The Exact Evaluation of Basic Two-Center Coulomb Integrals Appearing in Intermolecular Electrostatic Interaction Energy in Molecular Coordinate System

Mapping Intimacies ◽

10.22541/au.163293104.49456490/v1 ◽

2021 ◽

Author(s):

Ebru Çopuroğlu ◽

Bahtiyar Mamedov

Keyword(s):

Electrostatic Interaction ◽

Analytical Calculation ◽

Molecular Structures ◽

Slater Type Orbitals ◽

Interaction Energies ◽

Molecular Physics ◽

Auxiliary Functions ◽

Atomic And Molecular Physics ◽

Molecular Coordinate System ◽

Coulomb Integrals

We proposed a general and effective approach for accurate calculating method of the electron-electron, nuclear-electron and nuclear-nuclear Coulomb electrostatic interaction energies. It is well known that electron-electron, nuclear-electron and nuclear-nuclear Coulomb electrostatic interaction energies reduced to basic two-center Coulomb integrals. The analytical calculation of electrostatic interaction energies with respect to basic two-center Coulomb integrals over Slater type orbitals (STOs) in molecular coordinate systems allows us the routine evaluation of molecular structures and related properties. In this study we have introduced a new full analytical algorithm for calculation of the basic two-center Coulomb integrals over STOs by using Guseinov’s auxiliary functions especially interactions between electrons. The auxiliary functions has been calculated by using the exact recurrence relations which developed by Guseinov. The new approach is successfully tested on earlier published studies data and can be recommended for evaluation of related problems in atomic and molecular physics.

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Fast analytical evaluation of intermolecular electrostatic interaction energies using the pseudoatom representation of the electron density. II. The Fourier transform method

Acta Crystallographica Section A Foundations and Advances ◽

10.1107/s2053273319002535 ◽

2019 ◽

Vol 75 (3) ◽

pp. 448-464 ◽

Cited By ~ 1

Author(s):

Daniel Nguyen ◽

Anatoliy Volkov

Keyword(s):

Fourier Transform ◽

Electrostatic Interaction ◽

Multipole Moment ◽

Floating Point ◽

Interaction Energies ◽

Transform Method ◽

Fourier Transform Method ◽

The Fourier Transform ◽

Coulomb Integrals ◽

Löwdin Α Function

The Fourier transform method for analytical determination of the two-center Coulomb integrals needed for evaluation of the electrostatic interaction energies between pseudoatom-based charge distributions is presented, and its Fortran-based implementation using the 128-bit floating-point arithmetic in theXDPROPmodule of theXDsoftware is described. In combination with mathematical libraries included in the Lahey/Fujitsu LF64 Linux compiler, the new implementation outperforms the previously reported Löwdin α-function technique [Nguyenet al.(2018).Acta Cryst.A74, 524–536] in terms of precision of the determined individual Coulomb integrals regardless of whether the latter uses the 64-, 80- or 128-bit precision floating-point format, all the while being only marginally slower. When the Löwdin α-function or Fourier transform method is combined with a multipole moment approximation for large interatomic separations (such a hybrid scheme is called the analytical exact potential and multipole moment method, aEP/MM) the resulting electrostatic interaction energies are evaluated with a precision of ≤5 × 10−5 kJ mol−1for the current set of benchmark systems composed of H, C, N and O atoms and ranging in size from water–water to dodecapeptide–dodecapeptide dimers. Using a 2012 4.0 GHz AMD FX-8350 computer processor, the two recommended aEP/MM implementations, the 80-bit precision Löwdin α-function and 128-bit precision Fourier transform methods, evaluate the total electrostatic interaction energy between two 225-atom monomers of the benchmark dodecapeptide molecule in 6.0 and 7.9 s, respectively, versus 3.1 s for the previously reported 64-bit Löwdin α-function approach.

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Ion solvation by dipolar aprotic solvents. An ab initio study

Collection of Czechoslovak Chemical Communications ◽

10.1135/cccc19870006 ◽

1987 ◽

Vol 52 (1) ◽

pp. 6-13 ◽

Cited By ~ 2

Author(s):

Petr Kyselka ◽

Zdeněk Havlas ◽

Ivo Sláma

Keyword(s):

Ab Initio ◽

Geometry Optimization ◽

Molecular Structures ◽

Dimethyl Sulphoxide ◽

Ion Solvation ◽

Interaction Energies ◽

Ab Initio Study ◽

Solvation Energies ◽

Dipolar Aprotic Solvents ◽

Complete Geometry Optimization

The paper deals with the solvation of Li+, Be2+, Na+, Mg2+, and Al3+ ions in dimethyl sulphoxide, dimethylformamide, acetonitrile, and water. The ab initio quantum chemical method was used to calculate the solvation energies, molecular structures, and charge distributions for the complexes water···ion, acetonitrile···ion, dimethyl sulphoxide···ion, and dimethylformamide···ion. The interaction energies were corrected for the superposition error. Complete geometry optimization was performed for the complex water···ion. Some generalizations are made on the basis of the results obtained.

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