10.8 Ab Initio Path Integrals

10.8.2 Job Control and Examples

PIMC_NBEADSPERATOM
       Number of path integral time slices (“beads”) used on each atom of a PIMC simulation.
TYPE:
       INTEGER
DEFAULT:
       None.
OPTIONS:
       1 Perform classical Boltzmann sampling. >1 Perform quantum-mechanical path integral sampling.
RECOMMENDATION:
       This variable controls the inherent convergence of the path integral simulation. The one-bead limit represents classical sampling and the infinite-bead limit represents exact quantum-mechanical sampling. Using 32 beads is reasonably converged for room-temperature simulations of molecular systems.

PIMC_TEMP
       Temperature, in Kelvin (K), of path integral simulations.
TYPE:
       INTEGER
DEFAULT:
       None.
OPTIONS:
       User-specified number of Kelvin for PIMC or classical MC simulations.
RECOMMENDATION:
       None.

PIMC_MCMAX
       Number of Monte Carlo steps to sample.
TYPE:
       INTEGER
DEFAULT:
       None.
OPTIONS:
       User-specified number of steps to sample.
RECOMMENDATION:
       This variable dictates the statistical convergence of MC/PIMC simulations. For converged simulations at least 105 steps is recommended.

PIMC_WARMUP_MCMAX
       Number of Monte Carlo steps to sample during an equilibration period of MC/PIMC simulations.
TYPE:
       INTEGER
DEFAULT:
       None.
OPTIONS:
       User-specified number of steps to sample.
RECOMMENDATION:
       Use this variable to equilibrate the molecule/ring polymer before collecting production statistics. Usually a short run of roughly 10% of PIMC_MCMAX is sufficient.

PIMC_MOVETYPE
       Selects the type of displacements used in MC/PIMC simulations.
TYPE:
       INTEGER
DEFAULT:
       0
OPTIONS:
       0 Cartesian displacements of all beads, with occasional (1%) center-of-mass moves. 1 Normal-mode displacements of all modes, with occasional (1%) center-of-mass moves. 2 Levy flights without center-of-mass moves.
RECOMMENDATION:
       Except for classical sampling (MC) or small bead-number quantum sampling (PIMC), Levy flights should be used. For Cartesian and normal-mode moves, the maximum displacement is adjusted during the warm-up run to the desired acceptance rate (controlled by PIMC_ACCEPT_RATE). For Levy flights, the acceptance is solely controlled by PIMC_SNIP_LENGTH.

PIMC_ACCEPT_RATE
       Acceptance rate for MC/PIMC simulations when Cartesian or normal-mode displacements are used.
TYPE:
       INTEGER
DEFAULT:
       None
OPTIONS:
       0<n<100 User-specified rate, given as a whole-number percentage.
RECOMMENDATION:
       Choose acceptance rate to maximize sampling efficiency, which is typically signified by the mean-square displacement (printed in the job output). Note that the maximum displacement is adjusted during the warm-up run to achieve roughly this acceptance rate.

PIMC_SNIP_LENGTH
       Number of “beads” to use in the Levy flight movement of the ring polymer.
TYPE:
       INTEGER
DEFAULT:
       None
OPTIONS:
       3nPIMC_NBEADSPERATOM User-specified length of snippet.
RECOMMENDATION:
       Choose the snip length to maximize sampling efficiency. The efficiency can be estimated by the mean-square displacement between configurations, printed at the end of the output file. This efficiency will typically, however, be a trade-off between the mean-square displacement (length of statistical correlations) and the number of beads moved. Only the moved beads require recomputing the potential, i.e., a call to Q-Chem for the electronic energy. (Note that the endpoints of the snippet remain fixed during a single move, so n-2 beads are actually moved for a snip length of n. For 1 or 2 beads in the simulation, Cartesian moves should be used instead.)

Example 10.31  Path integral Monte Carlo simulation of H2 at room temperature

$comment
The number of Monte Carlo steps is deliberately set low, more typical
values would be:
   PIMC_WARMUP_MCMAX    10000   !Equilibration run
   PIMC_MCMAX           100000  !Production run
$end

$molecule
   0  1
   H
   H 1 0.75
$end

$rem
   JOBTYPE              pimc
   METHOD               hf
   BASIS                sto-3g
   PIMC_TEMP            298
   PIMC_NBEADSPERATOM   32
   PIMC_WARMUP_MCMAX    100     !Equilibration run
   PIMC_MCMAX           1000    !Production run
   PIMC_MOVETYPE        2         !Levy flights
   PIMC_SNIP_LENGTH     10        !Moves 8 beads per MC step (10-endpts)
$end

Example 10.32  Classical Monte Carlo simulation of a water molecule at 500K

$comment
The number of Monte Carlo steps is deliberately set low, more typical
values would be:
   PIMC_WARMUP_MCMAX    10000   !Equilibration run
   PIMC_MCMAX           100000  !Production run
$end

$molecule
   0  1
   H
   O 1 1.0
   H 2 1.0 1 104.5
$end

$rem
   JOBTYPE              pimc
   METHOD               rimp2
   BASIS                cc-pvdz
   AUX_BASIS            rimp2-cc-pvdz
   PIMC_TEMP            500
   PIMC_NBEADSPERATOM   1       !1 bead is classical sampling
   PIMC_WARMUP_MCMAX    100     !Equilibration run
   PIMC_MCMAX           1000    !Production run
   PIMC_MOVETYPE        0       !Cartesian displacements (ok for 1 bead)
   PIMC_ACCEPT_RATE     40      !During warm-up, adjusts step size to 40% acceptance
$end