Complete active space SCF, CASSCF

Some molecular species are not calculated properly by straightforward model chemistries these include singlet diradicals and some excited state species. For these the standard method is the complete active space approach, CAS (CASSCF, complete active space SCF). This is a limited version of configuration interaction, in which electrons are promoted from and to a carefully chosen set of molecular orbitals. 

MCSCF (multi-configuration SCF) methods are Cl in which not only the coefficients of the linear combination are optimized but also the MOs from which the excited configurations are constructed. Usually, the MOs are divided into active (FOs and some other nearby MOs) and inactive. If all the configurations generated from the active orbitals are taken into consideration, the model is called CASSCF (complete active space SCF).24... 

In Table 4.8 the lOTC CASSCF (complete active space SCF) and lOTC CASPT2 (CAS second-order perturbation theory) results have been compared with the corresponding nonrelativistic data. The ionization potential corresponding to the creation of a hole in the /-the orbital of a closed shell 2A -electron system was... 

If it were possible to carry out full Cl calculations (cf. Eq. [4] and the paragraph that follows it), artifactual symmetry breaking would, of course, not occur. Moreover, the variational principle would ensure that pure spin states were obtained, irrespective of whether one started with ROHF or UHF MOs, because in a full Cl calculation, the nature of the starting MOs is irrelevant. Although full Cl calculations are rarely practical, perhaps one might hope to reap some of their benefits without paying the entire cost. A method based on this idea is the so-called CASSCF (complete active space SCF) procedure. ... 

The equilibrium NH bond distance re(NH) = 1.038 to 1.043 A [18, 27 to 29] was calculated in ab initio studies at the MP2 (second-order Moller-Plesset perturbation theory) [27, 29], single-double Cl (configuration interaction) [18], and CASSCF (complete active space SCF) [28] levels. 

Of course, a proper treatment would utilize multireference methods, but these are very time consuming and limited to model stmctures only [36, 88). Furthermore, dynamic electron correlation is also very important in these reactions so that, for instance, simple CASSCF (complete active space SCF) computations are meaningless, as they mostly include static correlation. Perturbative corrections to CASSCF wavefunctions such as CASPT2 (CAS perturbation theory of second order) are necessary however, multireference perturbation methods do not improve significantly the singlet-triplet energy separations of many biradicals as compared to CASSCF results [89]. 

Roos B O, Taylor P R and Siegbahn P E M 1980 A complete active space SCF method (CASSCF) using a density matrix formulated super-CI approach Chem. Phys. 48 157-73... 

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. 

With regard to the former, one would like to include as many important configurations as possible. Unfortunately, the definition of an important configuration is often debatable. One popular remedy is the full-valence complete active space SCF (CASSCF) approach in which configurations arising from all excitations from valence-occupied to valence-virtual orbitals are chosen. [29] Since this is equivalent to performing a full Cl within the valence space, the full-valence CASSCF method is limited to small systems. Nevertheless, the CASSCF approach using a well-chosen (often chemically motivated) subspace of the valence orbitals has been shown to yield a much improved depiction of the wave function at all points on a potential surface. Furthermore, the choice of an active space can be adjusted to describe excited state wave functions. 

We shall not perform the somewhat elaborous calculation of the MC wave function in detail. A somewhat simpler example is the dissociation of a double bond and it is given as an exercise (exercise 2). Here we only note that the number of configuration state functions (CSF s) will increase very quickly with the number of active orbitals. In most cases we do not have to worry about the exact construction of the MC wave function that leads to correct dissociation. We simply use all CSFs that can be constructed by distributing the electrons among die active orbitals. This is the idea behind the Complete Active Space SCF (CASSCF) method. The total number of such CSFs is for N2 175 for a singlet wave function. A further reduction is obtained by imposing spatial symmetry. All these CSFs are not included in a wave... 

Multiconfiguration SCF (MCSCF) Theory and Complete Active Space SCF (CASSCF) Theory... 

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