Many-body Green's Function Theory Research Articles

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.

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.

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.

Theoretical Determination of Band Edge Alignments at the Water-CuInS2(112) Semiconductor Interface.

Knowledge of a semiconductor electrode's band edge alignment is essential for optimizing processes that occur at the semiconductor/electrolyte interface. Photocatalytic processes are particularly sensitive to such alignments, as they govern the transfer of photoexcited electrons or holes from the surface to reactants in the electrolyte solution. Reconstructions of a semiconductor surface during operation, as well as its interaction with the electrolyte solution, must be considered when determining band edge alignment. Here, we employ density functional theory + U theory to assess the stability of reconstructed CuInS2 surfaces, a system which has shown promise for the active and selective photoelectrocatalytic reduction of CO2 to CH3OH. Using many-body Green's function theory combined with calculations of surface work functions, we determine band edge positions of explicitly solvated, reconstructed CuInS2 surfaces. We find that there is a linear relationship between band edge position and net surface dipole, with the most stable solvent/surface structures tending to minimize this dipole because of generally weak interactions between the surface and solvating water molecules. We predict a conduction band minimum (CBM) of the solvated, reconstructed CuInS2 surface of -2.44 eV vs vacuum at the zero-dipole intercept of the dipole/CBM trendline, in reasonable agreement with the experimentally reported CBM position at -2.64 eV vs vacuum. This methodology offers a simplified approach for approximating the band edge positions at complex semiconductor/electrolyte interfaces.

Intermolecular Singlet and Triplet Exciton Transfer Integrals from Many-Body Green's Functions Theory.

A general approach to determine orientation and distance-dependent effective intermolecular exciton transfer integrals from many-body Green’s functions theory is presented. On the basis of the GW approximation and the Bethe–Salpeter equation (BSE), a projection technique is employed to obtain the excitonic coupling by forming the expectation value of a supramolecular BSE Hamiltonian with electron–hole wave functions for excitations localized on two separated chromophores. Within this approach, accounting for the effects of coupling mediated by intermolecular charge transfer (CT) excitations is possible via perturbation theory or a reduction technique. Application to model configurations of pyrene dimers shows an accurate description of short-range exchange and long-range Coulomb interactions for the coupling of singlet and triplet excitons. Computational parameters, such as the choice of the exchange-correlation functional in the density-functional theory (DFT) calculations that underly the GW-BSE steps and the convergence with the number of included CT excitations, are scrutinized. Finally, an optimal strategy is derived for simulations of full large-scale morphologies by benchmarking various approximations using pairs of dicyanovinyl end-capped oligothiophenes (DCV5T), which are used as donor material in state-of-the-art organic solar cells.

Low-rank canonical-tensor decomposition of potential energy surfaces: application to grid-based diagrammatic vibrational Green's function theory

ABSTRACTA new method is proposed for a fast evaluation of high-dimensional integrals of potential energy surfaces (PES) that arise in many areas of quantum dynamics. It decomposes a PES into a canonical low-rank tensor format, reducing its integral into a relatively short sum of products of low-dimensional integrals. The decomposition is achieved by the alternating least squares (ALS) algorithm, requiring only a small number of single-point energy evaluations. Therefore, it eradicates a force-constant evaluation as the hotspot of many quantum dynamics simulations and also possibly lifts the curse of dimensionality. This general method is applied to the anharmonic vibrational zero-point and transition energy calculations of molecules using the second-order diagrammatic vibrational many-body Green's function (XVH2) theory with a harmonic-approximation reference. In this application, high dimensional PES and Green's functions are both subjected to a low-rank decomposition. Evaluating the molecular integrals over a low-rank PES and Green's functions as sums of low-dimensional integrals using the Gauss–Hermite quadrature, this canonical-tensor-decomposition-based XVH2 (CT-XVH2) achieves an accuracy of 0.1 cm−1 or higher and nearly an order of magnitude speedup as compared with the original algorithm using force constants for water and formaldehyde.

Solvent effects on optical excitations of poly para phenylene ethynylene studied by QM/MM simulations based on many-body Green's functions theory

Electronic excitations in dilute solutions of poly para phenylene ethynylene (poly-PPE) are studied using a QM/MM approach combining many-body Green's functions theory within the $GW$ approximation and the Bethe-Salpeter equation with polarizable force field models. Oligomers up to a length of 7.5\,nm (10 repeat units) functionalized with nonyl side chains are solvated in toluene and water, respectively. After equilibration using atomistic molecular dynamics (MD), the system is partitioned into a quantum region (backbone) embedded into a classical (side chains and solvent) environment. Optical absorption properties are calculated solving the coupled QM/MM system self-consistently and special attention is paid to the effects of solvents. The model allows to differentiate the influence of oligomer conformation induced by the solvation from electronic effects related to local electric fields and polarization. It is found that the electronic environment contributions are negligible compared to the conformational dynamics of the conjugated PPE. An analysis of the electron-hole wave function reveals a sensitivity of energy and localization characteristics of the excited states to bends in the global conformation of the oligomer rather than to the relative of phenyl rings along the backbone.

Range-separated time-dependent density-functional theory with a frequency-dependent second-order Bethe-Salpeter correlation kernel.

We present a range-separated linear-response time-dependent density-functional theory (TDDFT) which combines a density-functional approximation for the short-range response kernel and a frequency-dependent second-order Bethe-Salpeter approximation for the long-range response kernel. This approach goes beyond the adiabatic approximation usually used in linear-response TDDFT and aims at improving the accuracy of calculations of electronic excitation energies of molecular systems. A detailed derivation of the frequency-dependent second-order Bethe-Salpeter correlation kernel is given using many-body Green-function theory. Preliminary tests of this range-separated TDDFT method are presented for the calculation of excitation energies of the He and Be atoms and small molecules (H2, N2, CO2, H2CO, and C2H4). The results suggest that the addition of the long-range second-order Bethe-Salpeter correlation kernel overall slightly improves the excitation energies.

Optical properties of acene molecules and pentacene crystal from the many-body Green's function method.

Acene is a type of important organic semiconductor which has promising applications in various optoelectronic devices. The fission of a singlet to triplet in it has been expected to elevate the quantum efficiency of organic solar cells. However, the quantum efficiency is still very low and the fission process is still under debate. Controversies also exist on the energies of the singlet and triplet states in acene. Using the many-body Green's function theory, which includes the GW method and Bethe-Salpeter equation (BSE), we compared the electronic excited states of several kinds of acene molecules (naphthalene to pentacene) at geometries optimized by different approaches. The energies of both the singlet and triplet depend strongly on the geometries of the molecules and their stacking. The non-negligible contribution from the resonant and anti-resonant transition coupling can cause large errors of the Tamm-Dancoff approximation, and the full BSE is required to get accurate results which are consistent with experiments. We found that accurate ionization energies and exciton energies can only be obtained when the geometries optimized by the Hartree-Fock approach are used. Singlet fission may be realized in isolated molecules, clusters, and surfaces, but it is hard in perfect pentacene crystals energetically. We provide a methodology for future research on acene-based solar cells and other optoelectronic devices.

Getting excited: challenges in quantum-classical studies of excitons in polymeric systems.

A combination of classical molecular dynamics (MM/MD) and quantum chemical calculations based on the density functional theory (DFT) was performed to describe the conformational properties of diphenylethyne (DPE), methylated-DPE and poly para phenylene ethynylene (PPE). DFT calculations were employed to improve and develop force field parameters for MM/MD simulations. Many-body Green's function theory within the GW approximation and the Bethe-Salpeter (GW-BSE) equation were utilized to describe the excited states of the systems. The reliability of the excitation energies based on the MM/MD conformations was examined and compared to the excitation energies from DFT conformations. The results show an overall agreement between the optical excitations based on MM/MD conformations and DFT conformations. This allows for the calculation of excitation energies based on MM/MD conformations.

Many-body Green's function theory for electron-phonon interactions: Ground state properties of the Holstein dimer.

We study ground-state properties of a two-site, two-electron Holstein model describing two molecules coupled indirectly via electron-phonon interaction by using both exact diagonalization and self-consistent diagrammatic many-body perturbation theory. The Hartree and self-consistent Born approximations used in the present work are studied at different levels of self-consistency. The governing equations are shown to exhibit multiple solutions when the electron-phonon interaction is sufficiently strong, whereas at smaller interactions, only a single solution is found. The additional solutions at larger electron-phonon couplings correspond to symmetry-broken states with inhomogeneous electron densities. A comparison to exact results indicates that this symmetry breaking is strongly correlated with the formation of a bipolaron state in which the two electrons prefer to reside on the same molecule. The results further show that the Hartree and partially self-consistent Born solutions obtained by enforcing symmetry do not compare well with exact energetics, while the fully self-consistent Born approximation improves the qualitative and quantitative agreement with exact results in the same symmetric case. This together with a presented natural occupation number analysis supports the conclusion that the fully self-consistent approximation describes partially the bipolaron crossover. These results contribute to better understanding how these approximations cope with the strong localizing effect of the electron-phonon interaction.

Comparison of the effect of the exchange and single-ion anisotropy on the magnetic properties of thin ferromagnetic films

Using the many-body Green function theory, we caculate the magnetic reorientation temperature and the anisotropic parallel susceptibility of ferromagnetic Heisenberg thin films with the exchange and single-ion anisotropy. Particularly, we compare the effect of these anisotropies on the above mentioned observables. On the basis of our results, one cannot generally claim that these anisotropies are equivalent in the whole rangle of their parameters.

Excitons and Davydov splitting in sexithiophene from first-principles many-body Green's function theory.

Organic semiconductors have promising and broad applications in optoelectronics. Understanding their electronic excited states is important to help us control their spectroscopic properties and performance of devices. There have been a large amount of experimental investigations on spectroscopies of organic semiconductors, but theoretical calculation from first principles on this respect is still limited. Here, we use density functional theory (DFT) and many-body Green's function theory, which includes the GW method and Bethe-Salpeter equation, to study the electronic excited-state properties and spectroscopies of one prototypical organic semiconductor, sexithiophene. The exciton energies of sexithiophene in both the gas and bulk crystalline phases are very sensitive to the exchange-correlation functionals used in DFT for ground-state structure relaxation. We investigated the influence of dynamical screening in the electron-hole interaction on exciton energies, which is found to be very pronounced for triplet excitons and has to be taken into account in first principles calculations. In the sexithiophene single crystal, the energy of the lowest triplet exciton is close to half the energy of the lowest singlet one. While lower-energy singlet and triplet excitons are intramolecular Frenkel excitons, higher-energy excitons are of intermolecular charge-transfer type. The calculated optical absorption spectra and Davydov splitting are in good agreement with experiments.

A systematic benchmark of the ab initio Bethe-Salpeter equation approach for low-lying optical excitations of small organic molecules.

The predictive power of the ab initio Bethe-Salpeter equation (BSE) approach, rigorously based on many-body Green's function theory but incorporating information from density functional theory, has already been demonstrated for the optical gaps and spectra of solid-state systems. Interest in photoactive hybrid organic/inorganic systems has recently increased and so has the use of the BSE for computing neutral excitations of organic molecules. However, no systematic benchmarks of the BSE for neutral electronic excitations of organic molecules exist. Here, we study the performance of the BSE for the 28 small molecules in Thiel's widely used time-dependent density functional theory benchmark set [Schreiber et al., J. Chem. Phys. 128, 134110 (2008)]. We observe that the BSE produces results that depend critically on the mean-field starting point employed in the perturbative approach. We find that this starting point dependence is mainly introduced through the quasiparticle energies obtained at the intermediate GW step and that with a judicious choice of starting mean-field, singlet excitation energies obtained from BSE are in excellent quantitative agreement with higher-level wavefunction methods. The quality of the triplet excitations is slightly less satisfactory.

Putting DFT to the test: a first-principles study of electronic, magnetic, and optical properties of Co3O4.

First-principles density functional theory (DFT) and a many-body Green's function method have been employed to elucidate the electronic, magnetic, and photonic properties of a spinel compound, Co3O4. Co3O4 is an antiferromagnetic semiconductor composed of cobalt ions in the Co(2+) and Co(3+) oxidation states. Co3O4 is believed to be a strongly correlated material, where the on-site Coulomb interaction (U) on Co d orbitals is presumably important, although this view has recently been contested. The suggested optical band gap for this material ranges from 0.8 to 2.0 eV, depending on the type of experiments and theoretical treatment. Thus, the correlated nature of the Co d orbitals in Co3O4 and the extent of the band gap are still under debate, raising questions regarding the ability of DFT to correctly treat the electronic structure in this material. To resolve the above controversies, we have employed a range of theoretical methods, including pure DFT, DFT+U, and a range-separated exchange-correlation functional (HSE06) as well as many-body Green's function theory (i.e., the GW method). We compare the electronic structure and band gap of Co3O4 with available photoemission spectroscopy and optical band gap data and confirm a direct band gap of ca. 0.8 eV. Furthermore, we have also studied the optical properties of Co3O4 by calculating the imaginary part of the dielectric function (Im(ε)), facilitating direct comparison with the measured optical absorption spectra. Finally, we have calculated the nearest-neighbor interaction (J1) between Co(2+) ions to understand the complex magnetic structure of Co3O4.

Ferromagnetism and metal-half-metal-insulator transitions in a frustrated periodic Anderson-like organic polymer

Abstract The ferromagnetism and quantum phase transitions of a periodic Anderson-like organic polymer, in which the next-nearest-neighboring hopping results in frustration, are investigated by means of many-body Green's function theory. It is found that the ground state lies in half-metallic and paramagnetic metallic states for weak and relatively strong frustrations, respectively. At finite temperatures, a ferrimagnetic order and two different ferromagnetic phases are unveiled. In a magnetic field, in addition to 1/3 magnetization plateau, it presents three cusps and three critical fields indicating metal-half-metal and half-metal-insulator transitions, respectively, which are closely related to the energy bands controlled by the field.

Electronic Excitations in Push–Pull Oligomers and Their Complexes with Fullerene from Many-Body Green’s Functions Theory with Polarizable Embedding

We present a comparative study of excited states in push-pull oligomers of PCPDTBT and PSBTBT and prototypical complexes with a C60 acceptor using many-body Green's functions theory within the GW approximation and the Bethe-Salpeter equation. We analyze excitations in oligomers up to a length of 5 nm and find that for both materials the absorption energy practically saturates for structures larger than two repeat units due to the localized nature of the excitation. In the bimolecular complexes with C60, the transition from Frenkel to charge transfer excitons is generally exothermic and strongly influenced by the acceptor's position and orientation. The high CT binding energy of the order of 2 eV results from the lack of an explicit molecular environment. External polarization effects are then modeled in a GW-BSE based QM/MM approach by embedding the donor-acceptor complex into a polarizable lattice. The lowest charge transfer exciton is energetically stabilized by about 0.5 eV, while its binding energy is reduced to about 0.3 eV. We also identify a globally unbound charge transfer state with a more delocalized hole at higher energy while still within the absorption spectrum, which opens another potential pathway for charge separation. For both PCPDTBT and PSBTBT, the energetics are largely similar with respect to absorption and the driving force to form intermediate charge transfer excitations for free charge generation. These results support that the higher power conversion efficiency observed for solar cells using PSBTBT as donor material is a result of molecular packing rather than of the electronic structure of the polymer.

Charge-transfer excited states in aqueous DNA: Insights from many-body Green's function theory.

Charge-transfer (CT) excited states play an important role in the excited-state dynamics of DNA in aqueous solution. However, there is still much controversy on their energies. By ab initio many-body Green's function theory, together with classical molecular dynamics simulations, we confirm the existence of CT states at the lower energy side of the optical absorption maximum in aqueous DNA as observed in experiments. We find that the hydration shell can exert strong effects (∼1 eV) on both the electronic structure and CT states of DNA molecules through dipole electric fields. In this case, the solvent cannot be simply regarded as a macroscopic screening medium as usual. The influence of base stacking and base pairing on the CT states is also discussed.

Ab Initio Geometry and Bright Excitation of Carotenoids: Quantum Monte Carlo and Many Body Green's Function Theory Calculations on Peridinin.

In this letter, we report the singlet ground state structure of the full carotenoid peridinin by means of variational Monte Carlo (VMC) calculations. The VMC relaxed geometry has an average bond length alternation of 0.1165(10) Å, larger than the values obtained by DFT (PBE, B3LYP, and CAM-B3LYP) and shorter than that calculated at the Hartree-Fock (HF) level. TDDFT and EOM-CCSD calculations on a reduced peridinin model confirm the HOMO-LUMO major contribution of the Bu(+)-like (S2) bright excited state. Many Body Green's Function Theory (MBGFT) calculations of the vertical excitation energy of the Bu(+)-like state for the VMC structure (VMC/MBGFT) provide an excitation energy of 2.62 eV, in agreement with experimental results in n-hexane (2.72 eV). The dependence of the excitation energy on the bond length alternation in the MBGFT and TDDFT calculations with different functionals is discussed.

Magnetic properties of ferromagnetic diluted Zn x Cd1–x Cr2Se4 spinels are studied by Green's functions, mean field theory and high temperature series expansions theories

The field induced reorientation of the magnetization of ferromagnetic (or antiferromagnetic) structure is treated within the framework of many-body Green's function theory by considering all components of the magnetization. The mean field theory is used to calculate the nearest neighbour and the next-neighbour super-exchange J1(Cr–Cr) and J2(Cr–(Zn(Cd)–Se)–Cr), respectively, for the Zn1–x Cd x Cr2Se4 in the range 0 < x < 1. The intraplanar and the interplanar interactions are deduced. The high temperature series expansions (HTSEs) are derived for the magnetic susceptibility and the two-spin correlation functions for a Heisenberg ferromagnetic model on the B-spinel lattice. The calculations are developed in the framework of the random phase approximation (RPA). The magnetic phase diagram is deduced. A spin glass phase is predicted for intermediate range of concentration. The obtained results are comparable with those obtained by magnetic measurements. The critical exponents associated with the magnetic susceptibility (γ) and the correlation lengths (ν) have been deduced. The obtained values are comparable to those of 3D Heisenberg model.