Transition between molecular electronic states

Problem 12.6. Show that in the limit where both A and are much smaller than 1, Eqs (12.55a) and(12.55b) yield the rates (12.47) and (12.48), respectively, where 2 inEq(12.46) is identified with 21 

The rate expressions (12.47) and (12.48) are thus seen to be limiting forms of (12.55), obtained in the low-temperature limit provided that A 1 for all a. On the other hand, the rate expression (12.55) is valid if F12 is small enough, irrespective of the temperature and the magnitudes of the shifts Aq,. 

Transitions between molecular electronic states are often described by focusing on the two electronic states involved, thus leading to a two-state model. When such transitions are coupled to molecular vibrations, environmental phonons or radiation-field photons the problem becomes a spin-boson-type. The examples discussed below reiterate the methodology described in this chapter in the context of physical applications pertaining to the dynamics of electronic transitions in molecular systems. 

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A term in photochemistry and photophysics describing an isoenergetic radiationless transition between two electronic states having different multiphcities. Such a process often results in the formation of a vibrationally excited molecular entity, at the lower electronic state, which then usually deactivates to its lowest vibrational energy level. See also Internal Conversion Fluorescence... 

For quite a few years we have been concerned with the use of molecular systems in memory devices. Whatever the final objective might be, a fundamental requirement for the system is to have an hysteresis effect with regard to a given perturbation. When it is so, a transition between two electronic states takes place for a certain value of the perturbation, /Vf, when the perturbation increases, and for another value of the perturbation, Pcl, when the perturbation decreases, with Pc[ < Pcf. Between those two critical values, the state of the system depends on its history or on the information which has been stored. It is of course well known that a hard magnetic material might be used for storing information. Our work provides evidence of the possibility that molecular chemistry might provide compounds of that kind. 

In the study of any radiative recombination process, one tries to answer a number of fairly well defined questions, mostly related to potential curves. From what electronic states is emission observed With what atomic states do these molecular states correlate Does the recombination take place on a single potential curve, or is a transition between two curves involved Is a potential curve with a significant maximum involved Is a third body necessary, either to stabilize the atom pair on a single curve, or to induce a transition to another curve In the case of a transition between two electronic states, is there an approximate equilibrium What is the vibrational and rotational distribution of newly formed molecules What is the recombination rate coefficient as a function of temperature or cross section as a function of energy In principle these questions can be answered either theoretically or experimentally. In fact, they have been answered experimentally in most cases, but the answers are seldom as certain or as numerous as one would wish. This becomes clear in the following discussion of particular cases. 

Besides its practical importance, photodissociation — especially of small polyatomic molecules — provides an ideal opportunity for the study of molecular dynamics on a detailed state-to-state level. We associate with molecular dynamics processes such as energy transfer between the various molecular modes, the breaking of chemical bonds and the creation of new ones, transitions between different electronic states etc. One goal of modern physical chemistry is the microscopical understanding of molecular reactivity beyond purely kinetic descriptions (Levine and Bernstein 1987). Because the initial conditions can be well defined (absorption of a single monochromatic photon, preparation of the parent molecule in selected quantum states), photodissociation is ideally suited to address questions which are unprecedented in chemistry. The last decade has witnessed an explosion of new experimental techniques which nowadays makes it possible to tackle questions which before were beyond any practical realization (Ashfold and Baggott 1987). 

This book is concerned primarily with the rotational levels of diatomic molecules. The spectroscopic transitions described arise either from transitions between different rotational levels, usually adjacent rotational levels, or from transitions between the fine or hyperfine components of a single rotational level. The electronic and vibrational quantum numbers play a different role. In the majority of cases the rotational levels studied belong to the lowest vibrational level of the ground electronic state. The detailed nature of the rotational levels, and the transitions between them, depends critically upon the type of electronic state involved. Consequently we will be deeply concerned with the many different types of electronic state which arise for diatomic molecules, and the molecular interactions which determine the nature and structure of the rotational levels. We will not, in general, be concerned with transitions between different electronic states, except for the double resonance studies described in the final chapter. The vibrational states of diatomic molecules are, in a sense, relatively uninteresting. 

Internal conversion A photophysical process. Isoenergetic radiationless transition between two electronic states of the same multiplicity. When the transition results in a vibrationally excited molecular entity in the lower electronic state, this usually undergoes deactivation to its lowest vibrational level, provided the final state is not unstable to dissociation. 

A direct consequence of the observation that Eqs. (12.55) provide also golden-rule expressions for transition rates between molecular electronic states in the shifted parallel harmonic potential surfaces model, is that the same theory can be applied to the calculation of optical absorption spectra. The electronic absorption lineshape expresses the photon-frequency dependent transition rate from the molecular ground state dressed by a photon, g) = g, hco ), to an electronically excited state without a photon, x). This absorption is broadened by electronic-vibrational coupling, and the resulting spectrum is sometimes referred to as the Franck-Condon envelope of the absorption lineshape. To see how this spectrum is obtained from the present formalism we start from the Hamiltonian (12.7) in which states L and R are replaced by g) and x) and Vlr becomes Pgx—the coupling between molecule and radiation field. The modes a represent intramolecular as well as intermolecular vibrational motions that couple to the electronic transition... 

The remarks in the previous paragraph apply, of course, only to the case of electronically adiabatic molecular collisions for which all degrees of freedom refer to the motion of nuclei (i.e. translation, rotation and vibration) if transitions between different electronic states are also involved, then there is no way to avoid dealing with an explicit mixture of a quantum description of some degrees of freedom (electronic) and a classical description of the others.9 The description of such non-adiabatic electronic transitions within the framework of classical S-matrix theory has been discussed at length in the earlier review9 and is not included here. 

Ultraviolet (UV) and visible spectra, also known as electronic spectra, involve transitions between different electronic states. The electronic transition is accompanied by the vibrational and rotational transitions so that what woidd otherwise be an absorption line becomes a broad peak containing vibrational and rotational fine structure. Furthermore, the molecular interaction between solute and solvent levels it to a smooth curve (envelope) for the absorption spectra in solutions. The accessible regions are 200-400nm for... 

The transition between different electronic states is an important phenomenon in molecular photodissociation processes. It is more the rule than the exception the validity of the Born-Oppenheimer approximation, that... 

Values of a and )3 are measured spectroscopically, and the electronic spectroscopy of many tt electron systems shows that the Hiickel approximation works fairly well. Many transitions between tt electronic states occur in the visible or ultraviolet region of the spectrum. These transitions are the cause of color in conjugated tt electron systems. In the Hiickel approximation, all of the tt molecular orbitals end up with a value of energy having the form E = a + K)8, where the value for K depends on the system. Therefore, only the values of K and )8 determine the molecule s tt energy level pattern, which is what is probed in an experimental spectrum. However, because of how it is defined, )3 has a similar value for most tt systems about —75 kj/mol. The value for a can be determined from atomic spectra. Because a specific value for a is not necessary in understanding the pattern of the tt electronic states, its value is not usually a matter of concern. (For carbon atoms, a is about — 1120 kJ/mol, which is much larger than )8.)... 

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