Linear Response Calculations Research Articles

DFT + U Study of Plutonium Hydrides with Occupation Matrix Control.

The magnetic order of plutonium hydrides (PuHx) has long been a subject of controversy, both experimentally and theoretically. The magnetic, structural, electronic, and thermodynamic properties of PuHx are investigated using Hubbard-corrected density functional theory (DFT + U), with U derived from linear response calculations. To address the issue of electronic metastable states within DFT + U, we employ an occupation matrix control method as well as allowing 5f orbitals to break the structural symmetry. This advanced computational approach establishes that the ground-state magnetic order for PuH2 is antiferromagnetic and that for PuH3 is ferromagnetic, consistent with Faraday and nuclear magnetic resonance experiments. Using the conventional hydrogen-vacancy model for PuHx, the hydrogen-content-induced magnetic transition and anomalous variation of the magnetic moment are successfully reproduced. In particular, the calculated transition point of x matches the experimental findings. Furthermore, the electronic configuration of the Pu atom in PuHx is determined to be 5f5, which is consistent with observations from X-ray photoemission spectroscopy. Our calculated values for enthalpy of formation, heat capacity, and entropy are in good agreement with experimental data, thereby validating the robustness of our theoretical framework.

A Constraint-Based Orbital-Optimized Excited State Method (COOX).

In this work, we present a novel method to directly calculate targeted electronic excited states within a self-consistent field calculation based on constrained density functional theory (cDFT). The constraint is constructed from the static occupied-occupied and virtual-virtual parts of the excited state difference density from (simplified) linear-response time-dependent density functional theory calculations (LR-TDDFT). Our new method shows a stable convergence behavior, provides an accurate excited state density adhering to the Aufbau principle, and can be solved within a restricted SCF for singlet excitations to avoid spin contamination. This also allows the straightforward application of post-SCF electron-correlation methods like MP2 or direct RPA methods. We present the details of our constraint-based orbital-optimized excited state method (COOX) and compare it to similar schemes. The accuracy of excitation energies will be analyzed for a benchmark of systems, while the quality of the resulting excited state densities is investigated by evaluating excited state nuclear forces and excited state structure optimizations. We also investigate the performance of the proposed COOX method for long-range charge transfer excitations and conical intersections with the ground-state.

Interplay between disorder and electronic correlations in compositionally complex alloys

Owing to their exceptional mechanical, electronic, and phononic transport properties, compositionally complex alloys, including high-entropy alloys, represent an important class of materials. However, the interplay between chemical disorder and electronic correlations, and its influence on electronic structure-derived properties, remains largely unexplored. This is addressed for the archetypal CrMnFeCoNi alloy using resonant and valence band photoemission spectroscopy, electrical resistivity, and optical conductivity measurements, complemented by linear response calculations based on density functional theory. Utilizing dynamical mean-field theory, correlation signatures and damping in the spectra are identified, highlighting the significance of many-body effects, particularly in states distant from the Fermi edge. Electronic transport remains dominated by disorder and potentially short-range order, especially at low temperatures, while visible-spectrum optical conductivity and high-temperature transport are influenced by short quasiparticle lifetimes. These findings improve our understanding of element-specific electronic correlations in compositionally complex alloys and facilitate the development of advanced materials with tailored electronic properties.

Symmetry, topology, and geometry: The many faces of the topological magnetoelectric effect

A delicate tension complicates the relationship between the topological magnetoelectric effect (TME) in three-dimensional (3D) Z2 topological insulators (TIs) and time-reversal symmetry (TRS). TRS underlies a particular Z2 topological classification of the electronic ground state of crystalline band insulators and the associated quantization of the magnetoelectric response coefficient calculated using bulk linear-response theory but, according to standard symmetry arguments, simultaneously forbids a nonzero magnetoelectric coefficient in any physical finite-size system. This contrast between theories of magnetoelectric response in formal bulk models and in real finite-sized materials originates from the distinct approaches required to introduce notions of (electronic) polarization and orbital magnetization in these fundamentally different environments. In this work we argue for a modified interpretation of the bulk linear-response calculations in nonmagnetic Z2 TIs that is more plainly consistent with TRS and use this interpretation to discuss the effect's observation—still absent over a decade after its prediction. Our analysis is reinforced by microscopic bulk and thin-film calculations carried out using a simplified but still realistic effective model for the well established V2VI3 [V=(Sb,Bi) and VI=(Se,Te)] family of nonmagnetic Z2 TIs. When a uniform dc magnetic field is included in this model, the anomalous n=0 Landau levels (LLs) play the central role, both in thin films and in bulk. In the former case, only the n=0 LL eigenfunctions can support a dipole moment, which vanishes if there are no magnetic surface dopants and is quantized in the thick-film limit if magnetic dopants at the top and bottom surfaces have opposite orientation. In the latter case, the Hamiltonian projected into the n=0 LL subspace is a one-dimensional Su-Schrieffer-Heeger model with ground-state polarization that is quantized in accordance with the bulk linear-response coefficient calculated for (a lattice regularization of) the starting 3D model. Motivated by analytical results, we conjecture a type of microscopic bulk-boundary correspondence: a bulk insulator with (generalized) TRS supports a magnetoelectric coefficient that is purely itinerant (which is generically related to the geometry of the ground state) if and only if magnetic surface dopants are required for the TME to manifest in finite samples thereof. We conclude that in nonmagnetic Z2 TIs the TME is activated by magnetic surface dopants, that the charge-density response to a uniform dc magnetic field is localized at the surface and specified by the configuration of those dopants, and that the TME is qualitatively less robust against disorder than the integer quantum Hall effect. Published by the American Physical Society 2024

Orbital-Resolved DFT+U for Molecules and Solids.

We present an orbital-resolved extension of the Hubbard U correction to density-functional theory (DFT). Compared to the conventional shell-averaged approach, the prediction of energetic, electronic and structural properties is strongly improved, particularly for compounds characterized by both localized and hybridized states in the Hubbard manifold. The numerical values of all Hubbard parameters are readily obtained from linear-response calculations. The relevance of this more refined approach is showcased by its application to bulk solids pyrite (FeS2) and pyrolusite (β-MnO2), as well as to six Fe(II) molecular complexes. Our findings indicate that a careful definition of Hubbard manifolds is indispensable for extending the applicability of DFT+U beyond its current boundaries. The present orbital-resolved scheme aims to provide a computationally undemanding yet accurate tool for electronic structure calculations of charge-transfer insulators, transition-metal (TM) complexes and other compounds displaying significant orbital hybridization.

Excitation energy transfer and vibronic relaxation through light-harvesting dendrimer building blocks: A nonadiabatic perspective.

The light-harvesting excitonic properties of poly(phenylene ethynylene) (PPE) extended dendrimers (tree-like π-conjugated macromolecules) involve a directional cascade of local excitation energy transfer (EET) processes occurring from the "leaves" (shortest branches) to the "trunk" (longest branch), which can be viewed from a vibronic perspective as a sequence of internal conversions occurring among a connected graph of nonadiabatically coupled locally excited electronic states via conical intersections. The smallest PPE building block that is able to exhibit EET, the asymmetrically meta-substituted PPE oligomer with one acetylenic bond on one side and two parallel ones on the other side (hence, 2-ring and 3-ring para-substituted pseudo-fragments), is a prototype and the focus of the present work. From linear-response time-dependent density functional theory electronic-structure calculations of the molecule as regards its first two nonadiabatically coupled, optically active, singlet excited states, we built a (1 + 2)-state-8-dimensional vibronic-coupling Hamiltonian model for running subsequent multiconfiguration time-dependent Hartree wavepacket relaxations and propagations, yielding both steady-state absorption and emission spectra as well as real-time dynamics. The EET process from the shortest branch to the longest one occurs quite efficiently (about 80% quantum yield) within the first 25fs after light excitation and is mediated vibrationally through acetylenic and quinoidal bond-stretching modes together with a particular role given to the central-ring anti-quinoidal rock-bending mode. Electronic and vibrational energy relaxations, together with redistributions of quantum populations and coherences, are interpreted herein through the lens of a nonadiabatic perspective, showing some interesting segregation among the foremost photoactive degrees of freedom as regards spectroscopy and reactivity.

Excitonic Effects of the Excited-State Photocatalytic Reaction at the Molecule/Metal Oxide Interface.

Excitonic effects caused by the Coulomb interaction between electrons and holes play a crucial role in photocatalysis at the molecule/metal oxide interface. As an ideal model for investigating the excitonic effect, coadsorption and photodissociation of water and methanol molecules on titanium dioxide involve complex ground-state thermalcatalytic and excited-state photocatalytic reaction processes. Herein, we systemically investigate the excited-state electronic structures of the coadsorption of H2O and CH3OH molecules on a rutile TiO2(110) surface by linear-response time-dependent density functional theory calculations and probe the reaction path for generating HCOOH or CO2, from ground-state and excited-state perspectives. The reaction barriers in excited-state calculations are significantly different from those in ground-state calculations during three processes, with the largest decrease being 0.94 eV for the Ti5c-O-CH2-O-Ti5c formation process.

Ab initio calculation of electron-phonon linewidths and molecular dynamics with electronic friction at metal surfaces with numeric atom-centred orbitals

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.

Gauge-Invariant Excited-State Linear and Quadratic Response Properties within the Meta-Generalized Gradient Approximation.

Gauge invariance is a fundamental symmetry connected to charge conservation and is widely accepted as indispensable for any electronic structure method. Hence, the gauge variance of the time-dependent kinetic energy density τ used in many meta-generalized gradient approximations (MGGAs) to the exchange-correlation (XC) functional presents a major obstacle for applying MGGAs within time-dependent density functional theory (TDDFT). Replacing τ by the gauge-invariant generalized kinetic energy density τ̂ significantly improves the accuracy of various functionals for vertical excitation energies [R. Grotjahn, F. Furche, and M. Kaupp. J. Chem. Phys. 2022, 157, 111102]. However, the dependence of the resulting current-MGGAs (cMGGAs) on the paramagnetic current density gives rise to new exchange-correlation kernels and hyper-kernels ignored in previous implementations of quadratic and higher-order response properties. Here we report the first implementation of cMGGAs and hybrid cMGGAs for excited-state gradients and dipole moments, as well as an extension to quadratic response properties including dynamic hyperpolarizabilities and two-photon absorption cross sections. In the first comprehensive benchmark study of MGGAs and cMGGAs for two-photon absorption cross sections, the M06-2X functional is found to be superior to the GGA hybrid PBE0. Additionally, two case studies from the literature for the practical prediction of nonlinear optical properties are revisited and potential advantages of hybrid (c)MGGAs compared to hybrid GGAs are discussed. The effect of restoring gauge invariance varies depending on the employed MGGA functional, the type of excitation, and the property under investigation: While some individual excited-state equilibrium structures are significantly affected, on average, these changes result in marginal improvements when compared against high-level reference data. Although the gauge-variant MGGA quadratic response properties are generally close to their gauge-invariant counterparts, the resulting errors are not bounded and significantly exceed typical method errors in some of the cases studied. Despite the limited effects seen in benchmark studies, gauge-invariant implementations of cMGGAs for excited-state properties are desirable from a fundamental perspective, entail little additional computational cost, and are necessary for response properties consistent with cMGGA linear response calculations such as excitation energies.

Connecting Higher-Order Topology with the Orbital Hall Effect in Monolayers of Transition Metal Dichalcogenides.

Monolayers of transition metal dichalcogenides (TMDs) in the 2H structural phase have been recently classified as higher-order topological insulators (HOTIs), protected by C_{3} rotation symmetry. In addition, theoretical calculations show an orbital Hall plateau in the insulating gap of TMDs, characterized by an orbital Chern number. We explore the correlation between these two phenomena in TMD monolayers in two structural phases: the noncentrosymmetric 2H and the centrosymmetric 1T. Using density functional theory, we confirm the characteristics of 2H TMDs and reveal that 1T TMDs are identified by a Z_{4} topological invariant. As a result, when cut along appropriate directions, they host conducting edge states, which cross their bulk energy-band gaps and can transport orbital angular momentum. Our linear response calculations thus indicate that the HOTI phase is accompanied by an orbital Hall effect. Using general symmetry arguments, we establish a connection between the two phenomena with potential implications for orbitronics and spin orbitronics.

Assignment of excitonic insulators in ab initio theories: The case of NiBr2

In this work we perform a detailed first-principles analysis of the electronic and optical properties of NiBr$_2$ within the state-of-the-art $GW$+BSE scheme to determine whether this system displays negative excitonic energies, which would identify it as an (half) excitonic insulator. Particular attention is payed to the convergence of the $GW$ band structure and to the consistency between approximations employed in the ground-state calculations and approximations employed in the linear response calculations. We show that these two issues play a crucial role in identifying the excitonic nature of NiBr$_2$.

Mean Value Ensemble Hubbard-U Correction for Spin-Crossover Molecules.

High-throughput searches for spin-crossover molecules require Hubbard-U corrections to common density functional exchange-correlation (XC) approximations. However, the Ueff values obtained from linear response or based on previous studies overcorrect the spin-crossover energies. We demonstrate that employing a linearly mixed ensemble average spin state as the reference configuration for the linear response calculation of Ueff resolves this issue. Validation on a commonly used set of spin-crossover complexes shows that these ensemble Ueff values consistently are smaller than those calculated directly on a pure spin state, irrespective of whether that be low- or high-spin. Adiabatic crossover energies using this methodology for a generalized gradient approximation XC functional are closer to the expected target energy range than with conventional Ueff values. Based on the observation that the Ueff correction is similar for different complexes that share transition metals with the same oxidation state, we devise a set of recommended averaged Ueff values for high-throughput calculations.

Evidence of direct charge transfer in plasmon-mediated photocatalytic water splitting: A time-dependent density functional theory study

Photocatalytic water splitting is a promising route for hydrogen production and solar energy storage. Plasmon-mediated water splitting has the potential to harvest photons with longer wavelengths compared with semiconductor-based photocatalysis. However, the mechanism of plasmon-induced charge transfer, the determining step of photochemistry, is not well understood. Here, we studied plasmon-mediated water splitting at atomic length scale and femtosecond timescale. Linear-response time-dependent density functional theory calculations and Ehrenfest dynamics simulations were performed for a realistic H2O@Au6 model excited by the femtosecond laser. Wavelength-dependent charge transfer mechanisms were demonstrated. Especially, for the excitation of 2.25 eV that falls into the visible spectrum, evidence was presented for the dominant direct transfer of d-orbital electrons from the gold cluster to the adsorbed water molecule. In this mechanism, the charge transfer leapfrogs the processes of excitation and thermalization within gold described in the classical theory. The results can assist the design of more energy-efficient solar water splitting.

Multiconfigurational SCF and Short-Range DFT Combined with Polarizable Density Embedding: Comparison of Linear-Response and State-Specific Solvatochromic Shifts of Acrolein and Para-nitrophenolate in Water.

The polarizable density embedding model is combined with the multiconfigurational self-consistent field and MC-srDFT electronic structure methods to calculate solvatochromic shifts of the n-π* absorption of acrolein and the π-π* absorption of the para-nitrophenolate anion in aqueous solution. Differences between linear-response (LR) and state-specific (SS) solvent shifts are analyzed by assessing the contributions of different terms in the solvent potential. This comparison shows that the differences are not only due to the intrinsically different response of LR and SS excitation energies to the polarizability of the environment but also due to a different response to the static part of the environment potential. These observations show that even in nonpolarizable environments, LR and SS calculations based on SCF (orbital optimization) methods do not necessarily agree on the spectral shift. The difference can be as large as, or even dominate, the difference due to dynamical polarization.

Site selective 5f electronic correlations in β-uranium

We investigate the electronic structure of β-uranium, which has five nonequivalent atomic sites in its unit cell, by means of the density functional theory plus Hubbard-U correction with U from linear response calculation. It is found that the 5f electronic correlations in β-uranium are moderate. More interestingly, their strengths are site selective, depending on the local atomic environment of the present uranium atom. As a consequence, the occupation matrices and partial 5f density of states of β-uranium manifest site dependence. In addition, the complicate experimental structure of β-uranium could be well reproduced within this theoretical framework.

Quantum Perturbation Theory Using Tensor Cores and a Deep Neural Network.

Time-independent quantum response calculations are performed using Tensor cores. This is achieved by mapping density matrix perturbation theory onto the computational structure of a deep neural network. The main computational cost of each deep layer is dominated by tensor contractions, i.e., dense matrix-matrix multiplications, in mixed-precision arithmetics, which achieves close to peak performance. Quantum response calculations are demonstrated and analyzed using self-consistent charge density-functional tight-binding theory as well as coupled-perturbed Hartree-Fock theory. For linear response calculations, a novel parameter-free convergence criterion is presented that is well-suited for numerically noisy low-precision floating point operations and we demonstrate a peak performance of almost 200 Tflops using the Tensor cores of two Nvidia A100 GPUs.

Inelastic scattering of electrons in water from first principles: cross sections and inelastic mean free path for use in Monte Carlo track-structure simulations of biological damage.

Modelling the inelastic scattering of electrons in water is fundamental, given their crucial role in biological damage. In Monte Carlo track-structure (MC-TS) codes used to assess biological damage, the energy loss function (ELF), from which cross sections are extracted, is derived from different semi-empirical optical models. Only recently have first ab initio results for the ELF and cross sections in water become available. For benchmarking purpose, in this work, we present ab initio linear-response time-dependent density functional theory calculations of the ELF of liquid water. We calculated the inelastic scattering cross sections, inelastic mean free paths, and electronic stopping power and compared our results with recent calculations and experimental data showing a good agreement. In addition, we provide an in-depth analysis of the contributions of different molecular orbitals, species and orbital angular momenta to the total ELF. Moreover, we present single-differential cross sections computed for each molecular orbital channel, which should prove useful for MC-TS simulations.

Comparing the nature of quantum plasmonic excitations for closely spaced silver and gold dimers.

In the new field of quantum plasmonics, plasmonic excitations of silver and gold nanoparticles are utilized to manipulate and control light-matter interactions at the nanoscale. While quantum plasmons can be described with atomistic detail using Time-Dependent Density Functional Theory (DFT), such studies are computationally challenging due to the size of the nanoparticles. An efficient alternative is to employ DFT without approximations only for the relatively fast ground state calculations and use tight-binding approximations in the demanding linear response calculations. In this work, we use this approach to investigate the nature of plasmonic excitations under the variation of the separation distance between two nanoparticles. We thereby provide complementary characterizations of these excitations in terms of Kohn-Sham single-orbital transitions, intrinsic localized molecular fragment orbitals, scaling of the electron-electron interactions, and probability of electron tunneling between monomers.

Linear response calculation with nonlocal van der Waals density functionals

The linear-response approach with the nonlocal van der Waals density functionals is presented, considering three kinds of perturbations: Atomic displacements, uniform electric fields, and strain. The formulas to compute the response with respect to strain are derived for the van der Waals density functionals as well as for the generalized gradient approximation. The linear-response method is implemented within the ultrasoft pseudopotential scheme. The method is applied to weak-coupled layered materials, graphite and ${\mathrm{MoS}}_{2}$. The results support the validity of the derived formulas and demonstrate the utilities of the linear-response method for weak-coupled van der Waals systems.

First-principles wave-vector- and frequency-dependent exchange-correlation kernel for jellium at all densities

We propose a spatially and temporally nonlocal exchange-correlation (xc) kernel for the spin-unpolarized fluid phase of ground-state jellium, for use in time-dependent density functional and linear response calculations. The kernel is constructed to satisfy known properties of the exact xc kernel, to accurately describe the correlation energies of bulk jellium, and to satisfy frequency-moment sum rules at a wide range of bulk jellium densities, including those low densities that display strong correlation and symmetry breaking. These effects are easier to understand in the simple jellium model than in real systems. All exact constraints satisfied by the recent MCP07 kernel [A. Ruzsinszky, et al., Phys. Rev. B 101, 245135 (2020)] are maintained in the new revised MCP07 (rMCP07) kernel, while others are added. The revision $f_\mathrm{xc}^\mathrm{rMCP07}(q,\omega)$ differs from MCP07 only for non-zero frequencies $\omega$. Only at densities much lower than those of real bulk metals is the frequency dependence of the kernel important for the correlation energy of jellium. As the wavevector $q$ tends to zero, the kernel has a $-4\pi \alpha(\omega)/q^2$ divergence whose frequency-dependent ultranonlocality coefficient $\alpha(\omega)$ vanishes in jellium, and is predicted by rMCP07 to be extremely small for the real metals Al and Na.}