C. Transition Potential Methods. As originally formulated, the STM and its generalizations require a separate calculations for each excited state of interest, i.e., for each virtual level ε v into which a fractional electron is promoted. The ∆SCF approach requires the same, with a full electron promoted for each individual state. This is a tedious and inconvenient way to compute an entire spectrum, and promotions beyond the LUMO are prone to variational collapse in the absence of symmetry constraints. Alternatives are to modify the core occupancy (n c ) only, leaving the virtual space empty (n v = 0), or else to promote an electron or fraction of an electron into the LUMO, then use the eigenvalue spectrum from that calculation to estimate excitation energies (∆E = ε v -ε c ). The latter approximation assumes that the potential generated by the LUMO is similar to that generated by the higher-lying virtual orbitals. The widely-used TPM corresponds to the first of these two alternatives, in which no electrons whatsoever are placed in the virtual space. The TPM formula for the lowest excitation energy is