Multiconfiguration method

Nonrelativistic quantum chemistry has been discussed so far. But transition metal (starting already from the first row) and actinide compounds cannot be studied theoretically without a detailed account of relativity. Thus, the multiconfigurational method needs to be extended to the relativistic regime. Can this be done with enough accuracy for chemical applications without using the four-component Dirac theory Much work has also been done in recent years to develop a reliable and computationally efficient four-component quantum chemistry.25,26 Nowadays it can be combined, for example, with the CC approach for electron correlation. The problem is that an extension to multiconfigurational... 

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>. 

A. Banerjee, F. Grein, Int. J. Quant. Chem. 10, 123 (1976). Convergence Behavior of Some Multiconfiguration Methods. 

The original Heitler-London treatment with its various extensions was a VB treatment that included several configurations, e.g., the total wave function is a sum of terms with spatial functions made up of different subsets of the orbitals. This is the essence of multiconfiguration methods. The most direct extension of this sort of approach is, of course, the inclusion of larger numbers of configurations and the application to larger molecules. The computational power allowed calculations of this sort. 

Jensen KP, Roos BO, Ryde U (2005) 02-binding to heme electronic structure and spectrum of oxyheme, studied by multiconfigurational methods. J Inorg Biochem 99 45-54... 

Grafenstein J, Cremer D (2000) The combination of density functional theory with multiconfigurational methods - CAS-DFT, Chem Phys Lett, 316 569-577... 

While the multiconfiguration methods lead to large and accurate descriptions of atomic states, formal insight that can lead to a productive understanding of structure-related reaction problems can be obtained from first-order perturbation theory. We consider the atomic states as perturbed frozen-orbital Hartree—Fock states. It is shown in chapter 11 on electron momentum spectroscopy that the perturbation is quite small, so it is sensible to consider the first order. Here the term Hartree—Fock is used to describe the procedure for obtaining the unperturbed determi-nantal configurations pk). The orbitals may be those obtained from a Hartree—Fock calculation of the ground state. A refinement would be to use natural orbitals. 

A size-consistent multiconfiguration method is the CAS-MC-SCF, which is a full Cl restricted to an active set of orbitals. 

It is clear from (A.8) and (A.9) that the gradient difference and derivative coupling in the adiabatic representation can be related to Hamiltonian derivatives in a quasidiabatic representation. In the two-level approximation used in Section 2, the crude adiabatic states are trivial diabatic states. In practice (see (A.9)), the fully frozen states at Qo are not convenient because the CSF basis set l Q) is not complete and the states may not be expanded in a CSF basis set evaluated at another value of Q (this would require an infinite number of states). However, generalized crude adiabatic states are introduced for multiconfiguration methods by freezing the expansion coefficients but letting the CSFs relax as in the adiabatic states ... 

CALCULATION OF ELECTRONIC SPECTRA WITH MULTICONFIGURATIONAL METHODS... 

Another simple system will be used to illustrate how multiconfigurational methods are used to describe radicals and at the same time to compute the electronic spectrum of an organic molecule. It is the allyl radical. 

We shall use the allyl radical to illustrate how one can treat planar unsaturated organic molecules using multiconfigurational methods. Some properties of the groimd state will be studied and, in addition, the electronic spectrum. The system has acmally been used as a example in a course given at the Department of Theoretical Chemistry in Lund called Quantum Chemistry at Work and a number of students have performed the calculations. We shall use their results. Some of them were recently published [69]. 

The examples given in the previous section were all for small molecules. This should not be misunderstood. The approach is not more restricted in size than other quanmm chemical methods. The limit is not the size of the basis set but rather the size of the active space. It is possible to develop linear scaling procedures that work well with the CASSCF/CASPT2 method. It is expected that it will be possible to use multiconfigurational methods to study molecular systems comprising several hundred atoms in the near future. 

Here, the reaction would appear to be required to follow the forbidden pathway. However, recent studies of the potential energy surface for this reaction with multiconfiguration methods find that the allowed pathway is utilized to produce a rra/i5, cw-l,3-cyclohexadiene which has only a 3 kcal/mol barrier to double bond isomerization to the all-c/5-l,3-cyclohexadiene (Scheme 5.6). 

However, at the CASSCF/6-31G level, the transition states are unsymmetrical with distances of 1.65 and 1.86 reflecting the formation of an intermediate C2 symmetric 1,4-cyclohexadiene-1,4-diyl. The apparent pathological predisposition for biradicals of multiconfiguration methods without inclusion of dynamic correlation is probably responsible for the latter result. 

Larsson et have employed a multiconfigurational method to investigate... 

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