Vibrations bending

Marquardt R, Quack M and Thanopoulos I 2000 Dynamical chirality and the quantum dynamics of bending vibrations of the CH chromophore In methane Isotopomers J. Phys. Chem. A 104 6129—49... 

Tunabie far-iR iaser speotrosoopy of ]et-oooied oarbon oiusters—the bending vibration of C3 Science 249 897-... 

The use of isotopic substitution to detennine stmctures relies on the assumption that different isotopomers have the same stmcture. This is not nearly as reliable for Van der Waals complexes as for chemically bound molecules. In particular, substituting D for H in a hydride complex can often change the amplitudes of bending vibrations substantially under such circumstances, the idea that the complex has a single stmcture is no longer appropriate and it is necessary to think instead of motion on the complete potential energy surface a well defined equilibrium stmcture may still exist, but knowledge of it does not constitute an adequate description of the complex. 

Figure C3.5.11. IR-Raman measurements of vibrational energy flow tlirough acetonitrile in a neat liquid at 300 K, adapted from [41], An ultrashort mid-IR pulse pumps the C-H stretch, which decays in 3 ps. Only 1% of the energy is transferred to the C N stretch, which has an 80 ps lifetime. Most of the energy is transferred to the C-H bend plus about four quanta of C-C=N bend. The daughter C-H bend vibration relaxes by exciting the C-C stretch. The build-up of energy in the C-C=N bend mirrors the build-up of energy in the bath, which continues for about 250 ps after C-H stretch pumping.

Explicit forms of the coefficients Tt and A depend on the coordinate system employed, the level of approximation applied, and so on. They can be chosen, for example, such that a part of the coupling with other degrees of freedom (typically stretching vibrations) is accounted for. In the space-fixed coordinate system at the infinitesimal bending vibrations, Tt + 7 reduces to the kinetic energy operator of a two-dimensional (2D) isotropic haiinonic oscillator. 

In this section, we briefly discuss spectroscopic consequences of the R-T coupling in tiiatomic molecules. We shall restrict ourselves to an analysis of the vibronic and spin-orbit structure, detennined by the bending vibrational quantum number o (in the usual spectroscopic notation 02) and the vibronic quantum numbers K, P. 

The first theoretical handling of the weak R-T combined with the spin-orbit coupling was carried out by Pople [71]. It represents a generalization of the perturbative approaches by Renner and PL-H. The basis functions are assumed as products of (42) with the eigenfunctions of the spin operator conesponding to values E = 1/2. The spin-orbit contribution to the model Hamiltonian was taken in the phenomenological form (16). It was assumed that both interactions are small compared to the bending vibrational frequency and that both the... 

After integrating over all electronic coordinates except for 0, the electronic operator transforms into the potential for bending vibrations has the fonn... 

The force constants kj,kc and the dimensionless Renner parameters r, c ate defined by the adiabatic potentials for the components of the II state at pure trans (Vj, Vj) and pure cis (V, V ) bending vibrations,... 

We introduce the dimensionless bending coordinates qr = t/XrPr anti qc = tAcPc ith Xt = (kT -r) = PrOir, Xc = sJ kcPc) = Pc nc. where cor and fOc are the harmonic frequencies for pure trans- and cis-bending vibrations, respectively. After integrating over 0, we obtain the effective Hamiltonian H = Ho + H, which is employed in the perturbative handling of the R-T effect and the spin-orbit coupling. Its zeroth-order pait is of the foim... 

This Schrodinger equation forms the basis for our thinking about bond stretching and angle bending vibrations as well as collective phonon motions in solids... 

The above figure shows part of the infrared absorption spectrum of HCN gas. The molecule has a CH stretching vibration, a bending vibration, and a CN stretching vibration. 

The 6(CH) bending vibrations have been located between 1250 and 1000 cm and show varying frequencies as a function of the nature and the position of substituents (203). It is possible, however, that the SC(2,H mode is located near 1220 cm and suffers the weakest influence from 4-or 5-Substitution. 

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