Electronic-vibrational coupling

Abstract Keeping in mind the pedagogical goal of the presentation the first third of the review is devoted to the basic definitions and to the description of the cooperative Jahn-Teller effect. Among different approaches to the intersite electron correlation in crystals the preference is with the most fundamental and systematic Hamiltonian shift transformation method. Order parameter equations and their connection to the crystal elastic properties and to the orbital ordering are considered. An especial attention is paid to the dynamics of Jahn-Teller crystals based on the coupled electronic, vibrational, and magnetic excitations which are of big interest nowadays in orbital physics. 

Figure 6 demonstrates the results of the neutron scattering measurements by Kjems, Hayes, and Smith [17] that clearly show the coupled electron-vibrational modes in TmV04. 

Here we discuss light absorption by various components of the cell and the effects caused by light absorption. Primary photoinduced cellular effects are produced by light absorption to induce transition between two electronic states (electronic or coupled electronic-vibrational [vibronic] transitions). Purely vibrational transitions (such as IR and Raman) are of significance only in stmctural identification and in conformational analysis. We first discuss the absorption by various constituent molecules and biopolymers. Subsequently we discuss the various photochemical and photophysical processes induced by light absorption. Then we discuss the effects produced from light absorption by an exogenous chromophore added to the cell. 

The coupling of vibrational and electronic motions in degenerate electronic states of inorganic complexes, part 1 state of double degeneracy. A. D. Liehr, Prog. Inorg. Chem., 1962, 3, 281-314 (25). 

However, others reached more ambiguous conclusions. Gates et al. developed a 2D model based on coupling NO vibration to surface phonons, but ignoring the possible role of electron-hole pairs, and successfully captured... 

Fig. 8. Scattering the transition state from the surface. Measured vibrational distribution of NO resulting from scattering of laser-prepared NO(v = 15) from Au (111) at incidence = 5 kJ mol-1. Only a small fraction of the laser-prepared population of v = 15 remains in the initial vibrational state. The most probable scattered vibrational level is more than 150 kJ mol-1 lower in energy than the initial state. Vibrational states below v = 5 could not be detected due to background problems. These experiments provide direct evidence that the remarkable coupling of vibrational motion to metallic electrons postulated by Luntz et al. can in fact occur. (See Refs. 44 and 59.)...

Equation 1 describes the radiationless decay rate for a single-frequency model with weak electron-vibration coupling in the low temperature limit as derived by Englman and Jortner. 

The reorganization free energy /.R represents the electronic-vibrational coupling, ( and y are fractions of the overpotential r] and of the bias voltage bias at the site of the redox center, e is the elementary charge, kB the Boltzmann constant, and coeff a characteristic nuclear vibration frequency, k and p represent, respectively, the microscopic transmission coefficient and the density of electronic levels in the metal leads, which are assumed to be identical for both the reduction and the oxidation of the intermediate redox group. Tmax and r max are the current and the overvoltage at the maximum. 

Hence, according to the symmetry selection rule, n —> n transitions are allowed but n —> ti transitions are forbidden. However, in practice the n —> it transition is weakly allowed due to coupling of vibrational and electronic motions in the molecule (vibronic coupling). Vibronic coupling is a result of the breakdown of the Born-Oppenheimer approximation. 

Figure 1. Relationship between activation free energy and overall free energy (values in units of electron-vibrational coupling energy x) n high-temperature...

In this expression A and Q are distance dispersion resulting from electron-vibrational coupling, and frequency tensor (assumed identical in reactant and product states), respectively (work of formation of precursor and successor states is omitted). If we assume that the frequency tensor is diagonal, then we have simply a sum of independent terms for all inner and outer contributing modes. At sufficiently high temperature, the hyperbolic tangents become unity and we obtain the usual (in this approximation) high-temperature expression ... 

There are at least two ways in which detailed information about electron-vibrational coupling strengths can be obtained for mixed-valence complexes. Both are based on the fact that such coupling will be reflected in modifications of the vibrational spectrum. Thus, for example, coupling to antisymmetric modes in a symmetric ion will modify intensities and frequencies of the modes involved. 

In the MQC mean-field trajectory scheme introduced above, all nuclear DoF are treated classically while a quantum mechanical description is retained only for the electronic DoF. This separation is used in most implementations of the mean-field trajectory method for electronically nonadiabatic dynamics. Another possibility to separate classical and quantum DoF is to include (in addition to the electronic DoF) some of the nuclear degrees of freedom (e.g., high frequency modes) into the quantum part of the calculation. This way, typically, an improved approximation of the overall dynamics can be obtained—albeit at a higher numerical cost. This idea is the basis of the recently proposed self-consistent hybrid method [201, 202], where the separation between classical and quantum DoF is systematically varied to improve the result for the overall quantum dynamics. For systems in the condensed phase with many nuclear DoF and a relatively smooth distribution of the electronic-vibrational coupling strength (e.g.. Model V), the separation between classical and quanmm can, in fact, be optimized to obtain numerically converged results for the overall quantum dynamics [202, 203]. 

Figure 32. Vibronic periodic orbits of a coupled electronic two-state system with a single vibrational mode (Model IVa). All orbits are displayed as a function of the nuclear position x and the electronic population N, where N = Aidia (left) and N = (right), respectively. As a further illustration, the three shortest orbits have been drawn as curves in between the diabatic potentials Vi and V2 (left) as well as in between the corresponding adiabatic potentials Wi and W2 (right). The shaded Gaussians schematically indicate that orbits A and C are responsible for the short-time dynamics following impulsive excitation of V2 at (xo,po) = (3,0), while orbit B and its symmetric partner determine the short-time dynamics after excitation of Vi at (xo,po) = (3, —2.45).

Non-Adiabatic Molecular Hamiltonian. Canonical Transformation Coupling Electronic and Vibrational... 

Eieiat. describes relativistic effects (such as variations in spin couplings - see Chap. A) and 8Econ. other electron-electron (and also electron-vibrational) many-body correlation effects (which are not included in Hartree-Fock calculations). 

Gas-phase photoelectron spectroscopy (PES) has been used in conjunction with theoretical calculations to investigate the hole-vibrational and electron-vibrational couplings in fused benzodithiophenes. The first ionization energies of benzojl,2- 5,4- ]dithiophene 21 and benzo[l,2-A4,5- ]dithiophene 22 were found to be to be 7.585 and 7.573eV, respectively <2006CEJ2073>. 

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