CASSCF configuration

As pointed out in the introduction, the CASSCF configuration space quickly becomes unmanageably large when the number of active orbitals is increased. While this does not create any serious problems in most applic-... 

The reference states are selected from the CASSCF configurations with a weight greater than 1%. As a but with the threshold 0.25%. 

Balasubramanian and Wang (1989a, b) carried out CASSCF followed by full second-order Cl (SOCI) calculations which included excitations from all CASSCF configurations. They used a (3s3p3dlf) valence Gaussian basis set together with RECPs which retained 4d 5s shells of the Y atom in the valence space. For the hydrogen... 

The construction of the Cl configuration list frequently involves problems in addition to those described above. For example, it will often be the case that a CASSCF configuration space of several thousand CSFs, in conjunction with a large one-particle basis, will generate several million or several tens of millions of CSFs in the SOCI (or CASSCF reference MRCI), making such a Cl calculation impossible. The most common approach is then to truncate the list of reference configurations. 

CASSCF is a version of MCSCF theory in which all possible configurations involving the active orbitals are included. This leads to a number of simplifications, and good convergence properties in the optimization steps. It does, however, lead to an explosion in the number of configurations being included, and calculations are usually limited to 14 elections in 14 active orbitals. 

A CASSCF calculation is a combination of an SCF computation with a full Configuration Interaction calculation involving a subset of the orbitals. The orbitals involved in the Cl are known as the active space. In this way, the CASSCF method optimizes the orbitals appropriately for the excited state. In contrast, the Cl-Singles method uses SCF orbitals for the excited state. Since Hartree-Fock orbitals are biased toward the ground state, a CASSCF description of the excited state electronic configuration is often an improvement. 

Table 4.3 Number of configurations generated in a [ , ]-CASSCF wave function...

It should be noted that CASSCF methods inherently tend to give an unbalanced description, since all the electron correlation recovered is in die active space, but none in the inactive space, or between the active and inactive electrons. This is not a problem if all the valence electrons are included in the active space, but this is only possible for small systems. If only part of die valence electrons are included in the active space, the CASSCF methods tend to overestimate the importance of biradical structures. Consider for example acetylene where the hydrogens have been bent 60° away from hnearity (this may be considered a model for ort/zo-benzyne). The in-plane jt-orbital now acquires significant biradical character. The true structure may be described as a hnear combination of the three configurations shown in Figure 4.11. 

The structure on the left is biradical, while the two others are ionic, corresponding to both electrons being at the same carbon. The simplest CASSCF wave function which qualitatively can describe this system has two electrons in two orbitals, giving the three configurations shown above. The dynamical correlation between die two active electrons will tend to keep them as far apart as possible, i.e. favouring the biradical structure. Now... 

Cl methods [21] add a certain number of excited Slater determinants, usually selected by the excitation type (e.g. single, double, triple excitations), which were initially not present in the CASSCF wave function, and treat them in a non-perturbative way. Inclusion of additional configurations allows for more degrees of freedom in the total wave function, thus improving its overall description. These methods are extremely costly and therefore, are only applicable to small systems. Among this class of methods, DDCI (difference-dedicated configuration interaction) [22] and CISD (single- and double excitations) [21] are the most popular. 

In a recent comprehensive study at the CASSCF level of ab initio theory, Cave and lohnson have carried out calculations for all six rotamers of the hexatriene radical cation. In agreement with experiment they found that the first excited state is hardly affected by the additional interactions which prevail in partially cA-configurated rotamers, whereas the energy of the second excited states decreases as the number of those cA-interactions increases. On this basis, they were able to confirm some of the original assignments of the observed spectra305 but proposed revisions for some of the others. 

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