Invariant Expansion for Two-Body Correlations: Thermodynamic Functions, Scattering, and the Ornstein—Zernike Equation

Blum, L.; Torruella, A. J.

doi:10.1063/1.1676864

Cited by 484 publications

(191 citation statements)

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“…That is, we choose to simultaneously represent the molecular distribution functions in the n 2 possible equivalent coordinate systems coincident with the site-site pairs between molecules, where there are n different sites on each molecule. In this case, the complete complement of direct correlation functions, c(r αγ , Ω 1 , Ω 2 ), can be generated at once through the mixture form of the molecular OZ equation in Fourier space, (1) where c represents the species labeled matrices whose elements are the Fourier transforms c( k αγ , Ω 1 , Ω 2 ), h represents the total correlation functions defined as h=g−1, and ρ is the diagonal matrix with ρ αα =ρ/n for ρ the molecular number density of the system and n the number of sites in the molecule. In a standard convention, the brackets represent the Ω=∫dΩ 3 -weighted average over the orientation of molecule 3.…”

Section: A Angular-dependent Site-site Correlationsmentioning

confidence: 99%

“…The molecular OZ equation (1) expands in the various site-site origin labels as a site-site labeled block matrix, such that the submatrices h αγ and c αγ are defined as (7) and ρ is now block diagonal, with ρ αγ =0 in all terms when α ≠ γ and, for this diatomic case, (8) This expansion can be used to diagrammatically resum, or angularly renormalize, the intermolecular distributions in a manner similar to the methods used to treat long-ranged Coulomb potentials in simple fluids. 16,23,24 For example, we consider the expansion of the left molecular diagrams.…”

Section: A Angular-dependent Site-site Correlationsmentioning

confidence: 99%

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A site-renormalized molecular fluid theory

Dyer

Perkyns

Pettitt

2007

The Journal of Chemical Physics

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The orientation-dependent pair distribution function for molecular fluids on site-site potentials is expanded in a topological analog of the diagrammatically proper site-site theory of liquids [D. Chandler et al., Mol. Phys. 46, 1335(1982]. The resulting functions are then used to diagrammatically renormalize the molecular fluid theory. A result is that the diagrammatically proper interaction site model theory is shown to be a linearized, minimal angular basis set approximation to this site-renormalized molecular theory. This framework is used to propose a new, exact, and proper closure to the diagrammatically proper interaction site model theory. The resulting equation system contains a bridge function expansion in the proper site-site theory. In addition, the construction of the theory is such that the molecular pair distribution function, in full dimensionality, is intrinsic to the theory. Furthermore, the theory is equivalent to the molecular Ornstein-Zernike treatment of site-site molecules in the basis set expansion of Blum and Torruella [J. Chem. Phys. 56, 303 (1971)]. A significant formal result of the theory is the demonstration that certain classes of diagrams which would otherwise be considered improper in the interaction site model formalism are included in the angular expansion of molecular interactions. Numerical results for several apolar homonuclear models and an apolar heteronuclear model are shown to quantitatively improve upon those of reference interaction site model and our recent proper variant with respect to simulation. Significant numerical results are that the various thermodynamic quantities obey the exact symmetries and sum rules within numerical error for the different sites in the heteronuclear case, even for the low order approximation used in this work, and the theory is independent of the so-called auxiliary site problem common to previous site-site theories.

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Section: A Angular-dependent Site-site Correlationsmentioning

confidence: 99%

Section: A Angular-dependent Site-site Correlationsmentioning

confidence: 99%

A site-renormalized molecular fluid theory

Dyer

Perkyns

Pettitt

2007

The Journal of Chemical Physics

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“…Variations with respect to the functions yield (12)+η (12) δη (12) ω1ω2 [18][19][20]. x mnl µν is the coefficient of the solvent-solvent total correlation function.…”

Section: Moz-scf Formalismmentioning

confidence: 99%

“…The MOZ theory allows us to treat the orientation dependence of intermolecular interactions through the rotational invariant expansions [18][19][20][21]. The MOZ theory turns out to be efficient in reproducing the thermodynamic, dielectric, and structural properties obtained from the simulations for aprotic solvents, though there is a controversy as to the accuracy of the HNC approximation for the dielectric constant of protic solvents [22,23].…”

Section: Introductionmentioning

confidence: 99%

Analytical free energy gradient for the molecular Ornstein-Zernike self-consistent-field method

Yoshida¹

2007

Condens. Matter Phys.

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An analytical free energy gradient for the molecular Ornstein-Zernike self-consistent-field (MOZ-SCF) method is presented. MOZ-SCF theory is one of the theories to considering the solvent effects on the solute electronic structure in solution. [Yoshida N. et al., J. Chem. Phys., 2000, 113, 4974] Molecular geometries of water, formaldehyde, acetonitrile and acetone in water are optimized by analytical energy gradient formula. The results are compared with those from the polarizable continuum model (PCM), the reference interaction site model (RISM)-SCF and the three dimensional (3D) RISM-SCF.

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“…The function should also be invariant for an arbitrary rotation of the laboratory frame. General rotationally invariant combinations can be constructed following Blum and Torruella [24] and Stone [25]. f (r 12 , ω r , ω 1 , ω 2 ) can be expanded in a basis of products of three Wigner rotation matrices…”

Section: Appendixmentioning

confidence: 99%

Liquid Crystal Observables: Static and Dynamic Properties

Zannoni

2000

Advances in the Computer Simulatons of Liquid Crystals

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Abstract. In this Chapter we introduce the description of single and pair particle static properties of liquid crystals, and discuss their calculation from computer simulations. We also briefly describe the calculation of dynamic properties from molecular dynamics simulations using Linear Response theory. Single particle propertiesWe consider a system of N molecules at certain specified thermodynamic conditions. Typically we shall consider that volume V and temperature T are fixed together with N (canonical conditions), but we shall also refer to the case where pressure P is fixed together with T (isobaric conditions). We assume the molecules to be classical, rigid particles with centre of mass at position r and orientation ω given for instance by a set of three Euler angles (α, β, γ), or only two angles (α, β) as illustrated in fig. 1 if we can assume that the molecules have cylindrical symmetry [1].We shall discuss the calculation of observables in liquid crystals [2] in fairly general terms, but adopting a rather special point of view, that of computer simulations. As will be clear from the contributions in this book, computer simulations techniques [3] actually generate configurations of the system, i.e. sets of positions r i = (x i , y i , z i ) and orientations ω i of all the particles. In particular the Monte Carlo (MC) method generates equilibrium configurations, albeit non necessarily in the proper time order, while Molecular Dynamics (MD) actually generates configurations time step after time step in their natural time sequence. In this last case configurations consists not only of positions and orientations, but also of the full set of linear and angular velocities.published as: C. Zannoni, Liquid crystal observables: static and dynamic

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Invariant Expansion for Two-Body Correlations: Thermodynamic Functions, Scattering, and the Ornstein—Zernike Equation

Cited by 484 publications

References 25 publications

A site-renormalized molecular fluid theory

A site-renormalized molecular fluid theory

Analytical free energy gradient for the molecular Ornstein-Zernike self-consistent-field method

Liquid Crystal Observables: Static and Dynamic Properties

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