Many-body Green Function Research Articles

Hybrid Materials: Electronic and Optical Excitations at the Pyridine/ZnO(101¯0) Hybrid Interface (Adv. Theory Simul. 2/2019)

Hybrid systems, combining inorganic and organic components, present an ex-citing pathway towards tailoring materials with specific desired properties. By a first-principles approach based on many-body Green function techniques, in article number 1800108, Olga Turkina, Claudia Draxl, and co-workers explore the opto-electronic spectra of pyridine/ZnO(1010). In this prototypical hybrid system, various kinds of novel exciton types are formed. The image shows the hole probability distribution of a hybrid charge-transfer exciton.

Magnetic Properties of Diluted Spinels Mg<i><sub>x</sub></i>Ni<sub>1−<i>x</i></sub>Fe<sub>2</sub>O<sub>4</sub> Systems: Are Studied by Green’s Functions and Mean Field Theories

Many-body Green's function, and mean field theories have been developed for magnetic systems MgxNi1−xFe2O4. We apply this theory to evaluate thermal magnetization and magnetic susceptibility for different values of magnetic field and dilution x, by considering all components of the magnetisation when an external magnetic field is applied in (x-z)-plane. The critical temperatures of MgxNi1−xFe2O4 systems in the range 0 ≤ x ≤ 1 have been deduced. The Green's function results are compared with the results of high temperature series expansion technique, and experimental magnetic measurements.

Development of the fragment-based COHSEX method for large and complex molecular systems

We present a fragment-based many-body Green's function method suitable for treating large molecular systems in heterogeneous polarizable environments. The Green's function for a total system is approximated from fragment Green's functions and is expanded up to two-body terms. The screened Coulomb potential is approximated from the sum of intrafragment density-response functions, with interfragment polarization terms being neglected. The approximations for the Green's function and screened Coulomb potential lead to a many-body expansion of the self-energy. This expansion is essentially equivalent to the many-body expansion of the Fock matrix in the fragment molecular orbital method. To handle large molecular systems, the present implementation relies on the Coulomb hole plus screened exchange (COHSEX) approximation for the $GW$ self-energy. The accuracy of the FMO-COHSEX method was demonstrated in comparison to conventional COHSEX results for organic molecular aggregates. We confirmed that the present fragmentation approximation can provide reasonably accurate results, and mean absolute errors for quasiparticle energies of less than 0.1 eV have been achieved for valence orbitals. We also assessed the accuracy of the COHSEX approximation to describe the effects of molecular aggregation of electronic states, by comparing them with the $GW$ method. The COHSEX approximation has been shown to successfully describe the induced polarization and dispersion effects. As an illustrative application of the present method, we considered the electronic states of the pentacene thin film, which contains 1476 atoms. We investigated the impact of the induced polarization effect in the heterogeneous environment, highlighting the gap renormalization and the polarization-induced localization. This application shows that the present fragment-based method is useful for studying electronic structures of molecular aggregates in complex environments.

Origin of the deep band-gap state in TiO2 (110): ddσ bonds between Ti-Ti pairs

Defects play crucial roles in the photonic and chemical activities of ${\mathrm{TiO}}_{2}$. The origin of the deep band-gap defect state ${S}_{bg}$ in the rutile ${\mathrm{TiO}}_{2}$(110) surface has remained controversial for quite a long time. Using many-body Green's function theory, we believe that ${S}_{bg}$ can be attributed only to $\ensuremath{\sigma}$ bonds formed between $3d$ orbitals at the Ti interstitial, while the nonbonded Ti $3d$ defect states from the oxygen vacancy and polaron, which are held to be responsible for ${S}_{bg}$ by the present prevailing view, are shallow regardless of their spatial distribution. Especially, we discover the defect-induced appreciable downshift of unoccupied Ti $3d$ bands which should be the key for accurately describing the electronic structure of ${\mathrm{TiO}}_{2}$ but was missed in previous studies based on density functional theory. Our model could more consistently and more reasonably account for various experimental phenomena on rutile (110) than the current model based on the oxygen vacancy and polaron.

Monte Carlo explicitly correlated many-body Green's function theory.

A highly scalable stochastic algorithm is proposed and implemented for computing the basis-set-incompleteness correction to the diagonal, frequency-independent self-energy of the second-order many-body Green's function (GF2) theory within the explicitly correlated (F12) formalism. The 6-, 9-, 12-, and 15-dimensional integrals comprising the F12 correction are directly evaluated by the Monte Carlo method using appropriate weight functions for importance sampling. The method is naturally and easily parallelized, involves minimal memory space and no disk I/O, and can use virtually any mathematical form of a correlation factor. Its computational cost to correct all ionization energies (IEs) is observed to increase as the fourth power of system size, as opposed to the fifth power in the case of the deterministic counterparts. The GF2 calculations and their F12 corrections for the first IEs of C60 and C70 were executed on 128 graphical processing units (GF2) and 896 central processing units (F12), respectively, to reach the results with statistical errors of 0.04 eV or less. They showed that the basis-set-incompleteness (from aug-cc-pVDZ) accounts for only 50%-60% of the deviations from experiments, suggesting the significance of higher-order perturbation corrections.

Electronic Excitations in Complex Molecular Environments: Many-Body Green's Functions Theory in VOTCA-XTP.

Many-body Green’s functions theory within the GW approximation and the Bethe-Salpeter Equation (BSE) is implemented in the open-source VOTCA-XTP software, aiming at the calculation of electronically excited states in complex molecular environments. Based on Gaussian-type atomic orbitals and making use of resolution of identity techniques, the code is designed specifically for nonperiodic systems. Application to a small molecule reference set successfully validates the methodology and its implementation for a variety of excitation types covering an energy range from 2 to 8 eV in single molecules. Further, embedding each GW-BSE calculation into an atomistically resolved surrounding, typically obtained from Molecular Dynamics, accounts for effects originating from local fields and polarization. Using aqueous DNA as a prototypical system, different levels of electrostatic coupling between the regions in this GW-BSE/MM setup are demonstrated. Particular attention is paid to charge-transfer (CT) excitations in adenine base pairs. It is found that their energy is extremely sensitive to the specific environment and to polarization effects. The calculated redshift of the CT excitation energy compared to a nucelobase dimer treated in vacuum is of the order of 1 eV, which matches expectations from experimental data. Predicted lowest CT energies are below that of a single nucleobase excitation, indicating the possibility of an initial (fast) decay of such an UV excited state into a binucleobase CT exciton. The results show that VOTCA-XTP’s GW-BSE/MM is a powerful tool to study a wide range of types of electronic excitations in complex molecular environments.

Resonant excitation of infrared emission in GaN:(Mn,Mg)

By combining experimental photoluminescence excitation spectroscopy and calculations based on density functional theory and many-body Green's functions, the most efficient excitation channels of infra-red (IR) emission from Mn-Mg$_{k}$ paramagnetic complexes stabilized in GaN:(Mn,Mg) are here identified. Moreover, a Tanabe-Sugano energy diagram for 3$d^{2}$Mn$ ^{5+}$ is reconstructed and Mn-Mg$_{3}$ are singled out as the predominant configurations responsible for the IR emission. The correlation of intensity of the individual emission lines as a function of temperature and excitation energy, allows assigning them to well defined and specific optical transitions.

Variation of optical spectra of water clusters with size from many-body Green's function theory.

Water clusters are an important species in the environment and atmosphere and take part in various chemical and biological reactions. How their optical properties vary with size is still an open question. Using the GW method and Bethe-Salpeter equation within the ab initio many-body Green's function theory, we study the electronic excitations in a series of water clusters (H2O)n with n = 1-48. We find that their absorption peaks blueshift with increasing cluster size due to the reducing electron-hole binding energy which arises from the enhanced electronic screening and gradually delocalized excitonic spatial distribution. The position of the first absorption peak has a close relation to the average number of hydrogen bonds per molecule. Off-diagonal matrix elements of the self-energy operator have pronounced effects on the unoccupied electronic levels and optical absorption for small clusters with n ≤ 10 when using density functional theory as the starting point for GW calculations. Although the optical absorption is predominated by delocalized excitons, highly localized excitons on a single water molecule are always present on the cluster surface in the vicinity of the absorption edge. These localized excitons may facilitate the photodissociation of water molecules. This can provide inspiration on the excited-state dynamics and photolysis in water clusters.

Tunable optical and excitonic properties of phosphorene via oxidation

The optical properties and excitonic wave function of phosphorene oxides (PO) are studied using the first principle many-body Green function and the Bethe–Salpeter equation formalism. In this work, the optical properties are determined using ab initio calculations of the dielectric function. At the long wavelength limit q of EM wave (i.e. ), the dielectric function, the absorption spectrum, the lectivity, the electron energy loss spectra (EELS) and the wave function are calculated. The results show an excitonic binding energy of 818 meV with a bright exciton located in the armchair direction in pristine phosphorene. For PO, the arrangement of the oxygen atoms significantly influences the optical properties. In particular, the absorption spectrum is extended along the solar spectrum, with a high absorption coefficient observed in the dangling structures. The maximum lectivity values are observed for the high energies of the light spectrum. Moreover, the first EELS peak is located in the visible region in all the structures except for one configuration that exhibits the same behavior as pure phosphorene. Finally, the exciton effect reveals that all PO conformers have a dark exciton state, which is suitable for long-lived applications.

Dynamical correlation effects in a weakly correlated material: Inelastic x-ray scattering and photoemission spectra of beryllium

Beryllium is a weakly correlated simple metal. Still we find that dynamical correlation effects, beyond the independent-particle picture, are necessary to successfully interpret the electronic spectra measured by inelastic x-ray scattering (IXS) and photoemission spectroscopies (PES). By combining ab initio time-dependent density-functional theory (TDDFT) and many-body Green's function theory in the $GW$ approximation ($GW\mathrm{A}$), we calculate the dynamic structure factor, the quasiparticle (QP) properties and PES spectra of bulk Be. We show that band-structure effects (i.e., due to interaction with the crystal potential) and QP lifetimes (LT) are both needed in order to explain the origin of the measured double-peak features in the IXS spectra. A quantitative agreement with experiment is obtained only when LT are supplemented to the adiabatic local-density approximation (ALDA) of TDDFT. Besides the valence band, PES spectra display a satellite, a signature of dynamical correlation due to the coupling of QPs and plasmons, which we are able to reproduce thanks to the combination of the $GW\mathrm{A}$ for the self-energy with the cumulant expansion of the Green's function.

A practical theoretical formalism for atomic multielectron processes: direct multiple ionization by a single auger decay or by impact of a single electron or photon

Multiple electron processes occur widely in atoms, molecules, clusters, and condensed matters when they are interacting with energetic particles or intense laser fields. Direct multielectron processes (DMEP) are the most complicated among the general multiple electron processes and are the most difficult to describe theoretically. In this work, a unified and accurate theoretical formalism is proposed on the DMEP of atoms including the multiple auger decay and multiple ionization by an impact of a single electron or a single photon based on the atomic collision theory described by a correlated many-body Green's function. Such a practical treatment is made possible by taking consideration of the different coherence features of the atoms (matter waves) in the initial and final states. We first explain how the coherence characteristics of the ejected continuum electrons is largely destructed, by taking the electron impact direct double ionization process as an example. The direct double ionization process is completely different from the single ionization where the complete interference can be maintained. The detailed expressions are obtained for the energy correlations among the continuum electrons and energy resolved differential and integral cross sections according to the separation of knock-out (KO) and shake-off (SO) mechanisms for the electron impact direct double ionization, direct double and triple auger decay, and double and triple photoionization (TPI) processes. Extension to higher order DMEP than triple ionization is straight forward by adding contributions of the following KO and SO processes. The approach is applied to investigate the electron impact double ionization processes of C+, N+, and O+, the direct double and triple auger decay of the K-shell excited states of C+ and , and the double and TPI of lithium. Comparisons with the experimental and other theoretical investigations wherever available in the literature show that our theoretical formalism is accurate and effective in treating the atomic multielectron processes.

Accurate description of charged excitations in molecular solids from embedded many-body perturbation theory

We present a novel hybrid quantum/classical approach to the calculation of charged excitations in molecular solids based on the many-body Green's function $GW$ formalism. Molecules described at the $GW$ level are embedded into the crystalline environment modeled with an accurate classical polarizable scheme. This allows the calculation of electron addition and removal energies in the bulk and at crystal surfaces where charged excitations are probed in photoelectron experiments. By considering the paradigmatic case of pentacene and perfluoropentacene crystals, we discuss the different contributions from intermolecular interactions to electronic energy levels, distinguishing between polarization, which is accounted for combining quantum and classical polarizabilities, and crystal field effects, that can impact energy levels by up to $\ifmmode\pm\else\textpm\fi{}0.6$ eV. After introducing band dispersion, we achieve quantitative agreement (within 0.2 eV) on the ionization potential and electron affinity measured at pentacene and perfluoropentacene crystal surfaces characterized by standing molecules.

The Bethe-Salpeter equation in chemistry: relations with TD-DFT, applications and challenges.

We review the many-body Green's function Bethe-Salpeter equation (BSE) formalism that is rapidly gaining importance for the study of the optical properties of molecular organic systems. We emphasize in particular its similarities and differences with time-dependent density functional theory (TD-DFT), both methods sharing the same formal O(N4) computing time scaling with system size. By comparison with higher level wavefunction based methods and experimental results, the advantages of BSE over TD-DFT are presented, including an accurate description of charge-transfer states and an improved accuracy for the challenging cyanine dyes. We further discuss the models that have been developed for including environmental effects. Finally, we summarize the challenges to be faced so that BSE reaches the same popularity as TD-DFT.

Where do photogenerated holes at the g-C3N4/water interface go for water splitting: H2O or OH-?

Graphitic carbon nitride (g-C3N4), a metal-free two-dimensional photocatalyst, has drawn increasing attention due to its application in photocatalytic water splitting. However, its quantum efficiency is limited by the poor performance of the oxygen evolution reaction (OER). Therefore, it is important to clarify the behavior of photogenerated holes in the OER. In this work, we investigate the energy level alignment using the GW method and the exciton properties using the Bethe-Salpeter equation within the ab initio many-body Green's function theory at the g-C3N4/water interface. We found that the g-C3N4 substrate can elevate energy levels of OH- and H2O molecules at the interface by up to 0.6 eV. This effect can make the electronic levels of OH- surpass the valence band maximum (VBM) of g-C3N4. However, orbital energies of H2O molecules remain far below the VBM of g-C3N4. This indicates that a photogenerated hole after exciting g-C3N4 can relax to OH- instead of neutral H2O. Moreover, OH- could be directly oxidized through electron transfer from OH- to g-C3N4 by light near the optical absorption edge of g-C3N4, which is beneficial for efficient carrier separation at the interface.

Quasiparticle Band Structures of Defects in Anatase TiO2 Bulk

Quasiparticle band structures of the defective anatase TiO2 bulk with O vacancy, Ti interstitial and H interstitial are investigated by the GW method within many-body Green's function theory. The computed direct band gap of the perfect anatase bulk is 4.3 eV, far larger than the experimental optical absorption edge (3.2 eV). We found that this can be ascribed to the inherent defects in anatase which drag the conduction band (CB) edge down. The occupied band-gap states induced by these defects locate close to the CB edge, excluding the possible contribution of these bulk defects to the deep band-gap state below CB as observed in experiments.

Combining Density Functional Theory and Green's Function Theory: Range-Separated, Nonlocal, Dynamic, and Orbital-Dependent Hybrid Functional.

We present a rigorous framework which combines single-particle Green's function theory with density functional theory based on a separation of electron-electron interactions into short- and long-range components. Short-range contribution to the total energy and exchange-correlation potential is provided by a density functional approximation, while the long-range contribution is calculated using an explicit many-body Green's function method. Such a hybrid results in a nonlocal, dynamic, and orbital-dependent exchange-correlation functional of a single-particle Green's function. In particular, we present a range-separated hybrid functional called srSVWN5-lrGF2 which combines the local-density approximation and the second-order Green's function theory. We illustrate that similarly to density functional approximations, the new functional is weakly basis-set dependent. Furthermore, it offers an improved description of the short-range dynamic correlation. The many-body contribution to the functional mitigates the many-electron self-interaction error present in many density functional approximations and provides a better description of molecular properties. Additionally, we illustrate that the new functional can be used to scale down the self-energy and, therefore, introduce an additional sparsity to the self-energy matrix that in the future can be exploited in calculations for large molecules or periodic systems.

Quasiparticle energies and dielectric functions of diamond polytypes

We perform ab initio many-body Green's function calculations to investigate the quasiparticle energies and optical properties of diamond polytypes that have been predicted to be producible via a pressure-induced structural phase transition from carbon nanotube solids. We find, through quasiparticle band-structure calculations within the $GW$ approximation, that the band gaps of two hexagonal $(2H$- and $4H$-type) polytypes of diamond differ significantly from that of cubic diamond as well as from that of the crystalline $s{p}^{3}$ carbon phase with a body-centered-tetragonal structure, called bct ${\mathrm{C}}_{4}$. We also examine the dielectric functions of three polytypes of diamond (cubic, $2H$, and $4H)$ by employing the $GW$ plus Bethe-Salpeter equation approach. The calculated optical absorption spectra are found to be distinct from each other. The lattice mismatches of carbon layers of these diamond polytypes are very small and the total-energy differences are also small. Our work opens up the possibility of fabricating diamond superlattices with various electronic and optoelectronic properties by utilizing and controlling the different stacking sequences of carbon layers.

Theoretical S1 ← S0 Absorption Energies of the Anionic Forms of Oxyluciferin by Variational Monte Carlo and Many-Body Green's Function Theory.

The structures of three negatively charged forms (anionic keto-1 and enol-1 and dianionic enol-2) of oxyluciferin (OxyLuc), which are the most probable emitters responsible for the firefly bioluminescence, have been fully relaxed at the variational Monte Carlo (VMC) level. Absorption energies of the S1 ← S0 vertical transition have been computed using different levels of theory, such as TDDFT, CC2, and many-body Green's function theory (MBGFT). The use of MBGFT, by means of the Bethe-Salpeter (BS) formalism, on VMC structures provides results in excellent agreement with the value (2.26(8) eV) obtained by action spectroscopy experiments for the keto-1 form (2.32 eV). To unravel the role of the quality of the optimized ground-state geometry, BS excitation energies have also been computed on CASSCF geometries, inducing a non-negligible blue shift (0.08 and 0.07 eV for keto-1 and enol-1 forms, respectively) with respect to the VMC ones. Structural effects have been analyzed in terms of over- or undercorrelation along the conjugated bonds of OxyLuc by using different methods for the ground-state optimization. The relative stability of the S1 state for the keto-1 and enol-1 forms depends on the method chosen for the excited-state calculation, thus representing a fundamental caveat for any theoretical study on these systems. Finally, Kohn-Sham HOMO and LUMO orbitals of enol-2 are (nearly) bound only when the dianion is embedded into a solvent (water and toluene in the present work); excited-state calculations are therefore meaningful only in the presence of a dielectric medium which localizes the electronic density. The combination of VMC for the ground-state geometry and BS formalism for the absorption spectra clearly outperforms standard TDDFT and quantum chemistry approaches.

The one step fermionic ladder

The one step fermionic ladder refers to two parallel Luttinger Liquids (poles of the ladder) placed such that there is a finite probability of electrons hopping between the two poles at a pair of opposing points along each of the poles. The many-body Green function for such a system is calculated in presence of forward scattering interactions using the powerful non-chiral bosonization technique (NCBT). This technique is based on a non-standard harmonic analysis of the rapidly varying parts of the density fields appropriate for the study of strongly inhomogeneous ladder systems. The closed analytical expression for the correlation function obtained from NCBT is nothing but the series involving the RPA (Random Phase Approximation) diagrams in powers of the forward scattering coupling strength resummed to include only the most singular terms with the source of inhomogeneities treated exactly. Finally the correlation functions are used to study physical phenomena such as Friedel oscillations and the conductance of such systems with the potential difference applied across various ends.

One-particle many-body Green's function theory: Algebraic recursive definitions, linked-diagram theorem, irreducible-diagram theorem, and general-order algorithms.

A thorough analytical and numerical characterization of the whole perturbation series of one-particle many-body Green's function (MBGF) theory is presented in a pedagogical manner. Three distinct but equivalent algebraic (first-quantized) recursive definitions of the perturbation series of the Green's function are derived, which can be combined with the well-known recursion for the self-energy. Six general-order algorithms of MBGF are developed, each implementing one of the three recursions, the ΔMPn method (where n is the perturbation order) [S. Hirata et al., J. Chem. Theory Comput. 11, 1595 (2015)], the automatic generation and interpretation of diagrams, or the numerical differentiation of the exact Green's function with a perturbation-scaled Hamiltonian. They all display the identical, nondivergent perturbation series except ΔMPn, which agrees with MBGF in the diagonal and frequency-independent approximations at 1≤n≤3 but converges at the full-configuration-interaction (FCI) limit at n=∞ (unless it diverges). Numerical data of the perturbation series are presented for Koopmans and non-Koopmans states to quantify the rate of convergence towards the FCI limit and the impact of the diagonal, frequency-independent, or ΔMPn approximation. The diagrammatic linkedness and thus size-consistency of the one-particle Green's function and self-energy are demonstrated at any perturbation order on the basis of the algebraic recursions in an entirely time-independent (frequency-domain) framework. The trimming of external lines in a one-particle Green's function to expose a self-energy diagram and the removal of reducible diagrams are also justified mathematically using the factorization theorem of Frantz and Mills. Equivalence of ΔMPn and MBGF in the diagonal and frequency-independent approximations at 1≤n≤3 is algebraically proven, also ascribing the differences at n = 4 to the so-called semi-reducible and linked-disconnected diagrams.