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Downfolding coupled cluster (CC) techniques are powerful tools for reducing the dimensionality of many-body quantum problems. This work investigates how ground-state downfolding formalisms can target excited states using non-Aufbau reference determinants, paving the way for applications of quantum computing in excited-state chemistry. This study focuses on doubly excited states for which canonical equation-of-motion CC approaches struggle to describe unless one includes higher-than-double excitations. The downfolding technique results in state-specific effective Hamiltonians that, when diagonalized in their respective active spaces, provide ground- and excited-state total energies (and therefore excitation energies) comparable to high-level CC methods. The performance of this procedure is examined with doubly excited states of H$_{2}$, Methylene, Formaldehyde, and Nitroxyl.

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.

Molecular structure plays an important role in the selectivity and performance of catalysts. Understanding the impact of structural differences on catalyst performance via quantitative structure-selectivity relationships is key to developing high-performing catalytic systems. There are several methods that have been introduced to quantify steric contributions, including Tolman cone angles, Charton parameters, and A-values. While these have shown promise in predicting selectivity, they access similar, general steric contributions and are largely empirically derived. Alternatively, Sterimol parameters offer a specific multi-directional measure of steric bulk in the form of three vectors in units of distance. Recently, these parameters revealed strong correlations between structure and selectivity in asymmetric catalysis. Yet, despite their demonstrated performance, Sterimol parameters are commonly derived using van der Waals radii, which approximate molecular size using hard-spheres. This method may not accurately describe highly polarized systems. Recently, a new chemical system size metric based on the electric-field of a molecule was developed, which accesses the occupied space of a molecule. Here, we demonstrate that the electric field-derived Sterimol parameters reveal similar structure-selectivity relationships in asymmetric catalysis as conventional Sterimol parameters. Specifically, we present a computational workflow for calculating Sterimol parameters based on the size of a molecule's electric field, and validate our method using several asymmetric catalysis reactions.

Synchrotron radiation-based methods, in particular photoemission spectroscopy, are very powerful tools for studying the electronic, chemical, and structural properties of materials and combinations of materials. Numerous experimental studies have been performed in the last decades using synchrotron radiation in physics, chemistry, material science, biology, medicine, and more. However, the advantage of high photon flux from synchrotron storage rings, which is beneficial or even crucial for many experiments, may impose new problems when sensitive samples are investigated, such as organic systems. They are prone to chemical changes when exposed to high photon fluxes. Here, we demonstrate how to identify beam-induced sample degradation and provide the best practice rules for reliable investigations and control experiments.

We present a comprehensive investigation of the electrical and thermal conductivity of iron under high pressures at ambient temperature, employing the real-time formulation of time-dependent density functional theory (RT-TDDFT). Specifically, we examine the influence of a Hubbard correction (+U) to account for strong electron correlations. Our calculations based on RT-TDDFT demonstrate that the evaluated electrical conductivity for both high-pressure body-centered cubic (BCC) and hexagonal close-packed (HCP) iron phases agrees well with experimental data. Furthermore, we explore the anisotropy in the thermal conductivity of HCP iron under high pressure, and our findings are consistent with experimental observations. Interestingly, we find that the incorporation of the +U correction significantly impacts the ground state and linear response properties of iron at pressures below 50 GPa, with its influence diminishing as pressure increases. This study offers valuable insights into the influence of electronic correlations on the electronic transport properties of iron under extreme conditions.

The propagation of general electronic quantum states provides information of the interaction of molecular systems with external driving fields. These can also offer understandings regarding non-adiabatic quantum phenomena. Well established methods focus mainly on propagating a quantum system that is initially described exclusively by the ground state wavefunction. In this work, we expand a previously developed size-extensive formalism within coupled cluster theory, called second response theory, so it propagates quantum systems that are initially described by a general linear combination of different states, which can include the ground state, and show how with a special set of time-dependent cluster operators such propagations are performed. Our theory shows strong consistency with numerically exact results for the determination of quantum mechanical observables, probabilities, and coherences. We discuss unperturbed non-stationary states within second response theory and their ability to predict matrix elements that agree with those found in linear and quadratic response theories. This work also discusses an approximate regularized methodology to treat systems with potential instabilities in their ground-state cluster amplitudes, and compares such approximations with respect to reference results from standard unitary theory.

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.

Despite rapid progress in the development of quantum algorithms in quantum computing as well as numerical simulation methods in classical computing for atomic and molecular applications, no systematic and comprehensive electronic structure study of atomic systems that covers almost all of the elements in the periodic table using a single quantum algorithm has been reported. In this work, we address this gap by implementing the recently-proposed quantum algorithm, the Bayesian phase difference estimation (BPDE) approach, to determine fine structure splittings of a wide range of boron-like atomic systems. Since accurate estimate of fine structure splittings strongly depend on the relativistic as well as quantum many-body effects, our study can test the potential of the BPDE approach to produce results close to the experimental values. Our numerical simulations reveal that the BPDE algorithm, in the Dirac–Coulomb–Breit framework, can predict fine structure splittings of ground states of the considered systems quite precisely. We performed our simulations of relativistic and electron correlation effects on Graphics Processing Unit by utilizing NVIDIA's cuQuantum, and observe a ×42.7 speedup as compared to the Central Processing Unit-only simulations in an 18-qubit active space.

Molecular motion at metallic surfaces is affected by nonadiabatic effects and electron-phonon coupling. The ensuing energy dissipation and dynamical steering effects are not captured by classical molecular dynamics simulations, but can be described with the molecular dynamics with electronic friction method and linear response calculations based on density functional theory. Herein, we present an implementation of electron-phonon response based on an all-electron numeric atomic orbital description in the electronic structure code FHI-aims. After providing details of the underlying approximations and numerical considerations, we present significant scalability and performance improvements of the new code compared to a previous implementation (Maurer et al 2016 Phys. Rev. B 94 115432). We compare convergence behaviour and results of our simulations for exemplary systems such as H₂ adsorption on Cu(111), and CO on Ru(0001) against existing plane wave implementations. We examine different expressions to calculate electronic friction and vibrational lifetimes for their reliability and ease of convergence. Finally, we show the capabilities of the new code by studying the contribution of interband and intraband excitations to the vibrational lifetime of aperiodic adsorbate motion in large, previously unfeasible, periodic surface models.

How fast a state of a system converges to a stationary state is one of the fundamental questions in science. Some Markov chains and random walks on finite groups are known to exhibit the non-asymptotic convergence to a stationary distribution, called the cutoff phenomenon. Here, we examine how quickly a random quantum circuit could transform a quantum state to a Haar-measure random quantum state. We find that random quantum states, as stationary states of random walks on a unitary group, are invariant under the quantum Fourier transform (QFT). Thus the entropic uncertainty of random quantum states has balanced Shannon entropies for the computational basis and the QFT basis. By calculating the Shannon entropy for random quantum states and the Wasserstein distances for the eigenvalues of random quantum circuits, we show that the cutoff phenomenon occurs for the random quantum circuit. It is also demonstrated that the Dyson-Brownian motion for the eigenvalues of a random unitary matrix as a continuous random walk exhibits the cutoff phenomenon. The results here imply that random quantum states could be generated with shallow random circuits.

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.