Analysis and optimisation of the basis set filtration algorithm

Abstract

The ltration algorithm has recently been introduced as a way of increasing the speed of ab initio modelling calculations using Cartesian Gaussian basis functions. It works by developing a novel set of basis functions which are constructed specifically for the system being modelled. It has been implemented in the ab initio density functional theory based modelling package AIMPRO. The standard ltration process is found to be accurate when the ltration radius is increased to at least 10 Bohr radii in silicon. The standard ltration process uses all the basis functions centred on points inside a sphere centred on each atom in turn. By rejecting some of these functions (a trimming process), the ltration process can be speeded up, however there will be a resulting loss of accuracy. Three approaches to developing a ltered basis for an atom are considered, and compared. The most successful criterion for function trimming is found to be where functions are kept which exceed a threshold value on the surface of a sphere. Structural optimisation using ltration produce accurate nal structures, even when using parameters that give rise to poorly converged absolute energies. For the most time consuming elements of a calculation, a rapid ltration process is possible. However, very poor ltration thresholds introduce small inconsistencies between energies and forces, which can make optimisation difficult if algorithms are chosen that use both the energy and force. Algorithms that only use forces are implemented, and shown to be stable and produce accurate structures. This is further demonstrated using a new implementation of the Lanczos method for determining transition states. This is compared against the current AIMPRO method, the nudged elastic band. The new method is far superior in terms of speed, and offers greater stability towards the end of calculations.