Electric and magnetic multipole integrals in STO basis sets: an analytical approach

ABSTRACT:A general formula has been established for the expansion of the product of two normalized associated Legendre functions centered on the nuclei a and b. This formula has been utilized for the evaluation of two-center overlap and nuclear attraction integrals over Slater-type orbitals (STOs) with integer and noninteger principal quantum numbers. The formulas given in this study for the evaluation of two-center overlap and nuclear attraction integrals show good rate of convergence and great numerical stability under wide range of quantum numbers, orbital exponents, and internuclear distances.

Section: Computational Results and Discussionsupporting

confidence: 86%

Evaluation of two‐center overlap and nuclear attraction integrals over Slater‐type orbitals with integer and noninteger principal quantum numbers

Özdoğan

Orbay

2001

“…In Table III we present the nuclear-attraction integrals associated with a two-center distribution of type 3d a -3d b , presented for the same set of parameters as treated by Ahmed and Meckellele [32], Rico et al [33], and Beck and Hohlneicher [34]. As can be seen from Table III, …”

Section: Numerical Results and Discussionmentioning

confidence: 95%

Calculation of nuclear‐attraction and modified overlap integrals using Gegenbauer coefficients*

Öztekin

Özcan

Orbay

et al. 2002

“…In principle, this expansion can be attained [18][19][20] provided that the expression of the potential is available and its derivatives can be obtained. However, this way is cumbersome because of the δ functions appearing in the derivatives of order higher than one.…”

Section: Electrostatic Potential and Its Derivativesmentioning

confidence: 99%

Auxiliary functions for molecular integrals with Slater‐type orbitals. II. Gauss transform methods

Ema

López

Fernández

et al. 2007

ABSTRACT:The Gauss transform of Slater-type orbitals is used to express several types of molecular integrals involving these functions in terms of simple auxiliary functions. After reviewing this transform and the way it can be combined with the shift operator technique, a master formula for overlap integrals is derived and used to obtain multipolar moments associated to fragments of two-center distributions and overlaps of derivatives of Slater functions. Moreover, it is proved that integrals involving two-center distributions and irregular harmonics placed at arbitrary points (which determine the electrostatic potential, field and field gradient, as well as higher order derivatives of the potential) can be expressed in terms of auxiliary functions of the same type as those appearing in the overlap. The recurrence relations and series expansions of these functions are thoroughly studied, and algorithms for their calculation are presented. The usefulness and efficiency of this procedure are tested by developing two independent codes: one for the derivatives of the overlap integrals with respect to the centers of the functions, and another for derivatives of the potential (electrostatic field, field gradient, and so forth) at arbitrary points.