Configuration interaction computational scaling

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... 

The electron correlation problem remains a central research area for quantum chemists, as its solution would provide the exact energies for arbitrary systems. Today there exist many procedures for calculating the electron correlation energy (/), none of which, unfortunately, is both robust and computationally inexpensive. Configuration interaction (Cl) methods provide a conceptually simple route to correlation energies and a full Cl calculation will provide exact energies but only at prohibitive computational cost as it scales factorially with the number of basis functions, N. Truncated Cl methods such as CISD (A cost) are more computationally feasible but can still only be used for small systems and are neither size consistent nor size extensive. Coupled cluster... 

The oscillator strengths obtained for the different transitions studied in the present work with the RQDO methodology, and the use of the two forms of the transition operator, the standard one, and that corrected for core-valence polarization, are collected in Tables 1 to 8, where other data, from several theoretical and experimental sources, have been included for comparative purposes. The former comprise the large-scale configuration interaction performed with the use of the CIVS computer package [19] by Hibbert and Hansen [20] The configuration interaction (Cl) procedure of... 

In the last few years, the improvements in computer hardware and software have allowed the simulation of molecules and materials with an increasing number of atoms. However, the most accurate electronic structure methods based on N-particle wavefunctions, for example, the configuration interaction (Cl) method or the coupled-cluster (CC) method, are computationally too expensive to be applied to large systems. There is a great need for treatments of electron correlation that scale favorably with the number of electrons. 

The second consideration in choosing a method is the level of electron correlation. A range of methods from no electron correlation (Hartree-Fock methods) to full configuration interaction is available however, the more extensive the electron correlation, the more computationally demanding the calculations become. Some electron correlation methods, such as the Mpller-Plesset method, can scale as N5 where N is the number of electrons.45 One can imagine that such methods become impractical for larger model systems. 

Full-scale treatments of correlation effects, found to be necessary to repair some of the known deficiencies of the HF model wavefunction, generally are done by Configuration Interaction theory [l),(5j. With highly developed computer codes it has been found possible to include more than 10s — 10 determinants, either explicitly or implicitly in the wavefunction expansion. Unfortunately, procedures for selecting the most important terms in the Cl expansion have proved to be a source of difficulty, despite successes of Coupled Cluster methods and related schemes (6],[7]. 

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