Electronic Transitions in Polyatomic Molecules

This brief allusion to types of transition will serve merely to give the reader an idea that the detailed description of electronic transitions in polyatomic molecules is complicated and for the moment not a realm of universal agreement. Zimmerman46 has extended the mechanistic ideas currently used by physico-organic chemists to organic photochemistry. It is possible in this way to give systematic descriptions of many organic photochemical phenomena. A systematization of this type will ultimately be necessary merely because of the multitude of facts which must be made useful. 

Transitions between electronic states are formally equivalent to transitions between different vibrational or rotational states which were amply discussed in Chapters 9 11. Computationally, however, they are much more difficult to handle because they arise from the coupling between electronic and nuclear motions. The rigorous description of electronic transitions in polyatomic molecules is probably the most difficult task in the whole field of molecular dynamics (Siebrand 1976 Tully 1976 Child 1979 Rebentrost 1981 Baer 1983 Koppel, Domcke, and Cederbaum 1984 Whetten, Ezra, and Grant 1985 Desouter-Lecomte et al. 1985 Baer 1985b Lefebvre-Brion and Field 1986 Sidis 1989a,b Coalson 1989). The reasons will become apparent below. The two basic approaches, the adiabatic and the diabatic representations, will be outlined in Sections 15.1 and 15.2, respectively. Two examples, the photodissociation of CH3I and of H2S, will be discussed in Section 15.3. 

Sensitivity levels more typical of kinetic studies are of the order of lO molecules cm . A schematic diagram of an apparatus for kinetic LIF measurements is shown in figure C3.I.8. A limitation of this approach is that only relative concentrations are easily measured, in contrast to absorjDtion measurements, which yield absolute concentrations. Another important limitation is that not all molecules have measurable fluorescence, as radiationless transitions can be the dominant decay route for electronic excitation in polyatomic molecules. However, the latter situation can also be an advantage in complex molecules, such as proteins, where a lack of background fluorescence allow s the selective introduction of fluorescent chromophores as probes for kinetic studies. (Tryptophan is the only strongly fluorescent amino acid naturally present in proteins, for instance.)... 

Hougen, J. T., Watson, J. K. G. Anomalous rotational line intensities in electronic transitions of polyatomic molecules Axis-switching. Can. J. Phys. 43, 298-320 (1965). 

In attempting to understand the properties of, and/or processes involving, excited electronic states in polyatomic molecules, it is often necessary to consider radiationless transitions. Radiationless processes can be classified into a number of types ... 

Fig. 1. The molecular energy level model used to discuss radiationless transitions in polyatomic molecules. 0O, s, and S0,S are vibronic components of the ground, an excited, and a third electronic state, respectively, in the Born-Oppenheimer approximation. 0S and 0 and 0j are assumed to be allowed, while transitions between j0,j and the thermally accessible 00 are assumed to be forbidden. The f 0n are the molecular eigenstates...

A previous review provides a description of the theory of electronic relaxation in polyatomic molecules with particular emphasis on the vibronic state dependence of radiationless transition rates. A sequal review considers the general question of collisional effects on electronic relaxation, while the present one covers only the special phenomenon of collision-induced intersystem crossing. It departs from the other collisional effects review in presenting only a qualitative description of the theory the full theoretical details can be obtained from the previous review and the original papers.As a review of the basic concepts of radiationless transitions theory is necessary as a prelude to a discussion of collision-induced intersystem crossing, considerable overlap exists between this section and Section II of the previous collision effects review. However, since many concepts from radiationless transition theory, such as the nature and criteria for irreversible decay, the role of the preparation of the initial state, the occurrence of intramolecular vibrational relaxation, etc. pervade the other papers on laser chemistry in these volumes, it is useful to recall the primary results of the theory of electronic relaxation in isolated molecules and its relevance to the material in the present volume as well as to this review. 

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... 

According to the selection rule for the harmonic oscillator, any transitions corresponding to An = 1 are allowed (Sec. I-2). Under ordinary conditions, however, only the fundamentah that originate in the transition from u = 0 to u = 1 in the electronic ground state can be observed because of the Maxwell-Boltzmann distribution law. In addition to the selection rule for the harmonic oscillator, another restriction results from the symmetry of the molecule (Sec. 1-9). Thus the number of allowed transitions in polyatomic molecules is greatly reduced. The overtones and combination bands of these fundamentals are forbidden by the selection rule of the harmonic oscillator. However, they are weakly observed in the spectrum because of the anharmonicity of the vibration... 

The substance of this section is based on the classic article by Herzberg and Teller (6) on vibronic transitions in polyatomic molecules. Some more specific aspects of the general theory are excellently described in recent articles (7, 8, 9). In the present section we wish to examine how symmetry arguments enter into the description and prediction of vibronic states, yet to attain this end it will be necessary to give a brief account of the quantum theory of the interaction between electronic and nuclear motion in molecules. 

The population probabilities Pn t) defined in Eqs. (8)-(13) should not be confused with the population probabilities which have been considered in the extensive earlier literature on radiationless transitions in polyatomic molecules, see Refs. 28 and 29 for reviews. There the population of a single bright (i.e. optically accessible from the electronic ground state) zero-order Born-Oppenheimer (BO) level is considered. Here, in contrast, we define the electronic population as the sum of all vibrational level populations within a given (diabatic or adiabatic) electronic state. These different definitions are adapted to different regimes of time scales of the system dynamics. If nonadiabatic interactions are relatively weak, and radiationless transitions relatively slow, the concept of zero-order BO levels is useful the populations of these levels can be prepared and probed using suitable laser pulses (typically of nanosecond duration). If the nonadiabatic transitions occur on femtosecond time scales, the preparation of individual zero-order BO levels is no longer possible. The total population of an electronic state then becomes the appropriate concept for the interpretation of time-resolved experiments. ° ... 

As in diatomics, vibrational transitions in polyatomic molecules are inevitably accompanied by rotational fine structure. In linear molecules, the vibrational and rotational selection rules in vibration-rotation spectra are closely analogous to the electronic and rotational selection rules, respectively, in diatomic electronic band spectra. When applied to a molecule, the general symmetry arguments of the previous Section lead to the El selection rules... 

Contents J.M.Bowman Introduction. - D.Secrest Inelastic Vibrational and Rotational Quantum Collisions. -G. C.Schatz Quasiclassical Trajectory Studies of State to State Collisional Energy Transfer in Polyatomic Molecules. - R. Schinke, J. M. Bowman Rotational Rainbows in Atom-Diatom Scattering. - M.Baer Quantum Mechanical Treatment of Electronic Transitions in Atom-Molecule Collisions. - Subject Index. 

As with diatomic molecules, vibrational and rotational transitions in polyatomic molecules take place along with electronic transitions. The Franck-Condon principle applies, so that the final state will usually be an excited vibrational state as well as an excited electronic state. Since there are several normal modes in any polyatomic molecule the simultaneous electronic, vibrational, and rotational transitions can give very complicated spectra. The most important selection rule is the same for all molecules and atoms The total spin quantum number is the same for the final as for the initial state ... 

If one of the components of this electronic transition moment is non-zero, the electronic transition is said to be allowed if all components are zero it is said to be forbidden. In the case of diatomic molecules, if the transition is forbidden it is usually not observed unless as a very weak band occurring by magnetic dipole or electric quadnipole interactions. In polyatomic molecules forbidden electronic transitions are still often observed, but they are usually weak in comparison with allowed 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. 

Figure 4.5 Jablonski diagram of electronic transitions in a polyatomic molecule which reacts chemically from the triplet state T...

This is generally known as Case I of predissociation it concerns an electronic transition. Case II, predissociation by vibration, can only take place in polyatomic molecules. Case III is predissociation by rotation, and concerns transitions in the same electronic level. The question is treated in detail by Herzberg i, ... 

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