*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)
@ -222,7 +223,7 @@ 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 +335,8 @@ 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*)
*keywords* = *integrator* or *fmass* or *temp* or *thermostat* or *tau* or *iso* or *aniso* or *barostat* or *taup* or *fixcom* or *lj*
*keywords* = *integrator* or *ensemble* or *fmass* or *temp* or *thermostat* or *tau* or *fixcom* or *lj*
*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
@ -39,10 +40,6 @@ Syntax
style value = *PILE_L*
seed = random number generator seed
*tau* value = thermostat damping parameter (time unit)
*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
epsilon = energy scale for reduced units (energy units)
@ -62,26 +59,17 @@ Examples
Description
"""""""""""
..versionchanged:: -
Fix *pimdb/nvt* and fix *pimdb/langevin* were added, inheriting fix *pimd/nvt* and fix *pimd/langevin*, respectively.
These fix commands are based on the fix *pimd/nvt* and fix *pimd/langevin* commands for
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 *pimdb/nvt* and fix *pimdb/langevin*support simulations of bosons by including exchange effects.
The *pimdb* commands share syntax with the equivalent *pimd* commands. The user is referred to the documentation of the *pimd*commands for a
while fix *pimdb/nvt* and fix *pimdb/langevin*perform simulations of bosons, including exchange effects.
The *pimdb* commands share syntax with the equivalent *pimd* commands. The user is referred to the documentation of the *pimd*fix for a
detailed syntax description and additional, general capabilities of the commands.
The major differences from fix *pimd* in terms of capabilities are:
..note::
* Fix *pimdb/nvt* the only supports the "pimd" and "nmpimd" methods. Fix *pimdb/langevin* only supports the "pimd" method, and the keyword *method* should not be used. 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 value other than *normal*.
* Fix *pimdb/langevin* currently does not support *ensemble* other than *nve*, *nvt*. The barostat related keywords *iso*, *aniso*, *barostat*, *taup* are not supported.
Currently, and fix *pimdb/nvt* only supports the "pimd" and "nmpimd" methods.
Fix *pimdb/langevin* only supports the "pimd" method, and the keyword *method* should not be used.
Trying to explicitly set a different method than "pimd" would raise an error.
Similarly, the keywords *ensemble* and *fmmode* should not be used, and would raise an error if set to values
other than *nvt* and *normal*, respectively.
Trying to use the *scale* keywords, that is not supported for "pimd" method, would also raise an error.
Finally, trying to use any of the barostat-related keywords supported for *pimd/langevin* would raise errors.
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`
@ -92,31 +80,33 @@ is given by :ref:`(Tuckerman) <book-Tuckerman>`:
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 different permutations:
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:
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.
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:`NP+N^2`:ref:`(Feldman) <Feldman>`.
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:`NP+N^2`:ref:`(Feldman) <Feldman>`.
through an algorithm that scales the same as the one for the potential calculation :math:`N^2+PN`:ref:`(Feldman) <Feldman>`.
Output
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 *pimdb/nvt* computes a global 4-vector, which can be accessed by
various :doc:`output commands <Howto_output>`. The three quantities in
the global vector are:
@ -124,9 +114,9 @@ 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) <Herman>`.
energy of the quantum system :ref:`(Herman) <HermanBB>`.
#. the current value of the scalar primitive estimator for the kinetic
energy of the quantum system :ref:`(Tuckerman) <book-Tuckerman>`.
energy of the quantum system :ref:`(Hirshberg) <Hirshberg>`.
The vector values calculated by fix *pimdb/nvt* are "extensive", except for the
temperature, which is "intensive".
@ -134,29 +124,44 @@ temperature, which is "intensive".
Fix *pimdb/langevin* 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 normal mode
#. spring elastic energy of the normal mode
#. kinetic energy of the beads
#. spring elastic energy of the beads
#. potential energy of the bead
#. total energy of all beads
#. primitive kinetic energy estimator
#. virial energy estimator
#. total energy of all beads (conserved if *ensemble* is *nve*)
#. primitive kinetic energy estimator:ref:`(Hirshberg) <Hirshberg>`
#. virial energy estimator:ref:`(Herman) <HermanBB>`
The first 3 are different for different log files, and the others are the same for different 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.
Default
"""""""
The keyword defaults for fix *pimdb/nvt* are method = pimd, fmass = 1.0, sp
= 1.0, temp = 300.0, and nhc = 2.
----------
..book-Tuckerman:
.. _book-Tuckerman:
**(Tuckerman)** M. Tuckerman, Statistical Mechanics: Theory and Molecular Simulation (Oxford University Press, 2010)
..Hirshberg:
.. _Hirshberg:
**(Hirshberg)** B. Hirshberg, V. Rizzi, and M.Parrinello, “Path integral molecular dynamics for bosons,” Proc. Natl. Acad. Sci. U. S. A. 116, 21445 (2019)
..Feldman:
.. _Feldman:
**(Feldman)** Y. M. Y. Feldman and B. Hirshberg, “Quadratic scaling bosonic path integral molecular dynamics,” J. Chem. Phys. 159, 154107 (2023)
.._Herman:
.._HermanBB:
**(Herman)** M. F. Herman, E. J. Bruskin, B. J. Berne, J Chem Phys, 76, 5150 (1982).
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