Ab Initio Multireference Approaches

Because the contribution of the external orbitals to the correlation energy is neglected, this missing dynamic correlation can be essentially recovered in two ways multireference configuration interaction (MRCI) or multireference perturbation theory (MRPT) approaches [53]. 

The most popular way of including dynamic correlation upon a CASSCF reference wave function [54-57] is the second-order perturbation theory (CASPT2) developed by Roos and coworkers [58]. However, in contrast to the single-configurational case, where the definition of the zeroth-order Hamiltonian is universal and taken as the sum of the one-electron Fock operators, the generalization of the zeroth-order Hamiltonian to the multiconfigurational case is not straightforward [59, 60]. A different, theoretically more justified approach is to 

The generalized valence bond (GVB) approach was one of the first methods where semilocalized orbitals, as developed by Coulson and Fischer, have been employed to polyatomic molecules [66-72]. GVB is typically applied within a restricted formulation introducing two simplifications for the construction of the VB structures (for a simple diatomic molecule AB, there are two VB structures the so-called ionic structures, and A B+, and a covalent structure, A-—B). In 

Typically, GVB-PP calculations are carried out within an orthogonal orbital basis, which is called the strong orthogonality constraint. This second simplification ensures that all orbitals are orthogonal to each other unless they are singlet paired. However, the strong orthogonality constraint was simply introduced for 

So far, we focused on conventional quantum chemical approaches that approximate the FCI wave function by truncating the complete N-particle Hilbert space based on predefined configuration selection procedures. In a different approach, the number of independent Cf coefficients can be reduced without pruning the FCI space. This is equivalent to seeking a more efficient parameterization of the wave function expansion, where the Cl coeflBcients are approximated by a smaller set of variational parameters that allow for an optimal representation of the quantum state of interest. Different approaches, which we will call modern solely to distinguish them from the standard quantum chemical methods, have emerged from solid-state physics. 

---