Ab Initio Prediction of a Negative Barkas Coefficient for Slow Protons and Antiprotons in LiF.

We report the ab initio prediction of a negative Barkas coefficient in lithium fluoride (LiF) insulator at low velocity (v<0.25 a.u., E_{kin}∼2 keV). The electronic stopping power of protons in LiF has been extensively studied both experimentally and theoretically because of a controversial threshold effect. While our time-dependent density-functional theory simulations confirm the presence of a velocity threshold below which the proton stopping power vanishes, our calculations demonstrate that the antiprotons do not experience such a threshold. The combination of those two contrasting behaviors gives rise to an unprecedented negative Barkas effect: the stopping power of antiprotons is larger than that of protons. We identify that the slow antiproton at close encounter destabilizes a p orbital of the F^{-} anion pointing toward the antiproton. This particular orbital becomes highly polarizable and hence contributes much to the stopping power.

An optimally tuned range-separated hybrid starting point for ab initio GW plus Bethe-Salpeter equation calculations of molecules.

The ab initio GW plus Bethe-Salpeter equation (GW-BSE, where G is the one particle Green's function and W is the screened Coulomb interaction) approach has emerged as a leading method for predicting excitations in both solids and molecules with a predictive power contingent upon several factors. Among these factors are the (1) generalized Kohn-Sham eigensystem used to construct the GW self-energy and to solve the BSE and (2) the efficacy and suitability of the Tamm-Dancoff approximation. Here, we present a detailed benchmark study of low-lying singlet excitations from a generalized Kohn-Sham (gKS) starting point based on an optimally tuned range-separated hybrid (OTRSH) functional. We show that the use of this gKS starting point with one-shot G0W0 and G0W0-BSE leads to the lowest mean absolute errors (MAEs) and mean signed errors (MSEs), with respect to high-accuracy reference values, demonstrated in the literature thus far for the ionization potentials of the GW100 benchmark set and for low-lying neutral excitations of Thiel's set molecules in the gas phase, without the need for self-consistency. The MSEs and MAEs of one-shot G0W0-BSE@OTRSH excitation energies are comparable to or lower than those obtained with other functional starting points after self-consistency. Additionally, we compare these results with linear-response time-dependent density functional theory (TDDFT) calculations and find GW-BSE to be superior to TDDFT when calculations are based on the same exchange-correlation functional. This work demonstrates tuned range-separated hybrids used in combination with GW and GW-BSE can greatly suppress starting point dependence for molecules, leading to accuracy similar to that for higher-order wavefunction-based theories for molecules without the need for costlier iterations to self-consistency.

ABINIT: Overview and focus on selected capabilities.

abinit is probably the first electronic-structure package to have been released under an open-source license about 20 years ago. It implements density functional theory, density-functional perturbation theory (DFPT), many-body perturbation theory (GW approximation and Bethe-Salpeter equation), and more specific or advanced formalisms, such as dynamical mean-field theory (DMFT) and the "temperature-dependent effective potential" approach for anharmonic effects. Relying on planewaves for the representation of wavefunctions, density, and other space-dependent quantities, with pseudopotentials or projector-augmented waves (PAWs), it is well suited for the study of periodic materials, although nanostructures and molecules can be treated with the supercell technique. The present article starts with a brief description of the project, a summary of the theories upon which abinit relies, and a list of the associated capabilities. It then focuses on selected capabilities that might not be present in the majority of electronic structure packages either among planewave codes or, in general, treatment of strongly correlated materials using DMFT; materials under finite electric fields; properties at nuclei (electric field gradient, Mössbauer shifts, and orbital magnetization); positron annihilation; Raman intensities and electro-optic effect; and DFPT calculations of response to strain perturbation (elastic constants and piezoelectricity), spatial dispersion (flexoelectricity), electronic mobility, temperature dependence of the gap, and spin-magnetic-field perturbation. The abinit DFPT implementation is very general, including systems with van der Waals interaction or with noncollinear magnetism. Community projects are also described: generation of pseudopotential and PAW datasets, high-throughput calculations (databases of phonon band structure, second-harmonic generation, and GW computations of bandgaps), and the library libpaw. abinit has strong links with many other software projects that are briefly mentioned.

Photoelectron spectra of copper oxide cluster anions from first principles methods.

We present results and analyses for the photoelectron spectra of small copper oxide cluster anions (CuO-, Cu O2- , Cu O3- , and Cu2O-). The spectra are computed using various techniques, including density functional theory (DFT) with semi-local, global hybrid, and optimally tuned range-separated hybrid functionals, as well as many-body perturbation theory within the GW approximation based on various DFT starting points. The results are compared with each other and with the available experimental data. We conclude that as in many metal-organic systems, self-interaction errors are a major issue that is mitigated by hybrid functionals. However, these need to be balanced against a strong role of non-dynamical correlation-especially in smaller, more symmetric systems-where errors are alleviated by semi-local functionals. The relative importance of the two phenomena, including practical ways of balancing the two constraints, is discussed in detail.

An assessment of low-lying excitation energies and triplet instabilities of organic molecules with an ab initio Bethe-Salpeter equation approach and the Tamm-Dancoff approximation.

The accurate prediction of singlet and triplet excitation energies is an area of intense research of significant fundamental interest and critical for many applications. Most calculations of singlet and triplet energies use time-dependent density functional theory (TDDFT) in conjunction with an approximate exchange-correlation functional. In this work, we examine and critically assess an alternative method for predicting low-lying neutral excitations with similar computational cost, the ab initio Bethe-Salpeter equation (BSE) approach, and compare results against high-accuracy wavefunction-based methods. We consider singlet and triplet excitations of 27 prototypical organic molecules, including members of Thiel's set, the acene series, and several aromatic hydrocarbons exhibiting charge-transfer-like excitations. Analogous to its impact in TDDFT, we find that the Tamm-Dancoff approximation (TDA) overcomes triplet instabilities in the BSE approach, improving both triplet and singlet energetics relative to higher level theories. Finally, we find that BSE-TDA calculations built on effective DFT starting points, such as those utilizing optimally tuned range-separated hybrid functionals, can yield accurate singlet and triplet excitation energies for gas-phase organic molecules.

Optimized virtual orbital subspace for faster GW calculations in localized basis.

The popularity of the GW approximation to the self-energy to access the quasiparticle energies of molecules is constantly increasing. As the other methods addressing the electronic correlation, the GW self-energy unfortunately shows a very slow convergence with respect to the basis complexity, which precludes the calculation of accurate quasiparticle energies for large molecules. Here we propose a method to mitigate this issue that relies on two steps: (i) the definition of a reduced virtual orbital subspace, thanks to a much smaller basis set; (ii) the account of the remainder through the simpler one-ring approximation to the self-energy. We assess the quality of the corrected quasiparticle energies for simple molecules, and finally we show an application to large graphene chunks to demonstrate the numerical efficiency of the scheme.

GW and Bethe-Salpeter study of small water clusters.

We study within the GW and Bethe-Salpeter many-body perturbation theories the electronic and optical properties of small (H2O)n water clusters (n = 1-6). Comparison with high-level CCSD(T) Coupled-Cluster at the Single Double (Triple) levels and ADC(3) Green's function third order algebraic diagrammatic construction calculations indicates that the standard non-self-consistent G0W0@PBE or G0W0@PBE0 approaches significantly underestimate the ionization energy by about 1.1 eV and 0.5 eV, respectively. Consequently, the related Bethe-Salpeter lowest optical excitations are found to be located much too low in energy when building transitions from a non-self-consistent G0W0 description of the quasiparticle spectrum. Simple self-consistent schemes, with update of the eigenvalues only, are shown to provide a weak dependence on the Kohn-Sham starting point and a much better agreement with reference calculations. The present findings rationalize the theory to experiment possible discrepancies observed in previous G0W0 and Bethe-Salpeter studies of bulk water. The increase of the optical gap with increasing cluster size is consistent with the evolution from gas to dense ice or water phases and results from an enhanced screening of the electron-hole interaction.

A systematic benchmark of the ab initio Bethe-Salpeter equation approach for low-lying optical excitations of small organic molecules.

The predictive power of the ab initio Bethe-Salpeter equation (BSE) approach, rigorously based on many-body Green's function theory but incorporating information from density functional theory, has already been demonstrated for the optical gaps and spectra of solid-state systems. Interest in photoactive hybrid organic/inorganic systems has recently increased and so has the use of the BSE for computing neutral excitations of organic molecules. However, no systematic benchmarks of the BSE for neutral electronic excitations of organic molecules exist. Here, we study the performance of the BSE for the 28 small molecules in Thiel's widely used time-dependent density functional theory benchmark set [Schreiber et al., J. Chem. Phys. 128, 134110 (2008)]. We observe that the BSE produces results that depend critically on the mean-field starting point employed in the perturbative approach. We find that this starting point dependence is mainly introduced through the quasiparticle energies obtained at the intermediate GW step and that with a judicious choice of starting mean-field, singlet excitation energies obtained from BSE are in excellent quantitative agreement with higher-level wavefunction methods. The quality of the triplet excitations is slightly less satisfactory.

Quasiparticle self-consistent GW method for the spectral properties of complex materials.

The GW approximation to the formally exact many-body perturbation theory has been applied successfully to materials for several decades. Since the practical calculations are extremely cumbersome, the GW self-energy is most commonly evaluated using a first-order perturbative approach: This is the so-called G 0 W 0 scheme. However, the G 0 W 0 approximation depends heavily on the mean-field theory that is employed as a basis for the perturbation theory. Recently, a procedure to reach a kind of self-consistency within the GW framework has been proposed. The quasiparticle self-consistent GW (QSGW) approximation retains some positive aspects of a self-consistent approach, but circumvents the intricacies of the complete GW theory, which is inconveniently based on a non-Hermitian and dynamical self-energy. This new scheme allows one to surmount most of the flaws of the usual G 0 W 0 at a moderate calculation cost and at a reasonable implementation burden. In particular, the issues of small band gap semiconductors, of large band gap insulators, and of some transition metal oxides are then cured. The QSGW method broadens the range of materials for which the spectral properties can be predicted with confidence.

Fully Dynamic G3W2 Self-Energy for Finite Systems: Formulas and Benchmark.

Over the years, Hedin's GW self-energy has been proven to be a rather accurate and simple approximation to evaluate electronic quasiparticle energies in solids and in molecules. Attempts to improve over the simple GW approximation, the so-called vertex corrections, have been constantly proposed in the literature. Here, we derive, analyze, and benchmark the complete second-order term in the screened Coulomb interaction W for finite systems. This self-energy named G3W2 contains all the possible time orderings that combine 3 Green's functions G and 2 dynamic W. We present the analytic formula and its imaginary frequency counterpart, with the latter allowing us to treat larger molecules. The accuracy of the G3W2 self-energy is evaluated on well-established benchmarks (GW100, Acceptor 24, and Core 65) for valence and core quasiparticle energies. Its link with the simpler static approximation, named SOSEX for static screened second-order exchange, is analyzed, which leads us to propose a more consistent approximation named 2SOSEX. In the end, we find that neither the G3W2 self-energy nor any of the investigated approximations to it improve over one-shot G0W0 with a good starting point. Only quasi-particle self-consistent GW HOMO energies are slightly improved by addition of the G3W2 self-energy correction. We show that this is due to the self-consistent update of the screened Coulomb interaction, leading to an overall sign change of the vertex correction to the frontier quasiparticle energies.

Influence of Electronic Correlations on Electron-Phonon Interactions of Molecular Systems with the GW and Coupled Cluster Methods.

Electron-phonon interactions are of great importance to a variety of physical phenomena, and their accurate description is an important goal for first-principles calculations. Isolated examples of materials and molecular systems have emerged where electron-phonon coupling is enhanced over density functional theory (DFT) when using the Green's-function-based ab initio GW method, which provides a more accurate description of electronic correlations. It is, however, unclear how general this enhancement is and how employing high-end quantum chemistry methods, which further improve the description of electronic correlations, might further alter electron-phonon interactions over GW or DFT. Here, we address these questions by computing the renormalization of the highest occupied molecular orbital energies of Thiel's set of organic molecules by harmonic vibrations using DFT, GW, and equation-of-motion coupled-cluster calculations. We find that, depending on the amount of exact exchange included in the DFT starting point, GW can increase the magnitude of the electron-phonon coupling across Thiel's set of molecules by an average factor of 1.1-1.8 compared to the underlying DFT, while equation-of-motion coupled-cluster leads to an increase of 1.4-2. The electron-phonon coupling predicted with the ab initio GW method is generally in much closer agreement to coupled cluster values compared to DFT, establishing GW as a promising route for accurately computing electron-phonon phenomena in molecules and beyond at a much lower computational cost than higher-end quantum chemistry techniques.

RPA, an Accurate and Fast Method for the Computation of Static Nonlinear Optical Properties.

The accurate computation of static nonlinear optical properties (SNLOPs) in large polymers requires accounting for electronic correlation effects with a reasonable computational cost. The Random Phase Approximation (RPA) used in the adiabatic connection fluctuation theorem is known to be a reliable and cost-effective method to render electronic correlation effects when combined with density-fitting techniques and integration over imaginary frequencies. We explore the ability of the RPA energy expression to predict SNLOPs by evaluating RPA electronic energies in the presence of finite electric fields to obtain (using the finite difference method) static polarizabilities and hyperpolarizabilities. We show that the RPA based on hybrid functional self-consistent field calculations yields accurate SNLOPs as the best-tuned double-hybrid functionals developed today, with the additional advantage that the RPA avoids any system-specific adjustment.

Range-separated approach to the RPA correlation applied to the van der Waals Bond and to diffusion of defects.

The random-phase approximation (RPA) is a promising approximation to the exchange-correlation energy of density functional theory, since it contains the van der Waals (vdW) interaction and yields a potential with the correct band gap. However, its calculation is computationally very demanding. We apply a range-separation concept to RPA and demonstrate how it drastically speeds up the calculations without loss of accuracy. The scheme is then successfully applied to a layered system subjected to weak vdW attraction and is used to address the controversy of the self-diffusion in silicon. We calculate the formation and migration energies of self-interstitials and vacancies taking into account atomic relaxations. The obtained activation energies deviate significantly from the earlier calculations and challenge some of the experimental interpretations: the diffusion of vacancies and interstitials has almost the same activation energy.

Ionization energy of atoms obtained from GW self-energy or from random phase approximation total energies.

A systematic evaluation of the ionization energy within the GW approximation is carried out for the first row atoms, from H to Ar. We describe a Gaussian basis implementation of the GW approximation, which does not resort to any further technical approximation, besides the choice of the basis set for the electronic wavefunctions. Different approaches to the GW approximation have been implemented and tested, for example, the standard perturbative approach based on a prior mean-field calculation (Hartree-Fock GW@HF or density-functional theory GW@DFT) or the recently developed quasiparticle self-consistent method (QSGW). The highest occupied molecular orbital energies of atoms obtained from both GW@HF and QSGW are in excellent agreement with the experimental ionization energy. The lowest unoccupied molecular orbital energies of the singly charged cation yield a noticeably worse estimate of the ionization energy. The best agreement with respect to experiment is obtained from the total energy differences within the random phase approximation functional, which is the total energy corresponding to the GW self-energy. We conclude with a discussion about the slight concave behavior upon number electron change of the GW approximation and its consequences upon the quality of the orbital energies.

The GW Miracle in Many-Body Perturbation Theory for the Ionization Potential of Molecules.

We use the GW100 benchmark set to systematically judge the quality of several perturbation theories against high-level quantum chemistry methods. First of all, we revisit the reference CCSD(T) ionization potentials for this popular benchmark set and establish a revised set of CCSD(T) results. Then, for all of these 100 molecules, we calculate the HOMO energy within second and third-order perturbation theory (PT2 and PT3), and, GW as post-Hartree-Fock methods. We found GW to be the most accurate of these three approximations for the ionization potential, by far. Going beyond GW by adding more diagrams is a tedious and dangerous activity: We tried to complement GW with second-order exchange (SOX), with second-order screened exchange (SOSEX), with interacting electron-hole pairs (W TDHF), and with a GW density-matrix (γ GW ). Only the γ GW result has a positive impact. Finally using an improved hybrid functional for the non-interacting Green's function, considering it as a cheap way to approximate self-consistency, the accuracy of the simplest GW approximation improves even more. We conclude that GW is a miracle: Its subtle balance makes GW both accurate and fast.

Coupling Natural Orbital Functional Theory and Many-Body Perturbation Theory by Using Nondynamically Correlated Canonical Orbitals.

We develop a new family of electronic structure methods for capturing at the same time the dynamic and nondynamic correlation effects. We combine the natural orbital functional theory (NOFT) and many-body perturbation theory (MBPT) through a canonicalization procedure applied to the natural orbitals to gain access to any MBPT approximation. We study three different scenarios: corrections based on second-order Møller-Plesset (MP2), random-phase approximation (RPA), and coupled-cluster singles doubles (CCSD). Several chemical problems involving different types of electron correlation in singlet and multiplet spin states have been considered. Our numerical tests reveal that RPA-based and CCSD-based corrections provide similar relative errors in molecular dissociation energies (De) to the results obtained using a MP2 correction. With respect to the MP2 case, the CCSD-based correction improves the prediction, while the RPA-based correction reduces the computational cost.

Improved One-Shot Total Energies from the Linearized GW Density Matrix.

The linearized GW density matrix (γGW) is an efficient method to improve the static portion of the self-energy compared to that of ordinary perturbative GW while keeping the single-shot simplicity of the calculation. Previous work has shown that γGW gives an improved Fock operator and total energy components that approach the self-consistent GW quality. Here, we test γGW for dimer dissociation for the first time by studying N2, LiH, and Be2. We also calculate a set of self-consistent GW results in identical basis sets for a direct and consistent comparison. γGW approaches self-consistent GW total energies for a starting point based on a high amount of exact exchange. We also compare the accuracy of different total energy functionals, which differ when evaluated with a non-self-consistent density or density matrix. While the errors in total energies among different functionals and starting points are small, the individual energy components show noticeable errors when compared to reference data. The energy component errors of γGW are smaller than functionals of the density and we suggest that the linearized GW density matrix is a route to improving total energy evaluations in the adiabatic connection framework.

Effects of electronic and lattice polarization on the band structure of delafossite transparent conductive oxides.

We use hybrid functionals and restricted self-consistent GW, state-of-the-art theoretical approaches for quasiparticle band structures, to study the electronic states of delafossite Cu(Al,In)O2, the first p-type and bipolar transparent conductive oxides. We show that a self-consistent GW approximation gives remarkably wider band gaps than all the other approaches used so far. Accounting for polaronic effects in the GW scheme we recover a very nice agreement with experiments. Furthermore, the modifications with respect to the Kohn-Sham bands are strongly k dependent, which makes questionable the common practice of using a scissor operator. Finally, our results support the view that the low energy structures found in optical experiments, and initially attributed to an indirect transition, are due to intrinsic defects in the samples.

Extrapolating Unconverged GW Energies up to the Complete Basis Set Limit with Linear Regression.

The GW approximation to the electronic self-energy is now a well-recognized approach to obtain the electron quasiparticle energies of molecules and, in particular, their ionization potential and electron affinity. Though much faster than the corresponding wavefunction methods, the GW energies are still affected by slow convergence with respect to the basis completeness. This limitation hinders a wider application of the GW approach. Here, we show that we can reach the complete basis set limit for the cumbersome GW calculations solely based on fast preliminary calculations with an unconverged basis set. We introduce a linear model that correlates the molecular orbital characteristics and the basis convergence error for a large database of approximately 600 states in 104 organic molecules that contain H, C, O, N, F, P, S, and Cl. The model employs molecular-orbital-based non-linear descriptors that encode efficiently the chemical space offering outstanding transferability. Using a low number of descriptors (17) the performance of this extrapolation procedure is superior to that of the earlier more physically motivated approaches. The predictive power of the method is finally demonstrated for a selection of large acceptor molecules.