Ab Initio Single-Reference Approaches

The simplest way of truncating the complete set of electronic configurations is to include those Slater determinants in the Cl expansion that differ by one, two, three, and so on spin orbitals compared to some reference configuration Oq. Truncated Cl expansions then are linear combinations of the reference determinant and aU singly, doubly, triply, and so on excited configurations. For instance, the Cl singles doubles (CISD) wave functions can be written as 

A different representation of the FCI wave function is obtained from the coupled cluster (CC) theory [25-27], where the CC wave function is expressed by means of an exponential function of the duster operator T, 

If the single-determinant model is a good approximation of the exact solution, the single-reference CC expansion, for which fl o is the Hartree-Fock determinant, is a convenient parameterization of the FCI coefficients. For open-shell molecules that exhibit a non-negligible multireference character, the standard single-reference CC approach should not yield reliable electronic energies and its multireference extensions should be employed instead [26-29]. Nevertheless, the unrestricted CC variant was shown to capture some of the multireference character [30]. 

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