Manuel Engel

Electron-phonon coupling (EPC) is key to understanding charge transport, band renormalization, and superconductivity in energy materials, including correlated transition-metal oxides, ferroelectric perovskites, optoelectronic semiconductors, and phonon-mediated superconductors. Although first-principles density functional theory (DFT)-based EPC calculations are used widely, their predictive power is limited by the accuracy, transferability, and efficiency of the underlying exchange-correlation functionals. These limitations become exacerbated in complex d - and f -electron materials, where beyond-DFT approaches and additional corrections, such as the Hubbard U , are commonly invoked. Here, using the examples of Co O and Ni O , we show how the r 2 SCAN density functional correctly captures strong EPC effects in transition-metal oxides without requiring the introduction of Hubbard U parameters. We also find that r 2 SCAN successfully describes the subtle interplay between ionic and covalent bonding, and strong EPC effects in the low-temperature rhombohedral phase of the prototypical ferroelectric Ba Ti O 3 , without requiring Hubbard U and intersite V corrections. We further demonstrate the ability of r 2 SCAN to accurately model the EPC of the main-group semiconductor Ga As and the phonon-mediated superconducting properties of Mg B 2 , with reliable electronic bands and phonons. Our study establishes r 2 SCAN-based EPC as a transferable, parameter-free, and computationally efficient framework for predictive material-specific modeling of EPC in energy materials, and opens a practical route toward high-throughput screening of superconductors, thermoelectrics, optoelectronic semiconductors, and oxide electrodes and catalysts.

Electron–phonon coupling (EPC) is fundamental for understanding the behavior of molecules and crystals, influencing phenomena such as charge transport, energy transfer, phase transitions, and polaron formation. Accurate computational methods to calculate EPCs from first principles are essential, but their complexity has resulted in a variety of computational strategies, raising concerns about their mutual consistency. In this study, we provide a systematic benchmark of methods for EPC calculation by comparing two fundamentally different ab initio methodologies. We investigate Gaussian-type orbital methods based on the CP2K code and plane-wave-based projector-augmented-wave methods combined with maximally localized Wannier functions, as implemented in VASP and wannier90 . In addition, we further distinguish between the derivative–of–Hamiltonian ( d H ) and derivative–of–states ( d ψ ) approaches for obtaining EPC parameters. The comparison is conducted on a representative set of organic molecules, including pyrazine, pyridine, bithiophene, and quarterthiophene, varying significantly in size and flexibility. We find excellent agreement across implementations and basis sets when employing the same computational approach ( d H or d ψ ), demonstrating robust consistency between the numerical schemes. However, noticeable deviations occur when comparing the d H and d ψ approaches within each code and for specific cases discussed in detail. Our findings emphasize the reliability of EPC computations using the d H method and caution against potential pitfalls associated with the d ψ approach, providing guidance for future EPC calculations and model parameterizations.

While the periodic equation-of-motion coupled-cluster (EOM-CC) method promises systematic improvement of electronic band gap calculations in solids, its practical application at the singles and doubles level (EOM-CCSD) is hindered by severe finite-size errors in feasible simulation cells. We present a hybrid approach combining EOM-CCSD with the computationally less demanding G W approximation to estimate thermodynamic limit band gaps for several insulators and semiconductors. Our method substantially reduces required cell sizes while maintaining accuracy. Comparisons with experimental gaps and self-consistent G W calculations reveal that deviations in EOM-CCSD predictions correlate with reduced single excitation character of the excited many-electron states. Our work not only provides a computationally tractable approach to EOM-CC calculations in solids but also reveals fundamental insights into the role of single excitations in electronic-structure theory.

We evaluate the zero-point renormalization (ZPR) due to electron-phonon interactions of 28 solids using the projector-augmented-wave (PAW) method. The calculations cover diamond, many zincblende semiconductors, rock-salt and wurtzite oxides, as well as silicate and titania. Particular care is taken to include long-range electrostatic interactions via a generalized Fröhlich model. The data are compared to recent calculations [Miglio et al., npj Comput. Mater. 6, 167 (2020)] and generally very good agreement is found. We discuss in detail the evaluation of the electron-phonon matrix elements within the PAW method. We show that two distinct versions can be obtained depending on when the atomic derivatives are taken. If the PAW transformation is applied before taking derivatives with respect to the ionic positions, then equations similar to the ones conventionally used in pseudopotential codes are obtained. If the PAW transformation is used after taking the derivatives, then the full-potential spirit is largely maintained. We show that both variants yield very similar ZPRs for selected materials when the rigid-ion approximation is employed. In practice, we find, however, that the pseudoversion converges more rapidly with respect to the number of included unoccupied states.

We present an ab initio density-functional-theory approach for calculating electron-phonon interactions within the projector augmented-wave (PAW) method. The required electron-phonon matrix elements are defined as the second derivative of the one-electron energies in the PAW method. As the PAW method leads to a generalized eigenvalue problem, the resulting electron-phonon matrix elements lack some symmetries that are usually present for simple eigenvalue problems and all-electron formulations. We discuss the relation between our definition of the electron-phonon matrix element and other formulations. To allow for efficient evaluation of physical properties, we introduce a Wannier-interpolation scheme, again adapted to generalized eigenvalue problems. To explore the method's numerical characteristics, the temperature-dependent band-gap renormalization of diamond is calculated and compared with previous publications. Furthermore, we apply the method to selected binary compounds and show that the obtained zero-point renormalizations agree well with other values found in literature and experiments.

Transition metal impurities are known to adversely affect the efficiency of electronic and optoelectronic devices by introducing midgap defect levels that can act as efficient Shockley-Read-Hall centers. Iron impurities in GaN do not follow this pattern: their defect level is close to the conduction band and hence far from midgap. Using hybrid functional first-principles calculations, we uncover the electronic properties of Fe and we demonstrate that its high efficiency as a nonradiative center is due to a recombination cycle involving excited states. Unintentional incorporation of iron impurities at modest concentrations (10¹⁵cm^–3) leads to nanosecond nonradiative recombination lifetimes, which can be detrimental for the efficiency of electronic and optoelectronic devices.