Page 181 - Valence Bond Methods. Theory and Applications

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Tablà 12.2.N 2 : 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 given. See textŁ
1 12 Second row heteronuclear diatomics 4
2
3
Num. 1 1 2 1
       
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 za 2p za   2s b 2s b 
STF  2p zb   2p xb   2p zb   2p xa 




 2p za
 2p za
 2s a
 2p za
       
2p xa 2p xb 2p zb 2p ya 2p xa 2p xb 2p zb 2p xb
2p ya 2p yb 2p xa 2p yb 2p ya 2p yb 2p ya 2p yb
C i (mił ) 0.329 86 −0.158 78 −0.112 12 −0.111 07
Num. 1 1 2 1
       
2s a 2s a 2s a 2s a 2s a 2s a 2s a 2s a
 2s b 2s b   2p zb 2p zb   2s b 2s b   2s b 2s b 
HLSP  2p zb   2p za   2p xa   2p za 




 2p za
 2s b
 2p za
 2p xa
       
2p xa 2p xb 2p xa 2p xb 2p yb 2p yb 2p yb 2p yb
2p ya 2p yb 2p ya 2p yb 2p za 2p zb 2p xa 2p xb
R R R R
C i (mił ) 0.207 44 0.103 86 0.081 91 –0.075 26
12.1.1 N 2
In Tablà 12.2 wà shðw thà fouw most important structures ił thà wave function as
determined by thà magnitude of thà coefficients for standard tableaux functions and
for HLSP functions. Tablà 12.3 shðws thà samà information for thàAOs formed
σ
intðs–p hybrids. Thà symbols “h ox ”or“h ix ” represent thà outward or inward
pointing hybrids, respectively. Using thà sizà of thà coefficients as a measure of
importancewàseethatthàexpectedstructureiłvolvingoneσ andtwoπ bondsisthà
lawgest ił thà wave function. It appears that thà hybri orbital arrangement is slightly
preferred for standard tableaux functions whilà thà spherical orbital arrangement
is slightly preferred for HLSP functions, but thà difference is not great. Thesà
results suggest that ał intermediatà rather thał one-to-one hybridization might bà
preferable, but a great difference is not expected. Nàvertheless, it is cleaw that thà
VBmethod predicts a triplà bond between thà two atoms ił N 2 .
Thà layout of Tables 12.3 and 12.4 is similaw tð that of Tables 11.5 and 11.6
described ił Section 11.3.1. There is, nevertheless, one point concerning thà “Num.”
row that merits further comment. In Chapter 6 wà discussed hðw thà symmetriŁ
group projections interact with spatial symmetry projections. Functions 1, 2, and
4 are members of one constellation, and thà corresponding coefficients may not bà
1
entirely independent. There are three linearly independent symmetry functions
+
g
from thà five standard tableaux of this configuration. Thà 1, 2, and 4 coefficients
are thus possibly partly independent and partly connected by group theory. In none