Question

2. In the LCAO method for Hy, it has been suggested to use the muclear charge Z as an additional parameter to bring the guess energy E, closer to the true ground-state energy Eo. In this case, the simple hydrogen 1s functions are replaced with vinz (r) and B2 (r) where 2 is now allowed to vary. If we assume that the overlap S can be neglected S 0), then the guess energy E, has the same general form E, CA+CHAA + 2C1CAHAB C+C Now, in addition to the two conditions dE,/dCA = 0 and dE,/dCn0, a third condition dE/dZ be included as part of the minimization condition. 0 would Thinking carefully about which factors in the expression for E, depend on Z. derive an expression for de/d2 Note that you do not need to do any integrals or introduce any explicit expressions for Is orbitals. Just leave your answer in terms of Ca. Ca. HAA. Han, and any nonzero derivatives of these quantities

Answer 1