Kesirli indisli slater fonksiyonlarını içeren öz-sürtünme örtme integrallerinin hesaplanması
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Date
2016
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Trakya Üniversitesi Fen Bilimleri Enstitüsü
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info:eu-repo/semantics/openAccess
Abstract
Atom ve moleküller için Hartree-Fock-Roothaan (HFR) denklemlerinde ortaya çıkan kesirli n Slater fonksiyonlarını içeren öz-sürtünme (SF) örtme integralleri standart konvensiyondaki tam ortonormal ( )-öz-sürtünme üstel tipli orbitaller ( ( ) ) kullanılarak hesaplanmıştır. Bu integrallerin hesabı için ( ) tam ortonormal baz setleri yardımıyla Guseinov tarafından önerilen tam ve kesirli n Slater tipi orbitallere ( ait tek bölgeli toplama teoremleri kullanıldı. Burada dır; , öz-sürtünme kuantum sayısıdır, tam ( ve kesirli ( değerler alır. SF örtme integralleri örtme integralleri vasıtasıyla ifade edildi. Elde edilen formüllere dayanan bilgisayar programı oluşturuldu. SF örtme integrallerinin etkinliği kuantum sayılarının çeşitli değerleri için incelendi. Serilerin yakınsaması ?ların parametrelerinin keyfi değerleri ve orbitallerinin konumu için farklı değerler hesaplanarak denendi. Elde edilen sonuçlar literatürle iyi uyumludur.
abstract
Self-frictional (SF) overlap integrals containing noninteger n Slater functions appearing in the HartreFock-Roothaan (HFR) equations for atoms and molecules have been evaluated using ( )-self-frictional exponential type orbitals ( ( ) ) in complete orthonormal standard convention. For the evaluation of these integrals, the one-range addition theorems with integer and noninteger n Slater type orbitals ( introduced by Guseinov with the help of complete orthonormal sets of ( ) are used, where ; is the SF quantum number with integer ( and noninteger ( . SF overlap integrals are expressed through the overlap integrals of . On the basis of the formulae obtained we constructed the computer programs. The accuracy of the SF overlap integrals was checked for various values of quantum numbers.The convergence of the series is tested by calculating concrete cases for arbitrary values of parameters of and location of orbitals. Obtained results are in good agreement with the literature.
abstract
Self-frictional (SF) overlap integrals containing noninteger n Slater functions appearing in the HartreFock-Roothaan (HFR) equations for atoms and molecules have been evaluated using ( )-self-frictional exponential type orbitals ( ( ) ) in complete orthonormal standard convention. For the evaluation of these integrals, the one-range addition theorems with integer and noninteger n Slater type orbitals ( introduced by Guseinov with the help of complete orthonormal sets of ( ) are used, where ; is the SF quantum number with integer ( and noninteger ( . SF overlap integrals are expressed through the overlap integrals of . On the basis of the formulae obtained we constructed the computer programs. The accuracy of the SF overlap integrals was checked for various values of quantum numbers.The convergence of the series is tested by calculating concrete cases for arbitrary values of parameters of and location of orbitals. Obtained results are in good agreement with the literature.
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Keywords
Öz-sürtünme Üstel Tipli Orbitaller, Tek Bölgeli Toplama Teoremleri, Öz-Sürtünme Örtme İnregralleri, Öz-Sürtünme Kuantum Sayısı, Self-Frictional Quantum Number, One-Range Addition Theorems, Self-Frictional Exponential Type Orbitals, Self-Frictional Overlap İntegrals
