On the Auxiliary Functions Used for the Evaluation of Two-Center Molecular Integrals over Slater-Type Orbitals using Elliptical Coordinates

Year 2017, Volume: 43 Issue: 1, 65 - 74, 28.04.2017

Erhan Akın

Abstract

In this study, a new form containing only binomial coefficients have been obtained for Iauxiliary functions proposed by Yakar et al. (Yakar et al., 2006)(Yakar et al., 2006)in the calculation of one- and two-electron two-center molecular integrals by using elliptical coordinates. Also new analytical expressions in the form of serial expansion have been given for the analytical expressions of J and K functions for negative n values which appears in the Iauxiliary function. Calculations of the analytical expressions obtained in this work and the analytical expressions given by Yakar et al. (Yakar et al., 2006)(Yakar et al., 2006)have been compared and it has been seen that the results from both expressions are in well agreement. Evaluation of two-center electric field gradient (EFG) integrals over Slater-type orbitals by using elliptical coordinates poses some difficulties, however these integrals have been easily evaluated by using the I, J and K auxiliary function obtained in this study. It has been seen that the results of this calculation are in good agreement with the results in the literature, too.

Keywords

Slater-type orbitals, Multicenter molecular integrals, Elliptical coordinates method

Slater-Tipi Orbitaller Üzerinden İki-Merkezli Moleküler İntegrallerin Eliptik Koordinatlar Kullanılarak Hesaplanması için Kullanılan Yadımcı Fonksiyonlar

Abstract

Bu çalışmada bir- ve
iki-elektron iki-merkezli moleküler integrallerin eliptik koordinatlar
kullanılarak hesaplanmasında Yakar ve ark. tarafından önerilen I yardımcı fonksiyonlarının yalnızca
binom katsayılarını içeren yeni bir formu elde edilmiştir. Aynı zamanda I yardımcı fonksiyonlarında görülen J ve K
fonksiyonlarının analitik ifadeleri için negatif n değerleri durumunda seri açılım şeklinde yeni analitik ifadeler
verilmiştir. Bu çalışmada elde edilen analitik ifadeler ile Yakar ve ark. tarafından
verilen analitik ifadelerin hesaplamaları karşılaştırılmış ve her iki ifadenin
sonuçlarının iyi uyum içinde olduğu görülmüştür. Slater-tipi atom orbitalleri üzerinden
iki-merkezli elektrik alan gradyenti integrallerinin eliptik koordinatlar
kullanılarak hesaplanması bazı zorluklar içerir, bununla birlikte bu
integraller bu çalışmada elde edilen I,
J ve K yardımcı fonksiyonları kullanılarak kolaylıkla hesaplanabilir. Bu
hesaplamanın sonuçlarının da literatürle iyi uyum içinde olduğu görülmüştür.

Keywords

Slater-tipi atom orbitalleri, Çokmerkezli moleküler integraller, Eliptik koordinatlar yöntemi

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