Question

The allyl cation C3H5+ has 2Pi electrons. Solving the Huckel MO secular equation yield E= {a+(sqrt2)*B,a,-(sqrt2)*B}

a) write the secular determinant

b) recalling that b,0, sketch the orbital energy diagram and fill in the Pi electrons. Indicate clearly which one is the HOMO and LUMO

c) in terms of a and B what does the HMO theory predict the HOMO-LUMO gap in allyl cation to be ?

d) what is the total energy of the molecule (in terms of a and b) ?