Perturbative Configuration Interaction potential energy calculations

If Fp and Fq (excited state) belong to the same electron configuration the potential energy curves are shifted by an equal amount due to vibronic coupling. Therefore no relative shifts are calculated for these states from first order perturbation theory in which configuration interaction (Cl) is neglected. 

In fact, for tightly localized electron pairs, the dominant excitation level is the value of k nearest "vO.OlN (i.e., for about 200 electrons the double excitations in aggregate are more important than the SCF configuration and for 400 electrons quadruple excitations should dominate). Even for molecules with only 40 electrons quadruple and higher excitations must be considered in order to reproduce excitation energies (30) or potential surfaces to an accuracy of 0.1 eV. Thus, configuration interaction calculations for very large molecules are hopeless unless perturbation theory can be used to correct for unlinked cluster effects. 

Our task is to find approximate solutions to the time-independent Schrodinger equation (Eq. (2)) subject to the Pauli antisymmetry constraints of many-electron wave functions. Once such an approximate solution has been obtained, we may extract from it information about the electronic system and go on to compute different molecular properties related to experimental observations. Usually, we must explore a range of nuclear configurations in our calculations to determine critical points of the potential energy surface, or to include the effects of vibrational and rotational motions on the calculated properties. For properties related to time-dependent perturbations (e.g., all interactions with radiation), we must determine the time development of the... 

Analytic gradient methods became widely used as a result of their implementation for closed-shell self-consistent field (SCF) wavefunctions by Pulay, who has reviewed the development of this topic. Since then, these methods have been extended to deal with all types of SCF wavefunctions, - as well as multi-configuration SCF (MC-SCF), - " configuration-interaction (Cl) wavefunctions, and various non-variational methods such as MoUer-Plesset (MP) perturbation theory - - and coupled-cluster (CC) techniques. - In short, it is possible to obtain analytic energy derivatives for virtually all the standard ab initio approaches. The main use of analytic gradient methods is, and will remain, the location of stationary points on a potential energy siuface, to obtain equilibrium and transition-state geometries. However, there is a specialized use in the calculation of quantities such as dipole derivatives. 

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