Linear-response Time-dependent Density Functional Theory Research Articles

Extending the limit of LR-TDDFT on two different approaches: Numerical algorithms and new Sunway heterogeneous supercomputer

First-principles time-dependent density functional theory (TDDFT) is a powerful tool to accurately describe the excited-state properties of molecules and solids in condensed matter physics, computational chemistry, and materials science. However, a perceived drawback in TDDFT calculations is its ultrahigh computational cost O(N5∼N6) and large memory usage O(N4) especially for plane-wave basis set, confining its applications to large systems containing thousands of atoms. Here, we present a massively parallel implementation of linear-response TDDFT (LR-TDDFT) and accelerate LR-TDDFT in two different aspects: (1) numerical algorithms on the X86 supercomputer and (2) optimizations on the heterogeneous architecture of the new Sunway supercomputer. Furthermore, we carefully design the parallel data and task distribution schemes to accommodate the physical nature of different computation steps. By utilizing these two different methods, our implementation can gain an overall speedup of 10x and 80x and efficiently scales to large systems up to 4096 and 2744 atoms within dozens of seconds.

Effects of Nanowire Doping on Plasmon-Enhanced N2 Dissociation.

Doping a transition metal element into plasmonic systems can tune the optical properties of the system, which will potentially facilitate the plasmon-enhanced catalytic process. In this study, we applied the linear-response time-dependent density functional theory (LR-TDDFT) method with real-time electron dynamics and mean-field Ehrenfest dynamics methods to computationally investigate the effects of doping silver nanowires on plasmon-enhanced N2 dissociation. We calculated the absorption spectra for different doped systems, applied an external electric field to the system, and performed mean-field Ehrenfest dynamics to examine how plasmonic excitation will affect the N2 activation or dissociation. In addition, we also studied how the transition metal dopant affects the system's electronic structure and potential energy surface.

Orbital-Optimized Versus Time-Dependent Density Functional Calculations of Intramolecular Charge Transfer Excited States.

The performance of time-independent, orbital-optimized calculations of excited states is assessed with respect to charge transfer excitations in organic molecules in comparison to the linear-response time-dependent density functional theory (TD-DFT) approach. A direct optimization method to converge on saddle points of the electronic energy surface is used to carry out calculations with the local density approximation (LDA) and the generalized gradient approximation (GGA) functionals PBE and BLYP for a set of 27 excitations in 15 molecules. The time-independent approach is fully variational and provides a relaxed excited state electron density from which the extent of charge transfer is quantified. The TD-DFT calculations are generally found to provide larger charge transfer distances compared to the orbital-optimized calculations, even when including orbital relaxation effects with the Z-vector method. While the error on the excitation energy relative to theoretical best estimates is found to increase with the extent of charge transfer up to ca. -2 eV for TD-DFT, no correlation is observed for the orbital-optimized approach. The orbital-optimized calculations with the LDA and the GGA functionals provide a mean absolute error of ∼0.7 eV, outperforming TD-DFT with both local and global hybrid functionals for excitations with a long-range charge transfer character. Orbital-optimized calculations with the global hybrid functional B3LYP and the range-separated hybrid functional CAM-B3LYP on a selection of states with short- and long-range charge transfer indicate that inclusion of exact exchange has a small effect on the charge transfer distance, while it significantly improves the excitation energy, with the best-performing functional CAM-B3LYP providing an absolute error typically around 0.15 eV.

Simulating X-ray Absorption Spectroscopy in Challenging Environments: Methodological Insights from Water-Solvated Ammonia and Ammonium Systems.

Core-electron excitations in solvated systems, influenced by solvent geometry and hydrogen bonding, make X-ray absorption spectroscopy (XAS) a valuable tool for assessing solvent-solute interactions. However, calculating XAS spectra with electronic-structure methods has proven challenging due to a delicate interplay between correlation and solvation effects. This study provides a computational procedure for XAS modeling in solvated systems, with water-solvated ammonia and ammonium systems serving as probes. Exploring methodological challenges, we investigate explicit embedding models, specifically the polarizable embedding family, including polarizable density embedding and extended polarizable density embedding. Our linear-response time-dependent density functional theory (LR-TDDFT) XAS calculations reveal the efficiency of this approach, with extended polarizable density embedding emerging as a robust improvement over polarizable density embedding. Contrary to some recent literature, our study challenges the belief that LR-TDDFT cannot accurately describe XAS spectra of ammonia and ammonium solvated in water.

Effects of Static Electric Fields on the Excitations of Silver Nanowire Dimers.

We theoretically studied the introduction of static electric fields to Ag10 nanowire dimer systems, including the effects of this field on optical absorption characteristics and the orbitals responsible for these excitations. Linear-response time-dependent density functional theory computations were performed on three distinct dimer systems: end-to-end, parallel, and 90° angle dimer systems separated by a closest interparticle distance of 7.0 Å. The calculations were performed in the presence of a 0.1 V/Å electric field strength applied in the z and y directions. The orientation of the dimer system and the direction of the applied static electric field each play a significant role in the resulting absorption spectra and the electronic structure of the nanowires. As a result, a dimer system can exhibit a blue shift for the longitudinal excitation and a red shift for the transverse excitation in the presence of one direction of the static electric field but not for the other direction. Notably, the electron density shifts from one nanowire to the other in the presence of the static electric field. Changes in optical characteristics and electronic structure suggest that the usage of a static electric field with a particular spatial configuration of nanowires provides a way to tune the optical properties of the system.

A mathematical analysis of the adiabatic Dyson equation from time-dependent density functional theory

In this article, we analyse the Dyson equation for the density–density response function (DDRF) that plays a central role in linear response time-dependent density functional theory (LR-TDDFT). First, we present a functional analytic setting that allows for a unified treatment of the Dyson equation with general adiabatic approximations for discrete (finite and infinite) and continuum systems. In this setting, we derive a representation formula for the solution of the Dyson equation in terms of an operator version of the Casida matrix. While the Casida matrix is well-known in the physics literature, its general formulation as an (unbounded) operator in the N-body wavefunction space appears to be new. Moreover, we derive several consequences of the solution formula obtained here; in particular, we discuss the stability of the solution and characterise the maximal meromorphic extension of its Fourier transform. We then show that for adiabatic approximations satisfying a suitable compactness condition, the maximal domains of meromorphic continuation of the initial DDRF and the solution of the Dyson equation are the same. The results derived here apply to widely used adiabatic approximations such as (but not limited to) the random phase approximation and the adiabatic local density approximation. In particular, these results show that neither of these approximations can shift the ionisation threshold of the Kohn–Sham system.

Green zinc/galactomannan-based hydrogels push up the photovoltage of quasi solid aqueous dye sensitized solar cells

In the present work, we implement environmentally friendly water-based Quasi-Solid Electrolytes (QSE) for Dye Sensitized Solar Cells (DSSCs), displaying an unprecedent open circuit voltage (VOC) as high as 750 mV. The production of the hydrogel for QSE-DSSCs is achieved by exploiting the concept of fully green design and fabrication, through the selection of components such as the natural polysaccharide galactomannan (GM), biocompatible zinc salts, and the employment of eco-friendly synthetic procedures to produce the hybrid gelating agents. In the process, moderate temperature (<40 °C), only aqueous solutions are employed, and, at most, ethanol is used in some phases of the procedure. Depending on the type of the initial salt, either zinc hydroxysulfate lamellae or zinc oxide nanoparticles are created within the gel matrix, with a more extended nanoporous structure in the latter case. The nanostructures and the gels are investigated by multiple techniques, including X-ray diffraction (XRD), infrared spectroscopy (IR), scanning electron microscopy (SEM) and thermogravimetric analysis (TGA). Upon ensuing addition of I-/I3- redox mediator and assembling of the device, state-of-the-art aqueous QSE-DSSCs are achieved. The latter couples a 2 % efficiency (limited by charge diffusion as proved by Electrochemical Impedance Spectroscopy) with a good Average Visible Transmittance (AVT), and Light Utilization Efficiency (LUE), a couple of coveted features in wave-selective or semi-transparent devices. Finally, Linear Response-Time Dependent DFT (LR-TDDFT) simulations are carried out on a model iodine/iodide layered zinc hydroxy sulphate structure towards a better understanding of the mechanism responsible for the high AVT.

Excitation energy transfer and vibronic relaxation through light-harvesting dendrimer building blocks: A nonadiabatic perspective.

The light-harvesting excitonic properties of poly(phenylene ethynylene) (PPE) extended dendrimers (tree-like π-conjugated macromolecules) involve a directional cascade of local excitation energy transfer (EET) processes occurring from the "leaves" (shortest branches) to the "trunk" (longest branch), which can be viewed from a vibronic perspective as a sequence of internal conversions occurring among a connected graph of nonadiabatically coupled locally excited electronic states via conical intersections. The smallest PPE building block that is able to exhibit EET, the asymmetrically meta-substituted PPE oligomer with one acetylenic bond on one side and two parallel ones on the other side (hence, 2-ring and 3-ring para-substituted pseudo-fragments), is a prototype and the focus of the present work. From linear-response time-dependent density functional theory electronic-structure calculations of the molecule as regards its first two nonadiabatically coupled, optically active, singlet excited states, we built a (1 + 2)-state-8-dimensional vibronic-coupling Hamiltonian model for running subsequent multiconfiguration time-dependent Hartree wavepacket relaxations and propagations, yielding both steady-state absorption and emission spectra as well as real-time dynamics. The EET process from the shortest branch to the longest one occurs quite efficiently (about 80% quantum yield) within the first 25fs after light excitation and is mediated vibrationally through acetylenic and quinoidal bond-stretching modes together with a particular role given to the central-ring anti-quinoidal rock-bending mode. Electronic and vibrational energy relaxations, together with redistributions of quantum populations and coherences, are interpreted herein through the lens of a nonadiabatic perspective, showing some interesting segregation among the foremost photoactive degrees of freedom as regards spectroscopy and reactivity.

Accurate Electronic and Optical Properties of Organic Doublet Radicals Using Machine Learned Range-Separated Functionals.

Luminescent organic semiconducting doublet-spin radicals are unique and emergent optical materials because their fluorescent quantum yields (Φfl) are not compromised by the spin-flipping intersystem crossing (ISC) into a dark high-spin state. The multiconfigurational nature of these radicals challenges their electronic structure calculations in the framework of single-reference density functional theory (DFT) and introduces room for method improvement. In the present study, we extended our earlier development of ML-ωPBE [J. Phys. Chem. Lett., 2021, 12, 9516-9524], a range-separated hybrid (RSH) exchange-correlation (XC) functional constructed using the stacked ensemble machine learning (SEML) algorithm, from closed-shell organic semiconducting molecules to doublet-spin organic semiconducting radicals. We assessed its performance for a new test set of 64 doublet-spin radicals from five categories while placing all previously compiled 3926 closed-shell molecules in the new training set. Interestingly, ML-ωPBE agrees with the nonempirical OT-ωPBE functional regarding the prediction of the molecule-dependent range-separation parameter (ω), with a small mean absolute error (MAE) of 0.0197 a0-1, but saves the computational cost by 2.46 orders of magnitude. This result demonstrates an outstanding domain adaptation capacity of ML-ωPBE for diverse organic semiconducting species. To further assess the predictive power of ML-ωPBE in experimental observables, we also applied it to evaluate absorption and fluorescence energies (Eabs and Efl) using linear-response time-dependent DFT (TDDFT), and we compared its behavior with nine popular XC functionals. For most radicals, ML-ωPBE reproduces experimental measurements of Eabs and Efl with small MAEs of 0.299 and 0.254 eV, only marginally different from those of OT-ωPBE. Our work illustrates a successful extension of the SEML framework from closed-shell molecules to doublet-spin radicals and will open the venue for calculating optical properties for organic semiconductors using single-reference TDDFT.

Excitonic Effects of the Excited-State Photocatalytic Reaction at the Molecule/Metal Oxide Interface.

Excitonic effects caused by the Coulomb interaction between electrons and holes play a crucial role in photocatalysis at the molecule/metal oxide interface. As an ideal model for investigating the excitonic effect, coadsorption and photodissociation of water and methanol molecules on titanium dioxide involve complex ground-state thermalcatalytic and excited-state photocatalytic reaction processes. Herein, we systemically investigate the excited-state electronic structures of the coadsorption of H2O and CH3OH molecules on a rutile TiO2(110) surface by linear-response time-dependent density functional theory calculations and probe the reaction path for generating HCOOH or CO2, from ground-state and excited-state perspectives. The reaction barriers in excited-state calculations are significantly different from those in ground-state calculations during three processes, with the largest decrease being 0.94 eV for the Ti5c-O-CH2-O-Ti5c formation process.

On the description of conical intersections between excited electronic states with LR-TDDFT and ADC(2).

Conical intersections constitute the conceptual bedrock of our working understanding of ultrafast, nonadiabatic processes within photochemistry (and photophysics). Accurate calculation of potential energy surfaces within the vicinity of conical intersections, however, still poses a serious challenge to many popular electronic structure methods. Multiple works have reported on the deficiency of methods like linear-response time-dependent density functional theory within the adiabatic approximation (AA LR-TDDFT) or algebraic diagrammatic construction to second-order [ADC(2)]-approaches often used in excited-state molecular dynamics simulations-to describe conical intersections between the ground and excited electronic states. In the present study, we focus our attention on conical intersections between excited electronic states and probe the ability of AA LR-TDDFT and ADC(2) to describe their topology and topography, using protonated formaldimine and pyrazine as two exemplar molecules. We also take the opportunity to revisit the performance of these methods in describing conical intersections involving the ground electronic state in protonated formaldimine-highlighting in particular how the intersection ring exhibited by AA LR-TDDFT can be perceived either as a (near-to-linear) seam of intersection or two interpenetrating cones, depending on the magnitude of molecular distortions within the branching space.

Nonadiabatic Dynamics Simulations for Photoinduced Processes in Molecules and Semiconductors: Methodologies and Applications.

Nonadiabatic dynamics (NAMD) simulations have become powerful tools for elucidating complicated photoinduced processes in various systems from molecules to semiconductor materials. In this review, we present an overview of our recent research on photophysics of molecular systems and periodic semiconductor materials with the aid of ab initio NAMD simulation methods implemented in the generalized trajectory surface-hopping (GTSH) package. Both theoretical backgrounds and applications of the developed NAMD methods are presented in detail. For molecular systems, the linear-response time-dependent density functional theory (LR-TDDFT) method is primarily used to model electronic structures in NAMD simulations owing to its balanced efficiency and accuracy. Moreover, the efficient algorithms for calculating nonadiabatic coupling terms (NACTs) and spin-orbit couplings (SOCs) have been coded into the package to increase the simulation efficiency. In combination with various analysis techniques, we can explore the mechanistic details of the photoinduced dynamics of a range of molecular systems, including charge separation and energy transfer processes in organic donor-acceptor structures, ultrafast intersystem crossing (ISC) processes in transition metal complexes (TMCs), and exciton dynamics in molecular aggregates. For semiconductor materials, we developed the NAMD methods for simulating the photoinduced carrier dynamics within the framework of the Kohn-Sham density functional theory (KS-DFT), in which SOC effects are explicitly accounted for using the two-component, noncollinear DFT method. Using this method, we have investigated the photoinduced carrier dynamics at the interface of a variety of van der Waals (vdW) heterojunctions, such as two-dimensional transition metal dichalcogenides (TMDs), carbon nanotubes (CNTs), and perovskites-related systems. Recently, we extended the LR-TDDFT-based NAMD method for semiconductor materials, allowing us to study the excitonic effects in the photoinduced energy transfer process. These results demonstrate that the NAMD simulations are powerful tools for exploring the photodynamics of molecular systems and semiconductor materials. In future studies, the NAMD simulation methods can be employed to elucidate experimental phenomena and reveal microscopic details as well as rationally design novel photofunctional materials with desired properties.

Tuning ultrafast time-evolution of photo-induced charge-transfer states: A real-time electronic dynamics study in substituted indenotetracene derivatives.

Photo-induced charge transfer (CT) states are pivotal in many technological and biological processes. A deeper knowledge of such states is mandatory for modeling the charge migration dynamics. Real-time time-dependent density functional theory (RT-TD-DFT) electronic dynamics simulations are employed to explicitly observe the electronic density time-evolution upon photo-excitation. Asymmetrically substituted indenotetracene molecules, given their potential application as n-type semiconductors in organic photovoltaic materials, are here investigated. Effects of substituents with different electron-donating characters are analyzed in terms of the overall electronic energy spacing and resulting ultrafast CT dynamics through linear response (LR-)TD-DFT and RT-TD-DFT based approaches. The combination of the computational techniques here employed provided direct access to the electronic density reorganization in time and to its spatial and rational representation in terms of molecular orbital occupation time evolution. Such results can be exploited to design peculiar directional charge dynamics, crucial when photoactive materials are used for light-harvesting applications.

Time-Dependent Density Functional Theory for X-ray Absorption Spectra: Comparing the Real-Time Approach to Linear Response.

We simulate X-ray absorption spectra at elemental K-edges using time-dependent density functional theory (TDDFT) in both its conventional linear-response implementation and its explicitly time-dependent or "real-time" formulation. Real-time TDDFT simulations enable broadband spectra calculations without the need to invoke frozen occupied orbitals ("core/valence separation"), but we find that these spectra are often contaminated by transitions to the continuum that originate from lower-energy core and semicore orbitals. This problem becomes acute in triple-ζ basis sets, although it is sometimes sidestepped in double-ζ basis sets. Transitions to the continuum acquire surprisingly large dipole oscillator strengths, leading to spectra that are difficult to interpret. Meaningful spectra can be recovered by means of a filtering technique that decomposes the spectrum into contributions from individual occupied orbitals, and the same procedure can be used to separate L- and K-edge spectra arising from different elements within a given molecule. In contrast, conventional linear-response TDDFT requires core/valence separation but is free of these artifacts. It is also significantly more efficient than the real-time approach, even when hundreds of individual states are needed to reproduce near-edge absorption features and even when Padé approximants are used to reduce the real-time simulations to just 2-4 fs of time propagation. Despite the cost, the real-time approach may be useful to examine the validity of the core/valence separation approximation.

Density Functional Treatment of Photoionization of Sodium Clusters: Effects of Cluster Size and Exchange–Correlation Framework

The ground state and photoionization properties of Nax (x = 20, 40, and 92) clusters are investigated using a method based on density functional theory (DFT) in a spherical jellium frame. Two different exchange–correlation treatments with the Gunnarsson–Lundqvist parametrization are used: (i) the electron self-interaction correction (SIC) scheme and (ii) the van Leeuwen–Baerends (LB94) scheme based on the gradient of the electron density. The shapes of the mean-field potentials and bound state properties, obtained in the two schemes, qualitatively agree, but differ in the details. The effect of the schemes on the photoionization dynamics, calculated in linear response time-dependent DFT is compared, in which the broader features are found to be universal. The general similarity of the results in SIC and LB94 demonstrates the reliability of DFT treatments. The study further elucidates the evolution of the ground state and ionization description as a function of the cluster size.

Averaging over atom snapshots in linear-response TDDFT of disordered systems: A case study of warm dense hydrogen.

Linear-response time-dependent density functional theory (LR-TDDFT) simulations of disordered extended systems require averaging over different snapshots of ion configurations to minimize finite size effects due to the snapshot-dependence of the electronic density response function and related properties. We present a consistent scheme for the computation of the macroscopic Kohn-Sham (KS) density response function connecting an average over snapshot values of charge density perturbations to the averaged values of KS potential variations. This allows us to formulate the LR-TDDFT within the adiabatic (static) approximation for the exchange-correlation (XC) kernel for disordered systems, where the static XC kernel is computed using the direct perturbation method [Moldabekov et al., J. Chem. Theory Comput. 19, 1286 (2023)]. The presented approach allows one to compute the macroscopic dynamic density response function as well as the dielectric function with a static XC kernel generated for any available XC functional. The application of the developed workflow is demonstrated for the example of warm dense hydrogen. The presented approach is applicable for various types of extended disordered systems, such as warm dense matter, liquid metals, and dense plasmas.

Efficient D-π-π-A-Type Dye Sensitizer Based on a Benzothiadiazole Moiety: A Computational Study.

The design of highly efficient sensitizers is one of the most significant areas in dye-sensitized solar cell (DSSC) research. We studied a series of benzothiadiazole-based D-π-π-A organic dyes, putting emphasis on the influence of the donor moiety on the DSSC's efficiency. Using (linear-response time-dependent) density functional theory ((TD)DFT)) with the CAM-B3LYP functional, different donor groups were characterized in terms of electronic absorption spectra and key photovoltaic parameters. As a reference, a dye was considered that had a benzothiadiazole fragment linked via thiophene rings to a diphenylamine donor and a cyanoacrylic-acid acceptor. The different systems were first studied in terms of individual performance parameters, which eventually aggregated into power conversion efficiency. Only the amino-substituted species showed a modest increase, whereas the dimethylamino case showed a decrease.

X-ray Thomson scattering spectra from density functional theory molecular dynamics simulations based on a modified Chihara formula.

We study ab initio approaches for calculating x-ray Thomson scattering spectra from density functional theory molecular dynamics simulations based on a modified Chihara formula that expresses the inelastic contribution in terms of the dielectric function. We study the electronic dynamic structure factor computed from the Mermin dielectric function using an ab initio electron-ion collision frequency in comparison to computations using a linear-response time-dependent density functional theory (LR-TDDFT) framework for hydrogen and beryllium and investigate the dispersion of free-free and bound-free contributions to the scattering signal. A separate treatment of these contributions, where only the free-free part follows the Mermin dispersion, shows good agreement with LR-TDDFT results for ambient-density beryllium, but breaks down for highly compressed matter where the bound states become pressure ionized. LR-TDDFT is used to reanalyze x-ray Thomson scattering experiments on beryllium demonstrating strong deviations from the plasma conditions inferred with traditional analytic models at small scattering angles.

Analytical excited state gradients for time-dependent density functional theory plus tight binding (TDDFT + TB).

Understanding photoluminescent mechanisms has become essential for photocatalytic, biological, and electronic applications. Unfortunately, analyzing excited state potential energy surfaces (PESs) in large systems is computationally expensive, and hence limited with electronic structure methods such as time-dependent density functional theory (TDDFT). Inspired by the sTDDFT and sTDA methods, time-dependent density functional theory plus tight binding (TDDFT + TB) has been shown to reproduce linear response TDDFT results much faster than TDDFT, particularly in large nanoparticles. For photochemical processes, however, methods must go beyond the calculation of excitation energies. Herein, this work outlines an analytical approach to obtain the derivative of the vertical excitation energy in TDDFT + TB for more efficient excited state PES exploration. The gradient derivation is based on the Z vector method, which utilizes an auxiliary Lagrangian to characterize the excitation energy. The gradient is obtained when the derivatives of the Fock matrix, the coupling matrix, and the overlap matrix are all plugged into the auxiliary Lagrangian, and the Lagrange multipliers are solved. This article outlines the derivation of the analytical gradient, discusses the implementation in Amsterdam Modeling Suite, and provides proof of concept by analyzing the emission energy and optimized excited state geometry calculated by TDDFT and TDDFT + TB for small organic molecules and noble metal nanoclusters.

Linear-response time-dependent density functional theory approach to warm dense matter with adiabatic exchange-correlation kernels

We present a new methodology for the linear-response time-dependent density functional theory (LR-TDDFT) calculation of the dynamic density response function of warm dense matter in an adiabatic approximation that can be used with any available exchange-correlation (XC) functional across Jacob's Ladder and across temperature regimes. The main novelty of the presented approach is that it can go beyond the adiabatic local density approximation (ALDA) and generalized LDA (AGGA) while preserving the self-consistence between the Kohn-Sham (KS) response function and adiabatic XC kernel for extended systems. The key ingredient for the presented method is the combination of the adiabatic XC kernel from the direct perturbation approach with the macroscopic dynamic KS response from the standard LR-TDDFT method using KS orbitals. We demonstrate the application of the method for the example of warm dense hydrogen, for which we perform a detailed analysis of the KS density response function, the RPA result, the total density response function and of the adiabatic XC kernel. The analysis is performed using LDA, GGA, and meta-GGA level approximations for the XC effects. The presented method is directly applicable to disordered systems such as liquid metals, warm dense matter, and dense plasmas.