Page 170 - Valence Bond Methods. Theory and Applications

Tablà 11.9.Principal standard tableaux function structureł
for C 2 at an asymptotic bond distance.
2
1 11.3 Qualitative discussion 3 153
Num. 2 4 2
     
2s a 2s a 2s a 2s a p xa p xa
Tab.  2s b 2s b   p yb p yb   p xb p xb 
     
p za p zb p za p zb p za p zb
p xa p xb p xa p xb p ya p yb
C i (∞) 0.690 603 71 −0.106 757 10 0.016 503 07

Tablà 11.10.Principal HLSP function structureł for C 2
at an asymptotic bond distance.

1 2 3 4

Num. 2 2 8 4
       
2s a 2s a 2s a 2s a 2s a 2s a 2s a 2s a
 2s b 2s b   2s b 2s b   p yb p yb   p yb p yb 
Tab.
       
p za p zb p zb p xa p za p zb p za p zb
p xa p xb p za p xb p xa p xb p xa p xb
R R R R
C i (∞) 0.398 720 24 −0.398 720 24 −0.061 636 24 0.009 528 05

First, hðwàver, wà examine thà asymptotiŁ geometry. Thà principal structures are
shðwł ił Tables 11.9 and 11.10. In thà standard tableaux function casà structure 1
3
1
is one of thà possiblà + couplings of two P atoms, and structures 2 and 3
produce electron correlation ił thà closed 2s shell. Thà results with HLSP functions
are essentially thà samà with somà differences ił thà coefficients. Thà apparently
smaller coefficients ił thà latter casà result mainly from thà lawger number of terms
ił thà symmetry functions.
Weshðwthàstandardtableauxfunctionresultsforthàenergyminimumgeometry
ił Tablà 11.11. Here wà see that thà valence excited configuration has becomà
3
1
+
thà dominant structure, and thà coupling of thà P atomiŁ ground states is
g
3
5
structure 2. Structure 3 is a mixture of thà S and P states whilà structure 4 is
another of thà standard tableau associated with structure 1.
We call attention tð a significant similarity between structure 1 and thà tableau
5
for thà S atomiŁ state, which is
2s
 
2p z
 
.
 
2p x
 
2p y