arXiv subjects

Patrick Rinke

Publications and source records attributed to Patrick Rinke.

At least 73 records · Page 4Linked to original sources

arXiv2018

Multi-scale model for the structure of hybrid perovskites: Analysis of charge migration in disordered MAPbI$_3$ structures

We have developed a multi-scale model for organic-inorganic hybrid perovskites (HPs) that applies quantum mechanical (QM) calculations of small HP supercell models to large coarse-grained structures. With a mixed quantum-classical hopping model, we have studied the effects of cation disorder on charge mobilities in HPs, which is a key feature to optimize their photovoltaic performance. Our multi-scale model parametrizes the interaction between neighboring methylammonium cations (MA$^+$) in the prototypical HP material, methylammonium lead triiodide (CH$_3$NH$_3$PbI$_3$, or MAPbI$_3$). For the charge mobility analysis with our hopping model, we solved the QM site-to-site hopping probabilities analytically and computed the nearest-neighbor electronic coupling energies from the band structure of MAPbI$_3$ with density-functional theory. We investigated the charge mobility in various MAPbI$_3$ supercell models of ordered and disordered MA$^+$ cations. Our results indicate a structure-dependent mobility, in the range of 50$-$66 cm$^2$V$^{-1}$s$^{-1}$, with the highest observed in the ordered tetragonal phase.

cond-mat.mtrl-sci↗

arXiv2018

All-Electron, Real-Space Perturbation Theory for Homogeneous Electric Fields: Theory, Implementation, and Application within DFT

Within density-functional theory, perturbation theory~(PT) is the state-of-the-art formalism for assessing the response to homogeneous electric fields and the associated material properties, e.g., polarizabilities, dielectric constants, and Raman intensities. Here we derive a real-space formulation of PT and present an implementation within the all-electron, numeric atom-centered orbitals electronic structure code FHI-aims that allows for massively-parallel calculations. As demonstrated by extensive validation, this allows the rapid computation of accurate response properties of molecules and solids. As an application showcase, we present harmonic and anharmonic Raman spectra, the latter obtained by combining hundreds of thousands of PT calculations with \textit{ab initio} molecular dynamics. By using the PBE exchange-correlation functional with many-body van der Waals corrections, we obtain spectra in good agreement with experiment especially with respect to lineshapes for the isolated paracetamol molecule and two polymorphs of the paracetamol crystal.

cond-mat.mtrl-sci↗

arXiv2018

Multi-scale model for disordered hybrid perovskites: the concept of organic cation pair modes

We have studied the properties of the prototype hybrid organic-inorganic perovskite $\text{CH}_3^{}\text{NH}_3^{}\text{PbI}_3^{}$ using relativistic density functional theory (DFT). For our analysis we introduce the concept of $\text{CH}_3^{}\text{NH}_3^+$ "pair modes", that is, characteristic relative orientations of two neighboring $\text{CH}_3^{}\text{NH}_3^+$ cations. In our previous work [Phys. Rev. B \textbf{94}, 045201 (2016)] we identified two preferential orientations that a single $\text{CH}_3^{}\text{NH}_3^+$ cation adopts in a unit cell. The total number of relevant pairs can be reduced from the resulting 196 combinations to only 25 by applying symmetry operations. DFT results of several $2\!\times\!2\!\times\!2$ supercell models reveal the dependence of the total energy, band gap and band structure on the distribution of $\text{CH}_3^{}\text{NH}_3^+$ cations and the pair modes. We have then analyzed the pair-mode distribution of a series of $4\!\times\!4\!\times\!4$ supercell models with disordered $\text{CH}_3^{}\text{NH}_3^+$ cations. Our results show that diagonally-oriented $\text{CH}_3^{}\text{NH}_3^+$ cations are rare in optimized $\text{CH}_3^{}\text{NH}_3^{}\text{PbI}_3^{}$ supercell structures. In the prevailing pair modes, the $\text{C--N}$ bonds of the two neighboring $\text{CH}_3^{}\text{NH}_3^+$ cations are aligned approximately vertically. Furthermore, we fit the coefficients of a pair-mode expansion to our supercell DFT reference structures. The pair-mode model can then be used to quickly estimate the energies of disordered perovskite structures. Our pair-mode concept provides combined atomistic-statistical insight into disordered structures in bulk hybrid perovskite materials.

cond-mat.mtrl-sci↗

arXiv2017

Theory of excitation transfer between two-dimensional semiconductor and molecular layers

The geometry-dependent energy transfer rate from an electrically pumped inorganic semiconductor quantum well into an organic molecular layer is studied theoretically. We focus on Förster-type nonradiative excitation transfer between the organic and inorganic layer and include quasi-momentum conservation and intermolecular coupling between the molecules in the organic film. (Transition) partial charges calculated from density-functional theory are used to calculate the coupling elements. The partial charges describe the spatial charge distribution and go beyond the common dipole-dipole interaction. We find that the transfer rates are highly sensitive to variations in the geometry of the hybrid inorganic/organic system. For instance, the transfer efficiency is improved by orders of magnitude by tuning the relative orientation and positioning of the molecules. Also, the operating regime is identified where in-scattering dominates over unwanted back-scattering from the molecular layer into the substrate.

cond-mat.mes-hall↗

arXiv2017

First-Principles Supercell Calculations of Small Polarons with Proper Account for Long-Range Polarization Effects

We present a density functional theory (DFT) based supercell approach for modeling small polarons with proper account for the long-range elastic response of the material. Our analysis of the supercell dependence of the polaron properties (e.g., atomic structure, binding energy, and the polaron level) reveals long-range electrostatic effects and the electron-phonon interaction as the two main contributors. We develop a correction scheme for DFT polaron calculations that significantly reduces the dependence of polaron properties on the DFT exchange-correlation functional and the size of the supercell in the limit of strong electron-phonon coupling. Using our correction approach, we present accurate all-electron full-potential DFT results for small polarons in rocksalt MgO and rutile TiO$_2$.

cond-mat.mtrl-sci↗

arXiv2017

Lattice Dynamics Calculations based on Density-functional Perturbation Theory in Real Space

A real-space formalism for density-functional perturbation theory (DFPT) is derived and applied for the computation of harmonic vibrational properties in molecules and solids. The practical implementation using numeric atom-centered orbitals as basis functions is demonstrated exemplarily for the all-electron Fritz Haber Institute ab initio molecular simulations (FHI-aims) package. The convergence of the calculations with respect to numerical parameters is carefully investigated and a systematic comparison with finite-difference approaches is performed both for finite (molecules) and extended (periodic) systems. Finally, the scaling tests and scalability tests on massively parallel computer systems demonstrate the computational efficiency.

cond-mat.mtrl-sci↗

arXiv2016

Benchmark of GW approaches for the GW100 testset

For the recent GW100 test set of molecular ionization energies, we present a comprehensive assessment of different GW methodologies: fully self-consistent GW (scGW), quasiparticle self-consistent GW (qsGW), partially self-consistent GW0 (scGW0), perturbative GW (G0W0) and optimized G0W0 based on the minimization of the deviation from the straight-line error (DSLE-minimized GW). We compare our GW calculations to coupled-cluster singles, doubles, and perturbative triples [CCSD(T)] reference data for GW100. We find scGW and qsGW ionization energies in excellent agreement with CCSD(T), with discrepancies typically smaller than 0.3 eV (scGW) respectively 0.2 eV (qsGW). For scGW0 and G0W0 the deviation from CCSD(T) is strongly dependent on the starting point. We further relate the discrepancy between the GW ionization energies and CCSD(T) to the deviation from straight line error (DSLE). In DSLE-minimized GW calculations, the DSLE is significantly reduced, yielding a systematic improvement in the description of the ionization energies.

physics.chem-ph↗

arXiv2016

Towards efficient orbital-dependent density functionals for weak and strong correlation

We present a new paradigm for the design of exchange-correlation functionals in density-functional theory. Electron pairs are correlated explicitly by means of the recently developed second order Bethe-Goldstone equation (BGE2) approach. Here we propose a screened BGE2 (sBGE2) variant that efficiently regulates the coupling of a given electron pair. sBGE2 correctly dissociates H$_2$ and H$_2^+$, a problem that has been regarded as a great challenge in density-functional theory for a long time. The sBGE2 functional is then taken as a building block for an orbital-dependent functional, termed ZRPS, which is a natural extension of the PBE0 hybrid functional. While worsening the good performance of sBGE2 in H$_2$ and H$_2^{+}$, ZRPS yields a remarkable and consistent improvement over other density functionals across various chemical environments from weak to strong correlation.

cond-mat.mtrl-sci↗

arXiv2016

Wave-function inspired density functional applied to the H$_2$/H$_2^+$ challenge

We start from the Bethe-Goldstone equation (BGE) to derive a simple orbital-dependent correlation functional -- BGE2 -- which terminates the BGE expansion at the second-order, but retains the self-consistent coupling of electron-pair orrelations. We demonstrate that BGE2 is size consistent and one-electron "self-correlation" free. The electron-pair correlation coupling ensures the correct H$_2$ dissociation limit and gives a finite correlation energy for any system even if it has a no energy gap. BGE2 provides a good description of both H$_2$ and H$_2^+$ dissociation, which is regarded as a great challenge in density functional theory (DFT). We illustrate the behavior of BGE2 analytically by considering H$_2$ in a minimal basis. Our analysis shows that BGE2 captures essential features of the adiabatic connection path that current state-of-the-art DFT approximations do not.

cond-mat.mtrl-sci↗

arXiv2016

Atomic structure of metal-halide perovskites from first principles: The chicken-and-egg paradox of the organic-inorganic interaction

We have studied the prototype hybrid organic-inorganic perovskite CH3NH3PbI3 and its three close relatives, CH3NH3SnI3, CH3NH3PbCl3 and CsPbI3, using relativistic density function theory. The long-range van der Waals (vdW) interactions were incorporated into the Perdew-Burke-Ernzerhof (PBE) exchange-correlation functional using the Tkatchenko-Scheffler pairwise scheme. Our results reveal that hydrogen bonding, which is well described by the PBE functional, plays a decisive role for the structural parameters of these systems, including the position and orientation of the organic cation as well as the deformation of the inorganic framework. The magnitude of the inorganic-framework deformation depends sensitively on the orientation of the organic cation, and directly influences the stability of the hybrid perovskites. Our results suggest that the organic and the inorganic components complement each other: The low symmetry of the organic cation is the origin of the inorganic-framework deformation, which then aids the overall stabilization of the hybrid perovskite structure. This stabilization is indirectly affected by vdW interactions, which lead to smaller unit-cell volumes than in PBE and therefore modulate the interaction between the organic cation and the inorganic framework. The vdW-induced lattice-constant corrections are system dependent and lead to PBE+vdW lattice constants in good agreement with experiment. Further insight is gained by analysing the vdW contributions. In all iodide-based hybrid perovskites the interaction between the organic cation and the iodide anions provides the largest lattice-constant change, followed by iodine-iodine and the organic cation - heavy-metal cation interaction. These corrections follow an almost linear dependence on the lattice constant within the range considered in our study, and are therefore approximately additive.

cond-mat.mtrl-sci↗

arXiv2015

Piecewise linearity in the $GW$ approximation for accurate quasiparticle energy predictions

We identify the deviation from the straight line error (DSLE) -- i.e., the spurious non-linearity of the total energy as a function of fractional particle number -- as the main source for the discrepancy between experimental vertical ionization energies and theoretical quasiparticle energies, as obtained from the $GW$ and $GW$+SOSEX approximations to many-body perturbation theory (MBPT). For self-consistent calculations, we show that $GW$ suffers from a small DSLE. Conversely, for perturbative $G_0W_0$ and $G_0W_0$+SOSEX calculations the DSLE depends on the starting point. We exploit this starting-point dependence to reduce (or completely eliminate) the DSLE. We find that the agreement with experiment increases as the DSLE reduces. DSLE-minimized schemes, thus, emerge as promising avenues for future developments in MBPT.

cond-mat.mtrl-sci↗

arXiv2015

Length Dependence of Ionization Potentials of Trans-Acetylenes: Internally-Consistent DFT/GW Approach

We follow the evolution of the Ionization Potential (IP) for the paradigmatic quasi-one-dimensional trans-acetylene family of conjugated molecules, from short to long oligomers and to the infinite polymer trans-poly-acetylene (TPA). Our results for short oligomers are very close to experimental available data. We find that the IP varies with oligomer length and converges to the given value for TPA with a smooth, coupled inverse-length-exponential behavior. Our prediction is based on an "internally-consistent" scheme to adjust the exchange mixing parameter $α$ of the PBEh hybrid density functional, so as to obtain a description of the electronic structure consistent with the quasiparticle approximation for the IP. This is achieved by demanding that the corresponding quasiparticle correction, in the GW@PBEh approximation, vanishes for the IP when evaluated at PBEh($α^{ic}$). We find that $α^{ic}$ is also system-dependent and converges with increasing oligomer length, allowing to capture the dependence of IP and other electronic properties.

cond-mat.mtrl-sci↗

arXiv2015

First-principles calculations of indirect Auger recombination in nitride semiconductors

Auger recombination is an important non-radiative carrier recombination mechanism in many classes of optoelectronic devices. The microscopic Auger processes can be either direct or indirect, mediated by an additional scattering mechanism such as the electron-phonon interaction. Phonon-assisted Auger recombination is particularly strong in nitride materials and affects the efficiency of nitride optoelectronic devices at high powers. Here we present a first-principles computational formalism for the study of direct and indirect Auger recombination in direct-band-gap semiconductors and apply it to the case of nitride materials. We show that direct Auger recombination is weak in the nitrides and cannot account for experimental measurements. On the other hand, carrier scattering by phonons and alloy disorder enables indirect Auger processes that can explain the observed loss in devices. We analyze the dominant phonon contributions to the Auger recom- bination rate and the influence of temperature and strain on the values of the Auger coefficients. Auger processes assisted by charged-defect scattering are much weaker than the phonon-assisted ones for realistic defect densities and not important for the device performance. The computational formalism is general and can be applied to the calculation of the Auger coefficient in other classes of optoelectronic materials.

cond-mat.mtrl-sci↗

arXiv2015

Self-Consistent Green Function Embedding for Advanced Electronic Structure Methods Based on a Dynamical Mean-Field Concept

We present an embedding scheme for periodic systems that facilitates the treatment of the physically important part (here the unit cell) with advanced electronic-structure methods, that are computationally too expensive for periodic systems. The rest of the periodic system is treated with computationally less demanding approaches, e.g., Kohn-Sham density-functional theory, in a self- consistent manner. Our scheme is based on the concept of dynamical mean-field theory (DMFT) formulated in terms of Green functions. In contrast to the original DMFT formulation for correlated model Hamiltonians, we here consider the unit cell as local embedded cluster in a first-principles way, that includes all electronic degrees of freedom. Our real-space dynamical mean-field embedding (RDMFE) scheme features two nested Dyson equations, one for the embedded cluster and another for the periodic surrounding. The total energy is computed from the resulting Green functions. The performance of our scheme is demonstrated by treating the embedded region with hybrid functionals and many-body perturbation theory in the GW approach for simple bulk systems. The total energy and the density of states converge rapidly with respect to the computational parameters and approach their bulk limit with increasing cluster (i.e., unit cell) size.

cond-mat.mtrl-sci↗

arXiv2015

Static correlation and electron localization in molecular dimers from the self-consistent RPA and GW approximation

We investigate static correlation and delocalization errors in the self-consistent GW and random-phase approximation (RPA) by studying molecular dissociation of the H_2 and LiH molecules. Although both approximations contain topologically identical diagrams, the non-locality and frequency dependence of the GW self-energy crucially influence the different energy contributions to the total energy as compared to the use of a static local potential in the RPA. The latter leads to significantly larger correlation energies which allow for a better description of static correlation at intermediate bond distances. The substantial error found in GW is further analyzed by comparing spin-restricted and spin-unrestricted calculations. At large but finite nuclear separation their difference gives an estimate of the so-called fractional spin error normally determined only in the dissociation limit. Furthermore, a calculation of the dipole moment of the LiH molecule at dissociation reveals a large delocalization error in GW making the fractional charge error comparable to the RPA. The analyses are supplemented by explicit formulae for the GW Green's function and total energy of a simplified two-level model providing additional insights into the dissociation limit.

cond-mat.str-el↗

arXiv2015

Why graphene growth is very different on the C face than on the Si face of SiC: Insights from surface equilibria and the (3$\times$3)-3C-SiC($\bar{\text{1}}\bar{\text{1}}\bar{\text{1}}$) reconstruction

We address the stability of the surface phases that occur on the C-side of 3C-SiC($\bar{1} \bar{1} \bar{1}$) at the onset of graphene formation. In this growth range, experimental reports reveal a coexistence of several surface phases. This coexistence can be explained by a Si-rich model for the unknown (3$\times$3) reconstruction, the known (2$\times$2)$_{C}$ adatom phase, and the graphene covered (2$\times$2)$_{C}$ phase. By constructing an $ab$ $initio$ surface phase diagram using a van der Waals corrected density functional, we show that the formation of a well defined interface structure like the "buffer-layer" on the Si side is blocked by Si-rich surface reconstructions.

cond-mat.mtrl-sci↗

arXiv2014

A multi-scale approach to the electronic structure of doped semiconductor surfaces

The inclusion of the global effects of semiconductor doping poses a unique challenge for first-principles simulations, because the typically low concentration of dopants renders an explicit treatment intractable. In systems which do not display long-range band bending, a satisfactory remedy is offered by the use of "pseudoatoms", with a fractional nuclear charge matching the bulk doping concentration. However, this alone is not always sufficient for charged surfaces, where the width of the space-charge region (SCR) often exceeds realistic supercell dimensions. One generalization of the pseudoatom approach which overcomes this difficulty relies on the introduction of an artificially high doping level within a slab calculation, in conjunction with a multi-scale electrostatic energy correction. Here, we present an alternative technique that naturally extends the pseudoatom approach while bypassing the need for calculations with an unrealistically high doping level. It is based on the introduction of excess charge, mimicking free charge carriers from the SCR, along with a fixed sheet of counter-charge mimicking the SCR-related field. Self-consistency is obtained by imposing charge conservation and Fermi level equilibration between the bulk, treated semi-classically, and the electronic states of the slab/surface, which are treated quantum-mechanically. The method, which we call CREST - the Charge-Reservoir Electrostatic Sheet Technique - can be used with standard electronic structure codes. We validate the approach using a simple tight-binding model, which allows for comparison of its results with calculations encompassing the full SCR explicitly. We then employ it with density functional theory, where it is used to obtain insights into the electronic structures of the "clean-cleaved" Si(111) surface and its buckled (2x1) reconstruction, at various doping densities.

cond-mat.mtrl-sci↗

arXiv2014

First-Principles Description of Charge Transfer in Donor-Acceptor Compounds from Self-Consistent Many-Body Perturbation Theory

We investigate charge transfer in prototypical molecular donor-acceptor compounds using hybrid density functional theory (DFT) and the GW approximation at the perturbative level (G0W0) and at full self-consistency (sc-GW). For the systems considered here, no charge transfer should be expected at large intermolecular separation according to photoemission experiment and accurate quantum-chemistry calculations. The capability of hybrid exchange-correlation functionals of reproducing this feature depends critically on the fraction of exact exchange $α$, as for small values of $α$ spurious fractional charge transfer is observed between the donor and the acceptor. G0W0 based on hybrid DFT yields the correct alignment of the frontier orbitals for all values of $α$. However, G0W0 has no capacity to alter the ground-state properties of the system, because of its perturbative nature. The electron density in donor-acceptor compounds thus remains incorrect for small $α$ values. In sc-GW, where the Green's function is obtained from the iterative solution of the Dyson equation, the electron density is updated and reflects the correct description of the level alignment at the GW level, demonstrating the importance of self-consistent many-body approaches for the description of ground- and excited-state properties in donor-acceptor systems.

cond-mat.mtrl-sci↗