A Multiconfigurational Study

As the accuracy of electron correlation methods is Hmited by the choice of the dimension of the active orbital space, the convergence behavior of the spin density with respect to the size of the active space must be studied to ensure that accurate ah initio spin densities are obtained. Although the CASSCF spin densities were quantitatively converged for medium-sized active orbital spaces, larger active spaces (more than 13 electrons correlated in 13 orbitals) were found to be unstable, that is, active space orbitals have been rotated out of the active space during the MCSCF procedure, while the spin densities started to diverge compared to the smaller sized CASSCF results. 

In this chapter, we reviewed different quantum chemical approaches to determine local quantities from (multireference) wave functions in order to provide a qualitative interpretation of the chemical bond in open-shell molecules. Chemical bonding in open-shell systems can be described by covalent interactions and electron-spin coupling schemes. For different definitions of the (effective) bond order as well as various decomposition schemes of the total molecular spin expectation value into local contributions, advantages and shortcomings have been pointed out. For open-sheU systems, the spin density distribution is an essential ingredient in the 

As an example of an open-shell transition-metal complex we discussed some of the pitfalls of present-day DFT and CASSCF calculations in determining accurate spin density distributions in open-shell transition-metal complexes. An accurate description of the spin density and of the electronic structure is mandatory for a subsequent qualitative analysis of the chemical bonding. This could only be accomplished by employing the DMRG algorithm to produce an accurate CASCI-type electronic wave function. 

It can thus be anticipated that theoretical research into the description of open-shell molecules, and especially into open-shell Transition-metal complexes and clusters, will continue to be important and successful in the future. 

We gratefully acknowledge financial support by a grant from the Swiss National Science Foundation (project 200020.144458/1). K.B. thanks the Fonds der Chemischen Industrie for a Chemiefonds scholarship. 

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