Nonlocal Exchange Research Articles

Role of spin currents on electron-electron interaction in the quantum spin Hall phase

The spin current density functional theory (SCDFT) is the generalization of the standard DFT to treat a fermionic system embedded in the effective external field produced by the spin-orbit coupling interaction. Even in the absence of a spin polarization, the SCDFT requires the electron-electron potential to depend on the spin currents ${\mathbf{J}}^{x}, {\mathbf{J}}^{y}$, and ${\mathbf{J}}^{z}$, which only recently was made possible for practical relativistic quantum-mechanical simulations, through the inclusion of a fraction of nonlocal Fock exchange into local-density or generalized-gradient density functional approximations [J. K. Desmarais, J.-P. Flament, and A. Erba, Phys. Rev. B 102, 235118 (2020)]. Here, we apply the SCDFT to the quantum spin Hall phase and show how it improves (even qualitatively) the description of its electronic features relative to the DFT. We study the Bi (001) 2D bilayer and its band insulator to topological insulator phase transition (via $s+{p}_{z}\ensuremath{\leftrightarrow}{p}_{x}+i{p}_{y}$ band inversion) as a function of mechanical strain. We show that the explicit account of spin currents in the electron-electron potential of the SCDFT is key to the appearance of a Dirac cone at the $\mathrm{\ensuremath{\Gamma}}$ point in the valence band structure at the onset of the topological phase transition. Finally, the valence band structure of this system is rationalized using a simple first-order $\mathbf{k}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{p}$ quasidegenerate perturbation theory model.

Effects of nonlocal interactions in describing V centers of MgO

The electronic structure and optical absorption spectrum of V 0 and center in MgO are investigated based on the density functional theory. The V-type centers are well described when the local symmetry around Mg vacancy is destroyed by using the nonlocal hybrid functionals. It is demonstrated that the holes are trapped on one (or two) O atoms around Mg vacancy for (or V 0) center. The defect states are separated from the valence bands due to the nonlocal exchange interactions involved in the hybrid functionals, which is the key to describing the optical properties correctly. At ambient condition, the absorption peaks ∼2.5 eV and ∼2.6 eV are assigned to V 0 and center, respectively, and they exhibit blue shift with increasing pressure.

Nonselfadjoint impedance in Generalized Optimized Schwarz Methods

Abstract We present a convergence theory for Optimized Schwarz Methods that rely on a nonlocal exchange operator and covers the case of coercive possibly nonselfadjoint impedance operators. This analysis also naturally deals with the presence of cross-points in subdomain partitions of arbitrary shape. In the particular case of hermitian positive definite impedance, we recover the theory proposed in Claeys & Parolin (2021).

Accelerating Linear-Response Time-Dependent Hybrid Density Functional Theory with Low-Rank Decomposition Techniques in the Plane-Wave Basis.

We present an efficient low-rank implementation of linear-response time-dependent density functional theory for hybrid functionals (hybrid-LR-TDDFT) within the plane-wave pseudopotential framework. The adaptively compressed exchange (ACE) operator and the natural transition orbitals (NTOs) are introduced to build the low-rank representation of the nonlocal exchange operator in the hybrid-LR-TDDFT Hamiltonian. Numerical tests demonstrate that the ACE approximation significantly reduces the computational cost of applying the nonlocal exchange operator without loss of accuracy, and the NTO approximation can further accelerate the hybrid-LR-TDDFT calculations by introducing an NTO cutoff parameter. This new method enables us to effectively study the excitonic properties of two-dimensional MoS2 consisting of 216 atoms and ∼1900 electrons with range-separated hybrid functionals on a single graphics processing unit.

Origin of contact polarity at metal-2D transition metal dichalcogenide interfaces

Using state-of-the-art ab initio GW many-body perturbation theory calculations, we show that monolayer MoS2 on Au is a p-type contact, in contrast to the vast majority of theoretical predictions using density functional theory. The predominantly n-type behaviour observed experimentally for MoS2/Au junctions can be attributed to the presence of sulfur vacancies, which pin the Fermi level. GW calculations on WSe2/Au junctions likewise predict p-type contacts for pristine WSe2 and n-type contacts for junctions with selenium vacancies. Experimentally, WSe2/metal junctions are predominantly p-type or ambipolar, with p-type junctions being observed for selenium-deficient WSe2, suggesting that selenium vacancies are not effective in pinning the Fermi level for WSe2/metal junctions. We rationalize these apparently contradictory results by noting that selenium vacancies in WSe2 are readily passivated by oxygen atoms. Taken together, our state-of-the-art calculations clearly elucidate the relation between contact polarity and atomic structure. We show that non-local exchange and correlation effects are critical for determining the energy level alignment and even the contact polarity (in the case of MoS2 on Au). We further reconcile a large body of experimental literature on TMDC/metal contact polarities by consideration of the defect chemistry.

The performance of exchange-correlation functionals in describing electron density parameters of saddle point structures along chemical reactions.

This work is focused on evaluating the performance of exchange-correlation functionals from density functional theory in providing descriptor values derived from the electron density of saddle point structures (transition states) in chemical reactions. The properties investigated were obtained from the quantum theory of atoms in molecules, including atomic charges and electron density topological data at the bond critical points. In addition, parameters from the Interacting quantum atom energy partition were used as well in this comparative study. The reference values are attained in coupled cluster calculations with iterative single and double excitations (CCSD). Six elementary reactions are considered here: CO + H2 ↔H2 CO, CO + H2 O↔HCOOH, HCN↔HNC, H + F2 ↔HF + F, H + N2 ↔HN2 , and H + CO↔HCO. In general, the BB1K functional (hybrid-meta-generalized gradient approximation) provides the best description of these properties. Our study indicates that an intermediate percentage of nonlocal exact exchange, around 40%-55% (perhaps even larger), is probably required for attaining more accurate values with actual functionals, although this condition is not able of explaining all the trends observed.

Electronic correlation in nearly free electron metals with beyond-DFT methods

For more than three decades, nearly free-electron elemental metals have been a topic of debate because the computed bandwidths are significantly wider in the local density approximation to density-functional theory (DFT) than indicated by angle-resolved photoemission (ARPES) experiments. Here, we systematically investigate this using first principles calculations for alkali and alkaline-earth metals using DFT and various beyond-DFT methods such as meta-GGA, G0W0, hybrid functionals (YS-PBE0, B3LYP), and LDA + eDMFT. We find that the static non-local exchange, as partly included in the hybrid functionals, significantly increase the bandwidths even compared to LDA, while the G0W0 bands are only slightly narrower than in LDA. The agreement with the ARPES is best when the local approximation to the self-energy is used in the LDA + eDMFT method. We infer that even moderately correlated systems with partially occupied s orbitals, which were assumed to approximate the uniform electron gas, are very well described in terms of short-range dynamical correlations that are only local to an atom.

Benchmarking exchange-correlation potentials with the mstar60 dataset: Importance of the nonlocal exchange potential for effective mass calculations in semiconductors

The accuracy of effective masses predicted by density functional theory depends on the exchange-correlation functional employed, with nonlocal hybrid functionals giving more accurate results than semilocal functionals. In this article, we benchmark the performance of the Perdew-Burke-Ernzerhof (PBE), Tran-Blaha modified Becke-Johnson (TB-mBJ), and the hybrid Heyd-Scuseria-Ernzerhof (HSE06) exchange-correlation functionals and potentials for the calculation of effective masses with perturbation theory. We introduce the mstar60 dataset, which contains 60 effective masses derived from 18 semiconductors. The ratio between experimental and calculated effective masses is $1.70 \pm 0.20$ for PBE, $0.76 \pm 0.04$ for TB-mBJ, $0.99 \pm 0.04$ for HSE06. We reveal that the nonlocal exchange in HSE06 enlarges the optical transition matrix elements leading to the superior accuracy of the hybrid functional in the calculation of effective masses. The omission of nonlocal exchange in the transition operator for HSE leads to serious errors. For the semilocal PBE functional, the errors in the bandgap and the optical transition matrix elements partially cancel out in the calculation of effective masses. The TB-mBJ functional yields PBE-like matrix elements paired with realistic bandgaps leading to a consistent overestimation of effective masses. However, if only limited computational resources are available, experimental masses can be estimated by multiplying TB-mBJ masses with the factor of 0.76. We then compare effective masses of transition metal dichalcogenide bulk and monolayer materials: we show that changes in the matrix elements are important in understanding the layer-dependent effective mass renormalization.

Effects of non-local exchange functionals in the density functional theories for the description of molecular vibrations

Effects of non-local exchange functionals in the density functional theories for the description of molecular vibrations

Theoretical study of the effect of nonlocal short-range exchange on calculations of molecular excitation energies in the dielectric screened-exchange method

We have previously proposed a dielectric screened-exchange approach in which the dielectric constant is used to describe system-dependent features of the electronic structures of materials (Chem. Phys. Lett., 466, pp. 91–94, 2008). In the present paper, we discuss the theoretical effects of the nonlocal short-range exchange term on molecular excitations and compare them with the effects of the local Slater approximation. We show that the nonlocal short-range term is useful in describing precisely the (excited) electronic structures of molecules with large HOMO–LUMO gaps. Conversely, the local Slater approximation works effectively for systems with small HOMO–LUMO gaps.

Multiconfiguration Pair-Density Functional Theory Calculations of Iron(II) Porphyrin: Effects of Hybrid Pair-Density Functionals and Expanded RAS and DMRG Active Spaces on Spin-State Orderings.

Iron(II) porphyrins play critical roles in enzymes and synthetic catalysts. Computationally determining the spin-state ordering for even the unsubstituted iron(II) porphyrin (FeP) is challenging due to its large size. Multiconfiguration pair-density functional theory (MC-PDFT), a method capable of accurately capturing correlation with lower cost than comparably accurate methods, was previously used to predict a triplet ground state for FeP across a wide range of active spaces up to (34e, 35o). The purpose of this present MC-PDFT study is to determine the effects of including nonlocal exchange in the energy calculation and of using a larger active space size [DMRG(40e, 42o) and RAS(40, 2, 2; 16, 6, 20)] on the calculated FeP spin-state ordering. The recently developed hybrid MC-PDFT method, which uses a weighted average of the MC-PDFT energy and the energy expectation value of the reference wave function, is applied with a weight of the reference wave function energy of λ. We find that increasing λ stabilizes the quintet relative to the triplets. The hybrid tPBE0 functional (tPBE with λ set to 0.25) consistently predicts a triplet ground state with the quintet lying above by 0.10-0.16 eV, depending on the reference wave function. These values are particularly interesting in light of tPBE0's very strong performance for a diverse set of other systems.

Note: Reproducibility of potential energy surfaces of organic/metal interfaces on the example of PTCDA on Ag(111).

We recently published a benchmark study of common local, semi-local, and non-local exchange correlation functionals in combination with various van der Waals (vdW) corrections, where we investigated the reproducibility of the potential energy surface of perylenetetracarboxylic dianhydride on Ag(111). This Note presents an additional benchmark of the recently developed non-local many body dispersion (MBD-NL) vdW correction, coupled with the Perdew-Burke-Ernzerhof (PBE) functional. We find that this computation method shows similar performance as the established approaches. Notably, it yields very similar results as PBE + MBD.

Spin current density functional theory of Weyl semimetals

Weyl fermions are massless solutions of the Dirac equation, described by two-component complex spinors. Such elusive objects emerge as quasiparticles in the so-called Weyl semimetals (WSM). The authors discuss the generalization of the standard one-component density functional theory to a two-component approach (the spin-current density functional theory) as well as its application to the practical quantum-mechanical description of WSMs through a self-consistent treatment of the spin-orbit coupling and nonlocal Fock exchange. In particular, the authors demonstrate the key role played by spin-current densities in the characterization of Weyl nodes in TaAs.

A general justification for hybrid functionals in DFT by means of linear response theory* *To the memory of Enrico Clementi, an outstanding human being; in recognition of his pioneering work in quantum chemistry and in tribute to his leadership and long-lasting accomplishments.

In the present work, resorting to linear response theory, we examine the plausibility of postulating Kohn–Sham (KS)-type equations which contain, by definition, an effective hybrid potential made up by some arbitrary mixture of local and non-local terms. In this way a general justification for the construction of hybrid functionals is provided without resorting to arguments based on the adiabatic connection, the generalized KS theory or the Levy’s constrained search (or its variations). In particular, we examine the cases of single-hybrid functionals, derived from non-local exchange and of double-hybrid functionals, emerging from non-local second-order expressions obtained from the KS perturbation theory. A further generalization for higher-order hybrid functionals is also included.

Non-covalent interactions between molecular dimers (S66) in electric fields

Fine tuning and microscopic control of van der Waals interactions through oriented external electric fields (OEEFs) mandates an accurate and systematic understanding of intermolecular response properties. Having taken exploratory steps into this direction, we present a systematic study of interaction induced dipole electric properties of all molecular dimers in the S66 set, relying on CCSD(T)-F12b/aug-cc-pVDZ-F12 as reference level of theory. For field strengths up to ≈5 GV m−1 the interaction induced electric response beyond second order is found to be insignificant. Large interaction dipole moments (i.e. dipole moment changes due to van der Waals binding) are observed in the case of hydrogen bonding oriented along the intermolecular axis, and mostly small interaction dipole moments are found in dimers bonded by π-stacking or London dispersion. The interaction polarizabilities (i.e. polarizability changes due to van der Waals binding) were generally found to be small but always with a positive-valued principal component approximately aligned with the intermolecular axis, and two other negative-valued components. Energy decompositions according to symmetry adapted perturbation theory (SAPT0/jun-cc-pVDZ) suggest that electrostatics dominates the interaction dipole moment, with exchange and induction contributing on a smaller scale, and with dispersion having the smallest effect. First-order SAPT0 decomposition into monomer-resolved contributions enables us to establish a quantitative link between electric properties of monomers and dimers, which is found to be in qualitative agreement with the coupled cluster reference method. Using the aug-cc-pVQZ basis and non-empirical Perdew–Burke–Ernzerhof (PBE) semilocal exchange–correlation kernels, we also assess how density functional approximations in the nonlocal exchange and correlation parts affect the predictive accuracy: while dRPA@PBE0 based predictions are in excellent overall agreement with coupled cluster results, the computationally more affordable LC-ωPBE0-D3 level of theory also yields reliable results with relative errors below 5%. PBE alone, even when dispersion corrected, produces larger errors in interaction dipole moments (≈10%) and polarizabilities (≈20%). We also resolve the mutual impact of the three dimensions of the OEEF, and we present a discussion of the intermolecular distance dependence of the perturbations.

Do any types of double-hybrid models render the correct order of excited state energies in inverted singlet-triplet emitters?

Organic emissive materials with the inverted singlet-triplet energy gaps, where in violation of Hund's multiplicity rule the lowest triplet excited-state is higher in energy than the lowest singlet excited-state, have recently come into the limelight. This unique feature is of important relevance, where the emitters meeting the singlet-triplet inversion have potential to usher in the next generation of organic light emitting diodes (OLEDs). Since experimental data in this context are currently sparse, necessity of the cost-effective theoretical tools able to provide reliable results seems to be evident. Following our recent endeavors on the spin-component-scaled (SCS), spin-opposite-scaled (SOS), and SOS-range separated exchange (SOS-RSX) double-hybrids (DHs) as well as other efforts revealing the superior performances of such models for time-dependent computations, in the present work, we develop and validate several models based on the SOS-configuration interaction singles with perturbative doubles correction [SOS-CIS(D)] devoid of any fitting procedure for describing the singlet-triplet inversion. Taking a series of emitters with the available reference values for the inverted singlet-triplet energy gaps as working models, it is unveiled that the extremes of the same-spin and opposite-spin parameters included in the direct and indirect terms of the SOS-CIS(D) correlation energy as well as the nonlocal exchange and correlation contributions do not necessarily work well for the inverted gaps, but particular proportions among them are needed to achieve a reliable accuracy. Perusing the results of our developed methods, the best one based on the Perdew-Burke-Ernzerhof (PBE) exchange and correlation terms and the quadratic integrand model, denominated as SOS0-CIS(D)-PBE-QIDH, is shown to be highly efficient and robust for computations of the inverted singlet-triplet energy gaps. Furthermore, through detailed comparisons, we have also evaluated the performances of a variety of the recently presented DHs, including parameterized, parameter-free, RSX, as well as spin-component and spin-opposite scaling models for the purpose. Dissecting all the findings, it is disclosed that the results of any type of the DHs cannot be reliable, leading to positive energy gaps in most cases. Nonetheless, there are still some approximations, including SCS-PBE-QIDH, dispersion corrected spin-component scaled double-hybrids (DSD) of DSD-PBEP86 and DSD-BLYP, SOS-PBE-QIDH, SOS-ωPBEPP86, and SOS-RSX-QIDH, that can predict the negative singlet-triplet energy gaps for all the considered emitters and provide comparable performances with respect to our proposed model. To wrap up, among the large panel of different families of DHs on the market, the newly proposed model herein alongside these latter functionals can be recommended as the currently best affordable methods for subsequent applications on the inverted singlet-triplet emitters in OLED materials.

Trions in MoS2 are quantum superpositions of intra- and intervalley spin states

We report magneto-photoluminescence spectroscopy of gated MoS$_2$ monolayers in high magnetic fields to 28 T. At B = 0T and electron density $n_s\sim 10^{12}cm^-2$, we observe three trion resonances that cannot be explained within a single-particle picture. Employing ab initio calculations that take into account three-particle correlation effects as well as local and non-local electron-hole exchange interaction, we identify those features as quantum superpositions of inter- and intravalley spin states. We experimentally investigate the mixed character of the trion wave function via the filling factor dependent valley Zeeman shift in positive and negative magnetic fields. Our results highlight the importance of exchange interactions for exciton physics in monolayer MoS$_2$ and provide new insights into the microscopic understanding of trion physics in 2D multi-valley semiconductors for low excess carrier densities.

Length-Gauge Optical Matrix Elements in WIEN2k

Hybrid exchange-correlation functionals provide superior electronic structure and optical properties of semiconductors or insulators as compared to semilocal exchange-correlation potentials due to admixing a portion of the non-local exact exchange potential from a Hartree–Fock theory. Since the non-local potential does not commute with the position operator, the momentum matrix elements do not fully capture the oscillator strength, while the length-gauge velocity matrix elements do. So far, length-gauge velocity matrix elements were not accessible in the all-electron full-potential WIEN2k package. We demonstrate the feasibility of computing length-gauge matrix elements in WIEN2k for a hybrid exchange-correlation functional based on a finite difference approach. To illustrate the implementation we determined matrix elements for optical transitions between the conduction and valence bands in GaAs, GaN, (CH3NH3)PbI3 and a monolayer MoS2. The non-locality of the Hartree–Fock exact exchange potential leads to a strong enhancement of the oscillator strength as noticed recently in calculations employing pseudopotentials (Laurien and Rubel: arXiv:2111.14772 (2021)). We obtained an analytical expression for the enhancement factor for the difference in eigenvalues not captured by the kinetic energy. It is expected that these results can also be extended to other non-local potentials, e.g., a many-body GW approximation.

Heisenberg Spin Hamiltonian Derived from a Multiple Grand Canonical Spin Density Functional Theory with a Principal Nonlocal Exchange–Correlation Energy Functional

Heisenberg Spin Hamiltonian Derived from a Multiple Grand Canonical Spin Density Functional Theory with a Principal Nonlocal Exchange–Correlation Energy Functional

Hard and soft materials: putting consistent van der Waals density functionals to work

We present the idea and illustrate potential benefits of having a tool chain of closely related regular, unscreened and screened hybrid exchange–correlation (XC) functionals, all within the consistent formulation of the van der Waals density functional (vdW-DF) method (Hyldgaard et al (2020 J. Phys.: Condens. Matter 32 393001)). Use of this chain of nonempirical XC functionals allows us to map when the inclusion of truly nonlocal exchange and of truly nonlocal correlation is important. Here we begin the mapping by addressing hard and soft material challenges: magnetic elements, perovskites, and biomolecular problems. We also predict the structure and polarization for a ferroelectric polymer. To facilitate this work and future broader explorations, we present a stress formulation for spin vdW-DF and illustrate the use of a simple stability-modeling scheme. The modeling supplements density functional theory (DFT) (with a specific XC functional) by asserting whether the finding of a soft mode (an imaginary-frequency vibrational mode, ubiquitous in perovskites and soft matter) implies an actual DFT-based prediction of a low-temperature transformation.