Assessment of the quality of orbital energies in resolution-of-the-identity Hartree-Fock calculations using deMon auxiliary basis sets

The Roothaan-Hartree-Fock (HF) method has been implemented in deMon-DynaRho within the resolution-of-the-identity (RI) auxiliary-function approximatio n. While previous studies have focused primarily upon the effect of the RI approximation on total energies, very little information has been available regarding the effect of the RI approximation on orbital energies, even tho ugh orbital energies play a central role in many theories of ionization and excitation. We fill this gap by testing the accuracy of the RI approximati on against non-RI-HF calculations using the same basis sets, for the occupi ed orbital energies and an equal number of unoccupied orbital energies of f ive small molecules, namely CO, N-2, CH2O, C2H4, and pyridine (in total 102 orbitals). These molecules have well-characterized excited states and so a re commonly used to test and validate molecular excitation spectra computat ions. Of the deMon auxiliary basis sets tested, the best results are obtain ed with the (44) auxiliary basis sets, yielding orbital energies to within 0.05 eV, which is adequate for analyzing typical low resolution polyatomic molecule ionization and excitation spectra. Interestingly, we find that the error in orbital energies due to the RI approximation does not seem to inc rease with the number of electrons. The absolute RI error in the orbital en ergies is also roughly related to their absolute magnitude, being larger fo r the core orbitals where the magnitude of orbital energy is large and smal lest where the molecular orbital energy is smallest. Two further approximat ions were also considered, namely uniterated ("zero-order") and single-iter ation ("first-order") calculations of orbital energies beginning with a loc al density approximation initial guess. We find that zero- and first-order orbital energies are very similar for occupied but not for unoccupied orbit als, and that the first-order orbital energies are fairly close to the corr esponding fully converged values. Typical root mean square errors for first -order calculations of orbital energies are about 0.5 eV for occupied and 0 .05 eV for unoccupied orbitals. Also reported are a few tests of the effect of the RI approximation on total energies using deMon basis sets, although this was not the primary objective of the present work. (C) 2001 American Institute of Physics.