The truncated configuration interaction (CI) approximations of the Hamiltonian eigenstates suffer from lack of simultaneous accuracy: If they are orthogonal as a result of optimization of one state, the other states are poorly approximated; and if they are independently optimized, then they cease to be mutually orthogonal. The fact that: Among all functions, orthogonal to an approximate ground state, the one closest to the (unknown) exact first excited state, of the same symmetry, has lower energy than the exact, leads to the conclusion that: Minimizing the energy of a first excited state approximation, orthogonally to an approximate ground state, should be avoided, because it will depart, instead of approaching, the exact first excited state. Further analysis suggests a method to construct CI approximations of the ground and of the first excited state, which are mutually orthogonal and both closer to the exact than the independently optimized (non‐orthogonal) ones.
Scitation: Utilizing the Fact that Among All Trial Functions Orthogonal to an Approximate Ground State,
to the Exact First Excited State,
has lower energy than the Exact: