Adiabatic Local Density Approximation Research Articles

Negative static permittivity and violation of Kramers-Kronig relations in quasi-two-dimensional crystals

We investigate the wave-vector and frequency-dependent screening of the electric field in atomically thin (quasi-two-dimensional) crystals. For graphene and hexagonal boron nitride we find that, above a critical wave-vector $q_c$, the static permittivity $\varepsilon(q \! > \!q_c,\omega \! = \!0)$ becomes negative and the Kramers-Kronig relations do not hold for $\varepsilon(q \! > \! q_c,\omega)$. Thus, in quasi-two-dimensional crystals, we reveal the physical confirmation of a proposition put forward decades ago (Kirzhnits, 1976), allowing for the breakdown of Kramers-Kronig relations and for the negative static permittivity. In the vicinity of the critical wave-vector, we find a giant growth of the permittivity. Our results, obtained in the {\it ab initio} calculations using both the random-phase approximation and the adiabatic time-dependent local-density approximation, and further confirmed with a simple slab model, allow us to argue that the above properties, being exceptional in the three-dimensional case, are common to quasi-two-dimensional systems.

Adiabatic-connection fluctuation-dissipation DFT for the structural properties of solids-The renormalized ALDA and electron gas kernels.

We present calculations of the correlation energies of crystalline solids and isolated systems within the adiabatic-connection fluctuation-dissipation formulation of density-functional theory. We perform a quantitative comparison of a set of model exchange-correlation kernels originally derived for the homogeneous electron gas (HEG), including the recently introduced renormalized adiabatic local-density approximation (rALDA) and also kernels which (a) satisfy known exact limits of the HEG, (b) carry a frequency dependence, or (c) display a 1/k(2) divergence for small wavevectors. After generalizing the kernels to inhomogeneous systems through a reciprocal-space averaging procedure, we calculate the lattice constants and bulk moduli of a test set of 10 solids consisting of tetrahedrally bonded semiconductors (C, Si, SiC), ionic compounds (MgO, LiCl, LiF), and metals (Al, Na, Cu, Pd). We also consider the atomization energy of the H2 molecule. We compare the results calculated with different kernels to those obtained from the random-phase approximation (RPA) and to experimental measurements. We demonstrate that the model kernels correct the RPA's tendency to overestimate the magnitude of the correlation energy whilst maintaining a high-accuracy description of structural properties.

First Principles Investigation of the Optical Properties of BN x P1−x (0 ≤ x ≤ 1) Boron Ternary Alloys

The effect of different concentrations of N on the electronic and optical properties of BN x P1−x (0 ≤ x ≤ 1) boron ternary alloys was studied using the full potential linearized augmented plane wave method within the density functional theory (DFT) and time-dependent DFT (TDDFT). The exchange–correlation potential is described in generalized gradient approximation (GGA) within the Perdew et al. scheme. Also, we have used the GW formalism to improve the band gap results, and the calculated band gap within GW shows substantial improvement over GGA. The real and imaginary parts of the dielectric function e(ω), optical reflectivity R(ω), absorption coefficient α(ω), refractive index and electron energy loss function are computed by random phase approximation for DFT and adiabatic local density approximation for TDDFT. The interband transitions responsible for the structures in the spectra are specified. It is shown that, for ternary alloys, N 2p states and N 2s, P 3d states play a major role in optical transitions as initial and final states, respectively. The results for these alloys indicate that the band gap increases, the static dielectric constant decreases, and all existing structures move toward higher energies by increasing the concentration of nitrogen atoms. The results are compared with other available theoretical and experimental data.

Towards time-dependent current-density-functional theory in the non-linear regime.

Time-Dependent Density-Functional Theory (TDDFT) is a well-established theoretical approach to describe and understand irradiation processes in clusters and molecules. However, within the so-called adiabatic local density approximation (ALDA) to the exchange-correlation (xc) potential, TDDFT can show insufficiencies, particularly in violently dynamical processes. This is because within ALDA the xc potential is instantaneous and is a local functional of the density, which means that this approximation neglects memory effects and long-range effects. A way to go beyond ALDA is to use Time-Dependent Current-Density-Functional Theory (TDCDFT), in which the basic quantity is the current density rather than the density as in TDDFT. This has been shown to offer an adequate account of dissipation in the linear domain when the Vignale-Kohn (VK) functional is used. Here, we go beyond the linear regime and we explore this formulation in the time domain. In this case, the equations become very involved making the computation out of reach; we hence propose an approximation to the VK functional which allows us to calculate the dynamics in real time and at the same time to keep most of the physics described by the VK functional. We apply this formulation to the calculation of the time-dependent dipole moment of Ca, Mg and Na2. Our results show trends similar to what was previously observed in model systems or within linear response. In the non-linear domain, our results show that relaxation times do not decrease with increasing deposited excitation energy, which sets some limitations to the practical use of TDCDFT in such a domain of excitations.

Electronic and optical properties of pure and modified diamondoids studied by many-body perturbation theory and time-dependent density functional theory.

Diamondoids are small diamond nanoparticles (NPs) that are built up from diamond cages. Unlike usual semiconductor NPs, their atomic structure is exactly known, thus they are ideal test-beds for benchmarking quantum chemical calculations. Their usage in spintronics and bioimaging applications requires a detailed knowledge of their electronic structure and optical properties. In this paper, we apply density functional theory (DFT) based methods to understand the electronic and optical properties of a few selected pure and modified diamondoids for which accurate experimental data exist. In particular, we use many-body perturbation theory methods, in the G0W0 and G0W0+BSE approximations, and time-dependent DFT in the adiabatic local density approximation. We find large quasiparticle gap corrections that can exceed thrice the DFT gap. The electron-hole binding energy can be as large as 4 eV but it is considerably smaller than the GW corrections and thus G0W0+BSE optical gaps are about 50% larger than the Kohn-Sham (KS) DFT gaps. We find significant differences between KS time-dependent DFT and GW+BSE optical spectra on the selected diamondoids. The calculated G0W0 quasiparticle levels agree well with the corresponding experimental vertical ionization energies. We show that nuclei dynamics in the ionization process can be significant and its contribution may reach about 0.5 eV in the adiabatic ionization energies.

Time-dependent potential-functional embedding theory

We introduce a time-dependent potential-functional embedding theory (TD-PFET), in which atoms are grouped into subsystems. In TD-PFET, subsystems can be propagated by different suitable time-dependent quantum mechanical methods and their interactions can be treated in a seamless, first-principles manner. TD-PFET is formulated based on the time-dependent quantum mechanics variational principle. The action of the total quantum system is written as a functional of the time-dependent embedding potential, i.e., a potential-functional formulation. By exploiting the Runge-Gross theorem, we prove the uniqueness of the time-dependent embedding potential under the constraint that all subsystems share a common embedding potential. We derive the integral equation that such an embedding potential needs to satisfy. As proof-of-principle, we demonstrate TD-PFET for a Na4 cluster, in which each Na atom is treated as one subsystem and propagated by time-dependent Kohn-Sham density functional theory (TDDFT) using the adiabatic local density approximation (ALDA). Our results agree well with a direct TDDFT calculation on the whole Na4 cluster using ALDA. We envision that TD-PFET will ultimately be useful for studying ultrafast quantum dynamics in condensed matter, where key regions are solved by highly accurate time-dependent quantum mechanics methods, and unimportant regions are solved by faster, less accurate methods.

First-principles simulation of the optical response of bulk and thin-film α-quartz irradiated with an ultrashort intense laser pulse

A computational method based on a first-principles multiscale simulation has been used for calculating the optical response and the ablation threshold of an optical material irradiated with an ultrashort intense laser pulse. The method employs Maxwell's equations to describe laser pulse propagation and time-dependent density functional theory to describe the generation of conduction band electrons in an optical medium. Optical properties, such as reflectance and absorption, were investigated for laser intensities in the range 1010 W/cm2 to 2 × 1015 W/cm2 based on the theory of generation and spatial distribution of the conduction band electrons. The method was applied to investigate the changes in the optical reflectance of α-quartz bulk, half-wavelength thin-film, and quarter-wavelength thin-film and to estimate their ablation thresholds. Despite the adiabatic local density approximation used in calculating the exchange–correlation potential, the reflectance and the ablation threshold obtained from our method agree well with the previous theoretical and experimental results. The method can be applied to estimate the ablation thresholds for optical materials, in general. The ablation threshold data can be used to design ultra-broadband high-damage-threshold coating structures.

On the Short-Range Behavior of Correlated Pair Functions from the Adiabatic-Connection Fluctuation-Dissipation Theorem of Density-Functional Theory.

The short-range behavior of correlated pair functions from the adiabatic-connection fluctuation-dissipation theorem (ACFD) of density functional theory (DFT) employing local exchange-correlation kernels has been analyzed. It has been found that for large basis sets the pair function exhibits unphysical humps for small interelectronic distances if the adiabatic local density approximation kernel is used in the ACFD scheme (this method is termed ACFD/ALDA in this work). However, up to basis set sizes of quadruple-ζ type quality, the correlated pair function of ACFD/ALDA behaves physically correct and the method yields reasonable results for atomization energies, ionization potentials, and intermolecular interaction energies. In order to correct the deficiencies of the pair function of ACFD/ALDA for large basis sets, a short-range correction scheme has been devised on the basis of a combination of the ACFD/ALDA pair function for the large distance regime with a proper physically correctly behaving pair function at smaller distances. While this approach, termed as ACFD/ALDAcorr, practically yields results close to those of the ACFD/ALDA method for finite basis sets, it enables basis set extrapolation techniques and thus can take dynamic correlation effects fully into account in contrast to the ACFD/ALDA approach. This work also presents an efficient density-fitting algorithm to compute the ACFD correlation energies that enables the calculation of correlation energies of extended molecular systems.

Beyond the random phase approximation: Improved description of short-range correlation by a renormalized adiabatic local density approximation

We assess the performance of a recently proposed renormalized adiabatic local density approximation (rALDA) for \textit{ab initio} calculations of electronic correlation energies in solids and molecules. The method is an extension of the random phase approximation (RPA) derived from time-dependent density functional theory and the adiabatic connection fluctuation-dissipation theorem and contains no fitted parameters. The new kernel is shown to preserve the accurate description of dispersive interactions from RPA while significantly improving the description of short range correlation in molecules, insulators, and metals. For molecular atomization energies the rALDA is a factor of 7(4) better than RPA(PBE) when compared to experiments, and a factor of 3(1.5) better than RPA(PBE) for cohesive energies of solids. For transition metals the inclusion of full shell semi-core states is found to be crucial for both RPA and rALDA calculations and can improve the cohesive energies by up to 0.4 eV. Finally we discuss straightforward generalizations of the method, which might improve results even further.

Action formalism of time-dependent density-functional theory

The Runge-Gross [E. Runge and E. K. U. Gross, Phys. Rev. Lett. 52, 997 (1984)] action functional of time-dependent density-functional theory leads to a well-known causality paradox; that is, a perturbation of the electronic density in the future affects the response of the system in the present. This paradox is known to be caused by an inconsistent application of the Dirac-Frenkel variational principle. In view of the recent solutions to this problem, the action functional employed by Runge and Gross in their formulation of time-dependent density-functional theory is analyzed in the context of the Keldysh contour technique. The time-dependent electronic density and the concept of causality are extended to the contour. We derive a variational equation that obeys causality and relates the exchange-correlation potential with its kernel and the functional derivative of the exchange-correlation action functional with respect to the density. It is shown that the adiabatic local-density approximation is a consistent solution of this equation and that the time-dependent optimized potential method can also be derived from it. The formalism presented here can be used to find new approximation methods for the exchange-correlation potential and to avoid the causality dilemma.

Assessment of range-separated time-dependent density-functional theory for calculating C6 dispersion coefficients

We assess a variant of linear-response range-separated time-dependent density-functional theory (TDDFT), combining a long-range Hartree-Fock (HF) exchange kernel with a short-range adiabatic exchange-correlation kernel in the local-density approximation (LDA) for calculating isotropic C6 dispersion coefficients of homodimers of a number of closed-shell atoms and small molecules. This range-separated TDDFT tends to give underestimated C6 coefficients of small molecules with a mean absolute percentage error of about 5%, a slight improvement over standard TDDFT in the adiabatic LDA which tends to overestimate them with a mean absolute percentage error of 8%, but close to time-dependent Hartree-Fock which has a mean absolute percentage error of about 6%. These results thus show that introduction of long-range HF exchange in TDDFT has a small but beneficial impact on the values of C6 coefficients. It also confirms that the present variant of range-separated TDDFT is a reasonably accurate method even using only a LDA-type density functional and without adding an explicit treatment of long-range correlation.

Nonlinear ionization mechanism dependence of energy absorption in diamond under femtosecond laser irradiation

We present first-principles calculations for nonlinear photoionization of diamond induced by the intense femtosecond laser field. A real-time and real-space time-dependent density functional theory with the adiabatic local-density approximation is applied to describe the laser-material interactions in the Kohn-Sham formalism with the self-interaction correction. For a certain laser wavelength, the intensity dependence of energy absorption on multiphoton and/or tunnel ionization mechanisms is investigated, where laser intensity regions vary from 1012 W/cm2 to 1016 W/cm2. In addition, the effect of laser wavelength on energy absorption at certain ionization mechanism is discussed when the Keldysh parameter is fixed. Theoretical results show that: (1) at the fixed laser wavelength, the relationship between the energy absorption and laser intensity shows a good fit of E = cMIN (N is the number of photons absorbed to free from the valence band) when multiphoton ionization dominates; (2) while when tunnel ionization becomes significant, the relationship coincides with the expression of E = cTIn (n < N).

Optimal control strategies for coupled quantum dots

AbstractSemiconductor quantum dots are ideal candidates for quantum information applications in solid-state technology. However, advanced theoretical and experimental tools are required to coherently control, for example, the electronic charge in these systems. Here we demonstrate how quantum optimal control theory provides a powerful way to manipulate the electronic structure of coupled quantum dots with an extremely high fidelity. As alternative control fields we apply both laser pulses as well as electric gates, respectively. We focus on double and triple quantum dots containing a single electron or two electrons interacting via Coulomb repulsion. In the two-electron situation we also briefly demonstrate the challenges of timedependent density-functional theory within the adiabatic local-density approximation to produce comparable results with the numerically exact approach.

Exchange-correlation asymptotics and high harmonic spectra

High harmonic spectra of N2 are calculated using time-dependent density functional theory. The adiabatic local density approximation (A-LDA) and the adiabatic van Leeuwen–Baerends (A-LB94) approximations are used to study effects of differing spatial asymptotics. The LB94 potential corrects the LDA potential to the exact -1/r decay, but does not satisfy the zero-force condition. The A-LB94 makes a significant change in ionization probabilities but not in the relevant orbital contributions to ionization. This leads to qualitatively similar spectra, the exception being harmonic intensities. We also discuss why spurious dipoles induced by the A-LB94 do not affect significantly the structure of the N2 harmonic spectrum.

First-principles investigation of transient dynamics of molecular devices

Based on the nonequilibrium Green's function (NEGF) and time-dependent density-functional theory (TDDFT), we propose a formalism to study the time-dependent transport behavior of molecular devices from first principles. While this approach is equivalent to the time-dependent wave-function approach within TDDFT, it has the advantage that the scattering states and bound states are treated on equal footing. Furthermore, it is much easier to implement our approach numerically. Different from the time-dependent wave-function $[\ensuremath{\psi}(t,E)$] approach, our formalism is in the time space [${\mathbf{G}}^{r}(t,{t}^{\ensuremath{'}})$], making this method superior in the time-dependent transport problem with many subbands in the transverse direction. For the purpose of numerical implementation on molecular devices, a computational tractable numerical scheme is discussed in detail. We have applied our formalism to calculate the transient current of two molecular devices Al-1,4-dimethylbenzene-Al and Al-benzene-Al from first principles. In the calculation, we have gone beyond the wideband limit and used the adiabatic local density approximation that was used within TDDFT. It is known that when the wideband limit is abandoned, the boundary condition of the transport problem is non-Markovian, resulting in a memory term in the effective Hamiltonian of the scattering region. To overcome the computational complexity due to the memory term, we have employed a fast algorithm to speed up the calculation and reduced the CPU time from the scaling ${N}^{3}$ to ${N}^{2}{\mathrm{log}}_{2}^{2}(N)$ for the steplike pulse, where $N$ is the number of time steps in the time evolution of the Green's function. To ensure the accuracy of our method, we have done a benchmark transient calculation on an atomic junction using a time-dependent wave-function approach within TDDFT in momentum space, which agrees very well with the result from our method.

Real-time real-space TD-DFT for atoms: Benchmark computations on a nonspherical logarithmic grid

We present the results of benchmark, all-electron computations for the optical properties of atoms with up to 30 electrons, carried out within the adiabatic local density approximation (ALDA) of time-dependent density functional theory. Following the original approach proposed by Janak and Williams, Phys. Rev. B 23, 6301 (1981), Kohn-Sham orbitals are tabulated on a logarithmic mesh along a discrete set of rays coming out of the atomic nucleus, selected in such a way to accurately represent the angular dependence of ground and excited states. Optical properties are obtained by real-time propagation of the electronic states represented on an extended basis of filled and empty Kohn-Sham orbitals. As expected, the comparison with experimental results is affected by the known drawbacks of the ALDA method. We apply the computational tool to carry out a real-time simulation of Auger processes, whose results, once again, highlight basic (but expected) limitations of the TD-DFT-ALDA approach. We define a novel set of atomic-like basis functions (response functions) meant to optimize the convergence of time-dependent computations, and we measure their performance by comparison with the results of the benchmark computations.

Correlation effects in bistability at the nanoscale: Steady state and beyond

The possibility of finding multistability in the density and current of an interacting nanoscale junction coupled to semi-infinite leads is studied at various levels of approximation. The system is driven out of equilibrium by an external bias and the nonequilibrium properties are determined by real-time propagation using both time-dependent density functional theory (TDDFT) and many-body perturbation theory (MBPT). In TDDFT the exchange-correlation effects are described within a recently proposed adiabatic local density approximation (ALDA). In MBPT the electron-electron interaction is incorporated in a many-body self-energy which is then approximated at the Hartree-Fock (HF), second-Born, and $GW$ level. Assuming the existence of a steady state and solving directly the steady-state equations we find multiple solutions in the HF approximation and within the ALDA. In these cases we investigate whether and how these solutions can be reached through time evolution and how to reversibly switch between them. We further show that for the same cases the inclusion of dynamical correlation effects suppresses bistability.

Theoretical and numerical assessments of spin-flip time-dependent density functional theory

Spin-flip time-dependent density functional theory (SF-TD-DFT) with the full noncollinear hybrid exchange-correlation kernel and its approximate variants are critically assessed, both formally and numerically. As demonstrated by the ethylene torsion and the C(2v) ring-opening of oxirane, SF-TD-DFT is very useful for describing nearly degenerate situations. However, it may occasionally yield unphysical results. This stems from the noncollinear form of the generalized gradient approximation, which becomes numerically instable in the presence of spin-flip excitations from the closed- to vacant-shell orbitals of an open-shell reference. To cure this defect, a simple modification, dubbed as ALDA0, is proposed in the spirit of adiabatic local density approximation (ALDA). It is applicable to all kinds of density functionals and yields stable results without too much loss of accuracy. In particular, the combination of ALDA0 with the Tamm-Dancoff approximation is a promising tool for studying global potential energy surfaces. In addition to the kernel problem, SF-TD-DFT is also rather sensitive to the choice of reference states, as demonstrated by the spin multiplet states of closed-shell molecules of H(2)O, CH(2)O, and C(2)H(4). Surprisingly, SF-TD-DFT with pure density functionals may also fail for valance excitations with large orbital overlaps, at variance with the spin-conserving counterpart (SC-TD-DFT). In this case, the inclusion of a large amount of Hartree-Fock exchange is mandatory for quantitative results. Nonetheless, for spatially degenerate cases such as CF, CH, and NH(+), SF-TD-DFT is more advantageous than SC-TD-DFT, unless the latter is also space adapted. These findings are very instructive for future development and applications of TD-DFT.

Different dimensionality trends in the Landau damping of magnons in iron, cobalt, and nickel: Time-dependent density functional study

We study the Landau damping of ferromagnetic magnons in Fe, Co, and Ni as the dimensionality of the system is reduced from three to two. We resort to the \textit{ab initio} linear response time dependent density functional theory in the adiabatic local spin density approximation. The numerical scheme is based on the Korringa-Kohn-Rostoker Green's function method. The key points of the theoretical approach and the implementation are discussed. We investigate the transition metals in three different forms: bulk phases, free-standing thin films and thin films supported on a nonmagnetic substrate. We demonstrate that the dimensionality trends in Fe and Ni are opposite: in Fe the transition from bulk bcc crystal to Fe/Cu(100) film reduces the damping whereas in Ni/Cu(100) film the attenuation increases compared to bulk fcc Ni. In Co, the strength of the damping depends relatively weakly on the sample dimensionality. We explain the difference in the trends on the basis of the underlying electronic structure. The influence of the substrate on the spin-wave damping is analyzed by employing Landau maps representing wave-vector resolved spectral density of the Stoner excitations.

Comparative study of many-body perturbation theory and time-dependent density functional theory in the out-of-equilibrium Anderson model

We study time-dependent electron transport through an Anderson model. The electronic interactions on the impurity site are included via the self-energy approximations at Hartree-Fock (HF), second Born (2B), GW, and T-Matrix level as well as within a time-dependent density functional (TDDFT) scheme based on the adiabatic Bethe-Ansatz local density approximation (ABALDA) for the exchange correlation potential. The Anderson model is driven out of equilibrium by applying a bias to the leads and its nonequilibrium dynamics is determined by real-time propagation. The time-dependent currents and densities are compared to benchmark results obtained with the time-dependent density matrix renormalization group (tDMRG) method. Many-body perturbation theory beyond HF gives results in close agreement with tDMRG especially within the 2B approximation. We find that the TDDFT approach with the ABALDA approximation produces accurate results for the densities on the impurity site but overestimates the currents. This problem is found to have its origin in an overestimation of the lead densities which indicates that the exchange correlation potential must attain nonzero values in the leads.