CHARMM (Chemistry at HARvard Macromolecular Mechanics) is a highly flexible computer program which uses empirical energy functions to model macromolecular systems. The program can read or model build structures, energy minimize them by first- or second-derivative techniques, perform a normal mode or molecular dynamics simulation, and analyze the structural, equilibrium, and dynamic properties determined in these calculations. The operations that CHARMM can perform are described, and some implementation details are given. A set of parameters for the empirical energy function and a sample run are included.

CHARMM: A program for macromolecular energy, minimization, and dynamics calculations

Molecular Dynamics

We propose modifications to the simple diffusion Monte Carlo algorithm that greatly reduce the time‐step error. The improved algorithm has a time‐step error smaller by a factor of 70 to 300 in the energy of Be, Li2 and Ne. For other observables the improvement is yet larger. The effective time step possible with the improved algorithm is typically a factor of a few hundred larger than the time step used in domain Green function Monte Carlo. We also present an optimized 109 parameter trial wave function for Be which, used in combination with our algorithm, yields an exceedingly accurate ground state energy. A simple solution to the population control bias in diffusion Monte Carlo is also discussed.

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A diffusion Monte Carlo algorithm with very small time-step errors

Polyethylene at equilibrium is studied by computer simulation. Configuration space is sampled efficiently by a novel Monte Carlo simulation scheme developed for the study of long molecules at high densities. Simulations are carried out in an isobaric‐isothermal statistical‐mechanical ensemble which permits calculation of the density of the polymer matrix at specified conditions of pressure and temperature. A systematic study of the polymer at different temperatures indicates a phase transition; in agreement with experiment, at low temperatures, the polyethylene model studied here crystallizes spontaneously. At temperatures above the melting point, the simulated melt is described accurately by the model.

Simulation of polyethylene above and below the melting point

Monte Carlo simulation of lattice models for macromolecules

The potential energy surface of the LiH molecule is calculated using the Green’s function Monte Carlo method. The calculated correlation energy is 0.078±0.001 hartree and the binding energy is 2.56 eV. These results are within 6% and 2% of the experimental values, respectively. The Green’s function Monte Carlo method is discussed in some detail with particular emphasis on problems of chemical interest.

A new look at correlation energy in atomic and molecular systems. II. The application of the Green’s function Monte Carlo method to LiH

The static properties of continuum, multichain systems are investigated by a ’’reptation’’ Monte Carlo algorithm. All beads interact via a repulsive (shifted) Lennard‐Jones potential. In addition, nearest neighbors along chains are linked by a quasiharmonic potential which permits limited pair extensions. Chain lengths of 5, 10, 20, 32, 50, and 70 beads have been studied. Studies at densities of 0.1, 0.3, and 0.5 demonstrate that chain dimensions are compressed as the concentration is increased. Both the mean square end‐to‐end distance, 〈R2〉, and the mean square radius of gyration, 〈S2〉, have a power law dependence upon l‐1, the number of bonds, with exponent approximately 1.16 for ρ=0.1 and 1.07 for ρ=0.3 and 0.5. 〈R2〉 and 〈S2〉 scale with density as ρ−γ where γ∼−0.22±0.02 for long chains, in reasonable agreement with the scaling prediction of −0.25. The asphericity ratios, the pair correlation functions of the center of masses, and the extent of chain overlaps indicate the nonideal behavior of these systems.

Investigations of static properties of model bulk polymer fluids

We report results of Monte Carlo variational calculations for a simple model of neutron matter for three different internuclear potentials. We have also done exact Monte Carlo calculations for the ground state of one of these systems. A wave function for the solid phase with full symmetry is proposed. None of the three systems crystallize. The validity of the Wu-Feenberg expansion and hard-sphere modeling for these systems are discussed. (AIP)

Exact calculations of the ground state of model neutron matter

A quantum hard-sphere system bounded by two parallel rigid walls is studied at absolute zero as a model of a helium film. A variational wave function is constructed which is of the Bijl-Dingle-Jastrow type modified by a one-body term which vanishes at the walls; Monte Carlo quadrature is used. We focus our attention particularly on the behavior of the single-particle density function and the condensed-state wave function, i.e., the order parameter. Both show significantly different behavior from that predicted by the Hartree theory. The healing length is calculated, we believe for the first time, and is rather small. The average condensate as a function of distance between two walls is also investigated. The calculation serves as a special probe for approximations to the ground-state wave function in a uniform system.

M. H. Kalos

Papers

A new look at correlation energy in atomic and molecular systems. II. The application of the Green’s function Monte Carlo method to LiH

Investigations of static properties of model bulk polymer fluids

Exact calculations of the ground state of model neutron matter

A hard-sphere model of the helium film