Z. Physik B 26, 257 -262 (1977) Zeitschrift for Physik B © by Springer-Verlag 1977 A Local Approach to the Computation of Correlation Energies of Molecules Gernot Stollhoff and Peter Fulde Max-Planck-Institut fiir FestkSrperforschung, Stuttgart, Germany Received November 25, 1976 A new variational approach is introduced for the calculation of correlation energies of molecules. It is based on the local character of the correlated electron motion. Based on the approach we calculate correlation energies for simple systems. These include various Hubbard models as well as a model of the H6-ring for which exact results are available. Our finding is that the proposed approach appears to be simpler and more economical for numerical work than conventional CI-methods. More than 90% of the correlation energy is obtained in all cases considered. I. Introduction One of the outstanding problems in quantum chem- istry is the economical calculation of correlation en- ergies for molecules. Correlation energies include all those energy contributions to the electronic state which result from the correlated motion of the elec- trons except for the Pauli exclusion principle. For describing this correlated motion one has either to go beyond the single particle picture or to make an ansatz for the electronic states which does not have the full symmetry of the Hamiltonian. An example is the Different Orbitals for Different Spins (DODS-)method [1], within which the ansatz for the ground state is not an eigenstate to the total electronic spin. Going beyond the single particle picture is equivalent to an electronic wave function which can not be represented by a single Slater determinant only. A method which aims at calculating the necessary superpositions of Slater determinants for the de- scription of the correlated electronic state is the widely used Configuration interaction (CI-)method [2]. It has been applied predominantly to the calculation of the ground state of atoms and molecules. Such CI-calculations can in principle yield the cor- relation energies to any required accuracy. In prac- tice however the computational efforts become enor- mous even for comparatively small molecules. Several techniques have been designed to reduce those efforts. By introducing suitable approximations and selection criteria one can limit the number of possible Slater determinants which are superposed. We refer to I-3, 4] for further informations on this subject. The aim of this paper is to present a new and promising approach to calculate correlation energies. It is a variational ansatz which is shown to be very economical and sufficiently accurate. Therefore it should be also applicable to larger molecules. Our new approach takes more consequently into account the physical picture of correlated electronic motion than the approaches just described. Therefore let us outline what this physical picture is before we discuss the basic idea for our new method. Correlated electronic motion results from the strong Coulomb repulsion of the electrons. Due to it elec- trons try to avoid each other during their motion in a molecule. While the Pauli principle ensures that elec- trons of equal spin do not come too close to each other (exchange hole), nothing prevents this in a HF- approximation for electrons of opposite spin. Thus this aplSroximation overrates the probabilities of elec- trons approaching each other. A simple and economical approach for treating cor- relations should therefore start out from this local picture of correlations and remedy the shortcoming of the HF-approximation accordingly. From this point of view the CI-methods do not start in an optimal way. By superposing Slater de- terminants constructed out of HF-single particle