Development of semi-empirical exchange- correlation functionals

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

Modelling the chemistry of Mn-doped MgO for bulk and (100) surfaces

We have investigated the energetic properties of Mn-doped MgO bulk and (100) surfaces using a QM/MM embedding computational method, calculating the formation energy for doped systems, as well as for surface defects, and the subsequent effect on chemical reactivity. Low-concentration Mn doping is endothermic for isovalent species in the bulk but exothermic for higher oxidation states under p-type conditions, and compensated by electrons going to the Fermi level rather than cation vacancies. The highest occupied dopant Mn 3d states are positioned in the MgO band gap, about 4.2 eV below the vacuum level. Surface Mn-doping is more favourable than subsurface doping, and marginally exothermic on a (100) surface at high O2 pressures. For both types of isovalent Mn-doped (100) surfaces, the formation energy for catalytically important oxygen defects is less than for pristine MgO, with F0 and F2+-centres favoured in n- and p-type conditions, respectively. In addition, F+-centres are stabilised by favourable exchange coupling between the Mn 3d states and the vacancy-localised electrons, as verified through calculation of the vertical ionisation potential. The adsorption of CO2 on to the pristine and defective (100) surface is used as a probe of chemical reactivity, with isovalent subsurface Mn dopants mildly affecting reactivity, whereas isovalent surface-positioned Mn strongly alters the chemical interactions between the substrate and adsorbate. The differing chemical reactivity, when compared to pristine MgO, justifies further detailed investigations for more varied oxidation states and dopant species

QM/MM Simulations of Protein Crystal Reactivity Guided by MSOX Crystallography: A Copper Nitrite Reductase Case Study.

The recently developed multiple structures from one crystal (MSOX) serial crystallography method can be used to provide multiple snapshots of the progress of enzymatic reactions taking place within a protein crystal. Such MSOX snapshots can be used as a reference for combined quantum mechanical/molecular mechanical (QM/MM) simulations of enzyme reactivity within the crystal. QM/MM calculations are used to identify details of reference states that cannot be directly observed by X-ray diffraction experiments, such as protonation and oxidation states. These reference states are then used as known fixed endpoints for the modeling of reaction paths. We investigate the mechanism of nitrite reduction in an Achromobacter cycloclastes copper nitrite reductase crystal using MSOX-guided QM/MM calculations, identifying the change in nitrite binding orientation with a change in copper oxidation state, and determining the reaction path to the final NO-bound MSOX structure. The results are compared with QM/MM simulations performed in a solvated environment

Bulk and Surface Contributions to Ionisation Potentials of Metal Oxides

Determining the absolute band edge positions in solid materials is crucial for optimising their performance in wide-ranging applications including photocatalysis and electronic devices. However, obtaining absolute energies is challenging, as seen in CeO2, where experimental measurements show substantial discrepancies in the ionisation potential (IP). Here, we have combined several theoretical approaches, from classical electrostatics to quantum mechanics, to elucidate the bulk and surface contributions to the IP of metal oxides. We have determined a theoretical bulk contribution to the IP of stoichiometric CeO2 of only 5.38 eV, while surface orientation results in intrinsic IP variations from 4.2 eV to 8.2 eV. Highly tuneable IPs were also found in TiO2, ZrO2, and HfO2, in which surface polarisation plays a pivotal role in long-range energy level shifting. Our analysis, in addition to rationalising the observed range of experimental results, provides a firm basis for future interpretations of experimental and computational studies of oxide band structures

Overcoming the compensation of acceptors in GaN:Mg by defect complex formation

In GaN:Mg, the MgGa acceptor is compensated extensively by the formation of nitrogen vacancies (VN) and Mg interstitials (Mgi). However, we show that such compensation can be overcome by forming two kinds of Mg-rich complexes: one that contains VN and the other that contains only MgGa and Mgi. Such complexing not only neutralizes VN and Mgi but also forms better complex acceptors that have lower formation energies and smaller hole localization energies than isolated MgGa. Our results help explain the different doping behaviors in samples grown by different methods

Hybrid-DFT modelling of lattice and surface vacancies in MnO

We have investigated the properties of defects in MnO bulk and at (100) surfaces, as used in catalytic applications, using hybrid-level density functional theory (i.e. inclusion of exact exchange within the exchange-correlation evaluation) in a hybrid QM/MM embedded-cluster approach. Initially, we calculate the formation energy for bulk Mn and O vacancies, comparing charged-defect compensation with charge carriers at the Fermi Level (εf) and through Schottky defect formation. Oxygen vacancies were also investigated at the (100) surface, where the vacancy formation energy is very similar to the bulk. Defect levels associated with the most stable vacancies are calculated using the ΔSCF method: all are positioned mid-bandgap, with surface environments failing strongly to alter the overall nature of the defect relative to bulk. Chemical activity of the (100) MnO surface was considered through the adsorption of a probe CO2 molecule, which is considered the initial step in the transformation of CO2 into hydrocarbons. CO2 adsorption was strongest over a neutral oxygen vacancy, where the associated trapped electrons of the defect transfer to the adsorbate and thus activate it; However, we have shown with our embedded-cluster approach that this defect is not necessarily the dominant species, which has implications when interpreting results for future catalytic applications

Atomic Simulation Interface (ASI) : application programming interface for electronic structure codes

The Atomic Simulation Interface (ASI) is a native C-style API for density functional theory (DFT) codes. ASI provides an efficient way to import and export large arrays that describe electronic structure (e.g. Hamiltonian, overlap, and density matrices) from DFT codes that are typically monolithic. The ASI API is designed to be implemented and used with minimal performance penalty, avoiding, where possible, unnecessary data copying. It provides direct access to the internal data structures of a code, and reuses existing data distribution over MPI nodes. The ASI API also defines a set of functions that support classical, AIMD (ab initio molecular dynamics), and hybrid QM/MM simulations: exporting potential energy, forces, atomic charges, and electrostatic potential at user defined points, as well as importing nuclear coordinates and arbitrary external electrostatic potentials. The ASI API is implemented in the DFTB+ (Hourahine et al., 2020) and FHI-aims (Blum et al., 2009) codes. A Python wrapper for easy access to ASI functions is also freely available (asi4py). We hope that the ASI API will be widely adopted and used for development of universal and interoperable DFT codes without sacrificing efficiency for portability

Toward a consistent prediction of defect chemistry in ceo2

Polarizable shell-model potentials are widely used for atomic-scale modeling of charged defects in solids using the Mott–Littleton approach and hybrid Quantum Mechanical/Molecular Mechanical (QM/MM) embedded-cluster techniques. However, at the pure MM level of theory, the calculated defect energetics may not satisfy the requirement of quantitative predictions and are limited to only certain charged states. Here, we proposed a novel interatomic potential development scheme that unifies the predictions of all relevant charged defects in CeO2 based on the Mott–Littleton approach and QM/MM electronic-structure calculations. The predicted formation energies of oxygen vacancies accompanied by different excess electron localization patterns at the MM level of theory reach the accuracy of density functional theory (DFT) calculations using hybrid functionals. The new potential also accurately reproduces a wide range of physical properties of CeO2, showing excellent agreement with experimental and other computational studies. These findings provide opportunities for accurate large-scale modeling of the partial reduction and nonstoichiometry in CeO2, as well as a prototype for developing robust interatomic potentials for other defective crystals

Computational infrared and Raman spectra by hybrid QM/MM techniques: a study on molecular and catalytic material systems

Vibrational spectroscopy is one of the most well-established and important techniques for characterizing chemical systems. To aid the interpretation of experimental infrared and Raman spectra, we report on recent theoretical developments in the ChemShell computational chemistry environment for modelling vibrational signatures. The hybrid quantum mechanical and molecular mechanical approach is employed, using density functional theory for the electronic structure calculations and classical forcefields for the environment. Computational vibrational intensities at chemical active sites are reported using electrostatic and fully polarizable embedding environments to achieve more realistic vibrational signatures for materials and molecular systems, including solvated molecules, proteins, zeolites and metal oxide surfaces, providing useful insight into the effect of the chemical environment on the signatures obtained from experiment. This work has been enabled by the efficient task-farming parallelism implemented in ChemShell for high-performance computing platforms.  This article is part of a discussion meeting issue 'Supercomputing simulations of advanced materials'