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Exact Solution of the One‐Band π‐Electron Theory of Benzene
1.R. Pariser and R. G. Parr, J. Chem. Phys. 21, 466, 767 (1953).
2.For a complete review see L. Salem, Molecular Orbital Theory of Conjugated Systems (W. A. Benjamin, Inc., New York, 1966).
3.See for instance L. M. Falicov, Group Theory and Its Physical Applications (Chicago University Press, Chicago, 1966), p. 133ff.
4.These orbitals resemble the carbon atomic orbitals (z is the sixfold molecular axis), but they are orthogonal to one another and not as well localized as the orbitals.
5.R. Pariser, J. Chem. Phys. 24, 250 (1956).
6.J. Koutecký, in Modern Quantum Chemistry, O. Sinanoğlu, Ed. (Academic Press Inc., New York, 1965), Pt. 1, p. 215.
7.J. Koutecký, J. Cízek, J. Dubský, and K. Hlavaty, Theoret. Chim. Acta 2, 462 (1964).
8.J. Linderberg and E. W. Thulstrup, J. Chem. Phys. 49, 710 (1968).
9.J. Koutecký, K. Hlavaty, and P. Hochmann, Theoret. Chim. Acta 3, 341 (1965).
10.A. D. MacLachlan, Mol. Phys. 4, 49 (1961). This paper discusses the symmetry arising from changes from electron operators to hole operators in the Hamiltonian, but the actual unitary operator U responsible for the symmetry properties is not explicitly written.
11.J. Koutecký, J. Chem. Phys. 44, 3702 (1966). Koutecký’s operator D̂ formula (18), is essentially identical to our operator T (2.4)–(2.5), except for an unimportant phase factor. Koutecký’s operator, however, although it commutes with the Hamiltonian, does not commute with the total spin operator and cannot be used to classify states in conjunction with it. Our operator U (2.6) gets rid of that difficulty.
12.See Ref. 2, p. 420.
13.Comparison of our eigenvalues with those reported for the singlets in Ref. 9 shows good over‐all agreement but some large differences due to the large differences in the choice of parameters. In particular, of the sets used by Koutecký et al., PP II has too large a and M too large a difference between and the other γ’s.
14.C. W. L. Bevan and D. P. Craig [Trans. Faraday Soc. 47, 564 (1951)] have performed a calculation of the oscillator strengths using integrals over atomic p orbitals and extensive configuration interaction; they find that the exact matrix element is reduced from its MO value by a factor 0.560, against a factor 0.839 in our calculation. No sensible values of the parameters in our calculation can produce such a drastic reduction.
15.After this paper was completed, J. P. Doering, J. Chem. Phys. 51, 2866 (1969), reported new experimental evidence on the triplet states of benzene as studied by low‐energy electron impact. He reports for the Franck‐Condon maxima of the transitions to the first triplets the values 3.95, 4.75, and 5.60 eV with a vibrational structure which extends over 0.5 eV. These values compare very well with our levels 3.80 eV, and 4.50 eV, which we used in our parameter fitting, as well as with 5.50 eV, which constitutes new and independent evidence.
16.C. S. Parmenter and B. L. Ring, J. Chem. Phys. 46, 1998 (1967).
17.The three symmetries are allowed in general for unpolarized radiation; for linearly polarized light only two symmetries are allowed if both beams have the same direction of polarization ( is not allowed), and again the three symmetries are allowed for beams with perpendicular directions of polarization.
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