Orbital active space

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 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... 

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. 

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 ... 

RASSCF calculations with large (27 orbitals) active spaces, all terms included. For clusters with n > 1 the calculations carried out on FHF with the geometry distorted to emulated larger cluster. 

AMPAC. Version 6.0, 1997. 7204 Mullen, Shawnee, KS 66216. In this approach, a subset of electronic configurations is selected using perturbation theory fi-om the list generated by a full configuration interaction over a defined window of molecular orbitals (active space). 

For saturated alkyl radical reactions, a simple 2 electron, 2 orbital active space is sufficient. For more complex radicals, such as resonantly stabilized radicals, it is important to include additional orbitals, such as the full set of n orbitals, in the active space. In the case of electronically degenerate radicals, it is again generally necessary to employ state averaged wavefunctions. 

The offending spherical harmonic contributions described by Fertig and Kohn [14] do not occur in the MCHF calculation of the density function, whatever the maximum /-value of the orbital active space [3]. 

CC2, CCS, etc.) can be devised offering a good balance between cost and accuracy. Other simple (second-order) perturbative approaches that are comparable to CC2 can be found in the ADC(2) [19] or CIS(D) [20] methods. As is the case for TDDFT, these linear response or propagator formulations are not only interesting from a formal perspective (by allowing one to obtain information from the excited states based on ground-state quantities) but also because of their black box nature, that is, one does not need to construct a complicated, multi-reference wavefunction via the definition of orbital active spaces. However, as we shall see, the restriction to closed-shell references somewhat limits their applicability to the actinides. 

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