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Evaluation of Some Electron Repulsion Integrals Needed in Molecular Quantum Mechanics. A Method of Calculation of Two Electron Multi‐Center Repulsion Integrals without the Use of the Neumann Expansion
1.See, for example, R. O. Brennan and J. F. Mulligan, J. Chem. Phys. 20, 1635 (1952);
1.C. C. J. Roothaan, J. Chem. Phys. 19, 1445 (1951).
2.M. P. Barnett and C. A. Coulson, Trans. Roy. Soc. (London) A243, 221 (1951).
3.S. O. Lundquist and P. O. Lowdin, Arkiv Fysik Stockholm 3, 147 (1951). This article has a bibliography on three and four centered integrals.
4.A. S. Coolidge, Phys. Rev. 42, 189 (1932).
5.Hirschfelder, Eyring, and Rosen, J. Chem. Phys. 4, 121 (1936).
6.Eyring, Walter, and Kimball, Quantum Chemistry (John Wiley and Sons, Inc., New York, 1947), p. 197.
7.Integration formulas which may be adapted for integration over the coordinates of the first electron for more complex AO’s have recently been tabulated by Roothaan (reference 1, equations 31). The integrals include all the orbital possibilities arising from the principle quantum numbers 1 and 2 using Slater‐type AO’s with arbitrary values for the effective nuclear charges.
8.R. S. Barker and H. Eyring, J. Chem. Phys. 21, 912–917 (1953).
9.This statement should not be interpreted as implying that elliptical coordinates are always the choice for such problems. There are frequently reasons for the use of other coordinate systems, bipolar coordinates being often preferable. See for example R. J. Buehler and J. O. Hirschfelder, Phys. Rev. 83, 623 (1951).
9.C. A. Coulson and his co‐workers have also made frequent use of bipolar coordinates in their work on similar problems from quantum mechanics.
10.The recurrence formula, , follows from definition and an elementary integration formula.
11.Kotani, Amemiya, and Simose, Proc. Phys.‐Math. Soc. Japan 20, Extra No. 1 (1938);
11.Kotani, Amemiya, and Simose, 22, Extra No. 1 (1940)., Proc. Phys. Math. Soc. Jpn.
12.V. Kourganoff, Ann. d’Astrophys. 10, 282 (1947).
13.J. O. Hirschfelder, dissertation, Princeton University (1935).
14.C. A. Coulson, Proc. Cambridge Phil. Soc. 33, 104 (1937).
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