Failure of density-matrix minimization methods for linear-scaling density-functional theory using the Kohn penalty-functional

Accepted versio

Implicit and explicit host effects on excitons in pentacene derivatives

An ab initio study of the effects of implicit and explicit hosts on the excited state properties of pentacene and its nitrogen-based derivatives has been performed using ground state density func- tional theory (DFT), time-dependent DFT and ∆SCF. We observe a significant solvatochromic redshift in the excitation energy of the lowest singlet state (S 1 ) of pentacene from inclusion in a p -terphenyl host compared to vacuum; for an explicit host consisting of six nearest neighbour p -terphenyls, we obtain a redshift of 65 meV while a conductor-like polarisable continuum model (CPCM) yields a 78 meV redshift. Comparison is made between the excitonic properties of pen- tacene and four of its nitrogen-based analogues, 1,8-, 2,9-, 5,12-, and 6,13-diazapentacene with the latter found to be the most distinct due to local distortions in the ground state electronic struc- ture. We observe that a CPCM is insufficient to fully understand the impact of the host due to the presence of a mild charge-transfer (CT) coupling between the chromophore and neighbouring p -terphenyls, a phenomenon which can only be captured using an explicit model. The strength of this CT interaction increases as the nitrogens are brought closer to the central acene ring of pentacene

Preconditioned iterative minimization for linear-scaling electronic structure calculations

Linear-scaling electronic structure methods are essential for calculations on large systems. Some of these approaches use a systematic basis set, the completeness of which may be tuned with an adjustable parameter similar to the energy cut-off of plane-wave techniques. The search for the electronic ground state in such methods suffers from an ill-conditioning which is related to the kinetic contribution to the total energy and which results in unacceptably slow convergence. We present a general preconditioning scheme to overcome this ill-conditioning and implement it within our own first-principles linear-scaling density functional theory method. The scheme may be applied in either real space or reciprocal space with equal success. The rate of convergence is improved by an order of magnitude and is found to be almost independent of the size of the basis

Single-electron induced surface plasmons on a topological nanoparticle

It is rarely the case that a single electron affects the behaviour of several hundred thousands of atoms. Here we demonstrate a phenomenon where this happens. The key role is played by topological insulators—materials that have surface states protected by time-reversal symmetry. Such states are delocalized over the surface and are immune to its imperfections in contrast to ordinary insulators. For topological insulators, the effects of these surface states will be more strongly pronounced in the case of nanoparticles. Here we show that under the influence of light a single electron in a topologically protected surface state creates a surface charge density similar to a plasmon in a metallic nanoparticle. Such an electron can act as a screening layer, which suppresses absorption inside the particle. In addition, it can couple phonons and light, giving rise to a previously unreported topological particle polariton mode. These effects may be useful in the areas of plasmonics, cavity electrodynamics and quantum information

Band structure interpolation using optimized local orbitals from linear-scaling density functional theory

© 2018 American Physical Society. Several approaches to linear-scaling density functional theory (LS-DFT) that seek to achieve accuracy equivalent to plane-wave methods do so by optimizing in situ a set of local orbitals in terms of which the density matrix can be accurately expressed. These local orbitals, which can also accurately represent the canonical Kohn-Sham orbitals, qualitatively resemble the maximally localized Wannier functions employed in band structure interpolation. As LS-DFT methods are increasingly being used in real-world applications demanding accurate band structures, it is natural to question the extent to which these optimized local orbitals can provide sufficient accuracy. In this paper, we present and compare, in principle and in practice, two methods for obtaining band structures. We apply these to a (10, 0) carbon nanotube as an example. By comparing with the results from a traditional plane-wave pseudopotential calculation, the optimized local orbitals are found to provide an excellent description of the occupied bands and some low-lying unoccupied bands, with consistent agreement across the Brillouin zone. However free-electron-like states derived from weakly bound states independent of the σ and π orbitals can only be found if additional local orbitals are included

Unravelling the roles of size, ligands and pressure in the piezochromic properties of CdS nanocrystals

Understanding the effects of pressure-induced deformations on the optoelectronic properties of nanomaterials is important not only from the fundamental point of view, but also for po- tential applications such as stress sensors and electromechanical devices. Here we describe the novel insights into these piezochromic ef- fects gained from using a linear-scaling den- sity functional theory framework and an elec- tronic enthalpy scheme, which allow us to ac- curately characterize the electronic structure of CdS nanocrystals with a zincblende-like core of experimentally relevant size. In particu- lar we focus on unravelling the complex inter- play of size and surface (phenyl) ligands with pressure. We show that pressure-induced de- formations are not simple isotropic scaling of the original structures and that the change in HOMO-LUMO gap with pressure results from two competing factors: (i) a bulk-like linear in- crease due to compression, which is offset by (ii) distortions/disorder and, to a lesser ex- tent, orbital hybridization induced by ligands affecting the frontier orbitals. Moreover, we observe that the main peak in the optical ab- sorption spectra is systematically red-shifted or blue-shifted, as pressure is increased up to 5 GPa, depending on the presence or absence of phenyl ligands. These heavily hybridize the frontier orbitals, causing a reduction in over- lap and oscillator strength, so that at zero pres- sure the lowest energy transition involves deeper hole orbitals than in the case of hydrogen- capped nanocrystals; the application of pressure induces greater delocalisation over the whole nanocrystals bringing the frontier hole orbitals into play and resulting in an unexpected red shift for the phenyl-capped nanocrystals, in part caused by distortions. In response to a growing interest in relatively small nanocrystals that can be difficult to accurately characterize with ex- perimental techniques, this work exemplifies the detailed understanding of structure-property re- lationships under pressure that can be obtained for realistic nanocrystals with state-of-the-art first principles methods and used for the charac- terization and design of devices based on these and similar nanomaterials

Simulations of nanocrystals under pressure: Combining electronic enthalpy and linear-scaling density-functional theory.

We present an implementation in a linear-scaling density-functional theory code of an electronic enthalpy method, which has been found to be natural and efficient for the ab initio calculation of finite systems under hydrostatic pressure. Based on a definition of the system volume as that enclosed within an electronic density isosurface [Phys. Rev. Lett., 94, 145501 (2005)], it supports both geometry optimizations and molecular dynamics simulations. We introduce an approach for calibrating the parameters defining the volume in the context of geometry optimizations and discuss their significance. Results in good agreement with simulations using explicit solvents are obtained, validating our approach. Size-dependent pressure-induced structural transformations and variations in the energy gap of hydrogenated silicon nanocrystals are investigated, including one comparable in size to recent experiments. A detailed analysis of the polyamorphic transformations reveals three types of amorphous structures and their persistence on depressurization is assessed.Comment: 11 pages and 13 figures (accepted for publication by The Journal of Chemical Physics on the 29th of July 2013

Linear-scaling time-dependent density-functional theory in the linear response formalism

We present an implementation of time-dependent density-functional theory (TDDFT) in the linear response formalism enabling the calculation of low energy optical absorption spectra for large molecules and nanostructures. The method avoids any explicit reference to canonical representations of either occupied or virtual Kohn-Sham states and thus achieves linear-scaling computational effort with system size. In contrast to conventional localised orbital formulations, where a single set of localised functions is used to span the occupied and unoccupied state manifold, we make use of two sets of in situ optimised localised orbitals, one for the occupied and one for the unoccupied space. This double representation approach avoids known problems of spanning the space of unoccupied Kohn-Sham states with a minimal set of localised orbitals optimised for the occupied space, while the in situ optimisation procedure allows for efficient calculations with a minimal number of functions. The method is applied to a number of medium sized organic molecules and a good agreement with traditional TDDFT methods is observed. Furthermore, linear scaling of computational cost with system size is demonstrated on a system of carbon nanotubes

Variational quantum algorithm with information sharing

We introduce an optimisation method for variational quantum algorithms and experimentally demonstrate a 100-fold improvement in efficiency compared to naive implementations. The effectiveness of our approach is shown by obtaining multi-dimensional energy surfaces for small molecules and a spin model. Our method solves related variational problems in parallel by exploiting the global nature of Bayesian optimisation and sharing information between different optimisers. Parallelisation makes our method ideally suited to the next generation of variational problems with many physical degrees of freedom. This addresses a key challenge in scaling-up quantum algorithms towards demonstrating quantum advantage for problems of real-world interest