Molecule electron-vibrational interaction

Owing to the electron-vibrational interaction in molecules, there is one more possible decay channel for SES. This is the nonradiative relaxation (internal conversion), in which the electron energy is transferred into vibrational energy of molecules (in the condensed phase, into thermal energy of the medium). If the molecule fluoresces, there may also occur fluorescence from the lowest excited state. (According to the empirical rule of Kasha,64 the molecular fluorescence occurs from the lowest excitation level irrespective of the wavelength of the exciting radiation.)... 

In this section, we introduce the working principle of vibrational spectroscopy. It will be compared with a parent technique called Inelastic Electron Tunneling Spectroscopy, which was developed in the 60 s. Although the working principle is similar in each of them, the specific nature of electron-vibration interaction differs. We shall conclude this section by reviewing the most important achievements of single-molecule vibrational spectroscopy. 

The physics of CITE looks very simple and clear. Because of the vibronic (electron-vibrational) interaction each Jahn-Teller (JT) molecule (center) is characterized with several energetically equivalent minima corresponding to a possible distortion of the initial (at the absence of the vibronic interaction) symmetry. In case of many JT centers in a crystal matrix an effective interaction caused by lattice strains around the centers takes place. This interaction breaks the equivalence of the minima. The preference of the specific distortions around each of the JT centers leads to the ordering of the local distortions - structural phase transitions. As each distortion is related to a specific electronic state (orbital) the JT structural transition is at the same time an ordering of orbitals. The last is a central question of the modern orbital physics. 

Nimzi et al. [53] showed the two-level model was well adapted for the 4-(N-(2-hydroxyethyl-J -ethyl)-amino-4 -nitrobenzene (DRl) dye, while a three-level model had to be considered for the 4-dibutylamino-4 -nitrobenzene (DEANS) system, due to electron-vibration interactions values of /zoi. and A/zoi could be deduced for both molecules. 

Significant advances have occurred of late in the computation of electron-vibration interactions in molecules. These are based on more or less sophisticated versions of the LCAO-method. A brief review of these works up to about 1978 is now available5 0c) (Chap. 8). 

The fundamentals of SSS are based on the theory of impurity centers in a crystal. The optical spectrum of an organic molecule embedded in a matrix is defined by electron-vibrational interaction with intramolecular vibrations (vibronic coupling) and interaction with vibrations of the solvent (electron-phonon coupling). Each vibronic band consists of a narrow zero-phonon line (ZPL) and a relatively broad phonon wing (PW). ZPL corresponds to a molecular transition with no change in the number of phonons in the matrix (an optical analogy of the resonance -line in the Mossbauer effect). PW is determined by a transition which is accompanied by creation or annihilation of matrix phonons. The relative distribution of the integrated intensity of a band between ZPL and PW is characterized by the Debye-Waller factor ... 

The final form of the Born-Handy formula consists of three terms The first one represents the electron-vibrational interaction. I will not present the numerical details for H2, HD and D2 molecules here, it can be found in our previous work. The most important result here is that the electron-vibrational Hamiltonian is totally inadequate for the description of the adiabatic correction to the molecular groundstates its contribution differs almost in one decimal place from the real values acquired from the Born-Handy formula. In the case of concrete examples -H2, HD and D2 molecules - the first term contributes only with ca 20% of the total value. The dominant rest - 80% of the total contribution - depends of the electron-translational and electron-rotational interaction [22]. This interesting effect occurs on the one-particle level, and it justifies the use of one-determinant expansion of the wave function (28.2). Of course, we can calculate the corrections beyond the Hartree-Fock approximation by means of many-body perturbation theory, as it was done in our work [22], but at this moment it is irrelevant to further considerations. 

The shielding at a given nucleus arises from the virtually instantaneous response of the nearby electrons to the magnetic field. It therefore fluctuates rapidly as the molecule rotates, vibrates and interacts with solvent molecules. The changes of shift widi rotation can be large, particularly when double bonds are present. For... 

Electronic structure theory describes the motions of the electrons and produces energy surfaces and wavefiinctions. The shapes and geometries of molecules, their electronic, vibrational and rotational energy levels, as well as the interactions of these states with electromagnetic fields lie within the realm of quantum stnicture theory. 

These so-called interaction perturbations Hint are what induces transitions among the various electronic/vibrational/rotational states of a molecule. The one-electron additive nature of Hint plays an important role in determining the kind of transitions that Hint can induce. For example, it causes the most intense electronic transitions to involve excitation of a single electron from one orbital to another (recall the Slater-Condon rules). 

If we deal with N isolated non-interacting entities such as the molecules in a gas at low density, we can further divide up molecular energies with reasonable accuracy into their electronic, vibrational and rotational contributions... 

Fig. 2. Surface temperature dependence of the vibrational excitation of NO(v = 0 — 1) in collisions with a clean Ag(lll) surface. The observed thermal activation was attributed to hot electron-hole-pair recombination transferring energy to NO vibration. This work provided some of the first strong evidence that metal electrons can interact with an adsorbate molecule strongly enough to change its vibrational quantum numbers. (See Ref. 24.)...

Experiments designed to probe these ideas have been carried out for NO colliding in high vibrational states on Au(lll). Before considering the results of these experiment, let us first look at how vibration might lead to unusual interactions with metal electrons. Molecules in vibrational states as high as NO(r = 15) undergo nuclear excursions that influence their... 

Fig. 10. The emerging picture of electronically nonadiabatic interactions of NO molecule scattering at a metal surfaces. Transition from the ground electronic state to an anionic state which is strongly attractive to the metal surface can be accomplished by high translational energy when vibrational excitation is low (black trajectory). When vibrational motion is highly excited, even low translational energies allow transition of the anionic state (red trajectory). Recently, Monte-Carlo wavepacket calculations have been carried out which tend to support this picture.63...

This arrangement may be the reason why the intensities of the CO vibrations are much less than the other modes in the molecule because tunneling electrons generally interact more strongly with dipoles perpendicular rather than parallel to the surface. 

Furthermore, as mentioned above the screening of the dipole field by the conduction electrons can be represented by an image dipole inside the metal. This complex of the chemisorbed molecule and its image has a vibration frequency different from that of the free molecule. The electrodynamic interaction between a dipole and its image has been discussed in many works. The theoretical problem is that the calculated frequency shift is extremely sensitive to the position of the image plane (Fig. 3a). One can with reasonable parameter values obtain a downward frequency shift of the order of 5-50 cm S but the latest work indicates that the shift due to this interaction is rather small. 

When the chemisorbed molecule is vibrationally excited this influences not only the metal electrons but also the ion cores in the neighbourhood. The vibrating ion cores can then in turn couple to other molecules and give rise to a short range interaction mediated via the substrate lattice. However, as Cl is much larger than the highest substrate phonon frequency the effect of this interaction is very small , but it can be important for low frequency modes . 

When the temperature of a molecule is increased, rotational and vibrational modes are excited and the internal energy is increased. The excitation of each degree of freedom as a function of temperature can be calculated by way of statis-hcal mechanics. Though the translational and rotational modes of a molecule are fully excited at low temperatures, the vibrational modes only become excited above room temperature. The excitation of electrons and interaction modes usually only occurs at well above combushon temperatures. Nevertheless, dissocia-hon and ionization of molecules can occur when the combustion temperature is very high. 

Since electrons are much faster than nuclei, owing to Wg Mj, ions can be considered as fixed and one can thus neglect the //ion-ion contribution (formally Mion-ion Hee, where Vion-ion is a Constant). This hrst approximation, as formulated by N. E. Born and J. R. Oppenheimer, reflects the instantaneous adaptation of electrons to atomic vibrations thus discarding any electron-phonon effects. Electron-phonon interactions can be a-posteriori included as a perturbation of the zero-order Hamiltonian Hq. This is particularly evident in the photoemission spectra of molecules in the gas phase, as already discussed in Section 1.1 for nJ, where the 7T state exhibits several lines separated by a constant quantized energy. 

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