Laura E. Ratcliff

Daubechies wavelets for linear scaling density functional theory

We demonstrate that Daubechies wavelets can be used to construct a minimal set of optimized localized adaptively contracted basis functions in which the Kohn-Sham orbitals can be represented with an arbitrarily high, controllable precision. Ground state energies and the forces acting on the ions can be calculated in this basis with the same accuracy as if they were calculated directly in a Daubechies wavelets basis, provided that the amplitude of these adaptively contracted basis functions is sufficiently small on the surface of the localization region, which is guaranteed by the optimization procedure described in this work. This approach reduces the computational costs of density functional theory calculations, and can be combined with sparse matrix algebra to obtain linear scaling with respect to the number of electrons in the system. Calculations on systems of 10,000 atoms or more thus become feasible in a systematic basis set with moderate computational resources. Further computational savings can be achieved by exploiting the similarity of the adaptively contracted basis functions for closely related environments, e.g., in geometry optimizations or combined calculations of neutral and charged systems.

Accurate and efficient linear scaling DFT calculations with universal applicability

Density functional theory calculations are computationally extremely expensive for systems containing many atoms due to their intrinsic cubic scaling. This fact has led to the development of so-called linear scaling algorithms during the last few decades. In this way it becomes possible to perform ab initio calculations for several tens of thousands of atoms within reasonable walltimes. However, even though the use of linear scaling algorithms is physically well justified, their implementation often introduces some small errors. Consequently most implementations offering such a linear complexity either yield only a limited accuracy or, if one wants to go beyond this restriction, require a tedious fine tuning of many parameters. In our linear scaling approach within the BigDFT package, we were able to overcome this restriction. Using an ansatz based on localized support functions expressed in an underlying Daubechies wavelet basis - which offers ideal properties for accurate linear scaling calculations - we obtain an amazingly high accuracy and a universal applicability while still keeping the possibility of simulating large system with linear scaling walltimes requiring only a moderate demand of computing resources. We prove the effectiveness of our method on a wide variety of systems with different boundary conditions, for single-point calculations as well as for geometry optimizations and molecular dynamics.

Calculating optical absorption spectra for large systems using linear-scaling density functional theory

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 fully functional 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.

Toward Fast and Accurate Evaluation of Charge On-Site Energies and Transfer Integrals in Supramolecular Architectures Using Linear Constrained Density Functional Theory (CDFT)-Based Methods

A fast and accurate scheme has been developed to evaluate two key molecular parameters (on-site energies and transfer integrals) that govern charge transport in organic supramolecular architecture devices. The scheme is based on a constrained density functional theory (CDFT) approach implemented in the linear-scaling BigDFT code that exploits a wavelet basis set. The method has been applied to model disordered structures generated by force-field simulations. The role of the environment on the transport parameters has been taken into account by building large clusters around the active molecules involved in the charge transfer.

MADNESS: A Multiresolution, Adaptive Numerical Environment for Scientific Simulation

MADNESS (multiresolution adaptive numerical environment for scientific simulation) is a high-level software environment for solving integral and differential equations in many dimensions that uses adaptive and fast harmonic analysis methods with guaranteed precision that are based on multiresolution analysis and separated representations. Underpinning the numerical capabilities is a powerful petascale parallel programming environment that aims to increase both programmer productivity and code scalability. This paper describes the features and capabilities of MADNESS and briefly discusses some current applications in chemistry and several areas of physics.

Challenges in large scale quantum mechanical calculations

During the past decades, quantum mechanical methods have undergone an amazing transition from pioneering investigations of experts into a wide range of practical applications, made by a vast community of researchers. First principles calculations of systems containing up to a few hundred atoms have become a standard in many branches of science. The sizes of the systems which can be simulated have increased even further during recent years, and quantum‐mechanical calculations of systems up to many thousands of atoms are nowadays possible. This opens up new appealing possibilities, in particular for interdisciplinary work, bridging together communities of different needs and sensibilities. In this review we will present the current status of this topic, and will also give an outlook on the vast multitude of applications, challenges, and opportunities stimulated by electronic structure calculations, making this field an important working tool and bringing together researchers of many different domains. WIREs Comput Mol Sci 2017, 7:e1290. doi: 10.1002/wcms.1290

Fragment approach to constrained density functional theory calculations using Daubechies wavelets

In a recent paper, we presented a linear scaling Kohn-Sham density functional theory (DFT) code based on Daubechies wavelets, where a minimal set of localized support functions are optimized in situ and therefore adapted to the chemical properties of the molecular system. Thanks to the systematically controllable accuracy of the underlying basis set, this approach is able to provide an optimal contracted basis for a given system: accuracies for ground state energies and atomic forces are of the same quality as an uncontracted, cubic scaling approach. This basis set offers, by construction, a natural subset where the density matrix of the system can be projected. In this paper, we demonstrate the flexibility of this minimal basis formalism in providing a basis set that can be reused as-is, i.e., without reoptimization, for charge-constrained DFT calculations within a fragment approach. Support functions, represented in the underlying wavelet grid, of the template fragments are roto-translated with high numerical precision to the required positions and used as projectors for the charge weight function. We demonstrate the interest of this approach to express highly precise and efficient calculations for preparing diabatic states and for the computational setup of systems in complex environments.

Chemically Selective Alternatives to Photoferroelectrics for Polarization-Enhanced Photocatalysis: the Untapped Potential of Hybrid Inorganic Nanotubes

Linear‐scaling density functional theory simulation of methylated imogolite nanotubes (NTs) elucidates the interplay between wall‐polarization, bands separation, charge‐transfer excitation, and tunable electrostatics inside and outside the NT‐cavity. The results suggest that integration of polarization‐enhanced selective photocatalysis and chemical separation into one overall dipole‐free material should be possible. Strategies are proposed to increase the NT polarization for maximally enhanced electron–hole separation.

Complexity Reduction in Large Quantum Systems: Fragment Identification and Population Analysis via a Local Optimized Minimal Basis

We present, within Kohn-Sham density functional theory calculations, a quantitative method to identify and assess the partitioning of a large quantum-mechanical system into fragments. We then show how within this framework simple generalizations of other well-known population analyses can be used to extract, from first-principles, reliable electrostatic multipoles for the identified fragments. Our approach reduces arbitrariness in the fragmentation procedure and enables the possibility to assess quantitatively whether the corresponding fragment multipoles can be interpreted as observable quantities associated with a system moiety. By applying our formalism within the code BigDFT, we show that the use of a minimal set of in situ-optimized basis functions allows at the same time a proper fragment definition and an accurate description of the electronic structure.

Simulation of electron energy loss spectra of nanomaterials with linear-scaling density functional theory

Experimental techniques for electron energy loss spectroscopy (EELS) combine high energy resolution with high spatial resolution. They are therefore powerful tools for investigating the local electronic structure of complex systems such as nanostructures, interfaces and even individual defects. Interpretation of experimental electron energy loss spectra is often challenging and can require theoretical modelling of candidate structures, which themselves may be large and complex, beyond the capabilities of traditional cubic-scaling density functional theory. In this work, we present functionality to compute electron energy loss spectra within the onetep linear-scaling density functional theory code. We first demonstrate that simulated spectra agree with those computed using conventional plane wave pseudopotential methods to a high degree of precision. The ability of onetep to tackle large problems is then exploited to investigate convergence of spectra with respect to supercell size. Finally, we apply the novel functionality to a study of the electron energy loss spectra of defects on the (1 0 1) surface of an anatase slab and determine concentrations of defects which might be experimentally detectable.