for virtual (ε v ) and core (ε c ) MO eigenvalues, computed using occupancies n v = 1/2 = n c . In this and subsequent equations, we will use the notation ε r (n c , n v ) to mean the Kohn-Sham eigenvalue for MO ψ r , obtained from an SCF calculation that employs occupancies n c and n v for the core and virtual orbitals, respectively. (We assume spinorbitals in this notation so 0 < n c ≤ 1 and 0 ≤ n v ≤ 1.) As seen in examples below, it may be the case that n v = n c , although this will create a charged excitation. The simple STM in eq 4 is known to overestimate excitation energies. This observation motivated a generalization in which the fractional-electron SCF calculation is mixed with a calculation involving a full core hole, which can be understood as a higher-order extension of Slater's method. For excitation energies, this generalized (G)STM takes the form