Problem 2. [25 points] Suppose that a molecular orbital has the unnormalized form $\psi_1 = 0.727\chi_{1sA} + 0.144\chi_{1sB} = 0.727A + 0.144B$. Find an unnormalized linear combination of the atomic orbitals A and B, $\psi_2 = aA + bB$, which is orthogonal to $\psi_1$. Also determine the normalization constants of $\psi_1$ and $\psi_2$, assuming that the overlap integral $S = 0.117$.