e-07 2.1181418e-07 0.00099042271
13 2.807392e-07 2.4218941e-07 0.00099012073
14 3.3827867e-07 2.7507982e-07 0.00098977876
15 3.9918359e-07 3.1771012e-07 0.00098940169
16 4.6034561e-07 3.6075963e-07 0.00098900826
17 5.2315136e-07 4.0059005e-07 0.00098859985
18 5.8457073e-07 4.3883585e-07 0.00098817535
19 6.5273892e-07 4.8036287e-07 0.00098770764
20 7.2150647e-07 5.2362451e-07 0.00098721266
21 8.0596691e-07 5.7705077e-07 0.00098670407
22 8.946994e-07 6.3271105e-07 0.00098617081
23 9.9120142e-07 6.9382916e-07 0.00098557406
24 1.09722e-06 7.5979853e-07 0.0009849612
25 1.2053692e-06 8.232213e-07 0.00098434971
26 1.3196547e-06 8.9901705e-07 0.0009836645
27 1.4380033e-06 9.7033126e-07 0.0009830068
28 1.5700587e-06 1.0444697e-06 0.00098229311
29 1.7089133e-06 1.1208219e-06 0.00098150213
30 1.839944e-06 1.1899315e-06 0.00098077686
31 1.9718088e-06 1.2560026e-06 0.00098003518
32 2.1244847e-06 1.3287355e-06 0.00097921099
33 2.2823018e-06 1.399856e-06 0.0009784037
34 2.4607034e-06 1.4769272e-06 0.00097754491
35 2.6410061e-06 1.5642459e-06 0.00097667479
36 2.8395019e-06 1.6571388e-06 0.00097572641
37 3.0476467e-06 1.7603492e-06 0.00097475881
38 3.2661567e-06 1.8666516e-06 0.00097373763
39 3.4857766e-06 1.9696572e-06 0.0009727081
40 3.7310241e-06 2.0910539e-06 0.00097155807
41 3.9947356e-06 2.2198868e-06 0.00097030871
42 4.2722057e-06 2.3576614e-06 0.00096896762
43 4.5444932e-06 2.496284e-06 0.00096760456
44 4.8307956e-06 2.637657e-06 0.00096619083
45 5.1356773e-06 2.795845e-06 0.00096470693
46 5.4835294e-06 2.9727162e-06 0.00096303835
47 5.8235502e-06 3.1451673e-06 0.00096140406
48 6.1541132e-06 3.3241907e-06 0.00095971129
49 6.4796693e-06 3.5094834e-06 0.00095790964
50 6.8009213e-06 3.7049195e-06 0.00095603039
51 7.1253629e-06 3.9139587e-06 0.0009540918
52 7.4712081e-06 4.1289537e-06 0.0009520767
53 7.8322309e-06 4.3481079e-06 0.00095003676
54 8.1941694e-06 4.5702968e-06 0.00094802906
55 8.579188e-06 4.7928135e-06 0.00094600351
56 8.9656493e-06 5.0253448e-06 0.0009438419
57 9.351102e-06 5.2569331e-06 0.00094169256
58 9.7645407e-06 5.4997767e-06 0.00093948055
59 1.0230434e-05 5.7547729e-06 0.00093714003
60 1.0724041e-05 6.0074589e-06 0.00093480857
61 1.1207453e-05 6.2647899e-06 0.00093244785
62 1.171285e-05 6.5384938e-06 0.00092998209
63 1.221299e-05 6.8124372e-06 0.00092751453
64 1.2743686e-05 7.0913777e-06 0.00092505171
65 1.3295725e-05 7.3773956e-06 0.00092256944
66 1.3906023e-05 7.6811232e-06 0.00091984092
67 1.4511348e-05 7.9951107e-06 0.0009170037
68 1.5116776e-05 8.3096758e-06 0.00091414977
69 1.571005e-05 8.6232285e-06 0.00091137219
70 1.6297136e-05 8.9388929e-06 0.00090857909
71 1.6849099e-05 9.2524846e-06 0.00090583473
72 1.7417168e-05 9.5688611e-06 0.00090308342
73 1.7971613e-05 9.8873586e-06 0.00090026584
74 1.8509472e-05 1.0203245e-05 0.00089755256
75 1.9047825e-05 1.0523755e-05 0.00089485804
76 1.9510646e-05 1.0848398e-05 0.00089217189
77 1.9903304e-05 1.1164286e-05 0.00088956967
78 2.0300948e-05 1.1466652e-05 0.00088700311
79 2.0696905e-05 1.177381e-05 0.00088439373
80 2.1058218e-05 1.2059606e-05 0.00088199635
81 2.139726e-05 1.233837e-05 0.0008797438
82 2.1755155e-05 1.261531e-05 0.00087745162
83 2.2051018e-05 1.2899972e-05 0.00087506863
84 2.2294567e-05 1.3160246e-05 0.00087288444
85 2.2559076e-05 1.3438712e-05 0.00087052617
86 2.2815918e-05 1.372546e-05 0.00086818634
87 2.3062616e-05 1.4017631e-05 0.00086572407
88 2.3324206e-05 1.4328439e-05 0.000862992
89 2.3559323e-05 1.4640964e-05 0.00086017364
90 2.3792776e-05 1.4978644e-05 0.0008570595
91 2.3990667e-05 1.5307214e-05 0.00085411601
92 2.4198637e-05 1.5649328e-05 0.00085112325
93 2.4419398e-05 1.6015833e-05 0.0008479391
94 2.4625252e-05 1.6393131e-05 0.00084474237
95 2.4816363e-05 1.674573e-05 0.00084165639
96 2.4982897e-05 1.7094435e-05 0.00083858996
97 2.5153682e-05 1.7451741e-05 0.00083536142
98 2.5288512e-05 1.780703e-05 0.00083221292
99 2.5384836e-05 1.8141862e-05 0.00082913227
100 2.5401412e-05 1.8457846e-05 0.00082619877
Loop time of 0.122921 on 1 procs for 100 steps with 3 atoms
Performance: 35144393.915 fs/day, 0.000 hours/fs, 813.528 timesteps/s, 2.441 katom-step/s
88.8% CPU use with 1 MPI tasks x no OpenMP threads
MPI task timing breakdown:
Section | min time | avg time | max time |%varavg| %total
---------------------------------------------------------------
Pair | 0 | 0 | 0 | 0.0 | 0.00
Neigh | 1.5885e-05 | 1.5885e-05 | 1.5885e-05 | 0.0 | 0.01
Comm | 9.4707e-05 | 9.4707e-05 | 9.4707e-05 | 0.0 | 0.08
Output | 0.0027076 | 0.0027076 | 0.0027076 | 0.0 | 2.20
Modify | 0.11993 | 0.11993 | 0.11993 | 0.0 | 97.57
Other | | 0.0001738 | | | 0.14
Nlocal: 3 ave 3 max 3 min
Histogram: 1 0 0 0 0 0 0 0 0 0
Nghost: 0 ave 0 max 0 min
Histogram: 1 0 0 0 0 0 0 0 0 0
Neighs: 0 ave 0 max 0 min
Histogram: 1 0 0 0 0 0 0 0 0 0
Total # of neighbors = 0
Ave neighs/atom = 0
Neighbor list builds = 42
Dangerous builds = 0

1
examples/PACKAGES/pimd_bosonic/harmonic_trap_langevin/run.sh Normal file
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mpirun -np $NBEADS $LMP -in in.lmp -partition ${NBEADS}x1

60
examples/PACKAGES/pimd_bosonic/harmonic_trap_nvt/in.lmp Normal file
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# Units and dimensions
units electron
dimension 3
boundary p p p
atom_style atomic
atom_modify map yes
pair_style none
# Time step (in femtoseconds)
timestep 0.5
# Temperature (in Kelvin)
variable Temp equal 17.4
# Number of Nose-Hoover chains
variable nhc equal 4
# Force constant (in Hartree energies per Bohr radius squared)
variable k equal 1.2154614120000001e-08
# Number of beads
variable Nbeads equal 4
variable ibead uloop ${Nbeads} pad
variable seed equal 18889
# Create box and atoms. All distances are in Bohr
region box block -1500 1500 -1500 1500 -1500 1500
create_box 1 box
variable a loop 3
label loop
variable x1 equal -15.0+0.5*v_a
variable y1 equal 10.0-0.5*v_a
variable z1 equal 1+0.5*v_a
create_atoms 1 single ${x1} ${y1} ${z1}
next a
jump SELF loop
# Electron mass (in amu)
mass 1 0.00054858
# Initialize velocities
velocity all create ${Temp} ${seed}${ibead} mom yes rot yes dist gaussian
# Add harmonic external force
fix harm all spring/self ${k}
# Add harmonic potential energy to total energy and potential energy
fix_modify harm energy yes
# PIMD command
fix pimdb all pimd/nvt/bosonic method pimd temp ${Temp} nhc ${nhc}
# Outputs
variable virial equal f_pimdb[3]
variable prim_kinetic equal f_pimdb[4]
thermo_style custom step pe v_virial v_prim_kinetic
thermo 1
run 100

236
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LAMMPS (4 Feb 2025)
Processor partition = 0
# Units and dimensions
units electron
dimension 3
boundary p p p
atom_style atomic
atom_modify map yes
pair_style none
# Time step (in femtoseconds)
timestep 0.5
# Temperature (in Kelvin)
variable Temp equal 17.4
# Number of Nose-Hoover chains
variable nhc equal 4
# Force constant (in Hartree energies per Bohr radius squared)
variable k equal 1.2154614120000001e-08
# Number of beads
variable Nbeads equal 4
variable ibead uloop ${Nbeads} pad
variable ibead uloop 4 pad
variable seed equal 18889
# Create box and atoms. All distances are in Bohr
region box block -1500 1500 -1500 1500 -1500 1500
create_box 1 box
Created orthogonal box = (-1500 -1500 -1500) to (1500 1500 1500)
1 by 1 by 1 MPI processor grid
variable a loop 3
label loop
variable x1 equal -15.0+0.5*v_a
variable y1 equal 10.0-0.5*v_a
variable z1 equal 1+0.5*v_a
create_atoms 1 single ${x1} ${y1} ${z1}
create_atoms 1 single -14.5 ${y1} ${z1}
create_atoms 1 single -14.5 9.5 ${z1}
create_atoms 1 single -14.5 9.5 1.5
Created 1 atoms
using lattice units in orthogonal box = (-1500 -1500 -1500) to (1500 1500 1500)
create_atoms CPU = 0.000 seconds
next a
jump SELF loop
variable x1 equal -15.0+0.5*v_a
variable y1 equal 10.0-0.5*v_a
variable z1 equal 1+0.5*v_a
create_atoms 1 single ${x1} ${y1} ${z1}
create_atoms 1 single -14 ${y1} ${z1}
create_atoms 1 single -14 9 ${z1}
create_atoms 1 single -14 9 2
Created 1 atoms
using lattice units in orthogonal box = (-1500 -1500 -1500) to (1500 1500 1500)
create_atoms CPU = 0.000 seconds
next a
jump SELF loop
variable x1 equal -15.0+0.5*v_a
variable y1 equal 10.0-0.5*v_a
variable z1 equal 1+0.5*v_a
create_atoms 1 single ${x1} ${y1} ${z1}
create_atoms 1 single -13.5 ${y1} ${z1}
create_atoms 1 single -13.5 8.5 ${z1}
create_atoms 1 single -13.5 8.5 2.5
Created 1 atoms
using lattice units in orthogonal box = (-1500 -1500 -1500) to (1500 1500 1500)
create_atoms CPU = 0.000 seconds
next a
jump SELF loop
# Electron mass (in amu)
mass 1 0.00054858
# Initialize velocities
velocity all create ${Temp} ${seed}${ibead} mom yes rot yes dist gaussian
velocity all create 17.4 ${seed}${ibead} mom yes rot yes dist gaussian
velocity all create 17.4 18889${ibead} mom yes rot yes dist gaussian
velocity all create 17.4 188891 mom yes rot yes dist gaussian
# Add harmonic external force
fix harm all spring/self ${k}
fix harm all spring/self 1.215461412e-08
# Add harmonic potential energy to total energy and potential energy
fix_modify harm energy yes
# PIMD command
fix pimdb all pimd/nvt/bosonic method pimd temp ${Temp} nhc ${nhc}
fix pimdb all pimd/nvt/bosonic method pimd temp 17.4 nhc ${nhc}
fix pimdb all pimd/nvt/bosonic method pimd temp 17.4 nhc 4
# Outputs
variable virial equal f_pimdb[3]
variable prim_kinetic equal f_pimdb[4]
thermo_style custom step pe v_virial v_prim_kinetic
thermo 1
run 100
WARNING: No fixes with time integration, atoms won't move (../verlet.cpp:60)
Fix pimd/nvt -P/(beta^2 * hbar^2) = -2.2139311e-05 (kcal/mol/A^2)
WARNING: No pairwise cutoff or binsize set. Atom sorting therefore disabled. (../atom.cpp:2444)
WARNING: Communication cutoff is 0.0. No ghost atoms will be generated. Atoms may get lost. (../comm_brick.cpp:212)
Per MPI rank memory allocation (min/avg/max) = 9.176 | 9.176 | 9.176 Mbytes
Step PotEng v_virial v_prim_kinetic
0 0 0 0.00024794798
1 8.5849317e-10 4.5664581e-10 0.00024794215
2 3.4338094e-09 1.3424585e-09 0.00024793325
3 7.7255501e-09 2.6573351e-09 0.00024792129
4 1.3733112e-08 4.4011211e-09 0.00024790626
5 2.1455686e-08 6.5736113e-09 0.00024788818
6 3.0892259e-08 9.1745487e-09 0.00024786704
7 4.2041614e-08 1.2203626e-08 0.00024784285
8 5.4902328e-08 1.5660483e-08 0.0002478156
9 6.9472776e-08 1.9544712e-08 0.00024778532
10 8.5751128e-08 2.385585e-08 0.00024775199
11 1.0373535e-07 2.8593386e-08 0.00024771564
12 1.234232e-07 3.3756758e-08 0.00024767626
13 1.4481225e-07 3.9345352e-08 0.00024763386
14 1.6789985e-07 4.5358504e-08 0.00024758844
15 1.9268316e-07 5.1795501e-08 0.00024754003
16 2.1915914e-07 5.8655576e-08 0.00024748862
17 2.4732452e-07 6.5937915e-08 0.00024743423
18 2.7717588e-07 7.3641654e-08 0.00024737686
19 3.0870956e-07 8.1765876e-08 0.00024731653
20 3.4192172e-07 9.0309618e-08 0.00024725324
21 3.7680831e-07 9.9271863e-08 0.00024718701
22 4.1336509e-07 1.0865155e-07 0.00024711785
23 4.5158762e-07 1.1844756e-07 0.00024704578
24 4.9147126e-07 1.2865874e-07 0.0002469708
25 5.3301119e-07 1.3928387e-07 0.00024689293
26 5.7620236e-07 1.5032169e-07 0.00024681218
27 6.2103957e-07 1.6177089e-07 0.00024672857
28 6.675174e-07 1.7363012e-07 0.00024664212
29 7.1563024e-07 1.8589798e-07 0.00024655283
30 7.6537229e-07 1.9857299e-07 0.00024646073
31 8.1673756e-07 2.1165368e-07 0.00024636584
32 8.6971988e-07 2.2513849e-07 0.00024626816
33 9.2431288e-07 2.3902582e-07 0.00024616772
34 9.8051001e-07 2.5331402e-07 0.00024606453
35 1.0383045e-06 2.6800143e-07 0.00024595862
36 1.0976895e-06 2.8308629e-07 0.00024585001
37 1.1586578e-06 2.9856682e-07 0.0002457387
38 1.2212021e-06 3.1444121e-07 0.00024562473
39 1.2853151e-06 3.3070757e-07 0.00024550812
40 1.350989e-06 3.4736399e-07 0.00024538888
41 1.4182159e-06 3.644085e-07 0.00024526703
42 1.4869879e-06 3.8183911e-07 0.00024514261
43 1.5572969e-06 3.9965375e-07 0.00024501562
44 1.6291343e-06 4.1785034e-07 0.0002448861
45 1.7024917e-06 4.3642673e-07 0.00024475406
46 1.7773604e-06 4.5538075e-07 0.00024461954
47 1.8537315e-06 4.7471016e-07 0.00024448255
48 1.9315959e-06 4.9441271e-07 0.00024434312
49 2.0109445e-06 5.1448608e-07 0.00024420127
50 2.0917677e-06 5.3492792e-07 0.00024405703
51 2.1740562e-06 5.5573584e-07 0.00024391043
52 2.2578001e-06 5.769074e-07 0.00024376149
53 2.3429895e-06 5.9844014e-07 0.00024361023
54 2.4296146e-06 6.2033154e-07 0.00024345669
55 2.5176649e-06 6.4257904e-07 0.00024330088
56 2.6071302e-06 6.6518005e-07 0.00024314285
57 2.6980001e-06 6.8813194e-07 0.00024298261
58 2.7902637e-06 7.1143203e-07 0.0002428202
59 2.8839103e-06 7.3507763e-07 0.00024265563
60 2.9789289e-06 7.5906598e-07 0.00024248895
61 3.0753084e-06 7.833943e-07 0.00024232018
62 3.1730376e-06 8.0805977e-07 0.00024214934
63 3.2721049e-06 8.3305953e-07 0.00024197647
64 3.372499e-06 8.5839069e-07 0.00024180161
65 3.474208e-06 8.8405032e-07 0.00024162477
66 3.5772201e-06 9.1003545e-07 0.00024144598
67 3.6815235e-06 9.3634309e-07 0.00024126529
68 3.7871058e-06 9.6297021e-07 0.00024108272
69 3.893955e-06 9.8991374e-07 0.0002408983
70 4.0020586e-06 1.0171706e-06 0.00024071206
71 4.1114041e-06 1.0447376e-06 0.00024052403
72 4.2219789e-06 1.0726116e-06 0.00024033425
73 4.3337702e-06 1.1007895e-06 0.00024014274
74 4.4467651e-06 1.1292679e-06 0.00023994955
75 4.5609507e-06 1.1580437e-06 0.0002397547
76 4.6763137e-06 1.1871136e-06 0.00023955822
77 4.792841e-06 1.2164741e-06 0.00023936014
78 4.9105191e-06 1.2461221e-06 0.00023916051
79 5.0293346e-06 1.276054e-06 0.00023895935
80 5.149274e-06 1.3062666e-06 0.00023875669
81 5.2703234e-06 1.3367563e-06 0.00023855257
82 5.392469e-06 1.3675198e-06 0.00023834703
83 5.515697e-06 1.3985535e-06 0.00023814009
84 5.6399934e-06 1.4298539e-06 0.00023793178
85 5.7653439e-06 1.4614174e-06 0.00023772215
86 5.8917344e-06 1.4932406e-06 0.00023751123
87 6.0191505e-06 1.5253199e-06 0.00023729904
88 6.1475779e-06 1.5576515e-06 0.00023708563
89 6.277002e-06 1.590232e-06 0.00023687102
90 6.4074081e-06 1.6230576e-06 0.00023665526
91 6.5387817e-06 1.6561246e-06 0.00023643837
92 6.6711079e-06 1.6894294e-06 0.00023622039
93 6.8043718e-06 1.7229682e-06 0.00023600135
94 6.9385585e-06 1.7567372e-06 0.00023578129
95 7.0736529e-06 1.7907328e-06 0.00023556024
96 7.2096401e-06 1.8249512e-06 0.00023533824
97 7.3465046e-06 1.8593885e-06 0.00023511531
98 7.4842314e-06 1.8940408e-06 0.0002348915
99 7.622805e-06 1.9289045e-06 0.00023466684
100 7.76221e-06 1.9639756e-06 0.00023444136
Loop time of 0.00940749 on 1 procs for 100 steps with 3 atoms
Performance: 459208566.791 fs/day, 0.000 hours/fs, 10629.828 timesteps/s, 31.889 katom-step/s
90.3% CPU use with 1 MPI tasks x no OpenMP threads
MPI task timing breakdown:
Section | min time | avg time | max time |%varavg| %total
---------------------------------------------------------------
Pair | 0 | 0 | 0 | 0.0 | 0.00
Neigh | 8.466e-06 | 8.466e-06 | 8.466e-06 | 0.0 | 0.09
Comm | 7.8365e-05 | 7.8365e-05 | 7.8365e-05 | 0.0 | 0.83
Output | 0.0012482 | 0.0012482 | 0.0012482 | 0.0 | 13.27
Modify | 0.0079193 | 0.0079193 | 0.0079193 | 0.0 | 84.18
Other | | 0.0001532 | | | 1.63
Nlocal: 3 ave 3 max 3 min
Histogram: 1 0 0 0 0 0 0 0 0 0
Nghost: 0 ave 0 max 0 min
Histogram: 1 0 0 0 0 0 0 0 0 0
Neighs: 0 ave 0 max 0 min
Histogram: 1 0 0 0 0 0 0 0 0 0
Total # of neighbors = 0
Ave neighs/atom = 0
Neighbor list builds = 24
Dangerous builds = 0
Total wall time: 0:00:00

234
examples/PACKAGES/pimd_bosonic/harmonic_trap_nvt/log.lammps.1 Normal file
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LAMMPS (4 Feb 2025)
Processor partition = 1
# Units and dimensions
units electron
dimension 3
boundary p p p
atom_style atomic
atom_modify map yes
pair_style none
# Time step (in femtoseconds)
timestep 0.5
# Temperature (in Kelvin)
variable Temp equal 17.4
# Number of Nose-Hoover chains
variable nhc equal 4
# Force constant (in Hartree energies per Bohr radius squared)
variable k equal 1.2154614120000001e-08
# Number of beads
variable Nbeads equal 4
variable ibead uloop ${Nbeads} pad
variable ibead uloop 4 pad
variable seed equal 18889
# Create box and atoms. All distances are in Bohr
region box block -1500 1500 -1500 1500 -1500 1500
create_box 1 box
Created orthogonal box = (-1500 -1500 -1500) to (1500 1500 1500)
1 by 1 by 1 MPI processor grid
variable a loop 3
label loop
variable x1 equal -15.0+0.5*v_a
variable y1 equal 10.0-0.5*v_a
variable z1 equal 1+0.5*v_a
create_atoms 1 single ${x1} ${y1} ${z1}
create_atoms 1 single -14.5 ${y1} ${z1}
create_atoms 1 single -14.5 9.5 ${z1}
create_atoms 1 single -14.5 9.5 1.5
Created 1 atoms
using lattice units in orthogonal box = (-1500 -1500 -1500) to (1500 1500 1500)
create_atoms CPU = 0.000 seconds
next a
jump SELF loop
variable x1 equal -15.0+0.5*v_a
variable y1 equal 10.0-0.5*v_a
variable z1 equal 1+0.5*v_a
create_atoms 1 single ${x1} ${y1} ${z1}
create_atoms 1 single -14 ${y1} ${z1}
create_atoms 1 single -14 9 ${z1}
create_atoms 1 single -14 9 2
Created 1 atoms
using lattice units in orthogonal box = (-1500 -1500 -1500) to (1500 1500 1500)
create_atoms CPU = 0.000 seconds
next a
jump SELF loop
variable x1 equal -15.0+0.5*v_a
variable y1 equal 10.0-0.5*v_a
variable z1 equal 1+0.5*v_a
create_atoms 1 single ${x1} ${y1} ${z1}
create_atoms 1 single -13.5 ${y1} ${z1}
create_atoms 1 single -13.5 8.5 ${z1}
create_atoms 1 single -13.5 8.5 2.5
Created 1 atoms
using lattice units in orthogonal box = (-1500 -1500 -1500) to (1500 1500 1500)
create_atoms CPU = 0.000 seconds
next a
jump SELF loop
# Electron mass (in amu)
mass 1 0.00054858
# Initialize velocities
velocity all create ${Temp} ${seed}${ibead} mom yes rot yes dist gaussian
velocity all create 17.4 ${seed}${ibead} mom yes rot yes dist gaussian
velocity all create 17.4 18889${ibead} mom yes rot yes dist gaussian
velocity all create 17.4 188892 mom yes rot yes dist gaussian
# Add harmonic external force
fix harm all spring/self ${k}
fix harm all spring/self 1.215461412e-08
# Add harmonic potential energy to total energy and potential energy
fix_modify harm energy yes
# PIMD command
fix pimdb all pimd/nvt/bosonic method pimd temp ${Temp} nhc ${nhc}
fix pimdb all pimd/nvt/bosonic method pimd temp 17.4 nhc ${nhc}
fix pimdb all pimd/nvt/bosonic method pimd temp 17.4 nhc 4
# Outputs
variable virial equal f_pimdb[3]
variable prim_kinetic equal f_pimdb[4]
thermo_style custom step pe v_virial v_prim_kinetic
thermo 1
run 100
WARNING: No fixes with time integration, atoms won't move (../verlet.cpp:60)
WARNING: No pairwise cutoff or binsize set. Atom sorting therefore disabled. (../atom.cpp:2444)
WARNING: Communication cutoff is 0.0. No ghost atoms will be generated. Atoms may get lost. (../comm_brick.cpp:212)
Per MPI rank memory allocation (min/avg/max) = 9.176 | 9.176 | 9.176 Mbytes
Step PotEng v_virial v_prim_kinetic
0 0 0 0.00024796164
1 8.5850843e-10 5.313724e-10 0.00024796083
2 3.4339027e-09 1.4919466e-09 0.00024795841
3 7.7257901e-09 2.8816048e-09 0.00024795438
4 1.3733516e-08 4.7001635e-09 0.00024794873
5 2.1456164e-08 6.9473741e-09 0.00024794148
6 3.0892555e-08 9.6229225e-09 0.00024793261
7 4.2041252e-08 1.2726429e-08 0.00024792214
8 5.4900553e-08 1.6257449e-08 0.00024791006
9 6.9468499e-08 2.0215473e-08 0.00024789638
10 8.5742867e-08 2.4599926e-08 0.0002478811
11 1.0372118e-07 2.9410168e-08 0.00024786422
12 1.2340069e-07 3.4645495e-08 0.00024784576
13 1.447784e-07 4.0305136e-08 0.0002478257
14 1.6785106e-07 4.6388259e-08 0.00024780406
15 1.9261515e-07 5.2893965e-08 0.00024778084
16 2.190669e-07 5.9821291e-08 0.00024775605
17 2.4720228e-07 6.7169211e-08 0.00024772969
18 2.7701701e-07 7.4936635e-08 0.00024770176
19 3.0850655e-07 8.312241e-08 0.00024767228
20 3.416661e-07 9.1725317e-08 0.00024764125
21 3.7649064e-07 1.0074408e-07 0.00024760868
22 4.1297485e-07 1.1017735e-07 0.00024757457
23 4.511132e-07 1.2002372e-07 0.00024753893
24 4.9089989e-07 1.3028173e-07 0.00024750177
25 5.3232887e-07 1.4094984e-07 0.0002474631
26 5.7539386e-07 1.5202647e-07 0.00024742293
27 6.2008832e-07 1.6350996e-07 0.00024738126
28 6.6640547e-07 1.7539859e-07 0.00024733811
29 7.1433828e-07 1.876906e-07 0.00024729348
30 7.6387949e-07 2.0038414e-07 0.00024724738
31 8.150216e-07 2.1347732e-07 0.00024719983
32 8.6775685e-07 2.2696818e-07 0.00024715084
33 9.2207727e-07 2.4085472e-07 0.0002471004
34 9.7797464e-07 2.5513485e-07 0.00024704855
35 1.0354405e-06 2.6980645e-07 0.00024699528
36 1.0944662e-06 2.8486732e-07 0.00024694061
37 1.1550427e-06 3.0031522e-07 0.00024688456
38 1.2171611e-06 3.1614785e-07 0.00024682713
39 1.2808118e-06 3.3236283e-07 0.00024676833
40 1.3459853e-06 3.4895776e-07 0.00024670818
41 1.4126717e-06 3.6593016e-07 0.0002466467
42 1.4808611e-06 3.832775e-07 0.0002465839
43 1.5505431e-06 4.009972e-07 0.00024651978
44 1.6217074e-06 4.1908663e-07 0.00024645437
45 1.6943431e-06 4.3754308e-07 0.00024638767
46 1.7684394e-06 4.5636381e-07 0.00024631971
47 1.8439852e-06 4.7554603e-07 0.0002462505
48 1.9209691e-06 4.9508689e-07 0.00024618005
49 1.9993796e-06 5.1498348e-07 0.00024610839
50 2.079205e-06 5.3523286e-07 0.00024603551
51 2.1604333e-06 5.5583202e-07 0.00024596145
52 2.2430524e-06 5.7677791e-07 0.00024588621
53 2.32705e-06 5.9806742e-07 0.00024580981
54 2.4124135e-06 6.1969741e-07 0.00024573228
55 2.4991302e-06 6.4166468e-07 0.00024565362
56 2.5871872e-06 6.6396597e-07 0.00024557386
57 2.6765714e-06 6.8659801e-07 0.00024549301
58 2.7672695e-06 7.0955745e-07 0.00024541108
59 2.859268e-06 7.328409e-07 0.00024532811
60 2.9525533e-06 7.5644494e-07 0.00024524409
61 3.0471115e-06 7.8036609e-07 0.00024515907
62 3.1429287e-06 8.0460083e-07 0.00024507304
63 3.2399907e-06 8.2914562e-07 0.00024498603
64 3.3382831e-06 8.5399683e-07 0.00024489807
65 3.4377915e-06 8.7915084e-07 0.00024480916
66 3.5385011e-06 9.0460395e-07 0.00024471933
67 3.6403972e-06 9.3035245e-07 0.0002446286
68 3.7434648e-06 9.5639257e-07 0.00024453698
69 3.8476886e-06 9.8272051e-07 0.0002444445
70 3.9530535e-06 1.0093324e-06 0.00024435118
71 4.0595439e-06 1.0362244e-06 0.00024425703
72 4.1671443e-06 1.0633926e-06 0.00024416208
73 4.275839e-06 1.0908331e-06 0.00024406635
74 4.3856121e-06 1.1185418e-06 0.00024396985
75 4.4964475e-06 1.1465147e-06 0.00024387262
76 4.6083292e-06 1.1747478e-06 0.00024377466
77 4.7212408e-06 1.2032371e-06 0.00024367601
78 4.835166e-06 1.2319783e-06 0.00024357668
79 4.9500883e-06 1.2609674e-06 0.00024347669
80 5.0659909e-06 1.2902001e-06 0.00024337607
81 5.1828572e-06 1.3196723e-06 0.00024327483
82 5.3006702e-06 1.3493797e-06 0.000243173
83 5.419413e-06 1.379318e-06 0.0002430706
84 5.5390685e-06 1.4094831e-06 0.00024296765
85 5.6596194e-06 1.4398705e-06 0.00024286417
86 5.7810485e-06 1.4704759e-06 0.00024276019
87 5.9033384e-06 1.501295e-06 0.00024265573
88 6.0264715e-06 1.5323234e-06 0.00024255081
89 6.1504303e-06 1.5635565e-06 0.00024244545
90 6.275197e-06 1.5949902e-06 0.00024233967
91 6.400754e-06 1.6266197e-06 0.0002422335
92 6.5270834e-06 1.6584408e-06 0.00024212696
93 6.6541672e-06 1.6904488e-06 0.00024202007
94 6.7819875e-06 1.7226394e-06 0.00024191285
95 6.9105262e-06 1.7550078e-06 0.00024180534
96 7.0397651e-06 1.7875497e-06 0.00024169754
97 7.169686e-06 1.8202604e-06 0.00024158948
98 7.3002707e-06 1.8531354e-06 0.00024148118
99 7.4315008e-06 1.88617e-06 0.00024137268
100 7.563358e-06 1.9193596e-06 0.00024126398
Loop time of 0.00941353 on 1 procs for 100 steps with 3 atoms
Performance: 458913876.206 fs/day, 0.000 hours/fs, 10623.006 timesteps/s, 31.869 katom-step/s
50.9% CPU use with 1 MPI tasks x no OpenMP threads
MPI task timing breakdown:
Section | min time | avg time | max time |%varavg| %total
---------------------------------------------------------------
Pair | 0 | 0 | 0 | 0.0 | 0.00
Neigh | 8.215e-06 | 8.215e-06 | 8.215e-06 | 0.0 | 0.09
Comm | 7.7692e-05 | 7.7692e-05 | 7.7692e-05 | 0.0 | 0.83
Output | 0.0047662 | 0.0047662 | 0.0047662 | 0.0 | 50.63
Modify | 0.004407 | 0.004407 | 0.004407 | 0.0 | 46.82
Other | | 0.0001545 | | | 1.64
Nlocal: 3 ave 3 max 3 min
Histogram: 1 0 0 0 0 0 0 0 0 0
Nghost: 0 ave 0 max 0 min
Histogram: 1 0 0 0 0 0 0 0 0 0
Neighs: 0 ave 0 max 0 min
Histogram: 1 0 0 0 0 0 0 0 0 0
Total # of neighbors = 0
Ave neighs/atom = 0
Neighbor list builds = 23
Dangerous builds = 0
Total wall time: 0:00:00

234
examples/PACKAGES/pimd_bosonic/harmonic_trap_nvt/log.lammps.2 Normal file
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LAMMPS (4 Feb 2025)
Processor partition = 2
# Units and dimensions
units electron
dimension 3
boundary p p p
atom_style atomic
atom_modify map yes
pair_style none
# Time step (in femtoseconds)
timestep 0.5
# Temperature (in Kelvin)
variable Temp equal 17.4
# Number of Nose-Hoover chains
variable nhc equal 4
# Force constant (in Hartree energies per Bohr radius squared)
variable k equal 1.2154614120000001e-08
# Number of beads
variable Nbeads equal 4
variable ibead uloop ${Nbeads} pad
variable ibead uloop 4 pad
variable seed equal 18889
# Create box and atoms. All distances are in Bohr
region box block -1500 1500 -1500 1500 -1500 1500
create_box 1 box
Created orthogonal box = (-1500 -1500 -1500) to (1500 1500 1500)
1 by 1 by 1 MPI processor grid
variable a loop 3
label loop
variable x1 equal -15.0+0.5*v_a
variable y1 equal 10.0-0.5*v_a
variable z1 equal 1+0.5*v_a
create_atoms 1 single ${x1} ${y1} ${z1}
create_atoms 1 single -14.5 ${y1} ${z1}
create_atoms 1 single -14.5 9.5 ${z1}
create_atoms 1 single -14.5 9.5 1.5
Created 1 atoms
using lattice units in orthogonal box = (-1500 -1500 -1500) to (1500 1500 1500)
create_atoms CPU = 0.000 seconds
next a
jump SELF loop
variable x1 equal -15.0+0.5*v_a
variable y1 equal 10.0-0.5*v_a
variable z1 equal 1+0.5*v_a
create_atoms 1 single ${x1} ${y1} ${z1}
create_atoms 1 single -14 ${y1} ${z1}
create_atoms 1 single -14 9 ${z1}
create_atoms 1 single -14 9 2
Created 1 atoms
using lattice units in orthogonal box = (-1500 -1500 -1500) to (1500 1500 1500)
create_atoms CPU = 0.000 seconds
next a
jump SELF loop
variable x1 equal -15.0+0.5*v_a
variable y1 equal 10.0-0.5*v_a
variable z1 equal 1+0.5*v_a
create_atoms 1 single ${x1} ${y1} ${z1}
create_atoms 1 single -13.5 ${y1} ${z1}
create_atoms 1 single -13.5 8.5 ${z1}
create_atoms 1 single -13.5 8.5 2.5
Created 1 atoms
using lattice units in orthogonal box = (-1500 -1500 -1500) to (1500 1500 1500)
create_atoms CPU = 0.000 seconds
next a
jump SELF loop
# Electron mass (in amu)
mass 1 0.00054858
# Initialize velocities
velocity all create ${Temp} ${seed}${ibead} mom yes rot yes dist gaussian
velocity all create 17.4 ${seed}${ibead} mom yes rot yes dist gaussian
velocity all create 17.4 18889${ibead} mom yes rot yes dist gaussian
velocity all create 17.4 188893 mom yes rot yes dist gaussian
# Add harmonic external force
fix harm all spring/self ${k}
fix harm all spring/self 1.215461412e-08
# Add harmonic potential energy to total energy and potential energy
fix_modify harm energy yes
# PIMD command
fix pimdb all pimd/nvt/bosonic method pimd temp ${Temp} nhc ${nhc}
fix pimdb all pimd/nvt/bosonic method pimd temp 17.4 nhc ${nhc}
fix pimdb all pimd/nvt/bosonic method pimd temp 17.4 nhc 4
# Outputs
variable virial equal f_pimdb[3]
variable prim_kinetic equal f_pimdb[4]
thermo_style custom step pe v_virial v_prim_kinetic
thermo 1
run 100
WARNING: No fixes with time integration, atoms won't move (../verlet.cpp:60)
WARNING: No pairwise cutoff or binsize set. Atom sorting therefore disabled. (../atom.cpp:2444)
WARNING: Communication cutoff is 0.0. No ghost atoms will be generated. Atoms may get lost. (../comm_brick.cpp:212)
Per MPI rank memory allocation (min/avg/max) = 9.176 | 9.176 | 9.176 Mbytes
Step PotEng v_virial v_prim_kinetic
0 0 0 0.00024796164
1 8.5850845e-10 -3.6831179e-10 0.0002479594
2 3.4338783e-09 -3.0736303e-10 0.00024795267
3 7.7256433e-09 1.8277487e-10 0.00024794145
4 1.3733026e-08 1.1019528e-09 0.00024792576
5 2.145494e-08 2.449944e-09 0.00024790558
6 3.0889985e-08 4.226444e-09 0.00024788093
7 4.2036455e-08 6.4310711e-09 0.00024785181
8 5.4892332e-08 9.0633658e-09 0.00024781823
9 6.9455288e-08 1.2122792e-08 0.00024778019
10 8.572269e-08 1.5608734e-08 0.0002477377
11 1.0369159e-07 1.9520504e-08 0.00024769077
12 1.2335875e-07 2.3857331e-08 0.00024763941
13 1.4472059e-07 2.8618373e-08 0.00024758363
14 1.6777327e-07 3.3802708e-08 0.00024752344
15 1.9251262e-07 3.940934e-08 0.00024745886
16 2.1893415e-07 4.5437194e-08 0.00024738989
17 2.4703311e-07 5.1885122e-08 0.00024731656
18 2.768044e-07 5.8751899e-08 0.00024723887
19 3.0824267e-07 6.6036227e-08 0.00024715685
20 3.4134222e-07 7.3736729e-08 0.00024707051
21 3.7609709e-07 8.1851958e-08 0.00024697986
22 4.1250102e-07 9.0380389e-08 0.00024688494
23 4.5054742e-07 9.9320426e-08 0.00024678575
24 4.9022945e-07 1.086704e-07 0.00024668231
25 5.3153996e-07 1.1842856e-07 0.00024657466
26 5.744715e-07 1.285931e-07 0.00024646281
27 6.1901635e-07 1.3916212e-07 0.00024634678
28 6.6516648e-07 1.5013367e-07 0.0002462266
29 7.1291361e-07 1.6150571e-07 0.00024610229
30 7.6224914e-07 1.7327614e-07 0.00024597388
31 8.1316422e-07 1.8544279e-07 0.0002458414
32 8.6564969e-07 1.9800342e-07 0.00024570487
33 9.1969614e-07 2.109557e-07 0.00024556432
34 9.7529388e-07 2.2429727e-07 0.00024541978
35 1.0324329e-06 2.3802567e-07 0.00024527128
36 1.0911031e-06 2.5213838e-07 0.00024511886
37 1.1512938e-06 2.6663282e-07 0.00024496253
38 1.2129943e-06 2.8150634e-07 0.00024480234
39 1.2761936e-06 2.9675622e-07 0.00024463831
40 1.3408803e-06 3.1237968e-07 0.00024447049
41 1.407043e-06 3.2837388e-07 0.0002442989
42 1.4746698e-06 3.447359e-07 0.00024412359
43 1.5437487e-06 3.6146277e-07 0.00024394458
44 1.6142674e-06 3.7855146e-07 0.00024376192
45 1.6862132e-06 3.9599886e-07 0.00024357564
46 1.7595735e-06 4.1380182e-07 0.00024338577
47 1.8343351e-06 4.3195711e-07 0.00024319237
48 1.9104848e-06 4.5046147e-07 0.00024299547
49 1.9880091e-06 4.6931154e-07 0.00024279511
50 2.0668943e-06 4.8850394e-07 0.00024259132
51 2.1471263e-06 5.0803521e-07 0.00024238416
52 2.228691e-06 5.2790184e-07 0.00024217367
53 2.311574e-06 5.4810027e-07 0.00024195988
54 2.3957606e-06 5.6862687e-07 0.00024174285
55 2.481236e-06 5.8947797e-07 0.00024152261
56 2.5679851e-06 6.1064984e-07 0.00024129922
57 2.6559926e-06 6.3213871e-07 0.00024107271
58 2.7452431e-06 6.5394073e-07 0.00024084313
59 2.8357209e-06 6.7605203e-07 0.00024061054
60 2.9274101e-06 6.9846868e-07 0.00024037498
61 3.0202947e-06 7.2118669e-07 0.00024013649
62 3.1143583e-06 7.4420204e-07 0.00023989513
63 3.2095846e-06 7.6751065e-07 0.00023965094
64 3.3059569e-06 7.911084e-07 0.00023940398
65 3.4034585e-06 8.1499113e-07 0.00023915429
66 3.5020722e-06 8.3915461e-07 0.00023890193
67 3.601781e-06 8.6359461e-07 0.00023864694
68 3.7025676e-06 8.8830681e-07 0.00023838939
69 3.8044144e-06 9.132869e-07 0.00023812931
70 3.9073038e-06 9.3853048e-07 0.00023786677
71 4.0112181e-06 9.6403314e-07 0.00023760182
72 4.1161392e-06 9.8979043e-07 0.00023733451
73 4.2220491e-06 1.0157978e-06 0.0002370649
74 4.3289295e-06 1.0420509e-06 0.00023679303
75 4.4367621e-06 1.068545e-06 0.00023651897
76 4.5455283e-06 1.0952755e-06 0.00023624277
77 4.6552095e-06 1.1222378e-06 0.00023596449
78 4.7657869e-06 1.1494273e-06 0.00023568418
79 4.8772416e-06 1.1768393e-06 0.0002354019
80 4.9895545e-06 1.2044689e-06 0.00023511771
81 5.1027067e-06 1.2323116e-06 0.00023483166
82 5.2166788e-06 1.2603625e-06 0.00023454381
83 5.3314515e-06 1.2886168e-06 0.00023425422
84 5.4470054e-06 1.3170697e-06 0.00023396295
85 5.5633208e-06 1.3457162e-06 0.00023367006
86 5.6803783e-06 1.3745516e-06 0.0002333756
87 5.798158e-06 1.403571e-06 0.00023307963
88 5.9166402e-06 1.4327693e-06 0.00023278222
89 6.0358049e-06 1.4621418e-06 0.00023248341
90 6.1556323e-06 1.4916833e-06 0.00023218329
91 6.2761023e-06 1.5213889e-06 0.00023188189
92 6.3971948e-06 1.5512537e-06 0.00023157929
93 6.5188897e-06 1.5812727e-06 0.00023127554
94 6.6411667e-06 1.6114407e-06 0.0002309707
95 6.7640056e-06 1.6417527e-06 0.00023066484
96 6.8873862e-06 1.6722038e-06 0.00023035801
97 7.011288e-06 1.7027888e-06 0.00023005028
98 7.1356907e-06 1.7335027e-06 0.0002297417
99 7.2605738e-06 1.7643404e-06 0.00022943234
100 7.3859169e-06 1.7952968e-06 0.00022912226
Loop time of 0.00941372 on 1 procs for 100 steps with 3 atoms
Performance: 458904516.311 fs/day, 0.000 hours/fs, 10622.790 timesteps/s, 31.868 katom-step/s
24.7% CPU use with 1 MPI tasks x no OpenMP threads
MPI task timing breakdown:
Section | min time | avg time | max time |%varavg| %total
---------------------------------------------------------------
Pair | 0 | 0 | 0 | 0.0 | 0.00
Neigh | 8.785e-06 | 8.785e-06 | 8.785e-06 | 0.0 | 0.09
Comm | 7.9921e-05 | 7.9921e-05 | 7.9921e-05 | 0.0 | 0.85
Output | 0.0071119 | 0.0071119 | 0.0071119 | 0.0 | 75.55
Modify | 0.0020558 | 0.0020558 | 0.0020558 | 0.0 | 21.84
Other | | 0.0001572 | | | 1.67
Nlocal: 3 ave 3 max 3 min
Histogram: 1 0 0 0 0 0 0 0 0 0
Nghost: 0 ave 0 max 0 min
Histogram: 1 0 0 0 0 0 0 0 0 0
Neighs: 0 ave 0 max 0 min
Histogram: 1 0 0 0 0 0 0 0 0 0
Total # of neighbors = 0
Ave neighs/atom = 0
Neighbor list builds = 24
Dangerous builds = 0
Total wall time: 0:00:00

234
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LAMMPS (4 Feb 2025)
Processor partition = 3
# Units and dimensions
units electron
dimension 3
boundary p p p
atom_style atomic
atom_modify map yes
pair_style none
# Time step (in femtoseconds)
timestep 0.5
# Temperature (in Kelvin)
variable Temp equal 17.4
# Number of Nose-Hoover chains
variable nhc equal 4
# Force constant (in Hartree energies per Bohr radius squared)
variable k equal 1.2154614120000001e-08
# Number of beads
variable Nbeads equal 4
variable ibead uloop ${Nbeads} pad
variable ibead uloop 4 pad
variable seed equal 18889
# Create box and atoms. All distances are in Bohr
region box block -1500 1500 -1500 1500 -1500 1500
create_box 1 box
Created orthogonal box = (-1500 -1500 -1500) to (1500 1500 1500)
1 by 1 by 1 MPI processor grid
variable a loop 3
label loop
variable x1 equal -15.0+0.5*v_a
variable y1 equal 10.0-0.5*v_a
variable z1 equal 1+0.5*v_a
create_atoms 1 single ${x1} ${y1} ${z1}
create_atoms 1 single -14.5 ${y1} ${z1}
create_atoms 1 single -14.5 9.5 ${z1}
create_atoms 1 single -14.5 9.5 1.5
Created 1 atoms
using lattice units in orthogonal box = (-1500 -1500 -1500) to (1500 1500 1500)
create_atoms CPU = 0.000 seconds
next a
jump SELF loop
variable x1 equal -15.0+0.5*v_a
variable y1 equal 10.0-0.5*v_a
variable z1 equal 1+0.5*v_a
create_atoms 1 single ${x1} ${y1} ${z1}
create_atoms 1 single -14 ${y1} ${z1}
create_atoms 1 single -14 9 ${z1}
create_atoms 1 single -14 9 2
Created 1 atoms
using lattice units in orthogonal box = (-1500 -1500 -1500) to (1500 1500 1500)
create_atoms CPU = 0.000 seconds
next a
jump SELF loop
variable x1 equal -15.0+0.5*v_a
variable y1 equal 10.0-0.5*v_a
variable z1 equal 1+0.5*v_a
create_atoms 1 single ${x1} ${y1} ${z1}
create_atoms 1 single -13.5 ${y1} ${z1}
create_atoms 1 single -13.5 8.5 ${z1}
create_atoms 1 single -13.5 8.5 2.5
Created 1 atoms
using lattice units in orthogonal box = (-1500 -1500 -1500) to (1500 1500 1500)
create_atoms CPU = 0.000 seconds
next a
jump SELF loop
# Electron mass (in amu)
mass 1 0.00054858
# Initialize velocities
velocity all create ${Temp} ${seed}${ibead} mom yes rot yes dist gaussian
velocity all create 17.4 ${seed}${ibead} mom yes rot yes dist gaussian
velocity all create 17.4 18889${ibead} mom yes rot yes dist gaussian
velocity all create 17.4 188894 mom yes rot yes dist gaussian
# Add harmonic external force
fix harm all spring/self ${k}
fix harm all spring/self 1.215461412e-08
# Add harmonic potential energy to total energy and potential energy
fix_modify harm energy yes
# PIMD command
fix pimdb all pimd/nvt/bosonic method pimd temp ${Temp} nhc ${nhc}
fix pimdb all pimd/nvt/bosonic method pimd temp 17.4 nhc ${nhc}
fix pimdb all pimd/nvt/bosonic method pimd temp 17.4 nhc 4
# Outputs
variable virial equal f_pimdb[3]
variable prim_kinetic equal f_pimdb[4]
thermo_style custom step pe v_virial v_prim_kinetic
thermo 1
run 100
WARNING: No fixes with time integration, atoms won't move (../verlet.cpp:60)
WARNING: No pairwise cutoff or binsize set. Atom sorting therefore disabled. (../atom.cpp:2444)
WARNING: Communication cutoff is 0.0. No ghost atoms will be generated. Atoms may get lost. (../comm_brick.cpp:212)
Per MPI rank memory allocation (min/avg/max) = 9.176 | 9.176 | 9.176 Mbytes
Step PotEng v_virial v_prim_kinetic
0 0 0 0.00024796164
1 8.5847879e-10 4.4463719e-10 0.00024796024
2 3.4336684e-09 1.3183829e-09 0.00024795602
3 7.7250055e-09 2.6210625e-09 0.000247949
4 1.3731669e-08 4.3524371e-09 0.00024793917
5 2.1452581e-08 6.5122035e-09 0.00024792653
6 3.0886407e-08 9.0999942e-09 0.0002479111
7 4.2031554e-08 1.2115377e-08 0.00024789287
8 5.4886174e-08 1.5557858e-08 0.00024787185
9 6.9448162e-08 1.9426875e-08 0.00024784804
10 8.5715159e-08 2.3721806e-08 0.00024782146
11 1.0368455e-07 2.8441963e-08 0.0002477921
12 1.2335346e-07 3.3586595e-08 0.00024775998
13 1.4471878e-07 3.9154888e-08 0.0002477251
14 1.6777712e-07 4.5145965e-08 0.00024768748
15 1.9252485e-07 5.1558884e-08 0.00024764712
16 2.1895809e-07 5.8392642e-08 0.00024760403
17 2.4707272e-07 6.5646173e-08 0.00024755823
18 2.7686434e-07 7.3318348e-08 0.00024750973
19 3.0832834e-07 8.1407976e-08 0.00024745854
20 3.4145982e-07 8.9913804e-08 0.00024740467
21 3.7625367e-07 9.8834518e-08 0.00024734813
22 4.127045e-07 1.0816874e-07 0.00024728895
23 4.5080671e-07 1.1791504e-07 0.00024722714
24 4.9055443e-07 1.2807191e-07 0.00024716271
25 5.3194155e-07 1.3863779e-07 0.00024709568
26 5.7496174e-07 1.4961107e-07 0.00024702607
27 6.1960841e-07 1.6099007e-07 0.00024695389
28 6.6587473e-07 1.7277305e-07 0.00024687917
29 7.1375365e-07 1.8495821e-07 0.00024680191
30 7.6323786e-07 1.975437e-07 0.00024672216
31 8.1431984e-07 2.1052759e-07 0.00024663991
32 8.6699183e-07 2.2390793e-07 0.0002465552
33 9.2124582e-07 2.3768267e-07 0.00024646805
34 9.7707361e-07 2.5184974e-07 0.00024637847
35 1.0344667e-06 2.6640698e-07 0.0002462865
36 1.0934165e-06 2.813522e-07 0.00024619215
37 1.1539141e-06 2.9668313e-07 0.00024609545
38 1.2159503e-06 3.1239747e-07 0.00024599643
39 1.2795157e-06 3.2849286e-07 0.00024589511
40 1.344601e-06 3.4496686e-07 0.00024579151
41 1.4111961e-06 3.61817e-07 0.00024568566
42 1.4792913e-06 3.7904076e-07 0.0002455776
43 1.5488762e-06 3.9663555e-07 0.00024546734
44 1.6199404e-06 4.1459874e-07 0.00024535492
45 1.6924734e-06 4.3292764e-07 0.00024524035
46 1.7664643e-06 4.5161952e-07 0.00024512369
47 1.841902e-06 4.7067159e-07 0.00024500494
48 1.9187753e-06 4.90081e-07 0.00024488415
49 1.9970729e-06 5.0984488e-07 0.00024476135
50 2.076783e-06 5.2996028e-07 0.00024463656
51 2.1578939e-06 5.5042422e-07 0.00024450981
52 2.2403935e-06 5.7123366e-07 0.00024438115
53 2.3242696e-06 5.9238553e-07 0.0002442506
54 2.4095099e-06 6.138767e-07 0.00024411819
55 2.4961017e-06 6.3570399e-07 0.00024398396
56 2.5840323e-06 6.5786419e-07 0.00024384795
57 2.6732887e-06 6.8035404e-07 0.00024371018
58 2.7638579e-06 7.0317021e-07 0.0002435707
59 2.8557265e-06 7.2630938e-07 0.00024342953
60 2.9488811e-06 7.4976814e-07 0.00024328672
61 3.0433081e-06 7.7354305e-07 0.0002431423
62 3.1389936e-06 7.9763065e-07 0.00024299631
63 3.2359238e-06 8.2202741e-07 0.00024284878
64 3.3340844e-06 8.4672977e-07 0.00024269976
65 3.4334612e-06 8.7173415e-07 0.00024254927
66 3.5340397e-06 8.970369e-07 0.00024239736
67 3.6358055e-06 9.2263435e-07 0.00024224406
68 3.7387437e-06 9.4852279e-07 0.00024208942
69 3.8428394e-06 9.7469849e-07 0.00024193348
70 3.9480777e-06 1.0011576e-06 0.00024177626
71 4.0544433e-06 1.0278964e-06 0.00024161782
72 4.1619211e-06 1.054911e-06 0.0002414582
73 4.2704954e-06 1.0821976e-06 0.00024129742
74 4.3801508e-06 1.1097521e-06 0.00024113554
75 4.4908716e-06 1.1375706e-06 0.0002409726
76 4.6026419e-06 1.1656492e-06 0.00024080863
77 4.7154459e-06 1.1939839e-06 0.00024064367
78 4.8292673e-06 1.2225706e-06 0.00024047778
79 4.9440901e-06 1.2514052e-06 0.00024031099
80 5.059898e-06 1.2804837e-06 0.00024014333
81 5.1766745e-06 1.309802e-06 0.00023997487
82 5.2944032e-06 1.3393558e-06 0.00023980562
83 5.4130674e-06 1.369141e-06 0.00023963565
84 5.5326505e-06 1.3991534e-06 0.00023946499
85 5.6531355e-06 1.4293887e-06 0.00023929369
86 5.7745057e-06 1.4598429e-06 0.00023912178
87 5.8967439e-06 1.4905114e-06 0.00023894931
88 6.0198332e-06 1.5213902e-06 0.00023877633
89 6.1437564e-06 1.5524748e-06 0.00023860287
90 6.2684962e-06 1.5837609e-06 0.00023842898
91 6.3940353e-06 1.6152441e-06 0.00023825471
92 6.5203562e-06 1.6469202e-06 0.0002380801
93 6.6474416e-06 1.6787847e-06 0.00023790518
94 6.7752739e-06 1.7108332e-06 0.00023773001
95 6.9038354e-06 1.7430613e-06 0.00023755463
96 7.0331085e-06 1.7754645e-06 0.00023737908
97 7.1630755e-06 1.8080385e-06 0.00023720341
98 7.2937187e-06 1.8407787e-06 0.00023702765
99 7.4250201e-06 1.8736806e-06 0.00023685186
100 7.5569619e-06 1.9067398e-06 0.00023667607
Loop time of 0.00939597 on 1 procs for 100 steps with 3 atoms
Performance: 459771778.655 fs/day, 0.000 hours/fs, 10642.865 timesteps/s, 31.929 katom-step/s
25.2% CPU use with 1 MPI tasks x no OpenMP threads
MPI task timing breakdown:
Section | min time | avg time | max time |%varavg| %total
---------------------------------------------------------------
Pair | 0 | 0 | 0 | 0.0 | 0.00
Neigh | 8.404e-06 | 8.404e-06 | 8.404e-06 | 0.0 | 0.09
Comm | 8.6872e-05 | 8.6872e-05 | 8.6872e-05 | 0.0 | 0.92
Output | 0.0071309 | 0.0071309 | 0.0071309 | 0.0 | 75.89
Modify | 0.0020085 | 0.0020085 | 0.0020085 | 0.0 | 21.38
Other | | 0.0001612 | | | 1.72
Nlocal: 3 ave 3 max 3 min
Histogram: 1 0 0 0 0 0 0 0 0 0
Nghost: 0 ave 0 max 0 min
Histogram: 1 0 0 0 0 0 0 0 0 0
Neighs: 0 ave 0 max 0 min
Histogram: 1 0 0 0 0 0 0 0 0 0
Total # of neighbors = 0
Ave neighs/atom = 0
Neighbor list builds = 24
Dangerous builds = 0
Total wall time: 0:00:00

1
examples/PACKAGES/pimd_bosonic/harmonic_trap_nvt/run.sh Normal file
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@ -0,0 +1 @@
mpirun -np $NBEADS $LMP -in in.lmp -partition ${NBEADS}x1

431
src/REPLICA/bosonic_exchange.cpp Normal file
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@ -0,0 +1,431 @@
/* ----------------------------------------------------------------------
LAMMPS - Large-scale Atomic/Molecular Massively Parallel Simulator
https://www.lammps.org/, Sandia National Laboratories
LAMMPS development team: developers@lammps.org
Copyright (2003) Sandia Corporation. Under the terms of Contract
DE-AC04-94AL85000 with Sandia Corporation, the U.S. Government retains
certain rights in this software. This software is distributed under
the GNU General Public License.
See the README file in the top-level LAMMPS directory.
------------------------------------------------------------------------- */
/* ----------------------------------------------------------------------
Package BosonicExchange
Purpose Handle Bosonic Exchange in Path Integral Molecular Dynamics
according to J. Chem. Phys. 159, 154107 (2023) (doi:10.1063/5.0173749)
Copyright Hirshberg lab @ Tel Aviv University
Authors Ofir Blumer, Jacob Higer, Yotam Feldman (yotam.feldman at gmail.com), Barak Hirshberg (hirshb at tauex.tau.ac.il)
Updated Jan-06-2025
Version 1.0
------------------------------------------------------------------------- */
#include "bosonic_exchange.h"
#include "domain.h"
#include "error.h"
#include "memory.h"
#include "universe.h"
using namespace LAMMPS_NS;
BosonicExchange::BosonicExchange(LAMMPS *lmp, int nbosons, int np, int bead_num, bool mic,
bool beta_convention) :
Pointers(lmp), nbosons(nbosons), np(np), bead_num(bead_num), apply_minimum_image(mic),
physical_beta_convention(beta_convention), x(nullptr), x_prev(nullptr), x_next(nullptr),
E_kn(nullptr), V(nullptr), V_backwards(nullptr), connection_probabilities(nullptr),
temp_nbosons_array(nullptr)
{
memory->create(temp_nbosons_array, nbosons + 1, "BosonicExchange: temp_nbosons_array");
memory->create(E_kn, (nbosons * (nbosons + 1) / 2), "BosonicExchange: E_kn");
memory->create(V, nbosons + 1, "BosonicExchange: V");
memory->create(V_backwards, nbosons + 1, "BosonicExchange: V_backwards");
memory->create(connection_probabilities, nbosons * nbosons,
"BosonicExchange: connection probabilities");
}
void BosonicExchange::prepare_with_coordinates(const double *x, const double *x_prev,
const double *x_next, double beta,
double spring_constant)
{
this->x = x;
this->x_prev = x_prev;
this->x_next = x_next;
this->beta = beta;
this->spring_constant = spring_constant;
if (bead_num == 0 || bead_num == np - 1) {
// exterior beads
evaluate_cycle_energies();
Evaluate_VBn();
Evaluate_V_backwards();
evaluate_connection_probabilities();
}
}
/* ---------------------------------------------------------------------- */
BosonicExchange::~BosonicExchange()
{
memory->destroy(connection_probabilities);
memory->destroy(V_backwards);
memory->destroy(V);
memory->destroy(E_kn);
memory->destroy(temp_nbosons_array);
}
/* ---------------------------------------------------------------------- */
void BosonicExchange::diff_two_beads(const double *x1, int l1, const double *x2, int l2,
double diff[3]) const
{
l1 = l1 % nbosons;
l2 = l2 % nbosons;
double delx2 = x2[3 * l2 + 0] - x1[3 * l1 + 0];
double dely2 = x2[3 * l2 + 1] - x1[3 * l1 + 1];
double delz2 = x2[3 * l2 + 2] - x1[3 * l1 + 2];
if (apply_minimum_image) { domain->minimum_image(delx2, dely2, delz2); }
diff[0] = delx2;
diff[1] = dely2;
diff[2] = delz2;
}
/* ---------------------------------------------------------------------- */
double BosonicExchange::distance_squared_two_beads(const double *x1, int l1, const double *x2,
int l2) const
{
double diff[3];
diff_two_beads(x1, l1, x2, l2, diff);
return diff[0] * diff[0] + diff[1] * diff[1] + diff[2] * diff[2];
}
/* ---------------------------------------------------------------------- */
void BosonicExchange::evaluate_cycle_energies()
{
const double *x_first_bead;
const double *x_last_bead;
if (bead_num == 0) {
x_first_bead = x;
x_last_bead = x_prev;
} else {
x_first_bead = x_next;
x_last_bead = x;
}
for (int i = 0; i < nbosons; i++) {
temp_nbosons_array[i] = distance_squared_two_beads(x_first_bead, i, x_last_bead, i);
}
for (int v = 0; v < nbosons; v++) {
set_Enk(v + 1, 1, 0.5 * spring_constant * (temp_nbosons_array[v]));
for (int u = v - 1; u >= 0; u--) {
double val = get_Enk(v + 1, v - u) +
0.5 * spring_constant *
(
// connect u to u+1
+distance_squared_two_beads(x_last_bead, u, x_first_bead, u + 1)
// break cycle [u+1,v]
- distance_squared_two_beads(x_first_bead, u + 1, x_last_bead, v)
// close cycle from v to u
+ distance_squared_two_beads(x_first_bead, u, x_last_bead, v));
set_Enk(v + 1, v - u + 1, val);
}
}
}
/* ---------------------------------------------------------------------- */
double BosonicExchange::get_Enk(int m, int k) const
{
int end_of_m = m * (m + 1) / 2;
return E_kn[end_of_m - k];
}
/* ---------------------------------------------------------------------- */
void BosonicExchange::set_Enk(int m, int k, double val)
{
int end_of_m = m * (m + 1) / 2;
E_kn[end_of_m - k] = val;
}
/* ---------------------------------------------------------------------- */
void BosonicExchange::Evaluate_VBn()
{
V[0] = 0.0;
for (int m = 1; m < nbosons + 1; m++) {
double Elongest = std::numeric_limits<double>::max();
for (int k = m; k > 0; k--) {
double val = get_Enk(m, k) + V[m - k];
Elongest = std::min(
Elongest, val); // Numerical stability (Xiong & Xiong, doi:10.1103/PhysRevE.106.025309)
temp_nbosons_array[k - 1] = val;
}
double sig_denom = 0.0;
for (int k = m; k > 0; k--) {
sig_denom += exp(-beta * (temp_nbosons_array[k - 1] - Elongest));
}
V[m] = Elongest - (1.0 / beta) * log(sig_denom / (double) m);
if (!std::isfinite(V[m])) {
error->universe_one(
FLERR,
fmt::format("Invalid sig_denom {} with Elongest {} in bosonic exchange potential",
sig_denom, Elongest));
}
}
}
/* ---------------------------------------------------------------------- */
void BosonicExchange::Evaluate_V_backwards()
{
V_backwards[nbosons] = 0.0;
for (int l = nbosons - 1; l > 0; l--) {
double Elongest = std::numeric_limits<double>::max();
for (int p = l; p < nbosons; p++) {
double val = get_Enk(p + 1, p - l + 1) + V_backwards[p + 1];
Elongest = std::min(Elongest, val);
temp_nbosons_array[p] = val;
}
double sig_denom = 0.0;
for (int p = l; p < nbosons; p++) {
sig_denom += 1.0 / (p + 1) * exp(-beta * (temp_nbosons_array[p] - Elongest));
}
V_backwards[l] = Elongest - log(sig_denom) / beta;
if (!std::isfinite(V_backwards[l])) {
error->universe_one(
FLERR,
fmt::format(
"Invalid sig_denom {} with Elongest {} in bosonic exchange potential backwards",
sig_denom, Elongest));
}
}
V_backwards[0] = V[nbosons];
}
/* ---------------------------------------------------------------------- */
double BosonicExchange::get_potential() const
{
return V[nbosons];
}
/* ---------------------------------------------------------------------- */
double BosonicExchange::get_interior_bead_spring_energy() const
{
double spring_energy_for_bead = 0.;
for (int i = 0; i < nbosons; i++) {
spring_energy_for_bead += 0.5 * spring_constant * distance_squared_two_beads(x, i, x_prev, i);
}
return spring_energy_for_bead;
}
/* ---------------------------------------------------------------------- */
double BosonicExchange::get_bead_spring_energy() const
{
double spring_energy_for_bead =
(bead_num == 0 ? get_potential() : get_interior_bead_spring_energy());
return spring_energy_for_bead;
}
/* ---------------------------------------------------------------------- */
void BosonicExchange::spring_force(double **f) const
{
if (bead_num == np - 1) {
spring_force_last_bead(f);
} else if (bead_num == 0) {
spring_force_first_bead(f);
} else {
spring_force_interior_bead(f);
}
}
/* ---------------------------------------------------------------------- */
void BosonicExchange::evaluate_connection_probabilities()
{
for (int l = 0; l < nbosons - 1; l++) {
double direct_link_probability =
1.0 - (exp(-beta * (V[l + 1] + V_backwards[l + 1] - V[nbosons])));
connection_probabilities[nbosons * l + (l + 1)] = direct_link_probability;
}
for (int u = 0; u < nbosons; u++) {
for (int l = u; l < nbosons; l++) {
double close_cycle_probability = 1.0 / (l + 1) *
exp(-beta * (V[u] + get_Enk(l + 1, l - u + 1) + V_backwards[l + 1] - V[nbosons]));
connection_probabilities[nbosons * l + u] = close_cycle_probability;
}
}
}
/* ---------------------------------------------------------------------- */
void BosonicExchange::spring_force_last_bead(double **f) const
{
const double *x_first_bead = x_next;
const double *x_last_bead = x;
for (int l = 0; l < nbosons; l++) {
double sum_x = 0.0;
double sum_y = 0.0;
double sum_z = 0.0;
for (int next_l = 0; next_l <= l + 1 && next_l < nbosons; next_l++) {
double diff_next[3];
diff_two_beads(x_last_bead, l, x_first_bead, next_l, diff_next);
double prob = connection_probabilities[nbosons * l + next_l];
sum_x += prob * diff_next[0];
sum_y += prob * diff_next[1];
sum_z += prob * diff_next[2];
}
double diff_prev[3];
diff_two_beads(x_last_bead, l, x_prev, l, diff_prev);
sum_x += diff_prev[0];
sum_y += diff_prev[1];
sum_z += diff_prev[2];
f[l][0] += sum_x * spring_constant;
f[l][1] += sum_y * spring_constant;
f[l][2] += sum_z * spring_constant;
}
}
/* ---------------------------------------------------------------------- */
void BosonicExchange::spring_force_first_bead(double **f) const
{
const double *x_first_bead = x;
const double *x_last_bead = x_prev;
for (int l = 0; l < nbosons; l++) {
double sum_x = 0.0;
double sum_y = 0.0;
double sum_z = 0.0;
for (int prev_l = std::max(0, l - 1); prev_l < nbosons; prev_l++) {
double diff_prev[3];
diff_two_beads(x_first_bead, l, x_last_bead, prev_l, diff_prev);
double prob = connection_probabilities[nbosons * prev_l + l];
sum_x += prob * diff_prev[0];
sum_y += prob * diff_prev[1];
sum_z += prob * diff_prev[2];
}
double diff_next[3];
diff_two_beads(x_first_bead, l, x_next, l, diff_next);
sum_x += diff_next[0];
sum_y += diff_next[1];
sum_z += diff_next[2];
f[l][0] += sum_x * spring_constant;
f[l][1] += sum_y * spring_constant;
f[l][2] += sum_z * spring_constant;
}
}
/* ---------------------------------------------------------------------- */
void BosonicExchange::spring_force_interior_bead(double **f) const
{
for (int l = 0; l < nbosons; l++) {
double sum_x = 0.0;
double sum_y = 0.0;
double sum_z = 0.0;
double diff_prev[3];
diff_two_beads(x, l, x_prev, l, diff_prev);
sum_x += diff_prev[0];
sum_y += diff_prev[1];
sum_z += diff_prev[2];
double diff_next[3];
diff_two_beads(x, l, x_next, l, diff_next);
sum_x += diff_next[0];
sum_y += diff_next[1];
sum_z += diff_next[2];
f[l][0] += sum_x * spring_constant;
f[l][1] += sum_y * spring_constant;
f[l][2] += sum_z * spring_constant;
}
}
/* ---------------------------------------------------------------------- */
double BosonicExchange::prim_estimator()
{
// In the "reduced-beta convention" [e.g., in J. Chem. Phys. 133, 124104 (2010); also J. Chem. Phys. 74, 4078-4095 (1981)],
// the Boltzmann exponents have the form exp[-(beta/P)H], where H is the classical Hamiltonian of the
// ring polymers. This results in a canonical distribution at P times the physical temperature.
// In contrast, the "physical-beta convention" [e.g., in J. Chem. Phys. 99, 2796-2808 (1993)] uses weights of the form exp(-beta*H),
// such that the temperature of the canonical ensemble coincides with the physical temperature.
// Notably, the classical Hamiltonians of the two conventions differ, with the spring constant
// in the reduced-beta convention being P times larger than that in the physical-beta convention. Additionally, the reduced-beta convention
// lacks a 1/P prefactor in front of the external potential. The Hamiltonians of the two conventions are related through
// H_physical = H_reduced / P. The code below was designed to be compatible with both conventions,
// and the choice of convention only affects a single calculation within it.
// Setting the following boolean variable to false amounts to adopting the reduced-beta convention.
double convention_correction = (physical_beta_convention ? 1 : 1.0 / np);
// Adds the contribution of an interior spring, which is the same as for distinguishable particles.
if (bead_num != 0) {
return convention_correction *
(0.5 * domain->dimension * nbosons / beta - get_interior_bead_spring_energy());
}
// For the first bead, add the contribution of the exterior bead (See Equations 4-5 in the
// Supporting Information of Hirshberg et. al., doi.org/10.1073/pnas.1913365116)
temp_nbosons_array[0] = 0.0;
for (int m = 1; m < nbosons + 1; ++m) {
double sig = 0.0;
temp_nbosons_array[m] = 0.0;
double Elongest = std::numeric_limits<double>::max();
// Numerical stability (Xiong & Xiong, doi:10.1103/PhysRevE.106.025309)
for (int k = m; k > 0; k--) { Elongest = std::min(Elongest, get_Enk(m, k) + V[m - k]); }
for (int k = m; k > 0; --k) {
double E_kn_val = get_Enk(m, k);
sig += (temp_nbosons_array[m - k] - E_kn_val) * exp(-beta * (E_kn_val + V[m - k] - Elongest));
}
double sig_denom_m = m * exp(-beta * (V[m] - Elongest));
temp_nbosons_array[m] = sig / sig_denom_m;
}
return convention_correction *
(0.5 * domain->dimension * nbosons / beta + temp_nbosons_array[nbosons]);
}
/* ---------------------------------------------------------------------- */

71
src/REPLICA/bosonic_exchange.h Normal file
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@ -0,0 +1,71 @@
/* ----------------------------------------------------------------------
LAMMPS - Large-scale Atomic/Molecular Massively Parallel Simulator
https://www.lammps.org/, Sandia National Laboratories
LAMMPS development team: developers@lammps.org
Copyright (2003) Sandia Corporation. Under the terms of Contract
DE-AC04-94AL85000 with Sandia Corporation, the U.S. Government retains
certain rights in this software. This software is distributed under
the GNU General Public License.
See the README file in the top-level LAMMPS directory.
------------------------------------------------------------------------- */
#ifndef BOSONIC_EXCHANGE_H
#define BOSONIC_EXCHANGE_H
#include "pointers.h"
namespace LAMMPS_NS {
class BosonicExchange : protected Pointers {
public:
BosonicExchange(class LAMMPS *, int nbosons, int np, int bead_num, bool mic,
bool beta_convention);
~BosonicExchange();
void prepare_with_coordinates(const double *x, const double *x_prev, const double *x_next,
double beta, double spring_constant);
double get_potential() const;
double get_bead_spring_energy() const;
void spring_force(double **f) const;
double prim_estimator();
private:
void evaluate_cycle_energies();
void diff_two_beads(const double *x1, int l1, const double *x2, int l2, double diff[3]) const;
double get_interior_bead_spring_energy() const;
double distance_squared_two_beads(const double *x1, int l1, const double *x2, int l2) const;
double get_Enk(int m, int k) const;
void set_Enk(int m, int k, double val);
void evaluate_connection_probabilities();
void spring_force_last_bead(double **f) const;
void spring_force_first_bead(double **f) const;
void spring_force_interior_bead(double **f) const;
void Evaluate_VBn();
void Evaluate_V_backwards();
const int nbosons;
const int np;
const int bead_num;
const bool apply_minimum_image;
const bool physical_beta_convention;
double spring_constant;
double beta;
const double *x;
const double *x_prev;
const double *x_next;
double *E_kn;
double *V;
double *V_backwards;
double *connection_probabilities;
double *temp_nbosons_array;
};
} // namespace LAMMPS_NS
#endif

32
src/REPLICA/fix_pimd_langevin.cpp
View File

@ -53,17 +53,12 @@ using MathConst::MY_SQRT2;
using MathConst::THIRD;
using MathSpecial::powint;
enum { PIMD, NMPIMD };
enum { PHYSICAL, NORMAL };
enum { BAOAB, OBABO };
enum { ISO, ANISO, TRICLINIC };
enum { PILE_L };
enum { MTTK, BZP };
enum { NVE, NVT, NPH, NPT };
enum { SINGLE_PROC, MULTI_PROC };
static std::map<int, std::string> Barostats{{MTTK, "MTTK"}, {BZP, "BZP"}};
static std::map<int, std::string> Ensembles{{NVE, "NVE"}, {NVT, "NVT"}, {NPH, "NPH"}, {NPT, "NPT"}};
static std::map<int, std::string> Barostats{{FixPIMDLangevin::MTTK, "MTTK"},
{FixPIMDLangevin::BZP, "BZP"}};
static std::map<int, std::string> Ensembles{{FixPIMDLangevin::NVE, "NVE"},
{FixPIMDLangevin::NVT, "NVT"},
{FixPIMDLangevin::NPH, "NPH"},
{FixPIMDLangevin::NPT, "NPT"}};
/* ---------------------------------------------------------------------- */
@ -248,7 +243,7 @@ FixPIMDLangevin::FixPIMDLangevin(LAMMPS *lmp, int narg, char **arg) :
removecomflag = 1;
else if (strcmp(arg[i + 1], "no") == 0)
removecomflag = 0;
} else {
} else if (strcmp(arg[i], "") != 0) {
error->universe_all(FLERR, fmt::format("Unknown keyword {} for fix {}", arg[i], style));
}
}
@ -445,7 +440,7 @@ void FixPIMDLangevin::init()
}
planck *= sp;
hbar = planck / (MY_2PI);
double beta = 1.0 / (force->boltz * temp);
beta = 1.0 / (force->boltz * temp);
double _fbond = 1.0 * np * np / (beta * beta * hbar * hbar);
omega_np = np / (hbar * beta) * sqrt(force->mvv2e);
@ -522,7 +517,7 @@ void FixPIMDLangevin::setup(int vflag)
else if (cmode == MULTI_PROC)
nmpimd_transform(bufbeads, x, M_x2xp[universe->iworld]);
} else if (method == PIMD) {
inter_replica_comm(x);
prepare_coordinates();
spring_force();
} else {
error->universe_all(
@ -679,6 +674,13 @@ void FixPIMDLangevin::final_integrate()
/* ---------------------------------------------------------------------- */
void FixPIMDLangevin::prepare_coordinates()
{
inter_replica_comm(atom->x);
}
/* ---------------------------------------------------------------------- */
void FixPIMDLangevin::post_force(int /*flag*/)
{
int nlocal = atom->nlocal;
@ -712,7 +714,7 @@ void FixPIMDLangevin::post_force(int /*flag*/)
if (mapflag) {
for (int i = 0; i < nlocal; i++) { domain->unmap(x[i], image[i]); }
}
inter_replica_comm(x);
prepare_coordinates();
spring_force();
compute_spring_energy();
compute_t_prim();

22
src/REPLICA/fix_pimd_langevin.h
View File

@ -29,6 +29,15 @@ class FixPIMDLangevin : public Fix {
FixPIMDLangevin(class LAMMPS *, int, char **);
~FixPIMDLangevin() override;
enum { PIMD, NMPIMD };
enum { PHYSICAL, NORMAL };
enum { BAOAB, OBABO };
enum { ISO, ANISO, TRICLINIC };
enum { PILE_L };
enum { MTTK, BZP };
enum { NVE, NVT, NPH, NPT };
enum { SINGLE_PROC, MULTI_PROC };
int setmask() override;
void init() override;
@ -94,8 +103,9 @@ class FixPIMDLangevin : public Fix {
int *counts, *displacements;
void comm_init();
virtual void prepare_coordinates();
void inter_replica_comm(double **ptr);
void spring_force();
void virtual spring_force();
/* normal-mode operations */
@ -165,12 +175,12 @@ class FixPIMDLangevin : public Fix {
class Compute *c_pe;
class Compute *c_press;
void compute_totke(); // 1: kinetic energy
void compute_spring_energy(); // 2: spring elastic energy
void compute_pote(); // 3: potential energy
void compute_tote(); // 4: total energy: 1+2+3 for all the beads
void compute_totke(); // 1: kinetic energy
virtual void compute_spring_energy(); // 2: spring elastic energy
void compute_pote(); // 3: potential energy
void compute_tote(); // 4: total energy: 1+2+3 for all the beads
void compute_stress_tensor();
void compute_t_prim();
virtual void compute_t_prim();
void compute_t_vir();
void compute_t_cv();
void compute_p_prim();

193
src/REPLICA/fix_pimd_langevin_bosonic.cpp Normal file
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@ -0,0 +1,193 @@
/* ----------------------------------------------------------------------
LAMMPS - Large-scale Atomic/Molecular Massively Parallel Simulator
https://www.lammps.org/, Sandia National Laboratories
LAMMPS development team: developers@lammps.org
Copyright (2003) Sandia Corporation. Under the terms of Contract
DE-AC04-94AL85000 with Sandia Corporation, the U.S. Government retains
certain rights in this software. This software is distributed under
the GNU General Public License.
See the README file in the top-level LAMMPS directory.
------------------------------------------------------------------------- */
/* ----------------------------------------------------------------------
Package FixPIMDBLangevin
Purpose Path Integral Molecular Dynamics of Bosons with Langevin Thermostat
Copyright Hirshberg lab @ Tel Aviv University
Authors Ofir Blumer, Jacob Higer, Yotam Feldman (yotam.feldman at gmail.com), Barak Hirshberg (hirshb at tauex.tau.ac.il)
Updated Jan-06-2025
Version 1.0
------------------------------------------------------------------------- */
#include "fix_pimd_langevin_bosonic.h"
#include "bosonic_exchange.h"
#include "atom.h"
#include "comm.h"
#include "domain.h"
#include "error.h"
#include "force.h"
#include "memory.h"
#include "universe.h"
#include "update.h"
#include <cmath>
#include <cstdlib>
#include <cstring>
using namespace LAMMPS_NS;
using namespace FixConst;
/* ---------------------------------------------------------------------- */
FixPIMDBLangevin::FixPIMDBLangevin(LAMMPS *lmp, int narg, char **arg) :
FixPIMDLangevin(lmp, narg, filtered_args = filter_args(narg, arg)), filtered_narg(narg),
nbosons(atom->nlocal)
{
bosonic_exchange = new BosonicExchange(lmp, atom->nlocal, np, universe->me, true, false);
synch_energies = true;
// Loop over the arguments with i++ instead of i+=2 like the parent,
// because the parent's loop has i++ inside some if blocks.
for (int i = 3; i < narg - 1; i++) {
if ((strcmp(arg[i], "method") == 0) && (strcmp(arg[i + 1], "pimd") != 0)) {
error->universe_all(FLERR, "Method not supported in fix pimdb/langevin; only method PIMD");
} else if (strcmp(arg[i], "scale") == 0) {
error->universe_all(FLERR,
"The scale parameter of the PILE_L thermostat is not supported for "
"pimdb, and should be removed.");
} else if ((strcmp(arg[i], "iso") == 0) || (strcmp(arg[i], "aniso") == 0) ||
(strcmp(arg[i], "barostat") == 0) || (strcmp(arg[i], "taup") == 0)) {
error->universe_all(FLERR, "Barostat parameters are not available for pimdb.");
} else if (strcmp(arg[i], "esynch") == 0) {
if (strcmp(arg[i + 1], "yes") == 0) {
synch_energies = true;
} else if (strcmp(arg[i + 1], "no") == 0) {
synch_energies = false;
} else {
error->universe_all(FLERR, "The esynch parameter can only receive yes or no!");
}
}
}
if (fmmode != PHYSICAL) {
error->universe_all(
FLERR,
"The only available fmmode for pimdb is physical, please remove the fmmode keyword.");
}
if (ensemble != NVE && ensemble != NVT) {
error->universe_all(FLERR,
"The only available ensembles for pimdb are nve and nvt, please choose one "
"of these ensembles.");
}
method = PIMD;
size_vector = 6;
memory->create(f_tag_order, nbosons, 3, "FixPIMDBLangevin:f_tag_order");
}
/* ---------------------------------------------------------------------- */
FixPIMDBLangevin::~FixPIMDBLangevin()
{
memory->destroy(f_tag_order);
for (int i = 0; i < filtered_narg; ++i) delete[] filtered_args[i];
memory->destroy(filtered_args);
delete bosonic_exchange;
}
/* ---------------------------------------------------------------------- */
char **FixPIMDBLangevin::filter_args(int narg, char **arg)
{
filtered_narg = narg;
char **filtered_args = new char *[narg];
for (int i = 0; i < narg; i++) {
if (strcmp(arg[i], "esynch") == 0) {
filtered_args[i] = utils::strdup("");
} else {
filtered_args[i] = utils::strdup(arg[i]);
}
}
return filtered_args;
}
/* ---------------------------------------------------------------------- */
void FixPIMDBLangevin::prepare_coordinates()
{
inter_replica_comm(atom->x);
double ff = fbond * atom->mass[atom->type[0]];
int nlocal = atom->nlocal;
double *me_bead_positions = *(atom->x);
double *last_bead_positions = &bufsortedall[x_last * nlocal][0];
double *next_bead_positions = &bufsortedall[x_next * nlocal][0];
bosonic_exchange->prepare_with_coordinates(me_bead_positions, last_bead_positions,
next_bead_positions, beta_np, ff);
}
/* ---------------------------------------------------------------------- */
void FixPIMDBLangevin::spring_force()
{
for (int i = 0; i < nbosons; i++) {
f_tag_order[i][0] = 0.0;
f_tag_order[i][1] = 0.0;
f_tag_order[i][2] = 0.0;
}
bosonic_exchange->spring_force(f_tag_order);
double **f = atom->f;
tagint *tag = atom->tag;
for (int i = 0; i < nbosons; i++) {
f[i][0] += f_tag_order[tag[i] - 1][0];
f[i][1] += f_tag_order[tag[i] - 1][1];
f[i][2] += f_tag_order[tag[i] - 1][2];
}
}
/* ---------------------------------------------------------------------- */
void FixPIMDBLangevin::compute_spring_energy()
{
se_bead = bosonic_exchange->get_bead_spring_energy();
if (synch_energies) {
MPI_Allreduce(&se_bead, &total_spring_energy, 1, MPI_DOUBLE, MPI_SUM, universe->uworld);
total_spring_energy /= universe->procs_per_world[universe->iworld];
} else {
total_spring_energy = 0;
}
}
/* ---------------------------------------------------------------------- */
void FixPIMDBLangevin::compute_t_prim()
{
if (synch_energies) {
double prim = bosonic_exchange->prim_estimator();
MPI_Allreduce(&prim, &t_prim, 1, MPI_DOUBLE, MPI_SUM, universe->uworld);
} else {
t_prim = bosonic_exchange->prim_estimator();
}
}
/* ---------------------------------------------------------------------- */
double FixPIMDBLangevin::compute_vector(int n)
{
if (0 <= n && n < 6) {
return FixPIMDLangevin::compute_vector(n);
} else {
error->universe_all(FLERR, "Fix only has 6 outputs!");
}
return 0.0;
}

55
src/REPLICA/fix_pimd_langevin_bosonic.h Normal file
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@ -0,0 +1,55 @@
/* ----------------------------------------------------------------------
LAMMPS - Large-scale Atomic/Molecular Massively Parallel Simulator
https://www.lammps.org/, Sandia National Laboratories
LAMMPS development team: developers@lammps.org
Copyright (2003) Sandia Corporation. Under the terms of Contract
DE-AC04-94AL85000 with Sandia Corporation, the U.S. Government retains
certain rights in this software. This software is distributed under
the GNU General Public License.
See the README file in the top-level LAMMPS directory.
------------------------------------------------------------------------- */
#ifdef FIX_CLASS
// clang-format off
FixStyle(pimd/langevin/bosonic, FixPIMDBLangevin);
// clang-format on
#else
#ifndef FIX_PIMDB_LANGEVIN_H
#define FIX_PIMDB_LANGEVIN_H
#include "fix_pimd_langevin.h"
namespace LAMMPS_NS {
class FixPIMDBLangevin : public FixPIMDLangevin {
public:
FixPIMDBLangevin(class LAMMPS *, int, char **);
~FixPIMDBLangevin();
double compute_vector(int) override;
void compute_spring_energy() override;
void compute_t_prim() override;
char **filtered_args;
int filtered_narg;
protected:
void prepare_coordinates() override;
void spring_force() override;
private:
const int nbosons;
bool synch_energies;
class BosonicExchange *bosonic_exchange;
double **f_tag_order;
char **filter_args(
int, char **); // for hold memory of filtered arguments when calling the parent constructor
};
} // namespace LAMMPS_NS
#endif
#endif

36
src/REPLICA/fix_pimd_nvt.cpp
View File

@ -43,8 +43,6 @@ using namespace MathConst;
using MathSpecial::powint;
enum { PIMD, NMPIMD, CMD };
/* ---------------------------------------------------------------------- */
FixPIMDNVT::FixPIMDNVT(LAMMPS *lmp, int narg, char **arg) : Fix(lmp, narg, arg)
@ -220,7 +218,7 @@ void FixPIMDNVT::init()
const double Plank = force->hplanck;
double hbar = Plank / (2.0 * MY_PI) * sp;
double beta = 1.0 / (Boltzmann * nhc_temp);
beta = 1.0 / (Boltzmann * nhc_temp);
double _fbond = 1.0 * np / (beta * beta * hbar * hbar);
omega_np = sqrt((double) np) / (hbar * beta) * sqrt(force->mvv2e);
@ -271,12 +269,20 @@ void FixPIMDNVT::final_integrate()
/* ---------------------------------------------------------------------- */
void FixPIMDNVT::prepare_coordinates()
{
comm_exec(atom->x);
}
/* ---------------------------------------------------------------------- */
void FixPIMDNVT::post_force(int /*flag*/)
{
for (int i = 0; i < atom->nlocal; i++)
for (int j = 0; j < 3; j++) atom->f[i][j] /= np;
comm_exec(atom->x);
prepare_coordinates();
pre_spring_force_estimators();
spring_force();
if (method == CMD || method == NMPIMD) {
@ -533,6 +539,24 @@ void FixPIMDNVT::nmpimd_transform(double **src, double **des, double *vector)
/* ---------------------------------------------------------------------- */
void FixPIMDNVT::pre_spring_force_estimators(){
vir_estimator();
}
/* ---------------------------------------------------------------------- */
void FixPIMDNVT::vir_estimator() {
double **x = atom->x;
double **f = atom->f;
int nlocal = atom->nlocal;
virial = 0.0;
for (int i = 0; i < nlocal; i++) {
virial += -0.5 * (x[i][0] * f[i][0] + x[i][1] * f[i][1] + x[i][2] * f[i][2]);
}
}
/* ---------------------------------------------------------------------- */
void FixPIMDNVT::spring_force()
{
spring_energy = 0.0;
@ -546,8 +570,6 @@ void FixPIMDNVT::spring_force()
double *xlast = buf_beads[x_last];
double *xnext = buf_beads[x_next];
virial = 0.0;
for (int i = 0; i < nlocal; i++) {
double delx1 = xlast[0] - x[i][0];
double dely1 = xlast[1] - x[i][1];
@ -567,8 +589,6 @@ void FixPIMDNVT::spring_force()
double dy = dely1 + dely2;
double dz = delz1 + delz2;
virial += -0.5 * (x[i][0] * f[i][0] + x[i][1] * f[i][1] + x[i][2] * f[i][2]);
f[i][0] -= (dx) *ff;
f[i][1] -= (dy) *ff;
f[i][2] -= (dz) *ff;

10
src/REPLICA/fix_pimd_nvt.h
View File

@ -30,6 +30,8 @@ class FixPIMDNVT : public Fix {
FixPIMDNVT(class LAMMPS *, int, char **);
~FixPIMDNVT() override;
enum { PIMD, NMPIMD, CMD };
int setmask() override;
void init() override;
@ -53,7 +55,6 @@ class FixPIMDNVT : public Fix {
void unpack_forward_comm(int, int, double *) override;
protected:
int method;
int np;
double inverse_np;
@ -62,8 +63,10 @@ class FixPIMDNVT : public Fix {
double omega_np, fbond, spring_energy, sp, virial;
int x_last, x_next;
void spring_force();
virtual void prepare_coordinates();
virtual void pre_spring_force_estimators();
virtual void spring_force();
void vir_estimator();
/* fictitious mass */
@ -101,6 +104,7 @@ class FixPIMDNVT : public Fix {
int nhc_nchain;
bool nhc_ready;
double nhc_temp, dtv, dtf, t_sys;
double beta;
double **nhc_eta; /* coordinates of NH chains for ring-polymer beads */
double **nhc_eta_dot; /* velocities of NH chains */

99
src/REPLICA/fix_pimd_nvt_bosonic.cpp Normal file
View File

@ -0,0 +1,99 @@
/* ----------------------------------------------------------------------
LAMMPS - Large-scale Atomic/Molecular Massively Parallel Simulator
https://www.lammps.org/, Sandia National Laboratories
LAMMPS development team: developers@lammps.org
Copyright (2003) Sandia Corporation. Under the terms of Contract
DE-AC04-94AL85000 with Sandia Corporation, the U.S. Government retains
certain rights in this software. This software is distributed under
the GNU General Public License.
See the README file in the top-level LAMMPS directory.
------------------------------------------------------------------------- */
/* ----------------------------------------------------------------------
Package FixPIMDBNVT
Purpose Path Integral Molecular Dynamics of Bosons with Nose-Hoover Thermostat
Copyright Hirshberg lab @ Tel Aviv University
Authors Ofir Blumer, Jacob Higer, Yotam Feldman (yotam.feldman at gmail.com), Barak Hirshberg (hirshb at tauex.tau.ac.il)
Updated Jan-06-2025
Version 1.0
------------------------------------------------------------------------- */
#include "fix_pimd_nvt_bosonic.h"
#include "bosonic_exchange.h"
#include "atom.h"
#include "error.h"
#include "force.h"
#include "universe.h"
using namespace LAMMPS_NS;
/* ---------------------------------------------------------------------- */
FixPIMDBNVT::FixPIMDBNVT(LAMMPS *lmp, int narg, char **arg) : FixPIMDNVT(lmp, narg, arg)
{
bosonic_exchange = new BosonicExchange(lmp, atom->nlocal, np, universe->me, true, true);
virial = 0.0;
prim = 0.0;
spring_energy = 0.0;
size_vector = 4;
if (method != PIMD && method != NMPIMD) {
error->universe_all(FLERR,
"Method not supported in fix pimdb/nvt; only methods PIMD and NMPIMD");
}
}
/* ---------------------------------------------------------------------- */
FixPIMDBNVT::~FixPIMDBNVT()
{
delete bosonic_exchange;
}
/* ---------------------------------------------------------------------- */
void FixPIMDBNVT::pre_spring_force_estimators()
{
FixPIMDNVT::pre_spring_force_estimators();
spring_energy = bosonic_exchange->get_bead_spring_energy();
prim = bosonic_exchange->prim_estimator();
}
/* ---------------------------------------------------------------------- */
void FixPIMDBNVT::prepare_coordinates()
{
comm_exec(atom->x);
double **x = atom->x;
double *xlast = buf_beads[x_last];
double *xnext = buf_beads[x_next];
double ff = fbond * atom->mass[atom->type[0]];
bosonic_exchange->prepare_with_coordinates(*x, xlast, xnext, beta, -ff);
}
void FixPIMDBNVT::spring_force()
{
double **f = atom->f;
bosonic_exchange->spring_force(f);
}
/* ---------------------------------------------------------------------- */
double FixPIMDBNVT::compute_vector(int n)
{
if (0 <= n && n < 3) { return FixPIMDNVT::compute_vector(n); }
if (n == 3) {
return prim;
} else {
error->universe_all(FLERR, "Fix only has 4 outputs!");
}
return 0.0;
}

46
src/REPLICA/fix_pimd_nvt_bosonic.h Normal file
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@ -0,0 +1,46 @@
/* ----------------------------------------------------------------------
LAMMPS - Large-scale Atomic/Molecular Massively Parallel Simulator
https://www.lammps.org/, Sandia National Laboratories
LAMMPS development team: developers@lammps.org
Copyright (2003) Sandia Corporation. Under the terms of Contract
DE-AC04-94AL85000 with Sandia Corporation, the U.S. Government retains
certain rights in this software. This software is distributed under
the GNU General Public License.
See the README file in the top-level LAMMPS directory.
------------------------------------------------------------------------- */
#ifdef FIX_CLASS
// clang-format off
FixStyle(pimd/nvt/bosonic,FixPIMDBNVT);
// clang-format on
#else
#ifndef FIX_PIMDB_NVT_H
#define FIX_PIMDB_NVT_H
#include "fix_pimd_nvt.h"
namespace LAMMPS_NS {
class FixPIMDBNVT : public FixPIMDNVT {
public:
FixPIMDBNVT(class LAMMPS *, int, char **);
~FixPIMDBNVT();
double compute_vector(int) override;
protected:
void prepare_coordinates() override;
void spring_force() override;
void pre_spring_force_estimators() override;
private:
class BosonicExchange *bosonic_exchange;
double prim;
};
} // namespace LAMMPS_NS
#endif
#endif