Exploring the statically screened G3W2 correction to the GW self-energy: Charged excitations and total energies of finite systems

Electron correlation in finite and extended systems is often described in an effective single-particle framework within the $GW$ approximation. Here, we use the statically screened second-order exchange contribution to the self-energy ($G3W2$) to calculate a perturbative correction to the $GW$ self-energy. We use this correction to calculate total correlation energies of atoms, relative energies, as well as charged excitations of a wide range of molecular systems. We show that the second-order correction improves correlation energies with respect to the RPA and also improves relative energies for many, but not all considered systems. While the full $G3W2$ contribution does not give consistent improvements over $GW$, taking the average of $GW$ and $GW + G3W2$ generally gives excellent results. Improvements over quasiparticle self-consistent $GW$, which we show to give very accurate charged excitations in small and medium molecules by itself, are only minor. $G_0W_0$ quasiparticle energies evaluated with eigenvalue and orbitals from range-separated hybrids, however, are tremendously improved upon: The second-order corrected $G_0W_0$ outperforms all existing $GW$ methods for the systems considered herein and also does not come with substantially increased computational cost compared to $G_0W_0$ for systems with up to 100 atoms.Comment: Revised version as accepted by Physical review B (Phys. Rev. B 2022, 105, 125121, 10.1103/PhysRevB.105.125121) Compared to our first submission, a programming mistake in our first implementation has been corrected leading to different (better) result

Low-order Scaling G0W0G_0W_0 by Pair Atomic Density Fitting

We derive a low-scaling $G_0W_0$ algorithm for molecules, using pair atomic density fitting (PADF) and an imaginary time representation of the Green's function and describe its implementation in the Slater type orbital (STO) based Amsterdam density functional (ADF) electronic structure code. We demonstrate the scalability of our algorithm on a series of water clusters with up to 432 atoms and 7776 basis functions and observe asymptotic quadratic scaling with realistic threshold qualities controlling distance effects and basis sets of triple-$\zeta$ (TZ) plus double polarization quality. Also owing to a very small prefactor, with these settings a $G_0W_0$ calculation for the largest of these clusters takes only 240 CPU hours. With errors of 0.24 eV for HOMO energies in the GW100 database on the quadruple-$\zeta$ level, our implementation is less accurate than canonical all-electron implementations using the larger def2-QZVP GTO-tpye basis set. Apart from basis set errors, this is related to the well-known shortcomings of the GW space-time method using analytical continuation techniques as well as to numerical issues of the PADF-approach of accurately representing diffuse AO-products. We speculate, that these difficulties might be overcome by using optimized auxiliary fit sets with more diffuse functions of higher angular momenta. Despite these shortcomings, for subsets of medium and large molecules from the GW5000 database, the error of our approach using basis sets of TZ and augmented DZ quality is decreasing with system size. On the augmented DZ level we reproduce canonical, complete basis set limit extrapolated reference values with an accuracy of 80 meV on average for a set of 20 large organic molecules. We anticipate our algorithm, in its current form, to be very useful in the study of single-particle properties of large organic systems such as chromophores and acceptor molecules.Comment: final version as accepted by JCTC https://pubs.acs.org/doi/10.1021/acs.jctc.0c0069

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, 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 $G_0W_0$ 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

GW100: A Slater Type Orbital Perspective

We calculate complete basis set (CBS) limit extrapolated ionization potentials (IP) and electron affinities (EA) with Slater Type Basis sets for the molecules in the GW100 database. To this end, we present two new Slater Type orbital (STO) basis sets of triple- (TZ) and quadruple-$\zeta$ (QZ) quality whose polarization is adequate for correlated-electron methods and which contain extra diffuse functions to be able to correctly calculate electron affinities of molecules with a positive Lowest Unoccupied Molecular Orbital (LUMO). We demonstrate, that going from TZ to QZ quality consistently reduces the basis set error of our computed IPs and EAs and we conclude that a good estimate of these quantities at the CBS limit can be obtained by extrapolation. With MADs from 70 to 85 meV, our CBS limit extrapolated ionization potentials are in good agreement with results from FHI-AIMS, TURBOMOLE, VASP and WEST while they differ by more than 130 meV on average from nanoGW. With a MAD of 160 meV, our electron affinities are also in good agreement with the WEST code. Especially for systems with positive LUMOs, the agreement is excellent. With respect to other codes, the STO type basis sets generally underestimate EAs of small molecules with strongly bound LUMOs. With 62 meV for IPs and 93 meV for EAs, we find much better agreement to CBS limit extrapolated results from FHI-AIMS for a set of 250 medium to large organic molecules.Comment: Published open access by Journal of chemical theory and computatio

Towards Pair Atomic Density Fitting for Correlation Energies with Benchmark Accuracy

Pair atomic density fitting (PADF) is a promising strategy to reduce the scaling with system size of quantum chemical methods for the calculation of the correlation energy like the direct random phase approximation (RPA) or second-order M{\o}ller-Plesset perturbation theory (MP2). PADF can however introduce large errors in correlation energies as the two-electron interaction energy is not guaranteed to be bounded from below. This issue can be partially alleviated by using very large fit sets, but this comes at the price of reduced efficiency and having to deal with near-linear dependencies in the fit set. In this work, we introduce an alternative methodology to overcome this problem that preserves the intrinsically favourable scaling of PADF. We first regularize the Fock matrix by projecting out parts of the basis set which gives rise to orbital products that are hard to describe by PADF. We then also apply this projector to the orbital coefficient matrix to improve the precision of PADF-MP2 and PADF-RPA. We systematically assess the accuracy of this new approach in a numerical atomic orbital framework using Slater Type Orbitals (STO) and correlation consistent Gaussian type basis sets up to quintuple-$\zeta$ quality for systems with more than 200 atoms. For the small and medium systems in the S66 database we show the maximum deviation of PADF-MP2 and PADF-RPA relative correlation energies to DF-MP2 and DF-RPA reference results to be 0.07 and 0.14 kcal/mol respectively. When the new projector method is used, the errors only slightly increase for large molecules and also when moderately sized fit sets are used the resulting errors are well under control. Finally, we demonstrate the computational efficiency of our algorithm by calculating the interaction energies of non-covalently bound complexes with more than 1000 atoms and 20000 atomic orbitals at the RPA@PBE/CC-pVTZ level of theory

Fluoxetine targets an allosteric site in the enterovirus 2C AAA+ ATPase and stabilizes a ring-shaped hexameric complex

Enteroviruses are globally prevalent human pathogens responsible for many diseases. The nonstructural protein 2C is a AAA+ helicase and plays a key role in enterovirus replication. Drug repurposing screens identified 2C-targeting compounds such as fluoxetine and dibucaine, but how they inhibit 2C is unknown. Here, we present a crystal structure of the soluble and monomeric fragment of coxsackievirus B3 2C protein in complex with (S)-fluoxetine (SFX), revealing an allosteric binding site. To study the functional consequences of SFX binding, we engineered an adenosine triphosphatase (ATPase)-competent, hexameric 2C protein. Using this system, we show that SFX, dibucaine, HBB [2-(α-hydroxybenzyl)-benzimidazole], and guanidine hydrochloride inhibit 2C ATPase activity. Moreover, cryo-electron microscopy analysis demonstrated that SFX and dibucaine lock 2C in a defined hexameric state, rationalizing their mode of inhibition. Collectively, these results provide important insights into 2C inhibition and a robust engineering strategy for structural, functional, and drug-screening analysis of 2C proteins

Search for dark matter produced in association with bottom or top quarks in √s = 13 TeV pp collisions with the ATLAS detector

A search for weakly interacting massive particle dark matter produced in association with bottom or top quarks is presented. Final states containing third-generation quarks and miss- ing transverse momentum are considered. The analysis uses 36.1 fb−1 of proton–proton collision data recorded by the ATLAS experiment at √s = 13 TeV in 2015 and 2016. No significant excess of events above the estimated backgrounds is observed. The results are in- terpreted in the framework of simplified models of spin-0 dark-matter mediators. For colour- neutral spin-0 mediators produced in association with top quarks and decaying into a pair of dark-matter particles, mediator masses below 50 GeV are excluded assuming a dark-matter candidate mass of 1 GeV and unitary couplings. For scalar and pseudoscalar mediators produced in association with bottom quarks, the search sets limits on the production cross- section of 300 times the predicted rate for mediators with masses between 10 and 50 GeV and assuming a dark-matter mass of 1 GeV and unitary coupling. Constraints on colour- charged scalar simplified models are also presented. Assuming a dark-matter particle mass of 35 GeV, mediator particles with mass below 1.1 TeV are excluded for couplings yielding a dark-matter relic density consistent with measurements

Fabrication and Characterisation of GaAs Gunn Diode Chips for Applications at 77 GHz in Automotive Industry

GaAs-based Gunn diodes with graded AlGaAs hot electron injectorheterostructures have been developed under the special needs in automotive applications.The fabrication of the Gunn diode chips was based on total substrate removal andprocessing of integrated Au heat sinks. Especially, the thermal and RF behavior of thediodes have been analyzed by DC, impedance and S-parameter measurements. Theelectrical investigations have revealed the functionality of the hot electron injector. Anoptimized layer structure could fulfill the requirements in adaptive cruise control (ACC)systems at 77 GHz with typical output power between 50 and 90 mW

Assessment of the Second-Order Statically Screened Exchange Correction to the Random Phase Approximation for Correlation Energies

With increasing interelectronic distance, the screening of the electron-electron interaction by the presence of other electrons becomes the dominant source of electron correlation. This effect is described by the random phase approximation (RPA) which is therefore a promising method for the calculation of weak interactions. The success of the RPA relies on the cancellation of errors, which can be traced back to the violation of the crossing symmetry of the 4-point vertex, leading to strongly overestimated total correlation energies. By the addition of second-order screened exchange (SOSEX) to the correlation energy, this issue is substantially reduced. In the adiabatic connection (AC) SOSEX formalism, one of the two electron-electron interaction lines in the second-order exchange term is dynamically screened (SOSEX(W, vc)). A related SOSEX expression in which both electron-electron interaction lines are statically screened (SOSEX(W(0), W(0))) is obtained from the G3W2 contribution to the electronic self-energy. In contrast to SOSEX(W, vc), the evaluation of this correlation energy expression does not require an expensive numerical frequency integration and is therefore advantageous from a computational perspective. We compare the accuracy of the statically screened variant to RPA and RPA+SOSEX(W, vc) for a wide range of chemical reactions. While both methods fail for barrier heights, SOSEX(W(0), W(0)) agrees very well with SOSEX(W, vc) for charged excitations and noncovalent interactions where they lead to major improvements over RPA