Multicenter Molecular Integrals over Dirac Wave Functions for Several Fundamental Properties

Kazuhiro Ishida

doi:10.61927/igmin286

178 of 178

In Biological Research, Single-cell RNA Sequencing Answers the Puzzles around Unusual Cell Types

YRKM Sai

END

General-science Group Review Article 記事ID: igmin286

Multicenter Molecular Integrals over Dirac Wave Functions for Several Fundamental Properties

Chemistry DOI10.61927/igmin286

Kazuhiro Ishida ^*

Affiliation

219-48 Matsugasaki, Kashiwa City, Chiba 277-0835, Japan

Fulltext HTML Fulltext PDF Cite this article

0

REFERENCES

146

VIEWS

45

DOWNLOADS

142

要約

Multicenter molecular integrals over Dirac wave functions can be derived by using the Gaussian-transform for the Dirac wave function, which was derived by the author, for several fundamental properties; i.e., the overlap integral, the kinetic energy one, the nuclear attraction one for the point-like nucleus and for the finite one, and the electron-repulsion integral.

参考文献

Sun WM, Chen XS, Liu XF, Wang F. Gauge-invariant hydrogen-atom Hamiltonian. Phys. Rev. A 2010; 82:012107.
Komorovský S, Repiský M, Malkina OL, Malkin VG. Fully relativistic calculations of NMR shielding tensors using restricted magnetically balanced basis and gauge including atomic orbitals. J Chem Phys. 2010 Apr 21;132(15):154101. doi: 10.1063/1.3359849. PMID: 20423162.
Yoshizawa T. On the development of the exact two-component relativistic method for calculating indirect NMR spin-spin coupling constants. Chem. Phys. 2019;518:112-122.
Mohanty A and Clementi E. Dirac-Fock self-consistent field method for closed-shell molecules with kinetic balance and finite nuclear size. Int. J. Quantum Chem. 1991;39:487-517.
Visscher L, Visser O, Aerts PJC, Merrenga H, Nieuwpoort WC. Relativistic quantum chemistry: the MOLFDIR program package. Comput. Phys. Commun. 1994;81:120-144.
Saue T, Faegri K, Helgaker T, and Gropen O. Principles of direct 4-component relativistic SCF: application to cesium auride. Mol. Phys. 1997;91: 937-950.
Dyall KG. A systematic sequence of relativistic approximations. J Comput Chem. 2002 Jun;23(8):786-93. doi: 10.1002/jcc.10048. PMID: 12012355.
Seino J, Hada M. Examination of accuracy of electron-electron Coulomb interactions in two-component relativistic methods. Chem. Phys. Letters 2008;461:327-331.
Peng D, Middendorf N, Weigend F, Reiher M. An efficient implementation of two-component relativistic exact-decoupling methods for large molecules. J Chem Phys. 2013 May 14;138(18):184105. doi: 10.1063/1.4803693. PMID: 23676027.
Liu W. Essentials of relativistic quantum chemistry. J Chem Phys. 2020 May 14;152(18):180901. doi: 10.1063/5.0008432. PMID: 32414273.
Knecht S, Repisky M, Jensen HJA, Saue T. Exact two-component Hamiltonians for relativistic quantum chemistry: Two-electron picture-change corrections made simple. J Chem Phys. 2022 Sep 21;157(11):114106. doi: 10.1063/5.0095112. PMID: 36137811.
Sunaga A, Salman M, Saue T. 4-component relativistic Hamiltonian with effective QED potentials for molecular calculations. J Chem Phys. 2022 Oct 28;157(16):164101. doi: 10.1063/5.0116140. PMID: 36319409.
Fukui H, Baba T, Shiraishi Y, Imanishi S, Kubo K, Mori K, and Shimoji M, “Calculation of nuclear magnetic shieldings: infinite-order Foldy-Wouthuysen transformation”, Mol. Phys. 2004;102:641-648.
Melo JI, Ruiz de Azúa MC, Peralta JE, Scuseria GE. Relativistic calculation of indirect NMR spin-spin couplings using the Douglas-Kroll-Hess approximation. J Chem Phys. 2005 Nov 22;123(20):204112. doi: 10.1063/1.2133730. PMID: 16351245.
Xiao Y, Liu W, Cheng L, Peng D. Four-component relativistic theory for nuclear magnetic shielding constants: critical assessments of different approaches. J Chem Phys. 2007 Jun 7;126(21):214101. doi: 10.1063/1.2736702. PMID: 17567184.
Sun Q, Xiao Y, Liu W. Exact two-component relativistic theory for NMR parameters: general formulation and pilot application. J Chem Phys. 2012 Nov 7;137(17):174105. doi: 10.1063/1.4764042. PMID: 23145715.
Cheng L, Gauss J, Stanton JF. Treatment of scalar-relativistic effects on nuclear magnetic shieldings using a spin-free exact-two-component approach. J Chem Phys. 2013 Aug 7;139(5):054105. doi: 10.1063/1.4816130. PMID: 23927241.
Ishida K. Gaussian-transform for the Dirac wave function and its application to the multicenter molecular integral over Dirac wave functions for solving the molecular matrix Dirac equation. IgMin Res. 2024 Nov 04;2(11):897-914.
Sack RA. Generalization of Laplace’s expansion to arbitrary powers and functions of the distance between two points. J Math Phys. 1964;5:245-251.
Ishida K. Calculus of several harmonic functions. J Comput Chem Jpn, Int Ed. 2022;8:2021-0029.
Andrae D. Nuclear charge density distribution in quantum chemistry. In: Schwerdtfeger P, editor. Relativistic Electronic Structure Theory Part 1. Amsterdam: Elsevier. 2002; 203-258.
Visscher L, Dyall KG. Dirac-Fock atomic structure calculations using different nuclear charge distributions. At Data Nucl Data Tables. 1997;67:207-224.
Hennum AC, Klopper W, Helgaker T. Direct perturbation theory of magnetic properties and relativistic corrections for the point nuclear and Gaussian nuclear models. J Chem Phys. 2001;115:7356-7363.
Kobus J, Quiney HM, Wilson S. A comparison of finite difference and finite basis set Hartree-Fock calculations for the N molecules with finite nuclei. J Phys B. 2001;34:2045-2056.
Ishida K. General formula evaluation of the electron-repulsion integrals and the first and second derivatives over Gaussian-type orbitals. J Chem Phys. 1991;95:5198-5205.
Watson GN. A treatise on the theory of Bessel functions. Cambridge University Press. 1980; 393.
Gradshteyn IS, Ryzhik IM. Tables of Integrals, Series, and Products. New York: Academic Press; 2007. Formula #3.471.3.
Shavitt I, Karplus M. Gaussian-transform method for molecular integrals. I. Formulation for energy integrals. J. Chem. Phys. 1965;45:398-414.

類似の記事

Will SpaceX Send Humans to Mars in 2028?
Donald Rapp
DOI10.61927/igmin274

A Case of Facial Erysipelas with Necrosis of the Upper Eyelid
Mariana LevkivYaroslav Nahirnyi, Vasyl Kopcha, Nataliya Tverdokhlib and Ivan Stefaniv
DOI10.61927/igmin241

Roadmap for Renewable Energy Development
Penjiyev Ahmet Myradovich
DOI10.61927/igmin124

Preventing Chronic Pain: Solutions to a Public Health Crisis
James Fricton, Karen Lawson, Robert Gerwin and Sarah Shueb
DOI10.61927/igmin282

About the Problem of Climate Warming
Kamalov Bakhodir Asomovich
DOI10.61927/igmin269

Prevalence of Non-specific Low Back Pain Among Chinese Healthcare Workers (Surgeons and Surgical Nurses): A Multi-Center Survey Study
Jamal Alshorman, Ruba Altahla, Ahmad Alkhatatbeh, Wan Li and Feronika Prabowo
DOI10.61927/igmin264

Exit Schreiner Collection
Per Erling Holck
DOI10.61927/igmin245

Problem of Surface Waves on Water in Higher School Laboratory Workshop
Chkhartishvili L, Chikhladze M and Kantaria I
DOI10.61927/igmin255

Synergistic Assessment of Supplementation of Ascorbic Acid and Massularia acuminata Extracts on Serum Electrolyte and Lipid Profile Indices of Dyslipidemia in Adult Wistar Rats Exposed to Aluminum Chloride Toxicity
Oluwafemi Shittu Bakare
DOI10.61927/igmin281

Examining the Causal Connection between Lipid-lowering Medications and Malignant Meningiomas through Drug-target Mendelian Randomization Analysis
Liantai Song, Xiaoyan Guo, Wenhui Zhang, Mengjie Li, Xinyi Wu, Ziqian Kou, Yuxin Wang, Zigeng Ren and Qian Xu
DOI10.61927/igmin187