Vibrational lowest frequency

Different motions of a molecule will have different frequencies. As a general rule of thumb, bond stretches are the highest energy vibrations. Bond bends are somewhat lower energy vibrations and torsional motions are even lower. The lowest frequencies are usually torsions between substantial pieces of large molecules and breathing modes in very large molecules. 

When the potential V Q) is symmetric or its asymmetry is smaller than the level spacing (Oq, then at low temperature (T cuo) only the lowest energy doublet is occupied, and the total energy spectrum can be truncated to that of a TLS. If V Q) is coupled to the vibrations whose frequencies are less than coq and co, it can be described by the spin-boson Hamiltonian... 

The damping material does not have to be a critical gel. Many applications do not require extra low damping frequencies. The lowest vibration damping frequency comin determines the longest relaxation time, Amax. A suitable damping material would be crosslinked beyond the gel point, with a 2max of about... 

The lowest frequency microwave transitions of HC,2NM and DC,2N14 occur at 88,631 and 72,415 MHz, respectively. (These are for the ground vibrational state.) Use the formula of Problem 5.6 to calculate the bond distances in HCN. (Ignore zero-point vibrations.)... 

An unresolved puzzle remains22 the first two vibrational peaks in the first band in the photoelectron spectrum are separated only by 360 20 cm4, less than the lowest frequency vibration observed in neutral propellane (529 cm4), and very much less than its lowest totally symmetric vibration (908 cm 1). Yet, the authors calculations22 suggest that the lowest frequency totally symmetrical vibration of the radical cation will be at higher and not lower frequencies. The authors suggested that the vibrational structure may be due to vibronic mixing with the lowest excited state of the radical cation. 

Note that in the present case, neither the Fukui theorem [Fukui, 1970] mentioned in Section 8.4 nor the similar statement concerning the initial direction of the instanton path (see Section 4.1) are valid. Both state that the reaction coordinate (IRC in the case of Fukui theorem or instanton) near the minimum of the surface is directed along the coordinate of the vibration with the lowest frequency. That would mean for our case that... 

The lowest frequencies v t g) 100-110 cm-1 and v( l u) 120-127 cm-1 correspond to rotational and translational vibrations of the icosahedral L Ali2 guest as a whole inside the AI20O30 cage. The largest IR-active frequency v(hu) within the range 340—470 cm-1 is related mostly to vibration... 

In addition, they predict that the ROA couplet due to the coupled C=C stretching vibrations should be the largest feature by far in the ROA spectmm of (+)-(P)-l,4-dimethylenespiropentane, with the exception of the lowest frequency vibration predicted to occur outside the presently measurable range. Higher quality computed data [38] give the same result. 

A fundamental prediction of the FrBhlich model then is that in subsystems which exchange photons with a thermal bath, in the nonlinear manner given by the set of Eqs.(14) and quantified by the magnitude of y in Eq. (18), a condensation of photons into the lowest-frequency vibration occurs as the rate of energy pumping from the thermal bath increases above a threshold value, S0 ... 

The structure of the lowest frequency vibrational bands of a helical chain is shown in Figure 1. The two zero frequency modes at 0 = 0 correspond to rotation and translation along the central helical axis. Translations perpendicular to the helical axis are... 

The lowest frequency at 335, 290 and 260 cm.-1 corresponding to 29.9, 34.5 and 38.5/u also had to be taken from Raman data alone since it is beyond the range of infrared spectrometers. The low frequency indicates that both atoms involved are heavy and the bending vibration of the halogen and the adjacent carbon atom was assigned to this frequency as shown in Fig. 37. 

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