Noninteger Bessel Type Orbitals for Two Electron Atomic Systems

Abstract

The aim of this study is to examine the applicability of Bessel type orbitals with non-integer principal quantum numbers to the atomic systems with the Hartree-Fock-Roothaan method and their superiority over other exponential orbitals used in the literature. By the use of combined Hartree-Fock-Roothaan method, the orbital and ground state energy values of two-electron atomic systems have been calculated using the newly proposed Bessel type orbitals. The results obtained with the new basis functions within the minimal basis sets framework are given comparatively in the tables. The results obtained give better values than the similar exponential type basis functions used in the literature and are in good agreement with numerical Hartree-Fock values.

Keywords

• Basis functions
• bessel functions
• hartree-fock-roothaan method
• isoelectronic series
• nonintegral principal quantum number

İki Elektronlu Atomik Sistemler için Baş kuantum Sayısı Kesir Değerli Bessel Tipli Orbitaller

Abstract

Bu çalışmanın amacı, baş kuantum sayısı tamsayı olmayan Bessel tipli orbitallerin Hartree-Fock-Roothaan yöntemi ile atomik sistemlere uygulanabilirliğini ve literatürdeki diğer üstel tipli orbitallerden üstünlüklerini incelemektir. Birleşik Hartree-Fock-Roothaan yönteminde yeni önerilen Bessel tipli orbitaller kullanılarak, iki elektronlu atomik sistemlerin orbital ve temel durum enerji değerleri hesaplanmıştır. Minimal baz çerçevesinde oluşturulan yeni baz fonksiyonları ile elde edilen değerler tablolarda karşılaştırmalı olarak verilmiştir. Elde edilen sonuçlar, literatürde kullanılan benzer üstel tipli baz fonksiyonlarına göre daha iyi değerler vermekte ve sayısal Hartree-Fock değerleri ile çok iyi uyum sağlamaktadır.

Keywords

• Baz fonksiyonu
• bessel fonksiyonu
• hartree-fock-roothaan yöntemi
• izoelektronik seriler
• kesir değerli baş kuantum sayısı

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