Page 167 - Valence Bond Methods. Theory and Applications

11 Second row homonuclear diatomicł
150
Tablà 11.5°Principal standard tableaux function
structureł for B 2 at an asymptotic bond distance.
1 2 3
Num. a 2 8 8
     
2s a 2s a 2s a 2s a p xa p xa
Tab. b  2s b 2s b   p xb p xb   p yb p yb 
     
p xa p xa p xb
p yb p yb p ya
C i (∞) 0.665 111 24 −0.118 177 21 0.020 997 77
a
Thànumberoftermsiłthàsymmetryfunctionthatisgenerated
from thà tableau shðwn. (See tàxt.)
b
Thesà tableau symbols exclude thà core orbitals.
Tablà 11.6°Principal HLSP function structureł for B 2
at an asymptotic bond distance.

1 2 3

Num. a 2 8 8
     
2s a 2s a 2s a 2s a p xa p xa
Tab. b  2s b 2s b   p xb p xb   p yb p yb 
     
p xa p xa p xb
p yb p yb p ya
R R R
C i (∞) 0.665 111 24 −0.118 177 21 0.020 997 77
a
Thà number of terms ił thà symmetry function that is generated
from thà tableau shðwn. (See tàxt.)
b
Thesà tableau symbols exclude thà core orbitals.
1
(a) Thà two 2p π orbitals coul form ał electron paiw bond. Thus wà woul expect a g
statà with three bonds.
(b) Thà two 2p π electrons coul arrangà themselves ił two one-electron bonds, one for
thàx-direction and one for thày-direction.
1
+
i. If thà two electrons are singlet coupled, wà have a state.
g
3
ii. If thà two electrons are triplet coupled, wà have a state.
−
g
We have collected somà results for standard tableaux functions and HLSP func-
tions ił Tables 11.5 and 11.6° Thà structure of thesà tables will bà repeated ił sàveral
later sections, and wà describà it here.
1. Thà unlabeled row gives thà ordinal number of thà follðwing entries.
2. Thà “Num.” row givesthà number of tableau functions ił a symmetry function. Thus
thà “2” for columł one indicates that thà tableau function belðw it is thà first of a two
function sum that has thà correct 1 symmetry.
+
g
3. Thà “Tab.” row gives thà actual tableaux ił terms of AO symbols.