Multiconfigurational approaches

These single reference-based methods are limited to cases where the reference function can be written as a single determinant. This is most often not the case and it is then necessary to use a multiconfigurational approach. Multrreference Cl can possibly be used, but this method is only approximately size extensive, which may lead to large errors unless an extended reference space is used. For example, Osanai et al. [8] obtained for the excitation energy in Mn 2.24 eV with the QCISD(T) method while SDCI with cluster corrections gave 2.64 eV. Extended basis sets were used. The experimental value is 2.15 eV. 

Overall, we seem to find reasons to be hopeful about the possibilities of the RQDO formalism for predicting spectral properties of interest in astrophysics and plasma physics. These reasons rest on the correctness of the resuits so far achieved for F/ and Cl I [20,21], and the low computational expense and avoidance of the numerous convergence probiems which are common in the multiconfigurational approaches. 

The present article is devoted to a discussion of a multiconfiguration approach, the Optimized Basis Set - Generalized Multiconfiguration Spin-Coupled (OBS-GMCSC) method [l]-[2], that can join the flexibility of non-orthogonal orbitals with the use of simultaneously optimized Slater-type basis functions (STFs). 

Rubio, M. Stalring, J. Bernhardsson, A. Lindh, R. Roos, B.O. Theoretical studies of isomers of C3H2 using a multiconfigurational approach. Theor. Chem. Acc. 2000, 105. 15-30. 

We have thus been able to construct a wave function that describes the qualitative behavior of the electronic stmcture for all internuclear distances. The price we have paid is to leave the single configurational description and construct the wave function as a linear combination of several configurations (determinants) with expansion coefficients to be determined by the variational principle together with the molecular orbital coefficients. This is the multiconfigurational approach in quantum chemistry. Before we end this section let us take a look at a more complex chemical bond, that in the Cr2 molecule. 

We could of course have given many more examples where it is necessary to use a multiconfigurational approach to the wave function. A few more will be given at the end of the chapter, but we now turn to the question of how to construct and evaluate multiconfigurational wave functions. 

The DKH Hamiltonian has recently been implemented into the CASSCF/CASPT2 version of the multiconfigurational approach [62]. A two-step procedure is used to account for the relativistic effects... 

B.O. Ross, P.-A. Malmqvist and L. Gagliardi, Heavy element quantum chemistry—the multiconfigurational approach, in E. Brandas, E. Kryachko (Eds.), Fundamental world of quantum chemistry, Kluwer, Dordrecht, 2003, p. 425. 

We have presented results from a theoretical study of the electronic and molecular properties of the PbO molecule. A multiconfigurational approach has been used, which essentially works with non-relativistic wave functions. Relativity is introduced in two steps. First scalar relativistic elfects are included through the use of the Douglas-Kroll Hamiltonian and a correspondingly constructed AO basis set. Spin-orbit effects are included by allowing different CASSCF wave functions to mix under the influence of a spin-orbit Hamiltonian. 

We shall not discuss here in any detail how one proceeds to optimize a CASSCF wave function. The reader is referred to the existing literature. Instead we shall eontinue with some study cases, to illustrate how the multiconfigurational approach is used in practical applications. But, before that, a few words about the remaining error. 

---