Relativistic Time-dependent Density Functional Theory Research Articles

Dirac-Coulomb-Breit Molecular Mean-Field Exact-Two-Component Relativistic Equation-of-Motion Coupled-Cluster Theory.

We present a relativistic equation-of-motion coupled-cluster with single and double excitation formalism within the exact two-component framework (X2C-EOM-CCSD), where both scalar relativistic effects and spin-orbit coupling are variationally included at the reference level. Three different molecular mean-field treatments of relativistic corrections, including the one-electron, Dirac-Coulomb, and Dirac-Coulomb-Breit Hamiltonian, are considered in this work. Benchmark calculations include atomic excitations and fine-structure splittings arising from spin-orbit coupling. Comparison with experimental values and relativistic time-dependent density functional theory is also carried out. The computation of the oscillator strength using the relativistic X2C-EOM-CCSD approach allows for studies of spin-orbit-driven processes, such as the spontaneous phosphorescence lifetime.

Core-Projected Hybrids Fix Systematic Errors in Time-Dependent Density Functional Theory Predicted Core-Electron Excitations.

Linear response time-dependent density functional theory (TDDFT) is widely applied to valence, Rydberg, and charge-transfer excitations but, in its current form, makes large errors for core-electron excitations. This work demonstrates that the admixture of nonlocal exact exchange in atomic core regions significantly improves TDDFT-predicted core excitations. Exact exchange admixture is accomplished using projected hybrid density functional theory [ J. Chem. Theory Comput. 2023, 19, 837-847]. Scalar relativistic TDDFT calculations using core-projected B3LYP accurately model core excitations of second-period elements C-F and third-period elements Si-Cl, without sacrificing performance for the relative shifts of core excitation energies. Predicted K-edge X-ray near absorption edge structure (XANES) of a series of sulfur standards highlight the value of this approach. Core-projected hybrids appear to be a practical solution to TDDFT's limitations for core excitations, in the way that long-range-corrected hybrids are a practical solution to TDDFT's limitations for Rydberg and charge-transfer excitations.

Accurate Relativistic Real-Time Time-Dependent Density Functional Theory for Valence and Core Attosecond Transient Absorption Spectroscopy

First principles theoretical modeling of out-of-equilibrium processes observed in attosecond pump-probe transient absorption spectroscopy (TAS) triggering pure electron dynamics remains a challenging task, especially for heavy elements and/or core excitations containing fingerprints of scalar and spin-orbit relativistic effects. To address this, we formulate a methodology for simulating TAS within the relativistic real-time, time-dependent density functional theory (RT-TDDFT) framework, for both the valence and core energy regimes. Especially for TAS, full four-component (4c) RT simulations are feasible but computationally demanding. Therefore, in addition to the 4c approach, we also introduce the atomic mean-field exact two-component (amfX2C) Hamiltonian accounting for one- and two-electron picture-change corrections within RT-TDDFT. amfX2C preserves the accuracy of the parent 4c method at a fraction of its computational cost. Finally, we apply the methodology to study valence and near-L2,3-edge TAS processes of experimentally relevant systems and provide additional physical insights using relativistic nonequilibrium response theory.

Optical Activity of Spin-Forbidden Electronic Transitions in Metal Complexes from Time-Dependent Density Functional Theory with Spin-Orbit Coupling.

The calculation of magnetic transition dipole moments and rotatory strengths was implemented at the zeroth‐order regular approximation (ZORA) two‐component relativistic time‐dependent density functional theory (TDDFT) level. The circular dichroism of the spin‐forbidden ligand‐field transitions of tris(ethylenediamine)cobalt(III) computed in this way agrees very well with available measurements. Phosphorescence dissymmetry factors glum and the corresponding lifetimes are evaluated for three N‐heterocyclic‐carbene‐based iridium complexes, two of which contain helicene moieties, and for two platinahelicenes. The agreement with experimental data is satisfactory. The calculations reproduce the signs and order of magnitude of glum , and the large variations of phosphorescence lifetimes among the systems. The electron spin contribution to the magnetic transition dipole moment is shown to be important in all of the computations.

Photoelectron angular distribution studies for two spin–orbit-split components of Xe 3d subshell: a critical comparison between theory and experiment

The photoelectron angular distribution asymmetry parameters β of the Xe 3d subshell were investigated using an x-ray free-electron laser (XFEL) at photon energies of 750 and 800 eV. Owing to the perfect polarization of the XFEL and two-dimensional momentum imaging capability of our velocity map imaging spectrometer, we determined the β values with high accuracy. The β values were also investigated based on relativistic time-dependent density functional theory calculations of up to 900 eV of photon energies. By comparing all the available experimental results including our data with the most reliable theories on the photon energy dependence of the β parameters, serious differences are noted between the experiments and theories. Further studies on resolving this difference will provide new insight into the photoionization processes of the deep inner shells.

Four-component relativistic time-dependent density-functional theory using a stable noncollinear DFT ansatz applicable to both closed- and open-shell systems.

We present a formulation of relativistic linear response time-dependent density functional theory for the calculation of electronic excitation energies in the framework of the four-component Dirac-Coulomb Hamiltonian. This approach is based on the noncollinear ansatz originally developed by Scalmani and Frisch [J. Chem. Theory Comput. 8, 2193 (2012)] and improves upon the past treatment of the limit cases in which the spin density approaches zero. As a result of these improvements, the presented approach is capable of treating both closed- and open-shell reference states. Robust convergence of the Davidson-Olsen eigenproblem algorithm for open-shell reference states was achieved through the use of a solver which considers both left and right eigenvectors. The applicability of the present methodology on both closed- and open-shell reference states is demonstrated on calculations of low-lying excitation energies for Group 3 atomic systems (Sc3+-Ac3+) with nondegenerate ground states, as well as for Group 11 atomic systems (Cu-Rg) and octahedral actinide complexes (PaCl6 2-, UCl6 -, and NpF6) with effective doublet ground states.

Size evolution study on the electronic and optical properties of gold-cluster complexes [formula omitted]-S-[formula omitted]-[formula omitted]-[formula omitted] (n = 2–5)

Relativistic unrestricted time-dependent density functional theory calculations were performed for obtaining the absorption spectra of gold-cluster complexes Au4-S-CnH2n-S′-Au4′ (n = 2–5). The range-separated exchange-correlation functional CAMYB3LYP was used to properly predict charge transfer excitations. The absorption UV–vis spectrum is not affected by size if structure and metal-molecule bonding remains similar. Changes in the ‘local’ structure and bonding have drastic effects on these systems’ electronic transitions. The HOMO-LUMO gap of the cluster complexes shows a zig-zag behavior typical of gold nanoclusters with respect to the size of the alkanedithiol chain (n).

Modeling L2,3-edge X-ray absorption spectroscopy with linear response exact two-component relativistic time-dependent density functional theory.

X-ray absorption spectroscopy (XAS) is a powerful tool that can provide physical insights into element-specific chemical processes and reactivities. Although relativistic time-dependent density functional theory (TDDFT) has been previously applied to model the L-edge region in XAS, there has not been a more comprehensive study of the choices of basis sets and density functional kernels available for variational relativistic excited state methods. In this work, we introduce the implementation of the generalized preconditioned locally harmonic residual algorithm to solve the complex-valued relativistic TDDFT for modeling the L-edge X-ray absorption spectra. We investigate the L2,3-edge spectra of a series of molecular complexes using relativistic linear response TDDFT with a hybrid iterative diagonalization algorithm. A systematic error analysis was carried out with a focus on the energetics, intensities, and magnitude of L2-L3 splitting compared to experiments. Additionally, the results from relativistic TDDFT calculations are compared to those computed using other theoretical methods, and the multideterminantal effects on the L-edge XAS were investigated.

Calculating transition dipole moments of phosphorescent emitters for efficient organic light-emitting diodes.

The out-coupling of light from an organic light-emitting diode, and thus its efficiency, strongly depends on the orientation of the transition dipole moment (TDM) of the emitting molecules with respect to the substrate surface. Despite the importance of this quantity, theoretical investigations of the direction of the TDM of phosphorescent emitters based on iridium(iii) complexes remain limited. One challenge is to find an appropriate level of theory able to accurately predict the direction of the TDM. Here, we report relativistic time-dependent density functional theory (TDDFT) calculations of the TDM, emission energies and lifetimes for both the ground-state (S0) and triplet (T1) excited-state geometries of fac-tris(2-phenylpyridyl)iridium(iii) (Ir(ppy)3), using the two-component zero-order regular approximation (ZORA) or including spin-orbit coupling (SOC) perturbatively using the simpler one-component (scalar) formulation. We show that the one- and two-component approaches give similar emission energies and overall radiative lifetimes for each individual geometry. Use of the S0 geometry leads to two of the excited triplet substates being degenerate, with the degeneracy lifted for the T1 geometry, with the latter matching experiment. Two-component calculations using the T1 geometry give results for the direction of the TDM more consistent with experiment than calculations using the S0 geometry. Finally, we show that adding a dielectric medium does not affect the direction of TDM significantly, but leads to better agreement with the experimentally measured radiative lifetime.

Excited-State Reactivity of [Mn(im)(CO)3 (phen)]+ : A Structural Exploration.

The electronic excited state reactivity of [Mn(im)(CO)3 (phen)]+ (phen = 1,10-phenanthroline; im = imidazole) ranging between 420 and 330 nm have been analyzed by means of relativistic spin-orbit time-dependent density functional theory and wavefunction approaches (state-average-complete-active-space self-consistent-field/multistate CAS second-order perturbation theory). Minimum energy conical intersection (MECI) structures and connecting pathways were explored using the artificial force induced reaction (AFIR) method. MECIs between the first and second singlet excited states (S1 /S2 -MECIs) were searched by the single-component AFIR (SC-AFIR) algorithm combined with the gradient projection type optimizer. The structural, electronic, and excited states properties of [Mn(im)(CO)3 (phen)]+ are compared to those of the Re(I) analogue [Re(im)(CO)3 (phen)]+ . The high density of excited states and the presence of low-lying metal-centered states that characterize the Mn complex add complexity to the photophysics and open various dissociative channels for both the CO and imidazole ligands. © 2018 Wiley Periodicals, Inc.

Computational simulation of vibrationally resolved spectra for spin-forbidden transitions.

In this computational study, we illustrate a method for computing phosphorescence and circularly polarized phosphorescence spectra of molecular systems, which takes into account vibronic effects including both Franck-Condon and Herzberg-Teller contributions. The singlet and triplet states involved in the phosphorescent emission are described within the harmonic approximation, and the method fully takes mode-mixing effects into account when evaluating Franck-Condon integrals. Spin-orbit couplings, which are responsible for these otherwise forbidden phenomena, are accounted for by means of a relativistic two-component time-dependent density functional theory method. The model is applied to two types of chiral systems: camphorquinone, a rigid organic system that allows for an extensive benchmark, and some members of a class of iridium complexes. The merits and shortcomings of the methods are discussed, and some perspectives for future developments are offered.

Multiphoton ionization of many-electron atoms and highly-charged ions in intense laser fields: a relativistic time-dependent density functional theory approach

We develop an efficient numerical implementation of the relativistic time-dependent density functional theory (RTDDFT) to study multielectron highly-charged ions subject to intense linearly-polarized laser fields. The interaction with the electromagnetic field is described within the electric dipole approximation. The resulting time-dependent relativistic Kohn–Sham (RKS) equations possess an axial symmetry and are solved accurately and efficiently with the help of the time-dependent generalized pseudospectral method. As a case study, we calculate multiphoton ionization probabilities of the neutral argon atom and argon-like xenon ion. Relativistic effects are assessed by comparison of our present results with existing non-relativistic data.

The Blue-Violet Color of Pentamethylbismuth: A Visible Spin-Orbit Effect.

Two‐component relativistic time‐dependent density functional theory calculations with spin‐orbit coupling predict yellow and orange–red absorption for BiPh5 and BiMe5, respectively, providing an excellent explanation for their respective violet and blue–violet colors. According to the calculations, the visible absorption is clearly attributable to a single transition from a ligand‐based HOMO to a low‐energy LUMO with a significant contribution from a relativistically stabilized Bi 6s orbital. Surprisingly, scalar releativistic calculations completely fail to reproduce the observed visible absorption and place it at the violet/near‐UV borderline instead.

Description of excited states in [Re(Imidazole)(CO)3 (Phen)](+) including solvent and spin-orbit coupling effects: Density functional theory versus multiconfigurational wavefunction approach.

The low-lying electronic excited states of [Re(imidazole)(CO)3 (phen)](+) (phen = 1,10-phenanthroline) ranging between 420 nm and 330 nm have been calculated by means of relativistic spin-orbit time-dependent density functional theory (TD-DFT) and wavefunction approaches (state-average-CASSCF/CASPT2). A direct comparison between the theoretical absorption spectra obtained with different methods including SOC and solvent corrections for water points to the difficulties at describing on the same footing the bands generated by metal-to-ligand charge transfer (MLCT), intraligand (IL) transition, and ligand-to-Ligand- charge transfer (LLCT). While TD-DFT and three-roots-state-average CASSCF (10,10) reproduce rather well the lowest broad MLCT band observed in the experimental spectrum between 420 nm and 330 nm, more flexible wavefunctions enlarged either by the number of roots or by the number of active orbitals and electrons destabilize the MLCT states by introducing IL and LLCT character in the lowest part of the absorption spectrum. © 2016 Wiley Periodicals, Inc.

Theoretical study on spin-forbidden transitions of osmium complexes by two-component relativistic time-dependent density functional theory

We study spin-forbidden transitions of Os polypyridyl sensitizers by two-component relativistic time-dependent density functional theory with the spin–orbit interaction based on Tamm–Dancoff approximation. The absorption spectra, including spin-forbidden-transition peaks, for the Os complexes are reasonably reproduced in comparison with the experimental ones. The extension of the conjugated lengths in the Os complexes is investigated and found to be effective to enhance photo absorption for spin-allowed transitions as well as spin-forbidden ones. This study provides fruitful information for a design of new dyes in terms of conjugation lengths.

Inter-Excited-State Phosphorescence in the Four-Component Relativistic Kohn-Sham Approximation: A Case Study on Lumiflavin.

Electronic transitions from one excited state to another excited state of different spin symmetry play important roles in many biochemical reactions. Although recent years have seen much progress in the elucidation of nonradiative (intersystem crossing) relaxation mechanisms for such transitions, there is presently a scarcity of data available to assess whether also radiative (phosphorescence) mechanisms are relevant for these processes. Here, we demonstrate that the well-established ability of quantum chemical methods to describe intersystem crossing events between excited states can be supplemented by the ability to also describe inter-excited-state phosphorescence. Specifically, by performing four-component relativistic time-dependent density functional theory calculations, we obtain rate constants for the radiative transitions from the absorbing (1)(πHπL*) singlet state of lumiflavin to the (3)(πHπL*), (3)(nN2πL*), and (3)(πH-1πL*) triplet states, and subsequently, we compare these results with rate constants calculated for the corresponding nonradiative transitions. Thereby, it is found that the radiative rate constants for these particular transitions are typically 2 to 5 orders of magnitude smaller than the nonradiative ones.

Two-component relativistic time-dependent density functional theory study on spin-forbidden transitions for metal polypyridyl complexes

Spin-forbidden transitions of metal polypyridyl sensitizers are studied by the two-component relativistic time-dependent density functional theory with spin–orbit interaction based on Tamm–Dancoff approximation. The spin-forbidden transitions for a phosphine-coordinated Ru(II), DX1, as well as the modified DX1 complexes whose Ru is replaced with Fe and Os, are calculated. The role of the central metals in spin-forbidden transitions is discussed toward the exploration for new efficient sensitizers.

Rational modifications on ruthenium terpyridine sensitizers with large Jsc for dye-sensitized solar cells: combined DFT and relativistic TDDFT studies

A series of ruthenium sensitizers DX2–DX5 derived from a phosphine-coordinated ruthenium sensitizer DX1 for dye sensitized solar cells (DSSCs) were designed and calculated based on density functional theory (DFT) and relativistic time-dependent DFT calculations.

Superatomic Orbitals under Spin-Orbit Coupling.

The Au25(SR)18(-) cluster has been the poster child of success in applying the superatom complex concept and remains the most studied system of all of the monolayer-protected metal clusters. In this Letter, we try to solve a mystery about this cluster: the low-temperature UV-vis absorption spectrum shows double peaks below 2.0 eV while simulation by scalar relativistic time-dependent density functional theory (TDDFT) shows only one peak in this region. Using a recently implemented two-component TDDFT, we show that spin-orbit coupling (SOC) leads to those two peaks by splitting the 1P superatomic HOMO orbitals. This work highlights the importance of SOC in understanding the electronic structure and optical absorption of thiolated gold nanoclusters, which has not been realized previously.

Impact of Spin-Orbit Coupling on Photocurrent Generation in Ruthenium Dye-Sensitized Solar Cells.

Relativistic TDDFT calculations have been performed employing a novel computational approach to evaluate the impact of spin-orbit coupling (SOC) in the optical and photovoltaic properties of panchromatic Ru(II) dyes for dye-sensitized solar cells (DSCs). The employed computational setup accurately reproduces the optical properties of the investigated dyes, allowing an assessment of the factors responsible for the varying SOC with the dye metal-ligand environment. While for the prototypical panchromatic black dye sensitizer a negligible SOC effect is found, the SOC-induced spectral broadening calculated for the recently reported DX1 dye partly enhances the light-harvesting efficiency and consequently the photocurrent generation in DSCs based on this dye.