The construction of the density functional for grand potential is fundamental in understanding a broad range of interesting physical phenomena, such as phase equilibrium, interfacial thermodynamics, and solvation. However, the knowledge of a general functional accurately describing the many-body correlation of molecules is far from complete. Here, we propose a self-consistent construction of the grand potential functional based on the weighted density approximation (WDA) utilizing hierarchical integral equations. Different from our previous study [T. Yagi and H. Sato, J. Chem. Phys. 154, 124113, (2021)], we apply the WDA to the excess Helmholtz free energy functional rather than the bridge functional. To assess the performance of the present functional, we apply it to the solvation thermodynamics of Lennard-Jones fluids. Compared to the modified Benedict–Webb–Rubin equation of state, the present functional qualitatively predicts the liquid–vapor equilibrium. The solvation free energy obtained from the present functional provides a much better agreement with the Monte Carlo simulation result than the hypernetted chain functionals. It constitutes a general starting point for a systematic improvement in the accuracy of the grand potential functional.
REFERENCES
1.
R.
Evans
, “The nature of the liquid-vapour interface and other topics in the statistical mechanics of non-uniform, classical fluids
,” Adv. Phys.
28
, 143
(1979
).2.
Fundamentals of Inhomogeneous Fluids
, edited by J. R.
Henderson
(Marcel Dekker
, New York
, 1992
).3.
J.-P.
Hansen
and I. R.
McDonald
, Theory of Simple Liquids
, 3rd ed. (Academic
, London
, 2006
).4.
R.
Evans
, P.
Tarazona
, and U. M. B.
Marconi
, “On the failure of certain integral equation theories to account for complete wetting at solid-fluid interfaces
,” Mol. Phys.
50
, 993
(1983
).5.
M.
Oettel
, “Integral equations for simple fluids in a general reference functional approach
,” J. Phys.: Condens. Matter
17
, 429
(2005
).6.
A.
Ayadim
, M.
Oettel
, and S.
Amokrane
, “Optimum free energy in the reference functional approach for the integral equations theory
,” J. Phys.: Condens. Matter
21
, 115103
(2009
).7.
M.
Levesque
, R.
Vuilleumier
, and D.
Borgis
, “Scalar fundamental measure theory for hard spheres in three dimensions: Application to hydrophobic solvation
,” J. Chem. Phys.
137
, 034115
(2012
).8.
G.
Jeanmairet
, M.
Levesque
, V.
Sergiievskyi
, and D.
Borgis
, “Molecular density functional theory for water with liquid-gas coexistence and correct pressure
,” J. Chem. Phys.
142
, 154112
(2015
).9.
T.
Sumi
, Y.
Maruyama
, A.
Mitsutake
, and K.
Koga
, “A reference-modified density functional theory: An application to solvation free-energy calculations for a Lennard-Jones solution
,” J. Chem. Phys.
144
, 224104
(2016
).10.
D.
Borgis
, S.
Luukkonen
, L.
Belloni
, and G.
Jeanmairet
, “Simple parameter-free bridge functionals for molecular density functional theory. Application to hydrophobic solvation
,” J. Phys. Chem. B
124
, 6885
–6893
(2020
).11.
D.
Borgis
, S.
Luukkonen
, L.
Belloni
, and G.
Jeanmairet
, “Accurate prediction of hydration free energies and solvation structures using molecular density functional theory with a simple bridge functional
,” J. Phys. Chem.
155
, 024117
(2021
).12.
P.
Tarazona
, “Free-energy density functional for hard spheres
,” Phys. Rev. A
31
, 2672
(1985
).13.
W. A.
Curtin
and N. W.
Ashcroft
, “Weighted-density-functional theory of inhomogeneous liquids and the freezing transition
,” Phys. Rev. A
32
, 2909
(1985
).14.
D. M.
Kroll
and B. B.
Laird
, “Comparison of weighted-density-functional theories for inhomogeneous liquids
,” Phys. Rev. A
42
, 4806
(1990
).15.
A. R.
Denton
and N. W.
Ashcroft
, “Weighted-density-functional theory of nonuniform fluid mixtures: Application to the structure of binary hard-sphere mixtures near a hard wall
,” Phys. Rev. A
44
, 8242
(1991
).16.
C. N.
Patra
and S. K.
Ghosh
, “A simple weighted-density-functional approach to the structure of inhomogeneous fluids
,” J. Chem. Phys.
116
, 8509
(2002
).17.
C. N.
Patra
and S. K.
Ghosh
, “A self-consistent weighted-density-functional approach to the structure of simple fluids
,” J. Chem. Phys.
116
, 9845
(2002
).18.
C. N.
Patra
and S. K.
Ghosh
, “Structure of nonuniform three-component fluid mixtures: A density-functional approach
,” J. Chem. Phys.
118
, 8326
(2003
).19.
T.
Sumi
and H.
Sekino
, “A self-consistent density-functional approach for homogeneous and inhomogeneous classical fluids
,” J. Phys. Soc. Jpn.
77
, 034605
(2008
).20.
A. R.
Denton
and N. W.
Ashcroft
, “Modified weighted-density-functional theory of nonuniform classical liquids
,” Phys. Rev. A
39
, 4701
(1989
).21.
J. F.
Lutsko
and M.
Baus
, “Nonperturbative density-functional theories of classical nonuniform systems
,” Phys. Rev. A
41
, 6647
(1990
).22.
C. N.
Likos
and N. W.
Ashcroft
, “Self-consistent theory of freezing of the classical one-component plasma
,” Phys. Rev. Lett.
69
, 316
(1992
).23.
R.
Leidl
and H.
Wagner
, “Hybrid WDA: A weighted-density approximation for inhomogeneous fluids
,” J. Chem. Phys.
98
, 4142
(1993
).24.
S. C.
Kim
and S. H.
Suh
, “Weighted-density approximation and its application to classical fluids
,” J. Chem. Phys.
104
, 7233
(1996
).25.
Y.
Rosenfeld
, “Free-energy model for the inhomogeneous hard-sphere fluid mixture and density-functional theory of freezing
,” Phys. Rev. Lett.
63
, 980
(1989
).26.
E.
Kierlik
and M. L.
Rosinberg
, “Free-energy density functional for the inhomogeneous hard-sphere fluid: Application to interfacial adsorption
,” Phys. Rev. A
42
, 3382
(1990
).27.
P.
Tarazona
, “Density functional for hard sphere crystals: A fundamental measure approach
,” Phys. Rev. Lett.
84
, 694
(2000
).28.
R.
Roth
, R.
Evans
, A.
Lang
, and G.
Kahl
, “Fundamental measure theory for hard-sphere mixtures revisited: The white bear version
,” J. Phys.: Condens. Matter
14
, 12063
(2002
).29.
Y.-X.
Yu
and J.
Wu
, “Structures of hard-sphere fluids from a modified fundamental-measure theory
,” J. Chem. Phys.
117
, 10156
(2002
).30.
H.
Hansen-Goos
and R.
Roth
, “A new generalization of the Carnahan-Starling equation of state to additive mixtures of hard spheres
,” J. Phys.: Condens. Matter
18
, 8413
(2006
).31.
H.
Hansen-Goos
and K.
Mecke
, “Fundamental measure theory for inhomogeneous fluids of nonspherical hard particles
,” Phys. Rev. Lett.
102
, 018302
(2009
).32.
R.
Roth
, “Fundamental measure theory for hard-sphere mixtures: A review
,” J. Phys.: Condens. Matter
22
, 063102
(2010
).33.
J. F.
Lutsko
, “Explicitly stable fundamental-measure-theory models for classical density functional theory
,” Phys. Rev. E
102
, 062137
(2020
).34.
T.
Yagi
and H.
Sato
, “Self-consistent construction of bridge functional based on the weighted density approximation
,” J. Chem. Phys.
154
, 124113
(2021
).35.
J. K.
Percus
, “Approximation methods in classical statistical mechanics
,” Phys. Rev. Lett.
8
, 462
(1962
).36.
R. J.
Baxter
, “Direct correlation functions and their derivatives with respect to particle density
,” J. Chem. Phys.
41
, 553
(1964
).37.
J. A.
Barker
and D.
Henderson
, “Perturbation theory and equation of state for fluids. II. A successful theory of liquids
,” J. Chem. Phys.
47
, 4714
(1967
).38.
J. D.
Weeks
, D.
Chandler
, and H. C.
Andersen
, “Role of repulsive forces in determining the equilibrium structure of simple liquids
,” J. Chem. Phys.
54
, 5237
(1971
).39.
A.
Kovalenko
, S.
Ten-no
, and F.
Hirata
, “Solution of the three-dimensional RISM/HNC equations for SPC water by the modified method of direct inversion in the iterative subspace
,” J. Comput. Chem.
20
, 928
(1999
).40.
J. K.
Johnson
, J. A.
Zollweg
, and K. E.
Gubbins
, “The Lennard-Jones equation of state revisited
,” Mol. Phys.
78
, 591
–618
(1993
).41.
D. M.
Huang
and D.
Chandler
, “Cavity formation and the drying transition in the Lennard-Jones fluid
,” Phys. Rev. E
61
, 1501
(2000
).42.
H. S.
Ashbaugh
, “Blowing bubbles in Lennard-Jonesium along the saturation curve
,” J. Chem. Phys.
130
, 204517
(2009
).43.
J.
Wu
, “Solvation of a spherical cavity in simple liquids: Interpolating between the limits
,” J. Phys. Chem. B
113
, 6813
–6818
(2009
).44.
T.
Miyata
and J.
Thapa
, “Accuracy of solvation free energy calculated by hypernetted chain and Kovalenko–Hirata approximations for two-component system of Lennard-Jones liquid
,” Chem. Phys. Lett.
604
, 122
(2014
).45.
T.
Miyata
and Y.
Ebato
, “Correction of Kovalenko-Hirata closure in Ornstein-Zernike integral equation theory for Lennard-Jones fluids
,” J. Mol. Liq.
245
, 2
–10
(2017
).© 2022 Author(s). Published under an exclusive license by AIP Publishing.
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