Renato Colle

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.

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.

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.

Correlation correction to the Hartree-Fock total energy of solids. II

A posteriori corrections to the Hartree-Fock total energy of crystalline compounds are obtained with the density functional proposed by Colle and Salvetti [Theor. Chem. Acta 37, 329 (1975)]. Results are presented for diamond, graphite and metallic lithium. For covalent systems, the error on the atomization energy is of the order of 8%, both with small and large basis sets. For metallic lithium the correlation energy is more severely underestimated but the error can be reduced to a few percent using a mixed scheme, which utilizes the CS functional within the ionic sphere, and the Wigner or Ceperley-Alder formula in the interstitial region.

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.

V-N vertical transition of planar ethylene

The V-N vertical transition of planar ethylene has been investigated by means of a large Gaussian basis set, taking into account both the SCF and correlation energies. It is shown that in this case the SCF function, which would lead to a valuation of the Rydberg character at around 80%, does not provide an adequate description of the V state. The correlative effects bring about a lowering of the percentage of the Rydberg character to 38%. The calculated value for the transition energy is in excellent accord with the experimental data.

MQDT analysis of predissociation. I. A two channel problem with semiclassical scattering parameters

Diatomic predissocitaion (case I) is treated in the framework of the multichannel quantum defect theory (MQDT) by adapting the Child and Bandrauk formulation. Analytical expressions are given for the scattering parameters of a two channel problem in terms of WKB phase integrals and of crossing parameters. Resonances in scattering and photoabsorption spectra are identified as the points of steepest rise of an effective phase shift, and analytical expessions are derived for both linewidths and energy shifts. A sample calculation shows the effects of coupling with the Bu20093Σ−u state upon the partial elastic cross section of two oxygen atoms colliding in the 5Πu channel.