Complexity reduction in density functional theory: Locality in space and energy.

We present recent developments of the NTChem program for performing large scale hybrid density functional theory calculations on the supercomputer Fugaku. We combine these developments with our recently proposed complexity reduction framework to assess the impact of basis set and functional choice on its measures of fragment quality and interaction. We further exploit the all electron representation to study system fragmentation in various energy envelopes. Building off this analysis, we propose two algorithms for computing the orbital energies of the Kohn-Sham Hamiltonian. We demonstrate that these algorithms can efficiently be applied to systems composed of thousands of atoms and as an analysis tool that reveals the origin of spectral properties.

Probing disorder in 2CzPN using core and valence states.

Molecules which exhibit thermally activated delayed fluorescence (TADF) show great promise for use in efficient, environmentally-friendly OLEDs, and thus the design of new TADF emitters is an active area of research. However, when used in devices, they are typically in the form of disordered thin films, where both the external molecular environment and thermally-induced internal variations in parameters such as the torsion angle can strongly influence their electronic structure. In this work, we use density functional theory and X-ray photoelectron spectroscopy to investigate the impact of disorder on both core and valence states in the TADF emitter 2CzPN (1,2-bis(carbazol-9-yl)-4,5-dicyanobenzene). By simulating gas phase molecules displaying varying levels of disorder, we assess the relative sensitivity of the different states to factors such as varying torsion angle. The theoretical results for both core and valence states show good agreement with experiment, thereby also highlighting the advantages of our approach for interpreting experimental spectra of large aromatic molecules, which are too complex to interpret based solely on experimental data.

Multi-phonon proton transfer pathway in a molecular organic ferroelectric crystal.

While the majority of ferroelectrics research has been focused on inorganic ceramics, molecular ferroelectrics can also combine large spontaneous polarization with high Curie temperatures. However, the microscopic mechanism of their ferroelectric switching is not fully understood. We explore proton tautomerism in the prototypical case of croconic acid, C5O5H2. In order to determine how efficiently ferroelectricity in croconic acid is described in terms of its Γ-point phonon modes, the minimum energy path between its structural ground states is approximated by projection onto reduced basis sets formed from subsets of these modes. The potential energy curve along the minimum energy path was found to be sensitive to the order of proton transfer, which requires a large subset (⪆8) of the modes to be approximated accurately. Our findings suggest rules for the construction of effective Hamiltonians to describe proton transfer ferroelectrics.

Structural and Electronic Effects of X-ray Irradiation on Prototypical [M(COD)Cl]2 Catalysts.

X-ray characterization techniques are invaluable for probing material characteristics and properties, and have been instrumental in discoveries across materials research. However, there is a current lack of understanding of how X-ray-induced effects manifest in small molecular crystals. This is of particular concern as new X-ray sources with ever-increasing brilliance are developed. In this paper, systematic studies of X-ray-matter interactions are reported on two industrially important catalysts, [Ir(COD)Cl]2 and [Rh(COD)Cl]2, exposed to radiation in X-ray diffraction (XRD) and X-ray photoelectron spectroscopy (XPS) experiments. From these complementary techniques, changes to structure, chemical environments, and electronic structure are observed as a function of X-ray exposure, allowing comparisons of stability to be made between the two catalysts. Radiation dose is estimated using recent developments to the RADDOSE-3D software for small molecules and applied to powder XRD and XPS experiments. Further insights into the electronic structure of the catalysts and changes occurring as a result of the irradiation are drawn from density functional theory (DFT). The techniques combined here offer much needed insight into the X-ray-induced effects in transition-metal catalysts and, consequently, their intrinsic stabilities. There is enormous potential to extend the application of these methods to other small molecular systems of scientific or industrial relevance.

Flexibilities of wavelets as a computational basis set for large-scale electronic structure calculations.

The BigDFT project was started in 2005 with the aim of testing the advantages of using a Daubechies wavelet basis set for Kohn-Sham (KS) density functional theory (DFT) with pseudopotentials. This project led to the creation of the BigDFT code, which employs a computational approach with optimal features of flexibility, performance, and precision of the results. In particular, the employed formalism has enabled the implementation of an algorithm able to tackle DFT calculations of large systems, up to many thousands of atoms, with a computational effort that scales linearly with the number of atoms. In this work, we recall some of the features that have been made possible by the peculiar properties of Daubechies wavelets. In particular, we focus our attention on the usage of DFT for large-scale systems. We show how the localized description of the KS problem, emerging from the features of the basis set, is helpful in providing a simplified description of large-scale electronic structure calculations. We provide some examples on how such a simplified description can be employed, and we consider, among the case-studies, the SARS-CoV-2 main protease.

The ONETEP linear-scaling density functional theory program.

We present an overview of the onetep program for linear-scaling density functional theory (DFT) calculations with large basis set (plane-wave) accuracy on parallel computers. The DFT energy is computed from the density matrix, which is constructed from spatially localized orbitals we call Non-orthogonal Generalized Wannier Functions (NGWFs), expressed in terms of periodic sinc (psinc) functions. During the calculation, both the density matrix and the NGWFs are optimized with localization constraints. By taking advantage of localization, onetep is able to perform calculations including thousands of atoms with computational effort, which scales linearly with the number or atoms. The code has a large and diverse range of capabilities, explored in this paper, including different boundary conditions, various exchange-correlation functionals (with and without exact exchange), finite electronic temperature methods for metallic systems, methods for strongly correlated systems, molecular dynamics, vibrational calculations, time-dependent DFT, electronic transport, core loss spectroscopy, implicit solvation, quantum mechanical (QM)/molecular mechanical and QM-in-QM embedding, density of states calculations, distributed multipole analysis, and methods for partitioning charges and interactions between fragments. Calculations with onetep provide unique insights into large and complex systems that require an accurate atomic-level description, ranging from biomolecular to chemical, to materials, and to physical problems, as we show with a small selection of illustrative examples. onetep has always aimed to be at the cutting edge of method and software developments, and it serves as a platform for developing new methods of electronic structure simulation. We therefore conclude by describing some of the challenges and directions for its future developments and applications.

Combining Pseudopotential and All Electron Density Functional Theory for the Efficient Calculation of Core Spectra Using a Multiresolution Approach.

Broadly speaking, the calculation of core spectra such as electron energy loss spectra (EELS) at the level of density functional theory (DFT) usually relies on one of two approaches: conceptually more complex but computationally efficient projector augmented wave based approaches or more straightforward but computationally more intensive all electron (AE) based approaches. In this work we present an alternative method, which aims to find a middle ground between the two. Specifically, we have implemented an approach in the multiwavelet madness molecular DFT code that permits a combination of atoms treated at the AE and pseudopotential (PSP) level. Atoms for which one wishes to calculate the core edges are thus treated at an AE level, while the remainder can be treated at the PSP level. This is made possible thanks to the multiresolution approach of madness, which permits accurate and efficient calculations at both the AE and PSP level. Through examples of a small molecule and a carbon nanotube, we demonstrate the potential applications of our approach.

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.

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.

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.

Ab initio calculations of the optical absorption spectra of C60-conjugated polymer hybrids.

A recently developed linear-scaling density-functional theory (LS-DFT) formalism is used to calculate optical absorption spectra of hybrids of C60 and the conjugated polymers poly(para-phenylene) (PPP) and poly(para-phenylene vinylene) (PPV). The use of a LS formalism allows calculations on large systems with realistic proportions of C60, which has been of interest for the use of such materials in photovoltaics. Two different bonding structures are tested for the hybrid PPP and for both systems additional peaks are present in the absorption spectra below the original onset of absorption. By identifying the eigenstates involved in the relevant transitions, a weighted density difference is formed, demonstrating the transfer of charge between the polymer chain and the C60, in agreement with experiment. For the hybrid PPV, no additional peaks are observed in the absorption spectrum.

Transition-Based Constrained DFT for the Robust and Reliable Treatment of Excitations in Supramolecular Systems.

Despite the variety of available computational approaches, state-of-the-art methods for calculating excitation energies, such as time-dependent density functional theory (TDDFT), are computationally demanding and thus limited to moderate system sizes. Here, we introduce a new variation of constrained DFT (CDFT), wherein the constraint corresponds to a particular transition (T), or a combination of transitions, between occupied and virtual orbitals, rather than a region of the simulation space as in traditional CDFT. We compare T-CDFT with TDDFT and ΔSCF results for the low-lying excited states (S1 and T1) of a set of gas-phase acene molecules and OLED emitters and with reference results from the literature. At the PBE level of theory, T-CDFT outperforms ΔSCF for both classes of molecules, while also proving to be more robust. For the local excitations seen in the acenes, T-CDFT and TDDFT perform equally well. For the charge transfer (CT)-like excitations seen in the OLED molecules, T-CDFT also performs well, in contrast to the severe energy underestimation seen with TDDFT. In other words, T-CDFT is equally applicable to both local excitations and CT states, providing more reliable excitation energies at a much lower computational cost than TDDFT cost. T-CDFT is designed for large systems and has been implemented in the linear-scaling BigDFT code. It is therefore ideally suited for exploring the effects of explicit environments on excitation energies, paving the way for future simulations of excited states in complex realistic morphologies, such as those which occur in OLED materials.

Tackling Disorder in γ-Ga2 O3.

Ga2 O3 and its polymorphs are attracting increasing attention. The rich structural space of polymorphic oxide systems such as Ga2 O3 offers potential for electronic structure engineering, which is of particular interest for a range of applications, such as power electronics. γ-Ga2 O3 presents a particular challenge across synthesis, characterization, and theory due to its inherent disorder and resulting complex structure-electronic-structure relationship. Here, density functional theory is used in combination with a machine-learning approach to screen nearly one million potential structures, thereby developing a robust atomistic model of the γ-phase. Theoretical results are compared with surface and bulk sensitive soft and hard X-ray photoelectron spectroscopy, X-ray absorption spectroscopy, spectroscopic ellipsometry, and photoluminescence excitation spectroscopy experiments representative of the occupied and unoccupied states of γ-Ga2 O3 . The first onset of strong absorption at room temperature is found at 5.1 eV from spectroscopic ellipsometry, which agrees well with the excitation maximum at 5.17 eV obtained by photoluminescence excitation spectroscopy, where the latter shifts to 5.33 eV at 5 K. This work presents a leap forward in the treatment of complex, disordered oxides and is a crucial step toward exploring how their electronic structure can be understood in terms of local coordination and overall structure.

Exploring metastable states in UO2using hybrid functionals and dynamical mean field theory.

A detailed exploration of thef-atomic orbital occupancy space for UO2is performed using a first principles approach based on density functional theory (DFT), employing a full hybrid functional within a systematic basis set. Specifically, the PBE0 functional is combined with an occupancy biasing scheme implemented in a wavelet-based algorithm which is adapted to large supercells. The results are compared with previous DFT +Ucalculations reported in the literature, while dynamical mean field theory is also performed to provide a further base for comparison. This work shows that the computational complexity of the energy landscape of a correlatedf-electron oxide is much richer than has previously been demonstrated. The resulting calculations provide evidence of the existence of multiple previously unexplored metastable electronic states of UO2, including those with energies which are lower than previously reported ground states.

Complexity Reduction in Density Functional Theory Calculations of Large Systems: System Partitioning and Fragment Embedding.

With the development of low order scaling methods for performing Kohn-Sham density functional theory, it is now possible to perform fully quantum mechanical calculations of systems containing tens of thousands of atoms. However, with an increase in the size of the system treated comes an increase in complexity, making it challenging to analyze such large systems and determine the cause of emergent properties. To address this issue, in this paper, we present a systematic complexity reduction methodology which can break down large systems into their constituent fragments and quantify interfragment interactions. The methodology proposed here requires no a priori information or user interaction, allowing a single workflow to be automatically applied to any system of interest. We apply this approach to a variety of different systems and show how it allows for the derivation of new system descriptors, the design of QM/MM partitioning schemes, and the novel application of graph metrics to molecules and materials.

Predicting Core Level Photoelectron Spectra of Amino Acids Using Density Functional Theory.

Core level photoelectron spectroscopy is a widely used technique to study amino acids. Interpretation of the individual contributions from functional groups and their local chemical environments to overall spectra requires both high-resolution reference spectra and theoretical insights, for example, from density functional theory calculations. This is a particular challenge for crystalline amino acids due to the lack of experimental data and the limitation of previous calculations to gas phase molecules. Here, a state of the art multiresolution approach is used for high-precision gas phase calculations and to validate core hole pseudopotentials for plane-wave calculations. This powerful combination of complementary numerical techniques provides a framework for accurate ΔSCF calculations for molecules and solids in systematic basis sets. It is used to successfully predict C and O 1s core level spectra of glycine, alanine, and serine and identify chemical state contributions to experimental spectra of crystalline amino acids.

Designing a bioremediator: mechanistic models guide cellular and molecular specialization.

Bioremediators are cells or non-living subcellular entities of biological origin employed to degrade target pollutants. Rational, mechanistic design can substantially improve the performance of bioremediators for applications, including waste treatment and food safety. We highlight how such improvements can be informed at the cellular level by theoretical observations especially in the context of phenotype plasticity, cell signaling, and community assembly. At the molecular level, we suggest enzyme design using techniques such as Small Angle Neutron Scattering and Density Functional Theory. To provide an example of how these techniques could be synergistically combined, we present the case-study of the interaction of the enzyme laccase with the food contaminant aflatoxin B1. In designing bioremediators, we encourage interdisciplinary, mechanistic research to transition from an observation-oriented approach to a principle-based one.

Pseudo-fragment approach for extended systems derived from linear-scaling DFT.

We present a computational approach which is tailored for reducing the complexity of the description of extended systems at the density functional theory level. We define a recipe for generating a set of localized basis functions which are optimized either for the accurate description of pristine, bulk-like Wannier functions, or for the in situ treatment of deformations induced by defective constituents such as boundaries or impurities. Our method enables one to identify the regions of an extended system which require dedicated optimization of the Kohn-Sham degrees of freedom, and provides the user with a reliable estimation of the errors-if any-induced by the locality of the approach. Such a method facilitates on the one hand an effective reduction of the computational degrees of freedom needed to simulate systems at the nanoscale, while in turn providing a description that can be straightforwardly put in relation to effective models, like tight binding Hamiltonians. We present our methodology with SiC nanotube-like cages as a test bed. Nonetheless, the wavelet-based method employed in this paper makes possible calculation of systems with different dimensionalities, including slabs and fully periodic systems.

Affordable and accurate large-scale hybrid-functional calculations on GPU-accelerated supercomputers.

Performing high accuracy hybrid functional calculations for condensed matter systems containing a large number of atoms is at present computationally very demanding or even out of reach if high quality basis sets are used. We present a highly optimized multiple graphics processing unit implementation of the exact exchange operator which allows one to perform fast hybrid functional density-functional theory (DFT) calculations with systematic basis sets without additional approximations for up to a thousand atoms. With this method hybrid DFT calculations of high quality become accessible on state-of-the-art supercomputers within a time-to-solution that is of the same order of magnitude as traditional semilocal-GGA functionals. The method is implemented in a portable open-source library.

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.