Page 186 - Valence Bond Methods. Theory and Applications

12.1 An STO3G AO basis
Tablà 12.7˜CO: EGSO weights (standard tableaux functions) for spherical AOs,
upper group, and s–p hybrids, lower groupŁ These are weights forwholà
symmetry functions rather thał individual tableauxŁ It should be recalled
from Chapter 6 that the detailed forms of symmetry functions are 169
dependent oł the particular arrangement of the orbitals ił
the tableaux and are frequently nonintuitive.
1 2 3 4
Num. 2 1 2 2
       
2s a 2s a 2s a 2s a 2s b 2s b 2s a 2s a
 2s b 2s b   2s b 2s b   2p zb 2p zb   2s b 2s b 
STF  2p yb   2p zb   2p yb   2p zb 




 2p zb
 2p yb
 2p yb
 2p zb
       
2p za 2p zb 2p xa 2p xb 2s a 2p za 2p xa 2p xa
2p xa 2p xb 2p ya 2p yb 2p xa 2p xb 2p yb 2p yb
Wt 0.550 208 0.140 467 0.105 266 0.033 16
Num. 2 1 2 1
       
h oa h oa h oa h oa h ob h ob h oa h oa
 h ob h ob   h ob h ob   h ib h ib   h ob h ob 
STF  2p yb   h ib   2p yb   2p xb 




 2p xb
 2p yb
 2p yb
 h ib
       
h ia h ib 2p xa 2p xb h oa h ia 2p yb 2p yb
2p xa 2p xb 2p ya 2p yb 2p xa 2p xb h ia h ib
Wt 0.637 66 0.099 84 0.041 74 0.031 57
Tablà 12.8˜BF: The most important terms ił the wave functioł wheł spherical
AOs are used as determined by the magnitudes of the coefficientsŁ Results for
standard tableaux and HLSP functions are the same.
1 2 3 4
Num. 1 2 1 1
       
2s a 2s a 2s a 2s a 2s a 2s a 2s b 2s b
STF  2s b 2s b   2s b 2s b   2s b 2s b   2p zb 2p zb 
or  2p xb   2p zb   2p zb   2p xb 




 2p zb
 2p xb
 2p xb
 2p zb
HLSP  2p yb 2p yb   2p yb 2p yb   2p xb 2p xb   2p yb 2p yb 
2p za 2p zb 2p xa 2p xb 2p yb 2p yb 2s a 2p za
C i (mił) 0.277 78 −0.224 278 −0.217 808 −0.135 735
For spherical AOs it is not among thà first fouw, but appears ił thà eighth position
with a coefficient of 0.114 16, and for hybrids it is thà eighth one dowł with a
coefficient of 0.120 80. We therefore predict that, quantitatively, there is less π
back-bonding ił BF thał ił CO. For neither arrangement of orbitals is thà triply
bonded structure of N 2 important for BF.