Abstract
In this study, the combined Hartree–Fock (HF) and Hartree–Fock–Roothaan equations are derived for multideterminantal single configuration states with any number of open shells of atoms, molecules and nuclei. It is shown that the postulated orbital-dependent energy and Fock operators are invariant to the unitary transformation of orbitals. This new methodology is based entirely on the spin-restricted HF theory. As an application of combined open shell theory of atomic–molecular and nuclear systems presented in this paper, we have solved Hartree–Fock–Roothaan equations for the ground state of electronic configuration C(1s 22s 22p 2) using Slater type orbitals as a basis.
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References
Negele J.W. (1982). Rev. Mod. Phys. 54:913
Aberg S., Flocard H., and Nazarewicz W. (1990). Annu. Rev. Nucl. Part. Sci 40:439
Butler P., and Nazarewicz W. (1996). Rev. Mod. Phys 68:349
Dobaczewski J., and Dudek J. (2000). Comput. Phys. Commun. 131:164
Teran E., Oberacker V.E., and Umar A.S. (2003). Phys. Rev. C 67:064314
Roothaan C.C.J. (1960). Rev. Mod. Phys. 32:179
Levine I.N. (2000). Quantum Chemistry, 5th ed. Prentice Hall, NJ
Bartlett B.J., in: Modern Electronic Structure Theory, Vol. 1, ed. Yarkony D.R., (World Scientific, Singapore), 1995.
Bishop R.F., in: Microscopic Quantum Many-Body Theories and Their Applications, Lecture Notes in Physics, Vol. 510, ed. Navarro J., and Polls A., (Springer, Berlin, 1998).
Piecuch P., and Bartlett R.J. (1999). Adv. Quantum Chem. 34:295
Paldus J., and Li X. (1999). Adv Chem Phys 110:1
Crawford T.D., and Schaefer H.F. III (2000). Rev. Comput. Chem. 14:33
Piecuch P., Kowalski K., Pimienta I.S.O. and McGuire M.J. (2002). Int. Rev. Phys. Chem 21:527
Piecuch P., Kowalski K., Fan P.D., and Pimienta I.S.O., in: Progress in Theoretical Chemistry and Physics, Vol. 12, ed. Maruani J., Lefebvre R., and Brandas E., (Kluwer, Dordrecht, 2003).
Kowalski K., Dean D.J., Hjorth-Jensen M., Papenbrock T., and Piecuch P. (2004). Phys. Rev. Lett. 92:132501-1
Roothaan C.C.J. (1951). Rev. Mod. Phys. 23:69
Silverstone H.J. (1977). J. Chem. Phys. 67:4172
Carbo R., and Riera J.M. (1978). Lecture Notes in Chemistry, Vol. 5: A General SCF Theory. Springer, Berlin
Fick G., and Wirsich J. (1980). Int. J. Quantum Chem. 18:753
Haser M. (1991). J. Chem. Phys. 95:8259
Murray C.W., and Davidson E.R. (1991). Chem. Phys Lett 187:451
Murray C.W., and Davidson E.R. (1992). Int. J. Quantum Chem. 43:755
Kozlowski P.M., and Davidson E.R. (1994). Chem. Phys. Lett. 226:440
Guseinov I.I. (1998). J. Mol. Struct. (Theochem) 422:69
Guseinov I.I. (1998). J. Mol. Struct. (Theochem) 422:75
Slater J.C. (1960). Quantum Theory of Atomic Structure, Vol II. McGraw-Hill, London
Slater J.C., Phys. Rev. 34 (1929) 1293; 38 (1931) 11109.
Clementi E., and Raimondi D.L. (1963). J. Chem. Phys. 38:2686
Ema I., Vega J., Miguel B., Dotterweich J., Meitner H., and Steinborn E.O. (1999). At. Data Nucl. Data Tables 72:57
I. I. Guseinov, Int. J. Quantum Chem. 90 (2002) 114, 90 (2002) 980; J. Mol. Model. 9 (2003) 135, 9 (2003) 190, 10 (2004) 19, 10 (2004) 212, 11 (2005) 124; J. Chem. Phys. 119 (2003) 4614, 120 (2004) 9454; J. Mol. Struct. (Theochem) 625 (2003) 221, 719 (2005) 53; J. Math. Chem. 36 (2004) 83, 38 (2005) 489; J. Phys. A. Math. Gen. 37 (2004) 957; Can. J. Phys. 82 (2004) 819; Chem. Phys. 309 (2005) 209; Bull. Chem. Soc. Jpn. 78 (2005) 611.
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Guseinov, I.I. Combined Open Shell Hartree–Fock Theory of Atomic–Molecular and Nuclear Systems. J Math Chem 42, 177–189 (2007). https://doi.org/10.1007/s10910-006-9090-0
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DOI: https://doi.org/10.1007/s10910-006-9090-0