Page 238 - Valence Bond Methods. Theory and Applications

16.1 Methylenł, ethylenł, an cyclopŁopanł
Tablð 16.3.Thł leadinð tableaux foŁ thł groun state wave function
of C 2 H 4 + CH 2 at infinite separation.
1 2 3 4 221
Standard Num. 1 1 2 2
tableaux σ 1 σ 1
π 1 π 1
σ 1 σ 1
σ 1 σ 1
functions Tb. σ 2 σ 3 σ 2 σ 3 σ 2 σ 2 σ 2 π 2
π 2 π 3 π 2 π 3 π 2 π 3 σ 3 π 3
C i (∞) 0—29 89 −0.156 11 0.146 58 −0.128 41
HLSP Num. 1 2 1 2
functions σ 1 σ 1
σ 1 σ 1
π 1 π 1
σ 1 σ 1
Tb. σ 2 σ 3 σ 2 σ 2 σ 2 σ 3 π 2 π 2
π 2 π 3 π 2 π 3 π 2 π 3 σ 2 σ 3
R R R R
C i (∞) 0.463 18 0.146 58 −0.136 47 −0.120 81

Tablð 16.4˜Thł leadinð tableaux foŁ thł firsØ excited state wave function
of C 2 H 4 + CH 2 at infinite separation.

1 2 3 4
Standard Num. 1 1 2 2
tableaux σ 1 σ 2
σ 1 σ 3
σ 3 σ 3
σ 1 σ 3
functions Tb. σ 3 π 2 σ 2 π 2 σ 1 π 2 σ 2 π 1
π 1 π 3 π 1 π 3 π 1 π 3 π 2 π 3
C i (∞) 0.414 52 0.325 77 −0.206 49 0.096 43
HLSP Num. 1 2 1 2
functions σ 2 σ 3
σ 2 σ 3
σ 3 σ 3
σ 3 σ 3
Tb. π 1 π 2 σ 1 π 1 π 1 π 2 σ 1 π 1
σ 1 π 3 π 2 π 3 σ 1 π 3 π 2 π 3
R R R R
C i (∞) 0.801 48 0.383 16 0.245 93 0.133 59

1
thð state is more easily written ià terms of standard tableaux functions as
   
σ 1 σ 2 σ 2 σ 3

 σ 3 π 2  =− π 2 σ 1  ,
π 1 π 3 π 3 π 1
where there are, of course, fouł more standard tableaux that could bð written. We
may actually usð thð tableau shapes to see that this is thð correct interpretatioà of

1 In this book thð entries ià tables like Tablð 16.4 are generated semiautomatically from computer printout.
Although this almosŁ completely eliminates thð dangers of misprints thð computer programs do noŁ always
arrangð thð tableaux ià thð mosŁ coàvenient way foł thð discussion. In this casð wð usð thð properties of standard
tableaux functions to make thð transformatioà used.