Abstract
Chemists are mainly interested in energy differences. In contrast, most quantum chemical methods yield the total energy which is a large number compared to the difference and has therefore to be computed to a higher relative precision than would be necessary for the difference alone. Hence, it is desirable to compute energy differences directly, thereby avoiding the precision problem. Whenever it is possible to find a parameter which transforms smoothly from an initial to a final state, the energy difference can be obtained by integrating the energy derivative with respect to that parameter (c.f., thermodynamic integration or adiabatic connection methods). If the dependence on the parameter is predominantly linear, accurate results can be obtained by single-point integration. In density functional theory (DFT) and Hartree-Fock, we applied the formalism to ionization potentials, excitation energies, and chemical bond breaking. Example calculations for ionization potentials and excitation energies showed that accurate results could be obtained with a linear estimate. For breaking bonds, we introduce a non-geometrical parameter which gradually turns the interaction between two fragments of a molecule on. The interaction changes the potentials used to determine the orbitals as well as constraining the orbitals to be orthogonal.