Force field models, empirical

Empirical Force Field Models Molecular Mechanics... 

A potentially much more adaptable technique is force-field vibrational modeling. In this method, the effective force constants related to distortions of a molecule (such as bond stretching) are used to estimate unknown vibrahonal frequencies. The great advantage of this approach is that it can be applied to any material, provided a suitable set of force constants is known. For small molecules and complexes, approximate force constants can often be determined using known (if incomplete) vibrational specha. These empirical force-field models, in effect, represent a more sophisticated way of exhapolating known frequencies than the rule-based method. A simple type of empirical molecular force field, the modified Urey-Bradley force field (MUBFF), is introduced below. 

Figure 5. Normal modes for vibration of tetrahedral [Cr04] (chromate). There are four distinct vibrational frequencies, including one doubly-degenerate vibration (E symmetry) and two triply-degenerate vibrations (F2 symmetry), for a total of nine vibrational modes. Arrows show the characteristic motions of each atom during vibration, and the length of each arrow is proportional to the magnitude of atomic motion. Only F2 modes involve motion of the central chromium atom, and as a result their vibrational frequencies are affected by Cr-isotope substitution. The normal modes shown here were calculated with an ab initio quantum mechanical model, using hybrid Hartree-Fock/Density Functional Theory (B3LYP) and the 6-31G(d) basis set—other ab initio and empirical force-field models give very similar results.

In this study the authors develop simplified equations relating equilibrium fractionations to mass-scaling factors and molecular force constants. Equilibrium isotopic fractionations of heavy elements (Si and Sn) are predicted to be small, based on highly simplified, one-parameter empirical force-field models (bond-stretching only) of Sip4, [SiFJ, SnCl4, and [SnCl,] -. 

Fractionation factors are calculated using measured vibrational spectra supplemented by simplified empirical force-field modeling (bond-stretching and bond-angle bending force constants only). 

It should be emphasized that solvation of excited electronic states is fundamentally different from the solvation of closed-shell solutes in the electronic ground state. In the latter case, the solute is nonreactive, and solvation does not significantly perturb the electronic structure of the solute. Even in the case of deprotonation of the solute or zwitterion formation, the electronic structure remains closed shell. Electronically excited solutes, on the other hand, are open-shell systems and therefore highly perceptible to perturbation by the solvent environment. Empirical force field models of solute-solvent interactions, which are successfully employed to describe ground-state solvation, cannot reliably account for the effect of solvation on excited states. In the past, the proven concepts of ground-state solvation often have been transferred too uncritically to the description of solvation effects in the excited state. In addition, the spectroscopically detectable excited states are not necessarily the photochemically reactive states, either in the isolated chromophore or in solution. Solvation may bring additional dark and photoreactive states into play. This possibility has hardly been considered hitherto in the interpretation of the experimental data. 

Raimondi, L., Brown, F.K., Gonzalez, J. and Houk, K.N. (1992) Empirical Force-Field Models for the Transition States of Intramolecular Diels-Alder Reactions Based upon Ab Initio Transition Structures, J. Am. Chem. Soc. 114, 4796—4804. 

Johannes Hunger (Chapter 7) takes on another of the standard topics in the philosophy of science, explanation. Hunger examines, in detail, various ways that chemists explain and predict the structural properties of molecules. We learn about ab initio methods, empirical force field models and neural network models, each of which have been used to explain and predict molecular structure. And we learn that none of these approaches can be subsumed under either hypothetico-deductive or causal models of explanation. Either chemistry does not offer proper explanations (the normative option) or our philosophical models for explanation are inadequate to cover explanation in chemistry (the descriptive option). Hunger takes the descriptive option and sketches a more pragmatic approach to the explanation that develops Bas van Fraassen s approach to explanation for chemistry. Once again, we find that the philosophy of science has much to learn from the philosophy of chemistry. 

One important point that we should bear in mind as we undertake a deeper analysis of molecular mechanics is that force fields are empirical-, there is no correct form for a force field. Of course, if one functional form is shown to perform better than another it is likely that form will be favoured. Most of the force fields in common use do have a very similar fqrm, and it is tempting to assume that this must therefore be the optimal functional form Certainly such models tend to conform to a useful picture of the interactions present in a system, but it should always be borne in mind that there may be better forms, particularly when developing a force field for new classes of molecule. The functional forms employed in molecular mechanics force fields are often a compromise between accuracy and computational efficiency the most accurate functional form may often be unsatisfactory for efficient computation. As the performance of computers increases so it becomes pcKsible to incorporate more sophisticated models. An additional consideration is that in order to use techniques such as energy minimisation and molecular dynamics, it is usually desirable to be able to calculate the first and second derivatives of the energy with respect to the atomic coordinates. 

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