P. N. Vorontsov-Velyaminov

New approach to Monte Carlo calculation of the free energy: Method of expanded ensembles

We propose a new effective Monte Carlo (MC) procedure for direct calculation of the free energy in a single MC run. The partition function of the expanded ensemble is introduced including a sum of canonical partition functions with a set of temperatures and additive factors (modification). Random walk in the space of both particle coordinates and temperatures provides calculation of free energy in a wide range of T. The method was applied to a primitive model of electrolyte including the region of low temperatures. In similar way other variants of expanded ensembles are constructed (e.g., over the number of particles N or volume V). Its facilities in quantum statistics (path integral Monte Carlo) and some other applications are also discussed.

A New Monte Carlo Method for Direct Calculation of the Critical Size and the Formation Work of a Microdrop

Abstract New Monte Carlo procedures in open ensembles are proposed. Non-stationary Markov chain procedure in the μl;pT - ensemble provides a direct estimation for the critical size of a condensation nucleus at given p and T. A stationary procedure in the μlpT ensemble with two allowed particle numbers n and n + 1 provides the direct way to calculate the chemical potential and Gibbs free energy of a cluster; in the grand canonical (μlVT) ensemble the same approach gives μl and the Helmholtz free energy. The same procedures are readily applicable to periodic systems representing bulk phases.

Free energy calculations for Lennard-Jones systems and water using the expanded ensemble method A Monte Carlo and molecular dynamics simulation study

The method of expanded ensembles for calculation of free energy in Monte Carlo simulations is incorporated into molecular dynamics simulations. Calculations of the free energy for the Lennard-Jones system are carried out using both variants of the expanded ensemble method (i.e. Monte Carlo and molecular dynamics simulations) and are shown to give identical results. The free energy for two variants of the simple point charge water (rigid and flexible) is calculated using the Lennard-Jones system as a reference. Numerically very accurate results for the free energy are obtained. The results are in accordance with results obtained using other methods for calculation of free energy in computer simulations. The advantages of the presented method and possible applications for calculation of free energies for more complicated molecular systems are discussed.

Determination of Free Energy from Chemical Potentials: Application of the Expanded Ensemble Method

Abstract The expanded ensemble method, previously developed for free energy calculation [J. Chem. Phys., 96, 1776 (1992)] is applied to calculate chemical potentials. The expanded ensemble is composed as a sum of canonical ensembles with gradually inserting the (N, + 1):th particle. The probability distribution over the subsensembles is directly related to the ratio of the partition functions and, hence, to the free energy difference. The gradual insertion eliminates the difficulties arising in using the standard particle insertion method at high densities. The problem of an optimal choice of subsensembles is studied in detail. Since the chemical potential is defined as the Gibbs free energy per particle for macroscopic systems, the present method allows calculation of free energies in a convenient way. The method is applied to calculate chemical potentials and free energies for a Lennard-Jones system and for the flexible SPC water model. The results are compared with corresponding direct free energy calc...

Entropic sampling of simple polymer models within Wang–Landau algorithm

In this paper we apply a new simulation technique proposed in Wang and Landau (WL) (2001 Phys. Rev. Lett. 86 2050) to sampling of three-dimensional lattice and continuous models of polymer chains. Distributions obtained by homogeneous (unconditional) random walks are compared with results of entropic sampling (ES) within the WL algorithm. While homogeneous sampling gives reliable results typically in the range of 4?5 orders of magnitude, the WL entropic sampling yields them in the range of 20?30 orders and even larger with comparable computer effort. A combination of homogeneous and WL sampling provides reliable data for events with probabilities down to 10?35.For the lattice model we consider both the athermal case (self-avoiding walks, SAWs) and the thermal case when an energy is attributed to each contact between nonbonded monomers in a self-avoiding walk. For short chains the simulation results are checked by comparison with the exact data. In WL calculations for chain lengths up to N = 300 scaling relations for SAWs are well reproduced. In the thermal case distribution over the number of contacts is obtained in the N-range up to N = 100 and the canonical averages?internal energy, heat capacity, excess canonical entropy, mean square end-to-end distance?are calculated as a result in a wide temperature range.The continuous model is studied in the athermal case. By sorting conformations of a continuous phantom freely joined N-bonded chain with a unit bond length over a stochastic variable, the minimum distance between nonbonded beads, we determine the probability distribution for the N-bonded chain with hard sphere monomer units over its diameter a in the complete diameter range, 0 ? a ? 2, within a single ES run. This distribution provides us with excess specific entropy for a set of diameters a in this range. Calculations were made for chain lengths up to N = 100 and results were extrapolated to N ? ? for a in the range 0 ? a ? 1.25.

Depletion and bridging forces in polymer systems: Monte Carlo simulations at constant chemical potential

A new Monte Carlo simulation method designed for polymer solutions confined to planar slits is presented. The slit is in equilibrium with a surrounding bulk solution and the method allows a variation of the slit width while maintaining the polymer chemical potential constant. This is achieved by changing the tangential pressure as a function of slit width. An analysis of chain parameters and monomer distribution within the slit has been carried out. The model system used is supposed to mimick a macromolecular solution whose stability is manipulated by addition of adsorbing and/or nonadsorbing polymers. Generally, for the nonadsorbing polymer an attractive depletion force is found. At high volume fractions the attraction is reduced and a repulsive force appears at short separations. The depletion force can also be extinguished in the case of an adsorption potential of intermediate strength, while strong adsorption gives rise to a significant attraction due to polymer bridges.

Path Integral Monte Carlo Simulation of an Electron Pair in a Cavity, Paramagnetic Susceptibility and Other Canonical Properties

Abstract The PIMC method is used to simulate an electron pair located in a spherical cavity in equilibrium with a thermal bath over a wide temperature range. Permutational symmetry, electron spin and interelectron Coulomb interaction are accounted for explicity. Spin “pairing” at low temperatures results in a fall in paramagnetic susceptibility in qualitative accordance with the experimental data for electrides. The method proves to be promising in solving various quantum statistical many electron problems.

Entropic sampling in the path integral Monte Carlo method

We have extended the entropic sampling Monte Carlo method to the case of path integral representation of a quantum system. A two-dimensional density of states is introduced into path integral form of the quantum canonical partition function. Entropic sampling technique within the algorithm suggested recently by Wang and Landau (Wang F and Landau D P 2001 Phys. Rev. Lett. 86 2050) is then applied to calculate the corresponding entropy distribution. A three-dimensional quantum oscillato ri sc onsidered as an example. Canonical distributions for a wide range of temperatures are obtained in a single simulation run, and exact data for the energy are reproduced.

Monte Carlo-Self Consistent Field Study of the Symmetrical Models of Polyelectrolytes

Abstract Time saving procedures unifying Monte Carlo and self consistent field approaches for the calculation of equilibrium potentials and density distributions of mobile ions around a polyion in a polyelectrolyte system are considered. In the final version of the method the region around the polyion is divided into two zones—internal and external; all the ions of the internal zone are accounted for explicitly in a Monte Carlo procedure, in the external zone the self consistent field approximation is applied with an exchange of ions between regions. Simulations are carried out for cylindrical and spherical polyions in solutions with mono-and divalent ions and their mixtures. The results are compared with Poisson—Boltzmann approximation and experimental data on intrinsic viscosity.

Monte-Carlo-self consistent field method in the polyelectrolyte theory.

A new time saving numerical method for calculation of equilibrium potential and density distribution of mobile ions around the polyion in a polyelectrolyte system is proposed: the region around the polyion is being divided into two zones-internal and external; in the internal zone all the ions are accounted explicity with the aid of Monte-Carlo procedure; in the external zone the combined Monte-Carlo-self consistent field method proposed earlier is applied, an exchange of ions between regions is being implied. For 1:1 electrolyte the optimal choice of the boundary between the zones has been demonstrated. As an example of a more complicated system calculation for 2:2:1:1 electrolyte was carried out.