272,583 research outputs found
Fast Computation of Solvation Free Energies with Molecular Density Functional Theory: Thermodynamic-Ensemble Partial Molar Volume Corrections
Molecular Density Functional Theory (MDFT) offers an efficient implicit-
solvent method to estimate molecule solvation free-energies whereas conserving
a fully molecular representation of the solvent. Even within a second order ap-
proximation for the free-energy functional, the so-called homogeneous reference
uid approximation, we show that the hydration free-energies computed for a
dataset of 500 organic compounds are of similar quality as those obtained from
molecular dynamics free-energy perturbation simulations, with a computer cost
reduced by two to three orders of magnitude. This requires to introduce the
proper partial volume correction to transform the results from the grand
canoni- cal to the isobaric-isotherm ensemble that is pertinent to experiments.
We show that this correction can be extended to 3D-RISM calculations, giving a
sound theoretical justifcation to empirical partial molar volume corrections
that have been proposed recently.Comment: Version with correct equation numbers is here:
http://compchemmpi.wikispaces.com/file/view/sergiievskyi_et_al.pdf/513575848/sergiievskyi_et_al.pdf
Supporting information available online at:
http://compchemmpi.wikispaces.com/file/view/SuppInf_sergiievskyi_et_al_07-04-2014.pdf/513576008/SuppInf_sergiievskyi_et_al_07-04-2014.pd
Variational Principle of Bogoliubov and Generalized Mean Fields in Many-Particle Interacting Systems
The approach to the theory of many-particle interacting systems from a
unified standpoint, based on the variational principle for free energy is
reviewed. A systematic discussion is given of the approximate free energies of
complex statistical systems. The analysis is centered around the variational
principle of N. N. Bogoliubov for free energy in the context of its
applications to various problems of statistical mechanics and condensed matter
physics. The review presents a terse discussion of selected works carried out
over the past few decades on the theory of many-particle interacting systems in
terms of the variational inequalities. It is the purpose of this paper to
discuss some of the general principles which form the mathematical background
to this approach, and to establish a connection of the variational technique
with other methods, such as the method of the mean (or self-consistent) field
in the many-body problem, in which the effect of all the other particles on any
given particle is approximated by a single averaged effect, thus reducing a
many-body problem to a single-body problem. The method is illustrated by
applying it to various systems of many-particle interacting systems, such as
Ising and Heisenberg models, superconducting and superfluid systems, strongly
correlated systems, etc. It seems likely that these technical advances in the
many-body problem will be useful in suggesting new methods for treating and
understanding many-particle interacting systems. This work proposes a new,
general and pedagogical presentation, intended both for those who are
interested in basic aspects, and for those who are interested in concrete
applications.Comment: 60 pages, Refs.25
Solvation in atomic liquids: connection between Gaussian field theory and density functional theory
For the problem of molecular solvation, formulated as a liquid submitted to
the external potential field created by a molecular solute of arbitrary shape
dissolved in that solvent, we draw a connection between the Gaussian field
theory derived by David Chandler [Phys. Rev. E, 1993, 48, 2898] and classical
density functional theory. We show that Chandler's results concerning the
solvation of a hard core of arbitrary shape can be recovered by either
minimising a linearised HNC functional using an auxiliary Lagrange multiplier
field to impose a vanishing density inside the core, or by minimising this
functional directly outside the core --- indeed a simpler procedure. Those
equivalent approaches are compared to two other variants of DFT, either in the
HNC, or partially linearised HNC approximation, for the solvation of a
Lennard-Jones solute of increasing size in a Lennard-Jones solvent. Compared to
Monte-Carlo simulations, all those theories give acceptable results for the
inhomogeneous solvent structure, but are completely out-of-range for the
solvation free-energies. This can be fixed in DFT by adding a hard-sphere
bridge correction to the HNC functional.Comment: 14 pages, 4 figure
Convergent series for lattice models with polynomial interactions
The standard perturbative weak-coupling expansions in lattice models are
asymptotic. The reason for this is hidden in the incorrect interchange of the
summation and integration. However, substituting the Gaussian initial
approximation of the perturbative expansions by a certain interacting model or
regularizing original lattice integrals, one can construct desired convergent
series. In this paper we develop methods, which are based on the joint and
separate utilization of the regularization and new initial approximation. We
prove, that the convergent series exist and can be expressed as the re-summed
standard perturbation theory for any model on the finite lattice with the
polynomial interaction of even degree. We discuss properties of such series and
make them applicable to practical computations. The workability of the methods
is demonstrated on the example of the lattice -model. We calculate the
operator using the convergent series, the comparison
of the results with the Borel re-summation and Monte Carlo simulations shows a
good agreement between all these methods.Comment: 25 pages, 14 figure
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