Active molecular orbitals, MCSCF methods

An MCSCF calculation in which all combinations of the active space orbitals are included is called a complete active space self-consistent held (CASSCF) calculation. This type of calculation is popular because it gives the maximum correlation in the valence region. The smallest MCSCF calculations are two-conhguration SCF (TCSCF) calculations. The generalized valence bond (GVB) method is a small MCSCF including a pair of orbitals for each molecular bond. 

When the HF wave function gives a very poor description of the system, i.e. when nondynamical electron correlation is important, the multiconfigurational SCF (MCSCF) method is used. This method is based on a Cl expansion of the wave function in which both the coefficients of the Cl and those of the molecular orbitals are variationally determined. The most common approach is the Complete Active Space SCF (CASSCF) scheme, where the user selects the chemically important molecular orbitals (active space), within which a full Cl is done. 

A conceptually straightforward improvement on the CI approximation is to reoptimize the molecular orbitals for a truncated CI expansion. This approach is called multi-configuration self-consistent field method (MCSCF) and its most prominent variant is the complete active space SCF method (CASSCF) [64]. In the first generation of MCSCF methods [65, 66], the CI coefficients C/ in Eq. 

Normally these molecular orbitals are obtained as expansions in a set of atom-centred basis functions (the linear combination of atomic orbitals (LCAO) method), m being the number of such functions. Recently, two-dimensional numerical integration methods have been developed to solve the MCSCF equations for linear molecules. The dimension m is then, in principle, infinite (practice, it is determined by the size of the grid used in the numerical integration). The molecular-orbital space is further divided into three subspaces the inactive, the active and the external orbitals. The inactive and active subspaces constitute the internal (occupied) orbital subspace, while the external orbitals are unoccupied. The CASSCF wavefunction is formed as a linear combination of configuration state functions (CSFs) generated from these orbitals in the following way. 

The MCSCF method is not a black-box method and cannot easily be applied by nonspecialists. The optimized MCSCF state should always be inspected carefully to ensure that it properly represents the desired electronic state. Nevertheless, the MCSCF model is a highly flexible one and it still constitutes the only approach that, in a balanced manner, can describe bond breakings and molecular dissociation processes, where an unbiased treatment of several electronic configurations is required. The small numbo- of active orbitals that can be treated in MCSCF theory usually makes it impossible to treat dynamical correlation and only a qualitatively correct description of the electronic system can therefore be expected. 

---