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An Extended Hückel Theory. I. Hydrocarbons
1.A. Streitwieser, Molecular Orbital Theory (John Wiley & Sons, Inc., New York, 1961). R. Daudel, R. Lefebvre, C. Moser, Quantum Chemistry (Interscience Publishers, Inc., New York, 1959). B. Pullman and A. Pullman, Les théories élecironiques de la chimie organique (Masson et Cie., Paris, 1952).
2.(a) G. G. Hall and J. Lennard‐Jones, Proc. Roy. Soc. (London) A202, 336 (1950);
2.G. G. Hall and J. Lennard‐Jones, 205, 357, 541 (1951); , Proc. R. Soc. London
2.(b) R. D. Brown, J. Chem. Soc. 1953, 2615;
2.(c) M. J. S. Dewar and R. Petitt, ibid. 1954, 1625;
2.(d) C. Sandorfy, Can. J. Chem. 33, 1337 (1955);
2.(e) K. Fukui, H. Kato, K. Morokuma, A. Imamura, and C. Nagata, Bull. Chem. Soc. Japan 35, 38 (1962) and references therein.
3.A recent example of the consequences of this attitude may be seen in the work of O. Sovers and W. Kauzmann, J. Chem. Phys. 38, 813 (1963).
4.H. A. Skinner and H. O. Pritchard, Trans. Faraday Soc. 49, 1254 (1953);
4.H. O. Pritchard and H. A. Skinner, Chem. Rev. 55, 745 (1955).
5.R. S. Mulliken, J. Chim. Phys. 46, 497, 675 (1949).
6.M. Wolfsberg and L. Helmholtz, J. Chem. Phys. 20, 837 (1952).
7.R. Hoffmann and W. N. Lipscomb, (a) J. Chem. Phys. 36, 2179, 3489 (1962);
7.(b) R. Hoffmann and W. N. Lipscomb, J. Chem. Phys. 37, 2872 (1962)., J. Chem. Phys.
8.R. S. Mulliken, J. Chem. Phys. 23, 1833, 18412338, 2343 (1955).
9.G. Herzberg, Molecular Spectra and Molecular Structure (D. Van Nostrand, Inc., New York, 1959), Vol. II.
10.The exceptions are some diatomics and triatomics for which this theory fails; for instance the obvious case of the ground state of the hydrogen molecule.
11.For the simplest LCAO and VB functions give a poor binding energy but an equilibrium separation within 10% of the correct value. Scaling, i.e., varying the Slater exponent, improves the energy somewhat and predicts the distance to 1% [see the review of calculations in A. D. McLean, A. Weiss, and M. Yoshimine, Rev. Mod. Phys. 32, 211 (1960)].
11.For the best simple LCAO function gives the internuclear separation to 10%, but fails to predict binding [B. T. Ransil, Rev. Mod. Phys. 32, 239, 245 (1960)].
12.(a) W. G. Dauben and K. S. Pitzer in Steric Effects in Organic Chemistry, edited by M. S. Newman (John Wiley & Sons, Inc., New York, 1956), p. 1;
12.(b) E. B. Wilson, Jr., Advan. Chem. Phys. 2, 367 (1959);
12.(c) D. J. Millen, Progr. Stereochem. 3, 138 (1962).
13.In the minimization procedure the staggered form stabilized at a slightly shorter C‐C distance than the eclipsed.
14.R. M. Pitzer (to be published).
15.D. R. Lide, J. Chem. Phys. 33, 1514 (1960).
16.E. L. Eliel, Stereochemistry of Carbon Compounds (McGraw‐Hill Book Company, Inc., New York, 1962).
17.D. R. Lide, J. Chem. Phys. 33, 1519 (1960).
18.F. R. Jensen, D. S. Noyce, C. H. Sederholm, and A. J. Berlin, J. Am. Chem. Soc. 84, 386 (1962).
19.F. V. Brutcher, Jr., and W. Bauer, Jr., J. Am. Chem. Soc. 84, 2233 (1962).
20.K. S. Pitzer and W. E. Donath, J. Am. Chem. Soc. 81, 3213 (1959).
21.R. S. Berry, J. Chem. Phys. 38, 1934 (1963).
22.R. S. Mulliken and C. C. J. Roothaan, Chem. Rev. 41, 219 (1947).
23.D. R. Herschbach and L. C. Krisher, J. Chem. Phys. 28, 728 (1958).
24.R. G. Parr and R. S. Mulliken, J. Chem. Phys. 18, 1338 (1950), obtained somewhat smaller estimates.
24.See also O. Polansky, Monatsh. Chem. 94, 23 (1963).
25.D. R. Lide and D. E. Mann, J. Chem. Phys. 27, 874 (1957).
26.D. R. Lide and D. E. Mann, J. Chem. Phys. 27, 868 (1957).
27.The acetylene wavefunction we obtain compares favorably with the SCF functions calculated by A. D. McLean, J. Chem. Phys. 32, 1595 (1960)
27.[see also A. D. McLean, B. J. Ransil, and R. S. Mulliken, J. Chem. Phys. 32, 1873 (1960)], , J. Chem. Phys.
27.and L. Burnelle, J. Chem. Phys. 35, 311 (1961). Our orbital energies, in eV, are The total C‐C overlap population is 1.93, of which 1.00 comes from the π orbitals. The charges and overlap population may be found in Table VII., J. Chem. Phys.
28.M. P. Gouterman has suggested that a careful search for transitions arising from excitations, and thus polarized perpendicular to the aromatic ring plane, would be useful in this respect. Our energy spectrum supports that given schematically by J. C. Slater, Quantum Theory of Molecules and Solids (McGraw‐Hill Book Company, Inc., New York, 1963), Vol. 1, p. 234.
29.K. Ruedenberg, J. Chem. Phys. 34, 1878 (1961).
30.R. McWeeny, J. Chem. Phys. 19, 1614 (1951).
31.J. Trotter, Acta Cryst. 14, 1135 (1961).
32.I. L. Karle and L. O. Brockway, J. Am. Chem. Soc. 66, 1974 (1944);
32.O. Bastiansen, Acta Chem. Scand. 3, 408 (1949).
33.C. A. Coulson, Conference on Quantum Mechanical Methods in Valence Theory, Shelter Island, New York, 1961, p. 42. F. J. Adrian, J. Chem. Phys. 28, 608 (1958).
34.E. Heilbronner in Nonbenzenoid Aromatic Compounds, edited by D. Ginsburg (Interscience Publishers, Inc., New York, 1959), p. 171.
35.J. H. Day and C. Oestreich, J. Org. Chem. 22, 214 (1956).
36.A. Magnus, H. Hartmann, and F. Becker, Z. Physik. Chem. 197, 75 (1951).
37.G. Ferguson and J. M. Robertson in Advances in Physical Organic Chemistry, edited by V. Gold (Academic Press Inc., New York, 1963), p. 203.
38.See, however, W. M. Schubert, R. B. Murphy, and J. Robins, Tetrahedron 17, 199 (1962).
39.T. J. Katz and M. Rosenberger, J. Am. Chem. Soc. 84, 865 (1962).
40.H. L. Strauss and G. K. Fraenkel, J. Chem. Phys. 35, 1738 (1961).
40.T. J. Katz and H. L. Strauss, J. Chem. Phys. 32, 1873 (1960)., J. Chem. Phys.
41.Note that as usual with LCAO‐MO calculations, the wave‐ function does not have the correct behavior at infinity.
42.It is interesting in this connection to note that in a calculation in which the Mulliken approximation was used for three‐ and four‐center integrals, the binding energy was also overestimated. (L. Burnelle, Ref. 27).
43.L. L. Lohr, Jr., has used a similar expression which differs from ours only in second order and has certain computational advantages. L. L. Lohr, Jr., and W. N. Lipscomb, J. Chem. Phys. 38, 1607 (1963).
43.T. Jordan, H. W. Smith, L. L. Lohr, Jr., and W. N. Lipscomb, J. Am. Chem. Soc. 85, 846 (1963).
43.L. L. Lohr, Jr. and W. N. Lipscomb, ibid. p. 240.
43.See also C. J. Ballhausen and H. B. Gray, Inorg. Chem. 1, 111 (1962).
44.J. C. Slater, Quantum Theory of Molecules and Solids (McGraw‐Hill Book Company, Inc., New York, 1963), Vol. I, p. 108.
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