By using the semiempirical VB theory described in Chapter 3, setting the sum of orbital energies to zero (Eq. 3.35) and neglecting squared overlap terms, derive the expression of the reduced Hamiltonian matrix element, in Equation 6.30, between $\boldsymbol{R}$ and $\boldsymbol{P}$ for the 3-orbital, 3-electrons reacting system $\left[\mathrm{H}_{\mathrm{a}} \ldots \mathrm{H}_{\mathrm{b}} \ldots \mathrm{H}_{\mathrm{c}}\right]^*$. From the sign of this integral, derive the expressions of $\Psi^{\neq}$and $\Psi^*$ in Equations 6.28 and 6.29 . Show that the reduced Hamiltonian matrix element is largest in the collinear transition state geometry, and drops to zero in the equilateral triangular structure.