Many-body Green's Function Theory Research Articles

Graphene with suitable-size nitrogen-doped cavity being an excellent photocatalyst for proton-coupled electron transfer in water splitting

Aiming to attain porous carbon nitride photocatalysts with high specific surface area, abundant active sites, broad absorption range and effective electron-hole separation, we remove carbon rings from graphene and replace all the edge carbon atoms of the cavity with nitrogen atoms. The accurate electronic structures and exciton properties of the proposed materials are revealed by the ab initio many-body Green's function theory. Computational results show that the absorption of the designed materials can cover both the visible and the near-infrared light region. The exciton binding energies of the materials are one order of magnitude lower than those of the typical two-dimensional photocatalyst graphitic carbon nitride. Due to the formation of hydrogen bonds between pyridinic nitrogen atoms and water molecules during water splitting, the key excited-state proton-coupled electron transfer reactions are barrierless. These findings could serve as guidelines for the realization of high-performance metal-free two-dimensional photocatalysts.

BSE@GW Prediction of Charge Transfer Exciton in Molecular Complexes: Assessment of Self-Energy and Exchange-Correlation Dependence.

The Bethe-Salpeter equation using the GW approximation to the self-energy (BSE@GW) is a computationally attractive method for studying electronic excitation from first principles within the many-body Green's function theory framework. We examine its dependence on the underlying exchange-correlation (XC) approximation as well as on the GW approximation for predicting the charge transfer exciton formation at representative type-II interfaces between molecular systems of tetrachloro-1,2-benzoquinone (TCBQ) and acene derivatives. For the XC approximation, we consider several widely used generalized gradient approximation (GGA) and hybrid GGA functionals. For the GW self-energy approximation, we examine the recently proposed renormalized singles approach by Yang and coauthors [J. Phys. Chem. Lett. 2019, 10 (3), 447-452; J. Chem. Theory Comput. 2022, 18, 7570-7585] in addition to other commonly employed approximated GW schemes. We demonstrate a reliable prediction of the charge transfer exciton within the BSE@GW level of theory.

Electronic Couplings and Conversion Dynamics between Localized and Charge Transfer Excitations from Many-Body Green's Functions Theory.

We investigate the determination of electronic coupling between localized excitations (LEs) and charge-transfer (CT) excitations based on many-body Green's functions theory in the GW approximation with the Bethe-Salpeter equation (GW-BSE). Using a small molecule dimer system, we first study the influence of different diabatization methods, as well as different model choices within GW-BSE, such as the self-energy models or different levels of self-consistency, and find that these choices affect the LE-CT couplings only minimally. We then consider a large-scale low-donor morphology formed from rubrene and fullerene and evaluate the LE-CT couplings based on coupled GW-BSE-molecular mechanics calculations. For these disordered systems of bulky molecules, we observe differences in the couplings based on the Edmiston-Ruedenberg diabatization compared to the more approximate Generalize Mulliken-Hush and fragment charge difference diabatization formalisms. In a kinetic model for the conversion between LE and CT states, these differences affect the details of state populations in an intermediate time scale but not the final populations.

Many-Body Green's Function Theory for Electronic Excitations in Complex Chemical Systems.

The GW method and the Bethe-Salpeter equation (BSE) have exhibited excellent performance in computing charged and neutral electronic excitations in materials of various dimensions in the past decades. Extensive benchmark studies have demonstrated that their precision can reach the level of high-level ab initio wave function approaches with a much lower computational cost. GW and BSE outperform the density functional theory because of both the more accurate electronic structures in GW and the capability to treat local, charge-transfer, and Rydberg excitations on the same footing in BSE. Presently, they are the only available first-principles approaches that can study electronic excitations at the surface and in the interior of periodic systems and at the interface between periodic systems with reliable accuracy. In this Perspective, a brief overview of GW and BSE and their applications in complex chemical systems is provided, with the goal of boosting their broader utilization in chemistry.

Exact factorization of the many-body Green's function theory of electrons and nuclei

We combine the recently developed many-body Green's function theory for electrons and nuclei with the exact factorization of the wave function. The existing Born-Oppenheimer Green's functions are shown to be special cases of our exact approach. We consider the limitations of the laboratory frame formulation of the Green's function theory and discuss why the body-fixed frame formulation is needed in order to go beyond the Born-Oppenheimer theory. We give exact forms of the electronic and nuclear Green's functions written in terms of the exact factorized states, providing a systematic approach beyond the Born-Oppenheimer approximation. The lowest order approximation to the exact electronic Green's function is found to be an expected value of the Born-Oppenheimer electronic Green's function with respect to the nuclear density.

The charge-transfer states and excitation energy transfers of halogen-free organic molecules from first-principles many-body Green’s function theory

The organic solar cells based on halogen-free components, have been the new favorites to develop green and renewable energy. PBDB-T and its derivatives are considered the superior electron donors to construct the solar cells. Although there are plenty of researches about them, the charge-transfer mechanisms and excitation energy transfers of relative organic solar cells are still unclear, the developments of photovoltaic devices are restricted consequently. In this work, we calculate the electronic structures and excited-state properties of PBDB-T, PBT1-C, PBT1-O and PBT1-S donors in the gas phase from the many-body Green's function theory. With BTP-IC and BTP-IS as the acceptors, we consider the Förster, Dexter, and overlap electronic couplings to compute the excitation energy transfers of the dimers. The ionization energies and excited-state energies of the four donors calculated by GW + BSE are in good agreement with experiments, and they are sensitive to the functionals in the computation. We find two charge transfer schemes. The thienyl of PBDB-T molecule makes its charge-transfer state at the lowest energy, and the total electronic coupling of PBDB-T based dimer is the strongest. The Dexter, and overlap types electronic couplings are significant to study the excitation energy transfer of organic heterojunctions. We provide a theoretical guide in the design and synthesis of higher-performance halogen-free donors.

Unified Approach to Polarons and Phonon-Induced Band Structure Renormalization.

Abinitio calculations of the phonon-induced band structure renormalization are currently based on the perturbative Allen-Heine theory and its many-body generalizations. These approaches are unsuitable to describe materials where electrons form localized polarons. Here, we develop a self-consistent, many-body Green's function theory of band structure renormalization that incorporates localization and self-trapping. We show that the present approach reduces to the Allen-Heine theory in the weak-coupling limit, and to total energy calculations of self-trapped polarons in the strong-coupling limit. To demonstrate this methodology, we reproduce the path-integral results of Feynman and diagrammatic MonteCarlo calculations for the Fröhlich model at all couplings, and we calculate the zero point renormalization of the band gap of an ionic insulator including polaronic effects.

Reactivity of anatase (001) surface from first-principles many-body Green's function theory

The anatase (001) surface has attracted a lot of interest in surface science due to its excellent performance. However, its reactivity is under debate since it can undergo a (1 × 4) reconstruction. Herein, we applied the many-body Green's function theory to investigate the electronic properties and excitons as well as the water adsorption behavior of the (1 × 4) unreconstructed anatase (001) surface and two reconstructed patterns, namely ADM and AOM. Our results revealed that the high reactivity of the (001) surface is probably not relevant to the reconstructed shape. The unreconstructed (001) surface and reconstructed ADM surface were very reactive for dissociating H2O molecules among three surfaces, but the lower-energy singlet exciton for ADM was completely confined within the inner atomic layers in TiO2, which is unfavorable for hole transfer to the reactant on the surface. Also, the required photon energy for initiating photochemical reactions on the reconstructed ADM surface should be higher than for the unreconstructed (001) surface, implying it is more difficult for the reaction to happen on the former surface. The unreconstructed (001) surface exhibited the highest reactivity due to the smaller optical absorption edge and the photoholes distributed on surface sites.

Ab initio modeling of phonon-assisted relaxation of electrons and excitons in semiconductor nanocrystals for multiexciton generation

Electron-phonon and exciton-phonon interactions in nanoclusters are formulated and computed under the framework of GW-BSE (Bethe-Salpeter equation) approach. The phonon effect is modeled with the two-particle representation for the first time. The nonradiative relaxation rates of electrons and excitons are calculated. It is uncovered that both single-phonon relaxation and multiple-phonon relaxation are significant in nanocrystals, and correspond to two types of physical processes that have totally different spectral lineshapes. Furthermore, the multiple-phonon relaxation always occurs and its rates are comparable to the corresponding single-phonon relaxation rates for both electrons and excitons in the system studied (Si46). The inelastic scattering rates of electrons and excitons are also calculated based on many-body Green function theory. For the electronic states in Si46, the inelastic scattering decay is predicted to be a primary decay mechanism for multiexciton relaxation, and nonradiative relaxation rates are larger than inelastic scattering rates for most excitonic states in Si46.

Many-body Green's function theory of electrons and nuclei beyond the Born-Oppenheimer approximation

The method of many-body Green's functions is developed for arbitrary systems of electrons and nuclei starting from the full (beyond Born-Oppenheimer) Hamiltonian of Coulomb interactions and kinetic energies. The theory presented here resolves the problems arising from the translational and rotational invariance of this Hamiltonian that afflict the existing many-body Green's function theories. We derive a coupled set of exact equations for the electronic and nuclear Green's functions and provide a systematic way to approximately compute the properties of arbitrary many-body systems of electrons and nuclei beyond the Born-Oppenheimer approximation. The case of crystalline solids is discussed in detail.

Multiscale simulations of singlet and triplet exciton dynamics in energetically disordered molecular systems based on many-body Green's functions theory

We present a multiscale model based on many-body Green’s functions theory in the GW approximation and the Bethe–Salpeter equation (GW-BSE) for the simulation of singlet and triplet exciton transport in molecular materials. Dynamics of coupled electron–hole pairs are modeled as a sequence of incoherent tunneling and decay events in a disordered morphology obtained at room temperature from molecular dynamics. The ingredients of the rates associated to the events, i.e. reorganization energies, site energies, lifetimes, and coupling elements, are determined from a combination of GW-BSE and classical polarizable force field techniques. Kinetic Monte Carlo simulations are then employed to evaluate dynamical properties such as the excitonic diffusion tensor and diffusion lengths. Using DCV5T-Me(3,3), a crystalline organic semiconductor, we demonstrate how this multiscale approach provides insight into the fundamental factors driving the transport processes. Comparing the results obtained via different calculation models, we investigate in particular the effects of charge-transfer mediated high exciton coupling and the influence of internal site energy disorder due to conformational variations. We show that a small number of high coupling elements indicative of delocalized exciton states does not impact the overall dynamics perceptively. Molecules with energies in the tail of the excitonic density of states dominate singlet decay, independent of the level of disorder taken into account in the simulation. Overall, our approach yields singlet diffusion lengths on the order of 10 nm as expected for energetically disordered molecular materials.

Quantitative predictions of photoelectron spectra in amorphous molecular solids from multiscale quasiparticle embedding

We present a first-principles-based multiscale simulation framework for quantitative predictions of the high-energy part of the Ultraviolet Photoelectron Spectroscopy (UPS) spectra of amorphous molecular solids. The approach combines a deposition simulation, many-body Green's Function Theory, polarizable film-embedding, and multimode electron-vibrational coupling and provides a molecular-level view on the interactions and processes giving rise to spectral features. This insight helps bridging the current gap between experimental UPS and theoretical models as accurate analyses are hampered by the energetic disorder, surface-sensitivity of the measurement and the complexity of excitation processes. In particular this is relevant for the unambiguous determination the highest occupied molecular orbital energy (HOMO) of organic semiconductors, a key quantity for tailoring and engineering new opto-electronic devices. We demonstrate the capabilities of the simulation approach studying the spectrum of two isomers of 2-methyl-9,10-bis(naphthalen-2-yl)anthracene (MADN) as archetypical materials showing a clearly separated HOMO peak in experiment. The agreement with experiment is excellent, suggesting that our approach provides a route for determining the HOMO energy with an accuracy better than 0.1eV.

Electronic energy transfer studied by many-body Green's function theory.

We present a combination of many-body Green's function theory and Förster-Dexter theory to estimate the excitation energy transfer (EET) coupling in both the isolated and condensed systems. This approach employs the accurate wave functions of excitons, which are derived from the Bethe-Salpeter equation, in the donor and acceptor to set up the electronic coupling terms. Dexter coupling, which arises from the exchange-correlation effect, is evaluated based on the GW method which is a state-of-the-art ab initio theory for the description of self-energy. This approach is applicable to various situations, especially for periodic systems. The approach is tested on some model molecular dimers and compared with other high-level quantum chemistry methods together with the exact supermolecule scheme. Finally, we apply it to study the EET between periodic single-walled carbon nanotubes, exploring the dependence of EET on the chirality of nanotubes and the type of excitation transferred, finding that dark states play key roles in the EET between nanotubes. The EET rate falls as ∼D-12 approximately with the distance D between nanotubes for small D, much faster than the traditional Förster model.

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.

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.

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.

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.