Potential, intermolecular vibrational states dependence

The form of this equation makes explicit the fact that intermolecular forces do depend upon their vibrational states as well as on their electronic states. Due to the antisymmetrization of the global electronic wave function, Vaia2(R R12) contains Coulomb exchange terms and a direct term formed by the Coulomb multipole interactions and the infinite order perturbation electrostatic effects embodied in the reaction field potential [21, 22],... 

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... 

All molecules undergo some sort of intermolecular interaction [1], These interactions must be attractive, at least along some specific intermolecular orientation, and consequently all known molecules aggregate to form solids and liquids. The preference for a specific condensed state depends on the relative effects of the interaction potential energy and of the thermal kinetic energy of nuclear vibrations, at the temperature considered. It is worth pointing out here that molecules, as we will see later, can also take relative orientations that give rise to repulsive intermolecular interactions. 

The intermolecular potential as it is given in Eq. (3) for example, does not depend explicitly on the (external) molecular displacements or on the (internal) normal coordinates as required by Eq. (10). The atom-atom potential in Eq. (5) does not even depend explicitly on the molecular orientations Q. All these dependencies have to be brought out, by expansion and transformation of the potentials in Eq. (3) and Eq. (5), before these can actually be used in lattice dynamics calculations. The way this is performed depends on the lattice dynamics method chosen (see below). If one is not interested in the internal molecular vibrations, the free-molecule Hamiltonians may be omitted from Eq. (10) and the potential may be averaged over the molecular vibrational states. The effective potential thus obtained no longer depends on the coordinates and Q. ... 

In the further discussion the authors assume that the parameter 8 deduced from experimental results using (28) gives directly the depth of the potential well for A -A interactions Ca-a - This statement is controversial experimental data for Ij show a strong dependence of 8 on the vibrational level in the + state. The same is true for the y4 w state of CO. This difference can be hardly explained by the dependence of the intermolecular forces on the vibrational quantum number. 

Even when the intramolecular vibrations do not mix with the phonons, they are coupled by the intermolecular potential, through its dependence on the internal molecular coordinates. This coupling determines the band structure of the vibrational excitons or vibrons in molecular crystals, which can be studied by inelastic neutron scattering (see Fig. 12). In the case of TCB crystals the vibron band structure has been observed recently by laser phosphorescence [59, 104]. This is a rather special achievement since, normally, optical techniques probe only the g = 0 excitations. It is related to the long lifetime of triplet electronic excitons in TCB, which are scattered into different q states. By phosphorescent de-excitation q 0 triplet excitons to the electronic ground state it is possible to detect the g 0 vibrons, with intensities controlled by the (very low) temperature and by the phosphorescence delay time. 

To see how we should be able to study the evolution of a collision let us consider first how intermolecular potentials between atoms bound together are studied. This is done, of course, via spectroscopy. One starts with the Born-Oppenheimer approximation for the total molecular wave function this enables one to describe the motion of the nuclei in a potential that depends on the separation between them. This result, the existence of a specific adiabatic potential, rests on there being no appreciable mixing between electronic states. One of its corollaries, the Franck-Condon Principle, enables one to interpret and invert (e.g. using the R.K.R. method) the vibrational spectra in terms of the interatomic potentials in different electronic states. To what extent can we extend such a technique to free-free spectra, in other words, to absorption in the middle of a transient molecule — a collision complex — and deduce information about the potentials between atoms as they collide ... 

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