Configuration interaction method efficiency

H.-J. Werner and P.J. Knowles, An Efficient Internally Contracted Multiconfiguration Reference Configuration Interaction Method, J. Chem. Phys. 89, 5803 (1988). 

The relative calculational efficiency of EOM-Green s function methods and conventional configuration interaction methods is a difficult matter to assess, since it is intimately bound to the question of optimization of computer codes. Our major emphasis has been on determining the requirements for an accurate and reliable EOM theory. Of necessity, the program optimization has to an extent taken a back seat to the constant changes introduced in the theory in the course of this work. However, the demonstrated ability to obtain accurate results for the simple ionization potentials of small molecules with very small primary operator spaces bodes well for the EOM method. 

Werner, H.-J., Knowles, P.J. An efficient internally contracted multiconfiguration reference configuration-interaction method, J. Chem. Phys. 1988,89,5803-14. 

An efficient internally contract multiconfiguration-reference configuration interaction method. J. Chem. Phys., 89, 5803-5814 (b) Knowles, P.J. and Werner, H.-J. (1988) An efficient method for the evaluation of coupling coefficients in configuration interaction calculations. Chem. Phys. Lett.,... 

Rhee YM, Head-Gordon M (2007) Scaled second-order perturbation corrections to configuration interaction singles efficient and reliable excitation energy methods. J Phys Chem A 111 5314... 

The idea of coupling variational and perturbational methods is nowadays gaining wider and wider acceptance in the quantum chemistry community. The background philosophy is to realize the best blend of a well-defined theoretical plateau provided by the application of the variational principle coupled to the computational efficiency of the perturbation techniques. [29-34]. In that sense, the aim of these approaches is to improve a limited Configuration Interaction (Cl) wavefunction by a perturbation treatment. 

Recently, quantum chemical computational techniques, such as density functional theory (DFT), have been used to study the electrode interface. Other methods ab initio methods based on Hartree-Fock (HF) theory,65 such as Mollcr-PIcsset perturbation theory,66,67 have also been used. However, DFT is much more computationally efficient than HF methods and sufficiently accurate for many applications. Use of highly accurate configuration interaction (Cl) and coupled cluster (CC) methods is prohibited by their immense computational requirements.68 Advances in computing capabilities and the availability of commercial software packages have resulted in widespread application of DFT to catalysis. 

Complete Cl, or full Cl, is configuration interaction with a configuration list which includes all possible configurations of proper spin and space symmetry in the chosen orbital space. As has been mentioned previously, the number of configurations in complete Cl will depend in an n-factorial way on the number of electrons and the number of orbitals and it will therefore quickly become too large to be handled. This method is therefore not very well suited as a standard model to solve quantum chemical problems. There are, however, two situations where an efficient complete Cl method is useful to have. The first of these is in connection with the CASSCF method which has been described in another chapter. The other is in connection with bench mark tests. Since any other Cl method selects configurations after some principle, a comparison to complete Cl is the way to check these principles out. We will therefore in this section briefly outline the main steps in the complete Cl method as it is carried out today. 

There have also been many more calculations in which geometry optimizations are carried out, and in which the basis sets in SCF calculations have been extended to DZ or DZ+P quality, and more recently one sees an increasing use of methods which include at least some electron correlation, especially via configuration interaction (Cl). Examples of the latter calculation were until recently restricted to molecules containing up to three atoms, but the recent development of efficient Cl programmes had enabled these calculations to be carried out without too great expense on a variety of larger molecules, and this work is referred to later on in this Report. 

As discussed in Chapter 9, the VBCI method provides results that are at par with the BOVB method, the difference being that the electrons of the spectator orbitals are correlated too in the VBCI method. The wave function starts from a VBSCF wave function and augments it with subsequent local configuration interaction that can be restricted to single excitations (VBCIS level), or single and double excitations (VBCISD), or higher excitations. Here, we will consider only the VBCISD level, which is a good compromise between accuracy and cost efficiency. 

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