Kohn-Sham Eigenvalues Research Articles

Chemical space-informed machine learning models for rapid predictions of x-ray photoelectron spectra of organic molecules

Abstract We present machine learning models based on kernel-ridge regression for predicting X-ray photoelectron spec- tra of organic molecules originating from the ionization energies of 1s electrons in carbon (C), nitrogen (N), oxygen (O), and fluorine (F) atoms. We constructed training dataset through high-throughput calculations of core-electron binding energies (CEBEs) for 12,880 small organic molecules in the bigQM7ω dataset, employing the ∆-SCF formalism coupled with meta-GGA-DFT and a variationally converged basis set. The models are cost-effective, as they require the atomic coordinates of a molecule generated using universal force fields while estimating the target-level CEBEs corresponding to DFT-level equilibrium geometry. We explore transfer learning by utilizing the atomic environment feature vectors learned using a graph neural network framework in kernel-ridge regression. Additionally, we enhance accuracy using the ∆-machine learning framework by leveraging inexpensive baseline spectra derived from Kohn–Sham eigenvalues. Upon application to 208 com- binatorially substituted uracil molecules, larger than those in the training set, our analyses reveal that while the models may not yield quantitatively accurate predictions of CEBEs on a molecule-by-molecule basis, they do exhibit a strong linear correlation, which proves valuable for virtual high-throughput screening purposes. We present the dataset and models as the Python module, cebeconf, to facilitate further explorations.

Many-Body Calculations of Excitons in Two-Dimensional GaN

We present an ab initio study on quasiparticle (QP) excitations and excitonic effects in two-dimensional (2D) GaN based on density-functional theory and many-body perturbation theory. We calculate the QP band structure using GW approximation, which generates an indirect band gap of 4.83 eV (K→Γ) for 2D GaN, opening up 1.24 eV with respect to its bulk counterpart. It is shown that the success of plasmon-pole approximation in treating the 2D material benefits considerably from error cancellation. On the other hand, much better gaps, comparable to GW ones, could be obtained by correcting the Kohn–Sham gap with a derivative discontinuity of the exchange–correlation functional at much lower computational cost. To evaluate excitonic effects, we solve the Bethe–Salpeter equation (BSE) starting from Kohn–Sham eigenvalues with a scissors operator to open the single-particle gap. This approach yields an exciton binding energy of 1.23 eV in 2D GaN, which is in good agreement with the highly demanding GW-BSE results. The enhanced excitonic effects due to reduced dimensionality are discussed by comparing the optical spectra from BSE calculations with that by random-phase approximation (RPA) for both the monolayer and bulk GaN in wurtzite phase. Additionally, we find that the spin–orbit splitting of excitonic peaks is noticeable in 2D GaN but buried in the bulk crystal.

Slater transition methods for core-level electron binding energies.

Methods for computing core-level ionization energies using self-consistent field (SCF) calculations are evaluated and benchmarked. These include a "full core hole" (or "ΔSCF") approach that fully accounts for orbital relaxation upon ionization, but also methods based on Slater's transition concept in which the binding energy is estimated from an orbital energy level that is obtained from a fractional-occupancy SCF calculation. A generalization that uses two different fractional-occupancy SCF calculations is also considered. The best of the Slater-type methods afford mean errors of 0.3-0.4eV with respect to experiment for a dataset of K-shell ionization energies, a level of accuracy that is competitive with more expensive many-body techniques. An empirical shifting procedure with one adjustable parameter reduces the average error below 0.2eV. This shifted Slater transition method is a simple and practical way to compute core-level binding energies using only initial-state Kohn-Sham eigenvalues. It requires no more computational effort than ΔSCF and may be especially useful for simulating transient x-ray experiments where core-level spectroscopy is used to probe an excited electronic state, for which the ΔSCF approach requires a tedious state-by-state calculation of the spectrum. As an example, we use Slater-type methods to model x-ray emission spectroscopy.

DFT-FE 1.0: A massively parallel hybrid CPU-GPU density functional theory code using finite-element discretization

We present DFT-FE 1.0, building on DFT-FE 0.6 Motamarri et al. (2020) [28], to conduct fast and accurate large-scale density functional theory (DFT) calculations (reaching ∼100,000 electrons) on both many-core CPU and hybrid CPU-GPU computing architectures. This work involves improvements in the real-space formulation—via an improved treatment of the electrostatic interactions that substantially enhances the computational efficiency—as well high-performance computing aspects, including the GPU acceleration of all the key compute kernels in DFT-FE. We demonstrate the accuracy by comparing the ground-state energies, ionic forces and cell stresses on a wide-range of benchmark systems against those obtained from widely used DFT codes. Further, we demonstrate the numerical efficiency of our GPU acceleration, which yields ∼20× speed-up on hybrid CPU-GPU nodes of the Summit supercomputer. Notably, owing to the parallel-scaling of the GPU implementation, we obtain wall-times of 80−140 seconds for full ground-state calculations, with stringent accuracy, on benchmark systems containing ∼6,000−15,000 electrons using 64−224 nodes of the Summit supercomputer. Program summaryProgram Title: DFT-FECPC Library link to program files:https://doi.org/10.17632/c5ghfc6ctn.1Developer's repository link:https://github.com/dftfeDevelopers/dftfeLicensing provisions: LGPL v3Programming language: C/C++External routines/libraries: p4est (http://www.p4est.org/), deal.II (https://www.dealii.org/), BLAS (http://www.netlib.org/blas/), LAPACK (http://www.netlib.org/lapack/), ELPA (https://elpa.mpcdf.mpg.de/), ScaLAPACK (http://www.netlib.org/scalapack/), Spglib (https://atztogo.github.io/spglib/), ALGLIB (http://www.alglib.net/), LIBXC (http://www.tddft.org/programs/libxc/), PETSc (https://www.mcs.anl.gov/petsc), SLEPc (http://slepc.upv.es), NCCL (optional-https://github.com/NVIDIA/nccl).Nature of problem: Density functional theory calculations.Solution method: We employ a local real-space variational formulation of Kohn-Sham density functional theory that is applicable for both pseudopotential and all-electron calculations on periodic, semi-periodic and non-periodic geometries. Higher-order adaptive spectral finite-element basis is used to discretize the Kohn-Sham equations. Chebyshev polynomial filtered subspace iteration procedure (ChFSI) is employed to solve the nonlinear Kohn-Sham eigenvalue problem self-consistently. ChFSI in DFT-FE employs Cholesky factorization based orthonormalization, and spectrum splitting based Rayleigh-Ritz procedure in conjunction with mixed precision arithmetic. Configurational force approach is used to compute ionic forces and periodic cell stresses for geometry optimization.Additional comments including restrictions and unusual features: Exchange correlation functionals are restricted to Local Density Approximation (LDA) and Generalized Gradient Approximation (GGA), with and without spin. The pseudopotentials available are optimized norm conserving Vanderbilt (ONCV) pseudopotentials and Troullier–Martins (TM) pseudopotentials. Calculations are non-relativistic.DFT-FE handles all-electron and pseudopotential calculations in the same framework, while accommodating periodic, non-periodic and semi-periodic boundary conditions.

Self-interaction-corrected Kohn-Sham effective potentials using the density-consistent effective potential method.

Density functional theory (DFT) and beyond-DFT methods are often used in combination with photoelectron spectroscopy to obtain physical insights into the electronic structure of molecules and solids. The Kohn-Sham eigenvalues are not electron removal energies except for the highest occupied orbital. The eigenvalues of the highest occupied molecular orbitals often underestimate the electron removal or ionization energies due to the self-interaction (SI) errors in approximate density functionals. In this work, we adapt and implement the density-consistent effective potential method of Kohut, Ryabinkin, and Staroverov [J. Chem. Phys. 140, 18A535 (2014)] to obtain SI-corrected local effective potentials from the SI-corrected Fermi-Löwdin orbitals and density in the Fermi-Löwdin orbital self-interaction correction scheme. The implementation is used to obtain the density of states (photoelectron spectra) and HOMO-LUMO gaps for a set of molecules and polyacenes. Good agreement with experimental values is obtained compared to a range of SI uncorrected density functional approximations.

Charge-Transfer Steps in Density Functional Theory from the Perspective of the Exact Electron Factorization.

When a molecule dissociates, the exact Kohn-Sham (KS) and Pauli potentials may form step structures. Reproducing these steps correctly is central for the description of dissociation and charge-transfer processes in density functional theory (DFT): The steps align the KS eigenvalues of the dissociating subsystems relative to each other and determine where electrons localize. While the step height can be calculated from the asymptotic behavior of the KS orbitals, this provides limited insight into what causes the steps. We give an explanation of the steps with an exact mapping of the many-electron problem to a one-electron problem, the exact electron factorization (EEF). The potentials appearing in the EEF have a clear physical meaning that translates to the DFT potentials by replacing the interacting many-electron system with the KS system. With a simple model of a diatomic, we illustrate that the steps are a consequence of spatial electron entanglement and are the result of a charge transfer. From this mechanism, the step height can immediately be deduced. Moreover, two methods to approximately reproduce the potentials during dissociation are proposed. One is based on the states of the dissociated system, while the other one is based on an analogy to the Born-Oppenheimer treatment of a molecule. The latter method also shows that the steps connect adiabatic potential energy surfaces. The view of DFT from the EEF thus provides a better understanding of how many-electron effects are encoded in a one-electron theory and how they can be modeled.

Investigating charge carrier scattering processes in anisotropic semiconductors through first-principles calculations: the case of p-type SnSe.

Efficient ab initio computational methods for the calculation of the thermoelectric transport properties of materials are of great interest for energy harvesting technologies. The constant relaxation time approximation (CRTA) has been largely used to efficiently calculate thermoelectric coefficients. However, CRTA usually does not hold for real materials. Here we go beyond the CRTA by incorporating realistic k-dependent relaxation time models of the temperature dependence of the main scattering processes, namely, screened polar and nonpolar scattering by optical phonons, scattering by acoustic phonons, and scattering by ionized impurities with screening. Our relaxation time models are based on a smooth Fourier interpolation of Kohn-Sham eigenvalues and its derivatives, taking into account non-parabolicity (beyond the parabolic or Kane models), degeneracy and multiplicity of the energy bands on the same footing, within very low computational cost. In order to test our methodology, we calculated the anisotropic thermoelectric transport properties of the low temperature phase (Pnma) of intrinsic p-type and hole-doped tin selenide (SnSe). Our results are in quantitative agreement with experimental data, regarding the evolution of the anisotropic thermoelectric coefficients with both temperature and chemical potential. Hence, from this picture, we also obtained the evolution and understanding of the main scattering processes of the overall thermoelectric transport in p-type SnSe.

Graphene–Iron(II) Phthalocyanine Hybrid Systems for Scalable Molecular Spintronics

Graphene - transition metal phthalocyanine (G-MPc) hybrid systems constitute promising platforms for densely-packed single-molecule magnets (SMMs). Here, we selected iron(II) phthalocyanine (FePc) and investigated its interaction with pristine and defective graphene layers employing density functional theory. Our calculations indicate that thorough proper dehydrogenation of the benzol rings in the FePc molecule its adsorption to graphene is thermodynamically favorable. In general, the presence of anchoring sites on the graphene layer, i.e. point defects, additionally facilitates the adsorption of FePc, allowing one to achieve high density of SMMs per unit area. Using the combination of group theory, ligand field splitting, and the calculated PBE0 Kohn-Sham eigenvalue spectrum, we resolved the electronic structure and predicted the spin states of both, the isolated FePc and G-FePc hybrid systems. Regardless of adsorption site and the number of removed hydrogen atoms from the benzol rings of FePc, the magnetic moment of the SMM remains unchanged with respect to free FePc. These results should mediate a successful synthesis of densely-packed G-MPc systems and may open up new avenue in designing scalable graphene - SMMs systems for spintronics applications.

Combined optical reflectivity measurement and ab initio simulation of expanded gold fluid across the metal–nonmetal transition regime

The metal–nonmetal transition is of fundamental interest in contemporary physics. We present a combination of the optical reflectivity measurement of an expanded gold fluid produced by gold L-band x-rays from a Hohlraum and the corresponding ab initio calculations to study the metal–nonmetal transition. The averaged density and temperature of the reflective layer are derived from 1D radiation hydrodynamic simulations constrained by matching the expansion velocity obtained from the fringe shift. A sharp change in time-resolved reflectivity occurs at one third of the initial density, near where the metal–nonmetal transition is predicted to occur. The reflectivity calculated based on the Helmholtz equations with the dielectric function from the density functional theory calculations is compared with the experimental measurement. Disagreement of reflectivity between calculation and measurement probably originates from the energy shift of the dielectric function due to the inaccurate Kohn–Sham eigenvalue. More accurate methods on calculating the dielectric function are still needed to improve the calculated reflectivity.

DFT-FE – A massively parallel adaptive finite-element code for large-scale density functional theory calculations

We present an accurate, efficient and massively parallel finite-element code, DFT-FE, for large-scale ab-initio calculations (reaching ∼100,000 electrons) using Kohn–Sham density functional theory (DFT). DFT-FE is based on a local real-space variational formulation of the Kohn–Sham DFT energy functional that is discretized using a higher-order adaptive spectral finite-element (FE) basis, and treats pseudopotential and all-electron calculations in the same framework, while accommodating non-periodic, semi-periodic and periodic boundary conditions. We discuss the main aspects of the code, which include, the various strategies of adaptive FE basis generation, and the different approaches employed in the numerical implementation of the solution of the discrete Kohn–Sham problem that are focused on significantly reducing the floating point operations, communication costs and latency. We demonstrate the accuracy of DFT-FE by comparing the energies, ionic forces and periodic cell stresses on a wide range of problems with popularly used DFT codes. Further, we demonstrate that DFT-FE significantly outperforms widely used plane-wave codes—both in CPU-times and wall-times, and on both non-periodic and periodic systems—at systems sizes beyond a few thousand electrons, with over 5−10 fold speedups in systems with more than 10,000 electrons. The benchmark studies also highlight the excellent parallel scalability of DFT-FE, with strong scaling demonstrated up to 192,000 MPI tasks. Program summaryProgram Title: DFT-FEProgram Files doi:http://dx.doi.org/10.17632/tgdmgvmfft.1Licensing provisions: LGPL v3Programming language: C/C++External routines/libraries: p4est (http://www.p4est.org/), deal.II (https://www.dealii.org/), BLAS (http://www.netlib.org/blas/), LAPACK (http://www.netlib.org/lapack/), ELPA (https://elpa.mpcdf.mpg.de/), ScaLAPACK (http://www.netlib.org/scalapack/), Spglib (https://atztogo.github.io/spglib/), ALGLIB (http://www.alglib.net/), LIBXC (http://www.tddft.org/programs/libxc/), PETSc (https://www.mcs.anl.gov/petsc), SLEPc (http://slepc.upv.es).Nature of problem: Density functional theory calculations.Solution method: We employ a local real-space variational formulation of Kohn–Sham density functional theory that is applicable for both pseudopotential and all-electron calculations with arbitrary boundary conditions. Higher-order adaptive spectral finite-element basis is used to discretize the Kohn–Sham equations. Chebyshev polynomial filtered subspace iteration procedure (ChFSI) is employed to solve the nonlinear Kohn–Sham eigenvalue problem self-consistently. ChFSI in DFT-FE employs Cholesky factorization based orthonormalization, and spectrum splitting based Rayleigh–Ritz procedure in conjunction with mixed precision arithmetic. Configurational force approach is used to compute ionic forces and periodic cell stresses for geometry optimization.Restrictions: Exchange–correlation functionals are restricted to Local Density Approximation (LDA) and Generalized Gradient Approximation (GGA), with and without spin. The pseudopotentials available are optimized norm conserving Vanderbilt (ONCV) pseudopotentials and Troullier–Martins (TM) pseudopotentials. Calculations are non-relativistic.Unusual features: DFT-FE handles all-electron and pseudopotential calculations in the same framework, while accommodating periodic, non-periodic and semi-periodic boundary conditions.Additional comments: DFT-FE github https://github.com/dftfeDevelopers/dftfe

Insights into Direct Methods for Predictions of Ionization Potential and Electron Affinity in Density Functional Theory.

Vertical ionization potential (IP) and electron affinity (EA) are fundamental molecular properties, while the Δ method and the direct method are the widely used approaches to compute these properties. The Δ method is calculated by taking the total energy difference of the initial and final states, whose reliability is seriously affected by the issue associated with the imbalanced treatment of these two states. The direct method based on the derivatives involving only one single-state calculation can yield a quasi-particle spectrum whose accuracy, on the other hand, is mostly affected by the levels of approximate molecular structure theories. Because of the aforementioned issues, EA prediction can be particularly problematic. Here we present, for the first time, an analytic theory on the derivation and realization of generalized Kohn-Sham (KS) eigenvalues of doubly hybrid (DH) functionals that depend on both occupied and unoccupied orbitals. The method based on the KS eigenvalues of neutral systems, termed the NKS method, is found to suffer little from the imbalance issue, while it is only the NKS method that can offer accurate EA prediction from a good functional approximation, such as the XYG3 type of DH functionals. Being less sensitive to the size of basis sets, the NKS method is of great significance for its application to large systems. The insights gained in this work are useful for the calculation of properties associated with small energy differences while emphasizing the importance of the development of generalized functionals that rely on both occupied and unoccupied orbitals.

Generalized Gradient Approximation Exchange Energy Functional with Near-Best Semilocal Performance.

We develop and validate a nonempirical generalized gradient approximation (GGA) exchange (X) density functional that performs as well as the SCAN (strongly constrained and appropriately normed) meta-GGA on standard thermochemistry tests. Additionally, the new functional (NCAP, nearly correct asymptotic potential) yields Kohn-Sham eigenvalues that are useful approximations of the density functional theory (DFT) ionization potential theorem values by inclusion of a systematic derivative discontinuity shift of the X potential. NCAP also enables time-dependent DFT (TD-DFT) calculations of good-quality polarizabilities, hyper-polarizabilities, and one-Fermion excited states without modification (calculated or ad hoc) of the long-range behavior of the exchange potential or other patches. NCAP is constructed by reconsidering the imposition of the asymptotic correctness of the X potential (-1/ r) as a constraint. Inclusion of derivative discontinuity and approximate integer self-interaction correction treatments along with first-principles determination of the effective second-order gradient expansion coefficient yields a major advance over our earlier correct asymptotic potential functional [CAP; J. Chem. Phys. 2015 , 142 , 054105 ]. The new functional reduces a spurious bump in the CAP atomic exchange potential and moves it to distances irrelevantly far from the nucleus (outside the tail of essentially all practical basis functions). It therefore has nearly correct atomic exchange-potential behavior out to rather large finite distances r from the nucleus but eventually goes as - c/ r with an estimated value for the constant c of around 0.3, so as to achieve other important properties of exact DFT exchange within the restrictions of the GGA form. We illustrate the results with the Ne atom optimized effective potentials and with standard molecular benchmark test data sets for thermochemical, structural, and response properties.

Thermoelectric properties of cuprous oxide by first-principles method

Electronic and thermoelectric properties of cubic cuprous oxide are investigated from the LAPW method. The calculations are performed taking the generalized gradient approximation together with Hubbard U scheme at the level of density functional theory. After settling the crystal structure, partial and total density of states are calculated. The Kohn-Sham eigenvalues spectra from the first-principles calculations are interfaced with the Boltzmann transport equations to find transport coefficients. This is achieved by coupling the E-k spectrum from LAPW method with the BoltzTraP. A number of transport coefficients namely, the Seebeck coefficient, power factor, electrical conductivity are reported utilizing GGA and the GGA+U approaches. The effect of temperature and doping on these transport coefficients is discussed. Our results are in better agreement with experimental results than the other theoretical calculations. The results eloquently demonstrate that the LAPW method embodied in the ElK can be deployed in conjunction with the BoltzTraP to investigate thermoelectric properties of other transition metal compounds.

Accurate computation of X-ray absorption spectra with ionization potential optimized global hybrid functional.

This manuscript presents the first consistent ionization potential (IP) optimized global hybrid functional to accurately estimate the vertical ionization and excitation energies of the inner-shell electrons in molecules. The new method fulfills the IP theorem that the Kohn-Sham eigenvalues of all the occupied orbitals (including the core orbitals) are good approximations to the exact vertical ionization energies. The accuracy of the one-particle spectrum is essential to enabling the one-particle density functional theory (DFT) to provide accurate results. Compared to its precursor, the range-separated hybrid functional CAM-QTP00, the new method is more computationally efficient. The IP theorem enables the new method to provide inner-shell ionization energies measured by X-ray photoelectron spectroscopy, and it can further accurately simulate the X-ray absorption spectrum (XAS, or NEXAFS). The simulated spectra can be compared to the experiment directly without shifting. In addition, the new method reduces the delocalization error (many-electron self-interaction error) which is a severe problem in DFT.

Linear response time-dependent density functional theory without unoccupied states: The Kohn-Sham-Sternheimer scheme revisited.

The Sternheimer approach to time-dependent density functional theory in the linear response regime is attractive because of its computational efficiency. The latter results from avoiding the explicit calculation of unoccupied orbitals and from the basic structure of the Sternheimer equations, which naturally lend themselves to far-reaching parallelization. In this article, we take a fresh look at the frequency-dependent Sternheimer equations. We first give a complete, self-contained derivation of the equations that complements previous derivations. We then discuss several aspects of an efficient numerical realization. As a worked example, we compute the photoabsorption spectra of small hydrogenated silicon clusters and confirm that for these the quality of the Kohn-Sham eigenvalues is more important than the effects of the exchange-correlation kernel. Finally, we demonstrate how triplet excitations can readily be computed from the Sternheimer approach.

Assessment of local density approximation based exchange–correlation functional for a two-dimensional spin polarized dipolar Fermi gas

In this paper we assess the accuracy of the local density approximation (LDA) based expressions for exchange and correlation functionals associated with a two-dimensional, spin-polarized, dipolar Fermi gas. For this purpose we consider and study an exactly solvable system of two interacting spin-polarized dipolar fermions confined in a two-dimensional harmonic oscillator potential. We determine the exact triplet ground state wavefunction, energy and the density by separating the time-independent Schrodinger equation in center-of-mass and relative coordinates and numerically solving the eigenvalue equation in relative coordinate. The exact Kohn–Sham orbitals, corresponding energies and exact Kohn–Sham potential are obtained from the exact density by inverting the Kohn–Sham equation. These results serve as benchmark data for assessing the accuracies of the LDA based expressions for a two-dimensional, spin-polarized, dipolar Fermi gas. We find that LDA results for total energy, interaction energy, and Kohn–Sham eigenvalues match well with the exact results for smaller values of dipole–dipole interaction strength. For higher values of interaction strength, LDA results for the total energy are underestimated. On the other hand, the LDA based interaction potentials overestimate the repulsion between the dipoles and their spatial profiles differ considerably from their exact counterparts and the discrepancy between them is higher for stronger interaction.

Density functional theory study on ruthenium dyes and dye@TiO2 assemblies for dye sensitized solar cell applications

Cyclometalated ruthenium dyes improve significantly the performance of dye sensitized solar cells (DSSCs) based on conventional ruthenium dyes. Here, this study examined four thiocyanate-free cyclometalated ruthenium dyes using the density functional theory (DFT). The geometrical, electronic structural, and photophysical propertiesof the dyes and the dyes tethered to a TiO2 surface were examined in both the presence and absence of an acetonitrile solvent. The Kohn-Sham eigenvalues of the molecular orbitals of the dyes were destabilized by ca. 2 eV in the presence of the solvent. The absorption peaks did not change significantly in position but hyperchromic shifts of more than two-fold occurred. When adsorbed on a TiO2 surface, the dyes showed redshifted absorption of approximately 20 nm. To the best of our knowledge, a systematic and comprehensive first-principles investigation on cyclometalated ruthenium dyes in vacuum, solvent, and tethered to TiO2 has been carried out for the first time.

ELSI: A unified software interface for Kohn–Sham electronic structure solvers

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. Program summaryProgram title: ELSI InterfaceProgram Files doi:http://dx.doi.org/10.17632/y8vzhzdm62.1Licensing provisions: BSD 3-clauseProgramming language: Fortran 2003, with interface to C/C++External routines/libraries: MPI, BLAS, LAPACK, ScaLAPACK, ELPA, libOMM, PEXSI, ParMETIS, SuperLU_DISTNature of problem: Solving the electronic structure from a generalized or standard eigenvalue problem in calculations based on Kohn–Sham density functional theory (KS-DFT).Solution method: To connect the KS-DFT codes and the KS electronic structure solvers, ELSI provides a unified software interface with reasonable default parameters, hierarchical control over the interface and the solvers, and automatic conversions between input and internal working matrix formats. Supported solvers are: ELPA (dense generalized eigensolver), libOMM (orbital minimization method), and PEXSI (pole expansion and selected inversion method).Restrictions: The ELSI interface requires complete information of the Hamiltonian matrix.

Accurate Valence Ionization Energies from Kohn-Sham Eigenvalues with the Help of Potential Adjustors.

An accurate yet computationally very efficient and formally well justified approach to calculate molecular ionization potentials is presented and tested. The first as well as higher ionization potentials are obtained as the negatives of the Kohn-Sham eigenvalues of the neutral molecule after adjusting the eigenvalues by a recently [ Görling Phys. Rev. B 2015 , 91 , 245120 ] introduced potential adjustor for exchange-correlation potentials. Technically the method is very simple. Besides a Kohn-Sham calculation of the neutral molecule, only a second Kohn-Sham calculation of the cation is required. The eigenvalue spectrum of the neutral molecule is shifted such that the negative of the eigenvalue of the highest occupied molecular orbital equals the energy difference of the total electronic energies of the cation minus the neutral molecule. For the first ionization potential this simply amounts to a ΔSCF calculation. Then, the higher ionization potentials are obtained as the negatives of the correspondingly shifted Kohn-Sham eigenvalues. Importantly, this shift of the Kohn-Sham eigenvalue spectrum is not just ad hoc. In fact, it is formally necessary for the physically correct energetic adjustment of the eigenvalue spectrum as it results from ensemble density-functional theory. An analogous approach for electron affinities is equally well obtained and justified. To illustrate the practical benefits of the approach, we calculate the valence ionization energies of test sets of small- and medium-sized molecules and photoelectron spectra of medium-sized electron acceptor molecules using a typical semilocal (PBE) and two typical global hybrid functionals (B3LYP and PBE0). The potential adjusted B3LYP and PBE0 eigenvalues yield valence ionization potentials that are in very good agreement with experimental values, reaching an accuracy that is as good as the best G0W0 methods, however, at much lower computational costs. The potential adjusted PBE eigenvalues result in somewhat less accurate ionization energies, which, however, are almost as accurate as those obtained from the most commonly used G0W0 variants.

General procedure for the calculation of accurate defect excitation energies from DFT-1/2 band structures: The case of the NV− center in diamond

A major challenge in creating a quantum computer is to find a quantum system that can be used to implement the qubits. For this purpose, deep centers are prominent candidates, and ab initio calculations are one of the most important tools to theoretically study their properties. However, these calculations are highly involved, due to the large supercell needed, and the computational cost can be even larger when one goes beyond the Kohn-Sham scheme to correct the band gap problem and achieve good accuracy. In this work, we present a method that overcomes these problems and provides the optical transition energies as a difference of Kohn-Sham eigenvalues; and even more, provides a complete and accurate band structure of the defect in the semiconductor. Despite the original motivations, the presented methodology is a general procedure, which can be used to systematically study the optical transitions between localized levels within the band gap of any system. The method is an extension of the low-cost and parameter-free DFT-1/2 approximate quasi-particle correction, and allows it to be applied in the study of complex defects. As a benchmark, we apply the method to the NV$^-$ center in diamond. The agreement with experiments is remarkable, with an accuracy of 0.1 eV. The band structure agrees with the expected qualitative features of this system, and thus provides a good intuitive physical picture by itself.