A quantum propagator for path-integral simulations of rigid molecules

The expression for the quantum propagator for rigid tops, proposed by Mu?ser and Berne [Phys. Rev. Lett. 77, 2638 (1996)], has been extended to asymmetric tops. Path-integral Monte Carlo simulations are provided that show that the quantum propagator proposed in this work exactly reproduces the rotational energy of free asymmetric tops as evaluated from the partition function. This propagator can subsequently be used in path-integral simulations of condensed phases if a rigid molecular model is used.     

Quantum Monte Carlo simulations of selected ammonia clusters (n = 2-5): isotope effects on the ground state of typical hydrogen bonded systems

Variational Monte Carlo, diffusion Monte Carlo, and stereographic projection path integral simulations are performed on eight selected species from the (NH(3))(n), (ND(3))(n), (NH(2)D)(n), and (NH(3))(n-1)(ND(3)) clusters. Each monomer is treated as a rigid body with the rotation spaces mapped by the stereographic projection coordinates. We compare the energy obtained from path integral simulations at several low temperatures with those obtained by diffusion Monte Carlo, for two dimers, and we find that at 4 K, the fully deuterated dimer energy is in excellent agreement with the ground state energy of the same. The ground state wavefunction for the (NH(3))(2-5) clusters is predominantly localized in the global minimum of the potential energy. In all simulations of mixed isotopic substitutions, we find that the heavier isotope is almost exclusively the participant in the hydrogen bond.     

Hybrid quantum/classical path integral approach for simulation of hydrogen transfer reactions in enzymes

A hybrid quantum/classical path integral Monte Carlo (QC-PIMC) method for calculating the quantum free energy barrier for hydrogen transfer reactions in condensed phases is presented. In this approach, the classical potential of mean force along a collective reaction coordinate is calculated using umbrella sampling techniques in conjunction with molecular dynamics trajectories propagated according to a mapping potential. The quantum contribution is determined for each configuration along the classical trajectory with path integral Monte Carlo calculations in which the beads move according to an effective mapping potential. This type of path integral calculation does not utilize the centroid constraint and can lead to more efficient sampling of the relevant region of conformational space than free-particle path integral sampling. The QC-PIMC method is computationally practical for large systems because the path integral sampling for the quantum nuclei is performed separately from the classical molecular dynamics sampling of the entire system. The utility of the QC-PIMC method is illustrated by an application to hydride transfer in the enzyme dihydrofolate reductase. A comparison of this method to the quantized classical path and grid-based methods for this system is presented.     

Stereographic projection path integral simulations of (HCl)n clusters (n=2-5): evidence of quantum induced melting in small hydrogen bonded networks

We investigate the quantum thermodynamic properties of small (HCl)(n) clusters using stereographic projection path integral simulations. The HCl stretches are rigid, the orientations are mapped with stereographic projection coordinates, and we make use of the reweighted random series techniques to obtain cubic convergence with respect to the number of path coefficients. Path integral simulations are converged at and above 10 K for the pentamer and above 15 K for the dimer and the trimer. None of the systems display a melting feature in the classical limit. We find an evidence of quantum induced melting between 15 and 45 K.     

Hybrid Monte Carlo implementation of the Fourier path integral algorithm

This paper formulates a hybrid Monte Carlo implementation of the Fourier path integral (FPI-HMC) approach with partial averaging. Such a hybrid Monte Carlo approach allows one to generate collective moves through configuration space using molecular dynamics while retaining the computational advantages associated with the Fourier path integral Monte Carlo method. In comparison with the earlier Metropolis Monte Carlo implementations of the FPI algorithm, the present HMC method is shown to be significantly more efficient for quantum Lennard-Jones solids and suggests that such algorithms may prove useful for efficient simulations of a range of atomic and molecular systems.     

A stereographic projection path integral study of the coupling between the orientation and the bending degrees of freedom of water

A Monte Carlo path integral method to study the coupling between the rotation and bending degrees of freedom for water is developed. It is demonstrated that soft internal degrees of freedom that are not stretching in nature can be mapped with stereographic projection coordinates. For water, the bending coordinate is orthogonal to the stereographic projection coordinates used to map its orientation. Methods are developed to compute the classical and quantum Jacobian terms so that the proper infinitely stiff spring constant limit is recovered in the classical limit, and so that the nonconstant nature of the Riemann Cartan curvature scalar is properly accounted in the quantum simulations. The theory is used to investigate the effects of the geometric coupling between the bending and the rotating degrees of freedom for the water monomer in an external field in the 250 to 500 K range. We detect no evidence of geometric coupling between the bending degree of freedom and the orientations.     

Path integral molecular dynamics methods: Application to neon

Feynman's path integral formulation of quantum statistical mechanics, which has commonly been applied be Monte Carlo methods, is now also implemented by traditional molecular dynamics simulations of the microcanonical ensemble and in the Nosé-Hoover method simulating the isothermal-isobaric ensemble. In this article these two methods are applied to solid and liquid neon, in which quantum effects are not negligible. The validity of the procedure is shown by comparison with Monte Carlo and Brownian Dynamics computer simulations and with experiment. © 1995 by John Wiley & Sons, Inc.     

The dynamo library for molecular simulations using hybrid quantum mechanical and molecular mechanical potentials

The Dynamo module library has been developed for the simulation of molecular systems using hybrid quantum mechanical (QM) and molecular mechanical (MM) potentials. Dynamo is not a program package but is a library of Fortran 90 modules that can be employed by those interested in writing their own programs for performing molecular simulations. The library supports a range of different types of molecular calculation including geometry optimizations, reaction‐path determinations and molecular dynamics and Monte Carlo simulations. This article outlines the general structure and capabilities of the library and describes in detail Dynamo's semiempirical QM/MM hybrid potential. Results are presented to indicate three particular aspects of this implementation—the handling of long‐range nonbonding interactions, the nature of the boundary between the quantum mechanical and molecular mechanical atoms and how to perform path‐integral hybrid‐potential molecular dynamics simulations. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 1088–1100, 2000     

Thermodynamic properties of small rare gas clusters by path integral Monte Carlo simulations: a preliminary study

A strategy for reducing the risk of non-ergodic simulations in Monte Carlo calculations of the thermodynamic properties of clusters is discussed with the support of some examples. The results obtained attest the significance of the approach for the low-temperature regime, as non-ergodic sampling of potential energy surfaces is a particularly insidious occurrence. Fourier path integral Monte Carlo techniques for taking into account quantum effects are adopted, in conjunction with suitable tricks for improving the procedure reliability. Applications are restricted to Lennard-Jones clusters of rare-gas systems.     

Efficient estimators for quantum instanton evaluation of the kinetic isotope effects: application to the intramolecular hydrogen transfer in pentadiene

The quantum instanton approximation is used to compute kinetic isotope effects for intramolecular hydrogen transfer in cis-1,3-pentadiene. Due to the importance of skeleton motions, this system with 13 atoms is a simple prototype for hydrogen transfer in enzymatic reactions. The calculation is carried out using thermodynamic integration with respect to the mass of the isotopes and a path integral Monte Carlo evaluation of relevant thermodynamic quantities. Efficient "virial" estimators are derived for the logarithmic derivatives of the partition function and the delta-delta correlation functions. These estimators require significantly fewer Monte Carlo samples since their statistical error does not increase with the number of discrete time slices in the path integral. The calculation treats all 39 degrees of freedom quantum mechanically and uses an empirical valence bond potential based on a molecular mechanics force field.     

Including quantum subsystem character within classical equilibrium simulations

A mixed quantum/classical density matrix approximation is derived. The density matrix makes use of quantum subsystem vibrational wave functions. The diagonal of the density matrix can be used as an equilibrium distribution in Monte Carlo simulations. The approximate distribution compares well with the path integral distribution for a model system. Since it includes quantum subsystem information, it performs much better than the quadratic Feynman-Hibbs distribution. These types of distributions can aid in including quantum vibrational information in otherwise classical simulations.     

Rotational fluctuation of molecules in quantum clusters. I. Path integral hybrid Monte Carlo algorithm

In this paper, we present a path integral hybrid Monte Carlo (PIHMC) method for rotating molecules in quantum fluids. This is an extension of our PIHMC for correlated Bose fluids [S. Miura and J. Tanaka, J. Chem. Phys. 120, 2160 (2004)] to handle the molecular rotation quantum mechanically. A novel technique referred to be an effective potential of quantum rotation is introduced to incorporate the rotational degree of freedom in the path integral molecular dynamics or hybrid Monte Carlo algorithm. For a permutation move to satisfy Bose statistics, we devise a multilevel Metropolis method combined with a configurational-bias technique for efficiently sampling the permutation and the associated atomic coordinates. Then, we have applied the PIHMC to a helium-4 cluster doped with a carbonyl sulfide molecule. The effects of the quantum rotation on the solvation structure and energetics were examined. Translational and rotational fluctuations of the dopant in the superfluid cluster were also analyzed.     

Accelerating molecular simulations by reversible mapping between local minima

A new framework is presented for performing Monte Carlo simulations of condensed matter based on a recently developed bijective mapping between local energy minima. The framework is used to implement a range of new multiparticle Monte Carlo moves, which are investigated by simulating atomic Lennard-Jones fluids in the canonical and grand canonical ensembles. Important aspects of the simulation protocol and their effect on performance are analyzed in detail. Using the mapping accelerates the simulations by many orders of magnitude when compared to the equivalent moves without the mapping, and leads to particularly efficient configurational sampling at low temperatures and high densities. The method appears to be suitable for adapting to quantitative simulations of more complex molecular systems over long effective time scales.     

Path integral ground state with a fourth-order propagator: application to condensed helium

Ground state properties of condensed helium are calculated using the path integral ground state (PIGS) method. A fourth-order approximation is used as short (imaginary) time propagator. We compare our results with those obtained with other quantum Monte Carlo (QMC) techniques and different propagators. For this particular application, we find that the fourth-order propagator performs comparably to the pair product approximation, and is far superior to the primitive approximation. Results obtained for the equation of state of condensed helium show that PIGS compares favorably to other QMC methods traditionally utilized for this type of calculation.     

First-principles simulation of molecular dissociation-recombination equilibrium

For the first time, the equilibrium composition of chemical dissociation-recombination reaction is simulated from first-principles, only. Furthermore, beyond the conventional ab initio Born-Oppenheimer quantum chemistry the effects from the thermal and quantum equilibrium dynamics of nuclei are consistently included, as well as, the nonadiabatic coupling between the electrons and the nuclei. This has been accomplished by the path integral Monte Carlo simulations for full NVT quantum statistics of the H(3)(+) ion. The molecular total energy, partition function, free energy, entropy, and heat capacity are evaluated in a large temperature range: from below room temperature to temperatures relevant for planetary atmospheric physics. Temperature and density dependent reaction balance of the molecular ion and its fragments above 4000 K is presented, and also the density dependence of thermal ionization above 10,000 K is demonstrated.     

Stereographic projection path-integral simulations of (HF)n clusters

We perform several quantum canonical ensemble simulations of (HF)(n) clusters. The HF stretches are rigid, and the stereographic projection path-integral method is employed for the simulation in the resulting curved configuration space. We make use of the reweighted random series techniques to accelerate the convergence of the path-integral simulation with respect to the number of path coefficients. We develop and test estimators for the total energy and heat capacity based on a finite difference approach for non-Euclidean spaces. The quantum effects at temperatures below 400 K are substantial for all sizes. We observe interesting thermodynamic behaviors in the quantum simulations of the octamer and the heptamer.     

Stereographic projections path integral for inertia ellipsoids: applications to Arn-HF clusters

The DeWitt formula for inertia ellipsoids mapped by stereographic projection coordinates is developed. We discover that by remapping the quaternion parameter space with stereographic projections, considerable simplification of the differential geometry for the inertia ellipsoid with spherical symmetry takes place. The metric tensor is diagonal and contains only one independent element in that case. We find no difficulties testing and implementing the DeWitt formula for the inertia ellipsoids of asymmetric tops mapped by stereographic projections. The path integral algorithm for the treatment of Rm x S2 manifolds based on a mixture of Cartesian and stereographic projection coordinates is tested for small Arn-HF clusters in the n = 2 to n = 5 range. In particular, we determine the quantum effects of the red shift and the isomerization patterns at finite temperatures. Our findings are consistent with previously reported computations and experimental data for small Arn-HF clusters.     

Extrapolation of the time-step bias in diffusion quantum Monte Carlo by a differential sampling technique

A new method of eliminating the finite-time-step error inherent in diffusion quantum Monte Carlo is presented, utilizing an improved version of the existing differential techniques. An implementation is described and results of several small but representative calculations are discussed. The pertinent computation requirements on these systems were reduced by up to a factor of five by the new algorithm. It is speculated that this method may be easily applied to other quantum Monte Carlo and discretized path integral Monte Carlo techniques having related finite step-size errors with a possibility of obtaining similar good results.     

A path integral influence functional for excess electron in fluids: Density-functional formulation

In this paper, we propose a path integral influence functional from a solvent to determine a self-correlation function of a quantum particle in classical simple fluid. It is shown that the influence functional is related to a grand potential functional of the pure solvent under a three-dimensional external field arising from a classical isomorphic polymer, on which the quantum particle is mapped. The influence functional can be calculated from the self-correlation function, the solute-solvent and the solvent-solvent pair correlation function. The obtained equation of the self-correlation function is applied to an excess electron problem in fluid helium. The Fourier path-integral Monte Carlo method is employed to perform the path integral of the electron. The solute-solvent pair correlation function is estimated from a reference interaction site model integral equation. These results obtained form our proposed influence functional and from that proposed by Chandler, Singh, and Richardson are compared with those provided by a path integral Monte Carlo simulation with the explicit helium solvent.