Perturbation Theory and the Triangular Well Potential

1975 ◽  
Vol 53 (1) ◽  
pp. 5-12 ◽  
Author(s):  
W. R. Smith ◽  
D. Henderson ◽  
J. A. Barker
Keyword(s):  
Free Energy ◽  
Distribution Function ◽  
Perturbation Theory ◽  
Radial Distribution Function ◽  
Radial Distribution ◽  
Order Term ◽  
Second Order ◽  
First Order ◽  
Triangular Well Potential

Accurate calculations of the second order term in the free energy and the first order term in the radial distribution function in the Barker–Henderson (BH) perturbation theory are presented for the triangular well potential. The BH theory is found to be fully satisfactory for this system. Thus, the conclusions of Card and Walkley regarding the accuracy of the BH theory are erroneous.

A note on the perturbation theory and the triangular well potential

1977 ◽  
Vol 55 (7-8) ◽  
pp. 632-634 ◽  
Author(s):  
P. C. Wankhede ◽  
K. N. Swamy
Keyword(s):  
Monte Carlo ◽  
Perturbation Theory ◽  
Order Term ◽  
Second Order ◽  
First Order ◽  
Monte Carlo Calculations ◽  
Theory Of Liquids ◽  
Compressibility Factors ◽  
Triangular Well Potential

The integrals which appear in the first order term and the macroscopic compressibility (mc) and the local compressibility (lc) approximation for the second order term in the Barker–Henderson (BH) perturbation theory of liquids are evaluated analytically for the triangular-well potential. The compressibility factors so calculated are compared with the Monte Carlo calculations.

Perturbation theory and the local compressibility approximation in classical statistical mechanics

1968 ◽  
Vol 46 (15) ◽  
pp. 1725-1727 ◽  
Author(s):  
W. R. Smith ◽  
D. Henderson ◽  
J. A. Barker
Keyword(s):  
Perturbation Theory ◽  
Statistical Mechanics ◽  
Order Term ◽  
Second Order ◽  
Three Dimensions ◽  
First Order ◽  
Classical Statistical Mechanics ◽  
Square Well ◽  
Exact Calculations

The integrals which appear in the first-order term and the local compressibility approximation to the second-order term in the Barker–Henderson perturbation theory of fluids are evaluated analytically for the square-well potential in one and three dimensions and are compared with exact calculations.

Perturbation theory for the radial distribution function

1971 ◽  
Vol 22 (6) ◽  
pp. 1089-1105 ◽  
Author(s):  
K.E. Gubbins ◽  
W.R. Smith ◽  
M.K. Tham ◽  
E.W. Tiepel
Keyword(s):  
Distribution Function ◽  
Perturbation Theory ◽  
Radial Distribution Function ◽  
Radial Distribution

Some Old and New Expansions in the Perturbation Theory of Fluids

1974 ◽  
Vol 52 (20) ◽  
pp. 2022-2029 ◽  
Author(s):  
William R. Smith
Keyword(s):  
Free Energy ◽  
Distribution Function ◽  
Perturbation Theory ◽  
Radial Distribution Function ◽  
Numerical Computation ◽  
Taylor Expansion ◽  
Helmholtz Free Energy ◽  
Fluid Mixtures ◽  
Pair Potentials ◽  
Present Formalism

A general functional Taylor expansion of the Helmholtz free energy and radial distribution function is derived for fluids and fluid mixtures. This gives rise to some known results for particular choices of expansion functional. The results are presented in a form convenient for numerical computation, and some calculations of g(r) for the fluid with potential u(r) = 4ε(σ/r)12 are presented. It is suggested that the present formalism may be useful for molecules with nonspherical pair potentials, and some new results are obtained for mixtures of such molecules.

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