Reference bond length

For each pair of interacting atoms (/r is their reduced mass), three parameters are needed D, (depth of the potential energy minimum, k (force constant of the par-tictilar bond), and l(, (reference bond length). The Morse ftinction will correctly allow the bond to dissociate, but has the disadvantage that it is computationally very expensive. Moreover, force fields arc normally not parameterized to handle bond dissociation. To circumvent these disadvantages, the Morse function is replaced by a simple harmonic potential, which describes bond stretching by Hooke s law (Eq. (20)). 

Table 4.1 Force constants and reference bond lengths for selected bonds [Allinger 1977],...

The 6th, 7th, and 8th terms of expression (9) are sometimes neglected or is related to (24,25). The potential constants of UBFF s, including the reference parameters, often deviate markedly from the corresponding VFF-constants. Especially the reference bond lengths b may assume values which hardly agree with intuitive ideas about strain-free bond lengths. 

In cases where the experimental and theoretical bond valences are different, the bond capacitances do not cancel, but the experimental bond valences continue to give a good estimate of the bond flux (Preiser et al. 1999). In these cases, discussed in Chapters 8 and 12, the theoretical bond valences can be used to determine a reference bond length against which the sizes of the strains in the observed bond lengths can be measured. 

Correlated calculations using SDCI plus generalized Davidson or MP2 corrections as described for the Hubbard model were first performed for buckminsterfiillerene using a standard literature set of PPP parameters [65], namely to = -2.6 ev at the benzene reference bond length To, y0 = 11.13 ev, and the Ohno form for the two center y s. While to is more commonly chosen as... 

In Tables P14 and P15, the van der Waals radii and the reference bond lengths used for P VS A calculations are collected. 

Table PIS Reference bond lengths (ir 1 Angstrom) used for P VSA ...

Each bond in a structure will contribute a stretch term to the total energy. Bonds are normally described as harmonic bonds, and like springs, are characterized by a preferred length. The resistance to change from the optimum value is then defined by a force constant, and each bond type is thus described by at least two parameters and the energies calculated by Hooke s law (Eq. (1)). Here the reference bond length is /0 (Fig. 1). 

Table III. Reference bond lengths and empirical parameters for the HOSE model [44-45] ...

The CH stretching frequencies (v2, v , V13, V20) calculated by the LDA method are close to the experimental fundamental frequencies, but are underestimated by 100 cm" compared to the harmonic frequencies. The large deviation from the experimental harmonic frequencies can be explained by the sensitivity of calculated CH-stretching frequencies to the applied reference geometry. We have shown in the previous section that the error in the reference bond length is the major source of error in the CH-stretching frequencies. 

In a recent study, we have determined a value of = 1.0 mdyn A for the Co—N stretch force constant, with a reference bond length of Tq = 1.881 A for an accurate... 

An empirical force field may contain hundreds or thousands of parameters. MMFF94 has roughly the following numbers of parameters 500 stretching force constants, 500 reference bond lengths, 2300 bending force constants, 2300 reference bond... 

Another approach based on bond lengths is the index HOMA. This index differs from all other geometry-based ones by assuming another reference bond length (bond order). Instead of the mean bond length (or bond order) taken as a reference, in the HOMA model a concept of the optimal bond length is proposed... 

Even if the choice of the reference bond lengths i (l) and R 2) in Table 6 is somewhat arbitrary and biased by some error (depending on the precision of measurements and the oice of model molecule(s) for a given bond length), a very narrow range of variation of the riopt values, between 1.584 and 1.602 A. makes the procedure encouraging. 

Applying the reference bond lengths and bond energies for CC single and double bonds, one obtains an expression for the bond energy, E(R, calculated directly from the bond length ... 

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