Calculation of overlap integrals between multiexponent atomic orbitals

The second part of this series on the field gradient in Fe(C5H5)2 and [Co(C5H5)2] + attains an improved choice of the radial parts of the atomic orbitals (AO’s) according to population analysis. Thus new overlap integrals are found which favour the use of BALLHAUSEN and DAHL coefficients for the LCAO expansion of the molecular orbitals (MO’s) of the molecules cited above. All contributions to the field gradients at the sites of the metal atom nuclei can be written down formally using these coefficients and the AO basis set. One-center integrals lead back to the 〈r-3〉nl-values obtained in part I of this series. COULSON’S Molecular Zeta Function is used in order to compute the occuring two-center integrals. The results are confirmed by the application of approximation formulas, especially one which takes account of the symmetry of the field gradient operator. Without inclusion of STERNHEIMER corrections the theoretical field gradients thus obtained are 2.367 a. u. in [Co (C5H5) 2] + and 1.58 a. u. in Fe(C5H5)2 compared with experimental values of 2.11 and 1.25 a. u. respectively.

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Overlap Integrals over Slater‐Type Atomic Orbitals

The Journal of Chemical Physics ◽

10.1063/1.1669874 ◽

1968 ◽

Vol 49 (10) ◽

pp. 4301-4305 ◽

Cited By ~ 37

Author(s):

David M. Silver ◽

Klaus Ruedenberg

Keyword(s):

Overlap Integrals ◽

Slater Type ◽

Atomic Orbitals

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Useful Integrals for Ab-Initio Molecular Quantum Similarity Measurements Using Slater Type Atomic Orbitals

Journal of Theoretical and Computational Chemistry ◽

10.1142/s0219633603000513 ◽

2003 ◽

Vol 02 (02) ◽

pp. 147-161 ◽

Cited By ~ 13

Author(s):

Lilian Berlu ◽

Philip Hoggan

Keyword(s):

Ab Initio ◽

Similarity Function ◽

Slater Type Orbitals ◽

Quantum Similarity ◽

Overlap Integrals ◽

Single Center ◽

Slater Type ◽

Atomic Orbitals ◽

Dirac Delta ◽

Molecular Quantum Similarity

Molecular quantum similarity measurements are based on a quantitative comparison of the one-electron densities of two molecules superposed and aligned to optimize a well-defined similarity function. In most previous work the densities have been related using a Dirac delta leading to the overlap-like quantum similarity function. The densities for the two molecules compared have generally been approximated often with a simple LCAO of s-gaussian functions. In this work, we present a one center two range expansion method for the evaluation of the overlap integrals involved in the overlap-like quantum similarity function over Slater type orbitals (STO). The single center and three types of two-center overlap integrals (involving four atomic orbitals; two in each molecule) have led to finite sums using a single center approach combined with selection rules obtained by analysis of orbital angular momentum (conservation). The three- and four-center integrals are also obtained analytically but involve infinite sums which require further study before leading to a complete set of integral codes for ab-initio quantum similarity.

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Overlap Integrals between Atomic Orbitals

Journal of Mathematical Physics ◽

10.1063/1.1704964 ◽

1966 ◽

Vol 7 (3) ◽

pp. 539-546 ◽

Cited By ~ 33

Author(s):

Klaus Ruedenberg ◽

Kiyosi O‐Ohata ◽

D. G. Wilson

Keyword(s):

Overlap Integrals ◽

Atomic Orbitals

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Smooth interpolation, Fourier transformation, and two-center overlap integrals for numerical atomic orbitals

International Journal of Quantum Chemistry ◽

10.1002/qua.560090504 ◽

1975 ◽

Vol 9 (5) ◽

pp. 789-795 ◽

Cited By ~ 4

Author(s):

Poul W. Thulstrup

Keyword(s):

Fourier Transformation ◽

Overlap Integrals ◽

Atomic Orbitals

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Erratum: Overlap Integrals over Slater‐Type Atomic Orbitals

The Journal of Chemical Physics ◽

10.1063/1.1678804 ◽

1972 ◽

Vol 57 (8) ◽

pp. 3585-3585

Author(s):

David M. Silver ◽

Klaus Ruedenberg

Keyword(s):

Overlap Integrals ◽

Slater Type ◽

Atomic Orbitals

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ANALYTICAL DEVELOPMENT OF MULTICENTER OVERLAP-LIKE QUANTUM SIMILARITY INTEGRALS OVER SLATER TYPE ORBITALS AND NUMERICAL EVALUATION

Journal of Theoretical and Computational Chemistry ◽

10.1142/s0219633605001866 ◽

2005 ◽

Vol 04 (03) ◽

pp. 787-801 ◽

Cited By ~ 5

Author(s):

LILIAN BERLU ◽

HASSAN SAFOUHI

Keyword(s):

Fourier Transform ◽

Linear Combination ◽

Slater Type Orbitals ◽

Quantum Similarity ◽

Overlap Integrals ◽

Slater Type ◽

Atomic Orbitals ◽

Dirac Delta ◽

Electronic Densities ◽

The Fourier Transform

Molecular overlap-like quantum similarity measurements imply the evaluation of overlap integrals of two molecular electronic densities related by the Dirac delta function. When the electronic densities are expanded over atomic orbitals using the usual LCAO (Linear Combination of Atomic Orbitals) scheme, overlap-like quantum similarity integrals could be expressed as a linear combination of four-center overlap integrals. In previous works, we showed that the one-center two-range expansion method leads to very complicated analytic expressions for three- and four-center terms. This is why its use has been prevented even for two-center integrals. We also showed that the use of the Fourier transform approach, combined with the so-called B functions, leads to great simplifications in both analytical and numerical development of overlap-like quantum similarity integrals over Slater type functions. In this work, a unified analytical treatment of multicenter overlap-like quantum similarity integrals over Slater type functions is described. The Fourier transform and nonlinear transformation methods are used. The numerical results section shows that the approach described in the present work can be applied to two-, three- and four-center integrals whatever nucleus positions might be.

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