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

Öz

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.

Anahtar Kelimeler

• 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

Öz

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.

Anahtar Kelimeler

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

Kaynakça

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