Vibration intermolecular

Tardy D C and Rabinovitch B S 1977 Intermolecular vibrational energy transfer in thermal unimolecular systems Chem. Rev. 77 369-408... 

Dvorak M A, Reeve S W, Burns W A, Grushow A and Leopold K R 1991 Observation of three intermolecular vibrational-states of Ar-HF Chem. Phys. Lett. 185 399-402... 

Chuang C, Andrews P M and Lester M I 1995 Intermolecular vibrations and spin-orbit predissooiation dynamios of NeOH J. Chem. Phys. 103 3418-29... 

Lotshaw WT, McMorrow D, Thantu N, Melinger J S and Kitchenbaum R 1995 Intermolecular vibrational coherence in molecular liquids J. Raman Spectrosc. 26 571-83... 

Zwitterionic L-alanine ( HjN—CfCHj)—CO2—) is a dipolar molecule that forms large well-ordered crystals in which the molecules form hydrogen-bonded columns. The strong interactions lead to the presence of well-defined intra- and intermolecular vibrations that can usefully be described using hannonic theory. 

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. 

A typical situation is when (5i > (5q, so that the tunneling distance Qo is overcome mostly at the expense of intermolecular vibration q. The probability p q) is exponentially small, but it is to be compared with the exponentially small barrier transparency, and reduction of the tunneling distance Qo — qhy promoting vibrations may be very large. 

It is noteworthy that it is the lower cross-over temperature T 2 that is usually measured. The above simple analysis shows that this temperature is determined by the intermolecular vibration frequencies rather than by the properties of the gas-phase reaction complex or by the static barrier. It is not surprising then, that in most solid state reactions the observed value of T 2 is of order of the Debye temperature of the crystal. Although the result (2.77a) has been obtained in the approximation < ojo, the leading exponential term turns out to be exact for arbitrary cu [Benderskii et al. 1990, 1991a]. It is instructive to compare (2.77a) with (2.27) and see that friction slows tunneling down, while the q mode promotes it. 

Let us now turn to the influence of vibrations on exchange chemical reactions, like transfer of hydrogen between two O atoms in fig. 2. The potential is symmetric and, depending on the coupling symmetry, there are two possible types of contour plot, schematically drawn in fig. 17a, b. The O atoms participate in different intra- and intermolecular vibrations. Those normal skeleton... 

When the mass of the tunneling particle is extremely small, it tunnels in the one-dimensional static barrier. With increasing mass, the contribution from the intermolecular vibrations also increases, and this leads to a weaker mass dependence of k, than that predicted by the onedimensional theory. That is why the strong isotope H/D effect is observed along with a weak k m) dependence for heavy transferred particles, as illustrated in fig. 18. It is this circumstance that makes the transfer of heavy reactants (with masses m < 20-30) possible. 

Such calculations have been performed by Takayanagi et al. [1987] and Hancock et al. [1989]. The minimum energy of the linear H3 complex is only 0.055 kcal/mol lower than that of the isolated H and H2. The intermolecular vibration frequency is smaller than 50cm L The height of the vibrational-adiabatic barrier is 9.4 kcal/mol, the H-H distance 0.82 A. The barrier was approximated by an Eckart potential with width 1.5-1.8 A. The rate constant has been calculated from eq. (2.1), using the barrier height as an adjustable parameter. This led to a value of Vq similar to that of the gas-phase reaction H -I- H2. 

Figure 1. Schematic of the radial cuts of the ground- and excited-state potential energy surfaces at the linear and T-shaped orientations. Transitions of the ground-state, T-shaped complexes access the lowest lying, bound intermolecular level in the excited-state potential also with a rigid T-shaped geometry. Transitions of the linear conformer were previously believed to access the purely repulsive region of the excited-state potential and would thus give rise to a continuum signal. The results reviewed here indicate that transitions of the linear conformer can access bound excited-state levels with intermolecular vibrational excitation.

The higher energy features can indeed be associated with transitions of He lCl(K,v" = 0) ground-state complexes with rigid He I—Cl linear geometries. In contrast to the T-shaped band that is associated with transitions to the most strongly bound intermolecular vibrational level in the excited state without intermolecular vibrational excitation, n = 0, the transitions of the linear conformer access numerous excited intermolecular vibrational levels, n > 1. These levels are delocalized in the angular coordinate and resemble hindered rotor levels with the He atom delocalized about the l Cl molecule. 

The angular-dependent adiabatic potential energy curves of these complexes obtained by averaging over the intermolecular distance coordinate at each orientation and the corresponding probability distributions for the bound intermolecular vibrational levels calculated by McCoy and co-workers provide valuable insights into the geometries of the complexes associated with the observed transitions. The He - - IC1(X, v" = 0) and He + 1C1(B, v = 3) adiabatic potentials are shown in Fig. 3 [39]. The abscissa represents the angle, 9,... 

Figure 12. Potential energy contour plots for He + I Cl(B,v = 3) and the corresponding probability densities for the n = 0, 2, and 4 intermolecular vibrational levels, (a), (c), and (e) plotted as a function of intermolecular angle, 0 and distance, R. Modified with permission from Ref. 40. The I Cl(B,v = 2/) rotational product state distributions measured following excitation to n = 0, 2, and 4 within the He + I Cl(B,v = 3) potential are plotted as black squares in (b), (d), and (f), respectively. The populations are normalized so that their sum is unity. The l Cl(B,v = 2/) rotational product state distributions calculated by Gray and Wozny [101] for the vibrational predissociation of He I Cl(B,v = 3,n = 0,/ = 0) complexes are shown as open circles in panel (b). Modified with permission from Ref. [51].

From the individual contributions of the modes to the msd along the c-axis ( 6 pm ) and along the a-axis ( 8 pm ), the corresponding calculated molecular Lamb-Mossbauer factors for the c-cut crystal (/Lm,c = 0.90) and for the a-cut crystal = 0.87) were derived. Comparison with the experimental /-factor, i.e., / P = 0.20(1) and/ N> = 0.12(1) [45], indicates that by far the largest part of the iron msd must be due to intermolecular vibrations (acoustic modes) of the nitroprusside anions and its counter ions. This behavior is reflected in the NIS spectrum of GNP by the considerable onset of absorption probability density below 30 meV in Fig. 9.36a. 

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... 

Intermolecular vibration involving nearest-neighbor molecules are easily excited in liquid hydrocarbons, since the de Broglie wavelength of the electron at a few tenths of electron-volt energy is comparable to the intermolecular separation. The quantum for this vibration lies in the far IR and can be observed indirectly by Raman spectra. Raman shifts in many hydrocarbon liquids have... 

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