On the Restricted and Combined Use of Rüdenberg's Approximations in Molecular Orbital Theories of Hartree-Fock Type

Zeitschrift fur Naturforschung - Section A Journal of Physical Sciences

Volumn 58, Issue 12, 2003, Pages 756-784

  Koch, Wolfhard ^a,b   Frey, Bastian ^b   Ruiz, Juan Francisco Sánchez ^a   Scior, Thomas ^c  

^a UNIVERSIDAD NACIONAL AUTÓNOMA DE MÉXICO   (Mexico)

^b UNIVERSITY OF TÜBINGEN   (Germany)

^c BENEMÉRITA UNIVERSIDAD AUTÓNOMA DE PUEBLA   (Mexico)

Author keywords

Extended H ckel Theory (EHT); Integral Approximations According to Mulliken and R denberg; Neglect of Diatomic Differential Overlap (NDDO); Unrestricted (and Restricted) Hartree Fock Molecular Orbitals; Zero Differential Overlap (ZDO)

Indexed keywords

EID: 0442307336     PISSN: 09320784     EISSN: None     Source Type: Journal    
DOI: 10.1515/zna-2003-1212     Document Type: Article

References (24)

1. K. Rüdenberg, J. Chem. Phys. 19, 1433 (1951).
2. R. S. Mulliken, J. Chim. Phys. 46, 500 and 521 (1949).
3. R. G. Parr, J. Chem. Phys. 20, 1499 (1952).
4. J. A. Pople, D. P. Santry, and G. A. Segal, J. Chem. Phys. 43, S 129 (1965).
5. C. C. J. Roothaan, Rev. Mod. Phys. 23, 69 (1951).
6. J. A. Pople and R. K. Nesbet, J. Chem. Phys. 22, 571 (1954).
7. W. Koch, Int. J. Quantum Chem. 76, 148 (2000).
8. G. Blyholder and C. A. Coulson, Theoret. Chim. Acta (Berl.) 10, 316 (1968). B. J. Nicholson, Adv. Chem. Phys. 18, 249 (1970).
9. G. Blyholder and C. A. Coulson, Theoret. Chim. Acta (Berl.) 10, 316 (1968). B. J. Nicholson, Adv. Chem. Phys. 18, 249 (1970).
10. M. Wolfsberg and L. Helmholz, J. Chem. Phys. 20, 837 (1952).
11. R. Hoffmann, J. Chem. Phys. 39, 1368 (1963).
12. P. J. A. Ruttink, Theoret. Chim. Acta (Berl.) 6, 83 (1966).
13. Improvements of Rüdenberg's truncated one-electron expansion have already been described in a paper entitled "Limited Expansion of Diatomic Overlap (LEDO): A Near-Accurate Approximate Ab Initio LCAO MO Method" of F. P. Billingsley II and J. E. Bloor, J. Chem. Phys. 55, 5178 (1971), and its predecessor F. P. Billingsley II and J. E. Bloor, Chem. Phys. Letters 4, 48 (1969). The LEDO technique has many points of similarity with the "Projection of Diatomic Differential Overlap" method (PDDO) of M. D. Newton, N. S. Ostlund, and J. A. Pople, J. Chem. Phys. 49, 5192 (1968), M. D. Newton, J. Chem. Phys. 51, 3917 (1969), and M. D. Newton, W. A. Lathan, W. J. Hehre, and J. A. Pople, J. Chem. Phys. 51, 3927 (1969). Another starting point for the LEDO procedure were the integral approximations of F. E. Harris and R. Rein, Theoret. Chim. Acta (Berl.) 6, 73 (1966).
14. Improvements of Rüdenberg's truncated one-electron expansion have already been described in a paper entitled "Limited Expansion of Diatomic Overlap (LEDO): A Near-Accurate Approximate Ab Initio LCAO MO Method" of F. P. Billingsley II and J. E. Bloor, J. Chem. Phys. 55, 5178 (1971), and its predecessor F. P. Billingsley II and J. E. Bloor, Chem. Phys. Letters 4, 48 (1969). The LEDO technique has many points of similarity with the "Projection of Diatomic Differential Overlap" method (PDDO) of M. D. Newton, N. S. Ostlund, and J. A. Pople, J. Chem. Phys. 49, 5192 (1968), M. D. Newton, J. Chem. Phys. 51, 3917 (1969), and M. D. Newton, W. A. Lathan, W. J. Hehre, and J. A. Pople, J. Chem. Phys. 51, 3927 (1969). Another starting point for the LEDO procedure were the integral approximations of F. E. Harris and R. Rein, Theoret. Chim. Acta (Berl.) 6, 73 (1966).
15. Improvements of Rüdenberg's truncated one-electron expansion have already been described in a paper entitled "Limited Expansion of Diatomic Overlap (LEDO): A Near-Accurate Approximate Ab Initio LCAO MO Method" of F. P. Billingsley II and J. E. Bloor, J. Chem. Phys. 55, 5178 (1971), and its predecessor F. P. Billingsley II and J. E. Bloor, Chem. Phys. Letters 4, 48 (1969). The LEDO technique has many points of similarity with the "Projection of Diatomic Differential Overlap" method (PDDO) of M. D. Newton, N. S. Ostlund, and J. A. Pople, J. Chem. Phys. 49, 5192 (1968), M. D. Newton, J. Chem. Phys. 51, 3917 (1969), and M. D. Newton, W. A. Lathan, W. J. Hehre, and J. A. Pople, J. Chem. Phys. 51, 3927 (1969). Another starting point for the LEDO procedure were the integral approximations of F. E. Harris and R. Rein, Theoret. Chim. Acta (Berl.) 6, 73 (1966).
16. Improvements of Rüdenberg's truncated one-electron expansion have already been described in a paper entitled "Limited Expansion of Diatomic Overlap (LEDO): A Near-Accurate Approximate Ab Initio LCAO MO Method" of F. P. Billingsley II and J. E. Bloor, J. Chem. Phys. 55, 5178 (1971), and its predecessor F. P. Billingsley II and J. E. Bloor, Chem. Phys. Letters 4, 48 (1969). The LEDO technique has many points of similarity with the "Projection of Diatomic Differential Overlap" method (PDDO) of M. D. Newton, N. S. Ostlund, and J. A. Pople, J. Chem. Phys. 49, 5192 (1968), M. D. Newton, J. Chem. Phys. 51, 3917 (1969), and M. D. Newton, W. A. Lathan, W. J. Hehre, and J. A. Pople, J. Chem. Phys. 51, 3927 (1969). Another starting point for the LEDO procedure were the integral approximations of F. E. Harris and R. Rein, Theoret. Chim. Acta (Berl.) 6, 73 (1966).
17. Improvements of Rüdenberg's truncated one-electron expansion have already been described in a paper entitled "Limited Expansion of Diatomic Overlap (LEDO): A Near-Accurate Approximate Ab Initio LCAO MO Method" of F. P. Billingsley II and J. E. Bloor, J. Chem. Phys. 55, 5178 (1971), and its predecessor F. P. Billingsley II and J. E. Bloor, Chem. Phys. Letters 4, 48 (1969). The LEDO technique has many points of similarity with the "Projection of Diatomic Differential Overlap" method (PDDO) of M. D. Newton, N. S. Ostlund, and J. A. Pople, J. Chem. Phys. 49, 5192 (1968), M. D. Newton, J. Chem. Phys. 51, 3917 (1969), and M. D. Newton, W. A. Lathan, W. J. Hehre, and J. A. Pople, J. Chem. Phys. 51, 3927 (1969). Another starting point for the LEDO procedure were the integral approximations of F. E. Harris and R. Rein, Theoret. Chim. Acta (Berl.) 6, 73 (1966).
18. Improvements of Rüdenberg's truncated one-electron expansion have already been described in a paper entitled "Limited Expansion of Diatomic Overlap (LEDO): A Near-Accurate Approximate Ab Initio LCAO MO Method" of F. P. Billingsley II and J. E. Bloor, J. Chem. Phys. 55, 5178 (1971), and its predecessor F. P. Billingsley II and J. E. Bloor, Chem. Phys. Letters 4, 48 (1969). The LEDO technique has many points of similarity with the "Projection of Diatomic Differential Overlap" method (PDDO) of M. D. Newton, N. S. Ostlund, and J. A. Pople, J. Chem. Phys. 49, 5192 (1968), M. D. Newton, J. Chem. Phys. 51, 3917 (1969), and M. D. Newton, W. A. Lathan, W. J. Hehre, and J. A. Pople, J. Chem. Phys. 51, 3927 (1969). Another starting point for the LEDO procedure were the integral approximations of F. E. Harris and R. Rein, Theoret. Chim. Acta (Berl.) 6, 73 (1966).
19. A. Szabo and N. S. Ostlund, Modern Quantum Chemistry, Macmillan, New York 1982.
20. Details of the formal deduction are available at the author's adress, or via e-mail: wolfhard.koch@unituebingen.de.
21. M. C. Zerner, Semiempirical Molecular Orbital Methods, in: K. B. Lipkowitz and D. B. Boyd (Eds.), Reviews in Computational Chemistry, Vol. 2, 313, VCH Publishers, New York 1991, and references therein. W. Thiel, Perspectives on Semiempirical Molecular Orbital Theory, in: I. Prigogine and S. A. Rice (Eds.), Advances in Chemical Physics, Vol. 93, 703, John Wiley & Sons, New York 1996, and references therein.
22. M. C. Zerner, Semiempirical Molecular Orbital Methods, in: K. B. Lipkowitz and D. B. Boyd (Eds.), Reviews in Computational Chemistry, Vol. 2, 313, VCH Publishers, New York 1991, and references therein. W. Thiel, Perspectives on Semiempirical Molecular Orbital Theory, in: I. Prigogine and S. A. Rice (Eds.), Advances in Chemical Physics, Vol. 93, 703, John Wiley & Sons, New York 1996, and references therein.
23. The interest in using Slater-type orbitals (STO) also in non-empirical calculations has been reanimated through "STOP: A Slater-Type Orbital Package for Molecular Electronic Structure Determination" by A. Bouferguene, M. Fares, and P. E. Hoggan, Int. J. Quantum Chem. 57, 801 (1996).
24. W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes, Cambridge University Press, Cambridge 1986.