Energy, Momentum, and Angular Momentum Transfer between Electrons and Nuclei.

The recently developed exact factorization approach condenses all electronic effects on the nuclear subsystem into scalar and vector potentials that appear in an effective time dependent Schrödinger equation. Starting from this equation, we derive subsystem Ehrenfest identities characterizing the energy, momentum, and angular momentum transfer between electrons and nuclei. An effective electromagnetic force operator induced by the electromagnetic field corresponding to the effective scalar and vector potentials appears in all three identities. The effective magnetic field has two components that can be identified with the Berry curvature calculated with (a) different Cartesian coordinates of the same nucleus and (b) arbitrary Cartesian coordinates of two different nuclei. (a) has a classical interpretation as the induced magnetic field felt by the nucleus, while (b) has no classical analog. Subsystem Ehrenfest identities are ideally suited for quantifying energy transfer in electron-phonon systems. With two explicit examples we demonstrate the usefulness of the new identities.

The 2021 room-temperature superconductivity roadmap.

Designing materials with advanced functionalities is the main focus of contemporary solid-state physics and chemistry. Research efforts worldwide are funneled into a few high-end goals, one of the oldest, and most fascinating of which is the search for an ambient temperature superconductor (A-SC). The reason is clear: superconductivity at ambient conditions implies being able to handle, measure and access a single, coherent, macroscopic quantum mechanical state without the limitations associated with cryogenics and pressurization. This would not only open exciting avenues for fundamental research, but also pave the road for a wide range of technological applications, affecting strategic areas such as energy conservation and climate change. In this roadmap we have collected contributions from many of the main actors working on superconductivity, and asked them to share their personal viewpoint on the field. The hope is that this article will serve not only as an instantaneous picture of the status of research, but also as a true roadmap defining the main long-term theoretical and experimental challenges that lie ahead. Interestingly, although the current research in superconductor design is dominated by conventional (phonon-mediated) superconductors, there seems to be a widespread consensus that achieving A-SC may require different pairing mechanisms.In memoriam, to Neil Ashcroft, who inspired us all.

Fock-Space Embedding Theory: Application to Strongly Correlated Topological Phases.

A many-body wave function can be factorized in Fock space into a marginal amplitude describing a set of strongly correlated orbitals and a conditional amplitude for the remaining weakly correlated part. The marginal amplitude is the solution of a Schrödinger equation with an effective Hamiltonian that can be viewed as embedding the marginal wave function in the environment of weakly correlated electrons. Here, the complementary equation for the conditional amplitude is replaced by a generalized Kohn-Sham equation, for which an orbital-dependent functional approximation is shown to reproduce the topological phase diagram of a multiband Hubbard model as a function of crystal field and Hubbard parameters. The roles of band filling and interband fluctuations are elucidated.

From Kohn-Sham to Many-Electron Energies via Step Structures in the Exchange-Correlation Potential.

Accurately describing excited states within Kohn-Sham (KS) density functional theory (DFT), particularly those which induce ionization and charge transfer, remains a great challenge. Common exchange-correlation (xc) approximations are unreliable for excited states owing, in part, to the absence of a derivative discontinuity in the xc energy (Δ), which relates a many-electron energy difference to the corresponding KS energy difference. We demonstrate, analytically and numerically, how the relationship between KS and many-electron energies leads to the step structures observed in the exact xc potential in four scenarios: electron addition, molecular dissociation, excitation of a finite system, and charge transfer. We further show that steps in the potential can be obtained also with common xc approximations, as simple as the LDA, when addressed from the ensemble perspective. The article therefore highlights how capturing the relationship between KS and many-electron energies with advanced xc approximations is crucial for accurately calculating excitations, as well as the ground-state density and energy of systems which consist of distinct subsystems.

Combining Eliashberg Theory with Density Functional Theory for the Accurate Prediction of Superconducting Transition Temperatures and Gap Functions.

We propose a practical alternative to Eliashberg equations for the ab initio calculation of superconducting transition temperatures and gap functions. Within the recent density functional theory for superconductors, we develop an exchange-correlation functional that retains the accuracy of Migdal's approximation to the many-body electron-phonon self-energy, while having a simple analytic form. Our functional is based on a parametrization of the Eliashberg self-energy for a superconductor with a single Einstein frequency, and enables density functional calculations of experimental excitation gaps. By merging electronic structure methods and Eliashberg theory, the present approach sets a new standard in quality and computational feasibility for the prediction of superconducting properties.

Extending Solid-State Calculations to Ultra-Long-Range Length Scales.

We present a method that enables solid-state density functional theory calculations to be applied to systems of almost unlimited size. Computations of physical effects up to the micron length scale but which nevertheless depend on the microscopic details of the electronic structure, are made possible. Our approach is based on a generalization of the Bloch state, which involves an additional sum over a finer grid in reciprocal space around each k point. We show that this allows for modulations in the density and magnetization of arbitrary length on top of a lattice-periodic solution. Based on this, we derive a set of ultra-long-range Kohn-Sham equations. We demonstrate our method with a sample calculation of bulk LiF subjected to an arbitrary external potential containing nearly 3500 atoms. We also confirm the accuracy of the method by comparing the spin density wave state of bcc Cr against a direct supercell calculation starting from a random magnetization density. Furthermore, the spin spiral state of γ-Fe is correctly reproduced.

Direct evaluation of the isotope effect within the framework of density functional theory for superconductors.

Within recent developments of density functional theory, its numerical implementation and of the superconducting density functional theory is nowadays possible to predict the superconducting critical temperature, [Formula: see text], with sufficient accuracy to anticipate the experimental verification. In this paper we present an analytical derivation of the isotope coefficient within the superconducting density functional theory. We calculate the partial derivative of [Formula: see text] with respect to atomic masses. We verified the final expression by means of numerical calculations of isotope coefficient in monatomic superconductors (Pb) as well as polyatomic superconductors (CaC6). The results confirm the validity of the analytical derivation with respect to the finite difference methods, with considerable improvement in terms of computational time and calculation accuracy. Once the critical temperature is calculated (at the reference mass(es)), various isotope exponents can be simply obtained in the same run. In addition, we provide the expression of interesting quantities like partial derivatives of the deformation potential, phonon frequencies and eigenvectors with respect to atomic masses, which can be useful for other derivations and applications.

Competing Spin Transfer and Dissipation at Co/Cu(001) Interfaces on Femtosecond Timescales.

By combining interface-sensitive nonlinear magneto-optical experiments with femtosecond time resolution and ab initio time-dependent density functional theory, we show that optically excited spin dynamics at Co/Cu(001) interfaces proceeds via spin-dependent charge transfer and back transfer between Co and Cu. This ultrafast spin transfer competes with dissipation of spin angular momentum mediated by spin-orbit coupling already on sub 100 fs timescales. We thereby identify the fundamental microscopic processes during laser-induced spin transfer at a model interface for technologically relevant ferromagnetic heterostructures.

Accurate Formula for the Macroscopic Polarization of Strongly Correlated Materials.

The many-body Berry phase formula for macroscopic polarization is approximated by a sum of natural orbital geometric phases with fractional occupation numbers accounting for the dominant correlation effects. This formula accurately reproduces the exact polarization in the Rice-Mele-Hubbard model across the band insulator-Mott insulator transition. A similar formula based on a reduced Berry curvature accurately predicts the interaction-induced quenching of Thouless topological charge pumping.

Experimental and theoretical structural/spectroscopical correlation of enterobactin and catecholamide.

Here we report the IR spectra of FeEnterobactin in catecholate conformations ([CatFeEB]3-) obtained by DFT calculations using PBE/QZVP and their correlation it with its experimental counterpart [SalH3FeEB]0. Fragments of FeEnterobactin and Enterobactin (H6EB) are elucidated from their MALDI-TOF mass spectrometry, and the dependence of the frontier orbitals (HOMO and LUMO) with the catecholamide dihedral angles of H6EB is reported. The frequency distribution of catecholamide dihedral angle of H6EB was carried-out using molecular dynamics (MD). The data presented enriches the understanding of [CatFeEB]3 - and H6EB frequency distribution and reactivity.

IR and NMR spectroscopic correlation of enterobactin by DFT.

Emerging and re-emerging epidemic diseases pose an ongoing threat to global health. Currently, Enterobactin and Enterobactin derivatives have gained interest, owing to their potential application in the pharmaceutical field. As it is known [J. Am. Chem. Soc (1979) 101, 20, 6097-6104], Enterobactin (H6EB) is an efficient iron carrier synthesized and secreted by many microbial species. In order to facilitate the elucidation of enterobactin and its analogues, here we propose the creation of a H6EB standard set using Density Functional Theory Infrared (IR) and NMR spectra. We used two exchange-correlation (xc) functionals (PBE including long-range corrections LC-PBE and mPW1), 2 basis sets (QZVP and 6-31G(d)) and 2 grids (fine and ultrafine) for most of the H6EB structures dependent of dihedral angles. The results show a significant difference between the OH and NH bands, while the CO amide and O(CO) IR bands are often found on top of each other. The NMR DFT calculations show a strong dependence on the xc functional, basis set, and grid used for the H6EB structure. Calculated 1H and 13C NMR spectra enable the effect of the solvent to be understood in the context of the experimental measurements. The good agreement between the experimental and the calculated spectra using LC-PBE/QZVP and ultrafine grid suggest the possibility of the systems reported here to be considered as a standard set. The dependence of electrostatic potential and frontier orbitals with the catecholamide dihedral angles of H6EB is described. The matrix-assisted laser desorption/ionization time of the flight mass spectrometry (MALDI-TOF MS) of H6EB is also reported of manner to enrich the knowledge about its reactivity.

Density functional theory of electron transfer beyond the Born-Oppenheimer approximation: Case study of LiF.

We perform model calculations for a stretched LiF molecule, demonstrating that nonadiabatic charge transfer effects can be accurately and seamlessly described within a density functional framework. In alkali halides like LiF, there is an abrupt change in the ground state electronic distribution due to an electron transfer at a critical bond length R = Rc, where an avoided crossing of the lowest adiabatic potential energy surfaces calls the validity of the Born-Oppenheimer approximation into doubt. Modeling the R-dependent electronic structure of LiF within a two-site Hubbard model, we find that nonadiabatic electron-nuclear coupling produces a sizable elongation of the critical Rc by 0.5 bohr. This effect is very accurately captured by a simple and rigorously derived correction, with an M-1 prefactor, to the exchange-correlation potential in density functional theory, M = reduced nuclear mass. Since this nonadiabatic term depends on gradients of the nuclear wave function and conditional electronic density, ∇Rχ(R) and ∇Rn(r, R), it couples the Kohn-Sham equations at neighboring R points. Motivated by an observed localization of nonadiabatic effects in nuclear configuration space, we propose a local conditional density approximation-an approximation that reduces the search for nonadiabatic density functionals to the search for a single function y(n).

Source-Free Exchange-Correlation Magnetic Fields in Density Functional Theory.

Spin-dependent exchange-correlation energy functionals in use today depend on the charge density and the magnetization density: Exc[ρ, m]. However, it is also correct to define the functional in terms of the curl of m for physical external fields: Exc[ρ,∇ × m]. The exchange-correlation magnetic field, Bxc, then becomes source-free. We study this variation of the theory by uniquely removing the source term from local and generalized gradient approximations to the functional. By doing so, the total Kohn-Sham moments are improved for a wide range of materials for both functionals. Significantly, the moments for the pnictides are now in good agreement with experiment. This source-free method is simple to implement in all existing density functional theory codes.

How Interatomic Steps in the Exact Kohn-Sham Potential Relate to Derivative Discontinuities of the Energy.

Accurate density functional calculations hinge on reliable approximations to the unknown exchange-correlation (xc) potential. The most popular approximations usually lack features of the exact xc potential that are important for an accurate prediction of the fundamental gap and the distribution of charge in complex systems. Two principal features in this regard are the spatially uniform shift in the potential, as the number of electrons infinitesimally surpasses an integer, and the spatial steps that form, for example, between the atoms of stretched molecules. Although both aforementioned concepts are well known, the exact relationship between them remained unclear. Here we establish this relationship via an analytical derivation. We support our result by numerically solving the many-electron Schrödinger equation to extract the exact Kohn-Sham potential and directly observe its features. Spatial steps in the exact xc potential of a full configuration-interaction (FCI) calculation of a molecule are presented in three dimensions.

Spin Flips versus Spin Transport in Nonthermal Electrons Excited by Ultrashort Optical Pulses in Transition Metals.

A joint theoretical and experimental investigation is performed to understand the underlying physics of laser-induced demagnetization in Ni and Co films with varying thicknesses excited by 10 fs optical pulses. Experimentally, the dynamics of spins is studied by determining the time-dependent amplitude of the Voigt vector, retrieved from a full set of magnetic and nonmagnetic quantities performed on both sides of films, with absolute time reference. Theoretically, ab initio calculations are performed using time-dependent density functional theory. Overall, we demonstrate that spin-orbit induced spin flips are the most significant contributors with superdiffusive spin transport, which assumes only that the transport of majority spins without spin flips induced by scattering does not apply in Ni. In Co it plays a significant role during the first ∼20 fs only. Our study highlights the material dependent nature of the demagnetization during the process of thermalization of nonequilibrium spins.

Ab Initio Nonadiabatic Dynamics with Coupled Trajectories: A Rigorous Approach to Quantum (De)Coherence.

We report the first nonadiabatic molecular dynamics study based on the exact factorization of the electron-nuclear wave function. Our approach (a coupled-trajectory mixed quantum-classical, CT-MQC, scheme) is based on the quantum-classical limit derived from systematic and controlled approximations to the full quantum-mechanical problem formulated in the exact-factorization framework. Its strength is the ability to correctly capture quantum (de)coherence effects in a trajectory-based approach to excited-state dynamics. We show this by benchmarking CT-MQC dynamics against a revised version of the popular fewest-switches surface-hopping scheme that is able to fix its well-documented overcoherence issue. The CT-MQC approach is successfully applied to investigation of the photochemistry (ring-opening) of oxirane in the gas phase, analyzing in detail the role of decoherence. This work represents a significant step forward in the establishment of the exact factorization as a powerful tool to study excited-state dynamics, not only for interpretation purposes but mainly for nonadiabatic ab initio molecular dynamics simulations.

Exact Single-Electron Approach to the Dynamics of Molecules in Strong Laser Fields.

We present an exact single-electron picture that describes the correlated electron dynamics in strong laser fields. Our approach is based on the factorization of the electronic wave function as a product of a marginal and a conditional amplitude. The marginal amplitude, which depends only on one electronic coordinate and yields the exact one-electron density and current density, obeys a time-dependent Schrödinger equation with an effective time-dependent potential. The exact equations are used to derive an approximation that is a step towards general and feasible ab initio single-electron calculations for molecules. The derivation also sheds new light on the usual interpretation of the single-active electron approximation. From the study of model systems, we find that the exact and approximate single-electron potentials for processes with negligible two-electron ionization lead to qualitatively similar dynamics, but that the ionization barrier in the exact single-electron potential may be explicitly time dependent.

Ultrafast demagnetization in bulk versus thin films: an ab initio study.

We report ab initio simulations of the quantum dynamics of electronic charge and spins when subjected to intense laser pulses. By performing these purely electron-dynamics calculations for a thin film and for the bulk of Ni, we conclude that formation of surfaces has a dramatic influence of amplifying the laser induced demagnetization. The reason for this amplification is enhanced spin-currents on the surface of the thin films. We show that the underlying physics of demagnetization for bulk is dominated by spin-flips induced by spin-orbit coupling. In the case of thin films, the dominant cause of demagnetization is a combination of the flow of spin-currents and spin-flips. Furthermore, a comparison of our results with experimental data shows that below ∼120 fs processes of demagnetization are entirely dominated by purely electronic processes followed by which dissipative effects like the Elliott-Yafet mechanism start to contribute significantly.

Electron-nuclear wave-packet dynamics through a conical intersection.

We investigate the coupled electron-nuclear dynamics in a model system showing a conical intersection (CoIn) between two excited state potential energy surfaces. Within the model, a single electron and nucleus move in two dimensions in an external static field. It is demonstrated that the nuclear density conserves its initial Gaussian shape when directly passing the CoIn, whereas the electronic density remains approximately constant. This is in sharp contrast to the picture which evolves from an analysis within the basis of adiabatic electronic states. There, dramatic changes are seen in the dynamics of the different nuclear components of the total wave function. It is thus documented that, in the case of a highly efficient population transfer between the respective adiabatic states, neither the nuclear nor the electronic density is influenced by the existence of a CoIn. This is the case because the nuclear-electronic wave packet moves on the complete potential energy surface which changes its topology smoothly as a function of all particle coordinates.

Ultrafast laser induced local magnetization dynamics in Heusler compounds.

The overarching goal of the field of femtomagnetism is to control, via laser light, the magnetic structure of matter on a femtosecond time scale. The temporal limits to the light-magnetism interaction are governed by the fact that the electron spin interacts indirectly with light, with current studies showing a laser induced global loss in the magnetic moment on a time scale of the order of a few 100 s of femtoseconds. In this work, by means of ab-initio calculations, we show that more complex magnetic materials - we use the example of the Heusler and half-Heusler alloys - allow for purely optical excitations to cause a significant change in the local moments on the order of 5 fs. This, being purely optical in nature, represents the ultimate mechanism for the short time scale manipulation of spins. Furthermore, we demonstrate that qualitative behaviour of this rich magnetic response to laser light can be deduced from the ground-state spectrum, thus providing a route to tailoring the response of some complex magnetic materials, like the Heuslers, to laser light by the well established methods for material design from ground-state calculations.