Bending vibrational frequencies

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... 

Table I. Interatomic distances, shrinkages, and bending vibrational frequencies of first row transition metal dihalides...

Box 3.4 Out-of-plane C-H Bending Vibration Frequencies of Mono- and Disubstituted Aromatic Rings... 

The proton of OH-II is additionally hydrogen bonded to the neighboring basic oxygen. Therefore, its stretching vibration frequency, vOH, should be lower and its bending vibration frequency higher than those of OH-II. On the other hand, vOH for OH-II should be higher than that for OH-I (Table III). 

TABLES. Calculated 2D OH-stretching and SOH-bending vibrational frequencies (in cm ) and... 

The W02(g) was assumed to have a symmetry with a bond angle O-W-0 = 110 . The bond distance W-0 was estimated to be the same as that in W0(g). The symmetric and asymmetric stretching frequencies were obtained from the infrared spectrum of WO2 in a neon matrix by Weltner and McLeod (3 ). The bending vibrational frequency (300 cm ... 

It is well known that the out-of-plane C—H bending vibration frequencies of olefins, and in particular ethylene derivatives, are indicative of the double-bond configuration of the olefin species [18]. These vibrational... 

Fig. 2.2 Variation of O-H bending vibration frequencies of physically adsorbed water and DMFC maximum power density vs. the pH of slurry of the fillers. The inset shows...

Asvany O, Giesen T, Redlich B, Schlemmer S (2005) Experimental determination of the Vs cis-bending vibrational frequency and Renner-Teller structure in ground state (X Hu) C2H2 using laser induced reactions. Phys Rev Lett 94 073001... 

Eq. (1) tells that the symmetrical and antisymmetrical AAX bending vibration frequencies directly depend upon the angle t, since the coefficients of Psaax and... 

The calculated barrier to the transition from a pyramidal to a planar configuration and in the opposite direction is very low and varies depending on the calculation procedure. In particular, according to Vetere et al. (2000), the DFT/PBEO procedure yields barrier values of 0.71, 0.33, 0.08, and 0.04 kj/mol for lanthanum trihalides from trifluoride to triiodide, respectively. Of greater importance is another conclusion made by Kovacs et al. (1997) and substantiated by theoretical calculations in more recent works. The low out-of-plane bending vibrational frequencies V2 obtained in calculations are caused by the use of the harmonic approximation. In reality, these vibrations are anharmonic, and the V2 values are much higher. Unfortunately, taking into account anharmonic effects is currently impracticable for lanthanide trichlorides. 

Much less experimental data are available for the bending vibrational frequencies vs and V4 of lanthanide trichlorides. 

FIGURE 4 Reduced Gibbs energies of LaCl3(g) calculated in the harmonic and anharmonic approximations for the out-of-plane bending vibration frequency V2. See text for explanations. 

The bending vibration frequency of Eup2 measured by Hastie et al. (1971) in two matrices is virtually the same, and the use of a mean value is recommended. 

Comparison of the experimental and theoretical data of Kovacs and Konings (2004) with the molecular constants for RF3 shows that the bending vibrational frequencies were not corrected for matrix shift. In the calculation of the molecular constants of RCI2, we also did not correct the V2 frequencies for matrix shift (Chervoimyi and Chervoimaya, 2004g) rather, we accepted that the V3/V2 and Vi /V2 ratios are constant for dichlorides and are equal to the same ratios as found for EUCI2. The calculation of... 

NDg and NHD Radicals. Experimental frequencies of the bending vibration were reported for gaseous ND2 and for NHD in a matrix. Stretching and bending vibrational frequencies of ND2 and NHD were derived from an ab initio-computed general valence force field of 4th order [22] which reproduces the experimental NH2 fundamentals to within a few cm" . The frequencies of Vi, V2, 2v2, and V3 vibrations (in cm" ) are compiled in the following table ... 

Additional Excited States. Vibrational frequencies of NH2 in the B B2 state were calculated by ab initio procedures [8]. Stretching and bending vibrational frequencies of NH2 were ab initio-calculated for the core-hole states Bi, B, 11, and [11]. 

Metal carbonyl compounds Approximate CO stretching vibration frequency Approximate M-C stretching MCO bending vibration frequencies (cm )... 

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