Many-body Perturbation Theory Methods Research Articles

Optical Gaps of Ionic Materials from GW/BSE-in-DFT and CC2-in-DFT.

This work presents a density functional theory (DFT)-based embedding technique for the calculation of optical gaps in ionic solids. The approach partitions the supercell of the ionic solid and embeds a small molecule-like cluster in a periodic environment using a cluster-in-periodic embedding method. The environment is treated with DFT, and its influence on the cluster is captured by a DFT-based embedding potential. The optical gap is estimated as the lowest singlet excitation energy of the embedded cluster, obtained using a wave function theory method: second-order approximate coupled-cluster singles and doubles (CC2), and a many-body perturbation theory method: GW approximation combined with the Bethe-Salpeter equation (GW/BSE). The calculated excitation energies are benchmarked against the periodic GW/BSE values, equation-of-motion coupled-cluster singles and doubles (EOM-CCSD) results, and experiments. Both CC2-in-DFT and GW/BSE-in-DFT deliver excitation energies that are in good agreement with experimental values for several ionic solids (MgO, CaO, LiF, NaF, KF, and LiCl) while incurring negligible computational costs. Notably, GW/BSE-in-DFT exhibits remarkable accuracy with a mean absolute error (MAE) of just 0.38 eV with respect to experiments, demonstrating the effectiveness of the embedding strategy. In addition, the versatility of the method is highlighted by investigating the optical gap of a 2D MgCl2 system and the excitation energy of an oxygen vacancy in MgO, with results in good agreement with reported values.

Fully relativistic energies, transition properties, and lifetimes of lithium-like germanium

Abstract Employing two fully relativistic methods, the multi-reference configuration Dirac–Hartree–Fock (MCDHF) method and the relativistic many-body perturbation theory (RMBPT) method, we report energies and lifetime values for the lowest 35 energy levels of the (1s2)nl configurations (where the principal quantum number n = 2–6 and the angular quantum number l = 0, …, n–1) of lithium-like germanium (Ge XXX), as well as complete data on the transition wavelengths, radiative rates, absorption oscillator strengths, and line strengths between the levels. Both the allowed (E1) and forbidden (magnetic dipole M1, magnetic quadrupole M2, and electric quadrupole E2) ones are reported. The results from the two methods are consistent with each other and align well with previous accurate experimental and theoretical findings. We assess the overall accuracies of present RMBPT results to be likely the most precise ones to date. The present fully relativistic results should be helpful for soft x-ray laser research, spectral line identification, plasma modeling and diagnosing. The datasets presented in this paper are openly available at https://doi.org/10.57760/sciencedb.j00113.00135.

Effect of the configuration mixing on the polarization and angular distribution of x-ray line emissions following electron-impact excitation of Ne-like ions.

We present a systematic theoretical study on the angular distribution and linear polarization of x-ray line emissions of neon-like ions following the electron-impact excitation from the ground state to the excited levels [(2p5)1/23d3/2]J=1, [(2p5)3/23d5/2]J=1, [(2p5)3/23d3/2]J=1, and [(2p5)1/23s]J=1. The cross sections are calculated by using the flexible atomic code under configuration-interaction plus many-body perturbation theory method. The angular distribution and linear polarization are obtained based on density matrix theory. Emphasis has been placed on the effect of the configuration mixing on the angular distribution and polarization. It has been proved that the strong mixing of configuration [(2p5)3/23d3/2]J=1 with configuration [(2p5)1/23s]J=1 can result in the abrupt change of Z-dependence of angular distribution and polarization. It indicates that angular distribution and polarization can be expected to serve as a tool for investigation of configuration mixing effect.

GPU acceleration of many‐body perturbation theory methods in MOLGW with OpenACC

AbstractQuasiparticle self‐consistent many‐body perturbation theory (MBPT) methods that update both eigenvalues and eigenvectors can calculate the excited‐state properties of molecular systems without depending on the choice of starting points. However, those methods are computationally intensive even on modern multi‐core central processing units (CPUs) and thus typically limited to small systems. Many‐core accelerators such as graphics processing units (GPUs) may be able to boost the performance of those methods without losing accuracy, making starting‐point‐independent MBPT methods applicable to large systems. Here, we GPU accelerate MOLGW, a Gaussian‐based MBPT code for molecules, with open accelerators (OpenACC) and achieve speedups of up to over 32 open multi‐processing (OpenMP) CPU threads.

K-shell X-Ray Emission from Lithium-like Nitrogen N v

We present laboratory measurements of n = 3 → n = 1 N v X-ray emission lines situated near 26 Å. The lines are excited by electron-impact collisions and are shown to reach a combined intensity of about a fifth of the combined strong N v 1s2s2p 2 P 1/2,3/2 → 1s 22s 2 S 1/2 resonance lines, commonly labeled q and r, at 29.4 Å. In addition, we present new experimental data for the wavelength of the blended q and r lines at 29.4 Å, as well as for that of the blended inner-shell-excited N v lines u and v at 30.0 Å. All of these collisional N v lines need to be included in astrophysical emission models in order to properly account for flux from N v in the soft X-ray region. The measured wavelengths provide benchmarks for testing atomic structure calculations and excellent agreement is found with our calculations using the many-body perturbation theory method. We provide a complete listing of the N v energy levels with valence electrons in the n = 2, 3, and 4 shells calculated with this approach. The experimental and theoretical data, thus, provide accurate rest-frame wavelengths needed for velocity determinations based on high-resolution absorption features in spectra of warm absorbers in active galactic nuclei and other astrophysical objects.

Extended calculations of energy levels, radiative properties, and lifetimes for oxygen-like Ge XXV

The calculations are performed for the lowest 427 fine-structure levels arising from the 2s22p4, 2s2p5, 2p6, 2s22p3nl (n=3−4, l≤n−1), 2s2p4nl (n=3−4, l≤n−1), and 2p5nl (n=3, l≤n−1) configurations in O-like Ge XXV using two state-of-the-art methods, namely the many-body perturbation theory (MBPT) method and the multiconfiguration Dirac–Hartree–Fock (MCDHF) method. A comprehensive set of atomic data for these 427 levels is presented, encompassing excitation energies, wavelengths, E1, E2, M1, M2 radiative transition data (line strengths, oscillator strengths, transition rates), and lifetimes. Thorough comparisons are made between the results obtained from the two methods, as well as with existing data. The accuracy of the present data set is deemed sufficient for precise identification and deblending of emission lines associated with the n=3,4 levels. Furthermore, these data can contribute to the modeling and diagnosis of fusion plasmas.

Theoretical calculation of “tune-out” wavelengths for clock states of Al<sup>+</sup>

In quantum optical experiments, the polarizabilities of atomic systems play a very important role, which can be used to describe the interactions of atomic systems with external electromagnetic fields. When subjected to a specific electric field such as a laser field with a particular frequency, the frequency-dependent electric-dipole (E1) dynamic polarizability of an atomic state can reach zero. The wavelength corresponding to such a frequency is referred to as the “turn-out” wavelength. In this work, the “turn-out” wavelengths for the 3s<sup>2</sup> <sup>1</sup>S<sub>0</sub> and 3s3p <sup>3</sup>P<sub>0</sub> clock states of Al<sup>+</sup> are calculated by using the configuration interaction plus many-body perturbation theory (CI+MBPT) method. The values of energy and E1 reduced matrix elements of low-lying states of Al<sup>+</sup> are calculated. By combining these E1 reduced matrix elements with the experimental energy values, the E1 dynamic polarizabilities of the 3s<sup>2</sup> <sup>1</sup>S<sub>0</sub> and 3s3p <sup>3</sup>P<sub>0</sub> clock states are determined in the angular frequency range of (0, 0.42 a.u.). The “turn-out” wavelengths are found at the zero-crossing points of the frequency-dependent dynamic polarizability curves for both the 3s<sup>2</sup> <sup>1</sup>S<sub>0</sub> and 3s3p <sup>3</sup>P<sub>0</sub> states. For the ground state 3s<sup>2</sup> <sup>1</sup>S<sub>0</sub>, a single “turn-out” wavelength at 266.994(1) nm is observed. On the other hand, the excited state 3s3p <sup>3</sup>P<sub>0</sub> exhibits four distinct “turn-out” wavelengths, namely 184.56(1) nm, 174.433(1) nm, 121.52(2) nm, and 119.71(2) nm. The contributions of individual resonant transitions to the dynamic polarizabilities at the “turn-out” wavelengths are examined. It is observed that the resonant lines situated near a certain “turn-out” wavelength can provide dominant contributions to the polarizability, while the remaining resonant lines generally contribute minimally. When analyzing these data, we recommend accurately measuring these “turn-out” wavelengths to accurately determine the oscillator strengths or reduced matrix elements of the relevant transitions. This is crucial for minimizing the uncertainty of the blackbody radiation (BBR) frequency shift in Al<sup>+</sup> optical clock and suppressing the systematic uncertainty. Meanwhile, precisely measuring these “turn-out” wavelengths is also helpful for further exploring the atomic structure of Al<sup>+</sup>.

Study of Electron Impact Excitation of Na-like Kr Ion for Impurity Seeding Experiment in Large Helical Device

In this work, a krypton gas impurity seeding experiment was conducted in a Large Helical Device. Emission lines from the Na-like Kr ion in the extreme ultraviolet wavelength region, such as 22.00 nm, 17.89 nm, 16.51 nm, 15.99 nm, and 14.08 nm, respective to 2p63p(2P1/2o)−2p63s(2S1/2), 2p63p(2P3/2o)−2p63s(2S1/2), 2p63d(2D3/2)−2p63p(2P3/2o), 2p63d(2D5/2)−2p63p(2P3/2o), and 2p63d(2D3/2)−2p63p(2P1/2o) transitions, are observed. In order to generate a theoretical synthetic spectrum, an extensive calculation concerning the excitation of the Kr25+ ion through electron impact was performed for the development of a suitable plasma model. For this, the relativistic multiconfiguration Dirac–Hartree–Fock method was employed along with its extension to the relativistic configuration interaction method to compute the relativistic bound-state wave functions and excitation energies of the fine structure levels using the General Relativistic Atomic Structure Package-2018. In addition, another set of calculations was carried out utilizing the relativistic many-body perturbation theory and relativistic configuration interaction methods integrated within the Flexible Atomic Code. To investigate the reliability of our findings, the results of excitation energies, transition probabilities, and weighted oscillator strengths of different dipole-allowed transitions obtained from these different methods are presented and compared with the available data. Further, the detailed electron impact excitation cross-sections and their respective rate coefficients are obtained for various fine structure resolved transitions using the fully relativistic distorted wave method. Rate coefficients, calculated using the Flexible Atomic Code for population and de-population kinetic processes, are integrated into the collisional-radiative plasma model to generate a theoretical spectrum. Further, the emission lines observed from the Kr25+ ion in the impurity seeding experiment were compared with the present plasma model spectrum, demonstrating a noteworthy overall agreement between the measurement and the theoretical synthetic spectrum.

Fully relativistic many-body perturbation energies, transition properties, and lifetimes of lithium-like iron Fe XXIV

Employing the advanced relativistic configuration interaction (RCI) combined with the many-body perturbation theory (RMBPT) method, we report energies and lifetime values for the lowest 35 energy levels from the (1s2)nl configurations (where the principal quantum number n = 2–6 and the angular quantum number l = 0,…,n–1) of lithium-like iron Fe XXIV, as well as complete data on the transition wavelengths, radiative rates, absorption oscillator strengths, and line strengths between the levels. Both the allowed (E1) and forbidden (magnetic dipole M1, magnetic quadrupole M2, and electric quadrupole E2) ones are reported. Through detailed comparisons with previous results, we assess the overall accuracies of present RMBPT results to be likely the most precise ones to date. Configuration interaction effects are found to be very important for the energies and radiative properties for the ion. The present RMBPT results are valuable for spectral line identification, plasma modeling, and diagnosing.

Toward more accurate surface properties of ceria using many-body perturbation theory.

Despite the wide applications, the abinitio modeling of the ceria based catalyst is challenging. The partial occupation in the 4f orbitals creates a fundamental challenge for commonly used density functional theory (DFT) methods, including semilocal functionals with Hubbard U correction to force localization and hybrid functionals. In this work, we benchmark the random phase approximation (RPA) for ceria surface properties, including surface energy and hydrogenation energy, compared to the results utilizing the DFT + U approach or hybrid functionals. We show that, for the latter approaches, different surface properties require opposite directions of parameter tuning. This forms a dilemma for the parameter based DFT methods, as the improvement of a certain property by tuning parameters will inevitably lead to the worsening of other properties. Our results suggest that the parameter-free many-body perturbation theory methods exemplified by RPA are a promising strategy to escape the dilemma and provide highly accurate descriptions, which will allow us to better understand the catalytic reactions in ceria related systems.

Modewise Johnson–Lindenstrauss embeddings for nuclear many-body theory

In this work, we explore modewise Johnson-Lindenstrauss embeddings (JLEs) as a tool to reduce the computational cost and memory requirements of nuclear many-body methods. JLEs are randomized projections of high-dimensional data tensors onto low-dimensional subspaces that preserve key structural features. Such embeddings allow for the oblivious and incremental compression of large tensors, e.g., the nuclear Hamiltonian, into significantly smaller random sketches that still allow for the accurate calculation of ground-state energies and other observables. Their oblivious character makes it possible to compress a tensor without knowing in advance exactly what observables one might want to approximate at a later time. This opens the door for the use of tensors that are much too large to store in memory, e.g., complete two-plus three-nucleon Hamiltonians in large, symmetry-unrestricted bases. Such compressed Hamiltonians can be stored and used later on with relative ease. As a first step, we analyze the JLE's impact on the second-order Many-Body Perturbation Theory (MBPT) corrections for nuclear ground-state observables. Numerical experiments for a wide range of closed-shell nuclei, model spaces and state-of-the-art nuclear interactions demonstrate the validity and potential of the proposed approach: We can compress nuclear Hamiltonians hundred- to thousand-fold while only incurring mean relative errors of 1\% or less in ground-state observables. Importantly, we show that JLEs capture the relevant physical information contained in the highly structured Hamiltonian tensor despite their random characteristics. In addition to the significant storage savings, the achieved compressions imply multiple order-of magnitude reductions in computational effort when the compressed Hamiltonians are used in higher-order MBPT or nonperturbative many-body methods.

Efficient GW calculations in two dimensional materials through a stochastic integration of the screened potential

Many-body perturbation theory methods, such as the G0W0 approximation, are able to accurately predict quasiparticle (QP) properties of several classes of materials. However, the calculation of the QP band structure of two-dimensional (2D) semiconductors is known to require a very dense BZ sampling, due to the sharp q-dependence of the dielectric matrix in the long-wavelength limit (q → 0). In this work, we show how the convergence of the QP corrections of 2D semiconductors with respect to the BZ sampling can be drastically improved, by combining a Monte Carlo integration with an interpolation scheme able to represent the screened potential between the calculated grid points. The method has been validated by computing the band gap of three different prototype monolayer materials: a transition metal dichalcogenide (MoS2), a wide band gap insulator (hBN) and an anisotropic semiconductor (phosphorene). The proposed scheme shows that the convergence of the gap for these three materials up to 50meV is achieved by using k-point grids comparable to those needed by DFT calculations, while keeping the grid uniform.

Identification of an Oxygen Defect in Hexagonal Boron Nitride.

Paramagnetic fluorescent defects in two-dimensional hexagonal boron nitride (hBN) are promising building blocks for quantum information processing. Although numerous defect-related single-photon sources and a few quantum bits have been found, except for the boron vacancy, their identification is still elusive. Here, we demonstrate that the comparison of experimental and first-principles simulated electron paramagnetic resonance (EPR) spectra is a powerful tool for defect identification in hBN, and first-principles modeling is inevitable in this process as a result of the dense nuclear spin environment of hBN. In particular, a recently observed EPR center is associated with the negatively charged oxygen vacancy complex by means of the many-body perturbation theory method on top of hybrid density functional calculations. To our surprise, the negatively charged oxygen vacancy complex produces a coherent emission around 2 eV with a well-reproducing previously recorded photoluminescence spectrum of some quantum emitters, according to our calculations.

Multiconfiguration Dirac–Hartree–Fock and Relativistic Many Body Perturbation Theory calculations of energy levels, wavelengths, weighted oscillator strengths, transitions rates, lifetimes, isotope shifts, hyperfine interaction constants and Landé g-factors of Zr XXXIX

An extensive and accurate data set of energy levels, wavelengths, weighted oscillator strengths, transitions rates, lifetimes, isotope shifts, hyperfine interaction constants and Landé g-factors have been calculated for the lowest 71 odd and even parity states arising from the 1s2 and 1snl(n=1−6,0≤l≤n−1) configurations of helium-like Zr. Calculations were performed using the Multiconfigurational Dirac–Hartree–Fock​ (MCDHF) followed by the Relativistic Configuration Interaction (RCI) method. Although no measurements or other theoretical results are available for comparison, we have implemented parallel calculations using a Flexible Atomic Code (FAC) by introducing the Relativistic Many-Body Perturbation Theory (RMBPT) method. Transition rates for electric-multipole (dipole (E1), quadrupole (E2)) and magnetic-multipole (dipole (M1), quadrupole (M2)) have been also calculated. Breit interactions and quantum electrodynamics effects (QED) have been included as perturbations in extensive relativistic configuration interaction (RCI) calculations. The results arising from the two sets of calculations MCDHF/RCI and RMBPT are quite close. Almost all atomic data of helium-like Zr ion presented in this paper are calculated for the first time. We expect that our results can be used as a reference point for any further calculations of plasma processes (electron impact excitation, dielectronic recombination). Furthermore, our values can contribute to the NIST database by essentially providing the data for the lowest singly excited states of Zr XXXIX.

K-shell Emission from O vi Near 19 Å

Laboratory measurements of O vi K-shell emission lines are presented that are situated near the O viii Lyα line at 19 Å. The data provide additional rest-frame references for velocity determinations based on absorption features in the spectra of warm absorbers in active galactic nuclei and other astrophysical objects. They also provide benchmarks for testing atomic structure calculations of energy levels with electrons in a high principal quantum number (n = 3, 4). Excellent agreement is found with our calculations using the many-body perturbation theory method, and we provide a complete listing of the O vi energy levels calculated with this approach.

Dynamic polarizabilities of the clock states of Al+

The dynamic polarizabilities of and states of Al+ are calculated using the hybrid configuration interaction and many-body perturbation theory method, and multiconfiguration Dirac–Hartree–Fock method in this work. Five ultraviolet magic wavelengths for the Al+ clock transition – are predicted. Although the suitable lasers are not available presently, the potential precision measurement on these magic wavelengths for the Al+ clock transition would be used to extract the ratios of several certain transition matrix elements with high accuracy, and then help to improve the precision and reliability of the estimate of the BBR shift of the Al+ clock transition. The differential dynamic polarizabilities at certain wavelengths are evaluated, which are useful to assess the ac Stark shift of the Al+ clock transition frequency and helpful in the clock experiments to suppress the ac Stark shift of the clock transition as possible as it can.

MacroQC 1.0: An electronic structure theory software for large-scale applications.

MacroQC is a quantum chemistry software for high-accuracy computations and large-scale chemical applications. MacroQC package features energy and analytic gradients for a broad range of many-body perturbation theory and coupled-cluster (CC) methods. Even when compared to commercial quantum chemistry software, analytical gradients of second-order perturbation theory, CC singles and doubles (CCSD), and CCSD with perturbative triples approaches are particularly efficient. MacroQC has a number of peculiar features, such as analytic gradients with the density-fitting approach, orbital-optimized methods, extended Koopman's theorem, and molecular fragmentation approaches. MacroQC provides a limited level of interoperability with some other software. The plugin system of MacroQC allows external interfaces in a developer-friendly way. The linear-scaling systematic molecular fragmentation (LSSMF) method is another distinctive feature of the MacroQC software. The LSSMF method enables one to apply high-level post-Hartree-Fock methods to large-sized molecular systems. Overall, we feel that the MacroQC program will be a valuable tool for wide scientific applications.

HYPERFINE STRUCTURE PARAMETERS FOR COMPLEX ATOMS WITHIN RELATIVISTIC MANY-BODY PERTURBATION THEORY

The calculational results for the hyperfine structure (HFS) parameters for the Mn atom (levels of the configuration 3d64s) and the results of advanced calculating the HFS constants and nuclear quadrupole moment for the radium isotope are obtained on the basis of computing within the relativistic many-body perturbation theory formalism with a correct and effective taking into account the exchange-correlation, relativistic, nuclear and radiative corrections. Analysis of the data shows that an account of the interelectron correlation effects is crucial in the calculation of the hyperfine structure parameters. The fundamental reason of physically reasonable agreement between theory and experiment is connected with the correct taking into account the inter-electron correlation effects, nuclear (due to the finite size of a nucleus), relativistic and radiative corrections. The key difference between the results of the relativistic Hartree-Fock Dirac-Fock and many-body perturbation theory methods calculations is explained by using the different schemes of taking into account the inter-electron correlations as well as nuclear and radiative ones.

Multicomponent MP4 and the inclusion of triple excitations in multicomponent many-body methods.

This study implements the full multicomponent third-order (MP3) and fourth-order (MP4) many-body perturbation theory methods for the first time. Previous multicomponent studies have only implemented a subset of the full contributions, and the present implementation is the first multicomponent many-body method to include any connected triples contribution to the electron-proton correlation energy. The multicomponent MP3 method is shown to be comparable in accuracy to the multicomponent coupled-cluster doubles method for the calculation of proton affinities, while the multicomponent MP4 method is of similar accuracy as the multicomponent coupled-cluster singles and doubles method. From the results in this study, it is hypothesized that the relative accuracy of multicomponent methods is more similar to their single-component counterparts than previously assumed. It is demonstrated that for multicomponent MP4, the fourth-order triple-excitation contributions can be split into electron-electron and electron-proton contributions and the electron-electron contributions ignored with very little loss of accuracy of protonic properties.

Superconductivity in the bilayer Hubbard model: Two Fermi surfaces are better than one

Fully occupied or unoccupied bands in a solid are often considered inert and irrelevant to a material's low-energy properties. But the discovery of enhanced superconductivity in heavily electron-doped FeSe-derived superconductors poses questions about the possible role of incipient bands (those laying close to but not crossing the Fermi level) in pairing. To answer this question, researchers have studied pairing correlations in the bilayer Hubbard model, which has an incipient band for large interlayer hopping ${t}_{\ensuremath{\perp}}$, using many-body perturbation theory and variational methods. They have generally found that superconductivity is enhanced as one of the bands approaches the Lifshitz transition and even when it becomes incipient. Here we address this question using the nonperturbative quantum Monte Carlo (QMC) dynamical cluster approximation (DCA) to study the bilayer Hubbard model's pairing correlations. We find that the model has robust ${s}^{\ifmmode\pm\else\textpm\fi{}}$ pairing correlations in the large ${t}_{\ensuremath{\perp}}$ limit, which can become stronger as one band is made incipient. While this behavior is linked to changes in the effective interaction, we further find that it is counteracted by a suppression of the intrinsic pair-field susceptibility and does not translate to an increased ${T}_{c}$. Our results demonstrate that the highest achievable transition temperatures in the bilayer Hubbard model occur when the system has two bands crossing the Fermi level.