Force fields bond stretching

The importance of the transferability of the geminals has been pointed out in [62], It was stated that the assumption of the transferability of the geminal amplitudes is a prerequisite for that of the bond energy. However, in [62] geminal transferability has not been proven and the authors concentrate on the statements equivalent to the transferability of the MM bond stretching force fields. Our proof of course strongly relies on the SLG form of the trial wave function. This may seem to be a very strong restriction on the proposed derivation scheme. However, it is not a restriction at all if... 

A selection of bond stretching force constants, G, taken from the literature is plotted in Fig. 9.2 as a function of the bond valence, S. What is surprising is not that there is some scatter (this is expected from the crudeness of the Urey-Bradley force field) but that an expression such as eqn (9.5) gives such a good fit ... 

Murrell 2S6> shows theoretically that for MX6 compounds the three bond stretching force constants can be calculated sufficiently accurately from IR and Raman spectra from this the complete harmonic force field can be deduced. This is an important simplification, and bond strengths can be more conveniently calculated. Murrell shows that e.g. in WFSC1 that replacement of F by Cl strengthens the trans WF bond and weakens the cis WF bonds. 

The set of functions, together with the collection of terms that parameterize them (kb, r0, etc.), is referred to as the force field. In some cases force field parameters can be related to experimentally determinable values. For example, the bond stretching force constant kb is approximately equivalent to the vibrational force constant derived from an infrared spectrum. However, in general die force field terms are derived empirically with the target of reproducing experimental structures and energy distributions. 

The vibrational problem of a symmetric molecule XY2 is most frequently described in terms of a quadratic valence force field. This is given in terms of a bond stretching force constant K1U the bond-bond interaction constant K12 and the bending force constant Koo ... 

The fact that the second derivative, d U/db in Eq. [24], contains a slight contamination from nonbonded interactions and third-order terms is an example of how parameter correlation can arise because it is not a pure bond stretch. If this derivative were simply used as the bond-stretching force constant, as in spectroscopic force fields, it would not be transferable to other molecules where the coupling or nonbonded interaction may differ. This problem is a general one and can be quite serious. As already discussed in previous sections, one possible resolution of this problem lies in the use of many molecular environments to determine all contributing terms. If we simultaneously fit many different alkanes, i.e., ethane, propane, butane, etc., with the full force field and assume... 

Fig. 1. The time evolution (top) and average cumulative difference (bottom) associated with the central dihedral angle of butane r (defined by the four carbon atoms), for trajectories differing initially in 10 , 10 , and 10 Angstoms of the Cartesian coordinates from a reference trajectory. The leap-frog/Verlet scheme at the timestep At = 1 fs is used in all cases, with an all-atom model comprised of bond-stretch, bond-angle, dihedral-angle, van der Waals, and electrostatic components, a.s specified by the AMBER force field within the INSIGHT/Discover program.

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)). 

Intensive use of cross-terms is important in force fields designed to predict vibrational spectra, whereas for the calculation of molecular structure only a limited set of cross-terms was found to be necessary. For the above-mentioned example, the coupling of bond-stretching (f and / and angle-bending (B) within a water molecule (see Figure 7-1.3, top left) can be calculated according to Eq. (30). 

Molecu lar mechari ical force fields use the equation s of classical mech an ics to describe th e poteri tial energy surfaces and physical properties of m olecii Ies. A molecu le is described as a collection of atom slhal in teracl with each other by sim pic an alytical fiiriclions. I h is description is called a force field. One component of a force field is th e eri ergy arisiri g from com pression and stretch in g a bond. 

The default parameters for bond stretching are an ec iiilibriiim bond length an d a stretch in g force eon starit. fb e fun etion al form isjiist that of the. M.M+ force field including a correction for cubic stretches. The default force constant depends only on the bond... 

A typical force field model for propane contains ten bond-stretching terms, eighteen angle-bending terms, eighteen torsional terms and 27 non-bonded interactions. 

The forces between bonded atoms are very strong and considerable energy is required to cause a bond to deviate significantly from its equilibrium value. This is reflected in the magnitude of the force constants for bond stretching some typical values from the MM2 force field are shown in Table 4.1, where it can be seen that those bonds one would... 

---