GPAW Setup Optimization Center for Atomicscale Materials Design

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?