Luis M. Sesé

Feynman-Hibbs potentials and path integrals for quantum Lennard-Jones systems: Theory and Monte Carlo simulations

This paper addresses unexplored aspects of the Feynman-Hibbs Gaussian picture and the ħ2- and ħ4-effective potentials obtainable from that model. Thermodynamic and structural properties are compared with their path-integral counterparts. In particular, a closed formula for the self-correlation (intranecklace) radial distribution function is derived from the Feynman-Hibbs model in view of, first, its importance in determining quantum structure factors and, second, the great difficulty in computing it accurately via path-integral calculations. In order to assess the reliability of the ħ2- and ħ4-potentials, neon liquid and helium-4 gas are studied for new state points with the corresponding semiclassical and ‘exact’ path-integral Monte Carlo simulations. As regards thermodynamics, energies, pressures and also specific heats at constant volume are reported. Structural results cover necklace radii of gyration, and instantaneous, linear response and self-correlation radial distribution functions. Comparison wi...

Heat capacity of water : a signature of nuclear quantum effects

In this note we present results for the heat capacity at constant pressure for the TIP4PQ/2005 model, as obtained from path-integral simulations. The model does a rather good job of describing both the heat capacity of ice I(h) and of liquid water. Classical simulations using the TIP4P/2005, TIP3P, TIP4P, TIP4P-Ew, simple point charge/extended, and TIP5P models are unable to reproduce the heat capacity of water. Given that classical simulations do not satisfy the third law of thermodynamics, one would expect such a failure at low temperatures. However, it seems that for water, nuclear quantum effects influence the heat capacities all the way up to room temperature. The failure of classical simulations to reproduce C(p) points to the necessity of incorporating nuclear quantum effects to describe this property accurately.

Quantum contributions in the ice phases: The path to a new empirical model for water—TIP4PQ/2005

With a view to a better understanding of the influence of atomic quantum delocalization effects on the phase behavior of water, path integral simulations have been undertaken for almost all of the known ice phases using the TIP4P/2005 model in conjunction with the rigid rotor propagator proposed by Muser and Berne [Phys. Rev. Lett. 77, 2638 (1996)]. The quantum contributions then being known, a new empirical model of water is developed (TIP4PQ/2005) which reproduces, to a good degree, a number of the physical properties of the ice phases, for example, densities, structure, and relative stabilities.

Study of the Feynman-Hibbs effective potential against the path-integral formalism for Monte Carlo simulations of quantum many-body Lennard-Jones systems

Approximate quantum pair radial correlation functions and thermodynamic quantities for Lennard-Jones systems can be computed with Monte Carlo simulation involving Feynman-Hibbs potentials. A convolution approach to produce the quantum pair radial function from the direct Monte Carlo structural results is presented by analysing its connection with the path-integral instantaneous and linear response pair radial functions. Several Lennard-Jones systems with substantial quantum behaviour: methane, argon, neon, deuterium and helium-4 (eighteen state points) are studied. For the sake of comparison, new path-integral simulations of helium-4 and improved path-integral results for methane are also reported. The effective potential results are in close agreement with experimental and exact path-integral data over a wide range of de Broglie wavelengths, densities and temperatures.

Feynman-Hibbs quantum effective potentials for Monte Carlo simulations of liquid neon

The quantum characteristics of liquid neon at four state points have been studied by means of Monte Carlo simulations involving two effective pair potentials arising from the path-integral formalis...

Path‐integral Monte Carlo energy and structure of the quantum hard‐sphere system using efficient propagators

Path‐integral Monte Carlo simulations neglecting exchange and involving different propagators (crude, Barker’s, Jacucci‐Omerti’s, and Cao‐Berne’s) have been performed to study the quantum hard‐sphere system at several state points ranging from the fluid to the solid phase (ρ*=0.7834; 0.1<λB*≤0.4). Energies, necklace radii of gyration and quantum pair radial distribution functions (instantaneous, linear response, self‐correlation, and necklace center of mass) have been computed and compared where possible with available data. The results indicate remarkably great performances for the efficient propagators as compared with the crude choice. Even though by lowering the temperature the three efficient propagators lead to the formation of a solid phase, quantitative differences between them are significant just from that stage (λB*≥0.3).

Quantum effects on the maximum in density of water as described by the TIP4PQ/2005 model.

Path integral simulations have been performed to determine the temperature of the maximum in density of water of the rigid, nonpolarizable TIP4PQ/2005 model treating long range Coulombic forces with the reaction field method. A maximum in density is found at 280 K, just 3 K above the experimental value. In tritiated water the maximum occurs at a temperature about 12 K higher than in water, in reasonable agreement with the experimental result. Contrary to the usual assumption that the maximum in classical water is about 14 K above that in water, we found that for TIP4PQ/2005 this maximum is about 30 K above. For rigid water models the internal energy and the temperature of maximum density do not follow a linear behavior when plotted as a function of the inverse of the hydrogen mass. In addition, it is shown that, when used with Ewald sums, the TIP4PQ/2005 reproduces quite nicely not only the maximum in density of water, but also the liquid densities, the structure of liquid water and the vaporization enthalpy. It was shown in a previous work that it also reproduces reasonably well the density and relative stabilities of ices. Therefore the TIP4PQ/2005 model, while still simple, allows one to analyze the interplay between quantum effects related to atomic masses and intermolecular forces in water.

Can gas hydrate structures be described using classical simulations

Quantum path-integral simulations of the hydrate solid structures have been performed using the recently proposed TIP4PQ/2005 model. By also performing classical simulations using this model, the impact of the nuclear quantum effects on the hydrates is highlighted; nuclear quantum effects significantly modify the structure, densities, and energies of the hydrates, leading to the conclusion that nuclear quantum effects are important not only when studying the solid phases of water but also when studying the hydrates. To analyze the validity of a classical description of hydrates, a comparison of the results of the TIP4P/2005 model (optimized for classical simulations) with those of TIP4PQ/2005 (optimized for path-integral simulations) was undertaken. A classical description of hydrates is able to correctly predict the densities at temperatures above 150 K and the relative stabilities between the hydrates and ice I(h). The inclusion of nuclear quantum effects does not significantly modify the sequence of phases found in the phase diagram of water at negative pressures, namely, I(h)-->sII-->sH. In fact the transition pressures are little affected by the inclusion of nuclear quantum effects; the phase diagram predictions for hydrates can be performed with reasonable accuracy using classical simulations. However, for a reliable calculation of the densities below 150 K, the sublimation energies, the constant pressure heat capacity, and the radial distribution functions, the incorporation of nuclear quantum effects is indeed required.

Thermodynamic and structural properties of the path-integral quantum hard-sphere fluid

An extensive study of the path-integral quantum hard-sphere fluid far from exchange is presented. The results cover the calculation of mechanical, thermal, r-space and k-space pair properties. Path-integral Monte Carlo simulations involving the Cao–Berne’s propagator provide the internal energies and pair radial distribution functions (instantaneous, linear response, and necklace center of mass). For the sake of comparison, Barker’s and Jaccuci–Omerti’s image propagators are also applied at several state points. To obtain k-space properties use of the Gaussian Feynman–Hibbs picture for representing quantum systems is made. This picture is known to yield two Ornstein–Zernike equations; one for true quantum particles (linear response) and the other for the centers of mass of quantum particles. Direct correlation functions and static structure factors are obtained via Baxter’s partition complemented with Dixon–Hutchinson’s variational procedure. Wherever possible, the present results are compared with semicl...

A quantum Monte Carlo study of liquid Lennard-Jones methane, path-integral and effective potentials

An intercomparative quantum study of liquid methane over a range of temperatures at zero experimental vapour pressure is presented. Interest is focused on the translational features. Classical, semi-classical (Wigner-Kirkwood (ħ2), Feynman-Hibbs) and path-integral Monte Carlo simulations have been performed. A basic one-centre Lennard-Jones potential has been used as the basic model to carry out computations. Energies, pressures and pair radial distribution functions are reported, and the reliability of the effective potentials is discussed. The results indicate, first, important quantum effects on the structure of this liquid and, second, that the Wigner-Kirkwood potential is a better semi-classical choice.