Correlated models full configuration interaction

Each cell in the chart defines a model chemistry. The columns correspond to differcni theoretical methods and the rows to different basis sets. The level of correlation increases as you move to the right across any row, with the Hartree-Fock method jI the extreme left (including no correlation), and the Full Configuration Interaction method at the right (which fuUy accounts for electron correlation). In general, computational cost and accuracy increase as you move to the right as well. The relative costs of different model chemistries for various job types is discussed in... 

Configuration Interaction. Provides an account of Electron Correlation by way of explicit promotion (excitation) of electrons from occupied molecular orbitals into unoccupied molecular orbitals. Full configuration interaction (all possible promotions) is not a practical method and limited schemes, for example, CIS, CID and CISD Models, need to be employed. 

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. 

It is well known that the major deficiency of the Hartree-Fock model is its incapacity to account for the correlation effect associated with the motions of electrons of opposite spin. In principle, this contribution can be computed using a full configuration interaction (Cl) method, where the wavefunction corresponds to a variationally optimized combination of all possible electronic configurations. However, the application of this method to molecules of chemical interest can involve a number of configurations which rapidly... 

Figure 4. Double bond dissociation of the water molecule using the perfect pairing (PP), imperfect pairing (IP) and restricted pairing (GVB-RCC) local correlation models, compared to full configuration interaction (FCI) and Hartree-Fock theory in a minimal (STO-3G) basis.

The other approach most frequently used to describe a correlated wavefunction beyond the independent-particle model is based on configuration interaction (Cl). (If the expansion is made on grounds of other basis sets, the approach is often called superposition of configurations, SOC, in order to distinguish it from the Cl method.) According to the general principles of quantum mechanics, the exact wavefunction which is a solution of the full Hamiltonian H can be obtained as an expansion in any complete set of basis functions which have the same symmetry properties ... 

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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