Benchmarking the accuracy of the separable resolution of the identity approach for correlated methods in the numeric atom-centered orbitals framework

Four-center two-electron Coulomb integrals routinely appear in electronic structure algorithms. The resolution-of-the-identity (RI) is a popular technique to reduce the computational cost for the numerical evaluation of these integrals in localized basis-sets codes. Recently, Duchemin and Blase proposed a separable RI scheme [J. Chem. Phys. 150, 174120 (2019)], which preserves the accuracy of the standard global RI method with the Coulomb metric and permits the formulation of cubic-scaling random phase approximation (RPA) and GW approaches. Here, we present the implementation of a separable RI scheme within an all-electron numeric atom-centered orbital framework. We present comprehensive benchmark results using the Thiel and the GW100 test set. Our benchmarks include atomization energies from Hartree-Fock, second-order Møller-Plesset (MP2), coupled-cluster singles and doubles, RPA, and renormalized second-order perturbation theory, as well as quasiparticle energies from GW. We found that the separable RI approach reproduces RI-free HF calculations within 9 meV and MP2 calculations within 1 meV. We have confirmed that the separable RI error is independent of the system size by including disordered carbon clusters up to 116 atoms in our benchmarks.

Accelerating Core-Level GW Calculations by Combining the Contour Deformation Approach with the Analytic Continuation of W

In recent years, the GW method has emerged as a reliable tool for computing core-level binding energies. The contour deformation (CD) technique has been established as an efficient, scalable, and numerically stable approach to compute the GW self-energy for deep core excitations. However, core-level GW calculations with CD face the challenge of higher scaling with respect to system size N compared to the conventional quartic scaling in valence-state algorithms. In this work, we present the CD-WAC method [CD with W analytic continuation (AC)], which reduces the scaling of CD applied to the inner shells from O(N5) to O(N4) by employing an AC of the screened Coulomb interaction W. Our proposed method retains the numerical accuracy of CD for the computationally challenging deep core case, yielding mean absolute errors <5 meV for well-established benchmark sets, such as CORE65, for single-shot GW calculations. More extensive testing for different GW flavors proves the reliability of the method. We have confirmed the theoretical scaling by performing scaling experiments on large acene chains and amorphous carbon clusters, achieving speedups of up to 10× for structures of only 116 atoms. This improvement in computational efficiency paves the way for more accurate and efficient core-level GW calculations on larger and more complex systems.

Benchmark of GW Methods for Core-Level Binding Energies

The GW approximation has recently gained increasing attention as a viable method for the computation of deep core-level binding energies as measured by X-ray photoelectron spectroscopy. We present a comprehensive benchmark study of different GW methodologies (starting point optimized, partial and full eigenvalue-self-consistent, Hedin shift, and renormalized singles) for molecular inner-shell excitations. We demonstrate that all methods yield a unique solution and apply them to the CORE65 benchmark set and ethyl trifluoroacetate. Three GW schemes clearly outperform the other methods for absolute core-level energies with a mean absolute error of 0.3 eV with respect to experiment. These are partial eigenvalue self-consistency, in which the eigenvalues are only updated in the Green's function, single-shot GW calculations based on an optimized hybrid functional starting point, and a Hedin shift in the Green's function. While all methods reproduce the experimental relative binding energies well, the eigenvalue self-consistent schemes and the Hedin shift yield with mean absolute errors <0.2 eV the best results.

Combining Renormalized Singles GW Methods with the Bethe-Salpeter Equation for Accurate Neutral Excitation Energies

We apply the renormalized singles (RS) Green's function in the Bethe-Salpeter equation (BSE)/GW approach to predict accurate neutral excitation energies of molecular systems. The BSE calculations are performed on top of the G_RSW_RS method, which uses the RS Green's function also for the computation of the screened Coulomb interaction W. We show that the BSE/G_RSW_RS approach significantly outperforms BSE/G₀W₀ for predicting excitation energies of valence, Rydberg, and charge-transfer (CT) excitations by benchmarking the Truhlar-Gagliardi set, Stein CT set, and an atomic Rydberg test set. For the Truhlar-Gagliardi test set, BSE/G_RSW_RS provides comparable accuracy to time-dependent density functional theory (TDDFT) and is slightly better than BSE starting from eigenvalue self-consistent GW (evGW). For the Stein CT test set, BSE/G_RSW_RS significantly outperforms BSE/G₀W₀ and TDDFT with the accuracy comparable to BSE/evGW. We also show that BSE/G_RSW_RS predicts Rydberg excitation energies of atomic systems well. Besides the excellent accuracy, BSE/G_RSW_RS largely eliminates the dependence on the choice of the density functional approximation. This work demonstrates that the BSE/G_RSW_RS approach is accurate and efficient for predicting excitation energies for a broad range of systems, which expands the applicability of the BSE/GW approach.

Accurate Computational Prediction of Core-Electron Binding Energies in Carbon-Based Materials: A Machine-Learning Model Combining Density-Functional Theory and GW

We present a quantitatively accurate machine-learning (ML) model for the computational prediction of core-electron binding energies, from which X-ray photoelectron spectroscopy (XPS) spectra can be readily obtained. Our model combines density functional theory (DFT) with GW and uses kernel ridge regression for the ML predictions. We apply the new approach to disordered materials and small molecules containing carbon, hydrogen, and oxygen and obtain qualitative and quantitative agreement with experiment, resolving spectral features within 0.1 eV of reference experimental spectra. The method only requires the user to provide a structural model for the material under study to obtain an XPS prediction within seconds. Our new tool is freely available online through the XPS Prediction Server.

Highly conducting single-molecule topological insulators based on mono- and di-radical cations

Single-molecule topological insulators are promising candidates as conducting wires over nanometre length scales. A key advantage is their ability to exhibit quasi-metallic transport, in contrast to conjugated molecular wires which typically exhibit a low conductance that decays as the wire length increases. Here, we study a family of oligophenylene-bridged bis(triarylamines) with tunable and stable mono- or di-radicaloid character. These wires can undergo one- and two-electron chemical oxidations to the corresponding mono-cation and di-cation, respectively. We show that the oxidized wires exhibit reversed conductance decay with increasing length, consistent with the expectation for Su-Schrieffer-Heeger-type one-dimensional topological insulators. The 2.6-nm-long di-cation reported here displays a conductance greater than 0.1G₀, where G₀ is the conductance quantum, a factor of 5,400 greater than the neutral form. The observed conductance-length relationship is similar between the mono-cation and di-cation series. Density functional theory calculations elucidate how the frontier orbitals and delocalization of radicals facilitate the observed non-classical quasi-metallic behaviour.

All-Electron BSE@GW Method for K-Edge Core Electron Excitation Energies

We present an accurate computational approach to calculate absolute K-edge core electron excitation energies as measured by X-ray absorption spectroscopy. Our approach employs an all-electron Bethe-Salpeter equation (BSE) formalism based on GW quasiparticle energies (BSE@GW) using numeric atom-centered orbitals (NAOs). The BSE@GW method has become an increasingly popular method for the computation of neutral valence excitation energies of molecules. However, it was so far not applied to molecular K-edge excitation energies. We discuss the influence of different numerical approximations on the BSE@GW calculation and employ in our final setup (i) exact numeric algorithms for the frequency integration of the GW self-energy, (ii) G₀W₀ and BSE starting points with ∼50% of exact exchange, (iii) the Tamm-Dancoff approximation and (iv) relativistic corrections. We study the basis set dependence and convergence with common Gaussian-type orbital and NAO basis sets. We identify the importance of additional spatially confined basis functions as well as of diffuse augmenting basis functions. The accuracy of our BSE@GW method is assessed for a benchmark set of small organic molecules, previously used for benchmarking the equation-of-motion coupled cluster method [Peng et al., J. Chem. Theory Comput., 2015, 11, 4146], as well as the medium-sized dibenzothiophene (DBT) molecule. Our BSE@GW results for absolute excitation energies are in excellent agreement with the experiment, with a mean average error of only 0.63 eV for the benchmark set and with errors <1 eV for the DBT molecule.

CP2K: An electronic structure and molecular dynamics software package - Quickstep: Efficient and accurate electronic structure calculations

CP2K is an open source electronic structure and molecular dynamics software package to perform atomistic simulations of solid-state, liquid, molecular, and biological systems. It is especially aimed at massively parallel and linear-scaling electronic structure methods and state-of-the-art ab initio molecular dynamics simulations. Excellent performance for electronic structure calculations is achieved using novel algorithms implemented for modern high-performance computing systems. This review revisits the main capabilities of CP2K to perform efficient and accurate electronic structure simulations. The emphasis is put on density functional theory and multiple post-Hartree-Fock methods using the Gaussian and plane wave approach and its augmented all-electron extension.

Accurate Absolute and Relative Core-Level Binding Energies from GW

We present an accurate approach to compute X-ray photoelectron spectra based on the GW Green's function method that overcomes the shortcomings of common density functional theory approaches. GW has become a popular tool to compute valence excitations for a wide range of materials. However, core-level spectroscopy is thus far almost uncharted in GW. We show that single-shot perturbation calculations in the G0W0 approximation, which are routinely used for valence states, cannot be applied for core levels and suffer from an extreme, erroneous transfer of spectral weight to the satellite spectrum. The correct behavior can be restored by partial self-consistent GW schemes or by using hybrid functionals with almost 50% of exact exchange as a starting point for G0W0. We also include relativistic corrections and present a benchmark study for 65 molecular 1s excitations. Our absolute and relative GW core-level binding energies agree within 0.3 and 0.2 eV with experiment, respectively.

Atomic structures and orbital energies of 61,489 crystal-forming organic molecules

Data science and machine learning in materials science require large datasets of technologically relevant molecules or materials. Currently, publicly available molecular datasets with realistic molecular geometries and spectral properties are rare. We here supply a diverse benchmark spectroscopy dataset of 61,489 molecules extracted from organic crystals in the Cambridge Structural Database (CSD), denoted OE62. Molecular equilibrium geometries are reported at the Perdew-Burke-Ernzerhof (PBE) level of density functional theory (DFT) including van der Waals corrections for all 62 k molecules. For these geometries, OE62 supplies total energies and orbital eigenvalues at the PBE and the PBE hybrid (PBE0) functional level of DFT for all 62 k molecules in vacuum as well as at the PBE0 level for a subset of 30,876 molecules in (implicit) water. For 5,239 molecules in vacuum, the dataset provides quasiparticle energies computed with many-body perturbation theory in the G0W0 approximation with a PBE0 starting point (denoted GW5000 in analogy to the GW100 benchmark set (M. van Setten et al. J. Chem. Theory Comput. 12, 5076 (2016))).

From flat to tilted: gradual interfaces in organic thin film growth

We investigate domain formation and local morphology of thin films of α-sexithiophene (α-6T) on Au(100) beyond monolayer coverage by combining high resolution scanning tunneling microscopy (STM) experiments with electronic structure theory calculations and computational structure search. We report a layerwise growth of highly-ordered enantiopure domains. For the second and third layer, we show that the molecular orbitals of individual α-6T molecules can be well resolved by STM, providing access to detailed information on the molecular orientation. We find that already in the second layer the molecules abandon the flat adsorption structure of the monolayer and adopt a tilted conformation. Although the observed tilted arrangement resembles the orientation of α-6T in the bulk, the observed morphology does not yet correspond to a well-defined surface of the α-6T bulk structure. A similar behavior is found for the third layer indicating a growth mechanism where the bulk structure is gradually adopted over several layers.

The GW Compendium: A Practical Guide to Theoretical Photoemission Spectroscopy

The GW approximation in electronic structure theory has become a widespread tool for predicting electronic excitations in chemical compounds and materials. In the realm of theoretical spectroscopy, the GW method provides access to charged excitations as measured in direct or inverse photoemission spectroscopy. The number of GW calculations in the past two decades has exploded with increased computing power and modern codes. The success of GW can be attributed to many factors: favorable scaling with respect to system size, a formal interpretation for charged excitation energies, the importance of dynamical screening in real systems, and its practical combination with other theories. In this review, we provide an overview of these formal and practical considerations. We expand, in detail, on the choices presented to the scientist performing GW calculations for the first time. We also give an introduction to the many-body theory behind GW, a review of modern applications like molecules and surfaces, and a perspective on methods which go beyond conventional GW calculations. This review addresses chemists, physicists and material scientists with an interest in theoretical spectroscopy. It is intended for newcomers to GW calculations but can also serve as an alternative perspective for experts and an up-to-date source of computational techniques.

Silver-Stabilized Guanine Duplex: Structural and Optical Properties

Recent experimental duplexes of DNA stabilized by Ag cations, pairing homostrands of guanine-guanine, cytosine-cytosine, adenine-thymine, and thymine-thymine, display much higher stability than the Watson-Crick paired DNA duplexes; these broaden the range of applications for DNA nanotechnology. Here we focus on silver-stabilized guanine duplexes in water. Using hybrid quantum mechanics/molecular mechanics simulations, we propose an atomic structure for the Ag⁺-mediated guanine duplex with two nucleobases per strand, G₂-Ag₂⁺-G₂. We then compare experimental and time-dependent density functional theory-simulated electronic circular dichroism (ECD) spectra to validate our results. Both experimental and simulated ECD share two negative peaks around 220 and 280 nm, with no positive signal in the measured wavelength range. We found that the left- or right-handed disposition of bases in the structure has a decisive effect on the signs of the ECD. We conclude that G₂-Ag₂⁺-G₂ is left-hand-oriented, and extrapolation of this orientation to longer strands gives rise to a left-hand-oriented parallel helix stabilized by interplanar H bonds.

Toward GW Calculations on Thousands of Atoms

The GW approximation of many-body perturbation theory is an accurate method for computing electron addition and removal energies of molecules and solids. In a canonical implementation, however, its computational cost is [Formula: see text] in the system size N, which prohibits its application to many systems of interest. We present a full-frequency GW algorithm in a Gaussian-type basis, whose computational cost scales with N² to N³. The implementation is optimized for massively parallel execution on state-of-the-art supercomputers and is suitable for nanostructures and molecules in the gas, liquid or condensed phase, using either pseudopotentials or all electrons. We validate the accuracy of the algorithm on the GW100 molecular test set, finding mean absolute deviations of 35 meV for ionization potentials and 27 meV for electron affinities. Furthermore, we study the length-dependence of quasiparticle energies in armchair graphene nanoribbons of up to 1734 atoms in size, and compute the local density of states across a nanoscale heterojunction.

Wetting of water on hexagonal boron nitride@Rh(111): a QM/MM model based on atomic charges derived for nano-structured substrates

The wetting of water on corrugated and flat hexagonal boron nitride (h-BN) monolayers on Rh(111) is studied within a hybrid quantum mechanics/molecular mechanics (QM/MM) approach. Water is treated by QM methods, whereas the interactions between liquid and substrate are described at the MM level. The electrostatic properties of the substrate are reproduced by assigning specifically generated partial charges to each MM atom. We propose a method to determine restrained electrostatic potential (RESP) charges that can be applied to periodic systems. Our approach is based on the Gaussian and plane waves algorithm and allows an easy tuning of charges for nano-structured substrates. We have successfully applied it to reproduce the electrostatic potential of the corrugated and flat h-BN/Rh(111) known as nanomesh. Molecular dynamics simulations of water films in contact with these substrates are performed and structural and dynamic properties of the interfaces are analyzed. Based on this analysis and on the interaction energies between water film and substrate, we found that the corrugated nanomesh is slightly more hydrophilic. On a macroscopic scale, we expect a smaller contact angle for a droplet on the corrugated surface.

Importance of dispersion forces for prediction of thermodynamic and transport properties of some common ionic liquids

An extensive study of interaction energies in ion pairs of pyrrolidinium and imidazolium ionic liquids is presented. The Cnmpyr and Cnmim cations with varying alkyl chains from Methyl, Ethyl, n-Propyl to n-Butyl were combined with a wide range of routinely used IL anions such as chloride, bromide, mesylate (CH3SO3 or Mes), tosylate (CH3PhSO3 or Tos), bis(trifluoromethanesulfonyl)amide (NTf2), dicyanamide (N(CN)2 or dca), tetrafluoroborate (BF4) and hexafluorophosphate (PF6). A number of energetically favourable conformations were studied for each cation-anion combination. The interaction energy and its dispersion component of the single ion pairs were calculated using a sophisticated state-of-the-art approach: a second-order of Symmetry Adapted Perturbation Theory (SAPT). A comparison of energetics depending on the cation-anion type, as well as the mode of interaction was performed. Dispersion forces were confirmed to be of importance for the overall stabilisation of ionic liquids contributing from 28 kJ mol(-1) in pyrrolidinium ion pairs to 59 kJ mol(-1) in imidazolium ion pairs. The previously proposed ratio of total interaction energy to dispersion components and melting points was assessed for this set of ionic liquids and was found to correlate with their melting points for the anionic series, producing separate trends for the Cnmim and Cmpyr series of cations. Chlorides, bromides and tetrafluoroborates formed close-to-ideal correlations when both types of cations, Cnmim and Cnmpyr, were combined in the same trend. Correlation of the dispersion component of the interaction energy with transport properties such as conductivity and viscosity was also considered. For imidazolium-based ionic liquids strong linear correlations were obtained, whereas pyrrolidinium ionic liquids appeared to be insensitive to this correlation.