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update fix pimd/langevin doc

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Yifan Li
2023-03-21 09:23:22 -04:00
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doc/src/fix_pimd.rst
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@ -30,7 +30,8 @@ Syntax
* 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 or *iso* or *aniso* or *barostat* or *taup* or *fixcom* or *lj*
*keywords* = *method* or *integrator* or *ensemble* or *fmmode* or *fmass* or *scale* or *temp* or *thermostat* or
*tau*or or *iso* or *aniso* or *barostat* or *taup* or *fixcom* or *lj*
*method* value = *nmpimd*
*integrator* value = *obabo* or *baoab*
*fmmode* value = *physical* or *normal*
@ -43,7 +44,7 @@ Syntax
*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
Pressure = scalar external pressure of the barostat
*barostat* value = *BZP* or *MTTK*
*taup* value = barostat damping parameter (time unit)
*fixcom* value = *yes* or *no*
@ -85,7 +86,7 @@ by the following equations:
H_{eff} = & \bigg(\sum_{i=1}^P \frac{p_i^2}{2M_i}\bigg) + V_{eff} \\
V_{eff} = & \sum_{i=1}^P \bigg[ \frac{mP}{2\beta^2 \hbar^2} (q_i - q_{i+1})^2 + \frac{1}{P} V(q_i)\bigg]
$M_i$ is the fictitious mass of the $i$-th mode, and m is the actual mass of the atoms.
:math:`M_i` is the fictitious mass of the :math:`i`-th mode, and m is the actual mass of the atoms.
The interested user is referred to any of the numerous references on
this methodology, but briefly, each quantum particle in a path integral
@ -109,8 +110,9 @@ would be 3 x N x P x Nc.
Fix *pimd/nvt* implements a complete velocity-verlet integrator
combined with NH massive chain thermostat, so no other time
integration fix should be used.
Fix *pimd/langevin* implements a complete velocity-verlet integrator
combined with Langevin thermostat in the normal mode representation, and
combined with Langevin thermostat in the normal mode representation, and
also provides a barostat to sample the NPH/NPT ensembles.
The *method* keyword determines what style of PIMD is performed. A
@ -136,7 +138,7 @@ normal-mode PIMD. A value of *cmd* is for centroid molecular dynamics
the real particle.
.. note::
Fix pimd/langevin only supports *method* value *nmpimd*. This should be enough
Fix pimd/langevin only supports *method* value *nmpimd*. This should be enough
for most PIMD applications for quantum thermodynamics purpose.
Motion of the centroid can be effectively uncoupled from the other
@ -155,42 +157,51 @@ masses of beads, which can be used for the Partial Adiabatic CMD
:ref:`(Hone) <Hone>`, or to be set as P, which results in the fictitious
masses to be equal to the real particle masses.
The keyword *fmmode* of *fix pimd/langevin* determines the mode of fictitious
mass preconditioning. There are two options: *physical* and *normal*. If *fmmode* is
The keyword *fmmode* of *fix pimd/langevin* determines the mode of fictitious
mass preconditioning. There are two options: *physical* and *normal*. If *fmmode* is
*physical*, then the physical mass of the particles are used (and then multiplied by
*fmass*). If *fmmode* is *normal*, then the physical mass is first multiplied by the
eigenvalue of each normal mode, and then multiplied by *fmass*. More precisely, the
*fmass*). If *fmmode* is *normal*, then the physical mass is first multiplied by the
eigenvalue of each normal mode, and then multiplied by *fmass*. More precisely, the
fictitious mass of *fix pimd/langevin* is determined by two factors: *fmmode* and *fmass*.
If *fmmode* is *physical*, then the fictitious mass is
.. math::
$M_i = \mathrm{fmass} \times m$
If *fmmode* is *normal*, then the fictitious mass is
.. math::
$M_i = \mathrm{fmass} \times \lambda_i \times m$
where $\lambda_i$ is the eigenvalue of the $i$-th normal mode.
.. math::
M_i = \mathrm{fmass} \times m
If *fmmode* is *normal*, then the fictitious mass is
.. math::
M_i = \mathrm{fmass} \times \lambda_i \times m
where :math:`\lambda_i` is the eigenvalue of the :math:`i`-th normal mode.
.. note::
Fictitious mass is only used in the momentum of the equation of motion
($\bf{p}_i=M_i\bf{v}_i$), and not used in the spring elastic energy
($\sum_{i=1}^P \frac{1}{2}m\omega_P^2(q_i - q_{i+1})^2$, $m$ is always the
actual mass of the particles).
(:math:`\mathbf{p}_i=M_i\mathbf{v}_i`), and not used in the spring elastic energy
(:math:`\sum_{i=1}^P \frac{1}{2}m\omega_P^2(q_i - q_{i+1})^2`, :math:`m` is always the
actual mass of the particles).
The keyword *sp* is a scaling factor on Planck's constant, which can
be useful for debugging or other purposes. The default value of 1.0
is appropriate for most situations.
The keyword *ensemble* for fix style *pimd/langevin* determines which ensemble is it
going to sample. The value can be *nve* (microcanonical), *nvt* (canonical), *nph* (isoenthalpic), and *npt* (isothermal-isobaric).
The keyword *ensemble* for fix style *pimd/langevin* determines which ensemble is it
going to sample. The value can be *nve* (microcanonical), *nvt* (canonical), *nph* (isoenthalpic),
and *npt* (isothermal-isobaric).
The keyword *temp* specifies temperature parameter for fix styles *pimd/nvt* and *pimd/langevin*. It should read
a positive floating-point number.
The keyword *temp* specifies temperature parameter for fix styles *pimd/nvt* and *pimd/langevin*. It should read a
positive floating-point number.
.. note::
For pimd simulations, a temperature values should be specified even for nve ensemble. Temperature will make a difference
for nve pimd, since the spring elastic frequency between the beads will be affected by the temperature.
The keyword *thermostat* reads *style* and *seed* of thermostat for fix style *pimd/langevin*. *style* can only
be *PILE_L* (path integral Langevin equation local thermostat, as described in :ref:`(Manolopoulos) <Manolopoulos>`), and *seed* should a positive integer number, which serves as the seed of the pseudo random number generator.
be *PILE_L* (path integral Langevin equation local thermostat, as described in :ref:`Ceriotti <Ceriotti>`), and *seed* should a positive integer number, which serves as the seed of the pseudo random number generator.
.. note::
The fix style *pimd/langevin* uses the stochastic PILE_L thermostat to control temperature. This thermostat works on the normal modes
@ -199,21 +210,21 @@ 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 $i$ is $\frac{P}{\beta\hbar}\sqrt{\lambda_i\times\mathrm{fmass}}$ (*fmmode* is *physical*) or $\frac{P}{\beta\hbar}\sqrt{\mathrm{fmass}}$ (*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*.
The barostat parameters for fix style *pimd/langevin* with *npt* or *nph* ensemble is specified using one of *iso* and *aniso*
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.
The keyword *barostat* reads *style* of barostat for fix style *pimd/langevin*. *style* can
be *BZP* (Bussi-Zykova-Parrinello, as described in :ref:`(Parrinello1) <Parrinello1>`) or *MTTK* (Martyna-Tuckerman-Tobias-Klein, as described in :ref:`(Tuckerman2) <Tuckerman2>`).
be *BZP* (Bussi-Zykova-Parrinello, as described in :ref:`Bussi <Bussi>`) or *MTTK* (Martyna-Tuckerman-Tobias-Klein, as described in :ref:`Martyna1 <Martyna1>` and :ref:`Martyna2 <Martyna2>`).
The keyword *taup* specifies the barostat damping time parameter for fix style *pimd/langevin*. It is in time unit.
The keyword *fixcom* specifies whether the center-of-mass of the extended ring-polymer system is fixed during the pimd simulation.
Once *fixcom* is set te be *yes*, the center-of-mass velocity will be distracted from the centroid-mode velocities in each step.
The keyword *fixcom* specifies whether the center-of-mass of the extended ring-polymer system is fixed during the pimd simulation.
Once *fixcom* is set to be *yes*, the center-of-mass velocity will be distracted from the centroid-mode velocities in each step.
The PIMD algorithm in LAMMPS is implemented as a hyper-parallel scheme
as described in :ref:`(Calhoun) <Calhoun>`. In LAMMPS this is done by using
as described in :ref:`Calhoun <Calhoun>`. In LAMMPS this is done by using
:doc:`multi-replica feature <Howto_replica>` in LAMMPS, where each
quasi-particle system is stored and simulated on a separate partition
of processors. The following diagram illustrates this approach. The
@ -340,18 +351,18 @@ Path Integrals, McGraw-Hill, New York (1965).
**(Herman)** M. F. Herman, E. J. Bruskin, B. J. Berne, J Chem Phys, 76, 5150 (1982).
.. _Parrinello1:
.. _Bussi:
**(Parrinello1)** G. Bussi, T. Zykova-Timan, M. Parrinello, J Chem Phys, 130, 074101 (2009).
**(Bussi)** G. Bussi, T. Zykova-Timan, M. Parrinello, J Chem Phys, 130, 074101 (2009).
.. _Manolopoulos:
.. _Ceriotti:
**(Manolopoulos)** M. Ceriotti, M. Parrinello, T. Markland, D. Manolopoulos, J. Chem. Phys. 133, 124104 (2010).
**(Ceriotti)** M. Ceriotti, M. Parrinello, T. Markland, D. Manolopoulos, J. Chem. Phys. 133, 124104 (2010).
.. _Klein:
.. _Martyna1:
**(Klein)** G. Martyna, D. Tobias, M. Klein, J. Chem. Phys. 101, 4177 (1994).
**(Martyna1)** G. Martyna, D. Tobias, M. Klein, J. Chem. Phys. 101, 4177 (1994).
.. _Tuckerman2:
.. _Martyna2:
**(Tuckerman2)** G. Martyna, A. Hughes, M. Tuckerman, J. Chem. Phys. 110, 3275 (1999).
**(Martyna2)** G. Martyna, A. Hughes, M. Tuckerman, J. Chem. Phys. 110, 3275 (1999).