Polyatomic systems electronic transitions

In electronic spectroscopy of polyatomic molecules the system used for labelling vibronic transitions employs N, to indicate a transition in which vibration N is excited with v" quanta in the lower state and v quanta in the upper state. The pure electronic transition is labelled Og. The system is very similar to the rather less often used system for pure vibrational transitions described in Section 6.2.3.1. 

In diatomic spectra, one distinguishes between individual bands each corresponding to a definite pair of quantum numbers v, v", and band systems, each composed of an ensemble of bands associated with a particular electronic transition. In polyatomic spectra, often (a), the individual bands of an electronic transition are so numerous and strongly overlapping that it is difficult or impossible to distinguish them individually, or (b), the electronic transition gives rise only to continuous absorption in both these situations the entire spectrum of an electronic transition is commonly called a band. IT IS RECOMMENDED (REC. 39) that the word band be reserved for definite individual bands, and that electronic transition or transition be used for the entire spectrum, whether discrete, pseudo-continuous, or strictly continuous, associated with an electronic transition or band system if the spectrum consists of discrete bands. ... 

B. Vibrational Structure of Electronic Transitions 1. Normal vibrations and their symmetry classification An electronic band system belonging to a polyatomic molecule normally contains a large number and variety of transitions in which vibrational quantum changes are superimposed on the electronic jump. The analysis, besides supplementing infrared and Raman evidence of the ground state frequencies, yields values for the fundamental frequencies of the excited state and is one of the principal sources of information as to its structure. 

A certain electronic transition in a polyatomic system can be equally described either within the adiabatic or within the diabatic basis set as the transitions can be induced either by the dynamic or by the static coupling,... 

If the regions of nonadiabatic behavior are well localized in the configuration space M, an (F — l)-dimensional hypersurface can be defined at which the nonadiabatic transitions may take place this hypersurface is referred to as the crossing seam. The coupled relations, Eq. (14), describing the corresponding nonseparable electronic and nuclear motion, are to be solved at the seam. Elsewhere, the evolution of the polyatomic system can be then treated adiabatically (49,50). 

For the treatment of large polyatomic systems, computational methodologies deal with a compromise between an overall description of the entire system and a more detailed handling of a properly selected part of it. This situation particularly applies to the transition metal structures that have to be drastically minimized for an adequate ob initio, local density functional, or even semiempirical calculation at a good correlation level. In contrast to this simplification of the system, the improvements of the simpler methods, which are capable of handling the system as a whole, have regained acceptability. This is the case of the EHMO method developed by Hoffman [19], which was initially used for a reasonable description of the structural and electronic properties of the systems at a frozen geometry. Improvements of this method are mainly related to the addition of the (two-body electrostatic correction) term as explained above [20,21],... 

Obviously, the electronic energies E (R) for n 0 corresponds in a similar manner to potential surfaces for electronically excited states. Each PES usually exhibits considerable structure for a polyatomic system and will provide useful pictures with reactant and product valleys, local minima corresponding to stable species, and transition states serving as gateways for the system to travel from one valley to another. However, for the number of nuclear degrees of freedom beyond six, i.e. for more than four-atom systems it becomes extremely cumbersome to produce the PES s and quite complicated to visuahze the topology. Furthermore, when more than one PES is needed, which is not unusual, there is a need for nonadiabatic coupling terms, which also may need interpolation in order to provide useful information. 

The Fermi Golden Rule (Merzbacher, 1970) is often used to interpret rate constants for electronically nonadiabatic transitions in polyatomic molecules. Figure 8.17 depicts vibrational/rotational levels for two electronic states 1 and 2. Unimolecular decomposition occurs on the ground electronic state 1. When the system is initially prepared in the electronically excited state, the complete unimolecular rate constant depends on both the rate constant k 2 for the electronic transition 1 <— 2 and the unimolecular rate constant for the ground electronic state. If a single vibrational/rotational state of electronic state 2 is initially excited, the Fermi Golden Rule expression for, 2 is... 

The extended formulation of the generalized JTE above states that the necessary and sufficient condition of instability of the high-symmetry configuration of any polyatomic system is the presence of two or more electronic states that interact sufficiently strongly under the nuclear displacements in the direction of instability. Configurational instabilities are present in a vast majority of processes in chemistry, physics, and biology, including, e.g., transition states of chemical reactions, con-... 

A very useful starting point for the study of non-adiabatic processes, which are common in photochemistry and photophysics, is the vibronic coupling model Hamiltonian. The model is based on a Taylor expansion of the potential surfaces in a diabatic electronic basis, and it is able to correctly describe the dominant feature resulting from vibronic coupling in polyatomic molecules a conical intersection. The importance of such intersections is that they provide efficient non-radiative pathways for electronic transitions. Not only is the position and shape of the intersection described by the model, but it also predicts which nuclear modes of motion are coupled to the electronic transition which takes place as the system evolves through the intersection. 

This example illustrates the general need for calculations, or even rough estimation, of potential surfaces of polyatomic systems correlating with different atomic states. Once these are known, the possible mechanisms of electronic energy conversion can be elucidated. Determination of the actual path of non-adiabatic processes must be based on molecular dynamics, i.e. on the study of motions of atom over different potential surfaces and transitions between these surfaces. 

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