Bending in-plane

It is common to use the symbols v(X-Y), i5(X-Y) and y(X-Y) for stretching, in-plane bending and out-of-plane bending, respectively, in the X-Y group. In addition, the word deformation is often used to imply a bending motion. 

Table IV. Calculated vibrational frequencies and IR intensities for the C5H7 to C H,3 The frequencies are given in cm > and the intensities are relative to the most intense mode for each molecule. The types represent the following vibrations SCI CH2 in plane bend, CCS = Carbon carbon stretching, CHB = CH in plane bend...

The v, i(b2) vibration featuring the asymmetric CC stretching vibration, which is strongly coupled with the asymmetric CH in-plane bending vibration (at 1061 cm- experimentally) is shifted by 20-25 cm towards lower frequencies, each time deuterium is incorporated in the molecule. The intensity ratio of V3 between the vs (ba) and the V4(a,) dominant feature is almost unchanged with deuteration. 

The vs(a ) vibration featuring the symmetric CH in-plane bending (at 886 cm- experimentally) is drastically shifted after deuteration because it implies mostly the CH bond. At the MP4 level our calculations show that v (a,) is shifted to 678 cnr in C3HD and to 648 cm- in C3D2 with weaker intensities of 9 and 7 Km/mol respectively. 

Figure 5. Pure torsional bands near the Si-So origin for three sixfold rotors as labeled. Band label my denotes a pure torsional transition from m = y in So to m = x in Si. The label bo denotes an increase from zero to one quantum of a low-frequency in-plane bending vibration.

The V3 and V4 bands are assigned to mixtures of CH in-plane bend and C=C and C—C stretches. The frequencies of these bands are affected significantly by the substitution of... 

In the MM3 program, the bending motions are divided into two separate descriptions in-plane and out-of-plane bending. The in-plane bending is shown in Equation 6. Depending on the geometry of the central atom in the... 

Fig. 5.4. Vibrational modes for CS2. (A) Represents the symmetrical stretch, (B) is the asymmetrical stretch, (C and D) are the out-of-plane and in-plane bending motions. The + and - symbols indicate motion toward and away from the viewer, respectively.

Ms, In-plane bending moment for the sustained condition being evaluated N-mm in.-lbf... 

Scissoring and rocking are called in Plane Bending while wagging and twisting are called out of plane Bending. 

In order to remove the spurious states, one takes advantage of the fact that the symmetry-adapted operators. S , S( ,. S(III), and their sum S are linear combinations of the projection operators on the symmetry species. If one rewrites Eq. (6.55) in terms of these operators, putting A - 0, one has for the C-C in-plane bend... 

Vibrational spectroscopy has been widely applied in the study of LDHs [161,162] but a somewhat confusing variety of spectral data and interpretations have appeared in the literature, hi this section, we focus on the information that can be obtained regarding the structure of the interlayer anions. The unperturbed carbonate ion has point symmetry Dsh. Group theoretical analysis predicts four normal modes the vi symmetric stretch of Aj symmetry at 1063 cm the V2 out of plane bend of A 2 symmetry at 880 cm the V3 asymmetric stretch of E symmetry at 1415 cm , and the V4 in plane bend of E symmetry at 680 cm [22]. The V2 mode is IR active only, the vi mode is Raman active only, whilst the two E modes are both IR and Ra-... 

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