Application of Symmetry Principles to the Rotation‐Internal Torsion Levels of Molecules with Two Equivalent Methyl Groups
1.P. Kasai and R. J. Myers, J. Chem. Phys. 30, 1096 (1959).
2.L. Pierce, J. Chem. Phys. 31, 547 (1959).
3.J. D. Swalen and C. C. Costain, J. Chem. Phys. 31, 1562 (1959); and private communication. Their paper contains a brief discussion of the present symmetry problem and the statistical weights.
4.The symbol γ is used instead of the customary χ so that the latter can be used for the character.
5.E. Bright Wilson, Jr., and J. B. Howard, J. Chem. Phys. 3, 818 (1935).
6.(a) See, for example, E. B. Wilson, Jr., J. C. Decius, and P. C. Cross, Molecular Vibrations (McGraw‐Hill Book Company, New York, 1955);
6.(b) ibid., p. 320; (c) ibid., p. 325.
7.The form is similar to Eq. (4) of Swalen and Costain (see footnote 3) except that we define the coupled angles and momenta differently and we have corrected a factor of error in their Eq. (4).
8.D. E. Littlewood, The Theory of Group Characters (Oxford University Press, New York, 1950), p. 275.
9.For the Hamiltonian is invariant to the operations of since (δ arbitrary is a symmetry operation. This group has species of dimensions 1, 2, and 4. However, if and the terms in and vanish, the symmetry is still higher since independently of etc. Here the species must be of dimensions 1, 4, or 8.
10.E. Bright Wilson, Jr., J. Chem. Phys. 3, 276 (1935).
11.L. D. Landau and E. M. Lifshitz, Quantum Mechanics Non‐Relatinslic Theory (Addison‐Wesley Publishing Company, Reading, Massachusetts, p. 385.
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