Active electrons, CASSCF/CASPT2 calculations

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). 

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... 

The complexity of choosing the active space was clear already in the first application of the CASSCF/CASPT2 method to a transition metal [4], The problem was to describe the electronic spectrum of the Ni atom. We present in Table 5-3 the results obtained with different active spaces (from Ref. [4]). Calculations were performed for each state separately. We note first the large errors obtained with the SCF method (open shell restricted SCF). The results are improved with the... 

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. 

We did some preliminary calculations for BCu (which still could be treated with rather large active spaces) with different partitioning of the orbital space in CAS calculations. The notation is (frozen(inactive active n el) for orbital subspaces and n correlated electrons in the active space. The C2v symmetry was used in all computations. For most distances the wave function has definitively a two configuration form. The smallest active space considered is (0000 9331 2000 2 el) in the CASSCF calculation while in the subsequent CASPT2 calculation we used the (6220 3111 2000 2 el) space. The best would be to choose as the active space the valence orbitals of boron (2110) and the 3d,4s and the correlating 4d shell for Cu (5222). 

Theoretical calculations were performed, initially with SCF-Xa-SW methods on a truncated model [16], and later with the complete active space self-consistent field (CASSCF) and mul-ticonfigurational complete active space second-order perturbation theory (CASPT2) methods on the full molecule [15]. The electronic structures from the two calculations were remarkably similar. The CASSCF/PT2 calculations predicted a single, dominant configuration (73%) with (a) (x) (x ) (a ) (8) (5 ). Although the formal bond order is 1.5, the effective bond order, which considers minor configurations that contribute to the ground-state wavefunction, is lower at 1.15. 

---