Reducing the expense of electronic structure calculations for larger molecules : optimized auxiliary basis sets, and system-specifically reparametrized semiempirical methods
Optimization approaches using several global and local algorithms (genetic algorithms, direct search, simplex and implicit filtering) in the search for a global minimum are applied to optimize auxiliary basis sets for quantum chemistry ab-initio calculations and to reparametrize semiempirical methods. We optimize auxiliary basis sets for RI-MP2 and RI-HF, by minimizing a suitable difference measure to the analogous calculations without the RI technique. It is shown that our methods of generating optimal auxiliary basis sets are more systematic and can be automatized more easily than the traditional approach. Hence, they can reasonably be expected to be faster and more reliable. At the same time, the quality of our basis sets is at least as good as that from the traditional approach. As an application, we present the first systematically optimized and complete set of mixed Poisson and density auxiliary basis sets for the atoms H, B, C, N, O and F, complementing the standard basis sets cc-pVXZ (X = D, T, Q and 5). As soon as efficient integral routines for this new basis function type become available, calculations with them will be much more efficient than with traditional basis sets. Similarly, these global and local optimization methods are also employed to reparametrize semiempirical methods for a difficult double proton transfer system. System-specific reparametrization of the well-known AM1, PM3 and PM5 methods is done by minimizing the error of the semiempirical calculations compared to ab-initio reference data at the MP2/aug-cc-pVDZ level. This is done at a small set of selected geometries, leading to one- and two-dimensional potential energy surfaces that are quantitatively in agreement with the ab-initio data over a much broader range of geometries. With this system-specific adaption, these reparametrized methods lead to results far superior to those obtainable with standard parameters. Nevertheless, the full speed advantage of the semiempirical approach is retained, offering the possibility to do direct dynamics studies with the potential energy surface calculated on the fly at ab-initio quality but at a fraction of the ab-initio cost. In both cases, our combination of genetic algorithm global search and Powell local search is the fastest and most robust choice for optimization, comparing with the other methods. Therefore, in these cases, a combination of global and local search is actually better than a purely local algorithm.
Use and reproduction:
No CC License (german copyright law applies)