Time-dependent Hybrid Density Functional Theory Research Articles

The role of the coupling matrix elements in time-dependent density functional theory on the simulation of core-level spectra of transition metal complexes

Time-dependent density functional theory (TD-DFT) stands out as an efficient tool for computing core-level spectra in large molecules, particularly transition metal complexes. However, despite their relatively moderate computational demands, TD-DFT methods can still pose challenges for typical computations involving transition metal complexes with over a thousand basis functions. In this study, we investigate the role of the Coulomb, Hartree–Fock exchange, and exchange-correlation kernel contributions to the TD-DFT coupling matrix elements when simulating core-level spectra in transition metal complexes. Our observations reveal that the exchange-correlation kernel contribution, responsible for more than 50% of the computational time in a hybrid TD-DFT calculation, surprisingly has no discernible impact on the qualitative aspects of the calculated spectra. While the Coulomb term plays a crucial role in describing L2,3 -edge spectra, its significance becomes negligible when considering K, L 1, and M4,5 edges. In contrast, the scaled Hartree–Fock exchange is demonstrated to be the most influential term, underscoring the necessity for hybrid density functional approximations in accurately simulating core-level spectra. These trends hold irrespective of the chosen basis set and exchange-correlation functional, providing valuable insights for the development of approximate methods for incorporating two-electron interactions within the realm of core-level spectroscopies.

Excited State Properties of Point Defects in Semiconductors and Insulators Investigated with Time-Dependent Density Functional Theory.

We present a formulation of spin-conserving and spin-flip hybrid time-dependent density functional theory (TDDFT), including the calculation of analytical forces, which allows for efficient calculations of excited state properties of solid-state systems with hundreds to thousands of atoms. We discuss an implementation on both GPU- and CPU-based architectures along with several acceleration techniques. We then apply our formulation to the study of several point defects in semiconductors and insulators, specifically the negatively charged nitrogen-vacancy and neutral silicon-vacancy centers in diamond, the neutral divacancy center in 4H silicon carbide, and the neutral oxygen-vacancy center in magnesium oxide. Our results highlight the importance of taking into account structural relaxations in excited states in order to interpret and predict optical absorption and emission mechanisms in spin defects.

Singlet-triplet energy gap of multiresonant molecular systems: A double hybrid time-dependent density functional theory study

Singlet–triplet energy gaps (ΔEST) for multiresonant molecular systems are investigated within time-dependent density functional theory (TDDFT), using conventional linear response TDDFT (LR-TDDFT) and double hybrid TDDFT (DH-TDDFT) schemes. LR-TDDFT methods systematically overestimate ΔEST; on the other hand, by explicitly taking double excitation characters into consideration, DH-TDDFT considerably improves the gap problem. Further theoretical analysis shows that DH-TDDFT calculations also work for the description of negative gap situations, which LR-TDDFT intrinsically fails. The present findings demonstrate the applicability of TDDFT-based methods for predicting ΔEST as a relatively low-cost computational approach, encouraging us to develop new exchange-correlation functionals suited for DH-TDDFT calculations.

Excitonic characteristics of blue-emitting quantum dot materials in group II-VI using hybrid time-dependent density functional theory

Colloidal quantum dots (QDs) of group II-VI are key ingredients of next-generation QD light-emitting diodes technology for display and lighting, yet the understanding of their luminescent characteristics are far from being mature. Using a hybrid time-dependent density functional theory, we have studied the electronic and excitonic properties of blue-emitting colloidal QDs within group II-VI containing a thousand atoms or more, including CdSe, CdS, ZnSe, and ZnS QDs, considering both quantum confinement and surface ligand effects. It is found that the calculated optical gaps are in excellent quantitative agreement with experiment, irrespective of the QD nature. Scaling laws of size-dependent energy gaps governed solely by quantum confinement effects have further been explored at both single-particle level and correlated excitonic level for all QDs. With concurrently stoichiometric control and enhancing quantum confinement effects, we have predicted an unusual switching of symmetry character of the highest occupied molecular orbital state from a ${\mathrm{\ensuremath{\Gamma}}}_{3}$ to a ${\mathrm{\ensuremath{\Gamma}}}_{1}$ symmetry at ultrasmall size ($\ensuremath{\sim}1$ nm) for all QDs. After the switching, pronounced linearly polarized band-edge excitonic emission is activated. The radiative exciton decay lifetime is found to increase monotonically with increasing the QD size and tends to saturate at larger sizes. Finally, we have explored the surface passivation mechanism of inorganic chloride ligand, and identified various favorable Cd-Cl bonding configurations which enable an effective surface passivation resembling the commonly applied pseudohydrogen passivation scheme. We find that chloride ligand serves as a hole delocalization ligand and tends to redshift the absorption spectra, reduce the absorption intensity, and significantly enhance the exciton decay lifetime. Our results provide a guideline for spectroscopic studies of excitonic characteristics of colloidal QDs within group II-VI.

Optical properties ofCsCu2X3(X=Cl, Br, and I): A comparative study between hybrid time-dependent density-functional theory and the Bethe-Salpeter equation

The cesium copper halides CsCu$_2$X$_3$ (X=Cl, Br and I) are a class of all-inorganic perovskites with interesting and potentially useful optical properties, characterized by distinct excitonic features. We present a computational study of the optical absorption spectra of CsCu$_2$X$_3$, comparing time-dependent density-functional theory (TDDFT) and the Bethe-Salpeter equation (BSE), using $GW$ quasiparticle band structures as input. The TDDFT calculations are carried out using several types of global hybrid exchange-correlation functionals. It is found that an admixture of nonlocal exchange determined by the dielectric constant produces optical spectra in excellent agreement with the BSE. Thus, hybrid TDDFT emerges as a promising first-principles approach for excitonic effects in solids.

Optical Gaps and Excitonic Properties of 2D Materials by Hybrid Time-Dependent Density Functional Theory: Evidences for Monolayers and Prospects for van der Waals Heterostructures.

The optical properties of two-dimensional (2D) materials are accurately described by many-body methods including specifically pronounced electron-electron and electron-hole effects. Such methods are, however, computationally demanding and applicable on small computational cells only. We provide approximate optical gaps for 2D materials from time-dependent (TD) density functional theory based on a set of specific screened hybrid functionals and show that this approach effectively accounts for all important physical effects including excitons. Optical gap values obtained from the TD-HSE06 approach for a broad gap range 1-6 eV of eight 2D materials are in agreement with both experimental optical gaps and accurate GW+BSE calculations. Further, we show that such an approach is eligible and practicable for van der Waals heterostructures containing incommensurate cells of different monolayers and enables detailed analysis of intra- and interlayer excitonic wave functions. TD-HSE06 is therefore a suitable method for a reliable description of the optical properties of extended periodic 2D systems.

5-Methoxyquinoline Photobasicity Is Mediated by Water Oxidation.

A mechanism explaining the photobasicity of 5-methoxyquinoline (5-MeOQ) is proposed on the basis of nonadiabatic molecular dynamics simulations using time-dependent hybrid density functional theory (TDDFT) and fewest switches surface hopping (SH) and analysis of existing ultrafast spectroscopy experiments. According to the TDDFT-SH simulations, the rate-determining step is hole transfer from photoexcited 5-MeOQ to adjacent water molecules within ∼5 ps followed by rapid electron-coupled proton transfer and deactivation to the ground state. This fast redox-catalyzed proton transfer mechanism is consistent with simple thermodynamic arguments, correlated wavefunction calculations, and recent isotope substitution time-resolved fluorescence experiments. Although energetically feasible, direct protonation of 5-MeOQ in the S1 state appears to be too slow to contribute significantly to 5-MeOQ photobasicity in aqueous solution.

Multistate hybrid time-dependent density functional theory with surface hopping accurately captures ultrafast thymine photodeactivation.

We report an efficient analytical implementation of first-order nonadiabatic derivative couplings between arbitrary Born-Oppenheimer states in the hybrid time-dependent density functional theory (TDDFT) framework using atom-centered basis functions. Our scheme is based on quadratic response theory and includes orbital relaxation terms neglected in previous approaches. Simultaneous computation of multiple derivative couplings and energy gradients enables efficient multistate nonadiabatic molecular dynamics simulations in conjunction with Tully's fewest switches surface hopping (SH) method. We benchmark the thus obtained multistate TDDFT-SH scheme by simulating ultrafast decay of UV-photoexcited thymine, for which accurate gas-phase data from ultrafast spectroscopy experiments are available. The calculations predict a fast 153 fs decay from the bright S2 to the dark S1 excited state, followed by a much slower 14 ps S1 deactivation to the ground state; statistical uncertainties were estimated using bootstrap sampling. These results agree well with the experimentally observed time constants of 100-200 fs and 5-7 ps, respectively, unlike previous multiconfigurational self-consistent field and second-order algebraic diagrammatic construction calculations. Furthermore, our results support the S1-trapping hypothesis [J. J. Szymczak et al., J. Phys. Chem. A, 2009, 113, 12686-12693]. For thymine, the computational cost of a single TDDFT-SH time-step including the lowest 3 states, all couplings and gradients, is ∼5 times larger than the cost of a single Born-Oppenheimer dynamics time step for the ground state in our implementation. Thus, ps nonadiabatic dynamics simulations using multistate hybrid TDDFT-SH for systems with up to ∼100 atoms are possible without drastic approximations on single workstation nodes. Our implementation will be made available through Turbomole.

Excited states of defect linear arrays in silicon: A first-principles study based on hydrogen cluster analogs

Excited states of a single donor in bulk silicon have previously been studied extensively based on effective mass theory. However, proper theoretical descriptions of the excited states of a donor cluster are still scarce. Here we study the excitations of lines of defects within a single-valley spherical band approximation, thus mapping the problem to a scaled hydrogen atom array. A series of detailed time-dependent Hartree-Fock, time-dependent hybrid density-functional theory and full configuration-interaction calculations have been performed to understand linear clusters of up to 10 donors. Our studies illustrate the generic features of their excited states, addressing the competition between formation of interdonor ionic states and intradonor atomic excited states. At short interdonor distances, excited states of donor molecules are dominant, at intermediate distances ionic states play an important role, and at long distances the intradonor excitations are predominant as expected. The calculations presented here emphasize the importance of correlations between donor electrons, and are thus complementary to other recent approaches that include effective mass anisotropy and multivalley effects. The exchange splittings between relevant excited states have also been estimated for a donor pair and for three-donor arrays; the splittings are much larger than those in the ground state in the range of donor separations between 10 and 20 nm. This establishes a solid theoretical basis for the use of excited-state exchange interactions for controllable quantum gate operations in silicon.

Combined TD-DFT-SOS-CIS(D) Study of BOPHY Derivatives with Potential Application in Biosensing.

A set of 13 bis(difluoroboron)-1,2-bis((pyrrol-2-yl)methylene)hydrazine (BOPHY) dyes is studied through a hybrid time-dependent density functional theory (TD-DFT)-scaled opposite spin-configuration interaction singles with a double correction [SOS-CIS(D)] approach accounting for solvent effects, to shed light onto the structure-property relationships of these recently developed chromophores. In the first step, we calculate the absorption-fluorescence crossing points with refined TD-DFT models considering the influences of both vibrational and solvent contributions. We found that the systematic overestimation of the 0-0 energies is effectively reduced by combining polarizable continuum model-TD-DFT with a scaled opposite spin-configuration interaction singles with a double correction [SOS-CIS(D)]. Next, for a representative system, the vibrationally resolved spectrum within the harmonic approximation is computed on the basis of TD-DFT vibrational signatures and an excellent match with experiment is found. Finally, the influence of different lateral groups on the spectroscopic properties is rationalized by investigating charge transfer parameters and examining electronic density difference maps. It is found that one can tune the position of the absorption/emission maxima by a judicious choice of the lateral substituents or by using π-extended segments. The largest absorption and emission wavelengths as well as the largest Stokes shifts are obtained for BOPHYs containing strong electron-donor dimethylaminophenyl groups attached to the α-positions of the pyrrole units through vinyl linkers, making these chromophores promising candidates for bioluminescence applications.

That Little Extra Kick: Nonadiabatic Effects in Acetaldehyde Photodissociation.

The effect of nonadiabatic transitions on branching ratios, kinetic and internal energy distribution of fragments, and reaction mechanisms observed in acetaldehyde photodissociation is investigated by nonadiabatic molecular dynamics (NAMD) simulations using time-dependent hybrid density functional theory and Tully surface hopping. Homolytic bond breaking is approximately captured by allowing spin symmetry to break. The NAMD simulations reveal that nonadiabatic transitions selectively enhance the kinetic energy of certain internal degrees of freedom within approximately 50 fs. Branching ratios from NAMD and conventional "hot" Born-Oppenheimer molecular dynamics (BOMD) are similar and qualitatively agree with experiment. However, as opposed to the BOMD simulations, NAMD captures the high-energy tail of the experimental kinetic energy distribution. The extra "kick" of the nuclei in the direction of the nonadiabatic coupling vector results from nonadiabatic transitions close to conical intersections. From a mechanistic perspective, the nonadiabatic effects favor asynchronous over synchronous fragmentation and tend to suppress roaming.

Optical properties of the organic-inorganic hybrid perovskiteCH3NH3PbI3: Theory and experiment

We perform a theoretical and experimental study of the optical properties of a $\mathrm{C}{\mathrm{H}}_{3}\mathrm{N}{\mathrm{H}}_{3}\mathrm{Pb}{\mathrm{I}}_{3}$ perovskite prepared by a vapor-assisted solution process, motivated in part by very high photovoltaic cell efficiencies. Several widespread theoretical approaches are used in an attempt to determine the most appropriate approach which would reproduce the experimental electronic structure and optical properties of the $\mathrm{C}{\mathrm{H}}_{3}\mathrm{N}{\mathrm{H}}_{3}\mathrm{Pb}{\mathrm{I}}_{3}$ perovskite. We compare a semilocal approximation to the density functional theory with hybrid functionals and time-dependent hybrid functional calculations, evaluating the effects of exchange tuning and spin-orbit coupling. Using these methods we calculate the electronic structure, optical absorption spectrum, and frequency-dependent dielectric function of the $\mathrm{C}{\mathrm{H}}_{3}\mathrm{N}{\mathrm{H}}_{3}\mathrm{Pb}{\mathrm{I}}_{3}$ perovskite. The results are compared to the experimentally obtained dielectric functions acquired from ellipsometry measurements. We demonstrate that inclusion of spin-orbit coupling in theoretical calculations is critical in describing the electronic and optical properties of the $\mathrm{C}{\mathrm{H}}_{3}\mathrm{N}{\mathrm{H}}_{3}\mathrm{Pb}{\mathrm{I}}_{3}$ perovskite. Good agreement with experimental data is achieved when the optical spectra are computed using time-dependent hybrid density functional theory with spin-orbit coupling.

Radiation damage in X-ray crystallography: a quantum-mechanical study of photoinduced defect formation in beeswax-analogue n-eicosane crystals

We study the nuclear dynamics of n-eicosane ( $$\hbox {C}_{20}\hbox {H}_{42}$$ ) in the crystalline state after photoirradation at room temperature using adiabatic ab initio excited-state dynamics based on hybrid time-dependent density-functional theory. We consider the weak perturbation (absorption) limit, in which an excited electron and a hole are simultaneously created in the system, and the strong perturbation (photoemission) regime, in which one electron is removed. We examine the changes in the carbon chain conformation occurring over timescales of the order of ca. 5 ps relative to the unperturbed (ground state) crystal structure at room temperature, which we simulate using standard ab initio molecular dynamics based on hybrid density-functional theory. Whereas the system retains its ground-state structure in the photoemission limit, the formation of structural defects, in the form of local distortions of the chain geometry, is observed in the absorption limit. We attribute the formation of these defects to the nuclear screening of the electron–hole pair created by photoexcitation. We discuss these findings in the context of radiation damage in organic/biological macromolecules and X-ray diffraction techniques.

Chaotic Soliton Dynamics in Photoexcited trans-Polyacetylene

We study the photogeneration of topological solitons in trans-polyacetylene and their time evolution using ab initio excited-state dynamics. The system is excited to the optically allowed 1(1)Bu state, and the atoms are then propagated classically using quantum mechanical forces computed using hybrid time-dependent density functional theory (TD-DFT). A soliton/antisoliton pair nucleates spontaneously and creates two independent solitons moving at constant velocity, similar to simulations based on uncorrelated lattice models like the Su-Schrieffer-Heeger (SSH) Hamiltonian [Su, W. P.; Schrieffer, J. R.; Heeger, A. J. Phys. Rev. Lett. 1979, 42, 1698]. At T = 0, the solitons coalesce into bound pairs with a two-soliton functional form, whereas chaotic dynamics, in the form of 2-bounce resonances, is observed at soliton/antisoliton collisions at T ≠ 0. This behavior is related to the onset of a strong correlation regime at short intersoliton distance, which is not accounted for by SSH simulations.

Two-component hybrid time-dependent density functional theory within the Tamm-Dancoff approximation.

We report the implementation of a two-component variant of time-dependent density functional theory (TDDFT) for hybrid functionals that accounts for spin-orbit effects within the Tamm-Dancoff approximation (TDA) for closed-shell systems. The influence of the admixture of Hartree-Fock exchange on excitation energies is investigated for several atoms and diatomic molecules by comparison to numbers for pure density functionals obtained previously [M. Kühn and F. Weigend, J. Chem. Theory Comput. 9, 5341 (2013)]. It is further related to changes upon switching to the local density approximation or using the full TDDFT formalism instead of TDA. Efficiency is demonstrated for a comparably large system, Ir(ppy)3 (61 atoms, 1501 basis functions, lowest 10 excited states), which is a prototype molecule for organic light-emitting diodes, due to its "spin-forbidden" triplet-singlet transition.

Protonation-induced modulation of one- and two-photon absorption properties for quadripolar dyes

The time-dependent hybrid density functional theory (TD-DFT) in combination with analytical response theory is used to explore the one-photon absorption (OPA) and emission as well as two-photon absorption (TPA) properties of quadripolar compounds with hydroxyl, amino or pyridyl end groups upon (de)protonation process. Both their one-photon absorption and emission as well as two-photon absorption properties show obvious changes upon passing from their neutral to their doubly (de)protonated state. The intramolecular charge-transfer (ICT) analysis demonstrates the variation of the electronic properties of the terminal groups by the (de)protonation process. The computational results are in reasonable agreement with the experimental ones.

Carbon K-Edge X-ray Absorption Spectroscopy and Time-Dependent Density Functional Theory Examination of Metal–Carbon Bonding in Metallocene Dichlorides

Metal-carbon covalence in (C5H5)2MCl2 (M = Ti, Zr, Hf) has been evaluated using carbon K-edge X-ray absorption spectroscopy (XAS) as well as ground-state and time-dependent hybrid density functional theory (DFT and TDDFT). Differences in orbital mixing were determined experimentally using transmission XAS of thin crystalline material with a scanning transmission X-ray microscope (STXM). Moving down the periodic table (Ti to Hf) has a marked effect on the experimental transition intensities associated with the low-lying antibonding 1a1* and 1b2* orbitals. The peak intensities, which are directly related to the M-(C5H5) orbital mixing coefficients, increase from 0.08(1) and 0.26(3) for (C5H5)2TiCl2 to 0.31(3) and 0.75(8) for (C5H5)2ZrCl2, and finally to 0.54(5) and 0.83(8) for (C5H5)2HfCl2. The experimental trend toward increased peak intensity for transitions associated with 1a1* and 1b2* orbitals agrees with the calculated TDDFT oscillator strengths [0.10 and 0.21, (C5H5)2TiCl2; 0.21 and 0.73, (C5H5)2ZrCl2; 0.35 and 0.69, (C5H5)2HfCl2] and with the amount of C 2p character obtained from the Mulliken populations for the antibonding 1a1* and 1b2* orbitals [8.2 and 23.4%, (C5H5)2TiCl2; 15.3 and 39.7%, (C5H5)2ZrCl2; 20.1 and 50.9%, (C5H5)2HfCl2]. The excellent agreement between experiment, theory, and recent Cl K-edge XAS and DFT measurements shows that C 2p orbital mixing is enhanced for the diffuse Hf (5d) and Zr (4d) atomic orbitals in relation to the more localized Ti (3d) orbitals. These results provide insight into how changes in M-Cl orbital mixing within the metallocene wedge are correlated with periodic trends in covalent bonding between the metal and the cyclopentadienide ancillary ligands.

Tetrahalide Complexes of the [U(NR)2]2+ Ion: Synthesis, Theory, and Chlorine K-Edge X-ray Absorption Spectroscopy

Synthetic routes to salts containing uranium bis-imido tetrahalide anions [U(NR)(2)X(4)](2-) (X = Cl(-), Br(-)) and non-coordinating NEt(4)(+) and PPh(4)(+) countercations are reported. In general, these compounds can be prepared from U(NR)(2)I(2)(THF)(x) (x = 2 and R = (t)Bu, Ph; x = 3 and R = Me) upon addition of excess halide. In addition to providing stable coordination complexes with Cl(-), the [U(NMe)(2)](2+) cation also reacts with Br(-) to form stable [NEt(4)](2)[U(NMe)(2)Br(4)] complexes. These materials were used as a platform to compare electronic structure and bonding in [U(NR)(2)](2+) with [UO(2)](2+). Specifically, Cl K-edge X-ray absorption spectroscopy (XAS) and both ground-state and time-dependent hybrid density functional theory (DFT and TDDFT) were used to probe U-Cl bonding interactions in [PPh(4)](2)[U(N(t)Bu)(2)Cl(4)] and [PPh(4)](2)[UO(2)Cl(4)]. The DFT and XAS results show the total amount of Cl 3p character mixed with the U 5f orbitals was roughly 7-10% per U-Cl bond for both compounds, which shows that moving from oxo to imido has little effect on orbital mixing between the U 5f and equatorial Cl 3p orbitals. The results are presented in the context of recent Cl K-edge XAS and DFT studies on other hexavalent uranium chloride systems with fewer oxo or imido ligands.

Solvent Effects on One- and Two-Photon Optical Properties of a Novel 2, 2':6', 2''-Terpyridine-Based Chromophore

At ab initio level, time-dependent hybrid density functional theory and re- sponse theory have been applied to study the solvent effect on the geometrical and elctronic structure as well as one- and two-photon absorption (TPA) properties of 2,2':6',2-terpyridine-based chromophore L. It is found that solvatochromic shift of charge-transfer (CT) appears nonmonotonic behavior with regard to the polarity of solvent. Besides, the one-photon absorption (OPA) strengths are enlarged slightly and are more dependent on the optical dielectric constant. The TPA cross sections are en- hanced when considering solvent effect compared to that in gas phase and the TPA cross sections show an increasing trend with the increase of solvent polarity. All the theoretical results are in reasonable agreement with experimental data.

A non-self-consistent range-separated time-dependent density functional approach for large-scale simulations

We propose an efficient method for carrying out time-dependent density functional theory (TDDFT) calculations using range-separated hybrid exchange–correlation functionals. Based on a non-self-consistent range-separated Hamiltonian, the method affords large-scale simulations at a fraction of the computational time of conventional hybrid TDDFT approaches. For typical benchmark molecules including N2, CO, C6H6, H2CO and the C2H4–C2F4 dimer, the method possesses the same level of accuracy as the conventional approaches for the valence, Rydberg, and charge-transfer excitation energies when compared to the experimental results. The method is used to determine π → π* excitations in both disordered and crystalline poly(3-hexylthiophene) (P3HT) conjugated polymers with more than six hundred atoms and it yields excitation energies and charge densities that are in excellent agreement with experiments. The simulation of the crystalline P3HT reveals that the phase of the wavefunctions could have an important effect on the excitation energy; a hypothesis based on π–π stacking is proposed to explain this novel effect in conjugated polymers.