Double shell effect

The CASSCF/CASPT2 calculations were performed with an active space including the five nd, the (n + l)s, the three (n+ l)p orbitals, and a second set of nd orbitals to account for the double shell effect. The importance of including a second 3d shell in the active space was detected in an early study of the electronic spectrum of the nickel atom [2]. This had already been suggested from MRCI results [1]. The results obtained by RT at about the same time indicated that such effects are effectively accounted for when a method is used that includes cluster corrections to all orders, like the QCI method used by them [3]. This result will hold true also for the less approximate coupled cluster method CCSD(T). 

In the tetrahedral Ni(CO)4 complex we have a formal d10 system and there is no CO to Ni a donation. We therefore need no CO a orbitals in the active space. Instead we add empty orbitals of the same symmetry as the 3d orbitals, e and t2. These orbital will turn out to be a mixture of CO tt orbitals and Cr 3d and thus include the double shell effect. The lOinlO active space turns out to be quite general and can be used for many transition metal complexes. This active space will allow studies of the ground state and ligand field excited states. If charge transfer states are considered, one has to extend the active space with the appropriate ligand orbitals. 

State average orbitals are not optimized for a specific electronic state. Normally, this is not a problem and a subsequent CASPT2 calculation will correct for most of it because the first order wave function contains CFs that are singly excited with respect to the CASSCF reference function. However, if the MOs in the different excited states are very different it may be needed to extend the active space such that it can describe the differences. A typical example is the double shell effect that appears for the late first row transition metals as described above. 

One of the most important correlation effects in transition metal systems is the so-called 3d double-shell effect. This correlation effect appears in particular in... 

Naturally, the double-shell effect should play a less important role for the Co 3d —> 3d transitions. Indeed, the difference between the CASSCF results (Table 1) obtained with or without the 3d shell is much more limited for the d ... 

Before finishing this section, we would like to remind the reader of another trend between different rows of the TM, i.e., the strongly reduced Ad as compared to M double-shell effect (see Sec. 2 and Table 1). The latter trend, together with... 

Lanthanide atoms and ions need the active space 4f, 5s, and 5p, in aU 11 active orbitals (for some elements also 5d has to be added). It is possible that a double shell effect obtains also here for atoms with many 4f electrons. Actinides are the most complicated atoms. The orbitals 5f, 6d, 7s, and 7p have similar energies and are occupied in low lying electronic states. One should, therefore, ideally use 16 active orbitals. Our experience in this part of the periodic table is, however, yet rather limited. 

What bonding mechanism will this active space result in Let us first look at the doubly occupied 3d-orbitals. 8 1 will only interact repulsively with the ring, because the ring rr-orbital of the same symmetry is also occupied. We thus expect a rather isolated orbital and the correlating orbital a will then describe the double-shell effect and also be localized to iron. The orbitals are shown in Figure 6. They have the expected shape. 

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