Chapter 15 Slater Determinants and WaveFunctions for “Increased-Valence”
Structures
We will now extend the Slater determinant theory of Section 3-7 to construct
wave-functions for “increased-valence” structures. Some of the theory for this
Chapter will be used again in Chapters 20, 23 and 24.
15-1 “Increased-Valence” Wave-Functions for 4-Electron
3-Centre and 6- Electron 4- Centre Bonding Units
In Chapters 11, 12 and 14, we have indicated that the “increased-valence” structure (1)
(with y(1)a(2) + a(1)y(2) as the wavefunction for the fractional Y-A electron-pair
bond) involves the electron spin distributions of structures (2) and (3), in which
the x and o represent electrons with α and β spin wave-functions. Here, we shall
construct Slater-determinantal wave-functions for (2) and (3), and hence for the
“increased-valence” structure (1).
The wave-functions for the Pauling “3-electron bond” components
O
O
A B
 and
O
O
A B

of the spin structures (2) and (3) are given by Eqs. (3-36) and (3-35). In
structures (2) and (3), we have a fourth electron with spin wave-function α or β,
which occupies the Y-atom atomic orbital y. Therefore, the wave-functions for
spin structures (2) and (3) are given by the Slater determinants of Eqs. (1) and (2),
Ó Springer International Publishing Switzerland 2016
R.D. Harcourt, Bonding in Electron-Rich Molecules,
Lecture Notes in Chemistry 90, DOI 10.1007/978-3-319-16676-6_15
205