Many-body Perturbation Theory Research Articles

Physical and unphysical regimes of self-consistent many-body perturbation theory

Physical and unphysical regimes of self-consistent many-body perturbation theory

Finite and high-temperature series expansion via many-body perturbation theory: application to Heisenberg spin-1/2 XXZ chain

We present a new algorithm to evaluate the grand potential at high and finite temperatures using many-body perturbation theory. This algorithm enables us to calculate the contribution of any Hugenholtz or Feynman vacuum diagrams and formulate the results as a sum of divided differences. Additionally, the proposed method is applicable to any interaction in any dimension, allowing us to calculate thermodynamic quantities efficiently at any given temperature, particularly at high temperatures.Furthermore, we apply this algorithm to the Heisenberg spin-1/2 XXZ chain. We obtain all coefficients of the high-temperature expansion of the free energy and susceptibility per site of this model up to the sixth order.

Going Beyond the GW Approximation Using the Time-Dependent Hartree-Fock Vertex.

The time-dependent Hartree-Fock (TDHF) vertex of many-body perturbation theory (MBPT) makes it possible to extend TDHF theory to charged excitations. Here we assess its performance by applying it to spherical atoms in their neutral electronic configuration. On a theoretical level, we recast the TDHF vertex as a reducible vertex, highlighting the emergence of a self-energy expansion purely in orders of the bare Coulomb interaction; then, on a numerical level, we present results for polarizabilities, ionization energies (IEs), and photoemission satellites. We confirm the superiority of THDF over simpler methods such as the random phase approximation for the prediction of atomic polarizabilities. We then find that the TDHF vertex reliably provides better IEs than GW and low-order self-energies do in the light-atom, few-electron regime; its performance degrades in heavier, many-electron atoms instead, where an expansion in orders of an unscreened Coulomb interaction becomes less justified. New relevant features are introduced in the satellite spectrum by the TDHF vertex, but the experimental spectra are not fully reproduced due to a missing account of nonlinear effects connected to hole relaxation. We also explore various truncations of the self-energy given by the TDHF vertex, but do not find them to be more convenient than low-order approximations such as GW and second Born (2B), suggesting that vertex corrections should be carried out consistently both in the self-energy and in the polarizability.

Converging many-body perturbation theory for ab-initio nuclear structure: Brillouin-Wigner perturbation series for closed-shell nuclei

Convergence aspects of nuclear many-body perturbation theory for ground states of closed-shell nuclei are explored using a Brillouin-Wigner formulation with a new vertex function enabling high-order calculations. A general formalism for Hamiltonian partitioning and a convergence criterion for the perturbation series are proposed. Analytical derivations show that with optimal partitioning, the convergence criterion for ground states can always be satisfied. This feature attributes to the variational principle and does not depend on the choice of an internucleon interaction or a many-body basis. Numerical calculations of the ground state energies of He4 and O16 with Daejeon16 and a bare N3LO potential in both harmonic-oscillator and Hartree-Fock bases confirm this finding.

Computational Discovery of Intermolecular Singlet Fission Materials Using Many-Body Perturbation Theory.

Intermolecular singlet fission (SF) is the conversion of a photogenerated singlet exciton into two triplet excitons residing on different molecules. SF has the potential to enhance the conversion efficiency of solar cells by harvesting two charge carriers from one high-energy photon, whose surplus energy would otherwise be lost to heat. The development of commercial SF-augmented modules is hindered by the limited selection of molecular crystals that exhibit intermolecular SF in the solid state. Computational exploration may accelerate the discovery of new SF materials. The GW approximation and Bethe-Salpeter equation (GW+BSE) within the framework of many-body perturbation theory is the current state-of-the-art method for calculating the excited-state properties of molecular crystals with periodic boundary conditions. In this Review, we discuss the usage of GW+BSE to assess candidate SF materials as well as its combination with low-cost physical or machine learned models in materials discovery workflows. We demonstrate three successful strategies for the discovery of new SF materials: (i) functionalization of known materials to tune their properties, (ii) finding potential polymorphs with improved crystal packing, and (iii) exploring new classes of materials. In addition, three new candidate SF materials are proposed here, which have not been published previously.

Unveiling the Electronic Structure of SnS for Photocatalytic Applications: A DFT Approach†

AbstractPhotocatalytic materials are of great scientific interest due to their potential applications in sustainable energy sources. Band gap and optical absorption of the materials are two core characteristics for photocatalysis that eventually depend on electronic structure. In order to accurately compute (predict) the electronic‐scale properties of a crystalline solid using first principles calculations, which might be costly to measure experimentally, large‐scale atomic level calculation frameworks have been made possible through the use of density functional theory (DFT). We have used DFT with many body perturbation theory (MBPT) by solving the bethe‐salpeter equation (BSE) to priorly predict the properties of bulk tin sulfide (SnS) as it meets the necessary requirements for photocatalytic applications. We fixed the DFT band gap underestimation by including the Hubbard parameter (U) and used projector augmented wave pseudo‐potentials with generalized‐gradient approximation (GGA) to calculate the electronic and optical properties of SnS. Optical properties were computed using independent particle approximation (IPA) and BSE with DFT+U wave functions. Our theoretical results align with experimental data for this material, demonstrating the potential for further research in validating experimental results with theoretical approximations and empirical relations.

Significant improvement in structural, electronic, optical and thermoelectric properties of PdTe2 in bulk and monolayer phase: A G0W0+BSE approach

Using first principles calculations structural, electronic, thermoelectric and optical properties of PdTe2 in bulk and monolayer were investigated. The calculated lattice parameters with different exchange correlation functionals show that the results obtained with addition of van der Waals corrections (vdW-DFC09x) are very well matched with the results obtained experimental. For correct prediction of electronic band gap, G0W0 approximation is used and the calculated band structure reveal that PdTe2 in bulk form has metallic nature as attained in experimental studies. In addition, the electronic band gap results with G0W0 approximation depicted that PdTe2 in monolayer phase is a semiconductor material with a direct band gap of 1.12 eV. The optical spectra have been calculated via many-body perturbation theory (MBPT) by solving Bethe-Salpeter equation (BSE) (G0W0+BSE). Ultimately, the results of optical spectra demonstrated that PdTe2 in monolayer phase has strong optical absorption within visible light wavelengths than the bulk phase which is good for solar cell applications. Thermoelectric (TE) properties of PdTe2 in bulk and monolayer structures have been studied using BoltzTraP code. The TE properties calculations indicated that better performance can be obtained by reducing the dimensionality of materials. The figure of merit was found to be above unity for monolayer phase. This paper successfully exploited the enhancement of the figure of merit values with the monolayer structure of PdTe2 material.

Tailoring the optoelectronic properties of MoS2 for broadband photodetection: Showcasing an Ab-into study involving the quasi-particle correction within the Green’s function-based approximation

In this study, the electronic and structural characteristics of both bulk and monolayer hexagonal MoS2 material are studied within and beyond density functional theory (DFT) by considering one-shot GW corrections for an accurate band gap prediction. Interestingly, our computed quasiparticle (QP) bandgap of 1.36 eV and 3.33 eV for bulk and monolayer, respectively, is in excellent agreement with the experimental finding. The elucidation of the optical properties was estimated with the aid of the Bethe–Salpeter equation within the many-body perturbation theory (MPB). The computed optical transitions such as absorption coefficient, extinction coefficient, refractive index, reflectivity, and electron energy loss function are in better agreement with the experimental data. Moreover, the new approach allows for the efficient inclusion of all conduction bands in GW calculations, significantly reducing computational costs compared to traditional methods. A good agreement of the lattice parameters, as well as the interlayer distance with the experimental findings, is observed by the inclusion of van der Waals (vdW) corrections. Besides the agreement with previously reported values, the evaluated band structure determined with the quasiparticle corrections shows that both bulk and monolayer MoS2 material exhibit semiconducting properties with direct and indirect band gaps, respectively. The calculation of the density of states reveals that the s-orbitals of S atoms and the d-orbitals of Mo are predominantly at the origin of the essential material properties secured at the Fermi level. The results of the study also point to the possibility of a foundation for creating physical structures with swift, decisive, directed, and long-range broadband photodetection capabilities.

Relativistic calculations of energy levels, lifetimes, transition parameters, and electron impact excitation cross sections for Kr XIX

In this study, we present a detailed analysis of atomic properties for Kr XIX, specifically focusing on the lowest 128 fine-structure levels originating from the 3s23p6, 3s23p53d, 3s3p63d and 3s23p43d2 configurations. We report energy levels, lifetimes, wavelengths, weighted oscillator strengths, and transition probabilities for multipole transition types (E1, E2, M1, and M2). To achieve this, we employed the GRASP2018 code, which implements the fully relativistic multiconfigurational Dirac–Hartree–Fock method and accounts for Breit interaction and quantum electrodynamic effects. We performed another set of calculations using the many-body perturbation theory implemented in the flexible atomic code (FAC). By comparing the results obtained from GRASP2018 and FAC, we established the accuracy and consistency of our calculations. Furthermore, using the relativistic distorted wave theory, we studied electron impact excitation of all transitions to upper levels from the ground and metastable levels and reported excitation cross sections for incident electron energies up to 5 keV. To enhance the practical utility of our findings, we also provided analytical fittings of these cross sections and excitation rate coefficients for their applications in plasma modeling. This work contributes to the atomic properties and excitation cross sections of Kr XIX, addressing a marked gap in the available atomic data.

Excitation and recombination studies with silicon and sulphur ions at an EBIT

Measurements of electron-impact excitation and recombination rate coefficients of highly charged Si and S ions at the Stockholm electron beam ion trap are reported. The experimental method was a combination of photon detection from the trapped ions during probing and subsequently extraction and time-of-flight (TOF) charge analysis of these ions. The TOF technique allows to measure recombination rate coefficients separately for every charge state, and together with the photon spectra of these ions also the excitation rate coefficients. In this paper, we present more details of the experimental procedure and summarize the experimental results in comparison with two different state-of-the-art calculations of recombination and excitation rates for Si10+–Si13+ and S12+–S15+ ions. One of these uses a relativistic configuration interaction approach (flexible atomic code) and the other is a relativistic many-body perturbation theory. A good to excellent agreement with both of them is found in energy and resonance strength for the investigated ions.

First-principles calculations into electronic, and excitonic effects of CH3NH3PbX3 (X = Br, I) perovskite solar cells

The orthorhombic phases of CH3NH3PbX3 (X = Br, I) have garnered significant research interest for their potential applications in optoelectronics. This work presents our findings regarding the geometric, electronic, and optical properties of CH3NH3PbX3 utilizing first-principles calculations based on density functions theory (DFT), and many-body perturbation theory (MBPT). Our investigation reveals that CH3NH3PbX3 exhibits direct band gap semiconductors, low effective mass, and high carrier mobility. Furthermore, CH3NH3PbX3 processes interesting optical properties, including a low exciton energy binding, and low reflectivity/high absorption efficiency. Additionally, the identified bound exciton states manifest as bright states in both materials. More importantly, the intimate correlation between optical and electronic characteristics is convincingly established through the orbital hybridization concept. These features suggest that CH3NH3PbX3 materials hold promise as an active layer for perovskite-based solar cells.

Noise-independent route toward the genesis of a COMPACT ansatz for molecular energetics: A dynamic approach.

Recent advances in quantum information and quantum science have inspired the development of various compact, dynamically structured ansätze that are expected to be realizable in Noisy Intermediate-Scale Quantum (NISQ) devices. However, such ansätze construction strategies hitherto developed involve considerable measurements, and thus, they deviate significantly in the NISQ platform from their ideal structures. Therefore, it is imperative that the usage of quantum resources be minimized while retaining the expressivity and dynamical structure of the ansatz that can adapt itself depending on the degree of correlation. We propose a novel ansatz construction strategy based on the abinitio many-body perturbation theory that requires no pre-circuit measurement and, thus, remains structurally unaffected by any hardware noise. The accuracy and quantum complexity associated with the ansatz are solely dictated by a pre-defined perturbative order, as desired, and, hence, are tunable. Furthermore, the underlying perturbative structure of the ansatz construction pipeline enables us to decompose any high-rank excitation that appears in higher perturbative orders into the product of various low-rank operators, and it thus keeps the execution gate-depth to its minimum. With a number of challenging applications on strongly correlated systems, we demonstrate that our ansatz performs significantly better, both in terms of accuracy, parameter count, and circuit depth, in comparison to the allied unitary coupled cluster based ansätze.

Benchmarking calculations of level energies, transition parameters and electron impact excitation cross sections of S-like Xe38+

Atomic structure parameters for levels corresponding to 2s22p63s23p4, 2s22p63s3p5, 2s22p63s23p23d2, 2s22p63s3p43d and 2s22p63s23p33d configurations of S-like Xe38+ are calculated using the fully relativistic multiconfiguration Dirac-Hatree-Fock (MCDHF) method followed by the subsequent relativistic configuration interaction (RCI) calculations. The parameters evaluated include energies of the lowest 75 levels and E1, M1, E2, and M2 transition parameters among these levels. The effect of the choice of virtual orbitals for generating the wavefunctions is discussed. The accuracy of our line strengths is established through the rigorous calculations of their associated uncertainties using three different methods. Another set of calculations using the many-body perturbation theory (MBPT) to validate the present MCDHF-RCI energies is carried out. Further, the electron impact excitation cross-sections using the relativistic distorted wave (RDW) theory are determined for all transitions from the ground and metastable states in the incident electron energy range from the excitation threshold to 10 keV. For plasma physics applications, the fitting parameters for these cross sections employing two distinct equations tailored for low and high-energy regimes are reported. Moreover, the rate coefficients are determined in the electron temperatures range of 15 eV to 100 eV by taking into account the Maxwellian electron energy distribution function and our computed cross-sections. In addition to addressing the atomic data gap in highly charged Xe ions, the present results are of good accuracy and can serve as benchmark tests for other theoretical evaluations. Moreover, they can also assist in line identification of the complex spectra of highly charged sulphur-like xenon ions.

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.

Absolute energy levels of liquid water from many-body perturbation theory with effective vertex corrections

We demonstrate the importance of addressing the Γ vertex and thus going beyond the GW approximation for achieving the energy levels of liquid water in many-body perturbation theory. In particular, we consider an effective vertex function in both the polarizability and the self-energy, which does not produce any computational overhead compared with the GW approximation. We yield the band gap, the ionization potential, and the electron affinity in good agreement with experiment and with a hybrid functional description. The achieved electronic structure and dielectric screening further lead to a good description of the optical absorption spectrum, as obtained through the solution of the Bethe-Salpeter equation. In particular, the experimental peak position of the exciton is accurately reproduced.

Second-order Rayleigh–Schrödinger perturbation theory for the GRASP2018 package: Core–valence correlations


 
 
 The General Relativistic Atomic Structure package [GRASP2018, C. Froese Fischer, G. Gaigalas, P. Jönsson, and J. Bieroń, Comput. Phys. Commun. (2019), DOI: 10.1016/j.cpc.2018.10.032] is based on multiconfiguration Dirac– Hartree–Fock and relativistic configuration interaction (RCI) methods for energy structure calculations. The atomic state function used in the program is built from the set of configuration state functions (CSFs). The valence–valence, core–valence and core–core correlations are explicitly included through expansions over CSFs in RCI. We present a combination of RCI and the stationary second-order Rayleigh–Schrödinger many-body perturbation theory in an irreducible tensorial form to account for electron core–valence correlations when an atom or ion has any number of valence electrons. This newly developed method, which offers two ways of use, allows a significant reduction of the CSF space for complex atoms and ions. We also demonstrate how the method and program works for the energy structure calculation of Cl III ion.
 
 

Anomalous isotope effect on the optical bandgap in a monolayer transition metal dichalcogenide semiconductor.

Isotope effects have received increasing attention in materials science and engineering because altering isotopes directly affects phonons, which can affect both thermal properties and optoelectronic properties of conventional semiconductors. However, how isotopic mass affects the optoelectronic properties in 2D semiconductors remains unclear because of measurement uncertainties resulting from sample heterogeneities. Here, we report an anomalous optical bandgap energy red shift of 13 (±7) milli-electron volts as mass of Mo isotopes is increased in laterally structured 100MoS2-92MoS2 monolayers grown by a two-step chemical vapor deposition that mitigates the effects of heterogeneities. This trend, which is opposite to that observed in conventional semiconductors, is explained by many-body perturbation and time-dependent density functional theories that reveal unusually large exciton binding energy renormalizations exceeding the ground-state renormalization energy due to strong coupling between confined excitons and phonons. The isotope effect on the optical bandgap reported here provides perspective on the important role of exciton-phonon coupling in the physical properties of two-dimensional materials.

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.

Electronic structure of Ta2O5 polymorphs: Variation trend of band gap and the role of oxygen vacancies

We provide a systematic study on the electronic structure of a series of Ta2O5 polymorphs using standard density functional theory (DFT) calculations as well as the more accurate many-body perturbation theory within the GW approximation. For the defect-free polymorphs, the variation trend of band gap can be microscopically related to the strength of orbital hybridization, and to the macroscopic bulk formation energy. The presence of oxygen vacancies is found to have profound effects on the electronic properties near the Fermi level, notably the reduction of band gap and gap closure (insulator-to-metal transition). Furthermore, depending on the vacancy sites, the band gap of some defective system may be enlarged with comparison to its defect-free counterpart. Such an anomalous behavior originates from the unexpected formation of Ta–Ta bonds.

Bistability between π-diradical open-shell and closed-shell states in indeno[1,2-a]fluorene.

Indenofluorenes are non-benzenoid conjugated hydrocarbons that have received great interest owing to their unusual electronic structure and potential applications in nonlinear optics and photovoltaics. Here we report the generation of unsubstituted indeno[1,2-a]fluorene on various surfaces by the cleavage of two C-H bonds in 7,12-dihydroindeno[1,2-a]fluorene through voltage pulses applied by the tip of a combined scanning tunnelling microscope and atomic force microscope. On bilayer NaCl on Au(111), indeno[1,2-a]fluorene is in the neutral charge state, but it exhibits charge bistability between neutral and anionic states on the lower-workfunction surfaces of bilayer NaCl on Ag(111) and Cu(111). In the neutral state, indeno[1,2-a]fluorene exhibits one of two ground states: an open-shell π-diradical state, predicted to be a triplet by density functional and multireference many-body perturbation theory calculations, or a closed-shell state with a para-quinodimethane moiety in the as-indacene core. We observe switching between open- and closed-shell states of a single molecule by changing its adsorption site on NaCl.