High frequency intramolecular modes

Ideally, one would like to study one single adsorbed molecule at 0 K but for practical reasons one has to study an ensemble of molecules at Anite temperatures. Even if it is feasible to cool the sample to very low temperatures. 

Molecule-molecule interactions can be direct (b) or mediated via the substrate (c). There may also be a substantial interaction wiA thermally excited, low frequency modes (d). 

It is a well known fact that the vibration frequency of the internal stretch mode of CO decreases from its gas phase value of 2143 cm on chemisorption onto a metal surface. In general terms, depending on the adsorption site it takes values between 2000-2100 cm Mn the ontop position, 1900-2000 cm when bridgebonded and 1800-1900 cm for molecules in the hollow site. The vibration frequency of a particular system is of course the total effect of the different kinds of interactions sketched in Fig. 2. For example, simply the fact that the oscillator is attached to a more or less rigid substrate so that the 

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. 

The situation is quite different for physisorbed molecules. In that case, there is no transfer of charge, the mechanical renormalization is weaker due to a much weaker metal-molecule bond and also the image interaction is smaller as the molecule probably is adsorbed further out from the surface. In a recent IRS investigation of CO physisorbed on Al(100) the measured frequency is only shifted down a few cm from the gasphase value. However, there is for this system also a short range intermolecular interaction that certainly will affect the vibrational frequency. As yet there exist no theoretical calculations for the van der Waals interaction between a CO molecule and a metal. 

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A covalent bond (or particular nomial mode) in the van der Waals molecule (e.g. the I2 bond in l2-He) can be selectively excited, and what is usually observed experimentally is that the unimolecular dissociation rate constant is orders of magnitude smaller than the RRKM prediction. This is thought to result from weak coupling between the excited high-frequency intramolecular mode and the low-frequency van der Waals intemiolecular modes [83]. This coupling may be highly mode specific. Exciting the two different HE stretch modes in the (HF)2 dimer with one quantum results in lifetimes which differ by a factor of 24 [84]. Other van der Waals molecules studied include (NO)2 [85], NO-HF [ ], and (C2i J )2 [87]. 

While being very similar in the general description, the RLT and electron-transfer processes differ in the vibration types they involve. In the first case, those are the high-frequency intramolecular modes, while in the second case the major role is played by the continuous spectrum of polarization phonons in condensed 3D media [Dogonadze and Kuznetsov 1975]. The localization effects mentioned in the previous section, connected with the low-frequency part of the phonon spectrum, still do not show up in electron-transfer reactions because of the asymmetry of the potential. 

To conclude, it seems that the nature of the anharmonic coupling between a high frequency intramolecular mode and a thermally excited low frequency mode is understood. It turns out that the strength of the influence on the infrared spectrum critically depends on the values of (Oq, Sm and t. However, we have to wait for more experimental data on these low frequency modes, probably obtained with the helium atom scattering technique, bdbre we can make more definite conclusions. 

Figure 2.4. The energy-gap dependence of the nuclear Franck-Condon factor, which incorporates the role of the high-frequency intramolecular modes. Sc = A/2 is the dimensionless electron-vibration coupling, given in terms which reduce replacement (A) between the minimum of the nuclear potential surfaces of the initial and final electronic states. (Bixon and Jortner, 1999) Reproduced with permission.

High-frequency intramolecular modes and shifts are represented by a single effective frequency. 

Early studies showed tliat tire rates of ET are limited by solvation rates for certain barrierless electron transfer reactions. However, more recent studies showed tliat electron-transfer rates can far exceed tire rates of diffusional solvation, which indicate critical roles for intramolecular (high frequency) vibrational mode couplings and inertial solvation. The interiDlay between inter- and intramolecular degrees of freedom is particularly significant in tire Marcus inverted regime [45] (figure C3.2.12)). 

In the examples smdied so far, the photoinduced short-time dynamics of a molecular system has been governed by a few high-frequency intramolecular vibrational modes that strongly couple to the electronic transition, a situation that... 

In Eq. (5b), /zw is the frequency and S is the unitless displacement of the high-frequency intramolecular vibrational mode which is coupled to the ET process,... 

Involvement of intramolecular high-frequency vibrational modes in electron transfer was considered (Efrima and Bixon, 1974 Nitzan et al., 1972 Neil et al., 1974, Jortner and Bixon, 1999b Hopfield, 1974 Grigorov and Chernyavsky, 1972 Miyashita et al. 2000). As an example, when the high-frequency mode (hvv) is in the low-temperature limit and solvent dynamic behavior can be treated classically (Jortner and Bixon, 1999 and references therein), the rate constant for non-adiabatic ET in the case of parabolic terms is given by... 

Three broad classes of vibrational modes may contribute to the thermally averaged Franck-Condon factor the high-frequency (fast) modes hv > 1000 cm ) which are mainly intraligand vibrations, intermediate modes (1000 cm > hv > 100 cm ) that typically include the metal-ligand stretching vibrations and higher frequency solvent orientational-vibrational modes, and the low-frequency (slow) modes hv < 100 cm ) which are primary solvent modes but can include low-frequency intramolecular modes. At ordinary temperatures hv kT k hv hv and the low-frequency modes can be treated using classical (continuum) expressions. 

Intramolecular vibrations strongly scatter electrons near the Femii-surfacc in doped fuUerenes. A simple expression for the electron-phonon coupling parameters for this case is derived and evaluated by quantum-chemical calculations. The observed superconducting transition temperatures and their variation with lattice constants can be understood on this basis. To test the ideas and calculations presented here, we predict that high frequency Hg modes acquire a width of about 20% of their frequency in superconductive foUerenes, and soften by about 5% compared to the insulating fuUerenes. 

An important achievement of the early theories was the derivation of the exact quantum mechanical expression for the ET rate in the Fermi Golden Rule limit in the linear response regime by Kubo and Toyozawa [4b], Levich and co-workers [20a] and by Ovchinnikov and Ovchinnikova [21], in terms of the dielectric spectral density of the solvent and intramolecular vibrational modes of donor and acceptor complexes. The solvent model was improved to take into account time and space correlation of the polarization fluctuations [20,21]. The importance of high-frequency intramolecular vibrations was fully recognized by Dogonadze and Kuznetsov [22], Efrima and Bixon [23], and by Jortner and co-workers [24,25] and Ulstrup [26]. It was shown that the main role of quantum modes is to effectively reduce the activation energy and thus to increase the reaction rate in the inverted... 

Fig. 5.5. Normal modes of the 4 atom hydrogen bonded (DF)2. The 6 vibrational degrees of freedom naturally separate into high frequency (intramolecular) and low frequency (intermolecular) modes. The intermolecular modes correspond to stretches and bends of the hydrogen bond, with typical frequencies of a few hundred cm s. The intramolecular modes, however, correspond to stretches of the covalent DF bonds and therefore absorb near the 3000cm free DF frequency. Shown at right is a schematic diagram illustrating how the far-IR intermolecular modes may be observed in the near-IR via combination bands built on the high frequency intramolecular vibrations.

The phonon frequencies Vpho on in proteins have the following characteristic values at acoustic modes they lie between 10" and 10" s" ( 0.0004-0.004 eV) in a polypeptide chain the acoustic modes are generated by vibrations, which cause changes in the relative distances and orientations of the side chains. The upper limit is given by the high-frequency intramolecular vibrational modes of hydrogen atoms with a frequency of 10 s" ( 0.4 eV). At body temperatures (k T ks 310 K 0.03 eV), the acoustic modes will be most active in the scattering of electrons. Therefore for the subsequent considerations Vphonon = 10 s has been taken as the characteristic value. 

Very fast processes like high frequency intramolecular vibrational modes contribute mainly to the Stokes shift occuring in an electron transfer process, but they are not necessarely very specific for the dynamics of proteins. 

At higher frequencies (above 200 cm ) the vibrational spectra for fullerenes and their cry.stalline solids are dominated by the intramolecular modes. Because of the high symmetry of the Cgo molecule (icosahedral point group Ih), there are only 46 distinct molecular mode frequencies corresponding to the 180 6 = 174 degrees of freedom for the isolated Cgo molecule, and of these only 4 are infrared-active (all with Ti symmetry) and 10 are Raman-active (2 with Ag symmetry and 8 with Hg symmetry). The remaining 32 eigcnfrequencies correspond to silent modes, i.e., they are not optically active in first order. 

Experimental studies of liquid crystals have been used for many years to probe the dynamics of these complex molecules [12]. These experiments are usually divided into high and low-frequency spectral regions [80]. This distinction is very important in the study of liquid crystalline phases because, in principle, it can discriminate between inter- and intramolecular dynamics. For many organic materials vibrations above about 150 cm are traditionally assigned to internal vibrations and those below this value to so-called lattice modes . However, the distinction is not absolute and coupling between inter- and intramolecular modes is possible. 

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