A new method for calculating optical absorption spectra within linear-scaling density-functional theory (LS-DFT) is presented, incorporating a scheme for optimizing a set of localized orbitals to accurately represent unoccupied Kohn-Sham states. Three different schemes are compared and the most promising of these, based on the use of a projection operator, has been implemented in a fullyfunctional LS-DFT code. The method has been applied to the calculation of optical absorption spectra for the metal-free phthalocyanine molecule and the conjugated polymer poly(para-phenylene). Excellent agreement with results from a traditional DFT code is obtained.

We present a comparison of methods for treating the electrostatic interactions of finite, isolated systems within periodic boundary conditions (PBCs), within density functional theory (DFT), with particular emphasis on linear-scaling (LS) DFT. Often, PBCs are not physically realistic but are an unavoidable consequence of the choice of basis set and the efficacy of using Fourier transforms to compute the Hartree potential. In such cases the effects of PBCs on the calculations need to be avoided, so that the results obtained represent the open rather than the periodic boundary. The very large systems encountered in LS-DFT make the demands of the supercell approximation for isolated systems more difficult to manage, and we show cases where the open boundary (infinite cell) result cannot be obtained from extrapolation of calculations from periodic cells of increasing size. We discuss, implement, and test three very different approaches for overcoming or circumventing the effects of PBCs: truncation of the Coulomb interaction combined with padding of the simulation cell, approaches based on the minimum image convention, and the explicit use of open boundary conditions (OBCs). We have implemented these approaches in the ONETEP LS-DFT program and applied them to a range of systems, including a polar nanorod and a protein. We compare their accuracy, complexity, and rate of convergence with simulation cell size. We demonstrate that corrective approaches within PBCs can achieve the OBC result more efficiently and accurately than pure OBC approaches.

While monolayer forms of 2D materials are well-characterised both experimentally and theoretically, properties of bilayer heterostructures are not nearly so well-known. We employ high-accuracy linear-scaling DFT calculations utilising non-local van-der-Waals functionals to explore the possible constructions of the MoS2/MoSe2 interface. Utilising large supercells, we vary rotation, translation and separation of the layers without introducing unrealistic strain. The energy landscape shows very low variations under rotation, with no strongly preferred alignments. By unfolding the spectral function into the primitive cells, we show that the monolayers are more independent than in homo-bilayers, and that the electronic bandstructure of each layer is tunable through rotation, thus influencing hole effective masses.

We investigate a recently developed approach [P. L. Silvestrelli, Phys. Rev. Lett. 100, 053002 (2008); J. Phys. Chem. A 113, 5224 (2009)] that uses maximally localized Wannier functions to evaluate the van der Waals contribution to the total energy of a system calculated with density-functional theory. We test it on a set of atomic and molecular dimers of increasing complexity (argon, methane, ethene, benzene, phthalocyanine, and copper phthalocyanine) and demonstrate that the method, as originally proposed, has a number of shortcomings that hamper its predictive power. In order to overcome these problems, we have developed and implemented a number of improvements to the method and show that these modifications give rise to calculated binding energies and equilibrium geometries that are in closer agreement to results of quantum-chemical coupled-cluster calculations.

We present an approach to the DFT+U method (Density Functional Theory + Hubbard model) within which the computational effort for calculation of ground state energies and forces scales linearly with system size. We employ a formulation of the Hubbard model using nonorthogonal projector functions to define the localized subspaces, and apply it to a local-orbital DFT method including in situ orbital optimization. The resulting approach thus combines linear-scaling and systematic variational convergence. We demonstrate the scaling of the method by applying it to nickel oxide nano-clusters with sizes exceeding 7, 000 atoms.

First-principles calculations of polar semiconductor nanorods reveal that their dipole moments are strongly influenced by Fermi level pinning. The Fermi level for an isolated nanorod is found to coincide with a significant density of electronic surface states at the end surfaces, which are either mid-gap states or band-edge states. These states pin the Fermi level, and therefore fix the potential difference across the rod. We provide evidence that this effect can have a determining influence on the polarity of nanorods, with consequences for the way a rod responds to changes in its surface chemistry, the scaling of its dipole moment with its size, and the dependence of polarity on its composition.

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In two-dimensional heterostructures, crystalline atomic layers with differing lattice parameters can stack directly one on another. The resultant close proximity of atomic lattices with differing periodicity can lead to new phenomena. For umklapp processes, this opens the possibility for interlayer umklapp scattering, where interactions are mediated by the transfer of momenta to or from the lattice in the neighbouring layer. Using angle-resolved photoemission spectroscopy to study a graphene on InSe heterostructure, we present evidence that interlayer umklapp processes can cause hybridization between bands from neighbouring layers in regions of the Brillouin zone where bands from only one layer are expected, despite no evidence for Moiré-induced replica bands. This phenomenon manifests itself as ‘ghost’ anti-crossings in the InSe electronic dispersion. Applied to a range of suitable two-dimensional material pairs, this phenomenon of interlayer umklapp hybridization can be used to create strong mixing of their electronic states, giving a new tool for twist-controlled band structure engineering.