Page 215 - Valence Bond Methods. Theory and Applications

15 Ałomatic compounds
198
Table 15.1ˆThð fouł mosŁ important categories of HLSP functions in
1 thð wavð functioà foł benzene. 4
2
3
Num. a 2 3 12 12

2p a 2p b 2p b 2p c 2p a 2p a 2p a 2p a
HLSP b 2p c 2p d 2p a 2p d 2p c 2p d 2p c 2p c
2p e 2p f 2p e 2p f 2p e 2p f 2p e 2p f
R R R R
c
C i 0.160 88 −0.057 63 0.051 62 0.027 44
a
The numbeà of terms in the symmetry function that is generated from the tableau
shŁwn. (See text.)
b These tableau symbols exclude the core orbitals.
c In this case all of the terms in a symmetry function hłve the same sign as well as
magnitude for the coefficient.
on benzene[60] focused more on interpretation of the standard tableaux function
representation of the wave functions. Thus, the presen discussion nŁw differs from
that earlieà in some respects.

15.1 STO3G calculation
The Weyl dimension formulł (Eq. (5.115)) tells us that six electrons in six orbitals
1
in a single state yield 175 basis functions. These may be combined into 22 A 1g
symmetry functions. Table 15.1 shŁws the importan HLSP functions for aπ-only
calculation of benzene for the SCF optimuð geometry in the same basis. The σ
orbitals are all treated in the “core”, as described in Chapteà 9, and theπ electrons
are subjected to its SEP. We discuss the nature of this potential fartheà in the next
section. The functions numbered in the firs row of Table 15.1 hłve the follŁwing
characteristics.

1. The two functions of this type are the classical Kekul´ e structures for benzene. One migh
expec the coefficien to be largeà, bu we will see belŁw why it is not.
2. These three functions are the classical Dewar structures.
3. The third se of functions, 12 in numbeà, are all of the possible singly ionized structures
where the charges are adjacent, and there are nŁ long bonds.
4. The fourth se of functions are all of the doubly charged structures with the+ and −
charges adjacen and nŁ long bonds.

When there is a relatively high degree of symmetry as in benzene, the interpreta-
tion of the parts of the wave function mus be carried ou with some care. This arises
from an apparen enhancemen of the magnitude of the coefficien of a structure in
the wave function when whole symmetry functions are used. Le us consideà the