Renormalized Singles with Correlation in <i>GW</i> Green’s Function Theory for Accurate Quasiparticle Energies

We apply the renormalized singles with the correlation (RSc) Green function in the GW approximation for accurate quasiparticle (QP) energies and orbitals. The RSc Green function includes singles contributions from the associated density functional approximation (DFA) and considers correlation contributions perturbatively. GRScWRSc uses the RSc Green function as the new starting point and in the formulation of the screened interaction. GRScW0 fixes the screened interaction at the DFA level. For the calculations of ionization potentials, GRScWRSc and GRScW0 significantly reduce the starting point dependence and provide accurate results with errors around 0.2  eV. For the calculations of core-level binding energies, GRScWRSc slightly overestimates the results because of underscreening, but GRScW0 with GGA functionals provides the optimal accuracy with errors of 0.40  eV. We also show that GRScWRSc predicts accurate dipole moments. GRScWRSc and GRScW0, are computationally favorable compared with any self-consistent GW methods. The RSc approach is promising for making GW and other Green function methods efficient and robust

Multireference Density Functional Theory for Describing Ground and Excited States with Renormalized Singles

We applied renormalized singles (RS) in the multireference density functional theory (DFT) to calculate accurate energies of ground and excited states. The multireference DFT approach determines the total energy of the N-electron system as the sum of the (N – 2)-electron energy from a density functional approximation (DFA) and the two-electron addition energies from the particle–particle Tamm–Dancoff approximation (ppTDA), naturally including multireference description. The ppTDA@RS-DFA approach uses the RS Hamiltonian capturing all singles contributions in calculating two-electron addition energies, and its total energy is optimized with the optimized effective potential method. It significantly improves the original ppTDA@DFA. For ground states, ppTDA@RS-DFA properly describes dissociation curves tested and the double bond rotation of ethylene. For excited states, ppTDA@RS-DFA provides accurate excitation energies and largely eliminates the DFA dependence. ppTDA@RS-DFA thus provides an efficient multireference approach to systems with static correlation

Combining Renormalized Singles <i>GW</i> 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 GRSWRS method, which uses the RS Green’s function also for the computation of the screened Coulomb interaction W. We show that the BSE/GRSWRS 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/GRSWRS 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/GRSWRS significantly outperforms BSE/G0W0 and TDDFT with the accuracy comparable to BSE/evGW. We also show that BSE/GRSWRS predicts Rydberg excitation energies of atomic systems well. Besides the excellent accuracy, BSE/GRSWRS largely eliminates the dependence on the choice of the density functional approximation. This work demonstrates that the BSE/GRSWRS approach is accurate and efficient for predicting excitation energies for a broad range of systems, which expands the applicability of the BSE/GW approach

Machine Learning Many-Body Green’s Functions for Molecular Excitation Spectra

We present a machine learning (ML) framework for predicting Green’s functions of molecular systems, from which photoemission spectra and quasiparticle energies at quantum many-body level can be obtained. Kernel ridge regression is adopted to predict self-energy matrix elements on compact imaginary frequency grids from static and dynamical mean-field electronic features, which gives direct access to real-frequency many-body Green’s functions through analytic continuation and Dyson’s equation. Feature and self-energy matrices are represented in a symmetry-adapted intrinsic atomic orbital plus projected atomic orbital basis to enforce rotational invariance. We demonstrate good transferability and high data efficiency of the proposed ML method across molecular sizes and chemical species by showing accurate predictions of density of states (DOS) and quasiparticle energies at the level of many-body perturbation theory (GW) or full configuration interaction. For the ML model trained on 48 out of 1995 molecules randomly sampled from the QM7 and QM9 data sets, we report the mean absolute errors of ML-predicted highest occupied and lowest unoccupied molecular orbital energies to be 0.13 and 0.10 eV, respectively, compared to GW@PBE0. We further showcase the capability of this method by applying the same ML model to predict DOS for significantly larger organic molecules with up to 44 heavy atoms

Linear Scaling Calculations of Excitation Energies with Active-Space Particle–Particle Random-Phase Approximation

We developed an efficient active-space particle–particle random-phase approximation (ppRPA) approach to calculate accurate charge-neutral excitation energies of molecular systems. The active-space ppRPA approach constrains both indexes in particle and hole pairs in the ppRPA matrix, which only selects frontier orbitals with dominant contributions to low-lying excitation energies. It employs the truncation in both orbital indexes in the particle–particle and the hole–hole spaces. The resulting matrix, whose eigenvalues are excitation energies, has a dimension that is independent of the size of the systems. The computational effort for the excitation energy calculation, therefore, scales linearly with system size and is negligible compared with the ground-state calculation of the (N – 2)-electron system, where N is the electron number of the molecule. With the active space consisting of 30 occupied and 30 virtual orbitals, the active-space ppRPA approach predicts the excitation energies of valence, charge-transfer, Rydberg, double, and diradical excitations with the mean absolute errors (MAEs) smaller than 0.03 eV compared with the full-space ppRPA results. As a side product, we also applied the active-space ppRPA approach in the renormalized singles (RS) T-matrix approach. Combining the non-interacting pair approximation that approximates the contribution to the self-energy outside the active space, the active-space GRSTRS@PBE approach predicts accurate absolute and relative core-level binding energies with the MAEs around 1.58 and 0.3 eV, respectively. The developed linear scaling calculation of excitation energies is promising for applications to large and complex systems

Tetrahedral Tilting and Oxygen Vacancy Stabilization and Migration in La_1–<i>x</i>Sr_2+<i>x</i>(GaO₄)O_{1–0.5<i>x</i>} Mixed Electronic/Oxide Ionic Conductors

The La2O3/SrO/Ga2O3 ternary system contains several compounds with remarkable oxide or proton ionic conduction. Among them, the layered LaSr2(GaO4)O compound is a less commonly studied material. Here, the crystal structure, electrical conduction properties, and ionic migration mechanism of the La1–xSr2+x(GaO4) O1–0.5x (0 ≤ x ≤ 0.3) system are thoroughly analyzed. Diffraction methods indicate that the system crystallizes in the tetragonal space group P4/ncc, which is compatible with the presence of a subtle GaO4 tetrahedral tilting along the c axis, leading to a slight deviation of the body-centered tetragonal structure previously reported. This feature is essential to further understanding the mixed p electronic/oxide ion-conducting behavior of the system. Upon La3+ for Sr2+ substitution, oxygen vacancies arise at the loosely bound oxide sublattice, which at high temperature go through the GaO4 tetrahedral layer, leading to the formation of intermediate corner-sharing Ga2O7 tetrahedral dimers, and migrate via the continuous breaking and re-formation of the dimers, assisted by the synergic rotation and deformation of neighboring GaO4 tetrahedra. The unique structural and electrical features of La1–xSr2+x(GaO4)­O1–0.5x materials within the La2O3/SrO/Ga2O3 ternary system emphasize their potential application as cathode materials in LaGaO3-based fuel cells

Monolithic Neat Graphene Oxide Aerogel for Efficient Catalysis of S → O Acetyl Migration

Graphene oxide (GO) is highly attractive for catalysis because of its large specific surface area and rich chemical structures. However, it has generally been used as a catalyst carrier. Here, we designed a three-dimensional monolith of neat GO aerogel as a fixed-bed carbocatalyst used in the reaction of S → O acetyl migration for the synthesis of thiol compounds, showing the merits of ultrafast catalytic speed (5–8 h), high selectivity (100%), high yields (near 100%), easy isolation of products, and long-life recyclability (>18 times). Particularly, we achieved for the first time thiol compounds containing functional groups of halogen and hydroxyl, which cannot be synthesized using other currently reported catalysts. Control experiments demonstrated that the efficient catalysis mechanism is mainly attributed to the protonic functional groups, ultralarge size, and unpaired electrons of GO, as well as the “cage effect” at nanoscale confined spaces of aerogel cells

Accurate Excitation Energies of Point Defects from Fast Particle–Particle Random Phase Approximation Calculations

We present an efficient particle–particle random phase approximation (ppRPA) approach that predicts accurate excitation energies of point defects, including the nitrogen-vacancy (NV–) and silicon-vacancy (SiV0) centers in diamond and the divacancy center (VV0) in 4H silicon carbide, with errors of ±0.2 eV compared with experimental values. Starting from the (N + 2)-electron ground state calculated with density functional theory (DFT), the ppRPA excitation energies of the N-electron system are calculated as the differences between the two-electron removal energies of the (N + 2)-electron system. We demonstrate that the ppRPA excitation energies converge rapidly with a few hundred canonical active-space orbitals. We also show that active-space ppRPA has weak DFT starting-point dependence and is significantly cheaper than the corresponding ground-state DFT calculation. This work establishes ppRPA as an accurate and low-cost tool for investigating excited-state properties of point defects and opens up new opportunities for applications of ppRPA to periodic bulk materials

Evaluating temporally decomposed associations between PM2.5 and hospitalisation risks of AECOPD: A case study in Beijing from 2010 to 2019

 Few studies investigated relative contributions of PM2.5 concentration at multiple time-scales (short-term, seasonal and long-term periods) on the hospitalisation risk for acute exacerbation of COPD (AECOPD). In this study, we specified and discriminated the short-term, seasonal and long-term trend effects of PM2.5 concentration on the hospitalisation for AECOPD in Beijing between 2010 and 2019. Daily PM2.5 observations from US Beijing Embassy from Jan 1, 2010, to Dec 31, 2019 (3652 days) were decomposed to short-term, seasonal and long-term trend components by using the robust Kolmogorov-Zurbenko filter. During the study period, daily counts of AECOPD hospitalisation were obtained from a database compiled by Beijing Public Health Information Center. Two separate generalized additive models were built to assess effects of raw PM2.5 concentrations and the three decomposed components of time-scales on hospitalisation of AECOPD in Beijing. We found raw PM2.5 concentrations were associated with AECOPD in Beijing with a 10 μg/m3 increase corresponding to 0.46% (95% CI: 0.40%–0.52%) increase in hospitalisation. In the model of decomposed PM2.5 time-series, both the short-term and long-term components exhibited statistically significant positive association with AECOPD, which, respectively, was associated to 0.42% (95% CI: 0.36%–0.48%) and 6.91% (95% CI: 6.08%–7.74%) increase in AECOPD hospitalisation per 10 μg/m3 increase. The seasonal trend had an insignificant U-shaped relationship with AECOPD. Our study simultaneously confirmed that a statistically significant positive association between the raw PM2.5 concentrations, the decomposed short-term and long-term trend of PM2.5 concentrations and increased risk for AECOPD hospitalisation. Strong long-term effects in this study indicated that stringent emission control measures would bring strong public health benefits concerning AECOPD. </p

Benchmark of <i>GW</i> 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