54
Chapter 3 Wave-Functions and Valence-Bond Structures for 1-Electron Bonds, …
{a(1)b(2) + b(1)a(2)}(φ* ab )
1 = (ψ ab )
1 (a)
1 (b)
1 = (a + kb)
1 (a)
1 (b)
1 = (a)
2 (b)
1 +
k(a)
1 (b)
2
is obtained, which is analogous to that of Eqn (18). The Slater-determinantal
derivation of this result goes as follows.
|a
α
b
β φ* ab
α
| + |b
α
a
β φ* ab
α
| = -k|a
α
b
β b
α
| + |b
α
a
β a
α
| = |(a + kb)
β a
α
b
α
| = |ψ ab
β a
α
b
α
|
A similar type of identity is obtained when the a and b atomic orbitals are
replaced by the Coulson-Fischer
22 type molecular orbitals a + k 1 b and b + k 2 a,
in which k 1 and k 2 are polarity parameters.
3) The Pauling “3-electron bond” valence bond structure (H  H)
(–) is also
appropriate for the ground-state of H 2
– . In Refs. 24 and 25, the non-Pauling
“3-electron bond” formulation of the wavefunction for the electronic structure
of H 2
– of Ref. 23 was shown to be fallacious.
21. R.D. Harcourt, (a) J. Chem. Educ. 62, 99 (1985). (b) J. Phys. Chem. A, 115, 6610, 8180
(2011) (In Eqs.(2) and (4), omit the negative signs.)
22. C.A. Coulson and I. Fischer, Phil. Mag. 40, 386 (1949).
23. R.D. Harcourt, J. Phys. B, 20, L617 (1987).
24. C.W. Bauschlicher, J. Phys. B, 21, L413 (1988).
25. R. McWeeny, J. Mol. Struct. (Theochem) 261, 403 (1992)