Development and testing of new exchange correlation functionals

Keld Troen Lundgård

Research output: Book/ReportPh.D. thesis

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Abstract

Catalysts are used in 90% of the world’s chemical processes to produce 60% of its chemical products, and they are thus very important to our modern society. We therefore seek to better understand current catalytic materials, so that we can find alternatives that will improve the energy efficiency, selectivity or similar of current chemical processes, or to make new technologies economical feasible. Kohn-Sham density functional theory (KS-DFT) has proven to be a powerful theory to find trends in current catalytic materials, which can empower a more informed search for better alternatives. KS-DFT relies on accurate and efficient approximations to the exchange correlation functional, yet these functional approximations have lacked a systematic way to estimate the underlying uncertainties. A Bayesian error estimation approach provides a mechanism for calculating approximative uncertainties, and so accurate, computationally feasible exchange-correlation approximations that incorporate it have been called for. This thesis presents significant steps forwards towards providing general applicable exchange-correlation functional approximations with Bayesian error estimation capabilities. A semi-empirical approach was used with a machine learning toolset to improve accuracy and transferability of the functional approximations. The toolset includes Tikhonov regularization of smoothness in a transformed model space, for ensuring sensible model solutions; an explicit model compromise with a geometric mean loss function, for ensuring generally applicable models; a robust MM-estimator loss function, for ensuring resistance to outliers in data; and a hierarchical bootstrap resampling estimating prediction error validation method, for selecting the model complexity that provide best transferability outside the training data. Three new semi-empirical functional approximations have been made: BEEF-vdW, mBEEF, and mBEEFvdW. It is shown that these functionals are able balance the accuracy of predicting energetics of covalent and non-covalent chemistry better than any comparative functional that we have tested, and they could therefore become the functional approximations of choice for understanding chemical processes at the solid-gas and solid-liquid interfaces.
Original languageEnglish
PublisherDepartment of Physics, Technical University of Denmark
Number of pages161
Publication statusPublished - 2014

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