Time-dependent Kohn-Sham Density Functional Theory Research Articles

Very-Large-Scale GPU-Accelerated Nuclear Gradient of Time-Dependent Density Functional Theory with Tamm-Dancoff Approximation and Range-Separated Hybrid Functionals.

Modern graphics processing units (GPUs) provide an unprecedented level of computing power. In this study, we present a high-performance, multi-GPU implementation of the analytical nuclear gradient for Kohn-Sham time-dependent density functional theory (TDDFT), employing the Tamm-Dancoff approximation (TDA) and Gaussian-type atomic orbitals as basis functions. We discuss GPU-efficient algorithms for the derivatives of electron repulsion integrals and exchange-correlation functionals within the range-separated scheme. As an illustrative example, we calculate the TDA-TDDFT gradient of the S1 state of a full-scale green fluorescent protein with explicit water solvent molecules, totaling 4353 atoms, at the ωB97X/def2-SVP level of theory. Our algorithm demonstrates favorable parallel efficiencies on a high-speed distributed system equipped with 256 Nvidia A100 GPUs, achieving >70% with up to 64 GPUs and 31% with 256 GPUs, effectively leveraging the capabilities of modern high-performance computing systems.

Kohn–Sham time-dependent density functional theory with Tamm–Dancoff approximation on massively parallel GPUs

We report a high-performance multi graphics processing unit (GPU) implementation of the Kohn–Sham time-dependent density functional theory (TDDFT) within the Tamm–Dancoff approximation. Our algorithm on massively parallel computing systems using multiple parallel models in tandem scales optimally with material size, considerably reducing the computational wall time. A benchmark TDDFT study was performed on a green fluorescent protein complex composed of 4353 atoms with 40,518 atomic orbitals represented by Gaussian-type functions, demonstrating the effect of distant protein residues on the excitation. As the largest molecule attempted to date to the best of our knowledge, the proposed strategy demonstrated reasonably high efficiencies up to 256 GPUs on a custom-built state-of-the-art GPU computing system with Nvidia A100 GPUs. We believe that our GPU-oriented algorithms, which empower first-principles simulation for very large-scale applications, may render deeper understanding of the molecular basis of material behaviors, eventually revealing new possibilities for breakthrough designs on new material systems.

Nonradiative relaxation of charge carriers at molecule-metal interfaces: Nonadiabatic molecular dynamics study

Nonadiabatic molecular dynamics simulations in combination with time-dependent Kohn-Sham density functional theory are used to study the nonradiative relaxation of charge carriers in 4-mercaptobenzonitrile (NCOPE1), 4-(mercaptomethyl) benzonitrile (NC-PT1), 4′-mercapto-[1,1′-biphenyl]-4-carbonitrile (NC-BP0) and 4-((4-mercaptophenyl) ethynyl) benzonitrile (NCOPE2) molecules absorbed on Au(111) surface. The fastest hot electron decay (∼30 fs) is obtained for the NCOPE1 molecule due to strong electron-phonon couplings. However, the relaxation kinetics strongly depends on the properties of the initially populated state (e.g., orbital-overlap/hybridization between the organic molecules and the substrate), on the proximity of neighboring electronic states (i.e., intraband gaps) and on the electron-phonon nonadiabatic couplings. The obtained orbital- and size-dependent relaxation dynamics is in qualitative agreement with the results of core-hole clock experiments, which indicates the possibility of modeling the interfacial electron transfer by the decay process of hot electrons.

Dependence between Structural and Electronic Properties of CsPbI3: Unsupervised Machine Learning of Nonadiabatic Molecular Dynamics.

Using unsupervised machine learning on the trajectories from a nonadiabatic molecular dynamics simulation with time-dependent Kohn-Sham density functional theory, we elucidated the structural parameters with the largest influence on nonradiative recombination of charge carriers in CsPbI3, which forms the basis for solar energy and optoelectronic applications. The I-I-I angles between PbI6 octahedra, followed by the Cs-I distance, have the strongest impact on the bandgap and the nonadiabatic coupling. The importance of the Cs-I distance is unexpected, because Cs does not contribute to electron and hole wave functions. The nonadiabatic coupling is most influenced by static properties, which is also surprising, given its explicit dependence on atomic velocities.

Linear-Response Time-Dependent Density Functional Theory with Stochastic Range-Separated Hybrids.

Generalized Kohn-Sham density functional theory is a popular computational tool for the ground state of extended systems, particularly within range-separated hybrid (RSH) functionals that capture the long-range electronic interaction. Unfortunately, the heavy computational cost of the nonlocal exchange operator in RSH-DFT usually confines the approach to systems with at most a few hundred electrons. A significant reduction in the computational cost is achieved by representing the density matrix with stochastic orbitals and a stochastic decomposition of the Coulomb convolution (J. Phys. Chem. A 2016, 120, 3071). Here, we extend the stochastic RSH approach to excited states within the framework of linear-response generalized Kohn-Sham time-dependent density functional theory (GKS-TDDFT) based on the plane-wave basis. As a validation of the stochastic GKS-TDDFT method, the excitation energies of small molecules N2 and CO are calculated and compared to the deterministic results. The computational efficiency of the stochastic method is demonstrated with a two-dimensional MoS2 sheet (∼1500 electrons), whose excitation energy, exciton charge density, and (excited state) geometric relaxation are determined in the absence and presence of a point defect.

Valence and core excitons in solids from velocity-gauge real-time TDDFT with range-separated hybrid functionals: An LCAO approach

An atomic-orbital basis set framework is presented for carrying out velocity-gauge real-time time-dependent density functional theory (TDDFT) simulations in periodic systems employing range-separated hybrid functionals. Linear optical response obtained from real-time propagation of the time-dependent Kohn-Sham equations including nonlocal exchange is considered in prototypical solid-state materials such as bulk Si, LiF and monolayer hexagonal-BN. Additionally core excitations in monolayer hexagonal-BN at the B and N K-edges are investigated and the role of long-range and short-range nonlocal exchange in capturing valence and core excitonic effects is discussed. Results obtained using this time-domain atomic orbital basis set framework are shown to be consistent with equivalent frequency-domain planewave results in the literature. The developments discussed lead to a time-domain generalized Kohn-Sham TDDFT implementation for the treatment of core and valence electron dynamics and light-matter interaction in periodic solid-state systems.

Investigation of Optimal Control Problems Governed by a Time-Dependent Kohn-Sham Model

Many application models in quantum physics and chemistry require to control multi-electron systems to achieve a desired target configuration. This challenging task appears possible in the framework of time-dependent density functional theory (TDDFT) that allows to describe these systems while avoiding the high dimensionality resulting from the multi-particle Schr\"{o}dinger equation. For this purpose, the theory and numerical solution of optimal control problems governed by a Kohn-Sham TDDFT model are investigated, considering different objectives and a bilinear control mechanism. Existence of optimal control solutions and their characterization as solutions to Kohn-Sham TDDFT optimality systems are discussed. To validate this control framework, a time-splitting discretization of the optimality systems and a nonlinear conjugate gradient scheme are implemented. Results of numerical experiments demonstrate the computational capability of the proposed control approach.

A QM/MM and QM/QM/MM study of Kerr, Cotton-Mouton and Jones linear birefringences in liquid acetonitrile.

QM/MM and QM/QM/MM protocols are applied to the ab initio study of the three linear birefringences Kerr, Cotton-Mouton, and Jones, as shown by acetonitrile in the gas and pure liquid phases. The relevant first-order properties as well as linear, quadratic, and cubic frequency-dependent response functions were computed using time-dependent Kohn-Sham density-functional theory with use of the standard CAM-B3LYP functional. In the liquid phase, a series of room temperature (293.15 K) molecular dynamics snapshots were selected, for which averaged values of the observables were obtained at an optical wavelength of 632.8 nm. The birefringences were computed for electric and magnetic induction fields corresponding to the laboratory setup previously employed by T. Roth and G. L. J. A. Rikken in Phys. Rev. Lett., 2000, 85, 4478. Under these conditions, acetonitrile is shown to exhibit a weak Jones response-in fact roughly 6.5 times smaller than the limit of detection of the apparatus employed in the measurements mentioned above. A comparison is made with the corresponding gas-phase results and an assessment is made of the index of measurability, estimating the degree of overlap of the three birefringences in actual measurements. For acetonitrile, it is shown that this index is a factor of 3.6 and 6.7 larger than that of methylcyclopentadienyl-Mn-tricarbonyl and cyclohexadienyl-Fe-tricarbonyl, respectively-two compounds reported in Phys. Rev. Lett., 2000, 85, 4478 to exhibit a strong Jones signal.

Plasmonic resonances of nanoparticles from large-scale quantum mechanical simulations

Plasmonic resonance of metallic nanoparticles results from coherent motion of its conduction electrons, driven by incident light. For the nanoparticles less than 10 nm in diameter, localized surface plasmonic resonances become sensitive to the quantum nature of the conduction electrons. Unfortunately, quantum mechanical simulations based on time-dependent Kohn–Sham density functional theory are computationally too expensive to tackle metal particles larger than 2 nm. Herein, we introduce the recently developed time-dependent orbital-free density functional theory (TD-OFDFT) approach which enables large-scale quantum mechanical simulations of plasmonic responses of metallic nanostructures. Using TD-OFDFT, we have performed quantum mechanical simulations to understand size-dependent plasmonic response of Na nanoparticles and plasmonic responses in Na nanoparticle dimers and trimers. An outlook of future development of the TD-OFDFT method is also presented.

Temperature Dependence of Electron–Phonon Interactions in Gold Films Rationalized by Time-Domain Ab Initio Analysis

The nonequilibrium dynamics of excited electrons in metals is probed by ultrafast laser measurements. Using a real-time Kohn–Sham time-dependent density functional theory and nonadiabatic molecular dynamics, we report direct modeling of such experiments, rationalizing the observed temperature dependence. Focusing on thin gold films, we analyze the effect of temperature on film structure, electronic state densities, nonadiabatic electron–phonon coupling, elastic electron–phonon scattering times, and electron–phonon relaxation rates. The effective electron–phonon coupling constants calculated at different temperatures are in good agreement with the values deduced from experiments and an alternative theory. A temperature increase accelerates both inelastic and elastic electron–phonon scattering and allows a larger number of higher-frequency phonon modes to couple to the electronic subsystem. The inelastic electron–phonon coupling is largest between nearest states, indicating that carrier relaxation involves ...

Dual-Functional Tamm-Dancoff Approximation: A Convenient Density Functional Method that Correctly Describes S1/S0 Conical Intersections.

Time-dependent Kohn-Sham density functional theory has been used successfully to compute vertical excitation energies, especially for large molecular systems. However, the lack of double excitation character in the excited amplitudes produced by linear response in the adiabatic approximation holds it back from broader applications in photochemistry; for example, it shows (3N - 7)-dimensional conical intersection seams (where N is the number of atoms) between ground and excited states, although the correct dimensionality is 3N - 8. In this letter, we present a new, conceptually simple, easy-to-implement, and easy-to-use way to employ time-dependent Kohn-Sham density functional theory that has global accuracy comparable with the conventional single-functional version and that recovers the double cone topology of the potential energy surfaces at S1/S0 conical intersection seams. The new method is called the dual-functional Tamm-Dancoff approximation (DF-TDA).

Multiconfiguration Pair-Density Functional Theory Spectral Calculations Are Stable to Adding Diffuse Basis Functions.

Time-dependent Kohn-Sham density functional theory (TD-KS-DFT) is useful for calculating electronic excitation spectra of large systems, but the low-energy spectra are often complicated by artificially lowered higher-energy states. This affects even the lowest energy excited states. Here, by calculating the lowest energy spin-conserving excited state for atoms from H to K and for formaldehyde, we show that this problem does not occur in multiconfiguration pair-density functional theory (MC-PDFT). We use the tPBE on-top density functional, which is a translation of the PBE exchange-correlation functional. We compare to a robust multireference method, namely, complete active space second-order perturbation theory (CASPT2), and to TD-KS-DFT with two popular exchange-correlation functionals, PBE and PBE0. We find for atoms that the mean unsigned error (MUE) of MC-PDFT with the tPBE functional improves from 0.42 to 0.40 eV with a double set of diffuse functions, whereas the MUEs for PBE and PBE0 drastically increase from 0.74 to 2.49 eV and from 0.45 to 1.47 eV, respectively.

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.

Size-Dependent Plasmonic Resonances from Large-Scale Quantum Simulations.

For metallic nanoparticles less than 10 nm in diameter, localized surface plasmon resonances (LSPRs) become sensitive to the quantum nature of conduction electrons. In this regime, experimental probes of size-dependent LSPRs are particularly challenging, and contradictory results are often reported. Unfortunately, quantum mechanical simulations based on time-dependent Kohn-Sham density functional theory (TD-KSDFT) are computationally too expensive to tackle metal particles larger than 2 nm. Herein, we present a time-dependent orbital-free density functional theory (TD-OFDFT) that accurately captures the dynamic response of electrons in the presence of realistic ionic potentials. The TD-OFDFT method offers a comparable accuracy as TD-KSDFT but with a much lower computational cost. Using TD-OFDFT, we study size-dependent LSPRs on Na nanoparticles with diameters from 0.7 to 12.3 nm. The optical absorption spectra exhibit a nonmonotonic behavior from blue shift to red shift and back to blue shift as the particle size decreases. Three principal plasmon modes are identified, and their physical origins are elucidated. Competing physical mechanisms responsible for the nonmonotonic size dependence are discussed. The TD-OFDFT provides a unified theoretical framework that bridges the gap between classical electromagnetic theory and quantum mechanical theory for plasmonics and nanophotonics.

Induced Optical Activity of DNA-Templated Cyanine Dye Aggregates: Exciton Coupling Theory and TD-DFT Studies

Certain cyanine dye molecules have been observed to self-assemble in DNA templates to form large chiral aggregates, which exhibit induced circular dichroism. The structure and circular dichroism (CD) of one such system, aggregates of a cationic DiSC2(5) cyanine dye, are investigated using the time-dependent Kohn-Sham density functional theory (TD-DFT) and exciton coupling model. A series of TD-DFT calculations on the aggregates with one, two, and four dye molecules clearly shows the onset of CD induced by the helically twisted structure compatible with the minor groove of DNA templates. More simplified exciton coupling model analysis successfully reproduces the major positive Cotton effect observed in the experiment as well as the TD-DFT calculations, but it is unable to capture minor features of the CD spectrum that are closely related to absolute configurations of constituent dyes in the complex. We assess the performance of various methods used for evaluation of the electronic coupling energies between interacting chromophores. Our results confirm that the interchromophore interactions in cyanine dye aggregates are primarily electrostatic in nature and indicate that the exciton coupling model is adequate for studying induced CD of self-assembled aggregates of cyanine dye molecules.

Electronic circular dichroism spectra from the complex polarization propagator

The complex linear polarization propagator approach has been applied to the calculation of electronic circular dichroism spectra of 3R-chloro-1-butyne, 3R-methylcyclopentanone, 3S-methylcyclohexanone, 4R-1,1-dimethyl-[3]-(1,2)ferrocenophan-2-on, S-3,3,3',3'-tetramethyl-1,1'-spirobi[3H,2,1]-benzoxaselenole, and the fullerene C84. Using time-dependent Kohn-Sham density functional theory, it is shown that a direct and efficient evaluation of the circular dichroism spectrum can be achieved. The approach allows for the determination of the circular dichroism at an arbitrary wavelength thereby, in a common formulation and implementation, covering the visible, ultraviolet, and x-ray regions of the spectrum. In contrast to traditional methods, the entire manifold of excited states is taken into account in the calculation of the circular dichroism at a given wavelength.

Calculation of excitation energies of open-shell molecules with spatially degenerate ground states. I. Transformed reference via an intermediate configuration Kohn-Sham density-functional theory and applications to d1 and d2 systems with octahedral and tetrahedral symmetries

A method for calculating the UV-vis spectra of molecules with spatially degenerate ground states using time-dependent density-functional theory (TDDFT) is proposed. The new transformed reference via an intermediate configuration Kohn-Sham TDDFT (TRICKS-TDDFT) method avoids the difficulties caused by the multireference nature of spatially degenerate states by rather than utilizing the ground state instead taking a nondegenerate excited state with desirable properties as the reference for the TDDFT calculation. The scope and practical application of the method are discussed. Like all open-shell TDDFT calculations this method at times suffers from the inability to produce transitions to states that are eigenfunctions of the total spin operator. A technique for alleviating this difficulty to some extent is proposed. The applicability and accuracy of the TRICKS-TDDFT method is demonstrated through example calculations of several d(1) and d(2) transition metal complexes with tetrahedral and octahedral symmetries. For the most part, the results of these calculations are similar in quality to to those obtained from standard TDDFT calculations.

Excitation energies of benzene from Kohn-Sham theory

Singlet and triplet vertical excitation energies are determined for benzene using time-dependent Kohn–Sham density functional theory. The potential of the HCTH continuum functional is explicitly corrected, using a recently developed procedure, to impose the appropriate −1/r+C asymptotic behavior. The 48 valence (π→π*) and Rydberg (π→n=3) excitation energies computed using this corrected potential have a mean absolute error of 0.12 eV. © 1999 John Wiley & Sons, Inc. J Comput Chem 20: 106–113, 1999

Time-dependent Kohn-Sham density-functional theory

A time-dependent Kohn-Sham theory is presented for obtaining the time-dependent density which has a periodic dependence on time. A set of coupled single-particle equations $\ensuremath{-}\frac{1}{2}{\ensuremath{\nabla}}^{2}{\ensuremath{\chi}}_{i}+{v}_{\mathrm{eff}}{\ensuremath{\chi}}_{i}={\ensuremath{\epsilon}}_{i}{\ensuremath{\chi}}_{i}$ and $\frac{\ensuremath{\partial}{\ensuremath{\chi}}_{i}^{2}}{\ensuremath{\partial}t}+\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\nabla}}\ifmmode\cdot\else\textperiodcentered\fi{}({\ensuremath{\chi}}_{i}^{2}\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\nabla}}{S}_{i})=0$ are obtained. The ${\ensuremath{\chi}}_{i}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}},t)$ and ${S}_{i}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}},t)$ are the phase and amplitude, respectively, of the time-dependent Kohn-Sham orbitals, ${v}_{\mathrm{eff}}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}},t)$ is the time-dependent Kohn-Sham effective potential, and ${\ensuremath{\epsilon}}_{i}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}},t)=\ensuremath{-}\frac{\ensuremath{\partial}{S}_{i}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}},t)}{\ensuremath{\partial}t}$. The density $\ensuremath{\rho}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}},t)$ is equal to the sum of the squares of the ${\ensuremath{\chi}}_{i}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}},t)$.