Simple pair distribution function theory for the calculation of Helmholtz free energy differences

1975 ◽  
Vol 62 (2) ◽  
pp. 630
Author(s):  
Joseph J. Chaback
Keyword(s):  
Free Energy ◽  
Distribution Function ◽  
Pair Distribution Function ◽  
Helmholtz Free Energy ◽  
Function Theory ◽  
Simple Pair

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.

A statistical-mechanical theory of surface tension

1952 ◽  
Vol 213 (1113) ◽  
pp. 274-284 ◽  
Keyword(s):  
Surface Tension ◽  
Free Energy ◽  
Distribution Function ◽  
Pair Distribution Function ◽  
Plane Surface ◽  
Phase System ◽  
Thermodynamic Quantities ◽  
Surface Tensions ◽  
Principal Coordinates ◽  
Derivatives Of

A system is studied which consists of a large number of molecules contained in a rectangular parallelepiped with rigid walls. Volume and surface area are taken as two principal coordinates, and pressure and surface tension are considered as isothermal derivatives of the free energy. It is shown that, for a one-phase system, the thermodynamic pressure so obtained depends on the values, at the centre of the container, of the number density and the pair-distribution function. Two types of surface tension are considered as derivatives of the free energy, that at the walls of the container and that at the surface between liquid and vapour. For the latter, the formula obtained agrees with that of Kirkwood & Buff (1949), who treated surface tension from the point of view of a stress, and it is shown how their treatment may be shortened considerably. The virial of the forces exerted by the container on the molecules is shown to include terms involving the surface tensions referred to above, and it is proved that the quantities, pressure and surface tensions, occurring in the expression of the Clausius virial theorem, agree with the corresponding thermodynamic quantities. For the tension of a plane surface between phases, an approximate formula is obtained which depends on a suggested approximate form for the pair-distribution function.

The pressure and temperature consistent Lennard-Jones liquid

1978 ◽  
Vol 56 (6) ◽  
pp. 696-699 ◽  
Author(s):  
Donald S. Hall ◽  
W. R. Conkie ◽  
P. Hutchinson
Keyword(s):  
Free Energy ◽  
Distribution Function ◽  
Radial Distribution Function ◽  
Radial Distribution ◽  
Virial Coefficient ◽  
Helmholtz Free Energy ◽  
Homogeneous System ◽  
Substantial Improvement ◽  
Approximate Theory ◽  
Lennard Jones

An approximate theory for the radial distribution function of a homogeneous system is presented that ensures consistency between the pressure and compressibility equations, and that the Helmholtz free energy has a unique value. The theory is applied to the fourth virial coefficient of a Lennard-Jones fluid in order to investigate the importance of the latter requirement.It is found that the resulting fourth virial coefficient shows a substantial improvement over that of theories that do not give a unique free energy.

On the relation between perturbation theory and distribution function theories of liquids

1969 ◽  
Vol 47 (19) ◽  
pp. 2009-2019 ◽  
Author(s):  
M. Chen ◽  
D. Henderson ◽  
J. A. Barker
Keyword(s):  
Free Energy ◽  
Distribution Function ◽  
Perturbation Theory ◽  
Equation Of State ◽  
Internal Energy ◽  
Pair Distribution Function ◽  
Energy Equation ◽  
Theory Of Liquids ◽  
Better Than

Perturbation theory of liquids and distribution function theories of liquids (as typified by the Percus–Yevick theory) are examined. It is shown that the energy equation, relating the pair distribution function to the internal energy, may be integrated to yield an expression for the free energy which is similar to that obtained from perturbation theory. The equation of state resulting from this approach, based on the energy equation, is shown to be better than that obtained from the pressure or compressibility equations. Finally, the similarity between perturbation theory and distribution function theories is exploited to provide simple improvements to either approach.

Real-Space X-Ray Pair Distribution Function Analysis and Molecular-Dynamics Modelling of Diflunisal Channel Hydrates

2020 ◽  
Author(s):  
Anuradha Pallipurath ◽  
Francesco Civati ◽  
Jonathan Skelton ◽  
Dean Keeble ◽  
Clare Crowley ◽  
...  
Keyword(s):  
Molecular Dynamics ◽  
Distribution Function ◽  
Structural Dynamics ◽  
First Principles ◽  
Pair Distribution Function ◽  
Function Analysis ◽  
Real Space ◽  
X Ray ◽  
Dynamics Modelling ◽  
Dynamics Simulations

X-ray pair distribution function analysis is used with first-principles molecular dynamics simulations to study the co-operative H<sub>2</sub>O binding, structural dynamics and host-guest interactions in the channel hydrate of diflunisal.

Engineering Porosity Through Defects in a Giant Pore Metal–Organic Framework

2020 ◽  
Author(s):  
Adam Sapnik ◽  
Duncan Johnstone ◽  
Sean M. Collins ◽  
Giorgio Divitini ◽  
Alice Bumstead ◽  
...  
Keyword(s):  
Distribution Function ◽  
Ball Milling ◽  
Local Structure ◽  
Pair Distribution Function ◽  
Function Analysis ◽  
Metal Organic Framework ◽  
Metal Organic Frameworks ◽  
Defect Engineering ◽  
Metal Organic ◽  
Unsaturated Metal Sites

<p>Defect engineering is a powerful tool that can be used to tailor the properties of metal–organic frameworks (MOFs). Here, we incorporate defects through ball milling to systematically vary the porosity of the giant pore MOF, MIL-100 (Fe). We show that milling leads to the breaking of metal–linker bonds, generating more coordinatively unsaturated metal sites, and ultimately causes amorphisation. Pair distribution function analysis shows the hierarchical local structure is partially</p><p>retained, even in the amorphised material. We find that the solvent toluene stabilises the MIL-100 (Fe) framework against collapse and leads to a substantial rentention of porosity over the non-stabilised material.</p>

A canonical ensemble derivation of the McMillan-Mayer solution theory

1983 ◽  
Vol 48 (10) ◽  
pp. 2888-2892 ◽  
Author(s):  
Vilém Kodýtek
Keyword(s):  
Free Energy ◽  
Partition Function ◽  
Energy Function ◽  
Special Function ◽  
Helmholtz Free Energy ◽  
Canonical Ensemble ◽  
Free Energy Function ◽  
Solution Theory ◽  
Pure Solvent ◽  
The Common

A special free energy function is defined for a solution in the osmotic equilibrium with pure solvent. The partition function of the solution is derived at the McMillan-Mayer level and it is related to this special function in the same manner as the common partition function of the system to its Helmholtz free energy.

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