fix quantum +Syntax: +fix ID group-ID quantum keyword values +ID, group-ID are documented in fix command +poems = style name of this fix command +keyword = group or file or molecule + method values = pimd or nmpimd or cmd + fmass values = real number for scaling factor of mass + sp values = real number for scaling factor of plank constant + temp values = real number for temperature in unit K + nhc values = N number of chains in Nose-Hoover chain thermostat +Examples: +fix 1 all quantum method nmpimd fmass 1.0 sp 2.0 temp 300.0 nhc 4 +Description: +
+This command conducts 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 the quantum +partition function of the original system and a classical partition +function of a ring-polymer system is exploited to efficiently sample +configurations from the canonical ensemble. Ref. 1, Chapter 7 +
+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 part of 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, the Nose-Hoover massive +chain thermostat is applied. Ref. 2 With this 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 of +thermostats in each chain. For example, if one simulated a system of N +particles with P beads in each ring-polymer, the total number of NH +thermostats equals 3 x N x P x nhc. +
+The selection of the bead’s mass (referred to as the fictitious mass) +is arbitrary according to the formula. A common choice is to use mi = +m/P, which results in the mass of the ring-polymer being equal to the +real quantum particle. It can be difficult to efficiently integrate +the equations of motion for the stiff harmonic interactions in the +ring polymers. A useful approach to resolve this is integrating the +equations of motion in a normal mode representation, which here is +referred to as Normal Mode Path-Integral Molecular Dynamics +(NMPIMD). Ref. 3 In NMPIMD, the NH chains are attached to each +normal mode of the ring-polymer and the fictitious mass of each mode +is chosen to be mk =, where is the eigen-value the k-th normal mode +for k>0. The mode of k=0, 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. In this +Centroid Molecular Dynamics (CMD) approximation Ref. 4, 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 keyword method is used to indicate the approach +PIMD, NMPIMD or CMD. 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 is used as a further +scaling factor for the fictitious masses of beads, which can be used +for the Partial Adiabatic CMD Ref. 5, or to be set as P, which +results in the fictitious masses to be equal to the real particle +masses. The last keyword sp is a scaling factor for Plank’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 Ref. 6 and use of +this fix command requires use of the multi-partition feature in +LAMMPS, where each quasi-particle system is calculated on a separate +partition of processors. For a quantum system that is discretized into +32 imaginary time slices (32 beads in a ring-polymer), 32 partitions +are required to run the simulation. Below is an example of running a +PIMD simulation with M quasi-beads in each ring polymer using N +MPI-tasks for the domain-decomposition on each partition. mpirun –np +P lmp_mpi –partition MxN –in script where, P = M x N. +
+In the LAMMPS input script, it is very useful to define a uloop type +variable such as, 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, such as read_data system_$ibead.restart dump dcd all dcd +10 system_$ibead.dcd restart 10 system_$ibead.restart1 +system_$ibead.restart2 +
+Restrictions: +
+To run PIMD simulations users must install the package +USER-QUANTUM. Users must use the multi-partition feature of LAMMPS and +the number of partitions needs to be consistent with the uloop +variable defined for the ring-polymer model. Meanwhile, USER-QUANTUM +is not compatible with any other modules that use the multi-partition +feature. The “quantum” fix-object already contains a complete +velocity-verlet integrator combined with NH massive chain thermostat, +so users shouldn’t use any other integration fix. The PIMD simulation +can be started with a single DATA file through the command +“read_data”, however, all the quasi-beads would then have identical +positions and velocities, resulting in identical trajectories for all +quasi-beads. To avoid this, users can simply initial a new set of +velocities with random number seeds defined by the uloop variable. +velocity all create 300.0 1234$ibead rot yes dist gaussian +
+The keyword defaults are method=pimd, fmass=1.0, sp=1.0, temp=300.0, +nhc=2. +
+1. Feynman, R. P. and Hibbs, A. R. (1965). Quantum Mechanics and Path Integrals. New York: McGraw-Hill. (PIMD) +
+2. Tuckerman, M. E., Berne, B. J., J. Chem. Phys. 99, 2796. (Nose-Hoove) +
+3. Cao, J, Berne, B. J., J. Chem. Phys. 99, 2902 (NMPIMD) +
+4. Cao, J.; Voth, G. A. , J. Chem. Phys. 100, 5093 (CMD) +
+5. Hone T. D., Rossky P. J., Voth G. A.., J. Chem. Phys. , 124, 154103. (PACMD) +
+6. Calhoun, A., Pavese, M., Voth, G. A., Chem. Phys. Let., 262, 415 +
+ diff --git a/doc/fix_pimd.txt b/doc/fix_pimd.txt new file mode 100644 index 0000000000..3350855f97 --- /dev/null +++ b/doc/fix_pimd.txt @@ -0,0 +1,121 @@ +fix quantum +Syntax: +fix ID group-ID quantum keyword values +ID, group-ID are documented in fix command +poems = style name of this fix command +keyword = group or file or molecule + method values = pimd or nmpimd or cmd + fmass values = real number for scaling factor of mass + sp values = real number for scaling factor of plank constant + temp values = real number for temperature in unit K + nhc values = N number of chains in Nose-Hoover chain thermostat +Examples: +fix 1 all quantum method nmpimd fmass 1.0 sp 2.0 temp 300.0 nhc 4 +Description: + +This command conducts 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 the quantum +partition function of the original system and a classical partition +function of a ring-polymer system is exploited to efficiently sample +configurations from the canonical ensemble. [Ref. 1, Chapter 7] + +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 part of 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, the Nose-Hoover massive +chain thermostat is applied. [Ref. 2] With this 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 of +thermostats in each chain. For example, if one simulated a system of N +particles with P beads in each ring-polymer, the total number of NH +thermostats equals 3 x N x P x nhc. + +The selection of the bead’s mass (referred to as the fictitious mass) +is arbitrary according to the formula. A common choice is to use mi = +m/P, which results in the mass of the ring-polymer being equal to the +real quantum particle. It can be difficult to efficiently integrate +the equations of motion for the stiff harmonic interactions in the +ring polymers. A useful approach to resolve this is integrating the +equations of motion in a normal mode representation, which here is +referred to as Normal Mode Path-Integral Molecular Dynamics +(NMPIMD). [Ref. 3] In NMPIMD, the NH chains are attached to each +normal mode of the ring-polymer and the fictitious mass of each mode +is chosen to be mk =, where is the eigen-value the k-th normal mode +for k>0. The mode of k=0, 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. In this +Centroid Molecular Dynamics (CMD) approximation [Ref. 4], 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 keyword method is used to indicate the approach +PIMD, NMPIMD or CMD. 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 is used as a further +scaling factor for the fictitious masses of beads, which can be used +for the Partial Adiabatic CMD [Ref. 5], or to be set as P, which +results in the fictitious masses to be equal to the real particle +masses. The last keyword sp is a scaling factor for Plank’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 [Ref. 6] and use of +this fix command requires use of the multi-partition feature in +LAMMPS, where each quasi-particle system is calculated on a separate +partition of processors. For a quantum system that is discretized into +32 imaginary time slices (32 beads in a ring-polymer), 32 partitions +are required to run the simulation. Below is an example of running a +PIMD simulation with M quasi-beads in each ring polymer using N +MPI-tasks for the domain-decomposition on each partition. mpirun –np +P lmp_mpi –partition MxN –in script where, P = M x N. + +In the LAMMPS input script, it is very useful to define a uloop type +variable such as, 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, such as read_data system_${ibead}.restart dump dcd all dcd +10 system_${ibead}.dcd restart 10 system_${ibead}.restart1 +system_${ibead}.restart2 + +Restrictions: + +To run PIMD simulations users must install the package +USER-QUANTUM. Users must use the multi-partition feature of LAMMPS and +the number of partitions needs to be consistent with the uloop +variable defined for the ring-polymer model. Meanwhile, USER-QUANTUM +is not compatible with any other modules that use the multi-partition +feature. The “quantum” fix-object already contains a complete +velocity-verlet integrator combined with NH massive chain thermostat, +so users shouldn’t use any other integration fix. The PIMD simulation +can be started with a single DATA file through the command +“read_data”, however, all the quasi-beads would then have identical +positions and velocities, resulting in identical trajectories for all +quasi-beads. To avoid this, users can simply initial a new set of +velocities with random number seeds defined by the uloop variable. +velocity all create 300.0 1234${ibead} rot yes dist gaussian + +The keyword defaults are method=pimd, fmass=1.0, sp=1.0, temp=300.0, +nhc=2. + +:line + +1. Feynman, R. P. and Hibbs, A. R. (1965). Quantum Mechanics and Path Integrals. New York: McGraw-Hill. (PIMD) + +2. Tuckerman, M. E., Berne, B. J., J. Chem. Phys. 99, 2796. (Nose-Hoove) + +3. Cao, J, Berne, B. J., J. Chem. Phys. 99, 2902 (NMPIMD) + +4. Cao, J.; Voth, G. A. , J. Chem. Phys. 100, 5093 (CMD) + +5. Hone T. D., Rossky P. J., Voth G. A.., J. Chem. Phys. , 124, 154103. (PACMD) + +6. Calhoun, A., Pavese, M., Voth, G. A., Chem. Phys. Let., 262, 415 +