Publication Date

April 2015


George Petersson




English (United States)


Modern semi-empirical methods are able to offer fast, approximate thermochemical data and can be useful tools for studying large systems. AM1, PM6, and methods such as these use fits to enormous amounts of experimental heats of formation in order to predict the properties of a given molecular system, as opposed to ab initio methods which use quantum mechanics to derive more exact properties. Due to the nature of experiment by which enthalpies are measured relative to the standard state rather than to the limit of infinite atomic separation, the experimental heats of formation used to parametrize semi-empirical data include but do not explicitly consider zero-point energies. A flaw in fitting experimental heats of formation in order to predict the thermochemical data of a given molecular system is that the matrix elements of the resulting Hamiltonian are constructed to predict correct bond dissociation energies and thus negative bond orders raise molecular energies while reducing the atomization energy of the molecule. This behavior is physically correct, but a problem arises in that the method does not recognize that negative bond orders simultaneously contribute positively to the zero-point energy of a molecule while weakening its overall atomization energy. The obvious reason zero-point energy computation is not offered in semi-empirical methods is that it is impractical to include; to get correct zero-point energies one must do a frequency calculation, yet the necessity of second derivatives in these calculations makes them slow enough that one might as well have chosen a more accurate computational method to begin with. We offer the zero-point energy from bond order method as a fast, accurate way to obtain zero-point energies by using fits to inexpensive Mulliken bond orders. This is achieved by using the relationship between bond order and bond energy to independently predict the stretching and bending contributions to the zero-point energy. The accuracy of the resulting energies rivals that of simple self-consistent field methods at a fraction of the computational cost. The error in modern semi-empirical methods contributed by the zero-point energy is a small enough percentage of the overall error that implementation of this method will not dramatically improve calculations. However, it is assumed that future semi-empirical methods will have improved to the point that the correction from the zero-point energy will be relevant in obtaining highly accurate energies at room temperature and beyond.



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