Recent developments in classical density functional theory: Internal energy functional and diagrammatic structure of fundamental measure theory

An overview of several recent developments in density functional theory for classical inhomogeneous liquids is given. We show how Levy's constrained search method can be used to derive the variational principle that underlies density functional theory. An advantage of the method is that the Hel...

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Дата:	2012
Автори:	Schmidt, M., Burgis, M., Dwandaru, W.S.B., Leithall, G., Hopkin, P.
Формат:	Стаття
Мова:	English
Опубліковано:	Інститут фізики конденсованих систем НАН України 2012
Назва видання:	Condensed Matter Physics
Онлайн доступ:	http://dspace.nbuv.gov.ua/handle/123456789/120308
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Назва журналу:	Digital Library of Periodicals of National Academy of Sciences of Ukraine
Цитувати:	Recent developments in classical density functional theory: Internal energy functional and diagrammatic structure of fundamental measure theory / M. Schmidt, M. Burgis, W.S.B. Dwandar, G. Leithall, P. Hopkins // Condensed Matter Physics. — 2012. — Т. 15, № 4. — С. 43603:1-15. — Бібліогр.: 65 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine

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spelling	irk-123456789-1203082017-06-12T03:04:55Z Recent developments in classical density functional theory: Internal energy functional and diagrammatic structure of fundamental measure theory Schmidt, M. Burgis, M. Dwandaru, W.S.B. Leithall, G. Hopkin, P. An overview of several recent developments in density functional theory for classical inhomogeneous liquids is given. We show how Levy's constrained search method can be used to derive the variational principle that underlies density functional theory. An advantage of the method is that the Helmholtz free energy as a functional of a trial one-body density is given as an explicit expression, without reference to an external potential as is the case in the standard Mermin-Evans proof by reductio ad absurdum. We show how to generalize the approach in order to express the internal energy as a functional of the one-body density distribution and of the local entropy distribution. Here the local chemical potential and the bulk temperature play the role of Lagrange multipliers in the Euler-Lagrange equations for minimiziation of the functional. As an explicit approximation for the free-energy functional for hard sphere mixtures, the diagrammatic structure of Rosenfeld's fundamental measure density functional is laid out. Recent extensions, based on the Kierlik-Rosinberg scalar weight functions, to binary and ternary non-additive hard sphere mixtures are described. Зроблено огляд декiлькох недавнiх праць з теорiї функцiоналу густини для класичних неоднорiдних рiдин. Ми показуємо яким чином метод Левi обмеженого пошуку може бути використаний для виведення варiацiйного принципу, який лежить в основi теорiї функцiоналу густини. Перевагою цього методу є те, що вiльна енергiя Гельмгольтца як функцiонал пробної одночастинкової густини задається у явному виглядi без вiдносно до зовнiшнього потенцiалу, як це є у вападку стандартного доведення Мермiна-Еванса через reductio ad absurdum. Ми показуємо як узагальнити пiдхiд для того, щоб виразити внутрiшню енергiю у виглядi функцiоналiв розподiлiв одночастинкової густини i локальної ентропiї. Тут локальний хiмi-чний потенцiал i температура в об’ємi вiдiграють роль множникiв Лагранжа в рiвняннi Ейлера-Лагранжа для мiнiмiзацiї функцiоналу. Як наближення для функцiоналу вiльної енергiї, показано дiаграмну структуру функцiоналу густини фундаментальної мiри Розенфельда для сумiшi твердих сфер. Описано недавнi узагальнення для бiнарних i потрiйних сумiшей твердих сфер, якi грунтуються на скалярних зважувальних функцiях Кiєрлiка-Розiнберга. 2012 Article Recent developments in classical density functional theory: Internal energy functional and diagrammatic structure of fundamental measure theory / M. Schmidt, M. Burgis, W.S.B. Dwandar, G. Leithall, P. Hopkins // Condensed Matter Physics. — 2012. — Т. 15, № 4. — С. 43603:1-15. — Бібліогр.: 65 назв. — англ. PACS: 61.25.-f, 61.20.Gy, 64.70.Ja DOI:10.5488/CMP.15.43603 arXiv:1212.6358 http://dspace.nbuv.gov.ua/handle/123456789/120308 en Condensed Matter Physics Інститут фізики конденсованих систем НАН України
institution	Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection	DSpace DC
language	English
description	An overview of several recent developments in density functional theory for classical inhomogeneous liquids is given. We show how Levy's constrained search method can be used to derive the variational principle that underlies density functional theory. An advantage of the method is that the Helmholtz free energy as a functional of a trial one-body density is given as an explicit expression, without reference to an external potential as is the case in the standard Mermin-Evans proof by reductio ad absurdum. We show how to generalize the approach in order to express the internal energy as a functional of the one-body density distribution and of the local entropy distribution. Here the local chemical potential and the bulk temperature play the role of Lagrange multipliers in the Euler-Lagrange equations for minimiziation of the functional. As an explicit approximation for the free-energy functional for hard sphere mixtures, the diagrammatic structure of Rosenfeld's fundamental measure density functional is laid out. Recent extensions, based on the Kierlik-Rosinberg scalar weight functions, to binary and ternary non-additive hard sphere mixtures are described.
format	Article
author	Schmidt, M. Burgis, M. Dwandaru, W.S.B. Leithall, G. Hopkin, P.
spellingShingle	Schmidt, M. Burgis, M. Dwandaru, W.S.B. Leithall, G. Hopkin, P. Recent developments in classical density functional theory: Internal energy functional and diagrammatic structure of fundamental measure theory Condensed Matter Physics
author_facet	Schmidt, M. Burgis, M. Dwandaru, W.S.B. Leithall, G. Hopkin, P.
author_sort	Schmidt, M.
title	Recent developments in classical density functional theory: Internal energy functional and diagrammatic structure of fundamental measure theory
title_short	Recent developments in classical density functional theory: Internal energy functional and diagrammatic structure of fundamental measure theory
title_full	Recent developments in classical density functional theory: Internal energy functional and diagrammatic structure of fundamental measure theory
title_fullStr	Recent developments in classical density functional theory: Internal energy functional and diagrammatic structure of fundamental measure theory
title_full_unstemmed	Recent developments in classical density functional theory: Internal energy functional and diagrammatic structure of fundamental measure theory
title_sort	recent developments in classical density functional theory: internal energy functional and diagrammatic structure of fundamental measure theory
publisher	Інститут фізики конденсованих систем НАН України
publishDate	2012
url	http://dspace.nbuv.gov.ua/handle/123456789/120308
citation_txt	Recent developments in classical density functional theory: Internal energy functional and diagrammatic structure of fundamental measure theory / M. Schmidt, M. Burgis, W.S.B. Dwandar, G. Leithall, P. Hopkins // Condensed Matter Physics. — 2012. — Т. 15, № 4. — С. 43603:1-15. — Бібліогр.: 65 назв. — англ.
series	Condensed Matter Physics
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first_indexed	2023-10-18T20:36:41Z
last_indexed	2023-10-18T20:36:41Z
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Recent developments in classical density functional theory: Internal energy functional and diagrammatic structure of fundamental measure theory

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