Single-reference configuration interaction expansion

SINGLE REFERENCE BRILLOUIN-WIGNER CONFIGURATION INTERACTION EXPANSION... 

Full configuration interaction does scale linearly with the size of the system but is only computationally tractable for small systems described by small basis sets. In practice, the configuration interaction expansions must be truncated. Truncation is effected by including only states which are singly and doubly excited with respect to some reference configuration(s). Shavitt continues... 

Configuration interaction (Cl) is conceptually the simplest procedure for improving on the Hartree-Fock approximation. Consider the determinant formed from the n lowest-energy occupied spin orbitals this determinant is o) and represents the appropriate SCF reference state. In addition, consider the determinants formed by promoting one electron from an orbital k to an orbital v that is unoccupied in these are the singly excited determinants ). Similarly, consider doubly excited (k, v,t) determinants and so on up to n-tuply excited determinants. Then use these many-electron wavefimctions in an expansion describing the Cl many-electron wavefunction [Pg.13]

The second step of the calculation involves the treatment of dynamic correlation effects, which can be approached by many-body perturbation theory (62) or configuration interaction (63). Multireference coupled-cluster techniques have been developed (64—66) but they are computationally far more demanding and still not established as standard methods. At this point, we will only focus on configuration interaction approaches. What is done in these approaches is to regard the entire zeroth-order wavefunc-tion Tj) or its constituent parts double excitations relative to these reference functions. This produces a set of excited CSFs ( Q) that are used as expansion space for the configuration interaction (Cl) procedure. The resulting wavefunction may be written as... 

An alternative method, named internally contracted Cl, was suggested by Meyer and was applied by Werner and Reinsch in the MCSCF self-consistent electron-pair (SCEP) approach. Here only one reference state is used, the entire MCSCF wavefunction. The Cl expansion is then in principle independent of the number of configurations used to build the MCSCF wavefunction. In practice, however, the complexity of the calculation also strongly depends on the size of the MCSCF expansion. A general configuration-interaction scheme which uses, for example, a CASSCF reference state, therefore still awaits development. Such a Cl wavefunction could preferably be used on the first-order interacting space, which for a CASSCF wavefunction can be obtained from single and double substitutions of the form ... 

A further restriction on the use of many-body perturbation techniques arises from the (quasi-) degenerate energy structure, which occurs for most open-shell atoms and molecules. In these systems, a single reference state fails to provide a good approximation for the physical states of interest. A better choice, instead, is the use of a multi-configurational reference state or model space, respectively. Such a choice, when combined with configuration interactions calculations, enables one to incorporate important correlation effects (within the model space) to all orders. The extension and application of perturbation expansions towards open-shell systems is of interest for both, the traditional order-by-order MBPT [1] as well as in the case of the CCA [17]. 

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