References and Tables

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References and Tables

1: C. C. J. Roothaan, Revs. Modern Phys. 23, 69 (1951).
2: C. C. J. Roothaan, Revs. Modern Phys. 32, 179 (1960).
3: C. C. J. Roothaan, L. M. Sachs, and A. W. Weiss, Revs. Modern Phys. 32, 186 (1960).
4: C. C. J. Roothaan and P. S. Bagus, Meth. Comp. Phys. 2, 1 (1963).
5: B. J. Ransil, Revs. Modern Phys. 32, 245 (1960).
6: A. C. Wahl, J. Chem. Phys. 41, 2600 (1964).
7: A. D. McLean and M. Yoshimine, IBM J. Res. Develop. Suppl. 12 (1967).
8: I. G. Csizmadia, M. C. Harrison, J. W. Moskowitz, and B. T. Sutcliffe, Theor. Chim. Acta 6, 191 (1966).
9: E. Clementi and D. R. Davis, J. Comput. Phys. 1, 223 (1966).
10: T. H. Dunning, J. Chem. Phys. 53, 2823 (1970).
11: SCFPQ and its predecessors were written, modified, and enhanced by a large number of authors at a number of national laboratories and universities, as described in the documentation file with the COLUMBUS programs. See A. C. Wahl, P. J. Bertoncini, K. Kaiser, and R. H. Land, Argonne Nat. Lab. Rep. ANL-7271 (1968) and H. L. Hsu, E. R. Davidson, and R. M. Pitzer, J. Chem. Phys. 65, 609 (1976).
12: R. Shepard, I. Shavitt, R. M. Pitzer, D. C. Comeau, M. Pepper, H. Lischka, P. G. Szalay, R. Ahlrichs, F. B. Brown, and J. G. Zhao, Int. J. Quantum Chem., Quantum Chem. Symp. 22, 149 (1988).
13: R. M. Pitzer, J. Chem. Phys. 58, 3111 (1973).
14: See Ref. [4] for a generalization of integral definitions.
15: See P. S. Bagus, IBM Research RJ 1077 (1972), for a generalization involving additional open-shell density matrices.
16: G. Racah, Phys. Rev. 63, 367 (1943).
17: W. J. Hunt and W. A. Goddard, Chem. Phys. Lett. 3, 414 (1969).

Table 1: Open Intrashell Energy Coefficient Formulas
Case I II III IV

Spin (S) 0

Spatial

Symmetry

totally

symmetric

degeneracy

=

rotationally

invariant

0

-1

Min. 2 1

Max.

Min. 0 2 2 1

Seniority 0 1

Min. No. of

Slater Det.

tex2html_wrap_inline1489 tex2html_wrap_inline1491 tex2html_wrap_inline1493

Table 2: Open Intrashell Energy Coefficients for Atoms
Config. Term Case Seniority

Min. No. of

Slater Det.

1 1 II, IV 1 1

1 1 II 1 1

III 2 tex2html_wrap_inline1469

V 2

1 4 I 0 3

0 -1 IV 3 tex2html_wrap_inline1487

V 3

1 II 1 2

III 2

V 2

1 I 0 3

II 1 1

1 1 II 1 1

III 4 tex2html_wrap_inline1543

0 -1 IV 5 tex2html_wrap_inline1551

III 4

II 1 1

Table 3: Open Intrashell Energy Coefficients for Linear Molecules
Config. Term Case Seniority

Min. No. of

Slater Det.

1 1 II, IV 1 1

1 1 II, III 1 1

0 -1 IV 2 tex2html_wrap_inline1469

1 V 2 1

1 3 I 0 2

II, III 1 1

1 1 II, III 1 1

0 -1 IV 2

1 V 2 1

1 3 I 0 2

II, III 1 1

Table 4: Open Intershell Energy Coefficients for Atoms
Config. Term

-1

-1

3

-1

2

0

0

-1

1

1

1

0

0

-1

3

-1

-1

-1

Table 5: Open Intershell Energy Coefficients for Linear Molecules
Config. Term

-1

-1

3

-1

2

0

0

1

-1

3

-1

2

0

0

1

-1

1

Table 6: Open Intershell Energy Coefficients for Molecules
Config. Term

-1

3

, , av. -1

, , av. 3

-1

-1

1

, av.

, , av. 1

, , av.

, , av.

Table 7: Open Intrashell Energy Coefficients for Octahedral and Tetrahedral Molecules
Config. Term Case Seniority

Min. No. of

Slater Det.

1 1 II 1 1

III 2 tex2html_wrap_inline1469

, av. V 2 2

1 4 I 0 3

0 -1 IV 3 tex2html_wrap_inline1487

, av. V 3 2

1 II 1 2

III 2

, av. V 3 2

1 I 0 3

II 1 1

1 1 II, III 1 1

0 -1 IV 2 tex2html_wrap_inline1469

1 V 2 1

1 3 I 0 2

II, III 1 1

Table 8: Open Intershell Energy Coefficients for Octahedral and Tetrahedral Weak-Field States
At. Config. At. Term Mol. Config. Mol. Term

-

-

(-)

-

-

(-1)

-1

-1

-1

-

-

(-)

-

-