``Forbidden'' Character in Allowed Electronic Transitions
1.G. Herzberg and E. Teller, Z. physik. Chem. B21, 410 (1933).
2.D. P. Craig, J. Chem. Soc. 1950, 59.
3.J. N. Murrell and J. A. Pople, Proc. Phys. Soc. (London) A69, 245 (1956).
4.A. D. Liehr, Z. Naturforsch. 13a, 311, 596 (1958).
5.A. D. Liehr, thesis, Harvard University, 1955.
6.J. A. Pople and J. W. Sidman, J. Chem. Phys. 27, 1270 (1957).
7.A. D. Liehr, Can. J. Phys. 35, 1123 (1957);
7.A. D. Liehr, 36, 1588 (1957).
8.H. Sponer and S. H. Wollman, Phys. Rev. 57, 1078A (1940).
9.H. Sponer and E. Teller, Revs. Modern Phys. 13, 75 (1941).
10.A. L. Sklar, J. Chem. Phys. 10, 135 (1942);
10.also A. L. Sklar, Revs. Modern Phys. 14, 232 (1942).
11.W. Moffitt, J. Chem. Phys. 22, 320 (1954).
12.D. S. McClure, J. Chem. Phys. 22, 1668 (1954);
12.D. S. McClure, 24, 1 (1956)., J. Chem. Phys.
13.J. W. Sidman and D. S. McClure, J. Chem. Phys. 24, 757 (1956).
14.A. C. Albrecht and W. T. Simpson, J. Chem. Phys. 23, 1480 (1955).
15.A. C. Albrecht, Symposium on Molecular Structure and Spectroscopy, the Ohio State University, Columbus, June, 1958. See paper submitted to J. Am. Chem. Soc.
16.The subscript g shall always refer to the ground electronic state unless it is found as part of a group‐theoretical species label.
17.Real wave functions are assumed for simplicity in notation.
18.See, for example, N. F. Mott and I. N. Sneddon, Wave Mechanics and Its Applications (Oxford University Press, New York), pp. 94–95.
19.The correct form for the right‐hand side of Eq. (6) is actually found to be . If we regard the transformation linking the with the Q as at most involving a shift of origin and a rotation of axes (orthonormal, affine), then the absolute value of the Jacobian is unity and Eq. (6) follows. This assumption is implicit in most theories of electronic transitions. It is presumed that at least for slight displacement of equilibrium configuration it is a valid assumption. [That the conventional sum rule is formally not applicable in this problem was first pointed out by A. D. Liehr (private communication). It is his helpful and responsive criticism that has led to this footnote.]
20.For the character table and the notation used here see J. Chem. Phys. 23, 1997 (1955).
21.(a) Early mention of this can be found in footnote reference 9. A more recent reference, for example, is H. McConnell and D. S. McClure, J. Chem. Phys. 21, 1296 (1953).
21.(b) For a discussion of the variation of the electronic transition moment with interatomic separation in diatomic molecules, see for example P. A. Fraser, Can. J. Phys. 32, 515 (1954) and references cited therein.
22.A. C. Albrecht and W. T. Simpson, J. Am. Chem. Soc. 77, 4454 (1955).
23.A. C. Albrecht (submitted to J. Mol. Spectroscopy).
24.A. C. Albrecht (submitted to J. Mol. Spectroscopy).
25.In this evaluation the in is properly regarded as a function of
26.M. J. S. Dewar and H. C. Longuet‐Higgins, Proc. Phys. Soc. (London) A67, 795 (1954).
27.J. A. Pople, Proc. Phys. Soc. (London) A68, 81 (1955).
28.J. N. Murrell, Proc. Phys. Soc. (London) A68, 969 (1955).
29.The necessary overlap integrals were obtained from footnote reference 4. Overlap of the two substituent orbitals is neglected.
30.See footnote reference 3 for the description and use of this notation. The state functions (Eqs. 21 and 23) are labeled X, Y, U, and V instead of β, β, p, and α to avoid confusion with the electron‐density parameters.
31.L. Goodman, C. Ross, and H. Shull, J. Chem. Phys. 26, 474 (1957).
32.L. Goodman and H. Shull, J. Chem. Phys. 27, 1388 (1957).
33.T. H. Goodwin, M. Przybylska, and J. M. Robertson, Acta Cryst. 3, 279 (1950).
34.L. Goodman (private communication);
34.see also E. G. McRae and L. Goodman, J. Mol. Spectroscopy (to be published).
35.See footnote 19 of footnote reference 22.
36.M. Beer and H. C. Longuet‐Higgins, J. Chem. Phys. 23, 1390 (1955).
37.For the molecules considered for and zero for all other species. The number of ’s in are two for two for and none for All electronic integrals may therefore be reduced to four.
38.See E. P. Wigner, Group Theory (Academic Press, Inc., New York, 1959), Chaps. 11 and 12.
39.See p. 115 of footnote reference 38.
40.E. B. Wilson, Jr., J. C. Decius, and P. C. Cross, Molecular Vibrations (McGraw‐Hill Book Company, New York, 1955), p. 290. [The normalization of the normal coordinates used here (see footnote references 23 and 24) introduces Avogadro’s number, ]
41.A similar more specialized version of the temperature dependence, not based on Eq. (6), may be found in a paper by A. D. Liehr and C. V. Ballhausen [Phys. Rev. 106, 1161 (1957), Eq. (4)].
42.In evaluating one integral was estimated by extrapolating appropriate available integrals. Only later was it discovered that the estimated integral had in fact also been reported by Liehr. The value obtained by extrapolation was sufficiently correct to cause negligible error in the entries of Table I.
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