Elektronik yapı hesabında ortaya çıkan örtme integrallerinin hesaplanması
Yükleniyor...
Dosyalar
Tarih
2015
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Trakya Üniversitesi Fen Bilimleri Enstitüsü
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
Moleküllerin relativistik ve relativistik olmayan elektronik yapılarının incelenmesinde Slater Tipi Orbitaller (STOs) üzerinden ?, (-?<??2) öz-sürtünme kuantum sayısını içeren örtme integrallerinin doğru ve etkin biçimde hesaplanması gereklidir. Bu integraller, yalnızca moleküller için Hartree-Fock-Roothaan denklemlerinde değil aynı zamanda yeni bir merkez civarında seri açılım formüllerine dayalı keyfi çok merkezli integrallerin hesabında ve özellikle büyük kuantum sayılı örtme integrallerinin etkin biçimde hesaplanmasının gerekli olduğu STO?ler için tek-bölgeli toplama teoremlerinde ortaya çıkmaktadır. Bu çalışmada, -üstel tipli orbitallerin (-ETOs) tam ortonormal kümelerinin yardımıyla I.I. Guseinov tarafından önerilen Slater Tipi Orbitallere (STOs) ait tek bölgeli toplama teoremleri kullanılarak -örtme integralleri yeniden incelendi. Elde edilen formüllere dayalı bilgisayar programları düzenlendi. -örtme integrallerinin etkinliği kuantum sayılarının çeGitli değerleri için kontrol edildi. Örtme integralleri atom, molekül ve katılarla ilgili elektronik yapı hesaplamalarının hem teorik hem de uygulamaları ile ilgili farklı kuantum mekaniksel problemlerin incelenmesinde kullanılabilir.
Abstract
In the study of the relativistic and non-relativistic electronic structure of molecules , one has to evaluate overlap integrals which depend on the self-frictional quantum number ?, where, (-?<??2) over Slater type orbitals ( STOs) accurately and efficiently, These integrals arise not only in the Hartree-Fock-Roothaan equations for molecules, are also central to the calculation of arbitrary multicenter integrals based on the series expansion formulas about a new center and one-range addition theorems for STOs which necessitate to accurately calculate the overlap integrals espectially for the large quantum numbers. The aim of study, using the one–range addition theorems of Slater type orbitals (STOs) introduced by I.I. Guseinov , with the help of complete orthonormal sets of -exponential type orbitals, the -overlap integrals are reinvestigated. On the basis of the formulate obtained we constructed the computer programs. The accuracy of the -overlap integrals was checked for various values of quantum numbers . The -overlap integrals can be used in the study of different quantum mechanical problems in both the theory and practice of electronic structure calculations dealing with atoms, molecules and solids.
Abstract
In the study of the relativistic and non-relativistic electronic structure of molecules , one has to evaluate overlap integrals which depend on the self-frictional quantum number ?, where, (-?<??2) over Slater type orbitals ( STOs) accurately and efficiently, These integrals arise not only in the Hartree-Fock-Roothaan equations for molecules, are also central to the calculation of arbitrary multicenter integrals based on the series expansion formulas about a new center and one-range addition theorems for STOs which necessitate to accurately calculate the overlap integrals espectially for the large quantum numbers. The aim of study, using the one–range addition theorems of Slater type orbitals (STOs) introduced by I.I. Guseinov , with the help of complete orthonormal sets of -exponential type orbitals, the -overlap integrals are reinvestigated. On the basis of the formulate obtained we constructed the computer programs. The accuracy of the -overlap integrals was checked for various values of quantum numbers . The -overlap integrals can be used in the study of different quantum mechanical problems in both the theory and practice of electronic structure calculations dealing with atoms, molecules and solids.
Açıklama
Yüksek Lisans Tezi
Anahtar Kelimeler
Slater Tipi Orbitaller, Öz Sürtünme Kuantum Sayısı, Örtme İntegralleri, Tek Bölgeli Toplama Teoremleri, Slater Type Orbitals, Self-Frictional Quantum Number, Overlap İntegrals, One-Range Addition Theorems
