Stretch-bend effect

It will be convenient to now discuss these equations in terms of the F matrix, which would then be used to actually solve the equations. We shall see later that it turns out that most of these troublesome cross terms result from the interaction of a lone pair of electrons with other nearby parts of the molecule. Since there are no lone pairs of electrons in hydrocarbons, this cross term problem is minimal in such compounds, and taking all of the cross terms equal to zero is a fair approximation. But a few of these terms are somewhat important, even in hydrocarbons. These few will be discussed here. 

Vibrational spectroscopy was a forerunner of molecular mechanics in the sense that spectroscopists used many of the basic methods used in molecular mechanics to calculate spectra, long before it was possible to calculate stiuctures. It was early found that a purely diagonal force field was less accurate than desired, and that cross terms could improve the quality of the spectra calculated. One of these cross terms was a stretch-bend term. It has the form shown in Eq. (4.12)  

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The number and type of cross terms vary among different force fields. Thus, AMBER2 contains no cross terms, MM23 uses stretch-bend interactions only and MM34 uses stretch-bend, bend-bend and stretch-torsion interactions. Cross terms are essential for an accurate reproduction of vibrational spectra and for a good treatment of strained molecular systems, but have only a small effect on conformational energies. 

Ideally, the Stanger demonstration should be an expression of the stretch-bend interaction in the Bj normal mode in benzene. Thus, it is instructive to examine the nature of the stretch-bend interaction in typical monocyclic and bicyclic alkenes. The IR spectra of monocyclic and bicyclic alkenes shift hypsochromically for exomethylenes and bathochromically for endocyclic alkenes with decreasing ring size. " This effect has been shown to be dominated by mode-coupling for the monocyclic series, but consistent with a pure angular effect or the bicyclic series.Further investigation in this vein is likely to resolve the paradox initiated by Stanger s work. 

To further characterize the effect of the ammonia hydrothermal treatment, we compared elemental analysis data and 1R spectra before and after ammonia hydrothermal treatment to quantitatively disclose the role of counterion between the silica framework and surfactants. In Table 2, the N/C molar ratio of the mesoporous materials prior to the ammonia hydrothermal treatment is nearly twice of that after the treatment. Moreover, the IR band at 1383 cm 1, which arises from the N03 stretch bending mode, completely disappears after ammonia hydrothermal treatment [20], These results verify that the existence of nitrate counterion (the nitrate/surfactant 1) between surfactant molecules and silica framework in the acid-made mesoporous materials. The bridging counterion N03 was completely removed after ammonia hydrothermal treatment. 

In MM3 a cross term involving torsional angles is also used[75] but in other programs it is neglected (exceptions are anomeric effects, e.g., with sugars). In other programs[52,5gJ, 1,3-interactions can be selectively included, e.g., to model the geometry of the chromophore of metal complexes. In these cases, an additional correction via a stretch-bend cross term is probably redundant. 

The CCSD(T)/aug-cc-pV(T d)Z calculated values of the G-matrix and force constant parameters used in Eqs. (5) and (9) are given in Table 8.1. From these parameters the effective stretch-bend coupling constants are calculated to be /r =... 

When complexed with HF, the stretching bends in NH3 were unshifted but intensified by upwards of thirty-fold. The situation is different when NH3 is bound to HjO, as the intensifications are much smaller, only an approximate doubling at the SCF level. However, correlation drastically enhances these bands, intensifying them by an order of magnitude, (Note that the lower symmetry of the HjN - HOH complex breaks the degeneracy of the pairs of vibrational levels in NH3.) The effects of complexation on the bending modes of NH3 are similar when either HF or H2O acts as proton donor. The lower-frequency bend is... 

Infrared spectra are potentially a very useful source of information on cis and trans effects. The frequency of a vibration is determined by the kinetic and potential energies of the nuclei involved (theoretically the whole complex, since all vibrations will couple to a certain extent) and the observed frequencies can be analyzed in terms of a generalized valence force field or some more approximate model to eliminate the kinetic energy and yield force constants (for stretching, bending, twisting, etc.) and interaction constants l iO)... 

This effective Hamiltonian will improve the taking into account of deformation vibrations [15,26,29,30], all of degrees of freedom of the system, namely vibronic effects [38,45-47]. However, the action of these factors (including stretch-bend resonance interactions, that perturb overtone part of vibrational spectra most of YCX3 molecules [15,26,29,30,48]) on vibrational... 

It is experimentally known that when a bond angle is reduced, the two bonds forming the angle will stretch in order to alleviate the resulting strain. Many force fields, including MM2 and MM3, use a stretch-bend term to account for this effect (Eq. [13]). 

The effect of this term is very similar to the effect of the stretch-bend interaction. The distance between atoms 1 and 3 is forced toward tq. If either the angle or the bond length is distorted, the other one adjusts to make r nearer to ro, so as to keep the energy at a minimum, similar to what happens with the stretch-bend interaction. 

C,H) and V(H,H) in CH4 and its isotopomers, /(C,H) was found to increase by 0.088 Hz on raising the temperature from 180 K to 380 K, which agrees with the observed increase of 0.083 Hz on raising the temperature from 200 K to 370 The D primary and secondary isotope effects on /(C,H) were predicted to decrease with increasing temperature. Table 18 shows the total values, separated into stretching, bending and the second-order stretch-bend contributions to /(C,H) and 7 (C,H) in each of the five isotopomers at 300 K, as well as the zero-point corrections. 7 (X,H) is defined as in Eq. (85). 

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