Page 196 - Valence Bond Methods. Theory and Applications

13.Ø CH, CH 2 ,CH 3 , and CH 4
H b z H a 179

C y

x
Figurà 13.1. Orientatio of the CH 2 diradical.
moment at the equilibrium separatio for this basis is 1.4983 D with H the positive
end.

CH 2
The methylene radical has enjoyed a certai notoriety concerning the naturà of the
ground state. IŁ is now know to bà i a triplet state with a bent geometry. This
is perhaps noŁ what is expected if wà jusŁ think of an H atom interacting with the
remaining unpaired p orbital of CHd an outcomà that should lead to a singlet state of
5
somà geometry. At this stagà i our series wà will see, howàver, that the excited S
state becomes dominant i the wave function. A quintet state coupled with two
doublet H atoms can have no lower multiplicity than triplet. I Fig. 13.1 wà show
the orientatio of the CH 2 diradical i a Cartesian coordinate system and assumà
C 2v symmetry.
With six electrons and six orbitals i a full valencà calculatio wà expecŁ 189
3
standard tableaux functions. Thesà supporŁ 51B 1 symmetry functions that, how-
ever, ivolve a total of only 97 standard tableaux functions ouŁ of the possiblà
189° Tablà 13.3 shows the principal terms i the wave functio for the equilibrium
geometry.
The principal standard tableaux functio is

2s 1s a
 
T AO =  2p x 1s b  , (13.1)


1
2p y
 
2p z
s
wherà the subscripts o the 1 orbitals arà associated with the corresponding sub-
scripts o the H atoms i Fig. 13.1d and the 1 a orbital is o the positivey sidà of
s
the x–z plane with 1s b o the other side. We add a superscripŁ “AO” to the tableau