Linear-response Density Functional Theory Research Articles

Collinear and noncollinear ferrimagnetic phases in Mn4N investigated by magneto-optical Kerr spectroscopy

Ferrimagnetic antiperovskite Mn4N has received growing interest due to room-temperature observation of large perpendicular magnetic anisotropy, low saturation magnetization, and ultrafast response to external magnetic fields. Comprehensive understanding of the underlying magnetic structure is instrumental in design and fabrication of computer memory and logic devices. Magneto-optical spectroscopy provides deeper insight into the magnetic and electronic structure than magnetometry. Simulations of a magneto-optical Kerr effect in biaxially strained Mn4N are performed using density functional theory and linear response theory. We consider three ferrimagnetic phases, two collinear and one noncollinear, which have been investigated separately by earlier studies. The simulated spectra are compared to measured magneto-optical data available in recent literature. One of the collinear ferrimagnetic phases is found to be consistent with the measured spectra. We show that an admixture of the noncollinear phase, which is the ground state of unstrained Mn4N, further improves the agreement with measured spectra, and at the same time, it could explain the lower than predicted net moment and magnetic anisotropy observed in thin films on various substrates.

Defect‐Induced Raman Scattering in Cu2O Nanostructures and Their Photocatalytic Performance

AbstractAdvanced oxidation processes using photogenerated charges in semiconductors constitute an approach to reduce and oxidize pollutants, with an efficiency that depends on the photo physics and defect chemistry of the photocatalyst. In this study, 2D Cu2O coatings on flat copper metal and on 3D copper nanopillars are created via low‐temperature oxidation and compared. The structures are characterized by X‐ray diffraction, Raman spectroscopy, and electron microscopy. The thickest surface oxide layers on the 3D structures show outgrowth of high‐aspect ratio CuO nano‐needles through the Cu2O layer, rationalized through a field‐induced copper ion diffusion mechanism. Raman scattering provides details about both the specific copper oxide phase present and the type and extent of defects, with a resolution spanning from hundreds of nanometers to micrometers. We show that defects in Cu2O induce Raman activity in several of its modes that are purely IR‐active or optically silent in pristine Cu2O. The experimental results are corroborated by linear response density functional theory (DFT) calculations for full vibrational mode analysis. The Cu‐supported 2D copper oxide systems exhibit effective photocatalytic performance at quite low probe pollution concentration (10 μM), while the 3D nanopillar structures enhance the photocatalytic efficiency by around 30 % compared to their planar counterpart under these conditions.

A novel two-dimensional superconducting Ti layer: density functional theory and electron-beam irradiation.

Since the discovery of graphene in an atomic thin layer format, many investigations have been conducted to search for two-dimensional (2D) layered materials, in which 3d-transition metals offer much new physics and great freedom of tunability. In this work, through electron-beam irradiation, we enable the manufacture of a new 2D Ti nanosheet from a suspension of Ti0.91O2 nanosheets. In state-of-the-art density functional theory (DFT), both empirical and linear response theory predicted that Hubbard Ueff values would be imposed, resulting in unstable phonon dispersion curves. In the end, the newly found Ti monolayer is confirmed to be a non-magnetic superconductor, with a medium level of electron-phonon coupling. The newly established Ti layer is quite robust under strain, and the evolution of local Dirac points in electronic bands is also analyzed in terms of linearity and energetic shift near the Fermi energy. As suggested by the Fermi surface, this metal monolayer experiences an electronic topological transition under strain. Our findings will encourage many more explorations of pure d metal-based isotopic monolayers with diverse structures and open a new playground for 2D superconductors and ultra-thin sensoring components.

Density Functional Response Calculations of Dispersion Coefficients C6 and C9 of Closed- and Open-Shell Systems.

Dipole polarizabilities and C6 and C9 dispersion coefficients are computed for closed- and open-shell atoms and molecules, using dynamic (time-dependent) density functional (TD-DFT) linear response theory as implemented in the response module of the NWChem quantum chemistry package. The response module is capable of accurate calculations of these properties, based on spin-restricted and spin-unrestricted formalisms. The calculated static polarizabilities and dispersion coefficients are compared to available experimental and other theoretical data. The behavior of the dynamic polarizability at imaginary frequencies is analyzed for differently sized closed- and open-shell systems. An interpolation method enforcing the monotonic decrease of the polarizability with increasing imaginary frequency is beneficial for the integration used to obtain C6 and C9. Scaling of the TD-DFT data by ratios of the static polarizability, which can be calculated with a variety of methods, including highly accurate theories, may be used as a leading-order correction.

Recent advances in ensemble density functional theory and linear response theory for strong correlation

AbstractThe formulations and performances of spin‐restricted ensemble‐referenced KS and mixed‐reference spin‐flip time‐dependent density functional theory incorporating strong correlations into density functional theories are documented. As a result of balanced dynamic and nondynamic correlation, they are capable of describing strongly correlated challenging systems including diradicals, bond dissociation, conical intersections, doubly excited states, and so on, overcoming the limitations of current density functional theories.

First-principles calculations on the spin anomalous Hall effect of ferromagnetic alloys

The spin anomalous Hall effect (SAHE) in ferromagnetic metals, which can generate a spin-orbit torque to rotate the magnetization of another ferromagnetic layer through a nonmagnetic spacer in magnetic junctions, has attracted much attention. We theoretically investigated the spin anomalous Hall conductivity (SAHC) of the $L{1}_{0}$-type alloys $X\mathrm{Pt}$ ($X=\mathrm{Fe},\mathrm{Co},\mathrm{Ni}$) on the basis of first-principles density functional theory and linear response theory. We found that the SAHC of FePt is much smaller than the anomalous Hall conductivity (AHC), leading to very small polarization for the anomalous Hall effect $\ensuremath{\zeta}=\mathrm{SAHC}/\mathrm{AHC}$ of around 0.1. On the other hand, the SAHC increases with an increasing number of valence electrons (${N}_{\mathrm{v}}$), and CoPt and NiPt show relatively large values of $|\ensuremath{\zeta}|$, greater than 1. The negative contribution of the spin-down-down component of AHC is the origin of the large SAHC and $\ensuremath{\zeta}$ in CoPt and NiPt, which is due to the antibonding states of Pt around the Fermi level in the minority-spin states.

Quantitative assessment of the role of spin fluctuations in 2D Ising superconductor NbSe2

Accurate determination of the full momentum-dependent spin susceptibility χ(q) is very important for the description of magnetism and superconductivity. While in principle the formalism for calculating χ(q) in the linear response density functional theory (DFT) is well established, hardly any publicly available code includes this capability. Here, we describe an alternative way to calculate the static χ(q), which can be applied to most common DFT codes without additional programming. The method combines standard fixed-spin-moment calculations of χ(0) with direct calculations of the energy of spin spirals stabilized by an artificial Hubbard interaction. From these calculations, χDFT(q) can be extracted by inverting the RPA formula. We apply this recipe to the recently discovered Ising superconductivity in NbSe2 monolayer, one of the most exciting findings in superconductivity in recent years. It was proposed that spin fluctuations may strongly affect the parity of the order parameter. Previous estimates suggested proximity to ferromagnetism, i.e., χ(q) peaked at q=0. We find that the structure of spin fluctuations is more complicated, with the fluctuation spectrum sharply peaked at q≈(0.2,0). Such a spectrum would change the interband pairing interaction and considerably affect the superconducting state.

Collective effects in photoionization of sodium clusters: plasmon resonance spill, induced attractive force and correlation minimum

Photoionization studies of Na20 and Na92 clusters are carried out in a framework of linear response density functional theory. Cross sections show substantial spillover of plasmon resonances to the near-threshold ionization energies which are in reasonable agreements with photoabsorption measurements. The analysis of the oscillator strength, consumed by the cross section, lends further detailed insights. The many-body interaction induced self-consistent field from density fluctuations suggests the existence of an attractive force. This may cause time-delayed plasmonic photoemissions in ultrafast measurements. At the waning end of the plasmon structure, a strong minimum in the cross sections from a correlation-driven coherence effect is predicted which can possibly be observed by the photoelectron spectroscopy.

Electronic and optical properties of two-dimensional ice I

Two-dimensional ice is a new type of atomic-scale material obtained by typical atomic manufacturing techniques. Its structure and nucleation growth play an essential role in many fields such as material science, tribology, biology, atmospheric science and planetary science. Although the structural properties of two-dimensional ice have been investigated extensively, little is known about its electronic and optical properties. In this paper, the main electronic, optical, dielectric properties and infrared spectra of two-dimensional ice I at zero temperature are calculated by density functional theory and linear response theory. The study reveals that the two-dimensional ice I is an indirect band gap and its optical properties show anisotropic lattice. And the absorption energy range for the two-dimensional ice I is in the ultraviolet region of the spectrum (> 3.2 eV) and the visible region of the spectrum (between 2 and 3.2 eV), respectively. Secondly, the radial distribution function and the vibrational density of states of the two-dimensional ice I at a finite temperature are simulated by <i>ab initio</i> molecular dynamics method. For the structure of the two-dimensional ice I, whether SCAN or PBE functional, after considering the vdW effect, there is almost no effect on the atomic distance, while by comparison, the SCAN functional and the PBE functional are quite different. Therefore, it can be seen that the main reason for affecting the distance between atoms in the structure is due to the consideration of the strong confinement effect of SCAN. In terms of the vibration characteristics of two-dimensional ice I, comparing with PBE and vdW-DF-ob86, the first two peaks of the IR spectrum of SCAN + rVV10 functional show blue shift, and the two peaks in the high frequency region present the red shift. Therefore, considering the strong confinement effect of SCAN, the intermolecular tensile vibration of two-dimensional ice I becomes stronger, while the intramolecular H—O—H bending vibration and O—H bond tensile vibration become weaker. The effect of van der Waals action on vibration properties is not obvious. Furthermore, we investigate the temperature effects on the vibration spectra of two-dimensional ice I. It is found that with the increase of temperature, the intermolecular librational mode weakens at a low frequency, the intramolecular bending and stretching bands gradually broaden, and the intramolecular O-H stretching peak presents the blue-shifts with temperature rising. The results of this paper reveal the electronic structure of atomic-scale two-dimensional ice I, and demonstrate its unique optical absorption mechanism, which is helpful in further experimentally characterizing and manipulating the two-dimensional ice on an atomic scale. Since the two-dimensional ice on the surface can promote or inhibit the formation of three-dimensional ice, it has potential applications in designing and developing the anti-icing materials. In addition, two-dimensional ice itself can also be used as a unique two-dimensional material, providing a brand-new standard material for high-temperature superconductivity, deep-ultraviolet detection, cryo-electron microscopy imaging.

First-Principles Method to Study Near-Field Radiative Heat Transfer

We present a general and convenient first principle method to study near-field radiative heat transfer. We show that the Landauer-like expression of heat flux can be expressed in terms of a frequency and wave-vector dependent macroscopic dielectric function which can be obtained from the linear response density functional theory. A random phase approximation is used to calculate the response function. We computed the heat transfer in three systems -- graphene, molybdenum disulfide (MoS$_2$), and hexagonal boron nitride (h-BN). Our results show that the near-field heat flux exceeds the blackbody limit up to four orders of magnitude. With the increase of the distances between two parallel sheets, a $1/d^2$ dependence of heat flux is shown, consistent with Coulomb's law. The heat transfer capacity is sensitive to the dielectric properties of materials. Influences from chemical potential and temperature are also discussed. Our method can be applied to a wide range of materials including systems with inhomogeneities.

Photoemission from hybrid states of Cl@C60 before and after a stabilizing charge transfer

Photoionization calculations of the endofullerene molecule Cl@C60 with an open-shell chlorine atom are performed in the linear response density functional theory based on a spherical jellium model of C60. Cross sections for atom–fullerene hybrid photoemission studied show the effects of the hybridization symmetry, the giant plasmon and the molecular cavity. Comparisons with the results of Ar@C60 provide insights into the role of a shell-closing electron and its influence on the dynamics. The results for Cl@C60 are further compared with those of a more stable configuration that results after a C60 electron transfers to Cl forming Cl−@. This comparison reveals noticeable differences in the ionization properties of the antibonding hybrid state while the bonding hybrid remains nearly unaltered showing a magnification covering the entire giant plasmon energy range. These predictions should raise interest in probing the molecular configuration using photoelectron spectroscopy.

On the performance of DFT/MRCI Hamiltonians for electronic excitations in transition metal complexes: The role of the damping function.

The combination of density functional theory and multireference configuration interaction (DFT/MRCI) is a well-established semi-empirical method suitable for computing spectral properties of large molecular systems. To this day, three different Hamiltonians and various parameter set combinations exist. These DFT/MRCI variants are well tried and tested when it comes to electronic excitations of organic molecules. For transition metal complexes, systematic benchmarks against experimental data are missing, however. Here we present an assessment of the DFT/MRCI variants and of time-dependent, linear-response density functional theory (TDDFT) for a diverse set of ligand-centered, metal-to-ligand charge transfer, metal-centered, and ligand-to-metal charge transfer (LMCT) excitations on 21 3d and 4d complexes comprising 10 small inorganic and 11 larger metalorganic compounds with closed-shell ground states. In the course of this assessment, we realized that the excitation energies of transition metal complexes can be very sensitive with respect to the details of the damping function that scales off-diagonal matrix elements. This scaling is required in DFT/MRCI to avoid double counting of dynamic electron correlation. These insights lead to a new Hamiltonian, denoted R2018, with improved performance on transition metal compounds, while the results for organic molecules are nearly unaffected by the modified damping function. Two parameter sets were optimized for this Hamiltonian: One set is to be used in conjunction with the standard configuration selection threshold of 1.0 E h and a second set is for use with a selection threshold of 0.8 E h which leads to shorter wave function expansions. The R2018 Hamiltonian in standard parameterization achieves root-mean-square errors (RMSEs) of merely 0.15 eV for the metalorganic complexes, followed by 0.20 eV for the original DFT/MRCI ansatz, and 0.25 eV for the redesigned DFT/MRCI approach. In comparison, TDDFT gives a much larger RMSE of 0.46 eV for metalorganic complexes. None of the DFT/MRCI variants yields convincing results for small oxides and fluorides which exhibit LMCT transitions. Here, TDDFT performs better. If the oxides and fluorides are excluded from the inorganic test set, satisfactory agreement can be achieved, with RMSE values between 0.26 eV and 0.30 eV for DFT/MRCI and 0.34 eV for TDDFT. The performance of the original and the new DFT/MRCI Hamiltonians deteriorates only slightly, when a tighter selection threshold is chosen, thus enabling the computation of reliable spectral properties even for large metalorganic complexes.

Can fused thiophene–pyrrole-containing rings act as possible new electrochromic dyes? A computational prediction

The computed electronic spectra of neutral, radical cation and dication species for a series of fused thiophene–pyrrole-containing ring systems clearly suggest that these molecules can be used as new electrochromic materials. The calculations have been performed in the framework of the time-dependent density functional linear response theory employing different exchange–correlation functionals. Based on our results, we can indicate the long-chain molecules with twelve and fourteen rings, not yet synthesized, as the best candidates for electrochromic devices operating in the near-infrared region. The calculated properties are in excellent agreement with the available experimental data.

First-principles study on lattice instabilities and structural phase transitions in Ba doped La2CuO4

We present linear-response density-functional theory calculations for the high-Tc superconductor La2−xBaxCuO4 to study the doping dependence of phonon dispersion. Using the virtual crystal approximation, the doping range up to x=0.20 is investigated. We find unstable phonon modes that soften around high-symmetry points of the Brillouin zone. These branches are analyzed as a function of doping and pressure. The structural distortions related to these phonons are in accordance with the observed phase transitions from the high-temperature tetragonal (HTT) phase to the low-temperature orthorhombic (LTO) and the low-temperature tetragonal (LTT) phases. The calculated tilting angles of the CuO6 octahedra corresponding to these phases are in good agreement with experiment. Our findings confirm that strong electron correlations have only minor impact on the structural properties of high-Tc cuprates.

Embedded correlated wavefunction schemes: theory and applications.

Conspectus Ab initio modeling of matter has become a pillar of chemical research: with ever-increasing computational power, simulations can be used to accurately predict, for example, chemical reaction rates, electronic and mechanical properties of materials, and dynamical properties of liquids. Many competing quantum mechanical methods have been developed over the years that vary in computational cost, accuracy, and scalability: density functional theory (DFT), the workhorse of solid-state electronic structure calculations, features a good compromise between accuracy and speed. However, approximate exchange-correlation functionals limit DFT's ability to treat certain phenomena or states of matter, such as charge-transfer processes or strongly correlated materials. Furthermore, conventional DFT is purely a ground-state theory: electronic excitations are beyond its scope. Excitations in molecules are routinely calculated using time-dependent DFT linear response; however applications to condensed matter are still limited. By contrast, many-electron wavefunction methods aim for a very accurate treatment of electronic exchange and correlation. Unfortunately, the associated computational cost renders treatment of more than a handful of heavy atoms challenging. On the other side of the accuracy spectrum, parametrized approaches like tight-binding can treat millions of atoms. In view of the different (dis-)advantages of each method, the simulation of complex systems seems to force a compromise: one is limited to the most accurate method that can still handle the problem size. For many interesting problems, however, compromise proves insufficient. A possible solution is to break up the system into manageable subsystems that may be treated by different computational methods. The interaction between subsystems may be handled by an embedding formalism. In this Account, we review embedded correlated wavefunction (CW) approaches and some applications. We first discuss our density functional embedding theory, which is formally exact. We show how to determine the embedding potential, which replaces the interaction between subsystems, at the DFT level. CW calculations are performed using a fixed embedding potential, that is, a non-self-consistent embedding scheme. We demonstrate this embedding theory for two challenging electron transfer phenomena: (1) initial oxidation of an aluminum surface and (2) hot-electron-mediated dissociation of hydrogen molecules on a gold surface. In both cases, the interaction between gas molecules and metal surfaces were treated by sophisticated CW techniques, with the remainder of the extended metal surface being treated by DFT. Our embedding approach overcomes the limitations of conventional Kohn-Sham DFT in describing charge transfer, multiconfigurational character, and excited states. From these embedding simulations, we gained important insights into fundamental processes that are crucial aspects of fuel cell catalysis (i.e., O2 reduction at metal surfaces) and plasmon-mediated photocatalysis by metal nanoparticles. Moreover, our findings agree very well with experimental observations, while offering new views into the chemistry. We finally discuss our recently formulated potential-functional embedding theory that provides a seamless, first-principles way to include back-action onto the environment from the embedded region.

Pressure-induced instability in CdO

The lattice dynamics of rocksalt CdO is studied as a function of pressure using density-functional linear-response theory. The predicted static phase-transition pressure from rocksalt (B1) to CsCl (B2) structures is 76.12 GPa. Analysis of the phonon calculations suggests that the pressure-induced instabilities at p = 78.26 GPa of the transverse acoustic (TA) modes in a large portion of the Brillouin zone are responsible for the phase transition from B1 → B2 phases of CdO. Moreover, the calculated partial phonon density of states at the precursor phase transition of p = 70 GPa reveals strong reduction of the longitudinal acoustic Cd-like modes and the existence of a large peak related to the longitudinal optic O-like mode.

A simplified time-dependent density functional theory approach for electronic ultraviolet and circular dichroism spectra of very large molecules

We present a simplified time-dependent density functional theory approach (sTD-DFT) that allows fast computation of electronic ultraviolet (UV) or circular dichroism (CD) spectra of molecules with 500–1000 atoms. The matrix elements are treated in the same way as in the recently proposed simplified Tamm-Dancoff approach (sTDA, S. Grimme, J. Chem. Phys., 138 (2013), 244104) but instead of applying the Tamm-Dancoff approximation, the standard linear-response density functional theory problem is solved. Compared to sTDA, the method leads to an increase in computation time (typically a factor of 2–5 compared to the corresponding sTDA) which is justified since the resulting transition dipole moments are in general of higher quality. This becomes important if spectral intensities (e.g. single-photon oscillator and rotatory transition strengths) are of interest. Comparison of UV and CD spectra obtained from sTD-DFT and sTDA for some typical systems employing standard hybrid functionals shows that both yield very similar excitation energies but the advantage of using the former approach for transition moments. In order to show the applicability of sTD-DFT to systems which are far beyond the scope of conventional TD-DFT, we present the CD spectrum of a substituted, chiral fullerene over a range of almost 1200 excited states. We propose this method as a more reliable alternative for the prediction especially of the more challenging CD spectra.

High pressure phase of pnictides yttrium YAs and YBi: first-principles studies

The high pressure phase transition in pnictides yttrium YAs and YBi has been investigated by a first-principles pseudopotential plane-wave method and density functional linear-response theory. Employing total energy calculations, the predicted rocksalt → CsCl phase transition pressure is found, respectively, at 63.3 and 23 GPa for YAs and YBi. A pressure-induced soft transverse acoustic (TA) phonon mode is identified at 92 GPa for YAs and at 47 GPa for YBi. Phonon calculations suggest that YAs becomes dynamically instable with respect to the TA [ε00] and TA [0εε] phonon modes, while YBi becomes dynamically instable with respect to the TA phonon mode at the zone boundary X point. Furthermore, it is found that the increase of anti-bonding Y-4d bands significantly weakens the stability of the rocksalt phase of YAs and YBi under pressure inducing, hence a structural phase transformation.

Ab initio investigations of phonons and thermodynamic properties of ScZn and YZn in the B2 structure

We have performed an ab initio investigation of structural, elastic, electronic, lattice dynamical, and thermodynamic properties of ScZn and YZn in B2 structure. The calculations was conducted within the density functional theory and linear response theory using the pseudopotentials and a plane wave basis set. The completely minimized structural parameters and elastic constants of ScZn and YZn compounds are in excellent agreement with previous theoretical and experimental data. The calculated phonon dispersion relations for YZn concur very well with experimental data available for main symmetry directions. Through the full quasi harmonic model, in which the phononic effects considered, the thermodynamic properties such as temperature dependence of the isothermal and adiabatic bulk modulus, thermal expansion coefficients, heat capacities, entropy and free energy have been successfully calculated in the whole temperature range from 0 to 1000K.

Fukui function and response function for nonlocal and fractional systems

We present extensions to our previous work on Fukui functions and linear-response functions [W. Yang, A. J. Cohen, F. D. Proft, and P. Geerlings, J. Chem. Phys. 136, 144110 (2012)]. Viewed as energy derivatives with respect to the number of electrons and the external potential, all second-order derivatives (the linear-response function, the Fukui function, and the chemical hardness) are extended to fractional systems, and all third-order derivatives (the second-order response function, the Fukui response function, the dual descriptor, and the hyperhardness) for integer systems are also obtained. These analytical derivatives are verified by finite difference numerical derivatives. In the context of the exact linearity condition and the constancy condition, these analytical derivatives enrich greatly the information of the exact conditions on the energy functional through establishing real-space dependency. The introduction of an external nonlocal potential defines the nonlocal Fukui function and the nonlocal linear-response function. The nonlocal linear-response function so defined also provides the precise meaning for the time-dependent linear-response density-functional theory calculations with generalized Kohn-Sham functionals. These extensions will be useful to conceptual density-functional theory and density functional development.