Many-body Green Function Research Articles

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.

B-spline algebraic diagrammatic construction: application to photoionization cross-sections and high-order harmonic generation.

We present the first implementation of the ab initio many-body Green's function method, algebraic diagrammatic construction (ADC), in the B-spline single-electron basis. B-spline versions of the first order [ADC(1)] and second order [ADC(2)] schemes for the polarization propagator are developed and applied to the ab initio calculation of static (photoionization cross-sections) and dynamic (high-order harmonic generation spectra) quantities. We show that the cross-section features that pose a challenge for the Gaussian basis calculations, such as Cooper minima and high-energy tails, are found to be reproduced by the B-spline ADC in a very good agreement with the experiment. We also present the first dynamic B-spline ADC results, showing that the effect of the Cooper minimum on the high-order harmonic generation spectrum of Ar is correctly predicted by the time-dependent ADC calculation in the B-spline basis. The present development paves the way for the application of the B-spline ADC to both energy- and time-resolved theoretical studies of many-electron phenomena in atoms, molecules, and clusters.

Probing excitonic dark states in single-layer tungsten disulphide.

Transition metal dichalcogenide (TMDC) monolayers have recently emerged as an important class of two-dimensional semiconductors with potential for electronic and optoelectronic devices. Unlike semi-metallic graphene, layered TMDCs have a sizeable bandgap. More interestingly, when thinned down to a monolayer, TMDCs transform from indirect-bandgap to direct-bandgap semiconductors, exhibiting a number of intriguing optical phenomena such as valley-selective circular dichroism, doping-dependent charged excitons and strong photocurrent responses. However, the fundamental mechanism underlying such a strong light-matter interaction is still under intensive investigation. First-principles calculations have predicted a quasiparticle bandgap much larger than the measured optical gap, and an optical response dominated by excitonic effects. In particular, a recent study based on a GW plus Bethe-Salpeter equation (GW-BSE) approach, which employed many-body Green's-function methodology to address electron-electron and electron-hole interactions, theoretically predicted a diversity of strongly bound excitons. Here we report experimental evidence of a series of excitonic dark states in single-layer WS2 using two-photon excitation spectroscopy. In combination with GW-BSE theory, we prove that the excitons are of Wannier type, meaning that each exciton wavefunction extends over multiple unit cells, but with extraordinarily large binding energy (∼0.7electronvolts), leading to a quasiparticle bandgap of 2.7electronvolts. These strongly bound exciton states are observed to be stable even at room temperature. We reveal an exciton series that deviates substantially from hydrogen models, with a novel energy dependence on the orbital angular momentum. These excitonic energy levels are experimentally found to be robust against environmental perturbations. The discovery of excitonic dark states and exceptionally large binding energy not only sheds light on the importance of many-electron effects in this two-dimensional gapped system, but also holds potential for the device application of TMDC monolayers and their heterostructures in computing, communication and bio-sensing.

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.

The excitonic effects in single and double-walled boron nitride nanotubes.

The electronic structures and excitonic optical properties of single- and double-walled armchair boron nitride nanotubes (BNNTs) [e.g., (5,5) and (10,10), and (5,5)@(10,10)] are investigated within many-body Green's function and Bethe-Salpeter equation formalism. The first absorption peak of the double-walled nanotube has almost no shift compared with the single-walled (5,5) tube due to the strong optical transition in the double-walled tube that occurs within the inner (5,5) one. Dark and semi-dark excitonic states are detected in the lower energy region, stemming from the charge transfer between inner and outer tubes in the double-walled structure. Most interestingly, the charge transfer makes the electron and the hole reside in different tubes. Moreover, the excited electrons in the double-walled BNNT are able to transfer from the outer tube to the inner one, opposite to that which has been observed in double-walled carbon nanotubes.

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.

Excited states properties of organic molecules: from density functional theory to the GW and Bethe–Salpeter Green's function formalisms

Many-body Green's function perturbation theories, such as the GW and Bethe-Salpeter formalisms, are starting to be routinely applied to study charged and neutral electronic excitations in molecular organic systems relevant to applications in photovoltaics, photochemistry or biology. In parallel, density functional theory and its time-dependent extensions significantly progressed along the line of range-separated hybrid functionals within the generalized Kohn-Sham formalism designed to provide correct excitation energies. We give an overview and compare these approaches with examples drawn from the study of gas phase organic systems such as fullerenes, porphyrins, bacteriochlorophylls or nucleobases molecules. The perspectives and challenges that many-body perturbation theory is facing, such as the role of self-consistency, the calculation of forces and potential energy surfaces in the excited states, or the development of embedding techniques specific to the GW and Bethe-Salpeter equation formalisms, are outlined.

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.

Many-body Green's function GW and Bethe-Salpeter study of the optical excitations in a paradigmatic model dipeptide

We study within the many-body Green's function GW and Bethe-Salpeter formalisms the excitation energies of a paradigmatic model dipeptide, focusing on the four lowest-lying local and charge-transfer excitations. Our GW calculations are performed at the self-consistent level, updating first the quasiparticle energies, and further the single-particle wavefunctions within the static Coulomb-hole plus screened-exchange approximation to the GW self-energy operator. Important level crossings, as compared to the starting Kohn-Sham LDA spectrum, are identified. Our final Bethe-Salpeter singlet excitation energies are found to agree, within 0.07 eV, with CASPT2 reference data, except for one charge-transfer state where the discrepancy can be as large as 0.5 eV. Our results agree best with LC-BLYP and CAM-B3LYP calculations with enhanced long-range exchange, with a 0.1 eV mean absolute error. This has been achieved employing a parameter-free formalism applicable to metallic or insulating extended or finite systems.

Quasiparticle band gaps of graphene nanowiggles and their magnetism on Au(111)

Periodic repetitions of nonaligned and finite-sized graphene nanoribbon domains, known as graphene nanowiggles, can be synthesized using a surface-assisted bottom-up approach. They have been predicted to possess unusual properties such as tunable band gaps and versatile magnetic behaviors. Here, a first-principles many-body Green's function approach within the $GW$ approximation is used to accurately compute their band gaps, which are in the range 0.00--3.65 eV depending on geometry and magnetism. We also perform spin-polarized density functional theory calculations to demonstrate that the previously predicted complex spin states for free-standing nanowiggles are not significantly altered by the presence of the gold substrate on which they are synthesized.

Resonant hot charge-transfer excitations in fullerene-porphyrin complexes: Many-body Bethe-Salpeter study

We study the neutral singlet excitations of the zinc-tetraphenylporphyrin and ${C}_{70}$-fullerene donor-acceptor complex within the many-body Green's-function $GW$ and Bethe-Salpeter approaches. The lowest transition is a charge-transfer excitation between the donor and the acceptor with an energy in excellent agreement with recent constrained density functional theory calculations. Beyond the lowest charge-transfer state, which can be determined with simple electrostatic models that we validate, the Bethe-Salpeter approach provides the full excitation spectrum. We evidence the existence of hot electron-hole states which are resonant in energy with the lowest donor intramolecular excitation and show a hybrid intramolecular and charge-transfer character, favoring the transition towards charge separation. Such findings, and the ability to describe accurately both low-lying and excited charge-transfer states, are important steps in the process of discriminating ``cold'' versus ``hot'' exciton dissociation processes.

Stochastic evaluation of second-order Dyson self-energies

A stochastic method is proposed that evaluates the second-order perturbation corrections to the Dyson self-energies of a molecule (i.e., quasiparticle energies or correlated ionization potentials and electron affinities) directly and not as small differences between two large, noisy quantities. With the aid of a Laplace transform, the usual sum-of-integral expressions of the second-order self-energy in many-body Green's function theory are rewritten into a sum of just four 13-dimensional integrals, 12-dimensional parts of which are evaluated by Monte Carlo integration. Efficient importance sampling is achieved with the Metropolis algorithm and a 12-dimensional weight function that is analytically integrable, is positive everywhere, and cancels all the singularities in the integrands exactly and analytically. The quasiparticle energies of small molecules have been reproduced within a few mEh of the correct values with 10(8) Monte Carlo steps. Linear-to-quadratic scaling of the size dependence of computational cost is demonstrated even for these small molecules.

Electronic and optical properties of fluorinated graphene: A many-body perturbation theory study

The electronic and optical properties of fully fluorinated graphene i.e. fluorographene (CF), and partially fluorinated graphene (C${}_{4}$F) are studied by means of the first-principles many-body Green's function method, i.e. $GW$--Bethe--Salpeter equation. In conformity with experimental observations, fluorination of graphene causes relatively wide quasiparticle band gaps, 7.01 eV for CF and 5.52 eV for C${}_{4}$F. The optical absorption properties of CF and C${}_{4}$F are of excitonic nature, leading to the formation of bound excitons with significantly high binding energies of 1.96 and 1.31 eV assigned to the first bright exciton of CF and C${}_{4}$F, respectively. The disagreement between the ab initio calculated electronic band gap and the experimentally optical gap seems to be mainly due to the binding energy of excitons rather than the presence of defects. Contrary to previous theoretical predictions, this paper demonstrates that CF seems to be less likely to realize the excitonic Bose--Einstein condensation because the exciton wave functions are relatively delocalized and not well separated. In the case of C${}_{4}$F, however, it indicates a charge-transfer excitation.

Strong excitonic effects in the optical properties of graphitic carbon nitrideg-C3N4from first principles

Graphitic carbon nitride ($g$-C${}_{3}$N${}_{4}$) has recently triggered extensive investigations due to its potential applications, such as in direct photochemical water splitting, CO${}_{2}$ activation, and transition-metal-free spintronics. However, electronic, and particularly the optical properties of $g$-C${}_{3}$N${}_{4}$ still have not been well established. Based on one of the state-of-the-art approaches---many-body Green's function theory (i.e., $GW$ $+$ BSE)---absorption of ultraviolet light by $g$-C${}_{3}$N${}_{4}$ is found to be determined by strong excitonic effects with a significantly large binding energy assigned to the bound excitons. Dark states have also been found in $g$-C${}_{3}$N${}_{4}$, which can affect the photoluminescence yield of $g$-C${}_{3}$N${}_{4}$. We find that the band gap of $g$-C${}_{3}$N${}_{4}$ probably can be tuned by adjusting the condensation (dimensionality) to initiate excitonic absorption in the visible light region, which might help improve the solar energy conversion efficiency.

Optical absorption spectrum of Ce@C82

Optical absorption spectrum for the Ce@C82 endohedral fullerene has been studied using the density-functional theory and the many-body Green's-function approaches. The geometry optimization was performed using the DMol3 software. A plane wave approach as implemented in the ABINIT package has been used to solve the Kohn-Sham equation. Self-energy was evaluated by the GW approximation. Finally the optical absorption spectra have been calculated using the random phase approximation (RPA), RPA plus self-energy correction (RPA-GW) and the Bethe-Salpeter equation (BSE-GW).

Strong charge-transfer excitonic effects in C4H-type hydrogenated graphene

The electronic and optical properties of a new type of hydrogenated graphene in the C${}_{4}$H phase have been studied using the first-principles many-body Green's function method ($\mathit{GW}$ approximation and Bethe--Salpeter equation). It demonstrates that strong charge-transfer excitonic effects dominate the optical properties of C${}_{4}$H. The binding energy of the first exciton, which turns out to be strongly localized, is as large as 1.67 eV. The spatial separation of exited electrons and holes makes C${}_{4}$H a candidate for the realization of excitonic Bose--Einstein condensate. Dark state provides a traveling path for the bound excitons. As the situation in graphane with H vacancies, changing H coverage changes the electronic and optical properties and the associated applications.

Many-body Green's function study of coumarins for dye-sensitized solar cells

We study within the many-body Green's function $GW$ and Bethe-Salpeter formalisms the excitation energies of several coumarin dyes proposed as an efficient alternative to ruthenium complexes for dye-sensitized solar cells. Due to their internal donor-acceptor structure, these chromophores present low-lying excitations showing a strong intramolecular charge-transfer character. We show that combining $GW$ and Bethe-Salpeter calculations leads to charge-transfer excitation energies and oscillator strengths in excellent agreement with reference range-separated functional studies or coupled-cluster calculations. The present results confirm the ability of this family of approaches to describe accurately Frenkel and charge-transfer photo-excitations in both extended and finite size systems without any system-dependent adjustable parameter, paving the way to the study of dye-sensitized semiconducting surfaces.

Pauli Exchange Correlated Composite-Boson Condensation: A Many-Body Green's Function Approach

In this research, we develop a many-body Green's function approach for interacting composite bosons in the Bose–Einstein condensed phase. The resummation scheme dealing with the carrier–carrier exchange between many-body composite bosons in cold condensation is manifested as a diagrammatic technique through the introduction of a set of Dyson equations for composite bosons. We diagrammatically calculate the specific heat capacity of neutral composite bosons, made of mass-imbalanced fermions with opposite charges, up to the first orders of the Pauli exchange and Coulomb interaction. Condensate phenomena due to the effect of the carrier–carrier exchange are discussed. In comparison with the approximation that composite bosons behave like interacting fundamental bosons, our result shows that the energy reduction from the carrier–carrier exchange stabilizes composite-boson condensates.