Ab Initio Based Force Fields

Although the use of quantum mechanical calculations, and in particular ab initio calculations, to derive force fields dates back to the 1960s, the number of apphcation has swelled in the last decade. - This is due to dramatic improvements of computer capabilities, allowing ab initio calculations to be 

Quantum mechanical calculations provide energies, first and second derivatives of the energy with respect to atomic coordinates, and dipole moments for the models. All these observables can also be calculated from a suitable force field. The force field parameters are determined by minimizing the sum in Eq. [25] 

The van der Waals parameters have usually been obtained by fitting to crystal structure data and to heats of sublimation of molecular crystals,77,93-97,101-103 but it is also possible to obtain parameters from quantum mechanical calculations. Because van der Waals interactions include dispersion, it would be necessary to use a correlated quantum mechanical method. Unfortunately, density functional methods do not describe dispersive interactions, and post-Hartree-Fock methods, capable of capturing this physical effect, are computationally expensive. The dispersion interactions are therefore often ignored. The repulsive part of the van der Waals interaction, on the other hand, can be determined from test particle calculations - using the Hartree-Fock method. 

As mentioned previously, molecular mechanics force fields use redundant internal coordinates. In a tetrahedrally coordinated center such as Si04, all six bond angles Aa, , Aog are used, but only five of them are independent. Thus correlations exist between the force constants and the reference values of the coordinates, and this poses a problem in the fitting process because there is no unambiguously optimal set of parameters. Hence, parameters fitted to redundant coordinates may not be transferable and also may lack a well-defined physical meaning. 

This correlation problem between force constants and reference values can be avoided by adding a linear term to each diagonal term of the force field. For instance, for bond angles we would write  

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