IR question on benzene

[dttom]

My question is short, how are the normal modes of stretching of C-H bonds in benzene look like?

I think there are 12 of them, my thinking is:

1) s orbital of H interact with sp2 orbital of C

2) there are 6 pairs of them

3) each pair can either exist in bonding or antibonding

so (A for antibonding; B for bonding):

a) BBBBBB

b) BBBBBA

c) BBBBAA

d) BBBABA

e) BBABBA

f) BBBAAA

g) BABABA

h) AAAABB

i) AAABAB

j) AABAAB

k) AAAAAB

l) AAAAAA

I don't know why, but I think this thinking is wrong, please point it out and illustrate how can I figure out the number of normal mode and how they are look like when a certain molecular is given. Thanks.