Response Time-dependent Density Functional Theory Research Articles

Ab initioelectronic stopping power of protons in bulk materials

The electronic stopping power is a crucial quantity for ion irradiation: it governs the deposited heat, the damage profile, and the implantation depth. Whereas experimental data are readily available for elemental solids, the data are much more scarce for compounds. Here we develop a fully ab initio computational scheme based on linear response time-dependent density-functional theory to predict the random electronic stopping power (RESP) of materials without any empirical fitting. We show that the calculated RESP compares well with experimental data, when at full convergence, with the inclusion of the core states and of the exchange correlation. We evaluate the unexpectedly limited magnitude of the nonlinear terms in the RESP by comparing with other approaches based on the time propagation of time-dependent density-functional theory. Finally, we check the validity of a few empirical rules of thumbs that are commonly used to estimate the electronic stopping power.

Photoinduced Absorption within Single-Walled Carbon Nanotube Systems

We study the photoabsorption properties of photoactive bulk polymer/fullerene/nanotube heterojunctions in the near-infrared region. By combining pump–probe spectroscopy and linear response time-dependent density functional theory within the random phase approximation (TDDFT-RPA) we elucidate the excited state dynamics of the E11 transition within (6,5) and (7,5) single-walled carbon nanotubes (SWNTs) and combined with poly(3-hexylthiophene-2,5-diyl) (P3HT) and [6,6]-phenyl-C61-butyric acid methyl ester (PCBM) in P3HT/PCBM/SWNT blended samples. We find the presence of a photoinduced absorption (PA) peak is related mainly to the width of the photobleach (PB) peak and the charge carrier density of the SWNT system. For mixed SWNT samples, the PB peak is too broad to observe the PA peak, whereas within P3HT/PCBM/SWNT blended samples P3HT acts as a hole acceptor, narrowing the PB peak by exciton delocalization, which reveals a PA peak. Our results suggest that the PA peak originates from a widening of the band gap in the presence of excited electrons and holes. These results have important implications for the development of new organic photovoltaic heterojunctions including SWNTs.

The adiabatic strictly-correlated-electrons functional: kernel and exact properties.

We investigate a number of formal properties of the adiabatic strictly-correlated electrons (SCE) functional, relevant for time-dependent potentials and for kernels in linear response time-dependent density functional theory. Among the former, we focus on the compliance to constraints of exact many-body theories, such as the generalised translational invariance and the zero-force theorem. Within the latter, we derive an analytical expression for the adiabatic SCE Hartree exchange-correlation kernel in one dimensional systems, and we compute it numerically for a variety of model densities. We analyse the non-local features of this kernel, particularly the ones that are relevant in tackling problems where kernels derived from local or semi-local functionals are known to fail.

Plasmonic and dielectric properties of ideal graphene

Graphene is a paradigm for 2D nano materials. We present electron energy loss spectra (EELS) and dielectric functions for graphene over several intervals of excitation energy and momentum transfer. We explore the difficulty of properly taking into account the vicinity of the Dirac point, which limits the resolution in the lower energy limit. For this we performed high resolution linear response time-dependent density functional theory (LRTDDFT) calculations of the dielectric function. Our results show a strong increase in the dielectric response approaching the static limit, which is linked to a Dirac-like cone, and which is not connected with plasmon resonances.

Efficient Algorithms for Estimating the Absorption Spectrum within Linear Response TDDFT.

We present a special symmetric Lanczos algorithm and a kernel polynomial method (KPM) for approximating the absorption spectrum of molecules within the linear response time-dependent density functional theory (TDDFT) framework in the product form. In contrast to existing algorithms, the new algorithms are based on reformulating the original non-Hermitian eigenvalue problem as a product eigenvalue problem and the observation that the product eigenvalue problem is self-adjoint with respect to an appropriately chosen inner product. This allows a simple symmetric Lanczos algorithm to be used to compute the desired absorption spectrum. The use of a symmetric Lanczos algorithm only requires half of the memory compared with the nonsymmetric variant of the Lanczos algorithm. The symmetric Lanczos algorithm is also numerically more stable than the nonsymmetric version. The KPM algorithm is also presented as a low-memory alternative to the Lanczos approach, but the algorithm may require more matrix-vector multiplications in practice. We discuss the pros and cons of these methods in terms of their accuracy as well as their computational and storage cost. Applications to a set of small and medium-sized molecules are also presented.

Energy-Specific Equation-of-Motion Coupled-Cluster Methods for High-Energy Excited States: Application to K-edge X-ray Absorption Spectroscopy

Single-reference techniques based on coupled-cluster (CC) theory, in the forms of linear response (LR) or equation of motion (EOM), are highly accurate and widely used approaches for modeling valence absorption spectra. Unfortunately, these equations with singles and doubles (LR-CCSD and EOM-CCSD) scale as O(N⁶), which may be prohibitively expensive for the study of high-energy excited states using a conventional eigensolver. In this paper, we present an energy-specific non-Hermitian eigensolver that is able to obtain high-energy excited states (e.g., XAS K-edge spectrum) at low computational cost. In addition, we also introduce an improved trial vector for iteratively solving the EOM-CCSD equation with a focus on high-energy eigenstates. The energy-specific EOM-CCSD approach and its low-scaling alternatives are applied to calculations of carbon, nitrogen, oxygen, and sulfur K-edge excitations. The results are compared to other implementations of CCSD for excited states, energy-specific linear response time-dependent density functional theory (TDDFT), and experimental results with multiple statistical metrics are presented and evaluated.

Dual fluorescence of 4-(dimethylamino)-pyridine: a comparative linear response TDDFT versus state-specific CASSCF study including solvent with the PCM model

Two different theoretical approaches have been used for the description of the experimentally observed dual luminescence of 4-(dimethylamino)pyridine (DMAP), introducing solvent effects with the polarizable continuum model (PCM), which seems needed to represent the dual fluorescence in polar media. These approaches are the linear response time-dependent density functional theory (TDDFT) and the state-specific complete active space self-consistent field. Both levels of theory represent the expected planar high-energy and the twisted intramolecular charge transfer (ICT) low-energy excited-state structures in the presence of solvent (toluene and acetonitrile). The comparison between both approaches shows that the main distortion of the ICT state is similar for both cases, i.e. twisting to almost 90o of the pyridine ring and the dimethylamino planes, but that other secondary distortions are slightly different. In the case of the TDDFT approach, the geometry optimizations of DMAP in the ground and excited states have been carried out using the conventional linear response approach (LR-PCM) for the solvent inclusion. The LR-PCM and the specific state (SS-PCM) approaches have been used for the prediction of the excitation and emission energies of DMAP in toluene and acetonitrile. The prediction of the emission energies at TDDFT/LR-PCM and CASPT2/PCM (complete active space perturbation theory) levels agrees with the experimental ones.

Impacts of Copper Position on the Electronic Structure of [Au25-xCux(SH)18]− Nanoclusters

Here, we use density functional theory to model the impact of heteroatom position on the optoelectronic properties of mixed metal nanoclusters. First, we consider the well-described [Au25(SH)18]− motif, and substitute Cu atoms at the three geometrically unique positions within the cluster. These clusters are atomically precise and show an electronic structure that is a function of both composition and heteroatom position. We then model clusters containing Cu substitutions at two positions, and demonstrate an additional and significant impact from heteroatom proximity with respect to one another. For each system, we report the formation energy, HOMO–LUMO gap, and energy level structure, and suggest how trends in these parameters may be explained using classic atomic descriptors such as electronegativity, analogous to design principles widely used in the field of organic electronics. Further, we use linear response time-dependent density functional theory to model the absorption behavior of each system in o...

The polarisability of atoms and molecules: a comparison between a conceptual density functional theory approach and time-dependent density functional theory

We investigate the local polarisability or polarisability density using both a conceptual density functional theory approach based on the linear response function and time-dependent density functional theory. Using a zero frequency in the latter, we can immediately compare both approaches. Using an analytical expression for the linear response kernel, we are able to systematically analyse α(r) throughout the periodic table. An extension to molecules is also made with a study of the CO molecule retrieving the connection between local softness and local polarisability.

First-order derivative couplings between excited states from adiabatic TDDFT response theory.

We present a complete derivation of derivative couplings between excited states in the framework of adiabatic time-dependent density functional response theory. Explicit working equations are given and the resulting derivative couplings are compared with derivative couplings from a pseudo-wavefunction ansatz. For degenerate excited states, i.e., close to a conical intersection (CI), the two approaches are identical apart from an antisymmetric overlap term. However, if the difference between two excitation energies equals another excitation energy, the couplings from response theory exhibit an unphysical divergence. This spurious behavior is a result of the adiabatic or static kernel approximation of time-dependent density functional theory leading to an incorrect analytical structure of the quadratic response function. Numerical examples for couplings close to a CI and for well-separated electronic states are given.

Computation of electron energy loss spectra by an iterative method

A method is presented to compute the dielectric function for extended systems using linear response time-dependent density functional theory. Localized basis functions with finite support are used to expand both eigenstates and response functions. The electron-energy loss function is directly obtained by an iterative Krylov-subspace method. We apply our method to graphene and silicon and compare it to plane-wave based approaches. Finally, we compute electron-energy loss spectrum of C60 crystal to demonstrate the merits of the method for molecular crystals, where it will be most competitive.

Theoretical electron energy loss spectroscopy of isolated graphene

A thorough understanding of the electronic structure is a necessary first step for the design of nanoelectronics, chemical/bio‐sensors, electrocatalysts and nanoplasmonics using graphene. As such, theoretical spectroscopic techniques to describe collective excitations of graphene are of fundamental importance. Starting from density functional theory (DFT), linear response time dependent DFT in frequency‐reciprocal space within the random phase approximation (TDDFT‐RPA) is used to describe the loss function for isolated graphene. To ensure any spurious interactions between layers are removed, both radial cutoff of the Coulomb kernel, and extra vacuum directly at the TDDFT‐RPA level are employed. A combination of both methods is found to provide a correct description of the electron energy loss spectra of isolated graphene, at a significant reduction in computational cost compared to standard methods.

Assessment of density functional theory based ΔSCF (self-consistent field) and linear response methods for longest wavelength excited states of extended π-conjugated molecular systems.

Computational investigation of the longest wavelength excitations in a series of cyanines and linear n-acenes is undertaken with the use of standard spin-conserving linear response time-dependent density functional theory (TD-DFT) as well as its spin-flip variant and a ΔSCF method based on the ensemble DFT. The spin-conserving linear response TD-DFT fails to accurately reproduce the lowest excitation energy in these π-conjugated systems by strongly overestimating the excitation energies of cyanines and underestimating the excitation energies of n-acenes. The spin-flip TD-DFT is capable of correcting the underestimation of excitation energies of n-acenes by bringing in the non-dynamic electron correlation into the ground state; however, it does not fully correct for the overestimation of the excitation energies of cyanines, for which the non-dynamic correlation does not seem to play a role. The ensemble DFT method employed in this work is capable of correcting for the effect of missing non-dynamic correlation in the ground state of n-acenes and for the deficient description of differential correlation effects between the ground and excited states of cyanines and yields the excitation energies of both types of extended π-conjugated systems with the accuracy matching high-level ab initio multireference calculations.

Effect of Excited-State Structural Relaxation on Midgap Excitations in Co2+-Doped ZnO Quantum Dots

The unique midgap excited states of Co2+-doped ZnO quantum dots have given rise to new applications in photocatalysis, sensing, magneto-optics, and magnetoelectronics. However, the electronic characteristics of these midgap transitions are not fully understood, and the uncertain interplay between these transitions has led to disagreement in the literature. In this work, midgap excited states of Co2+-doped ZnO quantum dots are analyzed using linear response time-dependent density functional theory and the effective mass theory with a focus on the geometry relaxation in the donor-type photoionization excited state. Relaxation of the excited-state geometry lowers the charge-transfer transition energy to be in the vicinity of the prominent spin-allowed 4A2 → 4T1 Co2+ d–d transition that gives this material its characteristic color. For large quantum dots, the excited-state population distribution between this Co2+ d–d excited state and the charge-transfer excited state can be tuned by thermal energy, resultin...

A divide-conquer-recombine algorithmic paradigm for large spatiotemporal quantum molecular dynamics simulations.

We introduce an extension of the divide-and-conquer (DC) algorithmic paradigm called divide-conquer-recombine (DCR) to perform large quantum molecular dynamics (QMD) simulations on massively parallel supercomputers, in which interatomic forces are computed quantum mechanically in the framework of density functional theory (DFT). In DCR, the DC phase constructs globally informed, overlapping local-domain solutions, which in the recombine phase are synthesized into a global solution encompassing large spatiotemporal scales. For the DC phase, we design a lean divide-and-conquer (LDC) DFT algorithm, which significantly reduces the prefactor of the O(N) computational cost for N electrons by applying a density-adaptive boundary condition at the peripheries of the DC domains. Our globally scalable and locally efficient solver is based on a hybrid real-reciprocal space approach that combines: (1) a highly scalable real-space multigrid to represent the global charge density; and (2) a numerically efficient plane-wave basis for local electronic wave functions and charge density within each domain. Hybrid space-band decomposition is used to implement the LDC-DFT algorithm on parallel computers. A benchmark test on an IBM Blue Gene/Q computer exhibits an isogranular parallel efficiency of 0.984 on 786 432 cores for a 50.3 × 10(6)-atom SiC system. As a test of production runs, LDC-DFT-based QMD simulation involving 16 661 atoms is performed on the Blue Gene/Q to study on-demand production of hydrogen gas from water using LiAl alloy particles. As an example of the recombine phase, LDC-DFT electronic structures are used as a basis set to describe global photoexcitation dynamics with nonadiabatic QMD (NAQMD) and kinetic Monte Carlo (KMC) methods. The NAQMD simulations are based on the linear response time-dependent density functional theory to describe electronic excited states and a surface-hopping approach to describe transitions between the excited states. A series of techniques are employed for efficiently calculating the long-range exact exchange correction and excited-state forces. The NAQMD trajectories are analyzed to extract the rates of various excitonic processes, which are then used in KMC simulation to study the dynamics of the global exciton flow network. This has allowed the study of large-scale photoexcitation dynamics in 6400-atom amorphous molecular solid, reaching the experimental time scales.

Nonlinear response time-dependent density functional theory combined with the effective fragment potential method.

This work presents an extension of the linear response TDDFT/EFP method to the nonlinear-response regime together with the implementation of nonlinear-response TDDFT/EFP in the quantum-chemistry computer package GAMESS. Included in the new method is the ability to calculate the two-photon absorption cross section and to incorporate solvent effects via the EFP method. The nonlinear-response TDDFT/EFP method is able to make correct qualitative predictions for both gas phase values and aqueous solvent shifts of several important nonlinear properties.

Simulating Cl K-edge X-ray absorption spectroscopy in MCl6 2− (M = U, Np, Pu) complexes and UOCl5 − using time-dependent density functional theory

We report simulations of the X-ray absorption near edge structure at the Cl K-edge of actinide hexahalides MCl6 2- (M = U, Np, Pu) and the UOCl5 – complex using linear response time-dependent density functional theory extended for core excitations. To the best of our knowledge, these are the first calculations of the Cl K-edge spectra of NpCl6 2- and PuCl6 2-. In addition, the spectra are simulated with and without the environmental effects of the host crystal as well as ab initio molecular dynamics to capture the dynamical effects due to atomic motion. The calculated spectra are compared with experimental results, where available and the observed trends are discussed.

Time-resolved photoelectron imaging spectra from non-adiabatic molecular dynamics simulations

We present an efficient method for the simulation of time-resolved photoelectron imaging (TRPEI) spectra in polyatomic molecules. Our approach combines trajectory-based molecular dynamics that account for non-adiabatic effects using surface hopping, with an approximate treatment of the photoionization process using Dyson orbitals as initial and Coulomb waves as final electron states. The method has been implemented in the frame of linear response time-dependent density functional theory. As an illustration, we simulate time- and energy-resolved anisotropy maps for the furan molecule and compare them with recent experimental data [T. Fuji, Y.-I. Suzuki, T. Horio, T. Suzuki, R. Mitrić, U. Werner, and V. Bonačić-Koutecký, J. Chem. Phys. 133, 234303 (2010)]. Our method can be generally used for the interpretation of TRPEI experiments allowing to shed light into the fundamental photochemical processes in complex molecules.

A Guided Self-Consistent-Field Method for Excited-State Wave Function Optimization: Applications to Ligand-Field Transitions in Transition-Metal Complexes.

A guided self-consistent field (SCF) method is presented in this paper. This method uses the eigenspace update-and-following idea to improve the SCF method for optimizing wave functions that are higher-energy solutions to the Roothaan-Hall equation. In this method, the eigenvectors of the previous SCF step are used to prediagonalize the current Fock/Kohn-Sham matrix, preserving the ordering of orbital occupations. When the subject of interest is an excited state of the same spin symmetry as the ground state, the initial guess of excited wave function is improved with a preconditioning step. The preconditioning step is an SCF iteration applied to the β spin manifold if the initial guess is generated by orbital permutation in the α spin manifold. This simple preconditioning step gives rise to more-stable SCF convergence using the algorithm presented herein. The guided SCF method is used to optimize ligand-field excited states in tetrahedral transition-metal complexes, and calculate ΔSCF excitation energies. The calculated ligand-field transition energies are compared with those obtained from orbital energy differences, linear response time-dependent density functional theory, and experiments. The excitation energies obtained using the method presented in this work show a significant improvement over orbital energy differences and linear response method.

Experimental and Theoretical Determination of the Optical Gap of the Au144(SC2H4Ph)60 Cluster and the (Au/Ag)144(SC2H4Ph)60 Nanoalloys.

Au144PET60 and Au144-xAgxPET60 (PET = SC2H4Ph, phenylethylthiolate, and 30 ≤ x ≤ 53) clusters were studied by optical spectroscopy and linear response time-dependent density functional theory. Spectra of thin dry films were measured in order to reveal the onset for electronic absorption. The optical gap of the Au144PET60 cluster was determined at 0.19 ± 0.01 eV, which agrees well with the computed energy for the first optical transition at 0.32 eV for a model cluster Au144(SH)60 when the line width of individual transitions is taken into account. The optical gaps for the Au144-xAgxPET60 alloy clusters were observed in a range of 0.12-0.26 eV, in good agreement with the calculations giving 0.16-0.36 eV for the lowest-energy optical transitions for corresponding Au144-xAgx(SH)60 models. This indicates that the gap is only moderately affected by doping Au with Ag. This work constitutes the first accurate determination of the fundamental spectroscopic gap of these compounds.