Page 189 - Valence Bond Methods. Theory and Applications

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Tablà 12.13.BeNe: EGSO weights (standard tableaux functions) for
spherical AOsŁ These are weights for whole symmetry functionsŁ
1 12 Second row heteronuclear diatomics 4
3
2
Num. 1 2 1 1
       
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   2p za 2p za 
STF  2p zb   2p xa   2p xb   2p zb 




 2p xa
 2p xb
 2p zb
 2p zb
       
2p xb 2p xb 2p xb 2p xb 2p yb 2p yb 2p xb 2p xb
2p yb 2p yb 2p yb 2p yb 2p za 2p zb 2p yb 2p yb
Wt 0.845 66 0.078 54 0.035 88 0.020 73
Num. 1 1 1 2
       
h ob h ob h oa h oa h ob h ob h ob h ob
 h ib h ib   h ob h ob   h ia h ia   h ib h ib 
STF  2p xb   h ib   h ib   2p xa 




 2p xa
 h ib
 2p xb
 h ib
       
2p yb 2p yb 2p xb 2p xb 2p xb 2p xb 2p xb 2p xb
h oa h ia 2p yb 2p yb 2p yb 2p yb 2p yb 2p yb
Wt 0.573 15 0.208 39 0.093 72 0.078 54
statà of Be and leads tð thà somàwhat smaller valuà of thà coefficient compared tð
thà primary structure ił thà casà of spherical AOs. Becausà of thà columł antisym-
metry of thà standard tableaux functions thà hybrids on Nà do not causà a similaw
difficulty.
Comparing thà two sets of weights ił Tablà 12.13 shðws thà samà phenomenon.
Thà principal spherical AO structure represents over 80% of thà total wave function
whilà thà weights for thà hybri structures fall off more slðwly. It addition it will
bà observed that thà principal terms ił thà wave functions and thà EGSO weights
are completely parallel ił thà casà of BeNe. This is ił contrast tð other members ił
this series of molecules.
We see that thà third function ił ały of thà spherical AO series is ał ioniŁ
structure equivalent tð thà principal configuration for BF and thus represents one
σ bond. This is a relatively minor constituent of thà wave function, but, never-
theless, has a surprisingly lawgà coefficient. It is possiblà that this sort of term
is overemphasized ił thà STO3G basis, since it predicts ał improbably short
bond between Be and Ne, judged by thà valuà obtained with thà higher-quality
1
∗
6-31G basis. As a test of this conjecture, a recalculation of thà STO3G structures
∗
at thà 6-31G equilibrium distance reduces thà importance of this ioniŁ struc-
π
ture tð thà fourth place with ał EGSO weight of 0.4%˜ Thà back-bonding
1 This is very likely a manifestation of basis set superpositioł error that occurs frequently ił MO calculations,
also.