Applications to Spin-Forbidden Reactions

There have been many calculations performed on diatomic molecules that include spin-orbit coupling. Hess, Marian, and Peyerimhoff have reviewed calculations of transition metal containing diatomic molecules using their Douglas-Kroll spin-orbit operators. A compilation of relativistic ECP-based spin-orbit Cl calculations for transition metal containing diatomics is given by Balasubramanian. More recent diatomic molecules that have been studied include N2 HI and DI, TeH and TeLi, HCl  

2 11 state, where the crossing points of two diabatic states are separated by at least three vibrational levels. This is the origin of the difference in the vibrational signature of the predissociation in the A state. 

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However, often the minimum in Si or Ti which is reached at first is shallow and thermal energy will allow escape into other areas on the Si or Ti surface before return to So occurs (Fig. 3, path e). This is particularly true in the Ti state which has longer lifetimes due to the spin-forbidden nature of both its radiative and non-radiative modes of return to So-The rate of the escape should depend on temperature and is determined in the simplest case by the height and shape of the wall around the minimum, similarly as in ground state reactions (concepts such as activation energy and entropy should be applicable). In cases of intermediate complexity, non-unity transmission coefficients may become important, as discussed above. Finally, in unfavorable cases, vibronic coupling between two or more states has to be considered at all times and simple concepts familiar from ground-state chemistry are not applicable. Pres-... 

Another rewarding field of applications is given by cluster simulations of the role of SOC in surface catalysis, for instance oxidation on the surface. Dissociative adsorption of O2 on metal surfaces leads to inclusion of atomic oxygen in the oxidation reaction. Ground state 0(3P) atom insertion in the C=C bond is spin forbidden, so the epoxidation of olefins on metal surfaces must find a way to overcome this prohibition. Other types of surface reactions can also illustrate the importance of SOC effects in spin catalysis [211]. 

One area of research that has not been explored very much by the techniques covered in this chapter is biological chemistry. Many enzymes carry out electron-transfer reactions, and can undergo intersystem crossing. Many of the methodologies discussed in this chapter are applicable to biological systems exhibiting spin-forbidden transitions. 

In (O Eq. 29.7) (a is a SOC constant for atom A (Co = 153 cm" ), //,a,s/ - are the orbital and spin angular momentum operators for the i-th electron, respectively. This is the effective singleelectron SOC approximation, which proved to be useful in many spectroscopic and chemical applications including oxygen spin-forbidden atmospheric bands (Minaev 1989 Minaev and Agren 1997 Minaev et al. 1997, 1996, 2008 Ogilby 1999 Paterson et al. 2006 Schweitzer and Schmidt 2003) and spin-forbidden enzyme reactions (Minaev 2002, 2007, 2010 Minaev et al. 2007 Prabhakar et al. 2003, 2004). 

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