Linear-response time-dependent density-functional theory with pairing fields.

For many types of vertical excitation energies, linear-response time-dependent density functional theory (LR-TDDFT) offers a useful degree of accuracy combined with unrivaled computational efficiency, although charge-transfer excitation energies are often systematically and dramatically underestimated, especially for large systems and those that contain explicit solvent. As a result, low-energy electronic spectra of solution-phase chromophores often contain tens to hundreds of spurious charge-transfer states, making LR-TDDFT needlessly expensive in bulk solution. Intensity borrowing by these spurious states can affect intensities of the valence excitations, altering electronic bandshapes. At higher excitation energies, it is difficult to distinguish spurious charge-transfer states from genuine charge-transfer-to-solvent (CTTS) excitations. In this work, we introduce an automated diabatization that enables fast and effective screening of the CTTS acceptor space in bulk solution. Our procedure introduces ``natural charge-transfer orbitals'' that provide a means to isolate orbitals that are most likely to participate in a CTTS excitation. Projection of these orbitals onto solvent-centered virtual orbitals provides a criterion for defining the most important solvent molecules in a given excitation and be used as an automated subspace selection algorithm for projection-based embedding of a high-level description of the CTTS state in a lower-level description of its environment. We apply this method to an ab initio molecular dynamics trajectory of I-(aq) and report the lowest-energy CTTS band in the absorption spectrum. Our results are in excellent agreement with experiment and only one-third of the water molecules in the I-(H2O)96 simulation cell need to be described with LR-TDDFT in order to obtain excitation energies that are converged to <0.1 eV. The tools introduced herein will improve the accuracy, efficiency, and usability of LR-TDDFT in solution-phase environments.

The asymmetric Hubbard dimer is used to study the density-dependence of the exact frequency-dependent kernel of linear-response time-dependent density functional theory. The exact form of the kernel is given, and the limitations of the adiabatic approximation utilizing the exact ground-state functional are shown. The oscillator strength sum rule is proven for lattice Hamiltonians, and relative oscillator strengths are defined appropriately. The method of Casida for extracting oscillator strengths from a frequency-dependent kernel is demonstrated to yield the exact result with this kernel. An unambiguous way of labelling the nature of excitations is given. The fluctuation-dissipation theorem is proven for the ground-state exchange-correlation energy. The distinction between weak and strong correlation is shown to depend on the ratio of interaction to asymmetry. A simple interpolation between carefully defined weak-correlation and strong-correlation regimes yields a density-functional approximation for the kernel that gives accurate transition frequencies for both the single and double excitations, including charge-transfer excitations. Many exact results, limits, and expansions about those limits are given in the appendices.

This article summarizes basic aspects of time‐dependent density functional theory (TD‐DFT) and its applications in inorganic chemistry. Sections titled TD‐DFT and Spectroscopic Properties outline some of the theoretical formalism and explain how excitation energies can be obtained from TD‐DFT linear response theory. Common approximations in density functional theory (DFT) exchange‐correlation (XC) potentials that might have adverse effects on the accuracy of computed results are explained. Sections titled Benchmark Data and Some Case Studies discuss a number of case studies, with emphasis on TD‐DFT excitation spectra computations in coordination chemistry. Computations of spectra and other properties of metals clusters are also discussed. Apart from excitation spectra, this section also describes TD‐DFT computations of Raman intensities (including resonance Raman and surface‐enhanced Raman spectra (SERS)), magnetic circular dichroism, optical rotatory dispersion (CD and ORD), and concludes with some comments on relativistic effects.

High performance computing is a powerful tool to accelerate the Kohn–Sham density functional theory calculations on modern heterogeneous supercomputers. Here, we describe a massively parallel implementation of large-scale linear-response time-dependent density functional theory (LR-TDDFT) to calculate the excitation energies and wave functions of solids with plane-wave basis set. We adopt a two-level parallelization strategy that combines the message passing interface with open multi-processing parallel programming to deal with the matrix operations and data communications of constructing and diagonalizing the LR-TDDFT Hamiltonian matrix. Numerical results illustrate that the LR-TDDFT calculations can scale up to 24 576 processing cores on modern heterogeneous supercomputers to study the excited state properties of bulky silicon systems containing thousands of atoms (4,096 atoms). We demonstrate that the LR-TDDFT calculations can be used to investigate the photoinduced charge separation of water molecule adsorption on rutile TiO2(110) surface from an excitonic perspective.

We present an efficient implementation of the analytical nuclear gradient of linear-response time-dependent density functional theory (LR-TDDFT) with the frozen core approximation (FCA). This implementation is realized based on the Hutter’s formalism and the plane wave pseudopotential method. Numerical results demonstrate that the LR-TDDFT/FCA method using a small subset of Kohn–Sham occupied orbitals are accurate enough to reproduce the LR-TDDFT results. Here, the FCA remarkably reduces the computational cost in solving the LR-TDDFT eigenvalue equation. Another challenge in the calculations of analytical nuclear gradients for LR-TDDFT is the solution of the Z-vector equation, for which the Davidson algorithm is a popular choice. While, for large systems the standard Davidson algorithm exhibits a low convergence rate. In order to overcome this problem, we generalize the two-level Davidson algorithm to solve linear equation problems. A more stable performance is achieved with this new algorithm. Our method should encourage further studies of excited-state properties with LR-TDDFT in the plane wave basis.

We present a range-separated linear-response time-dependent density-functional theory (TDDFT) which combines a density-functional approximation for the short-range response kernel and a frequency-dependent second-order Bethe-Salpeter approximation for the long-range response kernel. This approach goes beyond the adiabatic approximation usually used in linear-response TDDFT and aims at improving the accuracy of calculations of electronic excitation energies of molecular systems. A detailed derivation of the frequency-dependent second-order Bethe-Salpeter correlation kernel is given using many-body Green-function theory. Preliminary tests of this range-separated TDDFT method are presented for the calculation of excitation energies of the He and Be atoms and small molecules (H2, N2, CO2, H2CO, and C2H4). The results suggest that the addition of the long-range second-order Bethe-Salpeter correlation kernel overall slightly improves the excitation energies.

The ab initio GW plus Bethe-Salpeter equation (GW-BSE, where G is the one particle Green's function and W is the screened Coulomb interaction) approach has emerged as a leading method for predicting excitations in both solids and molecules with a predictive power contingent upon several factors. Among these factors are the (1) generalized Kohn-Sham eigensystem used to construct the GW self-energy and to solve the BSE and (2) the efficacy and suitability of the Tamm-Dancoff approximation. Here, we present a detailed benchmark study of low-lying singlet excitations from a generalized Kohn-Sham (gKS) starting point based on an optimally tuned range-separated hybrid (OTRSH) functional. We show that the use of this gKS starting point with one-shot G0W0 and G0W0-BSE leads to the lowest mean absolute errors (MAEs) and mean signed errors (MSEs), with respect to high-accuracy reference values, demonstrated in the literature thus far for the ionization potentials of the GW100 benchmark set and for low-lying neutral excitations of Thiel's set molecules in the gas phase, without the need for self-consistency. The MSEs and MAEs of one-shot G0W0-BSE@OTRSH excitation energies are comparable to or lower than those obtained with other functional starting points after self-consistency. Additionally, we compare these results with linear-response time-dependent density functional theory (TDDFT) calculations and find GW-BSE to be superior to TDDFT when calculations are based on the same exchange-correlation functional. This work demonstrates tuned range-separated hybrids used in combination with GW and GW-BSE can greatly suppress starting point dependence for molecules, leading to accuracy similar to that for higher-order wavefunction-based theories for molecules without the need for costlier iterations to self-consistency.

An efficient computational protocol for the prediction of vibrationally resolved phosphorescence spectra is developed and validated for five tris(2,2'-bipyridine)-metal complexes ([M(bpy)3]n+, where M = Zn, Ru, Rh, Os, Ir). The outstanding feature of this protocol is the use of full linear-response time-dependent density functional theory (TDDFT) for the excited-state triplet calculation, i.e., the commonly seen strategies employing the Tamm-Dancoff approximation (TDA) or unrestricted density functional theory (DFT) calculations for the T1 state are not needed. This is achieved by the use of a local hybrid functional (LH12ct-SsirPW92) that features a real-space dependent admixture of exact exchange governed by a local mixing function. The excellent performance of this LH for triplet excitation energies known from previous studies transfers to a remarkable mean absolute error of 0.06 eV for the phosphorescence 0-0 energies investigated herein, while the popular B3PW91 functional gives an error of 0.27 eV in TDDFT and 0.09 eV in unrestricted DFT calculations, respectively. The advantages of the local hybrid are particularly apparent for excited states with a mixed-valence character. The influence of spin-orbit coupling was found to be significant for [Os(bpy)3]2+ red-shifting the 0-0 energy for phosphorescence by 0.17 eV, while the effect is negligible for the other complexes (<0.03 eV). The influence of the basis-set and integration-grid sizes is evaluated, and a computationally lighter protocol is validated that leads to drastic savings in computation time with negligible loss in accuracy.

Inspired by the analysis of Kohn-Sham energy densities by Nakai et al, we extended the energy density analysis to linear-response time-dependent density functional theory (LR-TDDFT) calculations. Using ethylene-tetrafluoroethylene and oxyluciferin–water complexes as examples, distinctive distribution patterns were demonstrated for the excitation energy densities of local excitations (within a molecular fragment) and charge-transfer excitations (between molecular fragments). It also provided a simple way to compute the effective energy of both hot carriers (particle and hole) from charge-transfer excitations via an integration of the excitation energy density over the donorand acceptor grid points.

Linear-response time-dependent density-functional theory (TDDFT) can describe excitonic features in the optical spectra of insulators and semiconductors, using exchange-correlation (xc) kernels behaving as -1/k^{2} to leading order. We show how excitons can be modeled in real-time TDDFT, using an xc vector potential constructed from approximate, long-range corrected xc kernels. We demonstrate, for various materials, that this real-time approach is consistent with frequency-dependent linear response, gives access to femtosecond exciton dynamics following short-pulse excitations, and can be extended with some caution into the nonlinear regime.

Valence-to-core (VtC) X-ray emission spectroscopy (XES) has emerged as a powerful technique for the structural characterization of complex organometallic compounds in realistic environments. Since the spectrum represents electronic transitions from the ligand molecular orbitals to the core holes of the metal centers, the approach is more chemically sensitive to the metal-ligand bonding character compared with conventional X-ray absorption techniques. In this paper we study how linear-response time-dependent density functional theory (LR-TDDFT) can be harnessed to simulate K-edge VtC X-ray emission spectra reliably. LR-TDDFT allows one to go beyond the single-particle picture that has been extensively used to simulate VtC-XES. We consider seven low- and high-spin model complexes involving chromium, manganese, and iron transition metal centers. Our results are in good agreement with experiment.

Recent experimental and theoretical studies have shown several new organic molecules that violate Hund’s rule and have the first singlet excited state lower in energy than the first triplet excited state. While many correlated single reference wave function methods have successfully predicted excited-state energetics of these low-lying states, conventional linear-response time-dependent density functional theory (TDDFT) fails to predict the correct excited-state energy ordering. In this article, we have explored the performance of combined DFT and wave function methods like doubles-corrected TDDFT and multiconfiguration pair-density functional theory for the calculation of inverted singlet–triplet gaps. We have also tested the performance of the excited-state DFT (eDFT) method for this problem. Our results have shown that it is possible to obtain inverted singlet–triplet gaps both by using doubles-corrected TDDFT with a proper choice of double-hybrid functionals or by using eDFT.

Correction for 'Computational approaches for XANES, VtC-XES, and RIXS using linear-response time-dependent density functional theory based methods' by Daniel R. Nascimento et al., Phys. Chem. Chem. Phys., 2022, 24, 14680-14691, https://doi.org/10.1039/D2CP01132H.

The effect of a condensed-phase environment on the ultraviolet-visible (UV-vis) absorption spectra of chromophores is of fundamental interest in many phenomena, such as color tuning in photobiology and the solvatochromic shift in chemistry. The experimental measurement of UV-vis absorption spectra can provide the information on the spectral region of the absorption of the sample. While computer simulation of the UV-vis absorption spectra can provide the microscopic interpretation of the absorption bands. Moreover, computer simulations can be done for the cases that are impractical for experimental measurements. This thesis work aims to develop proper computational strategies to calculate the UV-vis absorption of organic chromophores in a condensed-phase environment, and to interpret the experimental results or to tackle problems that are difficult for experimental approaches. Simulation of the UV-vis absorption spectra typically involves modeling of the structure of the target system and the calculation of its vertical electronic excitation energies and oscillator strengths of the interesting part of the system. The large size of the condensed phase makes both parts of the simulation very challenging. In this thesis work, frozen-density embedding theory, one of the appropriate approaches on the market for tackling large systems, combined with linear-response time-dependent density-functional theory, is used to calculate the vertical electronic excitation energies and the oscillator strengths of the chromophores in condensed phases. This thesis work investigates the effect of condensed-phase environments on the UV-vis absorption spectra of organic chromophores for several systems, including a functional host-guest material (fluorenone in zeolite-L channel), a chemical solvation system (coumarin 153 in various solvents), and fundamental biological systems in the eye (retinal in rhodopsin and in three visual cone pigments).

In this paper, we demonstrate the performance of several density-based methods in predicting the inversion of S1 and T1 states of a few N-heterocyclic triangulene based fused ring molecules (popularly known as INVEST molecules) with an eye to identify a well performing but cost-effective preliminary screening method. Both conventional linear-response time-dependent density functional theory (LR-TDDFT) and ΔSCF methods (namely maximum overlap method, square-gradient minimization method, and restricted open-shell Kohn-Sham) are considered for excited state computations using exchange-correlation (XC) functionals from different rungs of Jacob's ladder. A well-justified systematism is observed in the performance of the functionals when compared against fully internally contracted multireference configuration interaction singles and doubles and/or equation of motion coupled-cluster singles and doubles (EOM-CCSD), with the most important feature being the capture of spin-polarization in the presence of correlation. A set of functionals with the least mean absolute error is proposed for both the approaches, LR-TDDFT and ΔSCF, which can be more cost-effective alternatives for computations on synthesizable larger derivatives of the templates studied here. We have based our findings on extensive studies of three cyclazine-based molecular templates, with additional studies on a set of six related templates. Previous benchmark studies for subsets of the functionals were conducted against the domain-based local pair natural orbital-similarity transformed EOM-CCSD (STEOM-CCSD), which resulted in an inadequate evaluation due to deficiencies in the benchmark theory. The role of exact-exchange, spin-contamination, and spin-polarization in the context of DFT comes to the forefront in our studies and supports the numerical evaluation of XC functionals for these applications. Suitable connections are drawn to two and three state exciton models, which identify the minimal physics governing the interactions in these molecules.