Analytical evaluation of multicenter integrals needed in molecular quantum mechanical calculations of some magnetic tensors over slater type basis functions
Other Title(s)
الحساب التحليلي لمتكاملات متعددة المراكز اللازمة للحسابات الميكانيكية الكمومية الجزيئية لبعض التنسورات المغناطيسية باستخدام توابع سلاتر كقاعدة
Author
Source
Damascus University Journal of Agricultural Sciences
Issue
Vol. 33, Issue 1 (30 Jun. 2017), pp.23-51, 29 p.
Publisher
Publication Date
2017-06-30
Country of Publication
Syria
No. of Pages
29
Main Subjects
Abstract EN
In the quantum theory of atoms or molecules in magnetic fields of different origin that can be an external homogenous field and that created by the nuclear magnetic moment of a nucleus, some important magnetic tensor appears.
The integrals due to magnetic perturbations appeared within coupled Hartree-Fock-Roothaan perturbation Gauge Invariant Atomic Orbitals or in Density Functional Theory (DFT) are analytically evaluated for Slater Type nsnp basis functions.
Reduced analytical formulas are obtained using properties of the Levi-Civita tensor of rank 3, properties of rotation matrix and symmetry properties of field-independent atomic orbitals.
The condensed formalism is expressed in term of auxiliary functions and integrals.
The angular dependence of integrals is also discussed in detail.
The multicenter integrals can be monocentric, bicentric or three centric.
All monocentric and bicentric integrals with monocentric electron distribution can be calculated rigorously in spherical polar coordinates with the nucleus as origin.
Bicentric integrals with bicentric electron distribution were also integrated using elliptic coordinates after an appropriate axis transformation.
The three centre integrals with bicentric electron distribution were determined analytically within the London Type approximation.
The resulting angular momentum and impulsion integrals whether dipolar or quadrupolar are all computed rigorously in elliptic coordinates
American Psychological Association (APA)
Juwaydah, Nabil Fadl Allah. 2017. Analytical evaluation of multicenter integrals needed in molecular quantum mechanical calculations of some magnetic tensors over slater type basis functions. Damascus University Journal of Agricultural Sciences،Vol. 33, no. 1, pp.23-51.
https://search.emarefa.net/detail/BIM-873883
Modern Language Association (MLA)
Juwaydah, Nabil Fadl Allah. Analytical evaluation of multicenter integrals needed in molecular quantum mechanical calculations of some magnetic tensors over slater type basis functions. Damascus University Journal of Agricultural Sciences Vol. 33, no. 1 (2017), pp.23-51.
https://search.emarefa.net/detail/BIM-873883
American Medical Association (AMA)
Juwaydah, Nabil Fadl Allah. Analytical evaluation of multicenter integrals needed in molecular quantum mechanical calculations of some magnetic tensors over slater type basis functions. Damascus University Journal of Agricultural Sciences. 2017. Vol. 33, no. 1, pp.23-51.
https://search.emarefa.net/detail/BIM-873883
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references : p. 50-51
Record ID
BIM-873883