Harmonic stretching constants

The harmonic force constants, frr and frr, are identical to those found when rectilinear coordinates are used. They may therefore be estimated from the observed stretching frequencies using A = (2 ircojk)2 and Eq. (5.3),... 

From calculations made for a number of simple molecules, it has become clear that in the cubic and quartic part of the potential written in curvilinear valence-force coordinates, the diagonal bond-stretching force constants (fm and fmr) are much larger than the bending and interaction constants. On this observation is based the simplest model potential, the anharmonic simple valence-force (SVF) model that consists of a complete harmonic potentialf with only the diagonal cubic and quartic stretching constants) and fmr added,... 

Representative force constants (/) for stretching of chemical bonds are listed in this table. Except where noted, all force constants are derived from values of the harmonic vibrational frequencies cd. Values derived from the observed vibrational fundamentals V, which are noted by a, are lower than the harmonic force constants, typically by 2 to 3% in the case of heavy atoms (often by 5 to 10% if one of the atoms is hydrogen). Values are given in the SI unit newton per centimeter (N/cm), which is identical to the commonly used cgs unit mdyn/A. 

The temperature dependence of QI rate constant, computed in Ref. [45], is shown in Figure 3.7. QI CCSD + B98 (HA) curve denotes HA result based on V2 (i.e., B98), and QI CCSD + B98 (HA) + EVB (PI anharm.) curve shows the full QI result, that is, including the anharmonicity PI correction computed with V3 (i.e., an EVB based on GAFF force field [86]). As GAFF force field considers only harmonic stretches, the only anharmonicities included are due to nonbonded interactions. Because of this, the final and presumably the most accurate curve is QI CCSD - -B98(HA) + EVB AMI (PI anharm.) that stiU uses EVB potential near the transition state, but computes the reactant PI anharmonicity corrections with the semiempirical AM 1 potential. It may seem more consistent to use AM 1 potential also in the constrained PI simulations however, this was computationally prohibitive. For simplicity, in the following discussion, CCSD + B98 (HA) is omitted as this part is common to all theoretical methods considered. 

The H-A bond is essentially a slightly stretched HA bond and the corresponding harmonic force constant (/ha)> equilibrium bond length (/nA.eq) and binding energy (Dha) can be taken from the isolated molecule. However, for the B - - H bond the quantities /hb+> /HB+,eq and Dhb+ are not readily... 

Resistance against change of bond order is measured as a harmonic stretching force constant. It depends on the relative energies of adjacent bond orders and on the slope of the linear curve that describes continuous change of bond order. In... 

The optimized quantized values of bond order correspond in an overwhelming majority of cases directly with the traditionally recognized single, double, triple and quadruple bonds that count electron pairs per interaction. Deformation of any diatomic system is resisted by the disturbance of an optimal arrangement and measured with a harmonic stretching force constant. Its value depends on the differences A D and Arf, and the slope, 5, of the line that represents the change between bond orders as a continuous function as shown in Fig. 2 of the covalence paper [38]. Calculation of AD is simplified by a special property of the golden ratio - t = = t+. In the common units of Ncm or mdyne/A, the... 

The selection rules provide crucial information for relating laboratory spectral results to molecular features such as bond lengths or harmonic force constants. To do that requires that we change our thinking somewhat. So far, we have learned how to predict a spectrum given the molecule s potential, V(s). But the stretching potentials of diatomic molecules are not known a priori. In fact, they are the very information that is to be extracted from experiment, not the... 

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