Employing general fit-bases for construction of potential energy surfaces with an adaptive density-guided approach.

Abstract

We present an approach to treat sets of general fit-basis functions in a single uniform framework, where the functional form is supplied on input, i.e., the use of different functions does not require new code to be written. The fit-basis functions can be used to carry out linear fits to the grid of single points, which are generated with an adaptive density-guided approach (ADGA). A non-linear conjugate gradient method is used to optimize non-linear parameters if such are present in the fit-basis functions. This means that a set of fit-basis functions with the same inherent shape as the potential cuts can be requested and no other choices with regards to the fit-basis functions need to be taken. The general fit-basis framework is explored in relation to anharmonic potentials for model systems, diatomic molecules, water, and imidazole. The behaviour and performance of Morse and double-well fit-basis functions are compared to that of polynomial fit-basis functions for unsymmetrical single-minimum and symmetrical double-well potentials. Furthermore, calculations for water and imidazole were carried out using both normal coordinates and hybrid optimized and localized coordinates (HOLCs). Our results suggest that choosing a suitable set of fit-basis functions can improve the stability of the fitting routine and the overall efficiency of potential construction by lowering the number of single point calculations required for the ADGA. It is possible to reduce the number of terms in the potential by choosing the Morse and double-well fit-basis functions. These effects are substantial for normal coordinates but become even more pronounced if HOLCs are used.