Evaluation of two-center Coulomb and hybrid integrals over complete orthonormal sets of $$ {\Psi^{\rm{\alpha }}} - {\hbox{ETO}} $$ using auxiliary functions
| Autor: | E. Sahin, I.I. Guseinov |
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| Rok vydání: | 2010 |
| Předmět: |
Physics
Organic Chemistry Center (category theory) Auxiliary function Type (model theory) Ellipsoidal coordinates Quantum number Catalysis Computer Science Applications Inorganic Chemistry Computational Theory and Mathematics Quantum mechanics Coulomb Orthonormal basis Physical and Theoretical Chemistry Ground state |
| Zdroj: | Journal of Molecular Modeling. 17:851-856 |
| ISSN: | 0948-5023 1610-2940 |
| DOI: | 10.1007/s00894-010-0777-6 |
| Popis: | By the use of ellipsoidal coordinates, the two-center Coulomb and hybrid integrals over complete orthonormal sets of $$ {\Psi^{\rm{\alpha }}} - {\hbox{exponential}} $$ type orbitals arising in ab initio calculations of molecules are evaluated, where $$ \alpha = 1,0, - 1, - 2,..., $$ . These integrals are expressed through the auxiliary functions $$ Q_{ns}^q $$ and $$ G_{ - ns}^q $$ . The comparison is made with some values of integrals for Slater type orbitals the computation results of which are in good agreement with those obtained in the literature. The relationships obtained are valid for the arbitrary quantum numbers, screening constants and location of orbitals. Closed form expressions for two-center Coulomb and hybrid integrals for 1s and 2s orbitals with α = 1 are also presented. As an example of application, the Hartree-Fock-Roothaan calculations for the ground state of H2 molecule are carried out with α = 1 and α = 0. |
| Databáze: | OpenAIRE |
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