$C_{2v}$ point group

$E_1{c}_2,{}_{in},{}_{yz}$

${}_{4}longrightarrow{A}_1$longleftarrow$++-$

${}_{3}longrightarrow{B}_1$larr$+-+-$

${}_{2}longrightarrow{A}_2$longleftarrow$++--$

$+-+-$

For every molecular obbital, we will find charaders according to $C_{2v}$ symmetiy. Then

find the possible possages:

${}_{1,3},{}_{1,4},{}_{2,3},{}_{2,4}$

We will we the following formula:

Exuple for ${}_{2,3}$ passege ${}_{2,3}$ Pasege ${?}_{(})$

$=A_{-}^{B_2}(B_2{B}_2)(A_2{A}_2)=A_1$ inided state

$IS{B}_2$

${}_{2,3}=A_2{B}_2=B_1$ exuited state

$x$ dirction $=B_1{B}_1=A_1$ orly permitted $inx$ drecectron$-$

$y$ direction $=B_1{B}_2=A_2$

$2$ dinction $=B_1{A}_1=B_1$

For a possage to be pemitted it has to be in $A_1$ choracter.

$(2)$ Firom the painitted passeges find the UV spectrem fo:

From the permitted passages find the UV spectrum for allyl anion $($propenyl anion$)$ using Q$=\backslash$Psi $\text{'}$ x $$ r$1$ x Qt x dz