Publications

Structural and electronic properties of lead chalcogenides from first principles

We present ab initio calculations on the structural and electronic properties of the narrow-gap lead chalcogenides $\mathrm{Pb}X$ ($X=\mathrm{S}$, Se, and Te). Particular emphasis is put on the correct description of their exceptional electronic properties compared to III-V and II-VI semiconductors, such as the very small magnitude of the band gap, the unusual order of the band gaps within the series $[{E}_{g}(\mathrm{Pb}\mathrm{S})>{E}_{g}(\mathrm{Pb}\mathrm{Te})>{E}_{g}(\mathrm{Pb}\mathrm{Se})]$, and the high effective charge-carrier masses. Within standard density-functional theory (DFT), the local-density approximation (LDA) as well as the generalized gradient approximation (GGA) to the exchange-correlation potential clearly fail to describe important aspects of the band structure of these materials. This problem is overcome by applying methods that go beyond the local or semilocal approximation. We show that hybrid functionals are very successful in giving the correct results for the electronic but also for the structural properties. The lattice constants and bulk moduli as well as the fundamental band gaps and effective masses are in much better agreement with experiment than within DFT-LDA/GGA. The order of the band gaps is also properly obtained. For comparison, partially self-consistent $G{W}_{0}$ calculations are reported, yielding highly accurate values for the band gaps.

The random phase approximation and beyond: an assessment for molecular binding energies and reaction barrier heights

No abstract is provided for this article.

Screened exchange corrections to the random phase approximation from many-body perturbation theory

The random phase approximation (RPA) systematically overestimates the magnitude of the correlation energy and generally underestimates cohesive energies. This originates in part from the complete lack of exchange terms, which would otherwise cancel Pauli exclusion principle violating (EPV) contributions. The uncanceled EPV contributions also manifest themselves in form of an unphysical negative pair density of spin-parallel electrons close to electron-electron coalescence. We follow considerations of many-body perturbation theory to propose an exchange correction that corrects the largest set of EPV contributions while having the lowest possible computational complexity. The proposed method exchanges adjacent particle/hole pairs in the RPA diagrams, considerably improving the pair density of spin-parallel electrons close to coalescence in the uniform electron gas (UEG). The accuracy of the correlation energy is comparable to other variants of Second Order Screened Exchange (SOSEX) corrections although it is slightly more accurate for the spin-polarized UEG. Its computational complexity scales as $\mathcal O(N^5)$ or $\mathcal O(N^4)$ in orbital space or real space, respectively. Its memory requirement scales as $\mathcal O(N^2)$.

Density isobar of water and melting temperature of ice: Assessing common density functionals

We investigate the density isobar of water and the melting temperature of ice using six different density functionals. Machine-learning potentials are employed to ensure computational affordability. Our findings reveal significant discrepancies between various base functionals. Notably, even the choice of damping can result in substantial differences. Overall, the outcomes obtained through density functional theory are not entirely satisfactory across most utilized functionals. All functionals exhibit significant deviations either in the melting temperature or equilibrium volume, with most of them even predicting an incorrect volume difference between ice and water. Our heuristic analysis indicates that a hybrid functional with 25% exact exchange and van der Waals damping averaged between zero and Becke–Johnson dampings yields the closest agreement with experimental data. This study underscores the necessity for further enhancements in the treatment of van der Waals interactions and, more broadly, density functional theory to enable accurate quantitative predictions for molecular liquids.

The cohesive energy of superheavy element copernicium determined from accurate relativistic coupled-cluster theory

The cohesive energy of bulk copernicium is accurately determined using the incremental method within a relativistic coupled-cluster approach. For the lowest energy structure of hexagonal close-packed (hcp) symmetry, we obtain a cohesive energy of -36.3 kJ mol-1 (inclusion of uncertainties leads to a lower bound of -39.6 kJ mol-1), in excellent agreement with the experimentally estimated sublimation enthalpy of -38 kJ mol-1 [R. Eichler et al., Angew. Chem. Int. Ed., 2008, 47, 3262]. At the coupled-cluster singles, doubles and perturbative triples level of theory, we find that the hcp structure is energetically quasi-degenerate with both face-centred and body-centred cubic structures. These results provide a basis for testing various density-functionals, of which the PBEsol functional yields a cohesive energy of -34.1 kJ mol-1 in good agreement with our coupled-cluster value.

Vanadium surface oxides on Pd(111): A structural analysis

Scanning tunneling microscopy studies of vanadium oxides grown on Pd(111) show interesting structures especially in the low-coverage region. Evaporation of V in an oxygen background at elevated sample temperature $(250\ifmmode^\circ\else\textdegree\fi{}\mathrm{C})$ results in the formation of a nonperiodic honeycomb-like structure growing from the steps, which starts to transform into an ordered phase at a vanadium coverage of $\ensuremath{\approx}0.2\mathrm{ML}$ (monolayer). At 0.31 ML the entire surface is covered by this well-ordered open $(4\ifmmode\times\else\texttimes\fi{}4)$ structure. Annealing this structure in ${\mathrm{H}}_{2}$ atmosphere transforms the phase into a ${\mathrm{V}}_{2}{\mathrm{O}}_{3}$ surface oxide with $(2\ifmmode\times\else\texttimes\fi{}2)$ periodicity, whose optimal coverage is reached at 0.5 ML vanadium. Models for both ordered structures have been suggested before on the basis of ab initio density-functional theory (DFT) calculations and molecular-dynamics simulations and these models are now unambiguously confirmed by quantitative low-energy electron-diffraction (LEED) analyses. In the $(4\ifmmode\times\else\texttimes\fi{}4)$ phase, the V atoms are surrounded by four oxygen atoms in an unusual tetrahedral coordination leading to a ${\mathrm{V}}_{5}{\mathrm{O}}_{14}$ stoichiometry. This tetrahedral coordination allows the oxide to adopt open loosely packed two-dimensional (2D) and 1D structures, which are stabilized by the surface-oxide interface energy. Furthermore, it is shown that state of the art DFT calculations can indeed predict complex structures exactly as well as that modern quantitative LEED is capable of dealing with very large unit cells.

Comparing GIPAW with numerically exact chemical shieldings: The role of two-center contributions to the induced current

In this study, we benchmark density functional theory gauge-including projector-augmented-wave (GIPAW) chemical shieldings against molecular shieldings for which basis set completeness has been achieved [Jensen et al., Phys. Chem. Chem. Phys. 18, 21145 (2016)]. We demonstrate the importance of two-center corrections for GIPAW hydrogen shieldings. For the other nuclei studied, standard GIPAW is sufficiently accurate. We find that GIPAW can be pushed to closely approach the basis set limit. The only source of small inaccuracies lies in the contribution to the shielding that is caused by surface currents, which we estimate comparing GIPAW susceptibilities to converged molecular magnetizabilities.

Temperature-dependent anharmonic phonons in quantum paraelectric KTaO$_3$ by first principles and machine-learned force fields

Understanding collective phenomena in quantum materials from first principles is a promising route toward engineering materials properties on demand and designing new functionalities. This work examines the quantum paraelectric state, an elusive state of matter characterized by the smooth saturation of the ferroelectric instability at low temperature due to quantum fluctuations associated with anharmonic phonon effects. The temperature-dependent evolution of the soft ferroelectric phonon mode in the quantum paraelectric KTaO$_3$ in the range 0-300 K is modelled by combining density functional theory (DFT) calculations with the stochastic self-consistent harmonic approximation assisted by an on-the-fly machine-learned force field. The calculated data show that including anharmonic terms is essential to stabilize the spurious imaginary ferroelectric phonon predicted by DFT, in agreement with experiments. Augmenting the DFT workflow with machine-learned force fields allows for efficient stochastic sampling of the configurational space using large supercells in a broad and dense temperature range, inaccessible by conventional ab initio protocols. This work proposes a robust computational workflow capable of accounting for collective behaviors involving different degrees of freedom and occurring at large time/length scales, paving the way for precise modeling and control of quantum effects in materials.

First-principles calculations for point defects in solids

Point defects and impurities strongly affect the physical properties of materials and have a decisive impact on their performance in applications. First-principles calculations have emerged as a powerful approach that complements experiments and can serve as a predictive tool in the identification and characterization of defects. The theoretical modeling of point defects in crystalline materials by means of electronic-structure calculations, with an emphasis on approaches based on density functional theory (DFT), is reviewed. A general thermodynamic formalism is laid down to investigate the physical properties of point defects independent of the materials class (semiconductors, insulators, and metals), indicating how the relevant thermodynamic quantities, such as formation energy, entropy, and excess volume, can be obtained from electronic structure calculations. Practical aspects such as the supercell approach and efficient strategies to extrapolate to the isolated-defect or dilute limit are discussed. Recent advances in tractable approximations to the exchange-correlation functional ($\mathrm{DFT}+U$, hybrid functionals) and approaches beyond DFT are highlighted. These advances have largely removed the long-standing uncertainty of defect formation energies in semiconductors and insulators due to the failure of standard DFT to reproduce band gaps. Two case studies illustrate how such calculations provide new insight into the physics and role of point defects in real materials.

Cohesive Properties and Asymptotics of the Dispersion Interaction in Graphite by the Random Phase Approximation

The structural properties of graphite, such as the interlayer equilibrium distance, the elastic constant, and the net layer binding energy, are obtained using the adiabatic-connection fluctuation-dissipation theorem in the random phase approximation. Excellent agreement is found with the available experimental data; however, our computed binding energy of 48 meV per atom is somewhat smaller than the one obtained by quantum Monte Carlo methods. The asymptotic behavior of the interlayer dispersion interaction, previously derived from analytic approximations, is explicitly demonstrated to follow a d-3 behavior at very large distances.

Finite-temperature structure of the MAPbI3 perovskite: Comparing density functional approximations and force fields to experiment

Determining the finite-temperature structure of the hybrid perovskite MAPbI3 is a challenge for both experimental and theoretical methods. A very powerful computational method that can resolve the atomic structure is molecular dynamics (MD). The resulting structure depends on the density functional approximation (DFA) in the case of ab initio MD and the force field in classical MD. We compare the structure between 250 and 400 K obtained with different DFAs and force fields in one consistent manner. The symmetry of the PbI3 framework is analyzed as well as the relative ordering of the neighboring organic molecules inside the framework. The distribution function of the molecules is used to map out an effective energy surface for the rotation of a single molecule. This surface is accurately modeled by a pair of cubic harmonics. Available experimental data in literature are discussed and compared to the structure obtained with the different methods. The spread in these data is still too large to uniquely determine the method that “best” describes the perovskite, however, promising candidates and outliers have been identified.

Heyd-Scuseria-Ernzerhof hybrid functional for calculating the lattice dynamics of semiconductors

We present an ab initio study of the lattice dynamics of group-IV elemental semiconductors and insulators using a finite differences approach. The investigated solids include cubic diamond (C), silicon (Si), germanium (Ge), and the zero-gap semiconductor gray tin $(\ensuremath{\alpha}\text{-Sn})$. The main objective of this work is to examine the performance of the screened hybrid functional (HSE) proposed by Heyd, Scuseria, and Ernzerhof [J. Chem. Phys. 118, 8207 (2003); J. Chem. Phys. 124, 219906(E) (2006)] for calculating phonon-dispersion relations. We find that all local and semilocal functionals tend to underestimate the phonon frequencies, with the errors increasing with increasing atomic mass. For $\ensuremath{\alpha}\text{-Sn}$, semilocal functionals even qualitatively fail to describe the dispersion of the highest optical phonon mode. We show that this is related to semilocal functionals predicting $\ensuremath{\alpha}\text{-Sn}$ to be a metal, whereas experimentally it is a zero-gap semiconductor. The HSE functional yields the correct electronic band structure resulting in qualitatively correct phonon-dispersion relations for all four solids. Quantitatively, the phonon frequencies are slightly overestimated using HSE, in particular for the lighter elements C and Si. Our results are compared to previously reported theoretical findings.

Thermodynamic properties by on-the-fly machine-learned interatomic potentials: thermal transport and phase transitions of zirconia

Descriptors representing two- and three-body atomic distributions and their effects on the accuracy of machine-learned inter-atomic potentials

When determining machine-learning models for inter-atomic potentials, the potential energy surface is often described as a non-linear function of descriptors representing two- and three-body atomic distribution functions. It is not obvious how the choice of the descriptors affects the efficiency of the training and the accuracy of the final machine-learned model. In this work, we formulate an efficient method to calculate descriptors that can separately represent two- and three-body atomic distribution functions, and we examine the effects of including only two- or three-body descriptors, as well as including both, in the regression model. Our study indicates that non-linear mixing of two- and three-body descriptors is essential for an efficient training and a high accuracy of the final machine-learned model. The efficiency can be further improved by weighting the two-body descriptors more strongly. We furthermore examine a sparsification of the three-body descriptors. The three-body descriptors usually provide redundant representations of the atomistic structure, and the number of descriptors can be significantly reduced without loss of accuracy by applying an automatic sparsification using a principal component analysis. Visualization of the reduced descriptors using three-body distribution functions in real-space indicates that the sparsification automatically removes the components that are less significant for describing the distribution function.

Brønsted Acid Sites in HSAPO-34 and Chabazite: An Ab Initio Structural Study

The structure of Brønsted acid sites and the effects of the Al → Si and Si → P substitution in chabazite and AlPO4-34 frameworks, respectively, have been studied by ab initio plane-wave calculations on periodic models. Geometry distortions remain well localized to the nearest neighborhood of the Brønsted acid site. The Si−O(H) and Al−O(H) distances of the common Si−O(H)−Al moiety are significantly different in the two kinds of materials. Calculated OH stretching frequencies of acidic protons, which could be assigned to the low- and high-frequency OH bands, in agreement with experimental infrared spectra of H-SSZ-13 (high silica chabazite) and HSAPO-34, correlate with OH bond lengths and Si−O(H)−Al angles.

Ab initio molecular dynamics: recent progresses and limitations

I will discuss recent developments in ab initio molecular dynamics (MD) based on the density functional theory (DFT). Presently, most such calculations are performed using the pseudopotential approximation. With the introduction of the projector augmented-wave method, the exact valence wave functions can be applied during MD without worsening the efficiency of the calculations significantly. Hence, calculations are now exact at least in the framework established by DFT. This allows attention to be turned to other limitations, such as system size or the present semilocal approximations used in DFT. I will show results of a comprehensive study for the liquid metallic (and semiconducting) p elements Al, Ga, In, Tl, Si, Ge, Sn, Pb, As, Sb, Bi, Se and Te. Compared to experiment, discrepancies in the structure factor are observed in particular for heavy elements and for As, Se and Te. Possible reasons for these discrepancies are discussed.

Optical and excitonic properties of transition metal oxide perovskites by the Bethe-Salpeter equation

We present a systematic investigation of the role and importance of excitonic effects on the optical properties of transitions metal oxide perovskites. A representative set of fourteen compounds has been selected, including 3$d$ (SrTiO$_3$, LaScO$_3$, LaTiO$_3$, LaVO$_3$, LaCrO$_3$, LaMnO$_3$, LaFeO$_3$ and SrMnO$_3$), 4$d$ (SrZrO$_3$, SrTcO$_3$ and Ca$_2$RuO$_4$) and 5$d$ (SrHfO$_3$, KTaO$_3$ and NaOsO$_3$) perovskites, covering a band gap ranging from 0.1 eV to 6.1 eV and exhibiting different electronic, structural and magnetic properties. Optical conductivities and optical transitions including electron-hole interactions are calculated through the solution of the Bethe-Salpeter equation (BSE) with quasi-particle energies evaluated by single-shot $G_0W_0$ approximation. The exciton binding energies are computed by means of a model-BSE (mBSE), carefully benchmarked against the full BSE method, in order to obtain well-converged results in terms of k-point sampling. The predicted results are compared with available measured data, with an overall satisfactory agreement between theory and experiment.

Hybrid functionals including random phase approximation correlation and second-order screened exchange

There has been considerable recent interest in density functionals incorporating random phase approximation (RPA) ground-state correlation. By virtue of its full nonlocality, RPA correlation is compatible with exact Hartree-Fock-type exchange and describes van der Waals interactions exceptionally well [B. G. Janesko et al., J. Chem. Phys. 130, 081105 (2009); J. Chem. Phys. 131, 034110 (2009)]. One caveat is that RPA correlation contains one-electron self-interaction error, which leads to disturbingly large correlation energies in the stretched bond situation of, e.g., H(2)(+), He(2)(+), or Ne(2)(+). In the present work, we show that inclusion of second-order screened exchange rectifies the aforementioned failure of RPA correlation. We present a large number of molecular benchmark results obtained using full-range as well as long-range corrected hybrids incorporating second-order screened exchange correlation. This correction has a generally small, and sometimes undesirable, effect on RPA predictions for chemical properties, but appears to be very beneficial for the dissociation of H(2)(+), He(2)(+), and Ne(2)(+).