Development of semi-empirical exchange- correlation functionals

Abstract

Kohn-Sham density functional theory (DFT) is the most widely-used method for quantum chemical calculations. For most chemical properties it offers relatively accurate results for a relatively low computational cost. This accuracy is governed by the quality of the exchange-correlation functional used. The development and assessment of new functionals is a vital aspect of DFT research, and is the focus of this thesis. In Chapter 1, the theory of traditional wavefunction-based quantum chemistry methods and of DFT is outlined, and the two approaches compared and contrasted. Chapter 2 considers the relatively poor performance of conventional DFT functionals for NMR shielding constants. A simple generalised gradient approximation (GGA) functional, denoted KTl, is developed, which improves this performance significantly. A more flexible functional fitted to experimental energetic data, denoted KT2, is also presented. In Chapter 3, KTl and KT2 are assessed for other magnetic properties, such as chemical shifts, magnetisabilities, and indirect spin-spin coupling constants. Chapter 4 details the development of a third GGA denoted KT3, which is designed to address the shortcomings of KT2 for non-magnetic properties. In Chapter 5, the more flexible functional form of KT3 is shown to give results competitive with the best GGAs for a wide range of chemical properties and for solid state calculations. In Chapter 6, we attempt to improve performance for classical chemical reaction barriers, for which KT3 is relatively poor. This requires a more flexible form in the resulting GGA functional, denoted KT4. A hybrid functional, B97- 3, is also developed with a similar emphasis on reaction barriers. Chapter 7 presents an extensive chemical assessment for KT4 and B97-3. For the systems considered, B97-3 is shown to be the most accurate semi-empirical functional developed to date. Concluding remarks are presented in Chapter 8.