Variational bounds to the overlap

Starting from a closed expression for the overlap, variational upper and lower bounds to the overlap are derived by means of operator inequalities.     

Angular parameters of the overlap integrals of f-orbitals

Angular parameters are calculated for these integrals for - and -types in the complexes MX₆ (O_h and D_3h symmetry), MX₈ (O_h, D_4d, D_2d, D_6h, C_2V, and D_3h), and MX₉ (D_3h). Examples are given of the use of the angular parameters in considering coordination compounds of the lanthanide elements: stabilization energy of the addend field and geometry of the compounds in the ground and excited states.     

配位多面体的群重叠积分

本文讨论了配位多面体的群重叠积分计算问题, 给出了这种群重叠积分的一般形式以及它们满足的一些关系, 用第一类点群将群重叠积分的计算化简, 由此定义了有关的几何参数并研究了它们的性质, 以正六面体为例说明了这些参数的具体计算。     

Semirigorous bounds for the overlap of approximate wavefunctions

Alexander's probable upper and lower bounds to the overlap S between an approximate and the true wavefunctions are based on second-order perturbation theory and a special ordering of configurations. These weak points are removed in the present treatment and replaced by an exact expression for the energy lowering, plus a very reasonable postulate. The resulting lower bound to the overlap S is illustrated with examples taken from the literature.     

Recursion formulae for calculation of overlap integrals

Multi-ζ Slater-type orbitals are frequently used in molecular orbital calculations. Master formulae and numerical tables are available in literature for overlap integrals between s, p, and d atomic orbitals up to principal quantum number (n) = 3 and for some other selected quantum numbers. However, no master formula or numerical table is available for quantum numbers n = 5 and above and involving ? orbitals. In this article recursion formulae have been presented for the calculation of the overlap integral between any two s, p, d, and ? atomic orbitals formed by a linear combination of Slater-type orbitals. These formulae, when expanded, would give rise to all the master formulae reported in the literature as well as formulae hitherto unreported.     

Error bounds for the overlap of approximate wave functions

Variational upper and lower bounds for the overlap between an approximate and the true wave function are proposed, and it is shown that the error bounds introduced recently by Gordon are special cases of the variational formulas.     

Computer-generated formulas for overlap integrals of slater-type orbitals

Using a modified form of Sharma's method for the expansion of a Slater-type orbital in spherical harmonics about a displaced center, a general expression for the overlap integral between two orbitals is derived that is equivalent to that given by Sharma. By use of a simple kind of “computer algebra” this expression is developed here into a formula that is equivalent to earlier known ones and may have computational advantages when the generated formula coefficients are stored. This method is capable of extension to more complicated integrals.     

A new expression for the vibrational overlap integrals between arbitrary one-dimensional harmonic oscillators

A new, compact formula for the vibrational overlap integrals between two harmonic potentials with both arbitrary curvatures and equilibrium positions is derived in a systematic manner with its several derivative formulas. Some mathematical properties of the overlap integrals obtained are discussed.     

A new method to evaluate the STO overlap integrals for compilation of an EHMO program containing f orbitals

In this paper, a calculation method to evaluate to STO overlap integrals that have integer or non-integer effective quantum number is reported. Using this method, the overlap integrals of 4f orbitals are calculated and some results are given.     

On a formula of Braun and Rebane for variational bounds to overlap

A recent formula of Braun and Rebane for variational bounds to overlap is shown to be closely related to the methods of Rayner and of Weinhold for the same problem, and is extended to give upper and lower bounds to overlap in both ground and excited states.     

Two-center overlap integrals in some acetylacetonates of f elements

Overlap integrals of the type 〈2s|f〉, 〈2pσ|f〉 and 〈2pπ|f〉 have been evaluated for certain lanthanide and actinide acetylacetonates. Slater-type orbitals with Burns's exponents, analytical Hartree-Fock wavefunctions and interatomic distances taken from known crystal structure determinations of the same complexes have been used. The results indicate that the decreasing f-electron density with increasing atomic number predominates over the corresponding contribution of the metal ion-oxygen distances.     

New translation method for STOs and its application to calculation of overlap integrals

A new translation method for Slater‐type orbitals (STOs) is proposed involving exact translation of the regular solid harmonic part of the orbital followed by the series expansion of the residual spherical part in powers of the radial variable. The method is positively tested in the case of the overlap integral, showing good rate of convergence and great numerical stability under wide changes in the relevant molecular parameters. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 73: 333–340, 1999