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Green's function theory has emerged as a powerful many-body approach not only in condensed matter physics but also in quantum chemistry in recent years. We have developed a new all-electron implementation of the BSE@GW formalism using numeric atom-centered orbital basis sets (Liu et al., J. Chem. Phys. 152, 044105 (2020)). We present our recent developments in implementing this formalism for extended systems with periodic boundary conditions. We discuss its numerical implementation and various convergence tests pertaining to numerical atom-centered orbitals, auxiliary basis sets for the resolution-of-identity formalism, and Brillouin zone sampling. Proof-of-principle examples are presented to compare with other formalisms, illustrating the new all-electron BSE@GW method for extended systems., Comment: 8 figures

Hybrid density functional approximations (DFAs) offer compelling accuracy for ab initio electronic-structure simulations of molecules, nanosystems, and bulk materials, addressing some deficiencies of computationally cheaper, frequently used semilocal DFAs. However, the computational bottleneck of hybrid DFAs is the evaluation of the non-local exact exchange contribution, which is the limiting factor for the application of the method for large-scale simulations. In this work, we present a drastically optimized resolution-of-identity-based real-space implementation of the exact exchange evaluation for both non-periodic and periodic boundary conditions in the all-electron code FHI-aims, targeting high-performance CPU compute clusters. The introduction of several new refined Message Passing Interface (MPI) parallelization layers and shared memory arrays according to the MPI-3 standard were the key components of the optimization. We demonstrate significant improvements of memory and performance efficiency, scalability, and workload distribution, extending the reach of hybrid DFAs to simulation sizes beyond ten thousand atoms. As a necessary byproduct of this work, other code parts in FHI-aims have been optimized as well, e.g., the computation of the Hartree potential and the evaluation of the force and stress components. We benchmark the performance and scaling of the hybrid DFA based simulations for a broad range of chemical systems, including hybrid organic-inorganic perovskites, organic crystals and ice crystals with up to 30,576 atoms (101,920 electrons described by 244,608 basis functions).

Science is and always has been based on data, but the terms "data-centric" and the "4th paradigm of" materials research indicate a radical change in how information is retrieved, handled and research is performed. It signifies a transformative shift towards managing vast data collections, digital repositories, and innovative data analytics methods. The integration of Artificial Intelligence (AI) and its subset Machine Learning (ML), has become pivotal in addressing all these challenges. This Roadmap on Data-Centric Materials Science explores fundamental concepts and methodologies, illustrating diverse applications in electronic-structure theory, soft matter theory, microstructure research, and experimental techniques like photoemission, atom probe tomography, and electron microscopy. While the roadmap delves into specific areas within the broad interdisciplinary field of materials science, the provided examples elucidate key concepts applicable to a wider range of topics. The discussed instances offer insights into addressing the multifaceted challenges encountered in contemporary materials research., Comment: Review, outlook, roadmap, perspective

The coupled quantum dynamics of electrons and protons is ubiquitous in many dynamical processes involving light-matter interaction, such as solar energy conversion in chemical systems and photosynthesis. A first-principles description of such nuclear-electronic quantum dynamics requires not only the time-dependent treatment of nonequilibrium electron dynamics but also that of quantum protons. Quantum mechanical correlation between electrons and protons adds further complexity to such coupled dynamics. Here we extend real-time nuclear-electronic orbital time-dependent density functional theory (RT-NEO-TDDFT) to periodic systems and perform first-principles simulations of coupled quantum dynamics of electrons and protons in complex heterogeneous systems. The process studied is electronically excited state intramolecular proton transfer of o-hydroxybenzaldehyde in water and at a silicon (111) semiconductor-molecule interface. These simulations illustrate how environments such as hydrogen-bonding water molecules and an extended material surface impact the dynamical process on the atomistic level. Depending on how the molecule is chemisorbed on the surface, excited state electron transfer from the molecule to the semiconductor surface can inhibit ultrafast proton transfer within the molecule. This work elucidates how heterogeneous environments influence the balance between the quantum mechanical proton transfer and excited electron dynamics. The periodic RT-NEO-TDDFT approach is applicable to a wide range of other photoinduced heterogeneous processes.

Electronic structure calculations have been instrumental in providing many important insights into a range of physical and chemical properties of various molecular and solid-state systems. Their importance to various fields, including materials science, chemical sciences, computational chemistry and device physics, is underscored by the large fraction of available public supercomputing resources devoted to these calculations. As we enter the exascale era, exciting new opportunities to increase simulation numbers, sizes, and accuracies present themselves. In order to realize these promises, the community of electronic structure software developers will however first have to tackle a number of challenges pertaining to the efficient use of new architectures that will rely heavily on massive parallelism and hardware accelerators. This roadmap provides a broad overview of the state-of-the-art in electronic structure calculations and of the various new directions being pursued by the community. It covers 14 electronic structure codes, presenting their current status, their development priorities over the next five years, and their plans towards tackling the challenges and leveraging the opportunities presented by the advent of exascale computing., Comment: Submitted as a roadmap article to Modelling and Simulation in Materials Science and Engineering; Address any correspondence to Vikram Gavini (vikramg@umich.edu) and Danny Perez (danny_perez@lanl.gov)

FHI-aims is a quantum mechanics software package based on numeric atom-centered orbitals (NAOs) with broad capabilities for all-electron electronic-structure calculations and ab initio molecular dynamics. It also connects to workflows for multi-scale and artificial intelligence modeling., Comment: 7 pages, 4 figures

Machine learning techniques have received growing attention as an alternative strategy for developing general-purpose density functional approximations, augmenting the historically successful approach of human designed functionals derived to obey mathematical constraints known for the exact exchange-correlation functional. More recently efforts have been made to reconcile the two techniques, integrating machine learning and exact-constraint satisfaction. We continue this integrated approach, designing a deep neural network that exploits the exact constraint and appropriate norm philosophy to deorbitalize the strongly constrained and appropriately normed SCAN functional. The deep neural network is trained to replicate the SCAN functional from only electron density and local derivative information, avoiding use of the orbital dependent kinetic energy density. The performance and transferability of the machine learned functional are demonstrated for molecular and periodic systems.

The nuclear-electronic orbital (NEO) method is a well-established approach for treating nuclei quantum mechanically in molecular systems beyond the usual Born-Oppenheimer approximation. In this work, we present a strategy to implement the NEO method for periodic electronic structure calculations, particularly focused on multicomponent density functional theory (DFT). The NEO-DFT method is implemented in an all-electron electronic structure code, FHI-aims, using a combination of analytical and numerical integration techniques as well as a resolution of the identity scheme to enhance computational efficiency. After validating this implementation, proof-of-concept applications are presented to illustrate the effects of quantized protons on the physical properties of extended systems such as two-dimensional materials and liquid-semiconductor interfaces. Specifically, periodic NEO-DFT calculations are performed for a trans-polyacetylene chain, a hydrogen boride sheet, and a titanium oxide-water interface. The zero-point energy effects of the protons, as well as electron-proton correlation, are shown to noticeably impact the density of states and band structures for these systems. These developments provide a foundation for the application of multicomponent DFT to a wide range of other extended condensed matter systems., Comment: 8 figures

In the field of van der Waals heterostructures, the twist angle between stacked two-dimensional (2D) layers has been identified to be of utmost importance for the properties of the heterostructures. In this context, we previously reported the growth of a single layer of unconventionally oriented epitaxial graphene that forms in a surfactant atmosphere [F. C. Bocquet, et al., Phys. Rev. Lett. 125, 106102 (2020)]. The resulting G-R0$^\circ$ layer is aligned with the SiC lattice, and hence represents an important milestone towards high quality twisted bilayer graphene (tBLG), a frequently investigated model system in this field. Here, we focus on the surface structures obtained in the same surfactant atmosphere, but at lower preparation temperatures at which a boron nitride template layer forms on SiC(0001). In a comprehensive study based on complementary experimental and theoretical techniques, we find -- in contrast to the literature -- that this template layer is a hexagonal B$_x$N$_y$ layer, but not high-quality hBN. It is aligned with the SiC lattice and gradually replaced by low-quality graphene in the 0$^\circ$ orientation of the B$_x$N$_y$ template layer upon annealing.

We demonstrate the use of Google's cloud-based Tensor Processing Units (TPUs) to accelerate and scale up conventional (cubic-scaling) density functional theory (DFT) calculations. Utilizing 512 TPU cores, we accomplish the largest such DFT computation to date, with 247848 orbitals, corresponding to a cluster of 10327 water molecules with 103270 electrons, all treated explicitly. Our work thus paves the way towards accessible and systematic use of conventional DFT, free of any system-specific constraints, at unprecedented scales.

We develop and implement a formalism which enables calculating the analytical gradients of particle-hole random-phase approximation (RPA) ground-state energy with respect to the atomic positions within the atomic orbital basis set framework. Our approach is based on a localized resolution of identity (LRI) approximation for evaluating the two-electron Coulomb integrals and their derivatives, and the density functional perturbation theory for computing the first-order derivatives of the Kohn-Sham (KS) orbitals and orbital energies. Our implementation allows one to relax molecular structures at the RPA level using both Gaussian-type orbitals (GTOs) and numerical atomic orbitals (NAOs). Benchmark calculations show that our approach delivers high numerical precision compared to previous implementations. A careful assessment of the quality of RPA geometries for small molecules reveals that post-KS RPA systematically overestimates the bond lengths. We furthermore optimized the geometries of the four low-lying water hexamers -- cage, prism, cyclic and book isomers, and determined the energy hierarchy of these four isomers using RPA. The obtained RPA energy ordering is in good agreement with that yielded by the coupled cluster method with single, double and perturbative triple excitations, despite that the dissociation energies themselves are appreciably underestimated. The underestimation of the dissociation energies by RPA is well corrected by the renormalized single excitation correction., Comment: 15 pages, 1 figure, five tables

We implement and benchmark the frozen core approximation, a technique commonly adopted in electronic structure theory to reduce the computational cost by means of mathematically fixing the chemically inactive core electron states. The accuracy and efficiency of this approach are well controlled by a single parameter, the number of frozen orbitals. Explicit corrections for the frozen core orbitals and the unfrozen valence orbitals are introduced, safeguarding against seemingly minor numerical deviations from the assumed orthonormality conditions of the basis functions. A speedup of over two-fold can be achieved for the diagonalization step in all-electron density-functional theory simulations containing heavy elements, without any accuracy degradation in terms of the electron density, total energy, and atomic forces. This is demonstrated in a benchmark study covering 103 materials across the periodic table, and a large-scale simulation of CsPbBr3 with 2,560 atoms. Our study provides a rigorous benchmark of the precision of the frozen core approximation (sub-meV per atom for frozen core orbitals below -200 eV) for a wide range of test cases and for chemical elements ranging from Li to Po. The algorithms discussed here are implemented in the open-source Electronic Structure Infrastructure software package.

We present an all-electron, periodic {\GnWn} implementation within the numerical atomic orbital (NAO) basis framework. A localized variant of the resolution-of-the-identity (RI) approximation is employed to significantly reduce the computational cost of evaluating and storing the two-electron Coulomb repulsion integrals. We demonstrate that the error arising from localized RI approximation can be reduced to an insignificant level by enhancing the set of auxiliary basis functions, used to expand the products of two single-particle NAOs. An efficient algorithm is introduced to deal with the Coulomb singularity in the Brillouin zone sampling that is suitable for the NAO framework. We perform systematic convergence tests and identify a set of computational parameters, which can serve as the default choice for most practical purposes. Benchmark calculations are carried out for a set of prototypical semiconductors and insulators, and compared to independent reference values obtained from an independent $G_0W_0$ implementation based on linearized augmented plane waves (LAPW) plus high-energy localized orbitals (HLOs) basis set, as well as experimental results. With a moderate (FHI-aims \textit{tier} 2) NAO basis set, our $G_0W_0$ calculations produce band gaps that typically lie in between the standard LAPW and the LAPW+HLO results. Complementing \textit{tier} 2 with highly localized Slater-type orbitals (STOs), we find that the obtained band gaps show an overall convergence towards the LAPW+HLO results. The algorithms and techniques developed in this work pave the way for efficient implementations of correlated methods within the NAO framework., Comment: 23 pages, 7 figures

A review of the present status, recent enhancements, and applicability of the SIESTA program is presented. Since its debut in the mid-nineties, SIESTA's flexibility, efficiency and free distribution has given advanced materials simulation capabilities to many groups worldwide. The core methodological scheme of SIESTA combines finite-support pseudo-atomic orbitals as basis sets, norm-conserving pseudopotentials, and a real-space grid for the representation of charge density and potentials and the computation of their associated matrix elements. Here we describe the more recent implementations on top of that core scheme, which include: full spin-orbit interaction, non-repeated and multiple-contact ballistic electron transport, DFT+U and hybrid functionals, time-dependent DFT, novel reduced-scaling solvers, density-functional perturbation theory, efficient Van der Waals non-local density functionals, and enhanced molecular-dynamics options. In addition, a substantial effort has been made in enhancing interoperability and interfacing with other codes and utilities, such as Wannier90 and the second-principles modelling it can be used for, an AiiDA plugin for workflow automatization, interface to Lua for steering SIESTA runs, and various postprocessing utilities. SIESTA has also been engaged in the Electronic Structure Library effort from its inception, which has allowed the sharing of various low level libraries, as well as data standards and support for them, in particular the PSML definition and library for transferable pseudopotentials, and the interface to the ELSI library of solvers. Code sharing is made easier by the new open-source licensing model of the program. This review also presents examples of application of the capabilities of the code, as well as a view of on-going and future developments., Comment: 29 pages, 23 figures

We present a relativistic correction scheme to improve the accuracy of 1s core-level binding energies calculated from Green's function theory in the $GW$ approximation, which does not add computational overhead. An element-specific corrective term is derived as the difference between the 1s eigenvalues obtained from the self-consistent solutions to the non- or scalar-relativistic Kohn-Sham equations and the four-component Dirac-Kohn-Sham equations for a free neutral atom. We examine the dependence of this corrective term on the molecular environment and on the amount of exact exchange in hybrid exchange-correlation functionals. This corrective term is then added as a perturbation to the quasiparticle energies from partially self-consistent and single-shot $GW$ calculations. We show that this element-specific relativistic correction, when applied to a previously reported benchmark set of 65 core-state excitations [J. Phys. Chem. Lett. 11, 1840 (2020)], reduces the mean absolute error (MAE) with respect to experiment from 0.55 to 0.30 eV and eliminates the species dependence of the MAE, which otherwise increases with the atomic number. The relativistic corrections also reduce the species dependence for the optimal amount of exact exchange in the hybrid functional used as starting point for the single-shot $G_0W_0$ calculations. Our correction scheme can be transferred to other methods, which we demonstrate for the Delta self-consistent field ($\Delta$SCF) approach based on density functional theory.

First-principles electronic structure calculations are very widely used thanks to the many successful software packages available. Their traditional coding paradigm is monolithic, i.e., regardless of how modular its internal structure may be, the code is built independently from others, from the compiler up, with the exception of linear-algebra and message-passing libraries. This model has been quite successful for decades. The rapid progress in methodology, however, has resulted in an ever increasing complexity of those programs, which implies a growing amount of replication in coding and in the recurrent re-engineering needed to adapt to evolving hardware architecture. The Electronic Structure Library (\esl) was initiated by CECAM (European Centre for Atomic and Molecular Calculations) to catalyze a paradigm shift away from the monolithic model and promote modularization, with the ambition to extract common tasks from electronic structure programs and redesign them as free, open-source libraries. They include "heavy-duty" ones with a high degree of parallelisation, and potential for adaptation to novel hardware within them, thereby separating the sophisticated computer science aspects of performance optimization and re-engineering from the computational science done by scientists when implementing new ideas. It is a community effort, undertaken by developers of various successful codes, now facing the challenges arising in the new model. This modular paradigm will improve overall coding efficiency and enable specialists (computer scientists or computational scientists) to use their skills more effectively. It will lead to a more sustainable and dynamic evolution of software as well as lower barriers to entry for new developers., Comment: Revised version as finally accepted by J. Chem. Phys. to appear within the Special Topic in Electronic Structure Software (version prior to JCP's typesetting and proofs)

The electronic properties of hybrid organic-inorganic semiconductor interfaces depend strongly on the alignment of the electronic carrier levels in the organic/inorganic components. In the present work, we address this energy level alignment from first principles theory for two paradigmatic organic-inorganic semiconductor interfaces, the singlet fission materials tetracene and pentacene on H/Si(111), using all-electron hybrid density functional theory. For isolated tetracene on H/Si(111), a type I-like heterojunction (lowest-energy electron and hole states on Si) is found. For isolated pentacene, the molecular and semiconductor valence band edges are degenerate. For monolayer films, we show how to construct supercell geometries with up to 1,192 atoms, which minimize the strain between the inorganic surface and an organic monolayer film. Based on these models, we predict the formation of type II heterojunctions (electron states on Si, hole-like states on the organic species) for both acenes, indicating that charge separation at the interface between the organic and inorganic components is favored. The paper discusses the steps needed to find appropriate low-energy interface geometries for weakly bonded organic molecules and films on inorganic substrates from first principles, a necessary prerequisite for any computational level alignment prediction., Comment: 36 pages, 15 figures, submitted v2: Corrected Affiliation No. 4

The solution of eigenproblems is often a key computational bottleneck that limits the tractable system size of numerical algorithms, among them electronic structure theory in chemistry and in condensed matter physics. Large eigenproblems can easily exceed the capacity of a single compute node, thus must be solved on distributed-memory parallel computers. We here present GPU-oriented optimizations of the ELPA two-stage tridiagonalization eigensolver (ELPA2). On top of cuBLAS-based GPU offloading, we add a CUDA kernel to speed up the back-transformation of eigenvectors, which can be the computationally most expensive part of the two-stage tridiagonalization algorithm. We benchmark the performance of this GPU-accelerated eigensolver on two hybrid CPU-GPU architectures, namely a compute cluster based on Intel Xeon Gold CPUs and NVIDIA Volta GPUs, and the Summit supercomputer based on IBM POWER9 CPUs and NVIDIA Volta GPUs. Consistent with previous benchmarks on CPU-only architectures, the GPU-accelerated two-stage solver exhibits a parallel performance superior to the one-stage counterpart. Finally, we demonstrate the performance of the GPU-accelerated eigensolver developed in this work for routine semi-local KS-DFT calculations comprising thousands of atoms.

Routine applications of electronic structure theory to molecules and periodic systems need to compute the electron density from given Hamiltonian and, in case of non-orthogonal basis sets, overlap matrices. System sizes can range from few to thousands or, in some examples, millions of atoms. Different discretization schemes (basis sets) and different system geometries (finite non-periodic vs. infinite periodic boundary conditions) yield matrices with different structures. The ELectronic Structure Infrastructure (ELSI) project provides an open-source software interface to facilitate the implementation and optimal use of high-performance solver libraries covering cubic scaling eigensolvers, linear scaling density-matrix-based algorithms, and other reduced scaling methods in between. In this paper, we present recent improvements and developments inside ELSI, mainly covering (1) new solvers connected to the interface, (2) matrix layout and communication adapted for parallel calculations of periodic and/or spin-polarized systems, (3) routines for density matrix extrapolation in geometry optimization and molecular dynamics calculations, and (4) general utilities such as parallel matrix I/O and JSON output. The ELSI interface has been integrated into four electronic structure code projects (DFTB+, DGDFT, FHI-aims, SIESTA), allowing us to rigorously benchmark the performance of the solvers on an equal footing. Based on results of a systematic set of large-scale benchmarks performed with Kohn-Sham density-functional theory and density-functional tight-binding theory, we identify factors that strongly affect the efficiency of the solvers, and propose a decision layer that assists with the solver selection process. Finally, we describe a reverse communication interface encoding matrix-free iterative solver strategies that are amenable, e.g., for use with planewave basis sets.

We present an implementation of all-electron density-functional theory for massively parallel GPGPU-based platforms, using localized atom-centered basis functions and real-space integration grids. Special attention is paid to domain decomposition of the problem on non-uniform grids, which enables compute- and memory-parallel execution across thousands of nodes for real-space operations, e.g. the update of the electron density, the integration of the real-space Hamiltonian matrix, and calculation of Pulay forces. To assess the performance of our GPGPU implementation, we performed benchmarks on three different architectures using a 103-material test set. We find that operations which rely on dense serial linear algebra show dramatic speedups from GPGPU acceleration: in particular, SCF iterations including force and stress calculations exhibit speedups ranging from 4.5 to 6.6. For the architectures and problem types investigated here, this translates to an expected overall speedup between 3-4 for the entire calculation (including non-GPU accelerated parts), for problems featuring several tens to hundreds of atoms. Additional calculations for a 375-atom Bi$_2$Se$_3$ bilayer show that the present GPGPU strategy scales for large-scale distributed-parallel simulations., Comment: 49 pages, 9 figures

The discovery of new materials as well as the determination of a vast set of materials properties for science and technology is a fast growing field of research, with contributions from many groups worldwide. Materials data from individual research groups is traditionally disseminated by means of loosely interconnected, peer-reviewed publications. MatD3 is an open-source, dedicated database and web application framework designed to store, curate and disseminate experimental and theoretical materials data generated by individual research groups or research consortia. A research group can set up its own instance of MatD3 and publish scientific results or simply use an existing online MatD3 instance. Disseminating research data in this form enables broader access, reproducibility, and repurposing of scientific products. MatD3 is a general purpose database that does not focus on any specific level of theory or experimental method. Instead, the focus is on storing and making accessible the data and making it straightforward to curate them.

Silicon carbide (SiC) is an excellent substrate for growth and manipulation of large scale, high quality epitaxial graphene. On the carbon face (the ($\bar{1}\bar{1}\bar{1}$) or $(000\bar{1}$) face, depending on the polytype), the onset of graphene growth is intertwined with the formation of several competing surface phases, among them a (3$\times$3) precursor phase suspected to hinder the onset of controlled, near-equilibrium growth of graphene. Despite more than two decades of research, the precise atomic structure of this phase is still unclear. We present a new model of the (3$\times$3)-SiC-($\bar{1}\bar{1}\bar{1}$) reconstruction, derived from an {\it ab initio} random structure search based on density functional theory including van der Waals effects. The structure consists of a simple pattern of five Si adatoms in bridging and on-top positions on an underlying, C-terminated substrate layer, leaving one C atom per (3$\times$3) unit cell formally unsaturated. Simulated scanning tunneling microscopy (STM) images are in excellent agreement with previously reported experimental STM images.

The Bethe-Salpeter equation (BSE) based on GW quasiparticle levels is a successful approach for calculating the optical gaps and spectra of solids and also for predicting the neutral excitations of small molecules. We here present an all-electron implementation of the GW+BSE formalism for molecules, using numeric atom-centered orbital (NAO) basis sets. We present benchmarks for low-lying excitation energies for a set of small organic molecules, denoted in the literature as "Thiel's set". Literature reference data based on Gaussian-type orbitals are reproduced to about one meV precision for the molecular benchmark set, when using the same GW quasiparticle energies and basis sets as the input to the BSE calculations. For valence correlation consistent NAO basis sets, as well as for standard NAO basis sets for ground state density-functional theory with extended augmentation functions, we demonstrate excellent convergence of the predicted low-lying excitations to the complete basis set limit. A simple and affordable augmented NAO basis set denoted "tier2+aug2" is recommended as a particularly efficient formulation for production calculations. We finally demonstrate that the same convergence properties also apply to linear-response time-dependent density functional theory within the NAO formalism.

The structure of the SiC(000-1) surface, the C-face of the {0001} SiC surfaces, is studied as a function of temperature and of pressure in a gaseous environment of disilane (Si2H6). Various surface reconstructions are observed, both with and without the presence of an overlying graphene layer (which spontaneously forms at sufficiently high temperatures). Based on cross-sectional scanning transmission electron microscopy measurements, the interface structure that forms in the presence of the graphene is found to contain 1.4 - 1.7 monolayers (ML) of Si, a somewhat counter-intuitive result since, when the graphene forms, the system is actually under C-rich conditions. Using ab initio thermodynamics, it is demonstrated that there exists a class of Si-rich surfaces containing about 1.3 ML of Si that are stable on the surface (even under C-rich conditions) at temperatures above about 400 K. The structures that thus form consist of Si adatoms atop a Si adlayer on the C-face of SiC, with or without the presence of overlying graphene., Comment: 19 pages with 8 figures, along with 6 pages of Supplemental Material; v2 adds refs. 56,59-62 all being prior work, along with several paragraphs in the Discussion or Summary sections of the manuscript discussing this prior work; v3 corrects several typographical errors

We describe an accurate and scalable implementation for the computation of molecular nuclear magnetic resonance shieldings, J-couplings, and magnetizabilities within nonrelativistic semilocal density functional theory, based on numeric atom-centered orbital (NAO) basis sets. We compare the convergence to the basis set limit for two established types of NAO basis sets, called NAO-VCC-nZ and FHI-aims-09, to several established Gaussian-type basis sets. The basis set limit is reached faster for the NAO basis sets than for standard correlation consistent Gaussian-type basis sets (cc-pVnZ, aug-cc-pVnZ, cc-pCVnZ, aug-cc-pCVnZ). For shieldings, the convergence properties and accuracy of the NAO-VCC-nZ basis sets are similar to Jensen's polarization consistent (pc) basis sets optimized for shieldings (pcS-n). For J-couplings, we develop a new type of NAO basis set (NAO-J-n) by augmenting the NAO-VCC-nZ basis sets with tight s-functions from Jensen's pcJ-n basis sets, which are optimized for J-couplings. We find the convergence of the NAO-J-n to be similar to the pcJ-n basis sets. Large scale applicability of the implementation is demonstrated for shieldings and J-couplings in a system of over 1,000 atoms.

For a class of 2D hybrid organic-inorganic perovskite semiconductors based on $\pi$-conjugated organic cations, we predict quantitatively how varying the organic and inorganic component allows control over the nature, energy and localization of carrier states in a quantum-well-like fashion. Our first-principles predictions, based on large-scale hybrid density-functional theory with spin-orbit coupling, show that the interface between the organic and inorganic parts within a single hybrid can be modulated systematically, enabling us to select between different type-I and type-II energy level alignments. Energy levels, recombination properties and transport behavior of electrons and holes thus become tunable by choosing specific organic functionalizations and juxtaposing them with suitable inorganic components.

Solving the electronic structure from a generalized or standard eigenproblem is often the bottleneck in large scale calculations based on Kohn-Sham density-functional theory. This problem must be addressed by essentially all current electronic structure codes, based on similar matrix expressions, and by high-performance computation. We here present a unified software interface, ELSI, to access different strategies that address the Kohn-Sham eigenvalue problem. Currently supported algorithms include the dense generalized eigensolver library ELPA, the orbital minimization method implemented in libOMM, and the pole expansion and selected inversion (PEXSI) approach with lower computational complexity for semilocal density functionals. The ELSI interface aims to simplify the implementation and optimal use of the different strategies, by offering (a) a unified software framework designed for the electronic structure solvers in Kohn-Sham density-functional theory; (b) reasonable default parameters for a chosen solver; (c) automatic conversion between input and internal working matrix formats, and in the future (d) recommendation of the optimal solver depending on the specific problem. Comparative benchmarks are shown for system sizes up to 11,520 atoms (172,800 basis functions) on distributed memory supercomputing architectures., Comment: 55 pages, 14 figures, 2 tables

We quantify the accuracy of different non-self-consistent and self-consistent spin-orbit coupling (SOC) treatments in Kohn-Sham and hybrid density-functional theory by providing a band structure benchmark set for the valence and low-lying conduction energy bands of 103 inorganic compounds, covering chemical elements up to Po. Reference energy band structures for the PBE density functional are obtained using the full-potential (linearized) augmented plane wave code Wien2k, employing its self-consistent treatment of SOC including Dirac-like p$^{1/2}$ orbitals in the basis set. We use this benchmark set to benchmark a computationally simpler, non-self-consistent all-electron treatment of SOC based on scalar-relativistic orbitals and numeric atom-centered orbital basis functions. For elements up to Z$\approx$50, both treatments agree virtually exactly. For the heaviest elements considered (Tl, Pb, Bi, Po), the band structure changes due to SOC are captured with a relative deviation of 11% or less. For different density functionals (PBE vs. the hybrid HSE06), we show that the effect of spin-orbit coupling is usually similar but can be dissimilar if the qualitative features of the predicted underlying scalar-relativistic band structures do not agree. All band structures considered in this work are available online via the NOMAD Repository to aid in future benchmark studies and methods development., Comment: 20 pages, 9 figures, 5 tables, supplemental material included in ancillary files

Using multiwavelets, we have obtained total energies and corresponding atomization energies for the GGA-PBE and hybrid-PBE0 density functionals for a test set of 211 molecules with an unprecedented and guaranteed $\mu$Hartree accuracy. These quasi-exact references allow us to quantify the accuracy of standard all-electron basis sets that are believed to be highly accurate for molecules, such as Gaussian-type orbitals (GTOs), all-electron numeric atom-centered orbitals (NAOs) and full-potential augmented plane wave (APW) methods. We show that NAOs are able to achieve the so-called chemical accuracy (1 kcal/mol) for the typical basis set sizes used in applications, for both total and atomization energies. For GTOs, a triple-zeta quality basis has mean errors of ~10kcal/mol in total energies, while chemical accuracy is almost reached for a quintuple-zeta basis. Due to systematic error cancellations, atomization energy errors are reduced by almost an order of magnitude, placing chemical accuracy within reach also for medium to large GTO bases, albeit with significant outliers. In order to check the accuracy of the computed densities, we have also investigated the dipole moments, where in general, only the largest NAO and GTO bases are able to yield errors below 0.01 Debye. The observed errors are similar across the different functionals considered here.

We derive structural and binding energy trends for twenty amino acids, their dipeptides, and their interactions with the divalent cations Ca$^{2+}$, Ba$^{2+}$, Sr$^{2+}$, Cd$^{2+}$, Pb$^{2+}$, and Hg$^{2+}$. The underlying data set consists of 45,892 first-principles predicted conformers with relative energies up to about 4 eV (about 400kJ/mol). We show that only very few distinct backbone structures of isolated amino acids and their dipeptides emerge as lowest-energy conformers. The isolated amino acids predominantly adopt structures that involve an acidic proton shared between the carboxy and amino function. Dipeptides adopt one of two intramolecular-hydrogen bonded conformations C$_5$ or equatorial C$_7$. Upon complexation with a divalent cation, the accessible conformational space shrinks and intramolecular hydrogen bonding is prevented due to strong electrostatic interaction of backbone and side chain functional groups with cations. Clear correlations emerge from the binding energies of the six divalent ions with amino acids and dipeptides. Cd$^{2+}$ and Hg$^{2+}$ show the largest binding energies - a potential correlation with their known high acute toxicities. Ca$^{2+}$ and Pb$^{2+}$ reveal almost identical binding energies across the entire series of amino acids and dipeptides. This observation validates past indications that ion-mimicry of calcium and lead should play an important role in a toxicological context., Comment: submitted, underlying data can be found here: http://aminoaciddb.rz-berlin.mpg.de/

The heptazine-based polymer melon (also known as graphitic carbon nitride, g-C3N4), is a promising photocatalyst for hydrogen evolution. Nonetheless, attempts to improve its inherently low activity are rarely based on rational approaches due to a lack of fundamental understanding of its mechanistic operation. Here, we employ molecular heptazine-based model catalysts to identify the cyanamide moiety as a photocatalytically relevant "defect". We exploit this knowledge for the rational design of a carbon nitride polymer populated with cyanamide groups, yielding a material with 12- and 16-times the hydrogen evolution rate and apparent quantum efficiency (400 nm), respectively, compared to the benchmark melon. Computational modelling and material characterization suggest this moiety improves co-ordination (and, in turn, charge transfer kinetics) to the platinum co-catalyst and enhances the separation of the photo-generated charge carriers. The demonstrated knowledge transfer for rational catalyst design presented here provides the conceptual framework for engineering high performance heptazine-based photocatalysts., Comment: Main article: 15 pages, 5 figures

The identification of low-energy conformers for a given molecule is a fundamental problem in computational chemistry and cheminformatics. We assess here a conformer search that employs a genetic algorithm for sampling the low-energy segment of the conformation space of molecules. The algorithm is designed to work with first-principles methods, facilitated by the incorporation of local optimization and blacklisting conformers to prevent repeated evaluations of very similar solutions. The aim of the search is not only to find the global minimum, but to predict all conformers within an energy window above the global minimum. The performance of the search strategy is: (i) evaluated for a reference data set extracted from a database with amino acid dipeptide conformers obtained by an extensive combined force field and first-principles search and (ii) compared to the performance of a systematic search and a random conformer generator for the example of a drug-like ligand with 43 atoms, 8 rotatable bonds and 1 cis/trans bond.

We present a structural data set of the 20 proteinogenic amino acids and their amino-methylated and acetylated (capped) dipeptides. Different protonation states of the backbone (uncharged and zwitterionic) were considered for the amino acids as well as varied side chain protonation states. Furthermore, we studied amino acids and dipeptides in complex with divalent cations (Ca2+, Ba2+, Sr2+, Cd2+, Pb2+, and Hg2+). The database covers the conformational hierarchies of 280 systems in a wide relative energy range of up to 4 eV (390 kJ/mol), summing up to an overall of 45,892 stationary points on the respective potential-energy surfaces. All systems were calculated on equal first-principles footing, applying density-functional theory in the generalized gradient approximation corrected for long-range van der Waals interactions. We show good agreement to available experimental data for gas-phase ion affinities. Our curated data can be utilized, for example, for a wide comparison across chemical space of the building blocks of life, for the parametrization of protein force fields, and for the calculation of reference spectra for biophysical applications., Comment: The reported data can be accessed in the NOMAD repository via the link http://dx.doi.org/10.17172/NOMAD/20150526220502 or on this website: http://aminoaciddb.rz-berlin.mpg.de

We address the stability of the surface phases that occur on the C-side of 3C-SiC($\bar{1} \bar{1} \bar{1}$) at the onset of graphene formation. In this growth range, experimental reports reveal a coexistence of several surface phases. This coexistence can be explained by a Si-rich model for the unknown (3$\times$3) reconstruction, the known (2$\times$2)$_{C}$ adatom phase, and the graphene covered (2$\times$2)$_{C}$ phase. By constructing an $ab$ $initio$ surface phase diagram using a van der Waals corrected density functional, we show that the formation of a well defined interface structure like the "buffer-layer" on the Si side is blocked by Si-rich surface reconstructions.

We follow the evolution of the Ionization Potential (IP) for the paradigmatic quasi-one-dimensional trans-acetylene family of conjugated molecules, from short to long oligomers and to the infinite polymer trans-poly-acetylene (TPA). Our results for short oligomers are very close to experimental available data. We find that the IP varies with oligomer length and converges to the given value for TPA with a smooth, coupled inverse-length-exponential behavior. Our prediction is based on an "internally-consistent" scheme to adjust the exchange mixing parameter $\alpha$ of the PBEh hybrid density functional, so as to obtain a description of the electronic structure consistent with the quasiparticle approximation for the IP. This is achieved by demanding that the corresponding quasiparticle correction, in the GW@PBEh approximation, vanishes for the IP when evaluated at PBEh($\alpha^{ic}$). We find that $\alpha^{ic}$ is also system-dependent and converges with increasing oligomer length, allowing to capture the dependence of IP and other electronic properties., Comment: 22 pages with 9 figures, submitted to Physical Review B

We integrate the all-electron electronic structure code FHI-aims into the general ChemShell package for solid-state embedding (QM/MM) calculations. A major undertaking in this integration is the implementation of pseudopotential functionality into FHI-aims to describe cations at the QM/MM boundary through effective core potentials and therewith prevent spurious overpolarization of the electronic density. Based on numeric atomic orbital basis sets, FHI-aims offers particularly efficient access to exact exchange and second order perturbation theory, rendering the established QM/MM setup an ideal tool for hybrid and double-hybrid level DFT calculations of solid systems. We illustrate this capability by calculating the reduction potential of Fe in the Fe-substituted ZSM-5 zeolitic framework and the reaction energy profile for (photo-)catalytic water oxidation at TiO2(110)., Comment: 12 pages, 4 figures

First-principles surface phase diagrams reveal that epitaxial monolayer graphene films on the Si side of 3C-SiC(111) can exist as thermodynamically stable phases in a narrow range of experimentally controllable conditions, defining a path to the highest-quality graphene films. Our calculations are based on a van der Waals corrected density functional. The full, experimentally observed (6 sqrt(3)x 6 sqrt(3))-R30 supercells for zero- to trilayer graphene are essential to describe the correct interface geometries and the relative stability of surface phases and possible defects.

Specific interactions between cations and proteins have a strong impact on peptide and protein structure. We here shed light on the nature of the underlying interactions, especially regarding the effects on the polyamide backbone structure. To do so, we compare the conformational ensembles of model peptides in isolation and in the presence of either Li+ or Na+ cations by state-of-the-art density-functional theory (including van der Waals effects) and gas-phase infrared spectroscopy. These monovalent cations have a drastic effect on the local backbone conformation of turn-forming peptides, by disruption of the H bonding networks and the resulting severe distortion of the backbone conformations. In fact, Li+ and Na+ can even have different conformational effects on the same peptide. We also assess the predictive power of current approximate density functionals for peptide-cation systems and compare to results from established protein force fields as well as to high-level quantum chemistry (CCSD(T))., Comment: 30 pages, 7 figures

Helices are a key folding motif in protein structure. The question which factors determine helix stability for a given polypeptide or protein is an ongoing challenge. Here we use van der Waals corrected density-functional theory to address a part of this question in a bottom-up approach. We show how intrinsic helical structure is stabilized with length and temperature for a series of experimentally well studied unsolvated alanine based polypeptides, Ac-Alan-LysH+. By exploring extensively the conformational space of these molecules, we find that helices emerge as the preferred structure in the length range n=4-8 not just due to enthalpic factors (hydrogen bonds and their cooperativity, van der Waals dispersion interactions, electrostatics), but importantly also by a vibrational entropic stabilization over competing conformers at room temperature. The stabilization is shown to be due to softer low-frequency vibrational modes in helical conformers than in more compact ones. This observation is corroborated by including anharmonic effects explicitly through \emph{ab initio} molecular dynamics, and generalized by testing different terminations and considering larger helical peptide models.

Efficient implementations of electronic structure methods are essential for first-principles modeling of molecules and solids. We here present a particularly efficient common framework for methods beyond semilocal density-functional theory, including Hartree-Fock (HF), hybrid density functionals, random-phase approximation (RPA), second-order M{\o}ller-Plesset perturbation theory (MP2), and the $GW$ method. This computational framework allows us to use compact and accurate numeric atom-centered orbitals (popular in many implementations of semilocal density-functional theory) as basis functions. The essence of our framework is to employ the "resolution of identity (RI)" technique to facilitate the treatment of both the two-electron Coulomb repulsion integrals (required in all these approaches) as well as the linear density-response function (required for RPA and $GW$). This is possible because these quantities can be expressed in terms of products of single-particle basis functions, which can in turn be expanded in a set of auxiliary basis functions (ABFs). The construction of ABFs lies at the heart of the RI technique, and here we propose a simple prescription for constructing the ABFs which can be applied regardless of whether the underlying radial functions have a specific analytical shape (e.g., Gaussian) or are numerically tabulated. We demonstrate the accuracy of our RI implementation for Gaussian and NAO basis functions, as well as the convergence behavior of our NAO basis sets for the above-mentioned methods. Benchmark results are presented for the ionization energies of 50 selected atoms and molecules from the G2 ion test set as obtained with $GW$ and MP2 self-energy methods, and the G2-I atomization energies as well as the S22 molecular interaction energies as obtained with the RPA method., Comment: 58 pages, 15 figures, and 7 tables

The low-index surfaces of Au and Pt all tend to reconstruct, a fact that is of key importance in many nanostructure, catalytic, and electrochemical applications. Remarkably, some significant questions regarding their structural energies remain even today, in particular for the large-scale quasihexagonal reconstructed (100) surfaces: Rather dissimilar reconstruction energies for Au and Pt in available experiments, and experiment and theory do not match for Pt. We here show by all-electron density-functional theory that only large enough "(5 x N)" approximant supercells capture the qualitative reconstruction energy trend between Au(100) and Pt(100), in contrast to what is often done in the theoretical literature. Their magnitudes are then in fact similar, and closer to the measured value for Pt(100); our calculations achieve excellent agreement with known geometric characteristics and provide direct evidence for the electronic reconstruction driving force., Comment: updated version - also includes EPAPS information as auxiliary file; related publications can be found at http://www.fhi-berlin.mpg.de/th/th.html

We employ a first-principles lattice-gas Hamiltonian (LGH) approach to determine the lateral interactions between O atoms adsorbed on the Pd(100) surface. With these interactions we obtain an ordering behavior at low coverage that is in quantitative agreement with experimental data. Uncertainties in the approach arise from the finite LGH expansion and from the approximate exchange-correlation (xc) functional underlying the employed density-functional theory energetics. We carefully scrutinize these uncertainties and conclude that they primarily affect the on-site energy, which rationalizes the agreement with the experimental critical temperatures for the order-disorder transition. We also investigate the validity of the frequently applied assumption that the ordering energies can be represented by a sum of pair terms. Restricting our LGH expansion to just pairwise lateral interactions, we find that this results in effective interactions which contain spurious contributions that are of equal size, if not larger than any of the uncertainties e.g. due to the approximate xc functional., Comment: 14 pages including 7 figures; related publications can be found at http://www.fhi-berlin.mpg.de/th/th.html