Molecules electronic states

Fig. 1. Schematic energy-level diagram for a dye molecule. Electronic states Sq = ground singlet state = first excited singlet state S2 = second excited singlet state Tj = first excited triplet state T2 = second excited triplet state EVS = excited vibrational states. Transitions A = absorption excited states ...

The molecular structure is assumed to be linear using the Walsh ( ) predictions for 16 valence electron XYg molecules electronic states, levels and vibrational frequencies are estimated by comparison with those for COg ( ). is estimated using the method of Krasnov (6). 

For some diatomic-molecule electronic states, solution of the electronic Schrodinger equation gives a U R) curve with no minimum. Such states are not bound and the molecule will dissociate. Examples are some of the states in Fig. 13.5. 

TERM SYMBOLS FOR LINEAR MOLECULES Electronic states of a linear molecule may be classified conveniently in terms of angular momentum and spin, analogous to the Russell-Saunders term-symbol scheme for atoms. The unique molecular axis in linear molecules is labeled the axis. The combining atomic orbitals in any given molecular orbital have the same mi value. Thus an mi quantum number is assigned to each different type of MO, as indicated in Table 2-3. The term designations are of the form... 

State Symbols Corresponding to M/, Values in Linear-Molecule Electronic-State Classification... 

SXES spectroscopy [111] ejects K electrons and the spectrum of the resulting x-rays is measured Spectroscopy of Emitted Electrons state of adsorbed molecules surface composition... 

The corresponding fiinctions i-, Xj etc. then define what are known as the normal coordinates of vibration, and the Hamiltonian can be written in tenns of these in precisely the fonn given by equation (AT 1.69). witli the caveat that each tenn refers not to the coordinates of a single particle, but rather to independent coordinates that involve the collective motion of many particles. An additional distinction is that treatment of the vibrational problem does not involve the complications of antisymmetry associated with identical fennions and the Pauli exclusion prmciple. Products of the nonnal coordinate fiinctions neveitlieless describe all vibrational states of the molecule (both ground and excited) in very much the same way that the product states of single-electron fiinctions describe the electronic states, although it must be emphasized that one model is based on independent motion and the other on collective motion, which are qualitatively very different. Neither model faithfully represents reality, but each serves as an extremely usefiil conceptual model and a basis for more accurate calculations. 

Much of the previous section dealt with two-level systems. Real molecules, however, are not two-level systems for many purposes there are only two electronic states that participate, but each of these electronic states has many states corresponding to different quantum levels for vibration and rotation. A coherent femtosecond pulse has a bandwidth which may span many vibrational levels when the pulse impinges on the molecule it excites a coherent superposition of all tliese vibrational states—a vibrational wavepacket. In this section we deal with excitation by one or two femtosecond optical pulses, as well as continuous wave excitation in section A 1.6.4 we will use the concepts developed here to understand nonlinear molecular electronic spectroscopy. 

As described at the end of section Al.6.1. in nonlinear spectroscopy a polarization is created in the material which depends in a nonlinear way on the strength of the electric field. As we shall now see, the microscopic description of this nonlinear polarization involves multiple interactions of the material with the electric field. The multiple interactions in principle contain infomiation on both the ground electronic state and excited electronic state dynamics, and for a molecule in the presence of solvent, infomiation on the molecule-solvent interactions. Excellent general introductions to nonlinear spectroscopy may be found in [35, 36 and 37]. Raman spectroscopy, described at the end of the previous section, is also a nonlinear spectroscopy, in the sense that it involves more than one interaction of light with the material, but it is a pathological example since the second interaction is tlirough spontaneous emission and therefore not proportional to a driving field... 

Figure Al.6.24. Schematic representation of a photon echo in an isolated, multilevel molecule, (a) The initial pulse prepares a superposition of ground- and excited-state amplitude, (b) The subsequent motion on the ground and excited electronic states. The ground-state amplitude is shown as stationary (which in general it will not be for strong pulses), while the excited-state amplitude is non-stationary. (c) The second pulse exchanges ground- and excited-state amplitude, (d) Subsequent evolution of the wavepackets on the ground and excited electronic states. Wlien they overlap, an echo occurs (after [40]).

Chemisorption occurs when the attractive potential well is large so that upon adsorption a strong chemical bond to a surface is fonued. Chemisorption involves changes to both the molecule and surface electronic states. For example, when oxygen adsorbs onto a metal surface, a partially ionic bond is created as charge transfers from the substrate to the oxygen atom. Other chemisorbed species interact in a more covalent maimer by sharing electrons, but this still involves perturbations to the electronic system. 

It is advantageous if the laser system pemiits rotation of the optical polarization. Detached electrons correlated witii different final electronic states of the neutral molecule will generally be emitted with different angular distributions about the direction of polarization. Measurement of the angular distribution helps in the interpretation of complex photoelectron spectra. The angular distribution/(0) of photoelectrons is [50]... 

There are significant differences between tliese two types of reactions as far as how they are treated experimentally and theoretically. Photodissociation typically involves excitation to an excited electronic state, whereas bimolecular reactions often occur on the ground-state potential energy surface for a reaction. In addition, the initial conditions are very different. In bimolecular collisions one has no control over the reactant orbital angular momentum (impact parameter), whereas m photodissociation one can start with cold molecules with total angular momentum 0. Nonetheless, many theoretical constructs and experimental methods can be applied to both types of reactions, and from the point of view of this chapter their similarities are more important than their differences. 

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

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