Wavelet algorithm for solving integral equations of molecular liquids. A test for the reference interaction site model

G N Chuev, M V Fedorov

Research output: Contribution to journalArticle

42 Citations (Scopus)

Abstract

A new efficient method is developed for solving integral equations based on the reference interaction site model (RISM) of molecular liquids. The method proposes the expansion of site-site correlation functions into the wavelet series and further calculations of the approximating coefficients. To solve the integral equations we have applied the hybrid scheme in which the coarse part of the solution is calculated by wavelets with the use of the Newton-Raphson procedure, while the fine part is evaluated by the direct iterations. The Coifman 2 basis set is employed for the wavelet treatment of the coarse solution. This wavelet basis set provides compact and accurate approximation of site-site correlation functions so that the number of basis functions and the amplitude of the fine part of solution decrease sufficiently with respect to those obtained by the conventional scheme. The efficiency of the method is tested by calculations of SPC/E model of water. The results indicated that the total CPU time to obtain solution by the proposed procedure reduces to 20% of that required for the conventional hybrid method. (C) 2004 Wiley Periodicals, Inc.

LanguageEnglish
Pages1369-1377
Number of pages9
JournalJournal of Computational Chemistry
Volume25
Issue number11
DOIs
Publication statusPublished - Aug 2004

Fingerprint

Integral equations
Integral Equations
Wavelets
Liquid
Correlation Function
Liquids
Interaction
Newton-Raphson
Wavelet Bases
CPU Time
Hybrid Method
Compact Set
Basis Functions
Model
Program processors
Iteration
Water
Decrease
Series
Coefficient

Keywords

  • integral equations
  • wavelet basis set
  • reference interaction model
  • water
  • hybrid scheme
  • modified broydon method
  • monte carlo simulation
  • extended rism equation
  • hydration free-energy
  • hypernetted chain
  • iterative subspace

Cite this

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title = "Wavelet algorithm for solving integral equations of molecular liquids. A test for the reference interaction site model",
abstract = "A new efficient method is developed for solving integral equations based on the reference interaction site model (RISM) of molecular liquids. The method proposes the expansion of site-site correlation functions into the wavelet series and further calculations of the approximating coefficients. To solve the integral equations we have applied the hybrid scheme in which the coarse part of the solution is calculated by wavelets with the use of the Newton-Raphson procedure, while the fine part is evaluated by the direct iterations. The Coifman 2 basis set is employed for the wavelet treatment of the coarse solution. This wavelet basis set provides compact and accurate approximation of site-site correlation functions so that the number of basis functions and the amplitude of the fine part of solution decrease sufficiently with respect to those obtained by the conventional scheme. The efficiency of the method is tested by calculations of SPC/E model of water. The results indicated that the total CPU time to obtain solution by the proposed procedure reduces to 20{\%} of that required for the conventional hybrid method. (C) 2004 Wiley Periodicals, Inc.",
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Wavelet algorithm for solving integral equations of molecular liquids. A test for the reference interaction site model. / Chuev, G N ; Fedorov, M V .

In: Journal of Computational Chemistry , Vol. 25, No. 11, 08.2004, p. 1369-1377.

Research output: Contribution to journalArticle

TY - JOUR

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AU - Fedorov, M V

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AB - A new efficient method is developed for solving integral equations based on the reference interaction site model (RISM) of molecular liquids. The method proposes the expansion of site-site correlation functions into the wavelet series and further calculations of the approximating coefficients. To solve the integral equations we have applied the hybrid scheme in which the coarse part of the solution is calculated by wavelets with the use of the Newton-Raphson procedure, while the fine part is evaluated by the direct iterations. The Coifman 2 basis set is employed for the wavelet treatment of the coarse solution. This wavelet basis set provides compact and accurate approximation of site-site correlation functions so that the number of basis functions and the amplitude of the fine part of solution decrease sufficiently with respect to those obtained by the conventional scheme. The efficiency of the method is tested by calculations of SPC/E model of water. The results indicated that the total CPU time to obtain solution by the proposed procedure reduces to 20% of that required for the conventional hybrid method. (C) 2004 Wiley Periodicals, Inc.

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KW - monte carlo simulation

KW - extended rism equation

KW - hydration free-energy

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