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Excitons with nonzero momenta and their energy dependence are important for time dependent phenomena such as transport properties or the coupling to external or internal fields, for example in electron energy loss spectroscopy. In this paper we calculate the momentum dependent energy landscape of excitons in rubrene single crystals. We show that singlet excitons exhibit a dispersion that is qualitatively similar to the electronic valence and conduction bands, namely a relatively large bandwidth along $\mathrm{\ensuremath{\Gamma}}$--Y and much flatter bands along $\mathrm{\ensuremath{\Gamma}}$--X and $\mathrm{\ensuremath{\Gamma}}$--Z. However, the absolute value of the bandwidths is significantly weaker than for both electronic bands. Triplet excitons, on the other hand, show much less dispersion and the exciton bands are much flatter than their singlet counterparts.

Subsystem Density-Functional Theory and its extension to excited states, namely, subsystem Time-Dependent Density-Functional Theory, have been proven to be efficient and accurate fragmentation approaches for ground and excited states. In the present study we extend this approach to the subsystem-based description of total systems by means of GW and the Bethe-Salpeter equation (BSE). For this, we derive the working equations starting from a subsystem-based partitioning of the screened-Coulomb interaction for an arbitrary number of subsystems. Making use of certain approximations, we develop a parameter-free approach in which environmental screening contributions are effectively included for each subsystem. We demonstrate the applicability of these approximations by comparing quasi-particle energies and excitation energies from subsystem-based GW/BSE calculations to the supermolecular reference. Furthermore, we demonstrate the computational efficiency and the usefulness of this method for the description of photoinduced processes in complex chemical environments.

How fast is the charge transfer between two layers of transition metal dichalcogenides and where does it take place in momentum space? Two-photon photoemission using high-harmonic probe pulses can answer this question, as the authors demonstrate here for the topmost layers of MoS${}_{2}$. By tuning pump pulses below the topmost-layer gap, they excite electrons in deeper layers and probe only the topmost layer. GW-based tight-binding calculations support the experimental findings and explain why the electron transfer takes place at $\overline{\mathrm{\ensuremath{\Sigma}}}$.

ACS nano 14(11), 15766-15775 (2020). doi:10.1021/acsnano.0c06798, Published by American Chemical Society, Washington, DC

We perform absorption and photoluminescence spectroscopy of trions in hBN-encapsulated WSe$_2$, WS$_2$, MoSe$_2$, and MoS$_2$ monolayers, depending on temperature. The different trends for W- and Mo-based materials are excellently reproduced considering a Fermi-Dirac distribution of bright and dark trions. We find a dark trion, $\rm{X_D^-}$ 19 meV $\textit{below}$ the lowest bright trion, $\rm{X}_1^-$ in WSe$_2$ and WS$_2$. In MoSe$_2$, $\rm{X_D^-}$ lies 6 meV $\textit{above}$ $\rm{X}_1^-$, while $\rm{X_D^-}$ and $\rm{X}_1^-$ almost coincide in MoS$_2$. Our results agree with GW-BSE $\textit{ab-initio}$ calculations and quantitatively explain the optical response of doped monolayers with temperature., Comment: 16 pages including supporting information, 4 figures in the main text, 10 figures in the supporting information

The effect of a magnetic field on the optical absorption in semiconductors has been measured experimentally and modeled theoretically for various systems in previous decades. We present a new first-principles approach to systematically determine the response of excitons to magnetic fields, i.e., exciton $g$ factors. By utilizing the $GW$-Bethe-Salpeter equation methodology we show that $g$ factors extracted from the Zeeman shift of electronic bands are strongly renormalized by many-body effects which we trace back to the extent of the excitons in reciprocal space. We apply our approach to monolayers of transition metal dichalcogenides (${\mathrm{MoS}}_{2}$, ${\mathrm{MoSe}}_{2}$, ${\mathrm{MoTe}}_{2}$, ${\mathrm{WS}}_{2}$, and ${\mathrm{WSe}}_{2}$) with strongly bound excitons for which $g$ factors are weakened by about 30%.

One- and two-dimensional materials are being intensively investigated due to their interesting properties for next-generation optoelectronic devices. Among these, armchair-edged graphene nanoribbons are very promising candidates with optical properties that are dominated by excitons. In the presence of additional charges, trions (i.e., charged excitons) can occur in the optical spectrum. With our recently developed first-principle many-body approach (Phys. Rev. Lett. 116, 196804), we predict strongly bound trions in free-standing nanoribbons with large binding energies of 140-660 meV for widths of 14.6-3.6 Å. Both for the trions and for the excitons, we observe an almost linear dependency of their binding energies on the band gap. We observe several trion states with different character derived from the corresponding excitons. Because of the large bindings energies, this opens a route to applications by which optical properties are easily manipulated, for example, by electrical fields.

Bound electron–hole pairs called excitons govern the electronic and optical response of many organic and inorganic semiconductors. Excitons with spatially displaced wave functions of electrons and holes (interlayer excitons) are important for Bose–Einstein condensation, superfluidity, dissipationless current flow, and the light-induced exciton spin Hall effect. Here we report on the discovery of interlayer excitons in a bulk van der Waals semiconductor. They form due to strong localization and spin-valley coupling of charge carriers. By combining high-field magneto-reflectance experiments and ab initio calculations for 2H-MoTe2, we explain their salient features: the positive sign of the g-factor and the large diamagnetic shift. Our investigations solve the long-standing puzzle of positive g-factors in transition metal dichalcogenides, and pave the way for studying collective phenomena in these materials at elevated temperatures. Excitons, quasi-particles of bound electron-hole pairs, are at the core of the optoelectronic properties of layered transition metal dichalcogenides. Here, the authors unveil the presence of interlayer excitons in bulk van der Waals semiconductors, arising from strong localization and spin-valley coupling of charge carriers.

We discover an excited bound three-particle state, the $2s$ trion, appearing energetically below the $2s$ exciton in monolayer ${\mathrm{WS}}_{2}$, using absorption spectroscopy and ab initio GW and Bethe-Salpeter equation calculations. The measured binding energy of the $2s$ trion (22 meV) is smaller compared to the $1s$ intravalley and intervalley trions (37 and 31 meV). With increasing temperature, the $1s$ and $2s$ trions transfer their oscillator strengths to the respective neutral excitons, establishing an optical fingerprint of trion-exciton resonance pairs. Our discovery underlines the importance of trions for the entire excitation spectrum of two-dimensional semiconductors.

Transition-metal dichalcogenides (TMDCs) are a focus of current research due to their fascinating optical and electronic properties with possible technical applications. ${\mathrm{ReSe}}_{2}$ is an interesting material of the TMDC family, with unique anisotropic properties originating from its distorted $1T$ structure ($1T$ '). To develop a fundamental understanding of the optical and electric properties, we studied the underlying electronic structure with angle-resolved photoemission (ARPES) as well as band-structure calculations within the density functional theory (DFT)--local density approximation (LDA) and GdW approximations. We identified the $\overline{\mathrm{\ensuremath{\Gamma}}}\phantom{\rule{0.28453pt}{0ex}}{\overline{M}}_{1}$ direction, which is perpendicular to the $a$ axis, as a distinct direction in k space with the smallest bandwidth of the highest valence band. Using photon-energy-dependent ARPES, two valence band maxima are identified within experimental limits of about 50 meV: one at the high-symmetry point $Z$, and a second one at a non-high-symmetry point in the Brillouin zone. Thus, the position in k space of the global valence band maximum is undecided experimentally. Theoretically, an indirect band gap is predicted on a DFT-LDA level, while quasiparticle corrections lead to a direct band gap at the $Z$ point.

We present a physically intuitive model of molecular quantum dots beyond the constant interaction approximation. It accurately describes their charging behavior and allows the extraction of important molecular properties that are otherwise experimentally inaccessible. The model is applied to data recorded with a noncontact atomic force microscope on three different molecules that act as a quantum dot when attached to the microscope tip. The results are in excellent agreement with first-principles simulations.

Monolayers of transition metal dichalcogenides (TMDCs) have unique optoelectronic properties. Density functional theory allows only for a limited description of the electronic excitation energies in these systems, while a more advanced treatment within many-body perturbation theory employing the $\mathit{GW}/\mathrm{BSE}$ approximation is often rather time consuming. Here, we show that the recently developed $\mathrm{LDA}+\mathit{GdW}$ approach provides an efficient and at the same time reliable description of one-particle energies, as well as optical properties including bound excitons in TMDCs. For five exemplary materials (${\mathrm{MoSe}}_{2}, {\mathrm{MoS}}_{2}, {\mathrm{WSe}}_{2}, {\mathrm{WS}}_{2}$, and ${\mathrm{ReSe}}_{2}$), we discuss the numerical convergence, in particular with respect to k-point sampling, and show that the $\mathit{GdW}/\mathrm{BSE}$ approximation gives results similar to common $\mathit{GW}/\mathrm{BSE}$ calculations. Such efficient approaches are essential to treat larger multilayer systems or defects.

The power of the $GW$ formalism is, to a large extent, based on the explicit treatment of dynamical correlations in the self-energy. This dynamics is taken into account by calculating the energy dependence of the screened Coulomb interaction $W$, followed by a convolution with the Green's function $G$. In order to obtain the energy dependence of $W$ the prevalent methods are plasmon-pole models and numerical integration techniques. In this paper, we discuss an alternative approach, in which the energy-dependent screening is calculated by determining the resolvent, which is set up from a matrix representation of the dielectric function. On the one hand, this refrains from a numerical energy convolution and allows one to actually write down the energy dependence of $W$ explicitly (like in the plasmon-pole models). On the other hand, the method is at least as accurate as the numerical approaches due to its multipole nature. We discuss the theoretical setup in some detail, give insight into the computational aspects, and present results for Si, C, GaAs, and LiF. Finally, we argue that the analytic representability is not only useful for educational purposes but may also be of avail for the development of theory that goes beyond $GW$.

Bound electron–hole pairs called excitons govern the electronic and optical response of many organic and inorganic semiconductors. Excitons with spatially displaced wave functions of electrons and holes (interlayer excitons) are important for Bose–Einstein condensation, superfluidity, dissipationless current flow, and the light-induced exciton spin Hall effect. Here we report on the discovery of interlayer excitons in a bulk van der Waals semiconductor. They form due to strong localization and spin-valley coupling of charge carriers. By combining high-field magneto-reflectance experiments and ab initio calculations for 2H-MoTe2, we explain their salient features: the positive sign of the g-factor and the large diamagnetic shift. Our investigations solve the long-standing puzzle of positive g-factors in transition metal dichalcogenides, and pave the way for studying collective phenomena in these materials at elevated temperatures., Excitons, quasi-particles of bound electron-hole pairs, are at the core of the optoelectronic properties of layered transition metal dichalcogenides. Here, the authors unveil the presence of interlayer excitons in bulk van der Waals semiconductors, arising from strong localization and spin-valley coupling of charge carriers.

Since their discovery single-layer semiconducting transition metal dichalcogenides have attracted much attention thanks to their outstanding optical and mechanical properties. Strain engineering in these two-dimensional materials aims to tune their bandgap energy and to modify their optoelectronic properties by the application of external strain. In this paper we demonstrate that biaxial strain, both tensile and compressive, can be applied and released in a timescale of a few seconds in a reproducible way on transition metal dichalcogenides monolayers deposited on polymeric substrates. We can control the amount of biaxial strain applied by letting the substrate expand or compress. To do this we change the substrate temperature and choose materials with a large thermal expansion coefficient. After the investigation of the substrate-dependent strain transfer, we performed micro-differential spectroscopy of four transition metal dichalcogenides monolayers (MoS2, MoSe2, WS2, WSe2) under the application of biaxial strain and measured their optical properties. For tensile strain we observe a redshift of the bandgap that reaches a value as large as 95 meV/% in the case of single-layer WS2 deposited on polypropylene. The observed bandgap shifts as a function of substrate extension/compression follow the order MoSe2 < MoS2 < WSe2 < WS2. Theoretical calculations of these four materials under biaxial strain predict the same trend for the material-dependent rates of the shift and reproduce well the features observed in the measured reflectance spectra., 10 pages, 5 figures, 2 tables, supporting information

Optická kontrola spinových prúdov v topologických izolátoroch je nová možnosť v spintronike. Na porozumenie týchto procesov je nutné zistiť elektrónovú štruktúru nad fermiho hladinou za použitia jednokrokového modelu a inverznej ARPES techniky The optical control of spin currents in topological surface states opens new perspectives in (opto-) spintronics. To understand these processes, a profound knowledge about the dispersion and the spin polarization of both the occupied and the unoccupied electronic states is required. We present a joint experimental and theoretical study on the unoccupied electronic states of the topological insulator Bi2Se3 . We discuss spin- and angle-resolved inverse-photoemission results in comparison with calculations for both the intrinsic band structure and, within the one-step model of (inverse) photoemission, the expected spectral intensities. This allows us to unravel the intrinsic spin texture of the unoccupied bands at the surface of Bi2 Se3.

Electronic excitations are often accompanied by displacement of the ions from their ground-state equilibrium positions. This leads to line broadening of optical spectra, Stokes shifts, conformational changes, and photoinduced reactions. Here we discuss approaches to these features within ab-initio methods, in particular within many-body perturbation theory. A number of various systems, including molecules, point defects, polymers, and surfaces, are discussed to illustrate issues like localization and self-trapping that are relevant for a detailed understanding of the interrelation between excited states and geometrical structure. To cite this article: M. Rohlfing, C. R. Physique 10 (2009).

Using a scanning tunneling microscope we have measured the quantum conductance through a PTCDA molecule for different configurations of the tip-molecule-surface junction. A peculiar conductance resonance arises at the Fermi level for certain tip to surface distances. We have relaxed the molecular junction coordinates and calculated transport by means of the Landauer/Keldysh approach. The zero bias transmission calculated for fixed tip positions in lateral dimensions but different tip substrate distances show a clear shift and sharpening of the molecular chemisorption level on increasing the STM-surface distance, in agreement with experiment., accepted for publication in Applied Physics A

Excited states of donor-acceptor dimers are studied using many-body Green's functions theory within the GW approximation and the Bethe-Salpeter equation. For a series of prototypical small-molecule based pairs, this method predicts energies of local Frenkel and intermolecular charge-transfer excitations with the accuracy of tens of meV. Application to larger systems is possible and allowed us to analyze energy levels and binding energies of excitons in representative dimers of dicyanovinyl-substituted quarterthiophene and fullerene, a donor-acceptor pair used in state of the art organic solar cells. In these dimers, the transition from Frenkel to charge transfer excitons is endothermic and the binding energy of charge transfer excitons is still of the order of 1.5-2 eV. Hence, even such an accurate dimer-based description does not yield internal energetics favorable for the generation of free charges either by thermal energy or an external electric field. These results confirm that, for qualitative predictions of solar cell functionality, accounting for the explicit molecular environment is as important as the accurate knowledge of internal dimer energies.

High-quality $G\phantom{\rule{0}{0ex}}W$ calculations of the quasiparticle band structure in thin films of topological insulator Bi${}_{2}$Se${}_{3}$ show that the topological nature of the surface states is $n\phantom{\rule{0}{0ex}}o\phantom{\rule{0}{0ex}}t$ the spin-polarized quantum spin Hall state, but the less interesting trivial topology. This is in strong contrast to the expected topology of the surface states of $b\phantom{\rule{0}{0ex}}u\phantom{\rule{0}{0ex}}l\phantom{\rule{0}{0ex}}k$ Bi${}_{2}$Se${}_{3}$ and the predictions of density functional theory and parametrized calculations for Bi${}_{2}$Se${}_{3}$ thin films, which produce fundamentally less accurate predictions of the band gap than the $G\phantom{\rule{0}{0ex}}W$ approach.

Trion states of three correlated particles (e.g., two electrons and one hole) are essential to understand the optical spectra of doped or gated nanostructures, like carbon nanotubes or transition-metal dichalcogenides. We develop a theoretical many-body description for such correlated states using an ab-initio approach. It can be regarded as an extension of the widely used $GW$ method and Bethe-Salpeter equation, thus allowing for a direct comparison with excitons. We apply this method to a semiconducting (8,0) carbon nanotube, and find that the lowest optically active trions are red-shifted by $\sim 130$ meV compared to the excitons, confirming experimental findings for similar tubes. Moreover, our method provides detailed insights in the physical nature of trion states. In the prototypical carbon nanotube we find a variety of different excitations, discuss the spectra, energy compositions, and correlated wave functions., main text, supplement

By means of low-temperature scanning tunneling microscopy (STM) and spectroscopy (STS), we have investigated the adsorption of single Au atoms on a PTCDA monolayer physisorbed on the Au(111) surface. A chemical reaction between the Au atom and the PTCDA molecule leads to the formation of a radical that has an unpaired electron in its highest occupied orbital. This orbital is a $\ensuremath{\pi}$ orbital that extends over the whole Au-PTCDA complex. Because of the large Coulomb repulsion in this orbital, the unpaired electron generates a local moment when the molecule is adsorbed on the Au(111) surface. We demonstrate the formation of the radical and the existence of the local moment after adsorption by observing a zero-bias differential conductance peak that originates from the Kondo effect. By temperature dependent measurements of the zero-bias differential conductance, we determine the Kondo temperature to be ${T}_{\mathrm{K}}=(38\ifmmode\pm\else\textpm\fi{}8)\phantom{\rule{0.16em}{0ex}}\mathrm{K}$. For the theoretical description of the properties of the Au-PTCDA complex we use a hierarchy of methods, ranging from density functional theory (DFT) including a van der Waals correction to many-body perturbation theory (MBPT) and the numerical renormalization group (NRG) approach. Regarding the high-energy orbital spectrum, we obtain an excellent agreement with experiments by both spin-polarized DFT/MBPT and NRG. Moreover, the NRG provides an accurate description of the low-energy excitation spectrum of the spin degree of freedom, predicting a Kondo temperature very close to the experimental value. This is achieved by a detailed analysis of the universality of various definitions of ${T}_{\mathrm{K}}$ and by taking into account the full energy dependence of the coupling function between the molecule-metal complex and the metallic substrate.

The topological crystalline insulator SnTe belongs to the recently discovered class of materials in which a crystalline symmetry ensures the existence of topologically protected surface states. The bulk band structure of SnTe is characterized by a band inversion at the four equivalent $L$ points, giving rise to a mirror Chern number of ${n}_{\mathcal{M}}=\ensuremath{-}2$. The (001) surface exhibits four Dirac cones which lie at non-time-reversal-invariant points close to $\overline{X}$ and $\overline{Y}$ and are protected by the $(\overline{1}10)$ and (110) mirror symmetries. In contrast to topological insulators, this symmetry can be broken via deformations of the crystal. This opens up new possibilities for manipulating the Dirac states and inducing a controllable gap. Here, we have employed density-functional theory to investigate the response of the Dirac states to applied distortions from first principles. Our calculations show that a local gap of up to $\ensuremath{\approx}30\phantom{\rule{0.28em}{0ex}}\mathrm{meV}$ can be introduced via lattice deformations that break at least one of the underlying mirror symmetries. It is formed at either all four or just two cones, depending on the direction of the displacement vector, making it possible to create either a global gap or a state where opened and intact Dirac cones coexist. Notably, applying these deformations at the surface only can already induce the gap. If the complete slab is distorted, bulk bands are pushed into the gap making the whole system metallic.

We investigate the influence of potassium adsorption and selenium vacancies in the surface layer on the electronic properties of the prototypical topological insulator ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$. These modifications of the surface give rise to oscillations in the charge density that extend deep into the crystal. They result in a long-ranged potential perpendicular to the surface (also referred to as band bending) and new states in the band structure that are reminiscent of the states of a two-dimensional electron gas. Very similar effects have been observed in several experiments. The reorganization of the charge deep inside the crystal as a reaction to the surface modification constitutes a remarkable property of ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$ and is closely related to its layered structure. The emergence of the long-ranged potential as a direct consequence of the charge reorganization turns out to be a generic property of ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$. However, calculations without spin-orbit coupling show that the band bending is not related to the nontrivial topological character of ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$.

The topological crystalline insulator SnTe belongs to the recently discovered class of materials in which a crystalline symmetry ensures the existence of topologically protected surface states. The bulk band structure of SnTe is characterized by a band inversion at the four equivalent $L$ points, giving rise to a mirror Chern number of ${n}_{\mathcal{M}}=\ensuremath{-}2$. The (001) surface exhibits four Dirac cones which lie at non-time-reversal-invariant points close to $\overline{X}$ and $\overline{Y}$ and are protected by the $(\overline{1}10)$ and (110) mirror symmetries. In contrast to topological insulators, this symmetry can be broken via deformations of the crystal. This opens up new possibilities for manipulating the Dirac states and inducing a controllable gap. Here, we have employed density-functional theory to investigate the response of the Dirac states to applied distortions from first principles. Our calculations show that a local gap of up to $\ensuremath{\approx}30\phantom{\rule{0.28em}{0ex}}\mathrm{meV}$ can be introduced via lattice deformations that break at least one of the underlying mirror symmetries. It is formed at either all four or just two cones, depending on the direction of the displacement vector, making it possible to create either a global gap or a state where opened and intact Dirac cones coexist. Notably, applying these deformations at the surface only can already induce the gap. If the complete slab is distorted, bulk bands are pushed into the gap making the whole system metallic.

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 ($\ensuremath{\sim}1\text{ }\text{ }\mathrm{eV}$) 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.

Van der Waals (vdW) forces act ubiquitously in condensed matter. Despite being weak on an atomic level, they substantially influence molecular and biological systems due to their long range and system-size scaling. The difficulty to isolate and measure vdW forces on a single-molecule level causes our present understanding to be strongly theory based. Here we show measurements of the attractive potential between differently sized organic molecules and a metal surface using an atomic force microscope. Our choice of molecules and the large molecule-surface separation cause this attraction to be purely of vdW type. The experiment allows testing the asymptotic vdW force law and its validity range. We find a superlinear growth of the vdW attraction with molecular size, originating from the increased deconfinement of electrons in the molecules. Because such non-additive vdW contributions are not accounted for in most first-principles or empirical calculations, we suggest further development in that direction., Van der Waals interactions are difficult to calculate at an atomistic level for moderate sized structures due to the many distinct atoms involved. Here, the authors measure the van der Waals force between an organic molecule and a metal surface, examining the non-additive part of these interactions.

Two state-of-the-art computational approaches: quantum Monte Carlo (QMC), based on accurate total energies, and GW with exciton effects (GW-BSE), based on perturbation theory are employed to calculate ionization potentials, electron affinities, and first excited singlet and triplet energies for the silane and methane molecules. Results are in excellent agreement between these dramatically different approaches and with available experiment. The optically forbidden triplet excitation in silane is predicted to lie roughly 1 eV higher than previously reported. For methane, the impact of geometry relaxation is shown to be $\sim$ 2 eV for excited states. Further, in the GW-BSE method, we demonstrate that inclusion of off-diagonal matrix elements in the self-energy operator is crucial for an accurate picture., Comment: Accepted to Physical Review Letters (11/15/00)

We present an ab initio study of the optical properties of $\ensuremath{\alpha}$-quartz. The absorption spectrum is calculated by solving the Bethe-Salpeter equation for the interacting electron-hole system and found to be in excellent agreement with the measured spectrum up to 10 eV above the absorption threshold. We find that excitonic effects are crucial in understanding the sharp features in the absorption spectrum in this energy range. They are also crucial in the ab initio computation of the static dielectric constant, significantly enhancing its value.

We present a recently developed approach to calculate electron-hole excitations and the optical spectra of condensed matter from first principles. The key concept is to describe the excitations of the electronic system by the corresponding one- and two-particle Green's function. The method combines three computational techniques. First, the electronic ground state is treated within density-functional theory. Second, the single-particle spectrum of the electrons and holes is obtained within the $\mathrm{GW}$ approximation to the electron self-energy operator. Finally, the electron-hole interaction is calculated and a Bethe-Salpeter equation is solved, yielding the coupled electron-hole excitations. The resulting solutions allow the calculation of the entire optical spectrum. This holds both for bound excitonic states below the band gap, as well as for the resonant spectrum above the band gap. We discuss a number of technical developments needed for the application of the method to real systems. To illustrate the approach, we discuss the excitations and optical spectra of spatially isolated systems (atoms, molecules, and semiconductor clusters) and of extended, periodic crystals (semiconductors and insulators).

The 6H-SiC(0001)-(sqrt[3]xsqrt[3])R30 degrees surface exhibits one half-filled localized dangling-bond orbital per surface unit cell. Its electronic structure can accurately be described as a Mott-Hubbard insulator. We investigate its spectrum by a spin-polarized ab initio quasiparticle calculation. The resulting band structure shows one occupied and one empty surface band, separated by a direct band gap of 1.95 eV. Since the band gap in the spectrum of the Hubbard model is directly given by the on-site Coulomb-interaction parameter U of the dangling-bond orbital, our results allow for a reliable determination of U = 1.95 eV.

We calculate the optical reflectivity of the Si(111)-(2x1) surface from first principles. To this end, we first calculate the quasiparticle band structure of the surface within the GW approximation for the electronic self energy. The band structure exhibits two surface bands inside the fundamental bulk band gap. Thereafter the electron-hole interaction is computed for transitions between the relevant bands, the Bethe-Salpeter equation for coupled electron-hole excitations is solved and the optical response is evaluated. In the energy range below the fundamental bulk band gap, the reflectivity spectrum is dominated by a surface exciton at 0.43 eV with an excitonic binding energy of 0.26 eV. Our calculated spectrum is in very good agreement with experimental data from differential reflectivity spectroscopy.

We investigate excitons at the $\mathrm{Si}(111)\ensuremath{-}(2\ifmmode\times\else\texttimes\fi{}1)$ surface and their optical spectrum from first principles. This is done by solving the Bethe-Salpeter equation for the two-particle Green's function, including the electron-hole interaction. The optical spectrum of the surface is dominated by a surface exciton formed from the $\ensuremath{\pi}$-bonded surface states. The excitonic binding energy is more than 1 order of magnitude larger than in bulk Si. The two-particle wave function of the exciton state is strongly localized at the surface and exhibits distinct anisotropy due to the surface reconstruction.

We investigate optical absorption spectra and excitons in conjugated polymers from first principles. This is done by calculating the one-particle and the two-particle Green{close_quote}s function, including relevant many-body effects, and evaluating quasiparticle and optical excitations. Trans-polyacetylene and poly-phenylene-vinylene are studied as prototype long chain polymers. The electron-hole interaction gives rise to large exciton binding energies ({approximately}1 thinspthinspeV) and dramatically alters the optical spectra. The calculated exciton wave functions are very extended in real space. {copyright} {ital 1999} {ital The American Physical Society}

We present a new {ital abthinspthinspinitio} approach to calculate the interaction between electrons and holes in periodic crystals and to evaluate the resulting coupled electron-hole excitations. This involves a novel interpolation scheme in reciprocal space in solving the Bethe-Salpeter equation for the two-particle Green{close_quote}s function. We apply this approach to the calculation of the entire optical absorption spectrum, as well as of the energies and wave functions of bound exciton states in GaAs and LiF. Very good agreement with experiment is observed. {copyright} {ital 1998} {ital The American Physical Society}

Motivated by a recent discussion about the existence of a fundamental gap in HgSe [Phys. Rev. Lett. {bold 78}, 3165 (1997)], we calculate the quasiparticle band structure of HgSe within the GW approximation for the electron self-energy. The band-structure results show that HgSe is a semimetal, which is in agreement with most experimental data. We observe a strong wave-vector dependence of the self-energy of the lowest conduction band, leading to an increased dispersion and a small effective mass. This may help to interpret recent photoemission spectroscopy measurements. {copyright} {ital 1998} {ital The American Physical Society}

We calculate the optical absorption spectrum of hydrogen-terminated silicon clusters by solving the Bethe-Salpeter equation for the two-particle Green{close_quote}s function using an {ital ab initio} approach. The one-particle Green{close_quote}s function and the electron-hole interaction kernel are calculated within the GW approximation for the electron self-energy operator. Very large exciton binding energies are observed. Our results for the one-particle properties and the optical absorption spectra of the clusters are in very good agreement with available experimental data. {copyright} {ital 1998} {ital The American Physical Society}

We have investigated the role of semicore $d$ electrons in the calculation of quasiparticle band structures within the $\mathrm{GW}$ approximation for a number of elemental and compound semiconductors, as well as for a semimetal. The systems studied comprise Ge, GaN, ZnS, CdS, and $\ensuremath{\alpha}$-Sn. Semicore $d$ states are explicitly taken into account as valence states in our investigations. Overall, they have a strong influence on the band structure of the compounds, but not on that of the elemental semiconductor Ge or of the semimetal $\ensuremath{\alpha}$-Sn. Nevertheless, there is a distinct influence on the Ge band structure to be noted, as well, in that the gap changes from direct to indirect by the inclusion of the semicore $d$ states. Our band-structure results are in very gratifying agreement with available experimental data.

We report the quasiparticle band structure and optical absorption spectrum of bulk LiBr calculated from first-principles approaches. The quasiparticle band structure is calculated within the GW approximation. Taking the electron-hole interaction into consideration, the optical excitation is investigated by solving the Bethe-Salpeter equation for the electron-hole two-particle Green’s function. The obtained results for the band gap and optical absorption spectrum are in good agreement with experimental measurements.

Optical excitations of molecular systems can be modified by their physical environment. We analyze the underlying mechanisms within many-body perturbation theory, which is particularly suited to study non-local polarizability effects on the electronic structure. Here we focus on the example of a semiconducting carbon nanotube, which observes redshifts of its excitons when the tube is touched by another nanotube or other physisorbates. We show that the redshifts mostly result from the polarizability of the attached ad-system. Electronic coupling may enhance the redshifts, but depends very sensitively on the structural details of the contact.

We discuss an efficient approach to excited electronic states within ab initio many-body perturbation theory (MBPT). Quasiparticle corrections to density-functional theory result from the difference between metallic and nonmetallic dielectric screening. They are evaluated as a small perturbation to the density-functional theory (within the local-density approximation) band structure rather than fully calculating the self-energy and evaluating its difference from the exchange-correlation potential. The dielectric screening is described by a model, which applies to bulk crystals, as well as, to systems of reduced dimension, like molecules, surfaces, interfaces, and more. The approach also describes electron-hole interaction. The resulting electronic and optical spectra are slightly less accurate but much faster to calculate than a full MBPT calculation. We discuss results for bulk silicon and argon, for the $\text{Si}(111)\text{\ensuremath{-}}(2\ifmmode\times\else\texttimes\fi{}1)$ surface, the ${\text{SiH}}_{4}$ molecule, an argon-aluminum interface, and liquid argon.

10 páginas, 6 figuras, 4 tablas.-- PACS number(s): 71.15.Ap, 71.20.-b.-- et al., We present the calculations of quasiparticle bandstructures and lifetimes for noble metals Cu and Ag within the GW approximation based on localized Gaussian orbital basis sets. For Cu, both the calculated positions of the d bands and the width of the d bands are within 0.1 eV compared to the experimental results. For Ag, partial core correction should be included in the pseudopotential to get reliable positions of the d bands. The calculated lifetimes agree with the experiment in the energy region away from the Fermi level, but deviate from the experimental results near the Fermi level where short-range interactions which GW approach fails to describe play an important role. For a better description of the lifetime near the Fermi level, terms beyond the GW approximation in the many-body perturbation theory need to be considered., This work has been supported by the Niedersachsen Ph. D. program ”Synthesis and Characterization of Surfaces and Interfaces assembled from Clusters and Molecules” and by the Deutsche Forschungsgemeinschaft (Bonn, Germany) by Grant No. Ro 1318/4–3.

We investigate the diabatic electronic states of a photoexcited molecule within a diabatization method originally proposed by Baer [Chem. Phys. Lett. 35, 112 (1975)]. A diabatization denotes a unitary transformation which allows for incorporating nonadiabatic effects into the quantum Hamiltonian, expressed in the adiabatic representation. A typical example is the treatment of avoided crossings in the potential-energy surface, for instance, in the case of the retinal chromophore. In this paper, we present analytical and numerical calculations for the diabatic states in the context of Green's-function-based ab initio many-body perturbation theory (density-functional theory plus GW method plus Bethe-Salpeter equation). We present the calculation of the adiabatic and diabatic lowest excited electronic states of the retinal chromophore molecule.

Excited states of the negatively charged nitrogen-vacancy color center in diamond are studied using ab initio many-body perturbation theory (within $GW$ approximation and Bethe-Salpeter equation), including electronic exchange, correlation, and electron-hole interaction effects. We find that three singlets, one of which exhibits an intersystem crossing with the excited triplet, may be relevant for the fluorescence process in a way which has never been considered before. The calculated zero-phonon line for the visible excitation and that for the transition among the singlets are in good agreement with the experiments.

The electronic spectrum of a chemically contacted molecule in the junction of a scanning tunneling microscope can be modified by tip retraction. We analyze this effect by a combination of density functional, many-body perturbation and numerical renormalization group theory, taking into account both the non-locality and the dynamics of electronic correlation. Our findings, in particular the evolution from a broad quasiparticle resonance below to a narrow Kondo resonance at the Fermi energy, correspond to the experimental observations., Comment: 4 pages, 3 figures

The excited states of model chromophores of the photoactive yellow protein and of rhodopsin are studied using ab initio many-body perturbation theory (within the GW approximation and Bethe-Salpeter equation). Calculations beyond the Tamm-Dancoff approximation, i.e., consideration of the resonant-antiresonant transition coupling, are needed for an accurate description of the lowest $\ensuremath{\pi}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{\ensuremath{\ast}}$ excitations due to the large exchange interaction between the electron and hole localized in the low-dimension systems. The inclusion of dynamical effect in the electron-hole screening is important for an accurate description of the lowest $n\ensuremath{\rightarrow}{\ensuremath{\pi}}^{\ensuremath{\ast}}$ excitations.

We discuss the adsorption of xenon and of PTCDA on the silver (111) surface within a first-principles approach, focusing on the adsorbate-substrate interaction energy as a function of distance. We combine exact exchange with correlation energy from the adiabatic-connection fluctuation-dissipation theorem. At a large distance Z from the surface, the correlation causes a van der Waals attraction [approximately -C3/(Z - Z0)3]. At a closer distance, the attraction deviates from its asymptotic form and, combined with the repulsive exact-exchange energy, yields an equilibrium in close agreement with experiment.