310
Chapter 23 Some Comparisons of Types of Wave-Funcions
References
1. W.H. Kirchhoff, J. Farren and J.W. Linnett, J. Chem. Phys., 42, 1410 (1965).
2. D.M. Hirst and J.W. Linnett, J. Chem. Phys., 43, S74 (1965).
3. R.D. Gould and J.W. Linnett, Trans. Faraday Soc., 59, 1001 (1963).
4. D.M. Hirst and J.W. Linnett, J. Chem. Soc., 1035, 3844, (1962); 1068 (1963).
5. H.C. Bowen and J.W. Linnett, Trans. Faraday Soc., 60, 1185 (1964).
6. See also (a) R. Pauncz, The Alternant Molecular Orbital Method (Saunders, 1967), p.
193; (b) B. Duke, Theor, Chim. Acta, 23, 175 (1971); (c) T. Okada and T. Fueno, Bull.
Chem. Soc. Jap. 49, 1524 (1976).
7. R.D. Harcourt and W. Roso, Canad. J. Chem., 56, 1093 (1978); Int. J. Quantum Chem.,
16, 1093 (1979).
8. P.C. Hiberty and C. Leforestier, J. Amer. Chem. Soc., 100, 2012 (1978).
9. (a) W.R. Wadt and W.A. Goddard III, J. Amer. Chem. Soc., 97, 3004 (1975); (b) W.A.
Goddard III and S.P. Walch, J. Amer. Chem. Soc., 97, 5319 (1975); (c) W.A. Goddard
III and B.D. Olafson, Proc. Natl, Acad. Sci. U.S.A., 72, 2335 (1975).
10. J.W. Sillitoe and R.D. Harcourt, Aust. J. Chem., 27, 691 (1974).
11. R.D. Harcourt, Aust. J. Chem., 31, 1635 (1978); 32, 933 (1979); 34, 231 (1981).
12. R.D. Harcourt, Aust. J. Chem., 22, 279 (1969).
13. R.D. Harcourt and A. Harcourt, J. Chem. Soc., Faraday II, 70, 743 (1974).
14. R.D. Harcourt, Int. J. Quantum Chem., 4, 173 (1970).
Addendum Chapter 23
1. Although the structural coefficients in Table 23-1 are now more than 40 years
old, it should be satisfactory to use them in order to illustrate aspects of theory.
2. In Refs. 13 and 15, it has been shown that the 1 (MO) of Eqn.(4) and the
(IVBO) of Eqn. (15), namely Eqs. (16) and (17) here
1 (MO) = 2k 1 I – k 1
2
II + 4 III + k 1
2
IV
(16)
(IVBO) (
)
2
4
2
k k k
kk
kk
II
III
IV
(17)
are equivalent when k = k 1 and k’ = k” = ½k 1 , i.e. Ψ(IVBO,k 1 ,½k 1 ,½k 1 ) =
1 (MO).
Also
16 , 1
1
1
2
2
(M )
for
with
1
1
y
a b
k
and
2
y – b
, is equivalent to |ψ L
α
ψ L
β ψ R
α
ψ R
β
|, with ψ L = a + 2k 1 y and
ψ L = a + 2k 1 b. Therefore for these sets of k 1 -dependent orbital parameters,
Chapter 23 Some Comparisons of Types of Wave-Funcions
References
1. W.H. Kirchhoff, J. Farren and J.W. Linnett, J. Chem. Phys., 42, 1410 (1965).
2. D.M. Hirst and J.W. Linnett, J. Chem. Phys., 43, S74 (1965).
3. R.D. Gould and J.W. Linnett, Trans. Faraday Soc., 59, 1001 (1963).
4. D.M. Hirst and J.W. Linnett, J. Chem. Soc., 1035, 3844, (1962); 1068 (1963).
5. H.C. Bowen and J.W. Linnett, Trans. Faraday Soc., 60, 1185 (1964).
6. See also (a) R. Pauncz, The Alternant Molecular Orbital Method (Saunders, 1967), p.
193; (b) B. Duke, Theor, Chim. Acta, 23, 175 (1971); (c) T. Okada and T. Fueno, Bull.
Chem. Soc. Jap. 49, 1524 (1976).
7. R.D. Harcourt and W. Roso, Canad. J. Chem., 56, 1093 (1978); Int. J. Quantum Chem.,
16, 1093 (1979).
8. P.C. Hiberty and C. Leforestier, J. Amer. Chem. Soc., 100, 2012 (1978).
9. (a) W.R. Wadt and W.A. Goddard III, J. Amer. Chem. Soc., 97, 3004 (1975); (b) W.A.
Goddard III and S.P. Walch, J. Amer. Chem. Soc., 97, 5319 (1975); (c) W.A. Goddard
III and B.D. Olafson, Proc. Natl, Acad. Sci. U.S.A., 72, 2335 (1975).
10. J.W. Sillitoe and R.D. Harcourt, Aust. J. Chem., 27, 691 (1974).
11. R.D. Harcourt, Aust. J. Chem., 31, 1635 (1978); 32, 933 (1979); 34, 231 (1981).
12. R.D. Harcourt, Aust. J. Chem., 22, 279 (1969).
13. R.D. Harcourt and A. Harcourt, J. Chem. Soc., Faraday II, 70, 743 (1974).
14. R.D. Harcourt, Int. J. Quantum Chem., 4, 173 (1970).
Addendum Chapter 23
1. Although the structural coefficients in Table 23-1 are now more than 40 years
old, it should be satisfactory to use them in order to illustrate aspects of theory.
2. In Refs. 13 and 15, it has been shown that the 1 (MO) of Eqn.(4) and the
(IVBO) of Eqn. (15), namely Eqs. (16) and (17) here
1 (MO) = 2k 1 I – k 1
2
II + 4 III + k 1
2
IV
(16)
(IVBO) (
)
2
4
2
k k k
kk
kk
II
III
IV
(17)
are equivalent when k = k 1 and k’ = k” = ½k 1 , i.e. Ψ(IVBO,k 1 ,½k 1 ,½k 1 ) =
1 (MO).
Also
16 , 1
1
1
2
2
(M )
for
with
1
1
y
a b
k
and
2
y – b
, is equivalent to |ψ L
α
ψ L
β ψ R
α
ψ R
β
|, with ψ L = a + 2k 1 y and
ψ L = a + 2k 1 b. Therefore for these sets of k 1 -dependent orbital parameters,