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.     

Quantum mechanical single molecule partition function from path integral Monte Carlo simulations

An algorithm for calculating the partition function of a molecule with the path integral Monte Carlo method is presented. Staged thermodynamic perturbation with respect to a reference harmonic potential is utilized to evaluate the ratio of partition functions. Parallel tempering and a new Monte Carlo estimator for the ratio of partition functions are implemented here to achieve well converged simulations that give an accuracy of 0.04 kcal/mol in the reported free energies. The method is applied to various test systems, including a catalytic system composed of 18 atoms. Absolute free energies calculated by this method lead to corrections as large as 2.6 kcal/mol at 300 K for some of the examples presented.     

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.     

Path integral Monte Carlo method for ab initio calculation

The Feynman path integral method is applied to the many-electron problem. We first give new closure relations in terms of ordinary complex and real numbers, which could be derived from an arbitrary complete set of state vectors. Then, in the path integral form, the partition function of the system and the ensemble average of energy are explicitly expressed in terms of these closure relations. It is impossible to evaluate the path integral by direct numerical integrations because of its huge amount of integration variables. Therefore, we develop an algorithm by the Monte Carlo method with constraints corresponding to the normalization condition of states to calculate the required integral. Finally, the ensemble average of energy for the hydrogen molecule is explicitly evaluated by the quantum Monte Carlo method and results are compared with the result obtained by the ordinary full configuration interaction (CI) method. © 1996 John Wiley & Sons, Inc.     

Electronic energy functionals: Levy–Lieb principle within the ground state path integral quantum Monte Carlo

We propose a theoretical/computational protocol based on the use of the Ground State Path Integral Quantum Monte Carlo for the calculation of the kinetic and Coulomb energy density for a system of N interacting electrons in an external potential. The idea is based on the derivation of the energy densities via the (N ? 1)‐conditional probability density within the framework of the Levy–Lieb constrained search principle. The consequences for the development of energy functionals within the context of density functional theory are discussed. We propose also the possibility of going beyond the energy densities and extend this idea to a computational procedure where the (N ? 1)‐conditional probability is an implicit functional of the electron density, independently from the external potential. In principle, such a procedure paves the way for an on‐the‐fly determination of the energy functional for any system. © 2012 Wiley Periodicals, Inc.     

Permeation and gating in proteins: kinetic Monte Carlo reaction path following

We present a new Monte Carlo technique, kinetic Monte Carlo reaction path following (kMCRPF), for the computer simulation of permeation and large-scale gating transitions in protein channels. It combines ideas from Metropolis Monte Carlo (MMC) and kinetic Monte Carlo (kMC) algorithms, and is particularly suitable when a reaction coordinate is well defined. Evolution of transition proceeds on the reaction coordinate by small jumps (kMC technique) toward the nearest lowest-energy uphill or downhill states, with the jumps thermally activated (constrained MMC). This approach permits navigation among potential minima on an energy surface, finding the minimum-energy paths and determining their associated free-energy profiles. The methodological and algorithmic strategies underlying the kMCRPF method are described. We have tested it using an analytical model and applied it to study permeation through the curvilinear ClC chloride and aquaporin pores and to gating in the gramicidin A channel. These studies of permeation and gating in real proteins provide extensive procedural tests of the method.     

Path integral hybrid Monte Carlo algorithm for correlated Bose fluids

Path integral hybrid Monte Carlo (PIHMC) algorithm for strongly correlated Bose fluids has been developed. This is an extended version of our previous method [S. Miura and S. Okazaki, Chem. Phys. Lett. 308, 115 (1999)] applied to a model system consisting of noninteracting bosons. Our PIHMC method for the correlated Bose fluids is constituted of two trial moves to sample path-variables describing system coordinates along imaginary time and a permutation of particle labels giving a boundary condition with respect to imaginary time. The path-variables for a given permutation are generated by a hybrid Monte Carlo method based on path integral molecular dynamics techniques. Equations of motion for the path-variables are formulated on the basis of a collective coordinate representation of the path, staging variables, to enhance the sampling efficiency. The permutation sampling to satisfy Bose-Einstein statistics is performed using the multilevel Metropolis method developed by Ceperley and Pollock [Phys. Rev. Lett. 56, 351 (1986)]. Our PIHMC method has successfully been applied to liquid helium-4 at a state point where the system is in a superfluid phase. Parameters determining the sampling efficiency are optimized in such a way that correlation among successive PIHMC steps is minimized.     

Finite temperature effects in Na3 and Na3: A path integral Monte Carlo study

Path integral Monte Carlo techniques are used to study Na₃⁺ and Na₃ at finite temperatures. In accord with previous classical trajectory calculations, we find that vibrational motion significantly distorts the clusters from the previously predicted zero temperature geometries, due to the flat Born-Oppenheimer potential energy surface. More importantly, these distorted clusters show significant localized electronic bonding, in contrast to the delocalized bonding found in previous studies of the zero temperature structures.     

Finite temperature path integral Monte Carlo simulations of structural and dynamical properties of Ar(N)-CO(2) clusters

We report finite temperature quantum mechanical simulations of structural and dynamical properties of Ar(N)-CO(2) clusters using a path integral Monte Carlo algorithm. The simulations are based on a newly developed analytical Ar-CO(2) interaction potential obtained by fitting ab initio results to an anisotropic two-dimensional Morse∕Long-range function. The calculated distributions of argon atoms around the CO(2) molecule in Ar(N)-CO(2) clusters with different sizes are consistent to the previous studies of the configurations of the clusters. A first-order perturbation theory is used to quantitatively predict the CO(2) vibrational frequency shift in different clusters. The first-solvation shell is completed at N = 17. Interestingly, our simulations for larger Ar(N)-CO(2) clusters showed several different structures of the argon shell around the doped CO(2) molecule. The observed two distinct peaks (2338.8 and 2344.5 cm(-1)) in the υ(3) band of CO(2) may be due to the different arrangements of argon atoms around the dopant molecule.     

Monte Carlo simulation and self-consistent integral equation theory for polymers in quenched random media

The conformational properties and static structure of freely jointed hard-sphere chains in matrices composed of stationary hard spheres are studied using Monte Carlo simulations and integral equation theory. The simulations show that the chain size is a nonmonotonic function of the matrix density when the matrix spheres are the same size as the monomers. When the matrix spheres are of the order of the chain size the chain size decreases monotonically with increasing matrix volume fraction. The simulations are used to test the replica-symmetric polymer reference interaction site model (RSP) integral equation theory. When the simulation results for the intramolecular correlation functions are input into the theory, the agreement between theoretical predictions and simulation results for the pair-correlation functions is quantitative only at the highest fluid volume fractions and for small matrix sphere sizes. The RSP theory is also implemented in a self-consistent fashion, i.e., the intramolecular and intermolecular correlation functions are calculated self-consistently by combining a field theory with the integral equations. The theory captures qualitative trends observed in the simulations, such as the nonmonotonic dependence of the chain size on media fraction.     

Path integral Monte Carlo study of CO2 solvation in 4He clusters

We present a finite temperature quantum mechanical study of the dynamical and structural properties of small (4)He(N)-CO(2) clusters (N< or =17) using a path integral Monte Carlo (PIMC) method. The simulations were based on a He-CO(2) interaction potential with explicit dependence on the asymmetric stretch of the CO(2) molecule obtained at the CCSD(T) level. The shift of the CO(2) antisymmetric stretching (nu(3)) band origin and effective rotational constant were calculated as a function of the cluster size. In excellent agreement with experimental observations, the CO(2) vibrational band origin shifts and rotational constant show a turnaround near N=5, corresponding to a donut structure with the He atoms in equatorial positions of the linear dopant molecule.     

Path integral Monte Carlo study of 4He clusters doped with alkali and alkali-earth ions

Path integral Monte Carlo calculations of (4)He nanodroplets doped with alkali (Na(+), K(+) and Cs(+)) and alkali-earth (Be(+) and Mg(+)) ions are presented. We study the system at T = 1 K and between 14 and 128 (4)He atoms. For all studied systems, we find that the ion is well localized at the center of the droplet with the formation of a "snowball" of well-defined shells of localized (4)He atoms forming solid-like order in at least the first surrounding shell. The number of surrounding helium shells (two or three) and the number of atoms per shell and the degree of localization of the helium atoms are sensitive to the type of ion. The number of (4)He atoms in the first shell varies from 12 for Na(+) to 18 for Mg(+) and depends weakly on the size of the droplet. The study of the density profile and of the angular correlations shows that the local solid-like order is more pronounced for the alkali ions with Na(+) giving a very stable icosahedral order extending up to three shells.     

Mercedes-Benz water molecules near hydrophobic wall: integral equation theories vs Monte Carlo simulations

Associative version of Henderson-Abraham-Barker theory is applied for the study of Mercedes-Benz model of water near hydrophobic surface. We calculated density profiles and adsorption coefficients using Percus-Yevick and soft mean spherical associative approximations. The results are compared with Monte Carlo simulation data. It is shown that at higher temperatures both approximations satisfactory reproduce the simulation data. For lower temperatures, soft mean spherical approximation gives good agreement at low and at high densities while in at mid range densities, the prediction is only qualitative. The formation of a depletion layer between water and hydrophobic surface was also demonstrated and studied.     

Path integral Monte Carlo simulation of the absorption spectra of an Al atom embedded in helium

We use a multilevel path integral Monte-Carlo (PIMC) method to simulate the arrangement of He atoms around a single Al atom doped in a He cluster. High-level ab initio Al-He pair potentials and a Balling and Wright pairwise Hamiltonian model are used to describe the full potential and the electronic asymmetry arising from the open-shell character of the Al atom in its ground and excited electronic states. Our calculations show that the doping of the Al 3p electron strongly influences the He packing. The results of the PIMC simulation are used to predict the electronic excitation spectrum of an Al atom embedded in He clusters. With inclusion of tail corrections for the ground and excited states potentials, the calculated 3d<--3p spectrum agrees reasonably well with the experimental spectrum. The blueshift of the calculated spectrum associated with the 4s<--3p transition of solvated Al is about 25 nm (2000 cm-1) larger than seen in experiments on Al embedded in bulk liquid He. We predict that the spectrum associated with the 4p<--3p transition will be blueshifted by approximately 7000 cm-1 (nearly 1 eV).     

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.     

Reactive Monte Carlo and grand-canonical Monte Carlo simulations of the propene metathesis reaction system

The influence of silicalite-1 pores on the reaction equilibria and the selectivity of the propene metathesis reaction system in the temperature range between 300 and 600 K and the pressure range from 0.5 to 7 bars has been investigated with molecular simulations. The reactive Monte Carlo (RxMC) technique was applied for bulk-phase simulations in the isobaric-isothermal ensemble and for two phase systems in the Gibbs ensemble. Additionally, Monte Carlo simulations in the grand-canonical ensemble (GCMC) have been carried out with and without using the RxMC technique. The various simulation procedures were combined with the configurational-bias Monte Carlo approach. It was found that the GCMC simulations are superior to the Gibbs ensemble simulations for reactions where the bulk-phase equilibrium can be calculated in advance and does not have to be simulated simultaneously with the molecules inside the pore. The confined environment can increase the conversion significantly. A large change in selectivity between the bulk phase and the pore phase is observed. Pressure and temperature have strong influences on both conversion and selectivity. At low pressure and temperature both conversion and selectivity have the highest values. The effect of confinement decreases as the temperature increases.     

DFT-LDA pseudopotentials in quantum Monte Carlo

We investigate the portability of standard norm-conserving pseudopotentials outside the density functional theory-local density approximation (DFT-LDA) framework, i.e., their use and interpretation as electron-ion effective potentials in valence-only diffusion Monte Carlo simulations. While first-principles many-body pseudopotentials are not available in the literature yet, the use of approximate pseudopotentials in quantum Monte Carlo simulations is becoming widespread. Here we attempt a systematic analysis of the portability of norm-conserving pseudopotentials generated within DFT-LDA, focusing on a model many-body system, the two-electron valence-only ion. Our results indicate that the portability is good in most cases, hence the use of pseudopotentials in quantum Monte Carlo simulations is in general a reasonable approximation but suggest that in some cases this approximation may be relevant. © 1997 John Wiley & Sons, Inc.     

Thermodynamic properties of van der Waals fluids from Monte Carlo simulations and perturbative Monte Carlo theory

Computer simulations have been performed for fluids with van der Waals potential, that is, hard spheres with attractive inverse power tails, to determine the equation of state and the excess energy. On the other hand, the first- and second-order perturbative contributions to the energy and the zero- and first-order perturbative contributions to the compressibility factor have been determined too from Monte Carlo simulations performed on the reference hard-sphere system. The aim was to test the reliability of this "exact" perturbation theory. It has been found that the results obtained from the Monte Carlo perturbation theory for these two thermodynamic properties agree well with the direct Monte Carlo simulations. Moreover, it has been found that results from the Barker-Henderson [J. Chem. Phys. 47, 2856 (1967)] perturbation theory are in good agreement with those from the exact perturbation theory.     

Higher order diffusion Monte Carlo propagators for linear rotors as diffusion on a sphere: development and application to O2@He(n)

Exploiting the theoretical treatment of particles diffusing on corrugated surfaces and the isomorphism between the "particle on a sphere" and a linear molecule rotation, a new diffusion kernel is introduced to increase the order of diffusion Monte Carlo (DMC) simulations involving linear rotors. Tests carried out on model systems indicate the superior performances of the new rotational diffusion kernel with respect to the simpler alternatives previously employed. In particular, it is evidenced a second order convergence toward exact results with respect to the time step of dynamical correlation functions, a fact that guarantees an identical order for the diffusion part of the DMC projector. The algorithmic advantages afforded by the latter are discussed, especially with respect to the "a posteriori" and "on the fly" extrapolation schemes. As a first application to the new algorithm, the structure and energetics of O(2)@He(n) (n = 1-40) clusters have been studied. This was done to investigate the possible cause of the quenching of the reaction between O(2) and Mg witnessed upon increasing the size of superfluid He droplets used as a solvent. With the simulations on O(2) indicating a strong localization in the cluster core, the behaviour as a function of n is ascribed to the extremely fluxional comportment of Mg@He(n), which dwells far from the droplet center, albeit being solvated, when n is large.