Spin-coupled theory

Modem valence bond (VB) theories such as Spin-Coupled theory, together with DFT and Molller-Plesset MO methods, and ab initio molecular dynamics, were employed to study structure/dynamics in representative carbonium ions. 

Spin-coupled theory has been used to smdy the changes that occur in the electronic wavefunction as a system moves along the intrinsic reaction coordinate for the case of the conrotatory and disrotatory pathways in the electrocyclization of cyclobutene to c/x-butadiene. Against intuitive expectations, conrotatory opening of cyclobutenes was found to be promoted by pressure. Ab initio MO and density functional calculations have indicated that the ring opening of the cyclobutene... 

T. Thorsteinsson Development of Methods in Spin-Coupled Theory (Ph.D. Thesis), University of Liverpool, Liverpool (1995). 

This description is furnished by spin-coupled theory, which represents the modern development of valent bond theory. The approach incorporates from the outset the chemically most important eifects of electron correlation, but it retains a simple, clear-cut visuality. 

The purpose of this review is to discuss the main conclusions for the electronic structure of benzenoid aromatic molecules of an approach which is much more general than either MO theory or classical VB theory. In particular, we describe some of the clear theoretical evidence which shows that the n electrons in such molecules are described well in terms of localized, non-orthogonal, singly-occupied orbitals. The characteristic properties of molecules such as benzene arise from a profoundly quantum mechanical phenomenon, namely the mode of coupling of the spins of the n electrons. This simple picture is furnished by spin-coupled theory, which incorporates from the start the most significant effects of electron correlation, but which retains a simple, clear-cut visuality. The spin-coupled representation of these systems is, to all intents and purposes, unaltered by the inclusion of additional electron correlation into the wavefunction. 

The spin-coupled wavefunction provides an improvement over the SCF energy of 199 kJ mol-1 (0.0758 hartree), which is considerable. This arises from the effects of electron correlation in the jr-electron system. The- distortion of the spin-coupled orbitals for benzene occurs because of the small amount of ionic character needed to describe the C — C n bonds. Ionic structures in spin-coupled theory are those in which one or more of the orbitals is allowed to be doubly occupied. Allowing for the different numbers of allowed spin functions, and including the spin-coupled configuration, a total of 175 VB structures can be generated in this way. A... 

The method is referred to simply as GMCSC when a fixed basis set is used. In this case, it can be viewed as a non-orthogonal variant of the Multiconfiguration Self-Consistent Field (MCSCF) approach. However, GMCSC s methodological roots are firmly planted in the Modem VB camp, and more specifically in the late Joe Gerratt s Spin-Coupled theory [3]-[4]. 

The c a are the spin-coupling coefficients of the a-th configuration. One should mention that in the earlier MCSC version of the method [1] all orbital configurations shared the same linear combination of the f(Ne,S) Yamanouchi-Kotani spin functions there was a single set of f(Ne,S) spin-coupling coefficients, denoted simply csk, just as in single-configuration spin-coupled theory. 

The aromaticity of benzene is linked, in spin-coupled theory, to the particular mode of coupling of the electron spins, and so it seems reasonable to suppose that the orbital descriptions of Dih cyclobutadiene and of benzene could be fairly similar, but for these to be associated with very different modes of spin coupling. To a first approximation, this indeed turns out to be the case. With benzene-like orbitals ordered a,b,c,d around the ring, the symmetry requirements of an overall Bu state are such that the electron spins associated with each diagonal (ale and bid) must be strictly triplet coupled. These two triplet subsystems combine to a net singlet. A characteristic feature of antiaromatic situations in spin-coupled theory is the presence of such triplet-coupled pairs of electrons. 

We initially believed [23] that a similar mode of description carries over to 03, but we now realise that this system is somewhat more complicated than we had first supposed. Calculations for the four out-of-plane n electron, whether using spin-coupled theory or at the CASSCF level, reveal that there exist two solutions that are remarkably close in energy. The one that lies lowest, provided we optimize properly the description of the inactive electrons, corresponds to a singlet diradical whereas the other corresponds to a hypercoordinate central atom [24]. It is clear that neither description carries much conviction on its own, and that we must consider expanding the active space. 

Keywords Valence bond, Spin-coupled theory, CASVB, Excited states, Intermolecular forces... 

As has been described in numerous review articles, approaches based on spin-coupled theory can provide highly visual representations of correlated electronic structure and have made important contributions to the development of ab initio modern valence bond theory. We have chosen in the present account to concentrate on certain recent developments. 

We now consider some of the technical aspects of the spin-coupled theory The total electronic energy given by the spin-coupled wavefunction (18) may be written as... 

Two properties of spin-coupled theory were crucial for all of these studies— namely, that the wavefunction is sufficiently flexible to allow for correct dissociation as bonds are broken and also that it is based on a simple orbital picture of singly occupied orbitals. 

In its simplest form (6), spin-coupled theory is based on a single product of N singly occupied nonorthogonal orbitals (Jy for the N active electrons ... 

The aromaticity of pyridazine was studied by the spin-coupled theory and it was shown that the Kekule structure with singlet coupling of 77-... 

The minimisation strategy is the specialisation to the case of a SCF-MI zero order waveflinction of the algorithm previously described by Raimondi et al. (1996) in the context of the Spin Coupled theory. Acceleration of the minimisation procedure now includes the approximate evaluation of the Hessian as described by Clarke et al. (1997). It should be underlined that in this scheme the a priori exclusion of BSSE is still operative, as the virtual orbitals are expanded on the two distinct subsets centred on A and B, see Eq. (10). 

J. Gerratt, D. L. Cooper, P. Karaddakov, M. Raimondi, Spin-coupled Theory. In Handbook of Molecular Physics and Quantum Chemistry, volume 2 Molecular Electronic Structure, chapter 12, p. 148, S. Wilson, P. F. Bernath, R. McWeeny, ed., John WUey, Chichester (2003) D. L. Cooper, Valence Bond Theory Other Methods. In Handbook of Molecular Physics and Quantum Chemistry, volume 2 Molecular Electronic Structure, chapter 13, p. 169, S. Wilson, R F. Bernath, R. McWeeny, eds., John WUey, Chichester (2003)... 

The gas-phase reaction of hydrochloric acid and ethylene to give chloroethane was investigated in the framework of spin-coupled theory. The authors found little evidenee supporting the occurrence of a four-membered transition state. AIM confirmed that the breaking of the H-Cl bond occurs before the C-Cl bond formation. 

Other theoretical treatments which have been applied to considerations of antiaromaticity include spin-coupled theory, topological methods,and quantum statistical definitions. The relevance of spin-coupled theory has been described The comparison between the (spin-coupled) descriptions of cyclobutadiene, benzene, and cyclooctatetraene clearly indicates that the reason for the lower stability and higher reactivity of antiaromatic systems is due to a simultaneous unfavorable coupling of the spins of all valence orbitals to triplet pairs, which discourages bonding interactions and suggests diradical character. ... 

Multi-configurational self-consistent field methods involving only the valence atomic orbitals, such as the generalized valence bond (GVB see Spin-coupled Theory)... 

Methods Spin-coupled Theory Transition State Theory TURBOMOLE. 

Benchmark Studies on Small Molecules Complete Active Space Self-consistent Field (CASSCF) Second-order Perturbation Theory (CASPT2) Configuration Interaction Conformational Analysis 3 Coupled-cluster Theory Density Functional Applications Density Functional Theory (DFT), Hartree-Fock (HF), and the Self-consistent Field Density Functional Theory Applications to Transition Metal Problems G2 Theory Heats of Formation Integrals of Electron Repulsion Localized MO SCF Methods M0ller-Plesset Perturbation Theory Spin Contamination Spin-coupled Theory. 

The interaction of the electron spin magnetic moment with the magnetic moment due to the orbital motion of the electron, and the consequent mixing of electronic states of different multiplicity. See Spin-coupled Theory. 

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