Stretch Stretched

Torsion-bend and torsion-bend-bend terms may also be included the latter, for example would couple two angles A-B-C and B-C-D to a torsion angle A-B-C-D. Maple, Dinu and Hagler used quantum mechanics calculations to investigate which of the cross term are most important and suggested that the stretch-stretch, stretch-bend, bend-bend stretch-torsion and bend-bend-torsion were most important [Dinur and Hagler 1991 (schematically illustrated in Figure 4.13). 

Here, f, /i2, /i3 and /33 are the stretching, stretching-stretching interaction, stretching-bending interaction, and bending force constants, respectively, and r (equilibrium distance) is multiplied to make /i3 and /33 dimensionally similar to the others. Using matrix expression, Eq. (1-86) is written as... 

Since there are two force constants and four frequencies, one can test the quality of this force field by determining k and kg/f separately from Eqs. (12) and (13) and from Eqs. (14) and (15). However, for some tetrahedral molecules, it is found that the latter two equations yield imaginary values for kmA kg, and this is an indication that stretch-stretch, stretch-bend, and bend-bend interaction terms may be important in U. Unfortunately addition of these terms leads to more complex expressions than Eqs. (12) to (15) and to more force constants than can be determined from the four observed frequencies. Use of frequencies of isotopic forms of the molecule is often helpful in such cases and can permit more accurate determination of potential functions. ... 

O II RCOR Carboxylic Esters (Section 18.1Q c=o sp - C—O sp C—O Stretching Stretching Stretching 1735-1800 1200-1250 1000-1100 Strong Strong Strong... 

Some of the modern force fields also include cross-terms to account for bond or angle distortions caused by nearby atoms. These terms are required to accurately reproduce experimental vibrational frequencies of molecules. Cross-terms may include stretch-stretch, stretch-bend-stretch, bend-bend, torsion-stretch, torsion-bend-bend, bend-torsion-bend, stretch-torsion-stretch terms. 

Cation Form) A-1 Opening Bend 6-Rings Stretch Stretch... 

McHugh (1975) has calculated the amount of extension as a function of deformation rate and molecular weight in polymer solutions. His results are presented in Fig. 19.18. They illustrate the enormous difference between shear and stretch. Stretch forces are far more conducive to chain extension and hence to fibrous nucleation than shear forces. 

The two Ai stretchings of axial (ax) and equatorial (eq) CO groups are extensively coupled84, 87> 216. Approximate force-field calculations have been made which neglect coupling with other molecular vibrations and take into account only two CO stretching force constants (/ax,/eq) and two CO/CO stretch-stretch interaction force constants (/ax,e9 To avoid vagueness,... 

This formula related the bending force constant to the stretching force constants. Now the stretch-stretch interaction force constant 12 is usually smaller by a factor of 10 or so than tl and hence often can be neglected. Then from equation (137) ... 

Compound N-H stretching asym sym N-H C-N deformation stretching c=o c-o stretching stretching Other vibrations and remarks... 

These approximations discussed above are important in attempting an assessment of the validity of the Cotton-Kraihanzel method. Thus, force constants calculated by this simplified approach for the compounds M(C0)e (M = Cr, Mo, or W) were compared with the values obtained using the complete secular equations and a more rigorous force field (195). Considerable discrepancies in the CO stretch-stretch interaction constants were noted. Furthermore, 8 values have been calculated (d ) and were found to be of the same order of magnitude as the CO stretch-stretch interaction constants. Thus, the possibility that 8 values are significant must be considered in discussing the applications of the Cotton-Kraihanzel force field. 

The construction of the F matrix is described first. The valence force constants are defined as and k referring to CO groups trans and cis to the ligand, X, respectively k, k and kt are CO stretch-stretch interaction constants between CO -CO, CO< -CO< (cis), and CO< >-CO< (trans), respectively. The F matrix elements can then be derived by setting up the following scheme and using the standard rules (S09). 

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