Orbital active

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. 

Clifford and co-workers [190] have performed complete active space self-consistent field (CASSCF) ab initio calculations on the photocycloaddition reactions of benzene and ethene. An eight-electron, eight-orbital active space involving the ir-orbitals of the benzene and ethene moieties was used. The geometries were optimized using the 4-31G basis set, and the energies were recomputed at the 6-31G level. 

The above best calculation [11] corresponds to the simplest level of the BOVB method, referred to as L-BOVB. All orbitals, active and inactive, are strictly local, and the ionic structures are of closed-shell type, as represented in 10 and 11. However the theory can be further improved, and the corresponding levels are displayed in Table 2. It appears that the L-BOVB/6-31+G level, yields a fair bonding energy, but an equilibrium distance that is rather too long compared to sophisticated estimations. This is the sign of an incomplete description of the bond. Indeed this simpler level does not fully account for the... 

The corresponding reaction with methane has PESs that are rather similar to those described here, so it will not be discussed in detail. It should, however, be pointed out that the description of the MECP in this system appears to have been one of the first such reports for a transition metal system in the literature (77). The study used CASSCF calculations with four electrons in an eight-orbital active space, combined with polarized double-zeta basis sets (77). Dynamic correlation is not very important in this system, partly because Sc+ has only one d electron, so this level of theory produces rather good agreement with experiment for quantities such as the D <— excitation energy, the complexation energy... 

Fig. 25.1. The eight first active orbitals in the water molecule obtained from a CASSCF calculation with these orbitals active and an ANO basis set of the size 0/4s2p2d, H/3s2p.

This is the simplest case. It is usually sufficient to have the valence orbitals active, perhaps with added Rydberg type orbitals for studies of excited states. One can normally leave the ns orbital inactive for main group atoms with more than three np electrons. First row transition metals are, however, more demanding. It has been shown that in order to be able to accurately describe the relative correlation effects in atomic states, which differ in the number of 3d electrons, one needs to use two sets of d-orbitals, 3d and 3d where the second set describes the strong radial correlation effects in the 3d shell [29]. Adding the 4s and 4p orbital one is faced with an active space of 14 orbitals. The importance of the second 3d orbital decreases for second and, in particular, for third row transition metals. 

Energy surfaces for chemical reactions involving three main group atoms can be performed with the 12 valence orbitals active. This will cover all possible reaction channels. Tetra-atomic molecules would need 12-16 orbitals depending on whether the ns orbitals have to be included or not. The problem is of course simplified if one or more of the atoms is hydrogen. Additional active orbitals may be needed for excited states surfaces where Rydberg states may become important. 

The results are shown in Table 25.2. We see that there is agreement between theory and experiment. This is typical for unsaturated hydrocarbons with the ir-orbitals active. 

Geometry optimizations for singlet and triplet nitrene 16 were performed with the standard 6-3IG basis set, using CASSCF(4,4) calculations with a four-electron and four-orbital active space. This active space consisted of two 2p AOs on nitrogen and the highest a and lowest unoccupied a MOs, formed from the two 3 C-C bonds of the cyclopropyl group. 

The procedure above was used in a recent study of the lower excited states of free-base porphin [35]. This molecule has 24 tt orbitals and 24 it electrons. It is clearly impossible to have all these orbitals and electrons active. Therefore, an SDCI-type RASSCF calculation was first performed with the 24 tt orbitals active. The occupation numbers were then used as a guidance in a series of CASSCF/CASPT2 calculations on the excited states. It was possible to increase the active space in a systematic way until the computed excitation energies had converged. There is no guarantee that this is always possible, however. If not, the CASSCF/ CASPT2 method cannot be used to study the electronic spectrum. One... 

For all octahedral molecules presented in Table XVI, the basic 10-orbital active space consists of the metal 3d orbitals, residing in the representations t2g 3d ) and as well as their bonding or antibond-... 

Only the 2t2g CO tt shell is included in the active space used for the calculation of the ligand field states. Thus the 10 orbitals should have to be extended with the other three CO tt shells to be able to calculate the full spectrum using the same active space for all states, ending up with an impossible number of 19 active orbitals. The only alternative is to use different active spaces for different excited states. Denoting the basic (5,6)gg, 2,3)t2g 10-orbital active space as active space A, we decided in favor of the following options ... 

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