Electronic states polyatomic molecules

For electronic states of polyatomic molecules for which the net electronic spin S is nonzero, we get an interaction between rotational and spin angular momenta. We shall not consider this case, but will restrict ourselves to rotational energies of singlet electronic states. Polyatomic molecules with nonsinglet ground electronic states are rare. 

Name the electronic states of molecules with the uppercase roman letters A, B, E, and T the ground state is X. Use the corresponding lowercase letters for one-electron orbitals. A tilde ( ) is added for polyatomic molecules. The subscripts describe the symmetry of the orbital. 

The electronic states of molecules are also given empirical single letter labels as follows. The ground electronic state is labelled X, excited states of the same multiplicity are labelled A, B, C,.. . , in ascending order of energy, and excited states of different multiplicity are labelled with lower case letters a, b, c,.. . . In polyatomic molecules (but not diatomic molecules) it is customary to add a tilde (e.g. X) to these empirical labels to prevent possible confusion with the symmetry species label. 

The title of this chapter seems to promise a general discussion of the nature of collision-induced intramolecular energy transfer in electronically excited polyatomic molecules. If interpreted as just stated, the title promises more than can be delivered at this time. It is only recently that advances in experimental technique have permitted the study of the pathways of intramolecular energy redistribution following collision, and the few results now available were neither anticipated nor can they yet be fully accounted for by the available theories of collision-induced energy transfer. This chapter describes a preliminary synthesis of the limited experimental and theoretical information in hand and discusses some of its implications. It will be seen that more questions are raised than are answered. 

In chapter 4 the data from investigations of radicals (non- I electronic states of molecules) have been compiled. The diatomic radicals are listed in 4.1, the polyatomic ones in 4.2. 

Weitz E and Flynn G W 1981 Vibrational energy flow in the ground electronic states of polyatomic molecules Adv. Chem. Rhys. 47 185-235... 

Most stable polyatomic molecules whose absorption intensities are easily studied have filled-shell, totally synuuetric, singlet ground states. For absorption spectra starting from the ground state the electronic selection rules become simple transitions are allowed to excited singlet states having synuuetries the same as one of the coordinate axes, v, y or z. Other transitions should be relatively weak. 

The selection rule for vibronic states is then straightforward. It is obtained by exactly the same procedure as described above for the electronic selection rules. In particular, the lowest vibrational level of the ground electronic state of most stable polyatomic molecules will be totally synnnetric. Transitions originating in that vibronic level must go to an excited state vibronic level whose synnnetry is the same as one of the coordinates, v, y, or z. 

Conical intersections, introduced over 60 years ago as possible efficient funnels connecting different elecbonically excited states [1], are now generally believed to be involved in many photochemical reactions. Direct laboratory observation of these subsurfaces on the potential surfaces of polyatomic molecules is difficult, since they are not stationary points . The system is expected to pass through them veiy rapidly, as the transition from one electronic state to another at the conical intersection is very rapid. Their presence is sunnised from the following data [2-5] ... 

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. 

As is the case for diatomic molecules, rotational fine structure of electronic spectra of polyatomic molecules is very similar, in principle, to that of their infrared vibrational spectra. For linear, symmetric rotor, spherical rotor and asymmetric rotor molecules the selection mles are the same as those discussed in Sections 6.2.4.1 to 6.2.4.4. The major difference, in practice, is that, as for diatomics, there is likely to be a much larger change of geometry, and therefore of rotational constants, from one electronic state to another than from one vibrational state to another. 

If we require similar information regarding the ground state potential energy surface in a polyatomic molecule the electronic emission specttum may again provide valuable information SVLF spectroscopy is a particularly powerful technique for providing it. 

Fig. 11. (a) Diagram of energy levels for a polyatomic molecule. Optical transition occurs from the ground state Ag to the excited electronic state Ai. Aj, are the vibrational sublevels of the optically forbidden electronic state A2. Arrows indicate vibrational relaxation (VR) in the states Ai and Aj, and radiationless transition (RLT). (b) Crossing of the terms Ai and Aj. Reorganization energy E, is indicated. 

In addition to the previously mentioned disadvantages, all of these methods have another drawback in the large molecule photofragment velocity measurements. For example, in the studies of UV photon photodissociation of polyatomic molecules, like alkene and aromatic molecules, molecules excited by the UV photons quickly become highly vibrationally excited in the ground electronic state through fast internal conversion, and dissociation occurs in the ground electronic state. 

After all, even in the first case we deal with the interaction of an electron belonging to the gas particle with all the electrons of the crystal. However, this formulation of the problem already represents a second step in the successive approximations of the surface interaction. It seems that this more or less exact formulation will have to be considered until the theoretical methods are available to describe the behavior both of the polyatomic molecules and the metal crystal separately, starting from the first principles. In other words, a crude model of the metal, as described earlier, constructed without taking into account the chemical reactivity of the surface, would be in this general approach (in the contemporary state of matter) combined with a relatively precise model of the polyatomic molecule (the adequacy of which has been proved in the reactivity calculations of the homogeneous reactions). 

Internal conversion refers to radiationless transition between states of the same multiplicity, whereas intersystem crossing refers to such transitions between states of different multiplicities. The difference between the electronic energies is vested as the vibrational energy of the lower state. In the liquid phase, the vibrational energy may be quickly degraded into heat by collision, and in any phase, the differential energy is shared in a polyatomic molecule among various modes of vibration. The theory of radiationless transitions developed by Robinson and Frosch (1963) stresses the Franck-Condon factor. Jortner et al. (1969) have extensively reviewed the situation from the photochemical viewpoint. 

Due to the simplicity and the ability to explain the spectroscopic and excited state properties, the MO theory in addition to easy adaptability for modern computers has gained tremendous popularity among chemists. The concept of directed valence, based on the principle of maximum overlap and valence shell electron pair repulsion theory (VSEPR), has successfully explained the molecular geometries and bonding in polyatomic molecules. 

In this chapter, the diverse coupling constants and MEC components identified in the combined electronic-nuclear approach to equilibrium states in molecules and reactants are explored. The reactivity implications of these derivative descriptors of the interaction between the electronic and geometric aspects of the molecular structure will be commented upon within both the EP and EF perspectives. We begin this analysis with a brief survey of the basic concepts and relations of the generalized compliant description of molecular systems, which simultaneously involves the electronic and nuclear degrees-of-freedom. Illustrative numerical data of these derivative properties for selected polyatomic molecules, taken from the recent computational analysis (Nalewajski et al., 2008), will also be discussed from the point of view of their possible applications as reactivity criteria and interpreted as manifestations of the LeChatelier-Braun principle of thermodynamics (Callen, 1962). 

Consider a di- or a polyatomic molecule AB in the gas phase, at T = 0. By means of an electron or a photon, this molecule can be ionized and excited to a state AB+, which subsequently decomposes into the fragments A+ and B ... 

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