Intramolecular/intermolecular vibrational

For aromatic hydrocarbon molecules, in particular, the main acceptor modes are strongly anharmonic C-H vibrations which pick up the main part of the electronic energy in ST conversion. Inactive modes are stretching and bending vibrations of the carbon skeleton. The value of Pf provided by these intramolecular vibrations is so large that they act practically as a continuous bath even without intermolecular vibrations. This is confirmed by the similarity of RLT rates for isolated molecules and the same molecules imbedded in crystals. 

To circumvent this difficulty, one has to take into account that the reactants themselves take part in intermolecular vibrations, which may bring them to distances sufficiently short so as to facilitate tunneling, as well as classical transition. Of course, such a rapprochement costs energy, but, because the intermolecular modes are much softer than the intramolecular ones, this energy is smaller than that required for the transition at a fixed intermolecular distance. 

In the molecular approximation used in (14) only the L = 3W — 6 (W is the number of atoms) discrete intramolecular vibrations of the molecular complex in vacuo are considered. In general these vibrations correspond to the L highest optical branches of the phonon spectrum. The intermolecular vibrations, which correspond to the three acoustical branches and to the three lowest optical branches are disregarded, i.e., the center of mass and - in case of small amplitudes - the inertial tensor of the complex are assumed to be fixed in space... 

First, we shall consider the model where the intermolecular vibrations A—B and intramolecular vibrations of the proton in the molecules AHZ,+1 and BHZ2+1 may be described in the harmonic approximation.48 In this case, using the Born-Oppenheimer approximation to separate the motion of the proton from the motion of the other atoms for the symmetric transition, Eq. (16) may be... 

In addition to the effects of motional narrowing, vibrational line shapes for the OH stretch region of water are complicated by intramolecular and intermolecular vibrational coupling. This is because (in a zeroth-order local-mode picture) all OH stretch transition frequencies in the liquid are degenerate, and so the effects of any... 

Coherent ion dip spectroscopy has been shown to be a versatile tool for the investigation of high-lying intramolecular vibrations in the ground state of molecules and of intermolecular vibrations of van der Waals complexes. 

We have presented a new technique for the investigation of intramolecular couplings in the electronic ground state 50. The new technique of CIS is based on the special population dynamics induced by the coherent excitation of a three-level system with two narrow-band Fourier-transform-limited laser pulses. It allows the investigation of high-lying intermolecular vibrational states in the electronic ground state of van der Waals complexes. These... 

Now, in aromatic hydrocarbons intramolecular skeletal vibrations, rather than C—H vibrations, dominate the vibronic coupling contribution to the term J m = — . Furthermore, intermolecular vibrations will have negligible effect on the coupling of the electronic states of interest. Thus, in the case of internal conversion, where the (relatively large) matrix elements are solely determined by intramolecular vibronic coupling, no appreciable medium effect on the nonradiative lifetime is to be expected. On the other hand, intersystem crossing processes are enhanced by the external heavy atom effect, which leads to a contribution to the electronic coupling term. 

Recent advances in spectroscopic methods have enabled the water pentamer to be studied experimentally. Infrared cavity ringdown spectroscopy has been used to examine the intramolecular absorption features of the gas-phase water pentamer, which match the spectral features of the pentamer rings in liquid water and amorphous ice (Paul et al., 1999 Burnham et al., 2002). Vibration Rotation Tunnelling (VRT) spectroscopy has been used to provide a more direct probe of the water pentamer intermolecular vibrations and fine structure in liquid water (Liu et al., 1997 Harker et al., 2005). The water pentamer was found to average out... 

If none of the partners is linear 6 degrees of rotational and translational degrees of freedom will be transformed into vibrational ones. The additional intermolecular vibration is a torsional motion. If the proton donor is polyatomic there will be vt and v2 and other essentially intramolecular vibrations while in the case of HC1 only vx can exist. 

This is the most puzzling requirement. It is not known why certain crystals—for example, HMTSF TCNQ or Cu(DMDCNQI)2—conduct very well at low temperatures but do not form Cooper pairs. One may wonder whether certain intramolecular or intermolecular vibrations or rigid-body librational modes must be "right" for superconductivity. 

Seihneier A, Kaiser W. Ultrashort intramolecular and intermolecular vibrational energy transfer of polyatomic molecules in liquids. In Kaiser W, ed. Ultrashort Laser Pulses and Applications. Vol. 60. Berlin Springer-Verlag, 1988 279-315. 

To analyze the density-dependent vibrational lifetime data displayed in Fig. 3, it is necessary to separate the contributions to Ti from intramolecular and intermolecular vibrational relaxation. The intermolecular component of the lifetime arises from the influence of the fluctuating forces produced by the solvent on the CO stretching mode. This contribution is density dependent and is determined by the details of the solute-solvent interactions. The intramolecular relaxation is density independent and occurs even at zero density through the interaction of the state initially prepared by the IR excitation pulse and the other internal modes of the molecule. Figure 5 shows the extrapolation of six density-dependent curves (Fig. 3 three solvents, each at two temperatures) to zero density. The spread in the extrapolations comes from making a linear extrapolation using only the lowest density data, which have the largest error bars. From the extrapolations, the zero density lifetime is —1.1 ns. To improve on this value, measurements were made of the vibrational relaxation at zero solvent density. 

The superconducting ability of [M(dmit)2] complexes, see Fig. 9, has prompted experimental and theoretical vibrational studies of [Ni(dmit)2]z and [Pd(dmit)2]z complexes (z is in the range 0-2—), in order to understand the mechanism of superconductivity in terms of electron-intramolecular and electron-intermolecular vibrational couplings (14, 21). These studies have... 

Let X = q,p) denote the one-degree-of-freedom reaction coordinate. For M-degrees-of-freedom vibrational modes, 7 e R" and 0 G T" denote their action and angle variables, respectively, where T = [0,27t]. These action and angle variables would be obtained by the Lie transformation, as we have discussed in Section IV. In reaction dynamics, the variables (/, 0) describe the degrees of freedom of the intramolecular and possibly the intermolecular vibrational modes that couple with the reaction coordinate. In the conventional reaction rate theory, these vibrational modes are supposed to play the role of a heat bath for the reaction coordinate x. 

We denote by G the set of all the experimentally observable quantities (called physical observables) which must be reproduced. Such quantities are, for instance, the collision energy, the quantum numbers defining the intramolecular state (vibrations and the principal quantum number of rotation), the total angular momentum etc... However, there are other dynamical variables which have a clear meaning in Classical Mechanics but correspond to no physical observable because of the Uncertainty Principle. We call them phase variables and denote them globally by g. The phase variables must be given particular values to obtain, at given G, a particular trajectory. Such variables are, for instance, the various intramolecular normal vibrational phases, the intermolecular orientation, the secondary rotation quantum numbers, the impact parameter, etc... Thus we look for relationships of the type qo = qq (G, g) and either qo = qo (G, g) or po = Po (G, g)... 

In this article, we have presented a series of LD and MD simulations for ice Ih using a variety of water potentials and the results were compared with INS measured DOS. Neutron measurements were shown to provide unique information on the fundamental intramolecular and intermolecular modes, some of which cannot be obtained from the standard IR and Raman techniques. A full knowledge of the intermolecular vibrations as modulated by the molecule s environment in the lattice systems is necessary for a complete analysis of the dynamics of these ice structures. Equipped with the precise knowledge of the structural information obtained by the diffraction measurements [81,82], one can model the system rigorously with suitable force fields or potential functions. The extensive simulation results show that classic pair-wise potentials were unsuccessful in reproducing the measured DOS for ice Ih. 

The main point of the preceding discussion is an assumption about the adiabaticity of intramolecular motion with reference to the intermolecular one, that is, division of the system into two subsystems the fast one involving electrons and intramolecular vibrations and the slow one incorporating the intermolecular vibrations. This division of the motions was called a double adiabatic approximation (DAA) and was applied earlier in the theory of proton transfer in the reorganizing medium (see, e.g., refs. 10, 14, 28, and 31-33). The wavefunctions in DAA are presented as the products of the wavefunctions of the fast and slow subsystems ... 

To calculate the static thermodynamic and molecular ordering properties of a system of molecules, the configurational partition function Qc of the system must be derived. Qc does not contain the kinetic energy, intramolecular and intermolecular vibrations, and very small rotations about molecular bonds. Qc does contain terms which deal with significant changes in the shapes of the molecules due to rotations about semiflexible bonds (such as about carbon-carbon bonds in n-alkyl [i.e., (-CH2-)X] sections) in a molecule. For mathematical tractability in deriving Qc, the description of the molecules in continuum space is mapped onto a... 

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... 

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