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

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

References

1. Bates, D. R. and Damgaard, A., The calculation of the absolute strengths of spectral lines, Philos. Trans. R. Soc. London Ser. A, 242, 101-122, 1949. 2. Kelly, P. S., Transition probabilities in nitrogen and oxygen from Hartree-Fock-Slater wave functions, J. Quant. Spectrose. Radiat. Transfer., 4, 117-148, 1964. 3. Beck, D. R. and Nicolaides, C. A., Theoretical oscillator strengths for the NI and OI resonance transitions, J. Quant. Spectrose. Radiat. Transfer., 16, 297-300, 1976. 4. Bell, K. L. and Berrington, K. A., Photoionization of the
2. S0 ground state of atomic nitrogen and atomic nitrogen 4S0-4P oscillator strengths, J. Phys. B: At.
3. Mol. Opt. Phys, 24, 933-941, 1991. 5.
4. Kostelecky, V. A. and Nieto, M. M., Evidence from
5. S,2P and2D states 8. 9.
6. Marxer, H. and Spruch, L., Semiclassical estimation of the radiative mean lifetimes of hydrogenlike states, Phys. Rev. A, 43, 1268-1274, 1991.
7. Robinson, D. J. R. and Hibbert, A., Quartet transitions in neutral nitrogen, J. Phys. B: At. Mol. Opt. Phys, 30, 4813-4825, 1997.
8. Tong, M., et al, Systematic transition probability studies for neutral nitrogen, J. Phys. B: At. Mol. Opt. Phys., 27, 4819-4828, 1994.

9. Zheng, N. W. and Wang, T., Theoretical resonance transition probabilities and lifetimes for atomic nitrogen, Chem. Phys., 282, 31-36, 2002.
10. Kostelecky, V. A. and Nieto, M. M., Analytical wave functions for atomic quantum-defect theory, Phys. Rev. A, 32, 3243-3246, 1985.
11. Clementi, E. and Raimondi, D.L., Atomic screening constants from SCF functions, J. Chem. Phys., 38, 2686-2689, 1963.
12. Clementi, E., et al, Accurate analytical self-consistenet field functions for atoms. II. lowest configurations of the neutral first row atoms, Phys. Rev., 127, 1618- 1620, 1962.
13. Hartmann, H. and Clementi E., Relativistic correction for analytic Hartree-Fock wave functions, Phys. Rev., 133, A1295-A1299, 1964.
14. Hartree, W., et al, Self-consistent field calculations for Zn, Ga, Ga+, Ga+++, As, As+, As++, As+++, Phys. Rev., 59, 299-305, 1941.
15. Hartree, W., et al, Self-consistent field calculations for Ge++ and Ge, Phys. Rev., 59, 306-307, 1941.
16. Hartree, W., et al, Self-consistent field, with exchange, for Si IV and Si V, Phys. Rev., 60, 857-865, 1941.
17. Hartree, D. R., Variation of atomic wave functions with atomic number, Rev. Mod. Phys., 30, 63-68, 1958.
18. Roothaan, C. C. J., et al, Analytical self-consistent field wave functions for the atomic configurations 1s2, 1s22s, and 1s22s2, Rev. Mod. Phys., 32, 186-194, 1960.
19. Roothaan, C. C. J., New developments in molecular orbital theory, Rev. Mod. Phys. 23, 69-89, 1951.
20. Roothaan, C. C. J., Self-consistent field theory for open shells of electronic systems, Rev. Mod. Phys., 32, 179-185, 1960.
21. Slater J. C., The self consistent field and the structure of atoms, Phys. Rev., 32, 339-348, 1928.
22. Slater J. C., Atomic sheilding constants, Phys. Rev., 36, 57-64, 1930.
23. Slater J. C., Analytic atomic wave functions, Phys. Rev., 42, 33-43, 1932.
24. Slater J. C., A simplification of the Hartree-Fock method, Phys. Rev., 81, 385-390, 1951.
25. Weinstein D. H., A lower limit for the ground state of the helium atom, Phys. Rev., 40, 797-799, 1932.
26. Zener, C., Analytic atomic wave functions, Phys. Rev., 36, 51-56, 1930.
27. Jones, M. D., et al, Theoretical atomic volumes of the light actinides, Phys. Rev. B, 61, 4644-4650, 2000.
28. Stanke, M., et al, Accuracy limits on the description of the lowest S excitation in the Li atom using explicitly correlated Gaussian basis functions, Phys. Rev. A, 78, 052507-052514, 2008.
29. Tachikawa, M. and Shiga, M., Evaluation of atomic integrals for hybrid Gaussian type and plane-wave basis functions via the McMurchie-Davidson recursion formula, Phys. Rev. E, 64, 056706-056709, 2001.
30. Winter, T. G., and Lin C. C., Electron capture by protons in helium and hdrogen atoms at intermediate energies, Phys. Rev. A, 10, 2141-2155, 1974.
31. Kavruk, A. E., Slater ve Gaussian Tipi Orbitalleri Kullanarak Baz Atomlar n Elektrik Dipol Geçi lerinin ncelenmesi, Yüksek Lisans Tezi, Selçuk Üniversitesi, Konya, 2003.
32. Atkins, P. and Friedman, R., Molecular Quantum Mechanics, p. 233, Oxford University Press, New York, 2005.
33. Arfken, G. B. and Weber, H. J., Mathematical Methods for Physicists, p. 644, Academic Press, Orlando, 2001.
34. Frisch, M. J., et al, GAUSSIAN98, Revision A.7, Gaussian Inc., Pittsburgh, PA, 1998.