Oriano Salvetti

Approximate calculation of the correlation energy for the closed shells

A formula is derived for the approximate calculation of the correlation energy, starting from knowledge of the one-electron and two-electron density matrices, calculated by the Hartree-Fock method.The results that we have obtained in test calculations seem to be accurate enough (average error 2.5%, highest error 8%)

Approximate calculation of the correlation energy for the closed and open shells

A formula is derived for the approximate calculation of the correlation energy of both open and closed shell systems. The formula integrates a functional of the one- and two-electron density matrices, obtained from a wavefunction built up by one or several Slater determinants.Some test calculations on the ground state of diatomic molecules at several internuclear distances and on many excited states of atoms and molecules show the goodness of this method.

A general method for approximating the electronic correlation energy in molecules and solids

A detailed analysis of a method proposed earlier for calculating a good approximation to the electronic correlation energy is presented here. The principal advantages of this method compared to the usual CI techniques are discussed.

SCF‐MO's and Molecular Properties of Methane

SCF‐MOs of the CH4 molecule have been calculated for the experimental geometry by using bases of up to 39 STOs. The best molecular energy obtained is −40.20452 a.u. The ground‐state wavefunctions have been utilized to compute some one‐electron properties, viz., the electric octupole moment, the electric field gradient at the protons, and the diamagnetic susceptibility. In addition, the electric polarizability and the paramagnetic susceptibility have been evaluated using a perturbed H–F calculation.

SCF MO's and Molecular Properties of H2O

SCF MOs of H2O molecule have been calculated for a geometry very close to the experimental one, using a basis set of 29 STOs. The evaluated HF energy is −76.0384 a.u. Several ground‐state one‐electron properties have also been computed, viz., the first three electric multipole moments, electric field and gradient field at the nuclei, electric polarizability, and magnetic susceptibility.

Generalization of the Colle–Salvetti correlation energy method to a many‐determinant wave function

The Colle–Salvetti method for calculating the correlation energy [Theor. Chim. Acta 37, 329 (1975)] is generalized to treat cases in which the reference function not a Hartree–Fock one, but a many‐determinant wave function. Through calculations on atoms and diatomic molecules it is shown that this generalized approach gives the ‘‘experimental,’’ non‐relativistic electronic energy at a millihartree level of accuracy also for internuclear distances far from the equilibrium positions.

SCF MO's and Molecular Properties of Methyl Fluoride

The SCF MOs of CH3F have been calculated by using bases of up to 47 STOs. The best molecular energy obtained is − 139.0612 a.u. The ground‐state wavefunctions have been utilized to compute several observables corresponding to one‐electron operators, viz., the electric dipole, quadrupole, and octopole moments, the electric field gradient at the carbon atom and at the proton, and the diamagnetic part of the susceptibility. In addition, by using the coupled HF perturbation theory, the electric polarizability and the paramagnetic part of the susceptibility have been computed.

An SCF technique for excited states

A method for deriving HF-SCF wave functions for excited states is presented here. All the active orbital transformations that are compatible with the orthogonality requirements are performed without unnecessary restrictions on the variational space and within a direct minimization approach. The method has been tested with an application on the first excited-singlet state of Be.

Calculation of some electronic excited states of formaldehyde

The optimized MOs of several excited states of formaldehyde have been calculated by means of a large basis set of modified Gaussian functions; particular attention has been paid to the π → π* transition. The total energy of the various states has been obtained as the sum of the SCF and correlation energies; the last one has been calculated as a functional of the electronic density. The calculated values for the transition energies are in good agreement with the experiment. A strong interaction of the π → π* state with the continuum is evidentiated; this fact can justify the absence of the π → π* band in the absorption spectrum.

Atoms in molecules. I. A charge conservation rule for taking into account the ‘‘orthogonality hole’’

An ab initio method for treating separately core and valence electrons in large systems by means of a generalized product function is presented here. The orthogonality constraints for each valence orbital with respect to the core orbitals are taken into account by means of an ‘‘orbital charge conservation’’ rule. Core functions and that part of each valence orbital, that is due to the orthogonality hole, are taken directly from atomic or molecular calculations.