Computation of the properties of liquid neon, methane, and gas helium at low temperature by the Feynman-Hibbs approach

The properties of liquid methane, liquid neon, and gas helium are calculated at low temperatures over a large range of pressure from the classical molecular-dynamics simulations. The molecular interactions are represented by the Lennard-Jones pair potentials supplemented by quantum corrections following the Feynman-Hibbs approach. The equations of state, diffusion, and shear viscosity coefficients are determined for neon at 45 K, helium at 80 K, and methane at 110 K. A comparison is made with the existing experimental data and for thermodynamical quantities, with results computed from quantum numerical simulations when they are available. The theoretical variation of the viscosity coefficient with pressure is in good agreement with the experimental data when the quantum corrections are taken into account, thus reducing considerably the 60% discrepancy between the simulations and experiments in the absence of these corrections.     

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.     

Accelerating the convergence of path integral dynamics with a generalized Langevin equation

The quantum nature of nuclei plays an important role in the accurate modelling of light atoms such as hydrogen, but it is often neglected in simulations due to the high computational overhead involved. It has recently been shown that zero-point energy effects can be included comparatively cheaply in simulations of harmonic and quasiharmonic systems by augmenting classical molecular dynamics with a generalized Langevin equation (GLE). Here we describe how a similar approach can be used to accelerate the convergence of path integral (PI) molecular dynamics to the exact quantum mechanical result in more strongly anharmonic systems exhibiting both zero point energy and tunnelling effects. The resulting PI-GLE method is illustrated with applications to a double-well tunnelling problem and to liquid water.     

Free energy derivatives: A new method for probing the convergence problem in free energy calculations

The convergence behavior of free energy calculations has been explored in more detail than in any previously reported work, using a model system of two neon atoms in a periodic box of water. We find that for thermodynamic integration-type free energy calculations as much as a nanosecond or more molecular dynamics sampling is required to obtain a fully converged value for a single λ point of the integrand. The concept of “free energy derivatives” with respect to the individual parameters of the force field is introduced. This formalism allows the total convergence of the simulation to be deconvoluted into components. A determination of the statistical “sampling ratio” from these simulations indicates that for window-type free energy calculations carried out in a periodic waterbox of typical size at least 0.6 ps of sampling should be performed at each window (0.7 ps if constraint contributions to the free energy are being determined). General methods to estimate and reduce the error in thermodynamic integration and free energy perturbation calculations are discussed. We show that the difficulty in applying such methods is determining a reliable estimate of the correlation length from a short series of data. © 1994 by John Wiley & Sons, Inc.     

Quantum effects on adsorption and diffusion of hydrogen and deuterium in microporous materials

Monte Carlo and molecular dynamics simulations and neutron scattering experiments are used to study the adsorption and diffusion of hydrogen and deuterium in zeolite Rho in the temperature range of 30-150 K. In the molecular simulations, quantum effects are incorporated via the Feynman-Hibbs variational approach. We suggest a new set of potential parameters for hydrogen, which can be used when Feynman-Hibbs variational approach is used for quantum corrections. The dynamic properties obtained from molecular dynamics simulations are in excellent agreement with the experimental results and show significant quantum effects on the transport at very low temperature. The molecular dynamics simulation results show that the quantum effect is very sensitive to pore dimensions and under suitable conditions can lead to a reverse kinetic molecular sieving with deuterium diffusing faster than hydrogen.     

Activation free energy for proton transfer in solution

Path integral molecular dynamics methods are employed to compute the free energy for proton transfer reactions for strongly hydrogen bonded systems in a polar solvent. The free energy profile is calculated using several different techniques, including: integration of the mean force acting on the proton path with its centroid constrained at different values, the integral form of the free energy calculation in the constrained-reaction-coordinate-dynamics ensemble and direct simulation of the unconstrained dynamics. The results show that estimates of the free energy barrier obtained by harmonic extrapolation are likely to be in error. Both quantum and classical results for the free energy are obtained and compared with simulations using adiabatic quantum dynamics. Comparison of the quantum and classical results show that there are quantum corrections to the solvent contributions to the free energy.     

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.     

Saddle-point expansion in molecular-orbital theory

We propose a novel method for calculation of the electronic correlation energy of molecular systems in the path integral formalism. The procedure consists of saddle-point expansion of the path integral around the Hartree–Fock energy. By one loop-expansion of the molecular path integral into the generalized space phase of the molecular orbitals, the shift energy is obtained.     

Many-body and quantum effects in the surface tension and surface energy of liquid neon and argon using the Fowler’s approximation

The Fowler’s expression for calculation of the reduced surface tension and surface energy has been used with Lennard-Jones (LJ) and two-body Hartree-Fock dispersion (HFD)-like potentials for neon and argon, respectively. The required radial distribution functions (RDFs) have been used from two recently determined expressions in the literature and a new equation proposed in this work. Quantum corrections for neon system have been considered using the Feynman-Hibbs (FH) and Wigner-Kirkwood (WK) approaches. To take many-body forces into account for argon system, the simple three-body potentials of Wang and Sadus (2006) [33] and Hauschild and Prausnitz (1993) [30] used with the HFD-like potential without requiring an expensive three-body calculation. The results show that the quantum and three-body effects improve the prediction of the surface tension of liquid neon and argon using the Fowler’s expression.     

Evaluation of the grand-canonical partition function using expanded Wang-Landau simulations. II. Adsorption of atomic and molecular fluids in a porous material

We propose to apply expanded Wang-Landau simulations to study the adsorption of atomic and molecular fluids in porous materials. This approach relies on a uniform sampling of the number of atoms and molecules adsorbed. The method consists in determining a high-accuracy estimate of the grand-canonical partition function for the adsorbed fluids. Then, using the formalism of statistical mechanics, we calculate absolute and excess thermodynamic properties relevant to adsorption processes. In this paper, we examine the adsorption of argon and carbon dioxide in the isoreticular metal-organic framework (IRMOF-1). We assess the reliability of the method by showing that the predicted adsorption isotherms and isosteric heats are in excellent agreement with simulation results obtained from grand-canonical Monte Carlo simulations. We also show that the proposed method is very efficient since a single expanded Wang-Landau simulation run at a given temperature provides the whole adsorption isotherm. Moreover, this approach provides a direct access to a wide range of thermodynamic properties, such as, e.g., the excess Gibbs free energy and the excess entropy of adsorption.     

A semiclassical study of the thermal conductivity of low temperature liquids

The conventional classical energy current auto-correlation function has been extended into a quantum mechanical version and then approximated by the linearized semiclassical initial value representation approach. Comparison of the thermal conductivity to simulation results shows that about 15% quantum correction to the classical molecular dynamics results for liquid neon are quantitatively predicted. For liquid para-hydrogen the quantum effects are sufficiently large that the linearized semiclassical approach is only 20% accurate, while for both liquid He(4) and He(3) the thermal conductivity disagrees by a factor of 2, although exchange effects appear to play a minor role.     

Path integral calculation of free energies: quantum effects on the melting temperature of neon

The path integral formulation has been combined with several methods to determine free energies of quantum many-body systems, such as adiabatic switching and reversible scaling. These techniques are alternatives to the standard thermodynamic integration method. A quantum Einstein crystal is used as a model to demonstrate the accuracy and reliability of these free energy methods in quantum simulations. Our main interest focuses on the calculation of the melting temperature of Ne at ambient pressure, taking into account quantum effects in the atomic dynamics. The free energy of the solid was calculated by considering a quantum Einstein crystal as reference state, while for the liquid, the reference state was defined by the classical limit of the fluid. Our findings indicate that, while quantum effects in the melting temperature of this system are small, they still amount to about 6% of the melting temperature, and are therefore not negligible. The particle density as well as the melting enthalpy and entropy of the solid and liquid phases at coexistence is compared to results obtained in the classical limit and also to available experimental data.     

The connected‐moments polynomial approach for Hamiltonian eigenvalues calculation and its application to the one‐particle systems

The new connected‐moments polynomial approach (CMP) is developed for evaluation of Hamiltonian eigenvalues. It is based on properties of specially designed polynomial and does not use any basis set and variational procedure. Like all the methods based on hamiltonain moments knowledge, the CMP is conceptually simple but is less tedious and is usually convergent even for very “crude” trial functions. This method is applicable not only to the ground state energy calculation but also to the excited states. The formalism is presented in two modifications: non‐local (integral) and local (integral‐free) ones. An accuracy of both versions is illustrated by numerical examples of Hamiltonian eigenvalues calculations for harmonic and anharmonic oscillators. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

Some remarks on the hydrogen atom

The path integral for the Green's function involving the Coulomb potential in combination with the Kustaanheimo-Stiefel transformation is used to generate the atomic orbitals of the nonrelativistic hydrogen atom as various combinations of the product of one-dimensional isotropic harmonic oscillator wave functions. The use of the transformation is justified, by connecting the homogeneous space with the quotient space in the Feynman quantization formalism.     

Rigid quantum Monte Carlo simulations of condensed molecular matter: water clusters in the n=2-->8 range

The numerical advantage of quantum Monte Carlo simulations of rigid bodies relative to the flexible simulations is investigated for some simple systems. The results show that if high frequency modes in molecular condensed matter are predominantly in the ground state, the convergence of path integral simulations becomes nonuniform. Rigid body quantum parallel tempering simulations are necessary to accurately capture thermodynamic phenomena in the temperature range where the dynamics are influenced by intermolecular degrees of freedom; the stereographic projection path integral adapted for quantum simulations of asymmetric tops is a significantly more efficient strategy compared with Cartesian coordinate simulations for molecular condensed matter under these conditions. The reweighted random series approach for stereographic path integral Monte Carlo is refined and implemented for the quantum simulation of water clusters treated as an assembly of rigid asymmetric tops.     

Molecular dynamics simulations and free energy calculations on the enzyme 4‐hydroxyphenylpyruvate dioxygenase

4‐Hydroxyphenylpyruvate dioxygenase is a relevant target in both pharmaceutical and agricultural research. We report on molecular dynamics simulations and free energy calculations on this enzyme, in complex with 12 inhibitors for which experimental affinities were determined. We applied the thermodynamic integration approach and the more efficient one‐step perturbation. Even though simulations seem well converged and both methods show excellent agreement between them, the correlation with the experimental values remains poor. We investigate the effect of slight modifications on the charge distribution of these highly conjugated systems and find that accurate models can be obtained when using improved force field parameters. This study gives insight into the applicability of free energy methods and current limitations in force field parameterization. © 2011 Wiley Periodicals, Inc. J Comput Chem 2011     

Integral equation theory for correcting truncation errors in molecular simulations

Various strategies for correcting structural and energetic artefacts of molecular simulations with truncated potentials based on integral equation theory are described and applied to liquid water. The performance of the methods is examined for a range of cutoff distances and different shifted-force potentials. With the recently enhanced damped Coulomb potential (D. Zahn, B. Schilling, S.M. Kast, J. Phys. Chem. B, 106 (2002) 10725), parameterised and corrected by integral equation theory, radial distribution functions and excess internal energy very close to the Ewald simulation limit are obtained from a simulation with a cutoff distance of only 6 Å.     

Improving the efficiency and convergence of geometry optimization with the polarizable continuum model: new energy gradients and molecular surface tessellation

New equations are derived and implemented for efficient and accurate computation of solvation energy derivatives for the conductor-like polarizable continuum model (C-PCM) and the isotropic integral equation formalism polarizable continuum model (IEF-PCM). Two new molecular surface tessellation procedures GEPOL-RT and GEPOL-AS that generate near continuous potential energy surfaces are proposed for PCM geometry optimization. The combined use of these new techniques leads to efficient and convergent geometry optimizations with the PCMs.     

Quantum path integral simulation of isotope effects in the melting temperature of ice Ih

The isotope effect in the melting temperature of ice Ih has been studied by free energy calculations within the path integral formulation of statistical mechanics. Free energy differences between isotopes are related to the dependence of their kinetic energy on the isotope mass. The water simulations were performed by using the q-TIP4P/F model, a point charge empirical potential that includes molecular flexibility and anharmonicity in the OH stretch of the water molecule. The reported melting temperature at ambient pressure of this model (T=251?K) increases by 6.5±0.5 and 8.2±0.5?K upon isotopic substitution of hydrogen by deuterium and tritium, respectively. These temperature shifts are larger than the experimental ones (3.8 and 4.5 K, respectively). In the classical limit, the melting temperature is nearly the same as that for tritiated ice. This unexpected behavior is rationalized by the coupling between intermolecular interactions and molecular flexibility. This coupling makes the kinetic energy of the OH stretching modes larger in the liquid than in the solid phase. However, the opposite behavior is found for intramolecular modes, which display larger kinetic energy in ice than in liquid water.