The Asymptotic Behavior of the Site-Site Ornstein-Zernike Equation and RISM-2 Approximations for Polyatomic Molecular Fluids

Ohba, Masaharu; Arakawa, Kiyoshi

doi:10.1143/jpsj.55.2955

Cited by 11 publications

(7 citation statements)

References 15 publications

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“…of molecule 2 are held at a fixed distance r from each other. It is worthwhile to note that the asymptotic form of the SSDCF-2 at large separation obtained from (3), the closure approximation, is in agreement with the exact one [14]. This fact clearly indicates that RISM-2 theory has no theoretical inconsistency similar to that of RISM-1 theory.…”

Section: The Rism-2 Theorysupporting

confidence: 73%

“…A similar relationship between the zeroth moment of SSDCF-2 and C~(r) can also be obtained from the compressibility equation [14]:…”

Section: Ramshaw's Equation and The Site-site Direct Correlation Funcmentioning

confidence: 70%

“…P is the matrix with elements P/j = 1, Q = P -I (l is the unit matrix), oJ ~2) = -12/6 and oJ (4} = 14/120. The expansion of pC in the small k regions can be written as [14]: pA' pC = K K 1 p 4-pC(Z)k 2 + ~-pk 3 + ... , (8) where K = pkB TXT, XT is the isothermal compressibility and C ~2) is the matrix whose ~7 element is the second moment of C~.(r). By using a method similar to the one used in [14], we obtain from (6) …”

Section: The Dielectric Constant In Terms Of the Ssdcf-2mentioning

confidence: 99%

“…The theory has some essential theoretical inconsistencies. The most important is the fact that the asymptotic forms of the site-site direct correlation functions obtained from the RISM-1 approximations at large separations are different from those of the exact functions [14][15][16][17]. Because of this inconsistency, all the RISM-1 theory lead to the same trivial result for the dielectric constant of polar fluids [18].…”

mentioning

confidence: 99%

“…The other is the RISM-2 theory based on the method of functional Taylor expansions [22,23]. Recently, one of the authors and Arakawa indicated that the RISM-2 theory is free from any theoretical inconsistencies similar to those of the RISM-1 theory [14]. This suggests that the RISM-2 theory will give a non-trivial result for the dielectric constant of polar fluids.…”

mentioning

confidence: 99%

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The dielectric constant and the site-site direct correlation function of the RISM-2 theory for polar polyatomic molecular fluids

Ohba

Nomura

1992

Molecular Physics

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The exact expression of the dielectric constant for polar polyatomic molecular fluids is obtained in terms of the site-site direct correlation function. This equation is closely related to the formula of the dielectric constant in terms of the molecular direct correlation function (the Ramshaw equation, Ramshaw, 1972, J. chem. Phys., 57, 2684. We discuss why RISM-l theory gives a trivial expression for the dielectric constant using equations obtained here, and show that RISM-2 theory leads to a non-trivial result for the dielectric constant of molecular liquids. IntroductionSince the proposal of the RISM integral equation by Chandler and Andersen [1], the theory based on the interaction site formalism has played an important role in the study of structure and thermodynamic properties of molecular liquids [2, 3]. The RISM-! type theory has been applied to many systems including polar liquids and ionic solutions [4][5][6][7][8][9][10][11][12][13]. It is well known that RISM-1 theory is successful in describing the short range structure and thermodynamic properties of these systems.However, the RISM-1 theory is obtained by direct application of the PY or HNC approximations for simple liquids to the theory of the molecular liquids without any theoretical justification. The theory has some essential theoretical inconsistencies. The most important is the fact that the asymptotic forms of the site-site direct correlation functions obtained from the RISM-1 approximations at large separations are different from those of the exact functions [14][15][16][17]. Because of this inconsistency, all the RISM-1 theory lead to the same trivial result for the dielectric constant of polar fluids [18].In order to overcome this difficulty, two types of theories have been proposed within the framework of the interaction site formalism. One is the theory based on the interaction site cluster expansion, that is, the proper integral equation theory by Chandler et al. [19] and Rossky and Chiles [20] and the optimized cluster expansion theory by Lupkowsky and Monson [21]. The other is the RISM-2 theory based on the method of functional Taylor expansions [22,23]. Recently, one of the authors and Arakawa indicated that the RISM-2 theory is free from any theoretical inconsistencies similar to those of the RISM-1 theory [14]. This suggests that the RISM-2 theory will give a non-trivial result for the dielectric constant of polar fluids. One of the purposes of this work is to obtain the expression for the dielectric constant of polar fluids, using the site-site direct correlation function of RISM-2 (SSDCF-2), and

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Section: The Rism-2 Theorysupporting

confidence: 73%

“…A similar relationship between the zeroth moment of SSDCF-2 and C~(r) can also be obtained from the compressibility equation [14]:…”

Section: Ramshaw's Equation and The Site-site Direct Correlation Funcmentioning

confidence: 70%