Exact expression for four-center integrals of slater orbitals obtained by symbolic computation

Semiconductor Institute, Academy of Sciences of the USSR. Translated from Zhurnal Strukturnoi Khimii, Vol. 30, No. 4, pp. 3–10, July–August, 1989.     

Automatic geometry optimization for molecules with d orbitals. I. General analytic formulas for derivatives of slater orbitals

General analytic formulas for derivatives of real Slater orbitals with respect to the Cartesian coordinates x and y have been derived. The application of this result to molecular geometry optimization or to the construction of a force constant matrix is briefly discussed.     

Semiempirical SCF theory with “scaled” slater orbitals

A self consistent quantum mechanical treatment of atomic structures is presented. The method which is suitable for molecular calculations involves the optimization (scaling) of exponents of a minimal basis set of Slater orbitals and accounts semiempirically for electron correlation.The calculation of successive ionization potentials as well as that of promotional energies lead to results in satisfactory agreement with experiment.

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Zusammenfassung Es wird ein selbstkonsistentes quantenmechanisches Verfahren für Atomstrukturen entwickelt, das auch für Moleküle geeignet ist, und eine Optimierung (scaling) der Exponenten von Slaterorbitalen in einem minimalen Satz der Basisvektoren sowie eine semiempirische Berücksichtigung der Elektronenkorrelation beinhaltet. p]Die berechneten Ionisierungs- und Anregungsenergien stimmen gut mit den experimentellen Werten überein.

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Résumé Un traitement quantique self consistent des structures atomiques est décrit. La méthode qui est aussi valable pour le calcul des molécules introduit l'optimalisation (scaling) des exposents d'un minimal basis set d'orbitales de Slater et prend en considération la corrélation électronique d'une manière semi empirique.Le calcul des potentiels d'ionisations successifs ainsi que celui des énergies de promotion conduit a des résultats en accord satisfaisant avec l'expérience.

     

Semiempirical SCF theory with “Scaled” slater orbitals

A new method is presented for the calculation of molecular properties in which the one center integrals are evaluated within their environment (scaled in the molecule) rather than carried over from atomic structures.The procedure can be incorporated into any SCF scheme using a minimal basis set of atomic orbitals. In this paper an INDO framework was chosen to illustrate the results. Both heats of formation and bond distances for various types of molecules were found in satisfactory agreement with experiment.

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Zusammenfassung Es wird eine neue Methode für die Berechnung von Moleküleigenschaften vorgeschlagen, in welcher die Einzentrenintegrale innerhalb ihrer Umgebung im Molekül bestimmt werden, statt sie von freien Atomen zu übernehmen.Diese Methode kann bei jedem SCF Verfahren angewandt werden, das auf einer minimalen Basis von Atomorbitalen aufbaut. Zur Illustration der Ergebnisse in dieser Arbeit wird das INDO-Verfahren gewählt. Sowohl Bildungswärmen als auch Bindungsabstände von verschiedenen Molekülarten sind in guter Übereinstimmung mit den experimentellen Daten.

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Résumé Une nouvelle méthode pour le calcul des propriétés moléculaires est présentée, dans laquelle les intégrales monocentriques sont évaluées dans leur environnement (ajustées à la molécule), au lieu d'être transférées du calcul atomique.Le procédé peut être incorporé dans n'importe quel schema SCF qui utilise un «basis set» minimal.Dans cet article, le procédé est illustré par l'utilisation d'un schema INDO.Les chaleurs de formation et les distances de liaison pour plusieurs types de molécules sont trouvées en accord satisfaisant avec l'experience.

     

All-electron density functional calculation on insulin with quasi-canonical localized orbitals

An all-electron density functional (DF) calculation on insulin was performed by the Gaussian-based DF program, ProteinDF. Quasi-canonical localized orbitals (QCLOs) were used to improve the initial guess for the self-consistent field (SCF) calculation. All calculations were carried out by parallel computing on eight processors of an Itanium2 cluster (SGI Altix3700) with a theoretical peak performance of 41.6 GFlops. It took 35 h for the whole calculation. Insulin is a protein hormone consisting of two peptide chains linked by three disulfide bonds. The numbers of residues, atoms, electrons, orbitals, and auxiliary functions are 51, 790, 3078, 4439, and 8060, respectively. An all-electron DF calculation on insulin was successfully carried out, starting from connected QCLOs. Regardless of a large molecule with complicated topology, the differences in the total energy and the Mulliken atomic charge between initial and converged wavefunctions were very small. The calculation proceeded smoothly without any trial and error, suggesting that this is a promising method to obtain SCF convergence on large molecules such as proteins.     

MBPT and coupled cluster calculation on the neon atom with numerical orbitals

Our diatomic coupled cluster method with numerical orbitals has been applied to the Ne atom. Second, third, and full fourth order MBPT correlation corrections as well as coupled cluster correlation energies are reported.     

Improvement of an integral approximation scheme based on semiorthogonalized orbitals

In a previous paper, a scheme of integral approximation was proposed, in which a large number of two-electron integrals containing a certain kind of orbital pairs, i.e., weakly related pairs, can be neglected. A new criterion for partitioning orbital pairs into two groups, i.e., strongly and weakly related pairs, is introduced in order to allow for neglect of more integrals without sacrificing the accuracy of a computation. Test calculations on the BH₃? C₂H₄ complex show that by the use of the new version, results of roughly the same accuracy as was obtained by the old version is obtained by retaining 80% of the integrals used in the old version. This kind of saving is more significant for larger molecules. For example, in a calculation on Cu-porphine with 203 CGTO 'S , the revised version will require about 2.0 × 10⁶ integrals, while the original version will require about 4.5 × 10⁶. And these two approximate calculations are expected to give the results of roughly the same accuracy.     

Exact formulas for overlap integrals of Slater-type orbitals with equal screening constants

Exact formulas for 147 overlap integrals between Slater-type orbitals with equal screening constants are presented in the most simplified form. This represents all combinations of orbitals with quantum numbers: 1 ≤ N ≤ 5, 0 ≤ L ≤ 3, and M ≤ L. The formulas are automatically generated by computer using the “C-matrix” single-center expansion method. There are no limitations to the applicability of this method to orbitals of higher quantum numbers.     

Exact solution of the adsorption integral equation for a heterogeneous surface

An exact method of solution of the adsorption integral equation using finite and realistic limits of the heats of adsorption and which is applicable to any analytic site-energy distribution is given. The optical feature is the postulation and use of a set of transformations to reduce the finite-limit problem to one of limits (0, ∞). The transformed integral equation is then inverted using the theory of Stieltjes transforms. The method thus avoids the limitations inherent in earlier work which employed restrictive assumptions about the heats of adsorption.     

Analytical calculation of two-center Coulomb and hybrid integrals with orbitals of the Slater type

Journal of Structural Chemistry -