Configuration interaction symmetry basis

The other approach most frequently used to describe a correlated wavefunction beyond the independent-particle model is based on configuration interaction (Cl). (If the expansion is made on grounds of other basis sets, the approach is often called superposition of configurations, SOC, in order to distinguish it from the Cl method.) According to the general principles of quantum mechanics, the exact wavefunction which is a solution of the full Hamiltonian H can be obtained as an expansion in any complete set of basis functions which have the same symmetry properties ... 

Quadratic Configuration Interaction with Singles and Doubles Quadratic Configuration Interaction with Singles, Doubles, and Noniterative Approximation of Triples Symmetry Adapted Cluster-Configuration Interaction Split-Valence basis set plus Polarisation functions Zero-Order Regular Approximation Zero-Point Energy... 

Predictions can be made about the suitability of different system trajectories on the basis of orbital symmetry conservation rules (207). The most suitable trajectory is an approximation to the reaction path of the reaction under study. The rules can also yield information about the possible structure of the activated complex. The correlation diagram technique has been improved in a series of books by Epiotis et al. (214-216). The method is based on self-consistent field-configuration interaction or valence bond (SCF-CI or VB) (including ionic structures) wave functions. Applications on reactions in the ground states as well as in the excited electronic states are impressive however, the price to be paid for the predictions seems to be rather high. 

Applying this projector on each of the terms of a rotational configuration interaction expansion, built up on the basis of the double free rotor solutions, the symmetry eigenvectors are obtained [21,22,34]. 

The configuration-interaction representation of the lower-energy states of an atom is the IV-electron analogue of the Sturmians in the hydrogen-atom problem. We choose an orbital basis of dimension P, form from them a subset of all possible A/ -electron determinants pk),k = 0,Mp, and use these determinants as a basis for diagonalising the IV-electron Hamiltonian. It may be convenient first to form symmetry configurations kfe) from the pfe). 

In general the observed ion states can be grouped into symmetry manifolds, characterised by the quantum numbers /,/ We consider each symmetry manifold separately. The configuration-interaction basis for the target consists of symmetry configurations r), which are linear combinations, with symmetry /,y, of determinants formed from the set of orbitals a). 

We have used a new seven-dimensional ab initio PES in which the CH3 group retains Csv symmetry and fixed CH bond lengths in our time-dependent calculations. [52] The energy near the minimum energy path (MEP) is described by a basis set corrected calculation using the quadratic configuration interaction treatment with all single and double excitations (QCISD) ... 

No improvement is obtained by replacing pure ji electron calculations by an all-electron SCF treatment thus, the assumption of a GMS potential can hardly be responsible for the failure of the theory. Furthermore, the theoretical predictions are not significantly altered by a configuration interaction limited to the 2pn orbital basis 59,83,84,85) oniy by combining the o- -o excitations and n+n excitations with the same symmetry properties can one succeed in reducing the 7z+n transition energy 86,87,88) Therefore, a satisfactory ah initio theory of spectra will probably need to go beyond the cr—n separation (see Sect. 6.4). 

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