One-range addition theorems for generalized integer and noninteger μ Coulomb, and exponential type correlated interaction potentials with hyperbolic cosine in position, momentum, and four-dimensional spaces

doi:10.1088/1674-1056/21/6/063101

中国物理B ›› 2012, Vol. 21 ›› Issue (6): 63101-063101.doi: 10.1088/1674-1056/21/6/063101

• ATOMIC AND MOLECULAR PHYSICS • 上一篇下一篇

One-range addition theorems for generalized integer and noninteger μ Coulomb, and exponential type correlated interaction potentials with hyperbolic cosine in position, momentum, and four-dimensional spaces

I. I. Guseinov

Department of Physics, Faculty of Arts and Sciences, Onsekiz Mart University, Canakkale, Turkey

收稿日期:2011-09-21 修回日期:2011-10-17 出版日期:2012-05-01 发布日期:2012-05-01

One-range addition theorems for generalized integer and noninteger μ Coulomb, and exponential type correlated interaction potentials with hyperbolic cosine in position, momentum, and four-dimensional spaces

I. I. Guseinov^†

Department of Physics, Faculty of Arts and Sciences, Onsekiz Mart University, Canakkale, Turkey

Received:2011-09-21 Revised:2011-10-17 Online:2012-05-01 Published:2012-05-01
Contact: I. I. Guseinov E-mail:isguseinov@yahoo.com

摘要/Abstract

摘要： The formulae are established in position, momentum, and four-dimensional spaces for the one-range addition theorems of generalized integer and noninteger μ Coulomb, and exponential type correlated interaction potentials with hyperbolic cosine (GCTCP and GETCP HC). These formulae are expressed in terms of one-range addition theorems of complete orthonormal sets of Ψ^α -exponential type orbitals (Ψ^α -ETO), φ^α -momentum space orbitals (φ^α -MSO), and z^α -hyperspherical harmonics (z^α-HSH) introduced. The one-range addition theorems obtained can be useful in the electronic structure calculations of atoms and molecules when the GCTCP and GETCP HC in position, momentum, and four-dimensional spaces are employed.

Abstract: The formulae are established in position, momentum, and four-dimensional spaces for the one-range addition theorems of generalized integer and noninteger μ Coulomb, and exponential type correlated interaction potentials with hyperbolic cosine (GCTCP and GETCP HC). These formulae are expressed in terms of one-range addition theorems of complete orthonormal sets of Ψ^α -exponential type orbitals (Ψ^α -ETO), φ^α -momentum space orbitals (φ^α -MSO), and z^α -hyperspherical harmonics (z^α-HSH) introduced. The one-range addition theorems obtained can be useful in the electronic structure calculations of atoms and molecules when the GCTCP and GETCP HC in position, momentum, and four-dimensional spaces are employed.

Key words: correlated interaction potentials, one-range additional theorems, complete orthonormal sets of orbitals, overlap integrals

中图分类号: (Theory of electronic structure, electronic transitions, and chemical binding)

31.10.+z

31.15.-p (Calculations and mathematical techniques in atomic and molecular physics)

I. I. Guseinov. One-range addition theorems for generalized integer and noninteger μ Coulomb, and exponential type correlated interaction potentials with hyperbolic cosine in position, momentum, and four-dimensional spaces[J]. 中国物理B, 2012, 21(6): 63101-063101.

I. I. Guseinov . One-range addition theorems for generalized integer and noninteger μ Coulomb, and exponential type correlated interaction potentials with hyperbolic cosine in position, momentum, and four-dimensional spaces[J]. Chin. Phys. B, 2012, 21(6): 63101-063101.

参考文献 22

[1]	Slater J C 1960 Quantum Theory of Atomic Sructure (New York: McGraw- Hill) p. 31
[2]	Hylleraas E A 1928 Z. Phys. 48 469
[3]	Hylleraas E A 1930 Z. Phys. 60 624
[4]	Hylleraas E A 1930 Z. Phys. 65 209
[5]	Löwdin PO 1955 Phys. Rev. 97 1474
[6]	Löwdin P O 1960 Rev. Mod. Phys. 32 328
[7]	Szasz L 1962 Phys. Rev. 126 169
[8]	James H M and Coolidge A S 1933 J. Chem. Phys. 1 825
[9]	L點how A and Kleindienst H 1993 Int. J. Quantum Chem. 45 445
[10]	Levine I N 2000 Quantum Chemistry (New Jersey: Prentice Hall) p. 305
[11]	Sims J S and Hagstrom S A 2002 Int. J. Quantum Chem. 90 1600
[12]	Guseinov I I 1988 Phys. Rev. A 37 2314
[13]	Guseinov I I 2002 Int. J. Quantum Chem. 90 114
[14]	Guseinov I I 2007 6th International Conference of the Balkan Physics Union, American Institue of Physics Conference Proceedings 899 65
[15]	Guseinov I I 2010 J. Math. Chem. 47 384
[16]	Guseinov I I 2010 J. Math. Chem. 48 812
[17]	Guseinov I I 2008 J. Math. Chem. 43 1024
[18]	Guseinov I I 2003 J. Mol. Model. 9 135
[19]	Guseinov I I 2006 J. Mol. Model. 12 757
[20]	Guseinov I I 2007 J. Math. Chem. 42 991
[21]	Guseinov I I 2008 J. Theor. Comput. Chem. 7 257
[22]	Guseinov I I 2008 Chin. Phys. Lett. 25 4240

One-range addition theorems for generalized integer and noninteger μ Coulomb, and exponential type correlated interaction potentials with hyperbolic cosine in position, momentum, and four-dimensional spaces

One-range addition theorems for generalized integer and noninteger μ Coulomb, and exponential type correlated interaction potentials with hyperbolic cosine in position, momentum, and four-dimensional spaces

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献 22

相关文章 15

Metrics

本文评价

推荐阅读 0

[1]	Ioan Baldea. Chemical bonding in representative astrophysically relevant neutral, cation, and anion HC_nH chains[J]. 中国物理B, 2022, 31(12): 123101-123101.
[2]	Meng-Nan Chen(陈梦南) and Wen-Chao Chen(陈文潮). Photoinduced Weyl semimetal phase and anomalous Hall effect in a three-dimensional topological insulator[J]. 中国物理B, 2021, 30(11): 110308-110308.
[3]	. [J]. 中国物理B, 2021, 30(4): 47501-.
[4]	. [J]. 中国物理B, 2021, 30(2): 23101-0.
[5]	Wan-Run Jiang(姜万润), Rui Wang(王瑞), Xue-Guang Ren(任雪光), Zhi-Yuan Zhang(张志远), Dan-Hui Li(李丹慧), Zhi-Gang Wang(王志刚). [J]. 中国物理B, 2020, 29(10): 103101-.
[6]	余维琪, 肖红君, 王戈明. Interface properties and electronic structures of aromatic molecules with anhydride and thio-functional groups on Ag (111) and Au (111) substrates[J]. 中国物理B, 2019, 28(10): 103101-103101.
[7]	Camile Rodolphe Tchenguem Kamto, Bridinette Thiodjio Sendja, Jeannot Mane Mane. Adsorption and desorption phenomena on thermally annealed multi-walled carbon nanotubes by XANES study[J]. 中国物理B, 2019, 28(9): 93101-093101.
[8]	胡静, 宋秀能, 王胜雨, 林娟, 张俊荣, 马勇. Landscape of s-triazine molecule on Si(100) by a theoretical x-ray photoelectron spectroscopy and x-ray absorption near-edge structure spectra study[J]. 中国物理B, 2018, 27(11): 113101-113101.
[9]	唐志明, 于艳梅, 董晨钟. Determination of static dipole polarizabilities of Yb atom[J]. 中国物理B, 2018, 27(6): 63101-063101.
[10]	田红春, 徐龙泉, 朱林繁. Selection rules for electric multipole transition of triatomic molecule in scattering experiments[J]. 中国物理B, 2018, 27(4): 43101-043101.
[11]	Tsogbayar Tsednee,Danny L Yeager. A numerical Hartree self-consistent field calculation of an autoionization resonance parameters for a doubly excited 2s², 3s², and 4s² states of He atom with a complex absorbing potential[J]. 中国物理B, 2017, 26(8): 83101-083101.
[12]	薛智琴, 郭永权. Correlation between valence electronic structure and magnetic properties in RCo₅ (R= rare earth) intermetallic compound[J]. 中国物理B, 2016, 25(6): 63101-063101.
[13]	王青青, 李鹏, 高涛, 王红艳, 敖冰云. Density function theoretical study on the complex involved in Th atom-activated C-C bond in C₂H₆[J]. 中国物理B, 2016, 25(6): 63102-063102.
[14]	张月霞, 张小龙. Influence of a strong magnetic field on the hydrogen molecular ion using B-spline-type basis-sets[J]. 中国物理B, 2015, 24(12): 123101-123101.
[15]	王立英, 代学芳, 王啸天, 林婷婷, 陈磊, 刘然, 崔玉亭, 刘国栋. Electronic structures and magnetisms of the Co₂TiSb_1-xSn_x (x=0, 0.25, 0.5) Heusler alloys: A theoretical study of the shape-memory behavior[J]. 中国物理B, 2015, 24(12): 126201-126201.