Fully optimized reaction space

One of the problems that the early applications of the MCSCF method faced was the construction of the wave function. It was necessary to keep it short in order to make the calculations feasible. Thus, one had to decide beforehand which where the most important CSFs to include in the Cl expansion. Even if this is quite simple in a molecule like H2 it quickly becomes ambiguous for larger systems. However, the development of more efficient techniques to solve large Cl problems made another approach possible. Instead of having to choose individual CSFs, one could choose only the orbitals that were involved and then make a full Cl expansion in this (small) orbital space. In 1976 Ruedenberg introduced the orbital reaction space in which a complete Cl expansion was used (in principle). All orbitals were optimized—the Fully Optimized Reaction Space— FORS [21]. 

A special case of full Cl is the complete active space self-consistent field (CASSCF) or fully optimized reaction space (FORS) approach in which one defines an active space of orbitals and corresponding electrons that are appropriate for a chemical process of interest [20]. The FORS wavefunction is then obtained as a linear combination of all possible electronic excitations (configurations) from the occupied to the unoccupied (virtual) orbitals in the active space, so a FORS wavefunction is a full Cl within the specified active space. Since a full Cl provides the exact wavefunction for a given atomic basis, there is no need to re-optimize the component molecular orbitals. On the other hand, a FORS wavefunction generally corresponds to an incomplete Cl, in the sense that only a subset of configuration (or determinant) space is included. Therefore, one also optimizes the molecular orbital coefficients to self-consistency. The calculation of a full Cl wavefunction is extremely computationally demanding, scaling exponentially with... 

EL-HAV = Eisenschitz, London-Hirschfelder, Amos, Van der Avoird FORS = fully optimized reaction space IMPT = intermolecular perturbation theory JS = Jeziorski-Kolos LCD = localized charge distribution MK = Morokuma-Ki-taura MS-MA = Murrell. Shaw-Musher, Amos RS-PT = Rayleigh-Schrodinger perturbation theory RVS = reduced variational space SA = symmetry-adapted perturbation theory SNOPT = symmetric non-orthogonal perturbation theory SRS = symmetrized Rayleigh-Schrddinger. 

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