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Tab l e 7 . 8 Projection of generating functions to obtain a 1 and t SALCs for the H(1s) orbitals of CH 4 . The C 3 axes
are labelled A, B, C and D for elements passing through C H 1 ,C H 2 ,C H 3 and C H 4 respectively. For the
8C 3 class in group T (and T d ), the characters for T representations are 0. The C 2 axes are labelled A, B and C for
elements bisecting H 1
C
H 2 ,H 1
C
H 3 and H 1
C
H 4 respectively.
P i s 1 = j
C 3 1(A,B,C,D)
C 3 2(A,B,C,D)
C 2 (A,B,C)
T subgroup of T d
E
χ i ( j ) T j s 1
A 1 T j s 1
s 1
s 1 , s 4 , s 2 , s 3
s 1 , s 3 , s 4 , s 2
s 2 , s 3 , s 4
3( s 1
+
s 2
+
s 3
+
s 4 )
T T j s 1
3 s 1
0
0
s 2 ,
s 3 ,
s 4
3 s 1
s 2
s 3
s 4
T T j ( s 1
+
s 3 )
3( s 1
+
s 3 )0
0
( s 3
+
s 1 ),
( s 2
+
s 4 ),
( s 4
+
s 2 )
( s 1
s 2
+
s 3
s 4 )
T T j ( s 1 +
s 4 )
3( s 1 +
s 4 )0
0
( s 3 +
s 2 ),
( s 2 +
s 3 ),
( s 4 +
s 1 )
( s 1
s 2
s 3 +
s 4 )
T T j ( s 1 +
s 2 )
3( s 1 +
s 2 )0
0
( s 3 +
s 4 ),
( s 2 +
s 1 ),
( s 4 +
s 3 )
( s 1 +
s 2
s 3
s 4 )
 
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