Pair potential for water from symmetry-adapted perturbation theory

1997 ◽  
Vol 107 (11) ◽  
pp. 4207-4218 ◽  
Author(s):  
Eric M. Mas ◽  
Krzysztof Szalewicz ◽  
Robert Bukowski ◽  
Bogumil Jeziorski
Keyword(s):  
Perturbation Theory ◽  
Pair Potential

Perturbation theory of the pair correlation function in molecular fluids

1978 ◽  
Vol 56 (5) ◽  
pp. 571-580 ◽  
Author(s):  
R. L. Henderson ◽  
C. G. Gray
Keyword(s):  
Perturbation Theory ◽  
Correlation Function ◽  
Pair Correlation Function ◽  
Pair Correlation ◽  
Mean Field ◽  
Pair Potential ◽  
Harmonic Series ◽  
Harmonic Space ◽  
Potential Symmetries ◽  
Harmonic Components

We study the perturbation theory of the angular pair correlation function g(rω1ω2)in a molecular fluid. We consider an anisotropic pair potential of the form u = u0 + ua, where u0 is an isotropic 'reference' potential, and for simplicity in this paper we assume the perturbation potential ua to be 'multipole-like', i.e., to contain no l = 0 spherical harmonics. We expand g in powers of ua about g0, the radial distribution function appropriate to u0. This series is examined by expanding ha = h−h0 (where h = g−1) and its corresponding direct correlation function ca in spherical harmonic components. We consider approximate summations of the series in ua that automatically truncate the corresponding harmonic series, so that the Ornstein–Zernike (OZ) equation relating ha and ca can be solved in closed form. We first expand ca = c1 + c2 + … where cn includes all terms in ca of order (ua)n. Taking ua to be a quadrupole–quadrupole interaction, we find that a 'mean field' (MF) approximation ca = c1 gives rise to only three nonvanishing harmonic components in ha, so that OZ is solved explicitly in Fourier space. The MF solution for multipoles of general order is given in an appendix. Graphical methods are then used to identify the class of all terms in the ua series that are restricted to the harmonic space defined by MF. A portion of this class can be summed by solving OZ with the closure ca = −βg0ua + h0(ha−ca), where β = (kT)−1, h0 = g0−1 This system is designated as generalized MF (GMF), and solved by numerical iteration. Numerical results from MF and GMF are presented for quadrupolar ua, taking u0 to be a Lennard-Jones potential. Symmetries imposed by the restricted harmonic space are foreign to the full g, yet harmonics within this space are sufficient for evaluation of many macroscopic properties. The results are therefore evaluated in harmonic form by comparison with the corresponding harmonic components of the 'correct' g as evaluated by Monte Carlo simulation.

Pair Potential for Liquid Nitrogen in the Perturbation Theory

1971 ◽  
Vol 55 (7) ◽  
pp. 3611-3612
Author(s):  
K. Rajagopal ◽  
T. M. Reed
Keyword(s):  
Perturbation Theory ◽  
Liquid Nitrogen ◽  
Pair Potential

An analytical equation derived from a perturbation theory to calculate Henry's constants for square well mixtures

1980 ◽  
Vol 45 (4) ◽  
pp. 1036-1046 ◽  
Author(s):  
M. I. Guerrero ◽  
L. Ponce ◽  
J. P. Monfort
Keyword(s):  
Perturbation Theory ◽  
Analytical Solution ◽  
Pair Potential ◽  
Analytic Form ◽  
Analytical Equation ◽  
Henry's Constant ◽  
Henry's Constants ◽  
Square Well

An analytic form for Henry's constant is derived and applied to several systems. The derivation is based on the use of Leonard-Henderson-Barker perturbation theory for a square well pair potential assuming the Ponce-Renon analytical solution of the square well fluid. Computed values of Henry's constants for CH4-Ar, CH4-N2, CH4-He, CH4-H2, C2H6-N2 and C2H6-CH4 mixtures are compared with experiment. The agreement is quite satisfactory, with mean relative deviations between 2.5 and 8 per cent. Heats of solutions are also computed and compared with experiment.

Radial Distribution Function of Liquid Sodium

1982 ◽  
Vol 37 (6) ◽  
pp. 594-597
Author(s):  
M. Rami Reddy
Keyword(s):  
Molecular Dynamics ◽  
Integral Equation ◽  
Distribution Function ◽  
Perturbation Theory ◽  
Radial Distribution Function ◽  
Radial Distribution ◽  
Pair Potential ◽  
Liquid Sodium ◽  
Oscillatory Potential ◽  
Molecular Dynamics Calculations

Abstract The radial distribution function of liquid sodium has been studied by considering the integral equation Perturbation Theory of Madden and Fitts for the reference part and the optimised cluster theory for the attractive part of the pair potential. Calculations were carried out for the long range oscillatory potential of Schiff. The calculated results are compared with the molecular dynamics calculations HTA, OCT and with experiment. The agreement was found to be satisfactory.

Pair potential for helium from symmetry-adapted perturbation theory calculations and from supermolecular data

2007 ◽  
Vol 127 (12) ◽  
pp. 124303 ◽  
Author(s):  
Małgorzata Jeziorska ◽  
Wojciech Cencek ◽  
Konrad Patkowski ◽  
Bogumił Jeziorski ◽  
Krzysztof Szalewicz
Keyword(s):  
Perturbation Theory ◽  
Pair Potential

Perturbation theory of solutions of non-electrolytes. The effect of permanent and induced multipole interactions on excess thermodynamic functions of binary systems

1979 ◽  
Vol 44 (12) ◽  
pp. 3541-3548 ◽  
Author(s):  
Miloš Ševčík ◽  
Tomáš Boublík
Keyword(s):  
Perturbation Theory ◽  
Thermodynamic Functions ◽  
Binary Systems ◽  
Pair Potential ◽  
Intermolecular Forces ◽  
Considerable Effect ◽  
Binary Solutions ◽  
Lennard Jones ◽  
Excess Thermodynamic Functions ◽  
Excess Quantities

Perturbation theory proposed to describe fluids with the multipole interactions was extended to the systems with significant induced interactions. The relations obtained were used to study the effect of the permanent and induced multipole interactions on excess thermodynamic functions of binary solutions formed by a simple fluid (interacting according to the Lennard-Jones pair potential) and a fluid with anisotropic intermolecular forces. Model solutions were studied first; the same procedure was then used to predict behaviour of the real systems cyclopentane-chloroform at 298.15 K and xenon-hydrogen chloride at 195.4 K. A considerable effect of anisotropic interaction on excess quantities of the model- as well as actual solutions was proved.

The second virial coefficient of a non-associating gas with anisotropic interactions

1980 ◽  
Vol 45 (9) ◽  
pp. 2375-2383 ◽  
Author(s):  
Miloš Ševčík ◽  
Tomáš Boublík
Keyword(s):  
Experimental Data ◽  
Perturbation Theory ◽  
Intermolecular Interactions ◽  
Virial Coefficient ◽  
Second Virial Coefficient ◽  
Pair Potential ◽  
Lennard Jones ◽  
Different Temperatures ◽  
Anisotropic Interactions ◽  
Experimental Values

The second virial coefficient in systems with permanent and induced multipole interactions was studied by using a statistical-thermodynamics correlation based on the perturbation theory of fluids. Several pair potential combinations of the Lennard-Jones function with different, subsequently more complex anisotropic contributions, were considered; the improvement in the description of intermolecular interactions due to these non-central contributions brought about an improvement in the interpretation of experimental data. The characteristic dependence of the parameters ε/k on σ at different temperatures was obtained for all of the three systems studied (Ar, CH4 and CH3F). It was found that if experimental values of the second virial coefficient of methyl fluoride are correlated by a relation derived from the Stockmayer potential, two sets of the ε/k and σ can be employed.

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