forked from lijiext/lammps
223 lines
7.5 KiB
Plaintext
223 lines
7.5 KiB
Plaintext
.. index:: fix pimd
|
|
|
|
fix pimd command
|
|
================
|
|
|
|
Syntax
|
|
""""""
|
|
|
|
.. parsed-literal::
|
|
|
|
fix ID group-ID pimd keyword value ...
|
|
|
|
* ID, group-ID are documented in :doc:`fix <fix>` command
|
|
* pimd = style name of this fix command
|
|
* zero or more keyword/value pairs may be appended
|
|
* keyword = *method* or *fmass* or *sp* or *temp* or *nhc*
|
|
.. parsed-literal::
|
|
|
|
*method* value = *pimd* or *nmpimd* or *cmd*
|
|
*fmass* value = scaling factor on mass
|
|
*sp* value = scaling factor on Planck constant
|
|
*temp* value = temperature (temperarate units)
|
|
*nhc* value = Nc = number of chains in Nose-Hoover thermostat
|
|
|
|
|
|
|
|
Examples
|
|
""""""""
|
|
|
|
.. parsed-literal::
|
|
|
|
fix 1 all pimd method nmpimd fmass 1.0 sp 2.0 temp 300.0 nhc 4
|
|
|
|
Description
|
|
"""""""""""
|
|
|
|
This command performs quantum molecular dynamics simulations based on
|
|
the Feynman path integral to include effects of tunneling and
|
|
zero-point motion. In this formalism, the isomorphism of a quantum
|
|
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
|
|
by the following equations:
|
|
|
|
.. image:: Eqs/fix_pimd.jpg
|
|
:align: center
|
|
|
|
The interested user is referred to any of the numerous references on
|
|
this methodology, but briefly, each quantum particle in a path
|
|
integral simulation is represented by a ring-polymer of P quasi-beads,
|
|
labeled from 1 to P. During the simulation, each quasi-bead interacts
|
|
with beads on the other ring-polymers with the same imaginary time
|
|
index (the second term in the effective potential above). The
|
|
quasi-beads also interact with the two neighboring quasi-beads through
|
|
the spring potential in imaginary-time space (first term in effective
|
|
potential). To sample the canonical ensemble, a Nose-Hoover massive
|
|
chain thermostat is applied :ref:`(Tuckerman) <Tuckerman>`. With the
|
|
massive chain algorithm, a chain of NH thermostats is coupled to each
|
|
degree of freedom for each quasi-bead. The keyword *temp* sets the
|
|
target temperature for the system and the keyword *nhc* sets the
|
|
number *Nc* of thermostats in each chain. For example, for a
|
|
simulation of N particles with P beads in each ring-polymer, the total
|
|
number of NH thermostats would be 3 x N x P x Nc.
|
|
|
|
.. note::
|
|
|
|
This fix implements a complete velocity-verlet integrator
|
|
combined with NH massive chain thermostat, so no other time
|
|
integration fix should be used.
|
|
|
|
The *method* keyword determines what style of PIMD is performed. A
|
|
value of *pimd* is standard PIMD. A value of *nmpimd* is for
|
|
normal-mode PIMD. A value of *cmd* is for centroid molecular dynamics
|
|
(CMD). The difference between the styles is as follows.
|
|
|
|
In standard PIMD, the value used for a bead's fictitious mass is
|
|
arbitrary. A common choice is to use Mi = m/P, which results in the
|
|
mass of the entire ring-polymer being equal to the real quantum
|
|
particle. But it can be difficult to efficiently integrate the
|
|
equations of motion for the stiff harmonic interactions in the ring
|
|
polymers.
|
|
|
|
A useful way to resolve this issue is to integrate the equations of
|
|
motion in a normal mode representation, using Normal Mode
|
|
Path-Integral Molecular Dynamics (NMPIMD) :ref:`(Cao1) <Cao1>`. In NMPIMD,
|
|
the NH chains are attached to each normal mode of the ring-polymer and
|
|
the fictitious mass of each mode is chosen as Mk = the eigenvalue of
|
|
the Kth normal mode for k > 0. The k = 0 mode, referred to as the
|
|
zero-frequency mode or centroid, corresponds to overall translation of
|
|
the ring-polymer and is assigned the mass of the real particle.
|
|
|
|
Motion of the centroid can be effectively uncoupled from the other
|
|
normal modes by scaling the fictitious masses to achieve a partial
|
|
adiabatic separation. This is called a Centroid Molecular Dynamics
|
|
(CMD) approximation :ref:`(Cao2) <Cao2>`. The time-evolution (and resulting
|
|
dynamics) of the quantum particles can be used to obtain centroid time
|
|
correlation functions, which can be further used to obtain the true
|
|
quantum correlation function for the original system. The CMD method
|
|
also uses normal modes to evolve the system, except only the k > 0
|
|
modes are thermostatted, not the centroid degrees of freedom.
|
|
|
|
The keyword *fmass* sets a further scaling factor for the fictitious
|
|
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 *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 PIMD algorithm in LAMMPS is implemented as a hyper-parallel scheme
|
|
as described in :ref:`(Calhoun) <Calhoun>`. In LAMMPS this is done by using
|
|
:ref:`multi-replica feature <howto_5>` in LAMMPS, where
|
|
each quasi-particle system is stored and simulated on a separate
|
|
partition of processors. The following diagram illustrates this
|
|
approach. The original system with 2 ring polymers is shown in red.
|
|
Since each ring has 4 quasi-beads (imaginary time slices), there are 4
|
|
replicas of the system, each running on one of the 4 partitions of
|
|
processors. Each replica (shown in green) owns one quasi-bead in each
|
|
ring.
|
|
|
|
.. image:: JPG/pimd.jpg
|
|
:align: center
|
|
|
|
To run a PIMD simulation with M quasi-beads in each ring polymer using
|
|
N MPI tasks for each partition's domain-decomposition, you would use P
|
|
= MxN processors (cores) and run the simulation as follows:
|
|
|
|
.. parsed-literal::
|
|
|
|
mpirun -np P lmp_mpi -partition MxN -in script
|
|
|
|
Note that in the LAMMPS input script for a multi-partition simulation,
|
|
it is often very useful to define a :doc:`uloop-style variable <variable>` such as
|
|
|
|
.. parsed-literal::
|
|
|
|
variable ibead uloop M pad
|
|
|
|
where M is the number of quasi-beads (partitions) used in the
|
|
calculation. The uloop variable can then be used to manage I/O
|
|
related tasks for each of the partitions, e.g.
|
|
|
|
.. parsed-literal::
|
|
|
|
dump dcd all dcd 10 system_${ibead}.dcd
|
|
restart 1000 system_${ibead}.restart1 system_${ibead}.restart2
|
|
read_restart system_${ibead}.restart2
|
|
|
|
Restrictions
|
|
""""""""""""
|
|
|
|
|
|
This fix is part of the USER-MISC package. It is only enabled if
|
|
LAMMPS was built with that package. See the :ref:`Making LAMMPS <start_3>` section for more info.
|
|
|
|
A PIMD simulation can be initialized with a single data file read via
|
|
the :doc:`read_data <read_data>` command. However, this means all
|
|
quasi-beads in a ring polymer will have identical positions and
|
|
velocities, resulting in identical trajectories for all quasi-beads.
|
|
To avoid this, users can simply initialize velocities with different
|
|
random number seeds assigned to each partition, as defined by the
|
|
uloop variable, e.g.
|
|
|
|
.. parsed-literal::
|
|
|
|
velocity all create 300.0 1234${ibead} rot yes dist gaussian
|
|
|
|
Default
|
|
"""""""
|
|
|
|
The keyword defaults are method = pimd, fmass = 1.0, sp = 1.0, temp = 300.0,
|
|
and nhc = 2.
|
|
|
|
|
|
----------
|
|
|
|
|
|
.. _Feynman:
|
|
|
|
|
|
|
|
**(Feynman)** R. Feynman and A. Hibbs, Chapter 7, Quantum Mechanics and
|
|
Path Integrals, McGraw-Hill, New York (1965).
|
|
|
|
.. _Tuckerman:
|
|
|
|
|
|
|
|
**(Tuckerman)** M. Tuckerman and B. Berne, J Chem Phys, 99, 2796 (1993).
|
|
|
|
.. _Cao1:
|
|
|
|
|
|
|
|
**(Cao1)** J. Cao and B. Berne, J Chem Phys, 99, 2902 (1993).
|
|
|
|
.. _Cao2:
|
|
|
|
|
|
|
|
**(Cao2)** J. Cao and G. Voth, J Chem Phys, 100, 5093 (1994).
|
|
|
|
.. _Hone:
|
|
|
|
|
|
|
|
**(Hone)** T. Hone, P. Rossky, G. Voth, J Chem Phys, 124,
|
|
154103 (2006).
|
|
|
|
.. _Calhoun:
|
|
|
|
|
|
|
|
**(Calhoun)** A. Calhoun, M. Pavese, G. Voth, Chem Phys Letters, 262,
|
|
415 (1996).
|
|
|
|
|
|
.. _lws: http://lammps.sandia.gov
|
|
.. _ld: Manual.html
|
|
.. _lc: Section_commands.html#comm
|