Multireference systems, dynamical correlation

In summary, it can be said that multireference Cl methods provide a balanced description of static and dynamic correlation effects. This comes at the cost of a considerably increased computational demand compared to single-reference methods. Nevertheless, a multireference approach is inevitable for systems with a genuine multiconfigurational character such as symmetric transition metal compounds. 

The non-relativistic CASPT2 method developed by Anderson et al. [11,12] is one of the most familiar multireference approaches. It is well established and has been applied to a large number of molecular systems with the non- or quasi-relativistic approaches. Because the CASPT2 method treats dynamic correlation effects pertur-batively, it is less expensive than the multireference Cl (MRCI) method. The... 

The main restriction of the methods discussed in the main part of this chapter is the assumption of a single dominant configuration. This requirement is not met for systems with strong non-dynamical correlation effects such as biradicals (e.g. in bond-breaking situations) or transition metal compounds. In this case the reference function must be a multireference expansion. The fixed-amplitude approximation lends itself very well to a multireference extension of the formalism, as demonstrated first by Ten-no who devised an F12-based internally contracted geminal correction to the multireference MP2 (MRMP2) method. A closely related approach was considered by Torheyden and Valeev, who proposed a generalized perturbative correction to arbitrary wavefunctions and which they applied to a MRCI wavefunction. A spin-free formulation was reported recently.The approach was also used by Booth et al. to get a basis set limit estimate for their full Cl quantum Monte Carlo method, which can also be seen as an approach to tackle systems with multireference character. 

Hamiltonian proposed by Muller and Plesset gives rise to a very successful and efficient method to treat electron correlation effects in systems that can be described by a single reference wave function. However, for a multireference wave function the Moller-Plesset division can no longer be made and an alternative choice of B(0> is needed. One such scheme is the Complete Active Space See-ond-Order Perturbation Theory (CASPT2) developed by Anderson and Roos [3, 4], We will briefly resume the most important definitions of the theory one is referred to the original articles for a more extensive description of the method. The reference wave function is a CASSCF wave function that accounts for the largest part of the non-dynamical electron correlation. The zeroth-order Hamiltonian is defined as follows and reduces to the Moller-Plesset operator in the limit of zero active orbitals ... 

Further developments in F12 theory mainly address three directions (1) Combination with strategies to treat large systems with wavefunction methods, (2) balanced treatment of dynamic and non-dynamic electron correlation in multireference methods, and (3) relativistic effects. 

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