Ruedenberg principle

All of these models are connected through the Ruedenberg principle, which states that the main part of the energy of the covalent bond between atoms is the lower kinetic energy of the valence electrons as they get more space. This is clear from the energy expression of a particle localized in a one-dimensional box that has a length L (derived in Section 2.2) ... 

In scheme (6) the basis set is optimized by invoking the variation principle for each state considered. For the ground state the optimized values of the even-tempered parameters ao and / o given by Schmidt and Ruedenberg [9] are used. We add the subscript 0 to distinguish ground state values. For the excited state optimal ai and / i values for a sequence of Mi values are determined. 

In 1963, Schwartz (48) emphasised the need to have a systematic scheme for extending basis sets. Ruedenberg and his co-workers (49-50) have recently reiterated this viewpoint. They developed a technique for systematically extending basis sets of the even-tempered type. In this scheme a and 3 are regarded as functions of the number of basis functions, N. This is necessary if the basis set is to be capable, in principle, of approaching a complete set. Specifically, Ruedenberg et al (49-50) proposed the empirical forms... 

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]. 

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