MRCI, CASSCF, theory

In practice, one often has to restrict the active space to include only a few of the highest occupied and lowest unoccupied molecular orbitals. The correlation effects not included in the CASSCF calculation can then be recovered by a multireference Cl (MRCI) calculation, in which all single and double excitations from the CASSCF reference are taken into account [27], A computationally more efficient way of including dynamical electron correlation effects is perturbation theory with respect to the CASSCF reference. The most widely employed method of this type is the CASPT2 method developed by Roos and collaborators [28], The CASSCF and CASPT2 methods have been essential tools for the calculations described in this contribution. 

The original procedure (Miertus et al., 1981) was expressed in the restricted Hartree-Fock (HF) formalism. Extensions to other levels of the quantum theory are easy, and there are versions of the PCM program accepting UHF, ROHF, MPn, CASSCF, SDCI, MRCI, and CASSCF-CI levels of quantum molecular theory. The extension to semiempirical quantum methods has been elaborated by several groups. We quote here Miertus et al. (1988) for CNDO methods, and Luque and Orozco (Luque et al., 1993 1995 Negre et al., 1992) for PM3 and AMI version. Both of them follow this approach. The computational codes are of public domain. The PM3 version has been included in MOPAC package (Stewart, 1990). 

Due to the inherent multireference nature of bond-breaking problems, it seems rather unlikely that single-determinant CC methods of any sort will ever provide a satisfactory solution to these problems. It seems much more sensible to use MR approaches to study problems of this sort when they are relevant for a particular chemical application. For small molecules, MRCI offers a suitable option, while CASSCF calculations corrected by perturbation theory are more generally useful for larger systems. 

Our group has already studied all the fluoro-, chloro-and bromo-carbenes [11-16]. We used the complete active space self-consistent field (CASSCF) method as well as complete active space second-order perturbation theory (CASPT2) and multi-reference configuration interaction (MRCI) approaches to compute the geometries, force constants, and vibrational frequencies of the (singlet) X and A states as well as the (triplet) a states. Our theoretical studies of most of these carbenes were carried out specifically to complement LIF studies that were pursued in our laboratories by Kable et al. [6]. In addition to the determination of spectroscopic constants, the spectroscopic and theoretical studies considered dynamics on the A surfaces, i.e. whether photodissociation or internal conversion to the ground state would occur. 

The CV correlation contributions were computed at the MRCI + Dav level of theory using the cc-pwCVQZ basis sets, where the CASSCF reference states were obtained by employing an active space of six electrons in six active orbitals. Unfortunately, MRCI calculations with a full-valence CASSCF reference state with all electrons correlated proved to be too demanding computationally, hence... 

Fig. 1 Distance dependence of SO correction in iodomethylidyne (Cl) computed at MRCI/cc-pVTZ level of theory. The SO Hamiltonians were constructed in bases of 2, 9, 18 and 36 electronic states, as indicated and as discussed in text. One set of results obtained at the CASSCF level is shown for comparison broken line)...

ABSTRACT. Recent advances in electronic structure theory and the availability of high speed vector processors have substantially increased the accuracy of ab initio potential energy surfaces. The recently developed atomic natural orbital approach for basis set contraction has reduced both the basis set incompleteness and superposition errors in molecular calculations. Furthermore, full Cl calculations can often be used to calibrate a CASSCF/MRCI approach that quantitatively accounts for the valence correlation energy. These computational advances also provide a vehicle for systematically improving the calculations and for estimating the residual error in the calculations. Cdculations on selected diatomic and triatomic systems will be used to illustrate the accuracy that currently can be achieved for molecular systems. In particular, the F-I-H2 - HF+H potential energy hypersurface is used to illustrate the impact of these computational advances on the calculation of potential energy surfaces. 

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