Slater ve gauss tipi orbitallerle Li, Na ve N atomlarında elektrik dipol geçişlerinin hesaplanmasi

Year 2011, Volume: 27 Issue: 3, 234 - 241, 01.06.2011

Ahmet Emre Kavruk Hüseyin Yüksel Ayhan Özmen Ülfet Atav

Abstract

Bu çalışmada Slater Tipi Orbitaller (STO) ve Gauss Tipi Orbitaller (GTO) kullanılarak Li (Lityum), Na
(Sodyum) ve N (Azot) atomlarında, elektrik dipol yaklaşıklığı altında ilk uyarılmış seviyeden temel
seviyeye kendiliğinden geçiş olasılıkları hesaplanmıştır. STO baz setleri kullanılarak gerçekleştirilen
hesaplamalarda, öncelikle tek elektronlu atom yaklaşımı altında kendiliğinden geçiş olasılıkları için
analitik ifadelerin türetilmiştir. Daha sonra bu analitik ifadeler çok elektronlu atomlara genişletilse de STO
baz setleri kullanılan hesaplamalarda elektronlar arası LS çiftlenimleri ve konfigürasyon etkileşmeleri
hesaba katılmamıştır. Elde edilen nihai ifadeler kullanılarak geçiş olasılıkları hesabı için C bilgisayar
programlama dilinde bir bilgisayar programı yazılmıştır. Yazılan bu program sayesinde STO baz setlerinin
kullanıldığı hesaplamalar gerçekleştirilmiştir. Ayrıca aynı hesaplamalar GTO baz setlerini kullanan
Gaussian 98 paket programı yardıPı ile tekrarlanmıştır. Fakat bu hesaplamalar esnasında Gaussian 98
paket programında tekli yerleşim etkileşmelerini hesaba katan CIS hesaplama yöntemi seçilerek bir
nebzede olsa yerleşim etkileşmeleri hesaba katılmıştır. STO ve GTO baz setleri kullanılarak elde edilen
sonuçları birbirleriyle ve literatürdeki mevcut sonuçlarla karşılaştıUılmıştır. Bu sonuçlar ışığında çeşitli
hesaplama teknikleri ve farklı baz setleri kullanılması arasındaki farklar tartışılmıştır.

Keywords

Elektrik dipol geçişleri, kendiliğinden geçiş olasılığı, elektrik dipol moment operatörünün beklenen değeri

Calculation of electric dipole moment transitions of Li, Na and N atoms by using slater and gaussian type orbitals

Abstract

In this study, spontaneous transition probabilities from the first excited state to the ground state of Li
(Lithium), Na (Sodium) and N (Nitrojen) atoms were calculated by using Slater Type Orbitals (STOs) and
Gaussian Type Orbitals (GTOs) in accordance with the electric dipole approximation. For the calculations
based on STO type orbitals analytic expressions were obtained for the spontaneous transition probabilities
within the single electron atom approximation. Although obtained analytical expressions were extended to
include many electron atoms, LS coupling among electrons and configuration interaction effects were not
taken into consideration. A computer program was written in C programming language by using these
analytical expressions and the calculations for STO type orbitals were performed by using this program.
Also similar calculations were performed using the Gaussian-98 software in which GTO basis functions are
employed. However, in the calculations with Gaussian-98 we have used CIS method which takes single
configuration interactions into account. The results obtained from the calculations with STO and GTO basis
sets were compared with each other and the values obtained from the literature. Considering these results,
the differences between different calculation methods and different basis sets were discussed.

Keywords

Electric dipol transitions, spontaneous transitions probability, expectation value of the electric dipole moment operator

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