Multiconfigurational treatment

In order to determine a transition probability, one usually uses a standard amplitude approach. Each of the theoretical approaches to calculation of transition probabilities contains critical factors (configuration interaction or multiconfiguration treatment, spectroscopic coupling schemes and relativistic corrections, exchange-correlation corrections, convergence of results and of the dipole length and velocity forms, accuracy of transition energies, etc.) which need to be adequately taken care of to obtain reliable results (look details in Refs. [2-5]). 

The molecular orbital (MO) is the basic concept in contemporary quantum chemistry. " It is used to describe the electronic structure of molecular systems in almost all models, ranging from simple Hiickel theory to the most advanced multiconfigurational treatments. Only in valence bond (VB) theory is it not used. Here, polarized atomic orbitals are instead the basic feature. One might ask why MOs have become the key concept in molecular electronic structure theory. There are several reasons, but the most important is most likely the computational advantages of MO theory compared to the alternative VB approach. The first quantum mechanical calculation on a molecule was the Heitler-London study of H2 and this was the start of VB theory. It was found, however, that this approach led to complex structures of the wave funetion when applied to many-electron systems and the mainstream of quantum ehemistry was to take another route, based on the success of the central-field model for atoms introduced by by Hartree in 1928 and developed into what we today know as the Hartree-Foek (HF) method, by Fock, Slater, and co-workers (see Ref. 5 for a review of the HF method for atoms). It was found in these calculations of atomic orbitals that a surprisingly accurate description of the electronic structure could be achieved by assuming that the electrons move independently of each other in the mean field created by the electron cloud. Some correlation was introduced between electrons with... 

Makri N, Miller WH (1987) Time-dependent self-consistent (TDSCF) approximation for a reaction coordinate coupled to a harmonic bath Single and multiconfiguration treatments. J Chem Phys 87 5781... 

The various response tensors are identified as terms in these series and are calculated using numerical derivatives of the energy. This method is easily implemented at any level of theory. Analytic derivative methods have been implemented using self-consistent-field (SCF) methods for a, ft and y, using multiconfiguration SCF (MCSCF) methods for ft and using second-order perturbation theory (MP2) for y". The response properties can also be determined in terms of sum-over-states formulation, which is derived from a perturbation theory treatment of the field operator — [iE, which in the static limit is equivalent to the results obtained by SCF finite field or analytic derivative methods. 

Our study has been restricted to molecules containing only first-row atoms and with wavefunctions dominated by one determinant. Molecules such as 03 are less accurately described, with an error of about 10 kJ/mol at the CCSD(T) level of theory. For such multiconfigurational systems, more elaborate treatments are necessary and no programs are yet available for routine applications. As we go down the periodic table, relativistic effects become more important and the electronic structures more complicated. Therefore, for such systems it is presently not possible to calculate thermochemical data to the same accuracy as for closed-shell molecules containing first-row atoms. Nevertheless, systems with wave-functions dominated by single determinant are by far the most abundant and it is promising that the accuracy of a few kJ/mol is obtainable for them. 

This is, of course, the approach used by all of the early VB workers. In more recent times, after computing machinery allowed ab initio treatments, this is the sort of wave function proposed by Balint-Kurti and Karplus[34], which they called a multi structure approach. The present author and his students have proposed the multiconfiguration valence bond (MCVB) approach, which differs from the Balint-Kurti-Karplus wave function principally in the way the , are chosen. 

For a reaction adequately described by just two configurations, reactant and product, the analysis of substituents effects is straightforward and was first treated by Horiuti and Polanyi (1935) almost 50 years ago. Subsequent contributions by Bell (1936) and Evans and Polanyi (1938) have led to these general ideas being jointly termed the Bell-Evans-Polanyi principle (Dewar, 1969). The treatment of multiconfiguration reactions is analogous and is illustrated in Fig. 12. Let us discuss this in detail. 

An analysis in terms of VB structures (see exercise 3) shows that this configurational mixing corresponds to approximately 40% diradical character in the wave function for ozone. The RHF wave function, on the other hand, contains only 12% of the diradical VB structure (the result was obtained using Hiickel values for the coefficients of the orbitals (2 11)). It is clear from these considerations that a correct treatment of the electronic structure for the ozone molecule must be based on a multiconfigurational wave function. 

There are some theoretical studies concerning the stability of 1,2-dithietenes and ethane-1,2-dithiones <1996IJQ859>. The valence isomerization of a series of 1,2-dithietes 19 to the open-chain dithiones 20 was studied by CASSI multiconfiguration methods, including the CASPT2 perturbational treatment <1996IJQ859>. 

---