### 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.

Language | English |
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Pages | 1369-1377 |

Number of pages | 9 |

Journal | Journal of Computational Chemistry |

Volume | 25 |

Issue number | 11 |

DOIs | |

Publication status | Published - Aug 2004 |

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### 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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*Journal of Computational Chemistry*, vol. 25, no. 11, pp. 1369-1377. https://doi.org/10.1002/jcc.20068

**Wavelet algorithm for solving integral equations of molecular liquids. A test for the reference interaction site model.** / Chuev, G N ; Fedorov, M V .

Research output: Contribution to journal › Article

TY - JOUR

T1 - Wavelet algorithm for solving integral equations of molecular liquids. A test for the reference interaction site model

AU - Chuev, G N

AU - Fedorov, M V

PY - 2004/8

Y1 - 2004/8

N2 - 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.

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.

KW - integral equations

KW - wavelet basis set

KW - reference interaction model

KW - water

KW - hybrid scheme

KW - modified broydon method

KW - monte carlo simulation

KW - extended rism equation

KW - hydration free-energy

KW - hypernetted chain

KW - iterative subspace

U2 - 10.1002/jcc.20068

DO - 10.1002/jcc.20068

M3 - Article

VL - 25

SP - 1369

EP - 1377

JO - Journal of Computational Chemistry

T2 - Journal of Computational Chemistry

JF - Journal of Computational Chemistry

SN - 0192-8651

IS - 11

ER -