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Use of Auxiliary Functions for Construction of Series Expansion Relations of Noninteger Slater Functions in Standard Convention
Author(s) -
Guseinov I. I.
Publication year - 2015
Publication title -
journal of the chinese chemical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.329
H-Index - 45
eISSN - 2192-6549
pISSN - 0009-4536
DOI - 10.1002/jccs.201400286
Subject(s) - orthonormal basis , exponential type , chemistry , atomic orbital , series (stratigraphy) , type (biology) , range (aeronautics) , integer (computer science) , slater type orbital , quantum mechanics , pure mathematics , computational chemistry , mathematical analysis , mathematics , physics , linear combination of atomic orbitals , electron , paleontology , ecology , materials science , computer science , composite material , biology , programming language
Using complete orthonormal sets of ψ (α*) ‐self‐frictional exponential type orbitals (ψ (α*) ‐SFETOs) and Q q ‐noninteger auxiliary functions ( Q q ‐NIAFs) introduced by the author, the combined formulas for the one‐ and two‐center one‐range addition theorems of χ‐noninteger Slater type orbitals (χ‐NISTOs) with arbitrary values of distances between centers R ab (for R ab = 0 and R ab ≠ 0), and of integer (for α* = α, –∞ < α ≤ 2) and noninteger (for α* ≠ α, –∞ < α* < 3) self‐frictional (SF) quantum numbers are suggested. The presented relations for the one‐range addition theorems can be useful tools especially in the electronic structure studies of atoms, molecules and solids when χ‐NISTOs are employed as basis functions.