Interaction correlation energy

Table 3. Interaction correlation energy (in kJ/mole) in van der Waals complexes75 ...

To exactly solve Eq. 1 the iterative Hartree-Fock (HF) procedure is the most widely used. To obtain exact results, a complete (i.e. infinite) basis set and a full Configuration Interactions (Cl) method would be needed. This is unattainable so a finite basis set is used. Methods that evaluate all the integrals needed to solve Eq. 1 are called ab initio methods. The HF method does not consider the instantaneous interaction within pairs of electrons but only an average force. Not considering this instantaneous interaction (correlation energy) may lead to severe errors. Different methods exist to include the correlation energy, the already cited Cl procedure (not at the usually unattainable full level) being the most evident way to overcome this problem. These methods, called post-HF, are quite costly in computational time so that they are restricted to small systems, well beyond the supramolecular level studied here. 

In Ecjuation (3.47) we have written the external potential in the form appropriate to the interaction with M nuclei. , are the orbital energies and Vxc is known as the exchange-correlation functional, related to the exchange-correlation energy by ... 

Cl calculations can be used to improve the quality of the wave-function and state energies. Self-consistent field (SCF) level calculations are based on the one-electron model, wherein each electron moves in the average field created by the other n-1 electrons in the molecule. Actually, electrons interact instantaneously and therefore have a natural tendency to avoid each other beyond the requirements of the Exclusion Principle. This correlation results in a lower average interelectronic repulsion and thus a lower state energy. The difference between electronic energies calculated at the SCF level versus the exact nonrelativistic energies is the correlation energy. 

Configuration interaction (Cl) is a systematic procedure for going beyond the Hartree-Fock approximation. A different systematic approach for finding the correlation energy is perturbation theory... 

Quadratic Configuration Interaction. A general technique for determining electron correlation energies... 

The Parameterized Configuration Interaction (PCI-X) method simply takes the correlation energy and scales it by a constant factor X (typical value 1.2), i.e. it is assumed that the given combination of method and basis set recovers a constant fraction of the correlation energy. 

Pople, J. A. Head-Gordon, M. Raghavachari, K. Quadratic configuration interaction. A general technique for determining electron correlation energies. J. Chem. Phys. 1987, 87, 5968-5975. 

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