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We describe a numerically robust strategy for implementing pseudopotentials in a way that is independent of the type of basis set employed. Applications of this method, within a fully optimized gaussian-orbital framework, are illustrated for many small molecules and compared to all-electron calculations determined from the same computer code. The type of bonding studied here includes both ionic and covalent systems and includes atoms from each of the first four rows of the periodic table. In addition to binding energies, structural parameters, electronic structures and vibrational frequencies we compare vibrational intensities (eg Raman and infrared Intensities) obtained from LDA within all-electron and pseudopotential methodologies. In addition to either pseudo-or all-electron calculations the methodology allows one to treat some atoms within an all-electron formalism and other atoms within a full potential …