Electronic Structure

In recent years, we have been witnessing a paradigm shift in computational materials science. In fact, traditional methods, mostly developed in the second half of the XXth century, are being complemented, extended, and sometimes even completely replaced by faster, simpler, and often more accurate approaches. The new approaches, that we collectively label by machine learning, have their origins in the fields of informatics and artificial intelligence, but are making rapid inroads in all other branches of science. With this in mind, this Roadmap article, consisting of multiple contributions from experts across the field, discusses the use of machine learning in materials science, and share perspectives on current and future challenges in problems as diverse as the prediction of materials properties, the construction of force-fields, the development of exchange correlation functionals for density-functional theory, the solution of the many-body problem, and more. In spite of the already numerous and exciting success stories, we are just at the beginning of a long path that will reshape materials science for the many challenges of the XXIth century.

The lattice vibrations (phonon modes) of crystals underpin a large number of material properties. The harmonic phonon spectrum of a solid is the simplest description of its structural dynamics and can be straightforwardly derived from the Hellman–Feynman forces obtained in a ground-state electronic structure calculation. The presence of imaginary harmonic modes in the spectrum indicates that a structure is not a local minimum on the structural potential-energy surface and is instead a saddle point or a hilltop, for example. This can in turn yield important insight into the fundamental nature and physical properties of a material. In this review article, we discuss the physical significance of imaginary harmonic modes and distinguish between cases where imaginary modes are indicative of such phenomena, and those where they reflect technical problems in the calculations. We outline basic approaches for exploring and renormalising imaginary modes, and demonstrate their utility through a set of three case studies in the materials sciences.

In this review, we present important concepts to describe inorganic–organic interfaces in hybrid solar cells. We discuss the formation of hybrid interfaces, provide an introduction to the ground-state electronic structure of the individual components, and detail the overall electronic landscape after combining into a hybrid material for different relevant cases. We then explore the impact of hybrid interfaces on photophysical processes that are crucial for the photovoltaic performance of hybrid solar cells. Within this framework, we discuss methods for hybrid interface modification toward the optimization of hybrid solar cells, such as doping, the application of interlayers, and morphological control.

The development of novel materials for vacuum electron sources in particle accelerators is an active field of research that can greatly benefit from the results of ab initio calculations for the characterization of the electronic structure of target systems. As state-of-the-art many-body perturbation theory calculations are too expensive for large-scale material screening, density functional theory offers the best compromise between accuracy and computational feasibility. The quality of the obtained results, however, crucially depends on the choice of the exchange–correlation potential, v_xc. To address this essential point, we systematically analyze the performance of three popular approximations of v_xc [PBE, strongly constrained and appropriately normed (SCAN), and HSE06] on the structural and electronic properties of bulk Cs₃Sb and Cs₂Te as representative materials of Cs-based semiconductors employed in photocathode applications. Among the adopted approximations, PBE shows expectedly the largest discrepancies from the target: the unit cell volume is overestimated compared to the experimental value, while the band gap is severely underestimated. On the other hand, both SCAN and HSE06 perform remarkably well in reproducing both structural and electronic properties. Spin–orbit coupling, which mainly impacts the valence region of both materials inducing a band splitting and, consequently, a band-gap reduction of the order of 0.2 eV, is equally captured by all functionals. Our results indicate SCAN as the best trade-off between accuracy and computational costs, outperforming the considerably more expensive HSE06.

This review outlines fundamental principles, instrumentation, and capabilities of angle-resolved photoemission spectroscopy (ARPES) and microscopy. We will present how high-resolution ARPES enables to investigate fine structures of electronic band dispersions, Fermi surfaces, gap structures, and many-body interactions, and how angle-resolved photoemission microscopy (spatially-resolved ARPES) utilizing micro/nano-focused light allows to extract spatially localized electronic information at small dimensions. This work is focused on specific results obtained by the author from strongly correlated copper and ruthenium oxides, to help readers to understand consistently how these techniques can provide essential electronic information of materials, which can, in principle, apply to a wide variety of systems.

Recent developments in fully numerical methods promise interesting opportunities for new, compact atomic orbital (AO) basis sets that maximize the overlap to fully numerical reference wave functions, following the pioneering work of Richardson and coworkers from the early 1960s. Motivated by this technique, we suggest a way to visualize the importance of AO basis functions employing fully numerical wave functions computed at the complete basis set limit: the importance of a normalized AO basis function $|\alpha\rangle$ centered on some nucleus can be visualized by projecting $|\alpha\rangle$ on the set of numerically represented occupied orbitals $|\psi_{i}\rangle$ as $I_{0}(\alpha) = \sum_{i}\langle\alpha|\psi_{i}\rangle\langle\psi_{i}|\alpha\rangle$. Choosing α to be a continuous parameter describing the AO basis, such as the exponent of a Gaussian-type orbital or Slater-type orbital basis function, one is then able to visualize the importance of various functions. The proposed visualization $I_{0}(\alpha)$ has the important property $0\unicode{x2A7D} I_{0}(\alpha)\unicode{x2A7D}1$ which allows unambiguous interpretation. We also propose a straightforward generalization of the importance profile for polyatomic applications $I(\alpha)$, in which the importance of a test function $\vert \alpha\rangle$ is measured as the increase in projection from the atomic minimal basis. We exemplify the methods with importance profiles computed for atoms from the first three rows, and for a set of chemically diverse diatomic molecules. We find that the importance profile offers a way to visualize the atomic basis set requirements for a given system in an a priori manner, provided that a fully numerical reference wave function is available.

We present a Floquet scheme for the ab-initio calculation of nonlinear optical properties in extended systems. This entails a reformulation of the real-time approach based on the dynamical Berry-phase polarisation (Attaccalite and Grüning 2013 Phys. Rev. B 88 1–9) and retains the advantage of being non-perturbative in the electric field. The proposed method applies to periodically-driven Hamiltonians and makes use of this symmetry to turn a time-dependent problem into a self-consistent time-independent eigenvalue problem. We implemented this Floquet scheme at the independent particle level and compared it with the real-time approach. Our reformulation reproduces real-time-calculated 2nd and 3rd order susceptibilities for a number of bulk and two-dimensional materials, while reducing the associated computational cost by one or two orders of magnitude.

Materials design based on density functional theory (DFT) calculations is an emergent field of great potential to accelerate the development and employment of novel materials. Magnetic materials play an essential role in green energy applications as they provide efficient ways of harvesting, converting, and utilizing energy. In this review, after a brief introduction to the major functionalities of magnetic materials, we demonstrated how the fundamental properties can be tackled via high-throughput DFT calculations, with a particular focus on the current challenges and feasible solutions. Successful case studies are summarized on several classes of magnetic materials, followed by bird-view perspectives.

The disproportionation of H₂O into solar fuels H₂ and O₂, or water splitting, is a promising strategy for clean energy harvesting and storage but requires the concerted action of absorption of photons, separation of excitons, charge diffusion to catalytic sites and catalysis of redox processes. It is increasingly evident that the rational design of photocatalysts for efficient water splitting must employ hybrid systems, where the different components perform light harvesting, charge separation and catalysis in tandem. In this topical review, we report on the recent development of a new class of hybrid photocatalysts that employs M_xV₂O₅ (M = p-block cation) nanowires in order to engineer efficient charge transfer from the photoactive chalcogenide quantum dots (QDs) to the water-splitting and hydrogen evolving catalysts. Herein, we summarize the oxygen-mediated lone pair mechanism used to modulate the energy level and orbital character of mid-gap states in the M_xV₂O₅ nanowires. The electronic structure of M_xV₂O₅ is discussed in terms of density functional theory and hard x-ray photoelectron spectroscopy (HAXPES) measurements. The principles of HAXPES are explained within the context of its unique sensitivity to metal 5(6)s orbitals and ability to non-destructively study buried interface alignments of quantum dot decorated nanowires i.e., M_xV₂O₅/CdX (X = S, Se, Te). We illustrate with examples how the M_xV₂O₅/CdX band alignments can be rationally engineered for ultra-fast charge-transfer of photogenerated holes from the quantum dot to the nanowires; thereby suppressing anodic photo-corrosion in the CdX QDs and enabling efficacious hydrogen evolution.

Quantum Monte Carlo (QMC) can play a very important role in generating accurate data needed for constructing potential energy surfaces. We argue that QMC has advantages in terms of a smaller systematic bias and an ability to cover phase space more completely. The stochastic noise can ease the training of the machine learning model. We discuss how stochastic errors affect the generation of effective models by analyzing the errors within a linear least squares procedure, finding that there is an advantage to having many relatively imprecise data points for constructing models. We then analyze the effect of noise on a model of many-body silicon finding that noise in some situations improves the resulting model. We then study the effect of QMC noise on two machine learning models of dense hydrogen used in a recent study of its phase diagram. The noise enables us to estimate the errors in the model. We conclude with a discussion of future research problems.

The wordwide energy demands and the surge towards a net-zero sustainable society let the researchers set a goal towards the end of carbon cycle. This has enormously exaggerated the electrocatalytic processes such as water splitting, CO₂ capture and reduction and nitrogen reduction reaction (NRR) as a safe and green alternative as these involve the utilization of renewable green power. Interestingly, the NH₃ produced from NRR has been realized as a future fuel in terms of safer green H₂ storage and transportation. Nevertheless, to scale up the NH₃ production electrochemically, a benevolent catalyst needs to be developed. More interestingly, the electronic features of the catalyst that actually contribute to the interaction and binding between the adsorbate and reaction intermediates should be analyzed such that these can be tuned based on our requirements to obtain the desired high-standard goals of NH₃ synthesis. The current topical review aims to provide an illustrative understanding on the experimental and theoretical descriptors that are likely to influence the electronic structure of catalysts for NRR. We have widely covered a detailed explanation regarding work function, d-band center and electronic effect on the electronic structures of the catalysts. While summarizing the same, we realized that there are several discrepancies in this field, which have not been discussed and could be misleading for the newcomers in the field. Thus, we have briefed the limitations and diverging explanations and have provided a few directions that could be looked upon to overcome the issues.

Variational Monte Carlo methods have recently been applied to the calculation of excited states; however, it is still an open question what objective function is most effective. A promising approach is to optimize excited states using a penalty to minimize overlap with lower eigenstates, which has the drawback that states must be computed one at a time. We derive a general framework for constructing objective functions with minima at the the lowest N eigenstates of a many-body Hamiltonian. The objective function uses a weighted average of the energies and an overlap penalty, which must satisfy several conditions. We show this objective function has a minimum at the exact eigenstates for a finite penalty, and provide a few strategies to minimize the objective function. The method is demonstrated using ab initio variational Monte Carlo to calculate the degenerate first excited state of a CO molecule.

The universal applicability of density functional approximations is limited by self-interaction error made by these functionals. Recently, a novel one-electron self-interaction-correction (SIC) method that uses an iso-orbital indicator to apply the SIC at each point in space by scaling the exchange-correlation and Coulomb energy densities was proposed. The locally scaled SIC (LSIC) method is exact for the one-electron densities, and unlike the well-known Perdew–Zunger SIC (PZSIC) method recovers the uniform electron gas limit of the uncorrected density functional approximation, and reduces to PZSIC method as a special case when isoorbital indicator is set to the unity. Here, we present a numerical scheme that we have adopted to evaluate the Coulomb potential of the electron density scaled by the iso-orbital indicator required for the self-consistent LSIC calculations. After analyzing the behavior of the finite difference method (FDM) and the green function solution to the radial part of the Poisson equation, we adopt a hybrid approach that uses the FDM for the Coulomb potential due to the monopole and the GF for all higher-order terms. The performance of the resultant hybrid method is assessed using a variety of systems. The results show improved accuracy than earlier numerical schemes. We also find that, even with a generic set of radial grid parameters, accurate energy differences can be obtained using a numerical Coulomb solver in standard density functional studies.

Recent developments in fully numerical methods promise interesting opportunities for new, compact atomic orbital (AO) basis sets that maximize the overlap to fully numerical reference wave functions, following the pioneering work of Richardson and coworkers from the early 1960s. Motivated by this technique, we suggest a way to visualize the importance of AO basis functions employing fully numerical wave functions computed at the complete basis set limit: the importance of a normalized AO basis function $|\alpha\rangle$ centered on some nucleus can be visualized by projecting $|\alpha\rangle$ on the set of numerically represented occupied orbitals $|\psi_{i}\rangle$ as $I_{0}(\alpha) = \sum_{i}\langle\alpha|\psi_{i}\rangle\langle\psi_{i}|\alpha\rangle$. Choosing α to be a continuous parameter describing the AO basis, such as the exponent of a Gaussian-type orbital or Slater-type orbital basis function, one is then able to visualize the importance of various functions. The proposed visualization $I_{0}(\alpha)$ has the important property $0\unicode{x2A7D} I_{0}(\alpha)\unicode{x2A7D}1$ which allows unambiguous interpretation. We also propose a straightforward generalization of the importance profile for polyatomic applications $I(\alpha)$, in which the importance of a test function $\vert \alpha\rangle$ is measured as the increase in projection from the atomic minimal basis. We exemplify the methods with importance profiles computed for atoms from the first three rows, and for a set of chemically diverse diatomic molecules. We find that the importance profile offers a way to visualize the atomic basis set requirements for a given system in an a priori manner, provided that a fully numerical reference wave function is available.

Quantum subspace methods (QSMs) are a class of quantum computing algorithms where the time-independent Schrödinger equation for a quantum system is projected onto a subspace of the underlying Hilbert space. This projection transforms the Schrödinger equation into an eigenvalue problem determined by measurements carried out on a quantum device. The eigenvalue problem is then solved on a classical computer, yielding approximations to ground- and excited-state energies and wavefunctions. QSMs are examples of hybrid quantum–classical methods, where a quantum device supported by classical computational resources is employed to tackle a problem. QSMs are rapidly gaining traction as a strategy to simulate electronic wavefunctions on quantum computers, and thus their design, development, and application is a key research field at the interface between quantum computation and electronic structure (ES). In this review, we provide a self-contained introduction to QSMs, with emphasis on their application to the ES of molecules. We present the theoretical foundations and applications of QSMs, and we discuss their implementation on quantum hardware, illustrating the impact of noise on their performance.

The wordwide energy demands and the surge towards a net-zero sustainable society let the researchers set a goal towards the end of carbon cycle. This has enormously exaggerated the electrocatalytic processes such as water splitting, CO₂ capture and reduction and nitrogen reduction reaction (NRR) as a safe and green alternative as these involve the utilization of renewable green power. Interestingly, the NH₃ produced from NRR has been realized as a future fuel in terms of safer green H₂ storage and transportation. Nevertheless, to scale up the NH₃ production electrochemically, a benevolent catalyst needs to be developed. More interestingly, the electronic features of the catalyst that actually contribute to the interaction and binding between the adsorbate and reaction intermediates should be analyzed such that these can be tuned based on our requirements to obtain the desired high-standard goals of NH₃ synthesis. The current topical review aims to provide an illustrative understanding on the experimental and theoretical descriptors that are likely to influence the electronic structure of catalysts for NRR. We have widely covered a detailed explanation regarding work function, d-band center and electronic effect on the electronic structures of the catalysts. While summarizing the same, we realized that there are several discrepancies in this field, which have not been discussed and could be misleading for the newcomers in the field. Thus, we have briefed the limitations and diverging explanations and have provided a few directions that could be looked upon to overcome the issues.

Quantum subspace methods (QSMs) are a class of quantum computing algorithms where the time-independent Schrödinger equation for a quantum system is projected onto a subspace of the underlying Hilbert space. This projection transforms the Schrödinger equation into an eigenvalue problem determined by measurements carried out on a quantum device. The eigenvalue problem is then solved on a classical computer, yielding approximations to ground- and excited-state energies and wavefunctions. QSMs are examples of hybrid quantum–classical methods, where a quantum device supported by classical computational resources is employed to tackle a problem. QSMs are rapidly gaining traction as a strategy to simulate electronic wavefunctions on quantum computers, and thus their design, development, and application is a key research field at the interface between quantum computation and electronic structure (ES). In this review, we provide a self-contained introduction to QSMs, with emphasis on their application to the ES of molecules. We present the theoretical foundations and applications of QSMs, and we discuss their implementation on quantum hardware, illustrating the impact of noise on their performance.

The recent progress in the studies of 2D materials placed in front many experimental and theoretical works on the interesting class of materials, the so-called transition metal phosphorus trichalcogenides with structural formula MPX₃ (M: transition metal, X: chalcogen). Here, the diversity in the M/X combination opens the possibility to tune the electronic and magnetic properties of these materials in a very wide range, resulting in many interesting physical phenomena followed by the promoting their use in different application areas. This review gives a timely overview of the recent progress in the fundamental studies of electronic structure and magnetic properties of MPX₃ materials (M: Mn, Fe, Co, Ni, X: S, Se) focusing on the results obtained by density functional theory, Raman spectroscopy and electron spectroscopy methods. We pay close attention to the large amount of theoretical and experimental data giving critical analysis of the previously obtained results. It is shown how the systematic fundamental studies of the electronic and magnetic properties of MPX₃ can help to understand the functionality of these interesting 2D materials in different applications, ranging from optoelectronics to catalysis.

Dispersed impurities in diamond present a flourishing platform for research in quantum informatics, spintronics and single phonon emitters. Based on the vast pool of experimental and theoretical work describing impurity atoms in diamond, we review the configurations by the chemical element discussing the relevant atomic configurations and most important properties. Dopant structures expand from single to co-doping configurations, also combined with carbon vacancies. Despite of their importance, not much is known about the exact atomic configurations associated with the dopant structures beyond computational models, partially due to difficulties in their microscopic observation. To assess the visibility of these structures, we carry out image simulations to show that the heavier dopants may be easily discernible in scanning transmission electron microscopy annular dark field images, with a window of visibility of up to over ${\pm}$10 nm in defocus. We further present the first atomic resolution images of an impurity atom configuration (substitutional Er atom) in the diamond lattice, confirmed by a comparison to the simulated images. Overall, our results demonstrate that there is a vast research field waiting for the microscopy community in resolving the exact atomic structure of various impurity atom configurations in diamond.

The development of advanced experimental and theoretical methods for the characterization of excitations in materials enables revisiting established concepts that are sometimes misleadingly transferred from one field to another without the necessary disclaimers. This is precisely the situation that occurs for excitons in organic materials: different states of matter and peculiarities related to their structural arrangements and their environment may substantially alter the nature of the photo-induced excited states compared to inorganic semiconductors for which the concept of an exciton was originally developed. Adopting the examples of tetracene and perfluorotetracene, in this review, we analyze the nature of the excitations in the isolated compounds in solution, in the crystalline materials, and in melt. Using single crystals or films with large crystalline domains enables polarization-resolved optical absorption measurements, and thus the determination of the energy and polarization of different excitons. These experiments are complemented by state-of-the-art first-principles calculations based on density-functional theory and many-body perturbation theory. The employed methodologies offer unprecedented insight into the optical response of the systems, allowing us to clarify the single-particle character of the excitations in isolated molecules and the collective nature of the electron–hole pairs in the aggregated phases. Our results reveal that the turning point between these two scenarios is the quantum-mechanical interactions between the molecules: when their wave-function distributions and the Coulomb interactions among them are explicitly described in the adopted theoretical scheme, the excitonic character of the optical transitions can be captured. Semi-classical models accounting only for electrostatic couplings between the photo-activated molecules and their environment are unable to reproduce these effects. The outcomes of this work offer a deeper understanding of excitations in organic semiconductors from both theoretical and experimental perspectives.

Solid state theory, density functional theory and its generalizations for correlated systems together with numerical simulations on supercomputers allow nowadays to model magnetic systems realistically and in detail and can be even used to predict new materials, paving the way for more rapid material development for applications in energy storage and conversion, information technologies, sensors, actuators etc. Modelling magnets on different length scales (between a few Angström and several micrometers) requires, however, approaches with very different mathematical formulations. Parameters defining the material in each formulation can be determined either by fitting experimental data or from theoretical calculations and there exists a well-established approach for obtaining model parameters for each length scale using the information from the smaller length scale. In this review, this approach will be explained step-by-step in textbook style with examples of successful multiscale modelling of different classes of magnetic materials from the research literature as well as based on results newly obtained for this review.

The universal applicability of density functional approximations is limited by self-interaction error made by these functionals. Recently, a novel one-electron self-interaction-correction (SIC) method that uses an iso-orbital indicator to apply the SIC at each point in space by scaling the exchange-correlation and Coulomb energy densities was proposed. The locally scaled SIC (LSIC) method is exact for the one-electron densities, and unlike the well-known Perdew–Zunger SIC (PZSIC) method recovers the uniform electron gas limit of the uncorrected density functional approximation, and reduces to PZSIC method as a special case when isoorbital indicator is set to the unity. Here, we present a numerical scheme that we have adopted to evaluate the Coulomb potential of the electron density scaled by the iso-orbital indicator required for the self-consistent LSIC calculations. After analyzing the behavior of the finite difference method (FDM) and the green function solution to the radial part of the Poisson equation, we adopt a hybrid approach that uses the FDM for the Coulomb potential due to the monopole and the GF for all higher-order terms. The performance of the resultant hybrid method is assessed using a variety of systems. The results show improved accuracy than earlier numerical schemes. We also find that, even with a generic set of radial grid parameters, accurate energy differences can be obtained using a numerical Coulomb solver in standard density functional studies.

Recent developments in fully numerical methods promise interesting opportunities for new, compact atomic orbital (AO) basis sets that maximize the overlap to fully numerical reference wave functions, following the pioneering work of Richardson and coworkers from the early 1960s. Motivated by this technique, we suggest a way to visualize the importance of AO basis functions employing fully numerical wave functions computed at the complete basis set limit: the importance of a normalized AO basis function $|\alpha\rangle$ centered on some nucleus can be visualized by projecting $|\alpha\rangle$ on the set of numerically represented occupied orbitals $|\psi_{i}\rangle$ as $I_{0}(\alpha) = \sum_{i}\langle\alpha|\psi_{i}\rangle\langle\psi_{i}|\alpha\rangle$. Choosing α to be a continuous parameter describing the AO basis, such as the exponent of a Gaussian-type orbital or Slater-type orbital basis function, one is then able to visualize the importance of various functions. The proposed visualization $I_{0}(\alpha)$ has the important property $0\unicode{x2A7D} I_{0}(\alpha)\unicode{x2A7D}1$ which allows unambiguous interpretation. We also propose a straightforward generalization of the importance profile for polyatomic applications $I(\alpha)$, in which the importance of a test function $\vert \alpha\rangle$ is measured as the increase in projection from the atomic minimal basis. We exemplify the methods with importance profiles computed for atoms from the first three rows, and for a set of chemically diverse diatomic molecules. We find that the importance profile offers a way to visualize the atomic basis set requirements for a given system in an a priori manner, provided that a fully numerical reference wave function is available.

The GW approximation has become an important tool for predicting charged excitations of isolated molecules and condensed systems. Its popularity can be attributed to many factors, including a favorable scaling and relatively good accuracy. In practical applications, the GW is often performed as a one-shot perturbation known as $G_0W_0$. Unfortunately, $G_0W_0$ suffers from a strong starting point dependence and is often not as accurate as one would need. Self-consistent GW methodologies alleviate these problems but come with a marked increase in computational cost. In this manuscript, we propose the use of an estimate of the exchange-correlation derivative discontinuity to provide a remarkably good starting point for $G_0W_0$ calculations, yielding ionization potentials and electron affinities with eigenvalue self-consistent GW quality at no additional cost. We assess the quality of the resulting methodology with the GW100 benchmark set and compare its advantages over other similar methods.

Quantum Monte Carlo (QMC) can play a very important role in generating accurate data needed for constructing potential energy surfaces. We argue that QMC has advantages in terms of a smaller systematic bias and an ability to cover phase space more completely. The stochastic noise can ease the training of the machine learning model. We discuss how stochastic errors affect the generation of effective models by analyzing the errors within a linear least squares procedure, finding that there is an advantage to having many relatively imprecise data points for constructing models. We then analyze the effect of noise on a model of many-body silicon finding that noise in some situations improves the resulting model. We then study the effect of QMC noise on two machine learning models of dense hydrogen used in a recent study of its phase diagram. The noise enables us to estimate the errors in the model. We conclude with a discussion of future research problems.

The last few decades has seen the rapid growth of interest in the bulk perovskite-type transition metal oxides SrVO₃ and SrTiO₃. The electronic configuration of these perovskites differs by one electron associated to the transition metal species which gives rise to the drastically different electronic properties. Therefore, it is natural to look into how the electronic structure transitions between these bulk structures by using doping. Measurements of the substitutional doped SrTi$_{{1-x}}$V$_{{{x}}}$O₃ shows an metal–insulator transition (MIT) as a function of doping. By using supercell density functional theory with dynamical mean field theory (DFT+DMFT), we show that the MIT is indeed the result of the combination of local electron correlation effects (Mott physics) within the $t_{{\mathrm{2g}}}$ orbitals and the atomic site configuration of the transition metals which may indicate dependence on site disorder. SrTi$_{{1-x}}$V$_{{{x}}}$O₃ may be an ideal candidate for benchmarking cutting-edge Mott–Anderson models of real systems. We show that applying an effective external perturbation on SrTi$_{{1-x}}$V$_{{{x}}}$O₃ can switch the system between the insulating and metallic phase, meaning this is a bulk system with the potential use in Mott electronic devices.

Phonons are quantized vibrations of a crystal lattice that play a crucial role in understanding many properties of solids. Density functional theory provides a state-of-the-art computational approach to lattice vibrations from first-principles. We present a successful software implementation for calculating phonons in the harmonic approximation, employing density-functional perturbation theory within the framework of the full-potential linearized augmented plane-wave method as implemented in the electronic structure package FLEUR. The implementation, which involves the Sternheimer equation for the linear response of the wave function, charge density, and potential with respect to infinitesimal atomic displacements, as well as the setup of the dynamical matrix, is presented and the specifics due to the muffin-tin sphere centered linearized augmented plane-wave basis-set and the all-electron nature are discussed. As a test, we calculate the phonon dispersion of several solids including an insulator, a semiconductor as well as several metals. The latter are comprised of magnetic, simple, and transition metals. The results are validated on the basis of phonon dispersions calculated using the finite displacement approach in conjunction with the FLEUR code and the phonopy package, as well as by some experimental results. An excellent agreement is obtained.

We present theoretical calculations of the optical spectrum of monolayer MoS₂ with a charged defect. In particular, we solve the Bethe–Salpeter equation based on an atomistic tight-binding model of the MoS₂ electronic structure which allows calculations for large supercells. The defect is modelled as a point charge whose potential is screened by the MoS₂ electrons. We find that the defect gives rise to new peaks in the optical spectrum approximately 100–200 meV below the first free exciton peak. These peaks arise from transitions involving in-gap bound states induced by the charged defect. Our findings are in good agreement with experimental measurements.

A typical task for classical and quantum computing in chemistry is finding a potential energy surface (PES) along a reaction coordinate, which involves solving the quantum chemistry problem for many points along the reaction path. Developing algorithms to accomplish this task on quantum computers has been an active area of development, yet finding all the relevant eigenstates along the reaction coordinate remains a difficult problem, and determining PESs is thus a costly proposal. In this paper, we demonstrate the use of a eigenvector continuation—a subspace expansion that uses a few eigenstates as a basis—as a tool for rapidly exploring PESs. We apply this to determining the binding PES or torsion PES for several molecules of varying complexity. In all cases, we show that the PES can be captured using relatively few basis states; suggesting that a significant amount of (quantum) computational effort can be saved by making use of already calculated ground states in this manner.

By exploiting the invariance of the molecular Hamiltonian by a unitary transformation of the orbitals it is possible to significantly shorter the depth of the variational circuit in the variational quantum eigensolver (VQE) algorithm by using the wavefunction adapted Hamiltonian through orbital rotation (WAHTOR) algorithm. This work introduces a non-adiabatic version of the WAHTOR algorithm and compares its efficiency with three implementations by estimating quantum processing unit (QPU) resources in prototypical benchmarking systems. Calculating first and second-order derivatives of the Hamiltonian at fixed VQE parameters does not introduce a significant QPU overload, leading to results on small molecules that indicate the non-adiabatic Newton–Raphson method as the more convenient choice. On the contrary, we find out that in the case of Hubbard model systems the trust region non-adiabatic optimization is more efficient. The preset work therefore clearly indicates the best optimization strategies for empirical variational ansatzes, facilitating the optimization of larger variational wavefunctions for quantum computing.