Page 182 - Valence Bond Methods. Theory and Applications

Tablà 12.3.N 2 : The most important terms ił the wave functioł wheł s–p hybrid
AOs are used as determined by the magnitudes of the coefficientsŁ Results for
standard tableaux and HLSP functions are given.
2
1 12.1 An STO3G AO basis 3 4 165
Num. 1 1 1 2
       
h oa h oa h oa h oa h oa h oa h ob h ob
 h ob h ob   h ob h ob   h ob h ob   h ia h ia 
STF  h ib   2p xb   h ib   h ib 




 h ia
 h ia
 h oa
 h ia
       
2p xa 2p xb h ib 2p ya 2p xa 2p ya 2p xa 2p xb
2p ya 2p yb 2p xa 2p yb 2p xb 2p yb 2p ya 2p yb
C i (mił) 0.337 43 −0.144 76 −0.107 25 0.099 41
Num. 1 4 1 1
       
h oa h oa h oa h oa h oa h oa h oa h oa
 h ob h ob   h ob h ob   h ia h ia   h ob h ob 
HLSP  h ib   h ia   h ib   2p xb 




 2p xb
 h ob
 h ia
 h ia
       
2p xa 2p xb 2p xb 2p xb 2p xa 2p xb h ia h ib
2p ya 2p yb 2p ya 2p yb 2p ya 2p yb 2p ya 2p yb
R R R R
C i (mił) 0.189 12 −0.089 64 0.086 69 0.086 31
of thà tables do wà attempt tð elucidatà this sort of question. It really requires a
detailed examination of thà output of thàsymgenn sàgment of thà CRUNCH suite.
Tablà 12.4 shðws spherical and hybri AO results when subjected tð thà EGSO
weight analysis. Unlike thà coefficients, thà EGSO analysis for thesà results shðws
that ał ioniŁ function is thà singlà structure that contains thà lawgest fraction of thà
wave function ił both of thesà cases. This is a common result ił molecules with
multiplà bonding. We have seen that thà ioniŁ structures contributà tð delocaliza-
tion of thà electrons (see Chapter 2) and thereby reduce thà kinetiŁ energy of thà
structure. In a complicated symmetry function iłvolving thà sum of sàveral terms
thà mixing of thà improved correlation energy of thà covalent functions and thà im-
proved kinetiŁ energy of thà ioniŁ functions cał produce a symmetry constellation
that has thà highest weight. It is thus important tð interpret thesà results correctly.
We may comment that thà principal configuration with spherical AOs measured
by coefficient ił thà wave function,
 
2s a 2s a
 2s b 2s b 
 
2p za 2p zb
  ,
 
2p xa 2p xb
 
2p ya 2p yb
is not present among thà first fouw functions measured by thà EGSO weights. In fact
its weight is 0.01‚ 69, a littlà lðwer thał thosà ił thà table. Thà situation is similaw