GPAW Setup Optimization Center for Atomic-scale Materials Design Technical University of Denmark Ask Hjorth Larsen

What is GPAW? – Density functional theory (DFT) is a method whereby quantum mechanical calculations are carried out using electron densities. – The projector augmented wave (PAW) method is a DFT method which works by augmenting solutions near/far from atom cores using different methods in the two regimes. – GPAW is a Python code library supporting PAW calculations using a real-space grid.

What is a GPAW setup? – A setup is an element-specific set of data that decides how atoms are represented in the calculations. – For example, the cut-off radius defining inner and outer regions around atoms is an important element-specific setting. – There are many other such parameters, and the optimal choice is far from trivial.

Project purpose and strategy ● Suppose we want to find optimal setups. We need to be able to evaluate the quality of a setup. ● We also need to select a number of parameters which should be optimized. ● Finally we need an algorithm to do things efficiently, since we cannot possibly check all the possible setups one by one.

Evaluating setup quality ● Physical characteristics – Deviation of atomization energy – Deviation of bond length ● Numerical behaviour – Convergence – Numerical “noise” due to finite grid ● These things can be expressed numerically and combined into a function which can be minimized.

Example: setup quality as a function of two variables. Blue is better.

Algorithm ● Downhill simplex algorithm – Select an initial simplex in the parameter space. A simplex in n dimensions is anything with n+1 vertices and non-zero n-volume. – Evaluate setup quality corresponding to each vertex – Repeatedly move the worst vertex in the general direction of the better ones ● This works in any number of dimensions.

Example: running the algorithm ● Five parameters as a function of evaluation count ● Setup “badness”

To do ● Find out how good the optimized setups actually are. ● Improve the setup quality evaluation functions. ● Perform calculations on other elements. ● Write tests suitable for crystals. ● Include more setup parameters. ● Etc.

Questions?