Cross-Comparisons between Experiment, TD-DFT, CC, and ADC for Transition Energies

Restricted open-shell time-dependent density functional theory with perturbative spin-orbit coupling

When using quantum chemical methods to study electronically excited states of open-shell molecules, it is often beneficial to start with wave functions that are spin eigenfunctions. For excited states of molecules containing heavy elements, spin-orbit coupling (SOC) is important and needs to be included as well. An efficient approach is to include SOC perturbatively on top of a restricted open-shell Kohn-Sham (ROKS) time-dependent density functional theory, which can be combined with the Tamm-Dancoff approximation (TDA) to suppress numerical instabilities. We implemented and assessed the potential of such a ROKS-TDA-SOC method, also featuring the possibility of calculating transition dipole moments between states to allow for full spectrum simulation. Our study shows that the ROKS-TDA-SOC formalism yields a clear and easy-to-use method to obtain electronically excited states of open-shell molecules that are of moderate size and contain heavy elements.

Spurious Oscillations Caused by Density Functional Approximations: Who is to Blame? Exchange or Correlation?

We analyze the varying susceptibilities of different density functional approximations (DFAs) to present spurious oscillations on the profiles of several vibrational properties. Among other problems, these spurious oscillations cause significant errors in harmonic and anharmonic IR and Raman frequencies and intensities. This work hinges on a judicious strategy to dissect the exchange and correlation components of DFAs and pinpoint the origins of these oscillations. We identify spurious oscillations in derivatives of all energy components with respect to nuclear displacements, including those energy terms that do not involve numerical integrations. These indirect spurious oscillations are attributed to suboptimal electron densities resulting from a self-consistent field procedure using a DFA that exhibits direct spurious oscillations. Direct oscillations stem from inaccurate numerical integration of the exchange and correlation energy density functionals. A thorough analysis of direct spurious oscillations reveals that only a handful of exchange and correlation components are insensitive to spurious oscillations, giving rise to three families of functionals, BH&H, LSDA, and BLYP. Among the functionals in these families, we encounter four widespread DFAs: BLYP, B3LYP, LC-BLYP, and CAM-B3LYP. Certain DFAs like PBE appear less sensitive to spurious oscillations due to compensatory cancellations between their energy components. Additionally, we found non-negligible but small oscillations in PBE and TPSS, which could be safely employed provided a sufficiently large integration grid is used in the calculations. These findings hint at the key components of current approximations to be improved and emphasize the necessity to develop accurate DFAs suitable for studying molecular spectroscopies.

Role of Singles Amplitudes in ADC(2) and CC2 for Low-Lying Electronically Excited States

The closely related second-order methods CC2 and ADC(2) usually perform very similarly for single excitations of organic molecules. However, as rationalized in this work, significant deviations between these two methods can arise if the ground state and a low-lying singly excited state arise from a strong coupling between their leading configurations. Such a configuration mixing is partially accounted for in CC2 through the ground-state singles amplitudes but is omitted in ADC(2). This can cause unusual deviations between the results obtained with these methods. In this work, we study how severe this effect can become at the example of two solvatochromic dyes: the negatively solvatochromic betaine dye N1-tBu and the positively solvatochromic bithiophene P1. These two dyes allow one to study the limits of both small and somewhat larger excitation energies and configuration mixing by tuning the S0 → S1 transition energy through the polarity of the environment. Higher-level calculations at the CC3 level provide information on the accuracy of ADC(2) and CC2 in these cases. The most extreme deviation between ADC(2) and CC2 is found for N1-tBu in vacuum, where the ADC(2) result is 0.45 eV below that of CC2. In this case, the methodical error of CC2 with respect to CC3 is only 0.05 eV. With increasing excitation energy in polar solvents, the CC2-ADC(2) deviation decreases and reaches a value of only 0.15 eV. For P1, which has larger excitation energies, these effects are reversed due to the opposite solvatochromism but also smaller in magnitude: the deviation increases from 0.08 eV in vacuum to 0.16 eV in the so-called conductor limit of the continuum solvation model. Although for these two dyes larger deviations are observed for smaller excitation energies, the extent of configuration mixing does not generally correlate with only the size of excitation energy. For example, s-triazine (0.15 eV), formamide (0.19 eV), and formaldehyde (0.23 eV) also show large deviations between CC2 and ADC(2) despite their much higher excitation energies compared to those of N1-tBu and P1.

DELFI: a computer oracle for recommending density functionals for excited states calculations

Density functional theory (DFT) is the workhorse of computational quantum chemistry. One of its main limitations is that choosing the right functional is a non-trivial task left for human experts. The choice is particularly hard for excited state calculations when using its time-dependent formulation (TD-DFT). This is due to the approximations of the method, but also because the photophysical properties of a molecule are defined by a manifold of states that all need to be properly described. This includes not only the relative energy of the states, but also capturing the correct character, order, and intensity of the transitions. In this work, we developed a neural network to recommend functionals to be used on molecules for TD-DFT calculations, by simultaneously considering all these properties for a manifold of states. This was possible by developing a scoring system to define the accuracy of an excited state's calculation against a higher-accuracy reference. The scoring system is generalizable to any level of theory; we here applied it to evaluate the performance of common functionals of different rungs against a higher accuracy method on a large set of organic molecules. The results are collected in a database that we released and made open, providing four million data points to the community for future applications. The scoring system assigns a value between zero and one hundred to each functional for each molecule, transforming the complicated task of learning photophysical properties into a simpler regression task. We used the dataset to train a graph attention neural network to predict the scores for unseen molecules. We call this oracle DELFI (Data-driven EvaLuation of Functionals by Inference), which can be used to quickly screen and predict the ranking of functionals to calculate the optical properties of organic molecules. We validated DELFI in two in silico experiments: choosing a common functional for a series of spiropyran-merocyanine isomers and a unique functional to screen a large dataset of over 50 000 organic photovoltaic molecules, for which an extensive benchmark would be unfeasible. A corresponding web application allows DELFI to be easily run and the results to be analyzed, alleviating the hurdle of choosing the right functional for TD-DFT calculations.

Non-linear light-matter interactions from the Bethe-Salpeter equation

A route to assess non-linear light-matter interactions from the increasingly popular GW-Bethe-Salpeter equation (GW-BSE) method is outlined. In the present work, the necessary analytic expressions within the static-screened exchange approximation of the BSE are derived. This enables a straightforward implementation of the computation of the first hyperpolarizability as well as two-photon absorption processes for molecular systems. Benchmark calculations on small molecular systems reveal that the GW-BSE method is intriguingly accurate for predicting both first hyperpolarizabilities and two-photon absorption strengths. Using state-of-the-art Kohn-Sham references as a starting point, the accuracy of the GW-BSE method rivals that of the coupled-cluster singles-and-doubles method, outperforming both second-order coupled-cluster and time-dependent density-functional theory.

Pitfall in simulations of vibronic TD-DFT spectra: diagnosis and assessment

In this Communication, we study the effect of spurious oscillations in the profiles of energy derivatives with respect to nuclear coordinates calculated with density functional approximations (DFAs) for formaldehyde, pyridine, and furan in their ground and electronic excited states. These spurious oscillations, which can only be removed using extensive integration grids that increase enormously the CPU cost of DFA calculations, are significant in the case of third- and fourth-order energy derivatives of the ground and excited states computed by M06-2X and ωB97X functionals. The errors in question propagate to anharmonic vibronic spectra computed under the Franck-Condon approximation, i.e., positions and intensities of vibronic transitions are affected to a large extent (shifts as significant as hundreds of cm-1 were observed). On the other hand, the LC-BLYP and CAM-B3LYP functionals show a much less pronounced effect due to spurious oscillations. Based on the results presented herein, we recommend either LC-BLYP or CAM-B3LYP with integration grids (250, 974) (or larger) for numerically stable simulations of vibronic spectra including anharmonic effects.

The Best Models of Bodipy's Electronic Excited State: Comparing Predictions from Various DFT Functionals with Measurements from Femtosecond Stimulated Raman Spectroscopy

Density functional theory (DFT) and time-dependent DFT (TD-DFT) are pivotal approaches for modeling electronically excited states of molecules. However, choosing a DFT exchange-correlation functional (XCF) among the myriad of alternatives is an overwhelming task that can affect the interpretation of results and lead to erroneous conclusions. The performance of these XCFs to describe the excited-state properties is often addressed by comparing them with high-level wave function methods or experimentally available vertical excitation energies; however, this is a limited analysis that relies on evaluation of a single point in the excited-state potential energy surface (PES). Different strategies have been proposed but are limited by the difficulty of experimentally accessing the electronic excited-state properties. In this work, we have tested the performance of 12 different XCFs and TD-DFT to describe the excited-state potential energy surface of Bodipy (2,6-diethyl-1,3,5,7-tetramethyl-8-phenyldipyrromethene difluoroborate). We compare those results with resonance Raman spectra collected by using femtosecond stimulated Raman spectroscopy (FSRS). By simultaneously fitting the absorption spectrum, fluorescence spectrum, and all of the resonance Raman excitation profiles within the independent mode displaced harmonic oscillator (IMDHO) formalism, we can describe the PES at the Franck-Condon (FC) region and determine the solvent and intramolecular reorganization energy after relaxation. This allows a direct comparison of the TD-DFT output with experimental observables. Our analysis reveals that using vertical absorption energies might not be a good criterion to determine the best XCF for a given molecular system and that FSRS opens up a new way to benchmark the excited-state performance of XCFs of fluorescent dyes.

Gas-phase C60Hn+q (n = 0-4, q = 0,1) fullerenes and fulleranes: spectroscopic simulations shed light on cosmic molecular structures

The discovery of C60, C60+, and C70 in the interstellar medium has ignited a profound interest in the astrochemistry of fullerene and related systems. In particular, the presence of diffuse interstellar bands and their association with C60+ has led to the hypothesis that hydrogenated derivatives, known as fulleranes, may also exist in the interstellar medium and contribute to these bands. In this study, we systematically investigated the structural and spectroscopic properties of C60Hn+q (n = 0-4, q = 0,1) using an automated global minimum search and density functional theory calculations. Our results revealed novel global minimum structures for C60H2 and C60H4, distinct from previous reports. Notably, all hydrogenated fullerenes exhibited lower ionization potentials and higher proton affinities compared to C60. From an astrochemical perspective, our results exposed the challenges in establishing definitive spectroscopic criteria for detecting fulleranes using mid-infrared and UV-Vis spectroscopies. However, we successfully identified distinct electronic transitions in the near-infrared range that serve as distinctive signatures of cationic fulleranes. We strongly advocate for further high-resolution experimental studies to fully explore the potential of these transitions for the interstellar detection of fulleranes.

Gauge-Invariant Excited-State Linear and Quadratic Response Properties within the Meta-Generalized Gradient Approximation

Gauge invariance is a fundamental symmetry connected to charge conservation and is widely accepted as indispensable for any electronic structure method. Hence, the gauge variance of the time-dependent kinetic energy density τ used in many meta-generalized gradient approximations (MGGAs) to the exchange-correlation (XC) functional presents a major obstacle for applying MGGAs within time-dependent density functional theory (TDDFT). Replacing τ by the gauge-invariant generalized kinetic energy density τ̂ significantly improves the accuracy of various functionals for vertical excitation energies [R. Grotjahn, F. Furche, and M. Kaupp. J. Chem. Phys. 2022, 157, 111102]. However, the dependence of the resulting current-MGGAs (cMGGAs) on the paramagnetic current density gives rise to new exchange-correlation kernels and hyper-kernels ignored in previous implementations of quadratic and higher-order response properties. Here we report the first implementation of cMGGAs and hybrid cMGGAs for excited-state gradients and dipole moments, as well as an extension to quadratic response properties including dynamic hyperpolarizabilities and two-photon absorption cross sections. In the first comprehensive benchmark study of MGGAs and cMGGAs for two-photon absorption cross sections, the M06-2X functional is found to be superior to the GGA hybrid PBE0. Additionally, two case studies from the literature for the practical prediction of nonlinear optical properties are revisited and potential advantages of hybrid (c)MGGAs compared to hybrid GGAs are discussed. The effect of restoring gauge invariance varies depending on the employed MGGA functional, the type of excitation, and the property under investigation: While some individual excited-state equilibrium structures are significantly affected, on average, these changes result in marginal improvements when compared against high-level reference data. Although the gauge-variant MGGA quadratic response properties are generally close to their gauge-invariant counterparts, the resulting errors are not bounded and significantly exceed typical method errors in some of the cases studied. Despite the limited effects seen in benchmark studies, gauge-invariant implementations of cMGGAs for excited-state properties are desirable from a fundamental perspective, entail little additional computational cost, and are necessary for response properties consistent with cMGGA linear response calculations such as excitation energies.

Cost-Effective Simulations of Vibrationally-Resolved Absorption Spectra of Fluorophores with Machine-Learning-Based Inhomogeneous Broadening

The results of electronic and vibrational structure simulations are an invaluable support for interpreting experimental absorption/emission spectra, which stimulates the development of reliable and cost-effective computational protocols. In this work, we contribute to these efforts and propose an efficient first-principle protocol for simulating vibrationally-resolved absorption spectra, including nonempirical estimations of the inhomogeneous broadening. To this end, we analyze three key aspects: (i) a metric-based selection of density functional approximation (DFA) so to benefit from the computational efficiency of time-dependent density function theory (TD-DFT) while safeguarding the accuracy of the vibrationally-resolved spectra, (ii) an assessment of two vibrational structure schemes (vertical gradient and adiabatic Hessian) to compute the Franck-Condon factors, and (iii) the use of machine learning to speed up nonempirical estimations of the inhomogeneous broadening. In more detail, we predict the absorption band shapes for a set of 20 medium-sized fluorescent dyes, focusing on the bright ππ^★ S₀ → S₁ transition and using experimental results as references. We demonstrate that, for the studied 20-dye set which includes structures with large structural variability, the preselection of DFAs based on an easily accessible metric ensures accurate band shapes with respect to the reference approach and that range-separated functionals show the best performance when combined with the vertical gradient model. As far as band widths are concerned, we propose a new machine-learning-based approach for determining the inhomogeneous broadening induced by the solvent microenvironment. This approach is shown to be very robust offering inhomogeneous broadenings with errors as small as 2 cm^-1 with respect to genuine electronic-structure calculations, with a total CPU time reduced by 98%.

Activating Electroluminescence of Charged Naphthalene Diimide Complexes Directly Adsorbed on a Metal Substrate

Electroluminescence from single molecules adsorbed on a conducting surface imposes conflicting demands for the molecule-electrode coupling. To conduct electrons, the molecular orbitals need to be hybridized with the electrodes. To emit light, they need to be decoupled from the electrodes to prevent fluorescence quenching. Here, we show that fully quenched 2,6-core-substituted naphthalene diimide derivative in a self-assembled monolayer directly deposited on a Au(111) surface can be activated with the tip of a scanning tunneling microscope to decouple the relevant frontier orbitals from the metallic substrate. In this way, individual molecules can be driven from a strongly hybridized state with quenched luminescence to a light-emitting state. The emission performance compares in terms of quantum efficiency, stability, and reproducibility to that of single molecules deposited on thin insulating layers. Quantum chemical calculations suggest that the emitted light originates from the singly charged cationic pair of the molecules.

Multiple Facets of Modeling Electronic Absorption Spectra of Systems in Solution

In this Perspective, we outline the essential physicochemical aspects that need to be considered when building a reliable approach to describe absorption properties of solvated systems. In particular, we focus on how to properly model the complexity of the solvation phenomenon, arising from dynamical aspects and specific, strong solute-solvent interactions. To this end, conformational and configurational sampling techniques, such as Molecular Dynamics, have to be coupled to accurate fully atomistic Quantum Mechanical/Molecular Mechanics (QM/MM) methodologies. By exploiting different illustrative applications, we show that an effective reproduction of experimental spectral signals can be achieved by delicately balancing exhaustive sampling, hydrogen bonding, mutual polarization, and nonelectrostatic effects.

A DFT Study on the Excited Electronic States of Cyanopolyynes: Benchmarks and Applications

Highly unsaturated chain molecules are interesting due to their potential application as nanowires and occurrence in interstellar space. Here, we focus on predicting the electronic spectra of polyynic nitriles HC2m+1N (m = 0–13) and dinitriles NC2n+2N (n = 0–14). The results of time-dependent density functional theory (TD-DFT) calculations are compared with the available gas-phase and noble gas matrix experimental data. We assessed the performance of fifteen functionals and five basis sets for reproducing (i) vibrationless electronic excitation energies and (ii) vibrational frequencies in the singlet excited states. We found that the basis sets of at least triple-ζ quality were necessary to describe the long molecules with alternate single and triple bonds. Vibrational frequency scaling factors are similar for the ground and excited states. The benchmarked spectroscopic parameters were shown to be acceptably reproduced with adequately chosen functionals, in particular ωB97X, CAM-B3LYP, B3LYP, B971, and B972. Select functionals were applied to study the electronic excitation of molecules up to HC27N and C30N2. It is demonstrated that optical excitation leads to a shift from the polyyne- to a cumulene-like electronic structure.

Evaluating the impact of Hartree-Fock exact exchange on the performance of global hybrid functionals for the vertical excited-state energies of fused-ring electron acceptors using TD-DFT

The acceptor-donor-acceptor structured fused-ring electron acceptors (FREAs) have piqued interest for organic solar cells. We herein employ time-dependent density functional theory to evaluate the effect of Hartree-Fock exact exchange (HFX) on the performance of 16 global hybrid functionals for computing the maximum absorption wavelengths (λ_ver-theo) and the vertical excitation energies (E_ver-theo) of 34 molecules. We customize the HFX ratio in the functionals used to perform an in-depth analysis of its impact on the E_ver-theo values. The computed λ_ver-theo values strictly follow an inverse proportionality to the HFX percentage. The performance of the methods with the same ratio of HFX is almost identical, such as B3LYP, B3PW91, and mPW3PBE containing 20% HFX. The performance enhances with a relatively higher HFX ratio of 21% in X3LYP, B971, B972, and 22% in B98 giving smaller deviations. APF and APFD containing 23% HFX provide the smallest deviations for all compounds, with a mean signed error limited to 0.02 eV and a mean absolute error (MAE) of 0.06 eV. The performance drops using M06 and M05 with comparatively higher HFX ratios providing MAE values of 0.07 eV and 0.1 eV, respectively. M06-2X with 54% HFX provides the largest MAE value of 0.35 eV. The lowest obtained MAE is 0.06 eV at 23 to 25% HFX in most of the functionals considered in this study, suggesting that these are the optimal values for the prediction of excitation energies of FREAs. It has also been found that global hybrids seem to be more efficient for larger-sized molecules with a smaller bandgap.

An optimally tuned range-separated hybrid starting point for ab initio GW plus Bethe–Salpeter equation calculations of molecules

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.

Theoretical study on the mechanism of hot excitons combined with aggregation-induced emission in efficient red fluorescent molecules

Fluorescent emitters with the hot exciton mechanism combined with aggregation induced emission (AIE) character show prospective applications in organic light emitting diodes (OLEDs). However, theoretical studies on amorphous states are limited. In this work, a theoretical study is performed on the photophysical properties of the reported compound 4-(7-(10-ethyl-10H-phenothiazin-3-yl)benzo[c][1,2,5]thiadiazol-4-yl)-N,N-diphenylaniline (PBTPA), which possesses a hot exciton mechanism and AIE. The aggregation states of this molecule in a film are given by molecular dynamics (MD) simulations, and then the photophysical properties are studied by using the QM/MM method with the consideration of the solid-state effect (SSE). The results explain the hot exciton and AIE mechanism of the molecule. First, there is a hot exciton channel between the S₁ and T₂ state of the PBTPA. Second, the conformational changes of PBTPA between the ground state and the excited state are restricted in the aggregate state. Last, in the low frequency region, the rotation motion is suppressed, and then the reorganization energy and Huang-Rhys (HR) factor in the aggregate state are much smaller. Therefore, the molecules show strong fluorescence efficiency in the aggregated state.

A Local Hybrid Exchange Functional Approximation from First Principles

Local hybrid functionals are a more flexible class of density functional approximations allowing for a position-dependent admixture of exact exchange. This additional flexibility, however, comes with a more involved mathematical form and a more complicated design. A common denominator for previously constructed local hybrid funtionals is usage of thermochemical benchmark data to construct these functionals. Herein, we design a local hybrid functional without relying on benchmark data. Instead, we construct it in a more ab initio manner, following the principles of modern meta-generalized gradient approximations and considering theoretical constrains. To achieve this, we make use of the density matrix expansion and a local mixing function based on an approximate correlation length. The accuracy of the developed density functional approximation is assessed for thermochemistry, excitation energies, polarizabilities, magnetizabilities, NMR spin-spincoupling constants, NMR shieldings and shifts, as well as EPR g-tensors and hyperfine coupling constants. Here, the new exchange functional shows a robust performance and is especially well suited for atomization energies, barrier heights, excitation energies, NMR coupling constants, and EPR properties, whereas it looses some ground for the NMR shifts.Therefore, the designed functional is a major step forwards for functionals that have been designed from first principles.

Linear Response of Current-Dependent Density Functional Approximations in Magnetic Fields

This Letter outlines the steps and derivations that are necessary to apply density functional approximations that depend on the current and kinetic energy density rigorously within the framework of linear-response methods, including adiabatic time-dependent current density functional theory. This includes systems with a non-zero current density in the ground state. The necessary exchange-correlation kernel for these density functional approximations is derived, and the matrix elements are given explicitly. Due to the gauge variance of the kinetic energy density in an external magnetic field, having access to the proper current-dependent exchange-correlation kernel is necessary to recover gauge invariance for excited states. As a proof of principle application, the excited states of two small molecules in strong external magnetic fields are calculated using linear-response time-dependent current density functional theory. Finally, the implications of the derived current density-dependent exchange-correlation kernel for systems with strong spin-orbit coupling are discussed.

Automated Generation of Optimized Auxiliary Basis Sets for Long-Range-Corrected TDDFT Using the Cholesky Decomposition

Range-separated hybrid functionals making use of a smooth separation of the Coulomb operator in terms of the error function and its complement have proven to be a valuable tool for improving Kohn-Sham density functional theory (DFT) calculations. This holds in particular for obtaining accurate excitation energies from linear-response time-dependent DFT. Evaluating the long-range exchange contributions represents one of the most time-consuming tasks in such calculations. Prefitted auxiliary basis sets can be employed to speed up this step. Here, we present a way to generate auxiliary basis sets optimized to fit the long-range exchange contributions only, contrary to the common optimization strategies on the basis of the full Coulomb operator. For this purpose, we use the atomic Cholesky decomposition technique. The basis sets are generated on-the-fly using the specific range-separation parameter defined in the exchange-correlation functional. We obtain excitation energies and oscillator strengths which are of similar or better accuracy than those obtained with conventional resolution-of-the-identity auxiliary basis sets while drastically reducing the number of auxiliary functions required. This is demonstrated for the QUESTDB#5 benchmark set. In addition, we outline the benefits of this approach in sequences of calculations employing varying range-separation parameters, as is the case in the optimally tuned range-separation strategy. Finally, we illustrate the efficiency of this approach for real-world examples, namely, a chlorophyll tetramer from photosystem II and a carotenoid-porphyrin-C₆₀ triad.

Revisiting the Performance of Time-Dependent Density Functional Theory for Electronic Excitations: Assessment of 43 Popular and Recently Developed Functionals from Rungs One to Four

In this paper, the performance of more than 40 popular or recently developed density functionals is assessed for the calculation of 463 vertical excitation energies against the large and accurate QuestDB benchmark set. For this purpose, the Tamm-Dancoff approximation offers a good balance between computational efficiency and accuracy. The functionals ωB97X-D and BMK are found to offer the best performance overall with a root-mean square error (RMSE) of around 0.27 eV, better than the computationally more demanding CIS(D) wave function method with a RMSE of 0.36 eV. The results also suggest that Jacob's ladder still holds for time-dependent density functional theory excitation energies, though hybrid meta generalized-gradient approximations (meta-GGAs) are not generally better than hybrid GGAs. Effects of basis set convergence, gauge invariance correction to meta-GGAs, and nonlocal correlation (VV10) are also studied, and practical basis set recommendations are provided.

Machine learned calibrations to high-throughput molecular excited state calculations

Understanding the excited state properties of molecules provides insight into how they interact with light. These interactions can be exploited to design compounds for photochemical applications, including enhanced spectral conversion of light to increase the efficiency of photovoltaic cells. While chemical discovery is time- and resource-intensive experimentally, computational chemistry can be used to screen large-scale databases for molecules of interest in a procedure known as high-throughput virtual screening. The first step usually involves a high-speed but low-accuracy method to screen large numbers of molecules (potentially millions), so only the best candidates are evaluated with expensive methods. However, use of a coarse first-pass screening method can potentially result in high false positive or false negative rates. Therefore, this study uses machine learning to calibrate a high-throughput technique [eXtended Tight Binding based simplified Tamm-Dancoff approximation (xTB-sTDA)] against a higher accuracy one (time-dependent density functional theory). Testing the calibration model shows an approximately sixfold decrease in the error in-domain and an approximately threefold decrease in the out-of-domain. The resulting mean absolute error of ∼0.14 eV is in line with previous work in machine learning calibrations and out-performs previous work in linear calibration of xTB-sTDA. We then apply the calibration model to screen a 250k molecule database and map inaccuracies of xTB-sTDA in chemical space. We also show generalizability of the workflow by calibrating against a higher-level technique (CC2), yielding a similarly low error. Overall, this work demonstrates that machine learning can be used to develop a cost-effective and accurate method for large-scale excited state screening, enabling accelerated molecular discovery across a variety of disciplines.

Choosing Bad versus Worse: Predictions of Two-Photon-Absorption Strengths Based on Popular Density Functional Approximations

We present a benchmark study of density functional approximation (DFA) performances in predicting the two-photon-absorption strengths in π-conjugated molecules containing electron-donating/-accepting moieties. A set of 48 organic molecules is chosen for this purpose, for which the two-photon-absorption (2PA) parameters are evaluated using different DFAs, including BLYP, PBE, B3LYP, PBE0, CAM-B3LYP, LC-BLYP, and optimally tuned LC-BLYP. Minnesota functionals and ωB97X-D are also used, applying the two-state approximation, for a subset of molecules. The efficient resolution-of-identity implementation of the coupled-cluster CC2 model (RI-CC2) is used as a reference for the assessment of the DFAs. Two-state models within the framework of both DFAs and RI-CC2 are used to gain a deeper insight into the performance of different DFAs. Our results give a clear picture of the performance of the density functionals in describing the two-photon activity in dipolar π-conjugated systems. The results show that global hybrids are best suited to reproduce the absolute values of 2PA strengths of donor–acceptor molecules. The range-separated functionals CAM-B3LYP and optimally tuned LC-BLYP, however, show the highest linear correlations with the reference RI-CC2 results. Hence, we recommend the latter DFAs for structure–property studies across large series of dipolar compounds.

Surface modeling of photocatalytic materials for water splitting

The photocatalyst surface is central to photocatalytic reactions. However, it has been a challenge to explicitly understand both the surface configuration and the structure-dependent photocatalytic properties at the atomic level. First-principles density functional theory (DFT) calculations provide a versatile method that makes up for the lack of experimental surface studies. In DFT calculations, the initial surface model greatly affects the accuracy of the calculation results. Consequently, establishing a more realistic and more reliable material surface models is undoubtedly the first step and the most important link in theoretical calculations. The aim of this Perspective is to provide a general understanding of the methods for the surface modeling of photocatalytic materials in recent years. We begin with a discussion of the basic theories applied in photocatalytic surface research, followed by an explanation of the importance of surface modeling in photocatalysis. We then elaborate on the advantages and disadvantages of the basic surface model and briefly describe the latest surface modeling methods. Finally, we evaluate the rationality of current surface modeling methods. We summarize this Perspective by prospecting the developing directions of photocatalytic surface research in the future. It is believed that a reasonable surface model should be verified by both experimental characterization and theoretical computation with negative feedback.

The GW/BSE Method in Magnetic Fields

The GW approximation and the Bethe–Salpeter equation have been implemented into the Turbomole program package for computations of molecular systems in a strong, finite magnetic field. Complex-valued London orbitals are used as basis functions to ensure gauge-invariant computational results. The implementation has been benchmarked against triplet excitation energies of 36 small to medium-sized molecules against reference values obtained at the approximate coupled-cluster level (CC2 approximation). Finally, a spectacular change of colour from orange to green of the tetracene molecule is induced by applying magnetic fields between 0 and 9,000 T perpendicular to the molecular plane.

Benchmarking Density Functional Approximations for Excited-State Properties of Fluorescent Dyes

This study presents an extensive analysis of the predictive power of time-dependent density functional theory in determining the excited-state properties of two groups of important fluorescent dyes, difluoroboranes and hydroxyphenylimidazo[1,2-a]pyridine derivatives. To ensure statistically meaningful results, the data set is comprised of 85 molecules manifesting diverse photophysical properties. The vertical excitation energies and dipole moments (in the electronic ground and excited states) of the aforementioned dyes were determined using the RI-CC2 method (reference) and with 18 density functional approximations (DFA). The set encompasses DFAs with varying amounts of exact exchange energy (EEX): from 0% (e.g., SVWN, BLYP), through a medium (e.g., TPSSh, B3LYP), up to a major contribution of EEX (e.g., BMK, MN15). It also includes range-separated hybrids (CAM-B3LYP, LC-BLYP). Similar error profiles of vertical energy were obtained for both dye groups, although the errors related to hydroxyphenylimidazopiridines are significantly larger. Overall, functionals including 40-55% of EEX (SOGGA11-X, BMK, M06-2X) ensure satisfactory agreement with the reference vertical excitation energies obtained using the RI-CC2 method; however, MN15 significantly outperforms them, providing a mean absolute error of merely 0.04 eV together with a very high correlation coefficient (R2 = 0.98). Within the investigated set of functionals, there is no single functional that would equally accurately determine ground- and excited-state dipole moments of difluoroboranes and hydroxyphenylimidazopiridine derivatives. Depending on the chosen set of dyes, the most accurate μGS predictions were delivered by MN15 incorporating a major EEX contribution (difluoroboranes) and by PBE0 containing a minor EEX fraction (hydroxyphenylimidazopiridines). Reverse trends are observed for μES, i.e., for difluoroboranes the best results were obtained with functionals including a minor fraction of EEX, specifically PBE0, while in the case of hydroxyphenylimidazopiridines, much more accurate predictions were provided by functionals incorporating a major EEX contribution (BMK, MN15).

Dye-sensitized solar cells strike back

Dye-sensitized solar cells (DSCs) are celebrating their 30th birthday and they are attracting a wealth of research efforts aimed at unleashing their full potential. In recent years, DSCs and dye-sensitized photoelectrochemical cells (DSPECs) have experienced a renaissance as the best technology for several niche applications that take advantage of DSCs' unique combination of properties: at low cost, they are composed of non-toxic materials, are colorful, transparent, and very efficient in low light conditions. This review summarizes the advancements in the field over the last decade, encompassing all aspects of the DSC technology: theoretical studies, characterization techniques, materials, applications as solar cells and as drivers for the synthesis of solar fuels, and commercialization efforts from various companies.

Modeling Spectral Tuning in Red Fluorescent Proteins Using the Dipole Moment Variation upon Excitation

We describe a model for spectral tuning in red fluorescent proteins (RFPs) based on the relation between an electronic structure descriptor, the dipole moment variation upon excitation (DMV), and the excitation energy of a protein. This approach aims to overcome the problem of accurate prediction of excitation energies in RFPs, which span a very narrow window of band maxima. The latter roughly corresponds to the energy range of 0.1 eV, which is comparable with typical errors in calculations of the excitation energy by conventional quantum chemistry methods. In this work, we demonstrate a strong quantitative correlation between DMV values, obtained computationally with modest efforts, and excitation energies ΔE_ex at the experimental excitation band maxima for a series of RFPs with bands between 570 and 605 nm. Protein models are constructed by motifs of the relevant crystal structures, and atomic coordinates are optimized in quantum mechanics/molecular mechanics (QM/MM) calculations with QM-subsystems composed of large chromophore-containing regions. DMV values are evaluated with the electron density computed at the time-dependent density functional theory (TDDFT) level using several functionals and basis sets. We show that the results obtained with the CAM-B3LYP, BHHLYP, and M06-2X functionals demonstrate favorable correlations between DMV and ΔE_ex with the mean absolute error less than 0.01 eV. Taking into account the solid theoretical grounds of the relation between the DMV and the excitation energy in fluorescent proteins, the described modeling strategy presents a rational tool for spectral tuning in these efficient markers for in vivo imaging.

Optimizing the Cosensitization Effect of SQ02 Dye on BP-2 Dye-Sensitized Solar Cells: A Computational Quantum Chemical Study

Cosensitization of the semiconducting electrode in dye-sensitized solar cells (DSCs), with two or more light-harvesting dyes, is a chemical fabrication method that aims to achieve a panchromatic absorption spectrum emulating that of the solar emission spectrum. In this paper, SQ02 and BP-2 cosensitizers have been investigated, as isolated monomers/dimer and adsorbed monomers/dimer on the TiO₂ (101) anatase surface, by employing density functional theory (DFT) and time-dependent DFT calculations. Computed results showed that the dominant electron injection pathway is direct injection from each dye into the conduction band of TiO₂. The almost complete spectral overlap between the simulated absorption spectrum of BP-2 and fluorescence emissions of SQ02 implies that excitation energy transfer occurs between cosensitizers via the trivial reabsorption mechanism. However, the results showed very limited unidirectional intermolecular charge transfer (CT) from SQ02 dye to BP-2 dye (0.04 |e^-|). Therefore, this study also presents a stepwise molecular engineering of BP-2 dye, aiming at optimizing the cosensitization functionality. First, 14 redesigned dye candidates are reported to identify dyes with photophysical properties matching the requirements for efficient DSCs. Second, the four most promising dyes are shortlisted for testing as cosensitizers with the SQ02 dye. The molecular design factors of cosensitization that need validation are chemical compatibility, availability of CT between cosensitizers, and complementarity of the absorption spectra. This screening suggests the judicious choice of the modeled difluorenyl amine donor-based dye (BP-D4) as a very promising cosensitizer. In particular, the SQ02/BP-D4 dimer showed 10 times larger (0.53 |e^-|) unidirectional CT than that of SQ02/BP-2 dimer, in addition to the maximum increased electron population of acceptor moieties upon photoexcitation.

Multiscale Modeling of Electronic Spectra Including Nuclear Quantum Effects

Theoretical prediction of electronic absorption spectra without input from experiments is no easy feat, as it requires addressing all of the factors that affect line shapes. In practice, however, the methodologies are limited to treat these ingredients only to a certain extent. Here, we present a multiscale protocol that addresses the temperature, solvent, and nuclear quantum effects as well as anharmonicity and the reconstruction of the final spectra from individual transitions. First, quantum mechanics/molecular mechanics (QM/MM) molecular dynamics is conducted to obtain trajectories of solute-solvent configurations, from which the corresponding quantum-corrected ensembles are generated through the generalized smoothed trajectory analysis (GSTA). The optical spectra of the ensembles are then produced by calculating vertical transitions using time-dependent density-functional theory (TDDFT) with implicit solvation. To obtain the final spectral shapes, the stick spectra from TDDFT are convoluted with Gaussian kernels where the half-widths are determined by a statistically motivated strategy. We have tested our method by calculating the UV-vis spectra of a recently discovered acridine photocatalyst in two redox states. Vibronic progressions and broadenings due to the finite lifetime of the excited states are not included in the methodology yet. Nuclear quantization affects the relative peak intensities and widths, which is necessary to reproduce the experimental spectrum. We have also found that using only the optimized geometry of each molecule works surprisingly well if a proper empirical broadening factor is applied. This is explained by the rigidity of the conjugated chromophore moieties of the selected molecules, which are mainly responsible for the excitations in the spectra. In contrast, we have also shown that other parts of the molecules are flexible enough to feature anharmonicities that impair the use of other techniques such as Wigner sampling.

Assessment of hybrid functionals for singlet and triplet excitations: Why do some local hybrid functionals perform so well for triplet excitation energies?

The performance of various hybrid density functionals is assessed for 105 singlet and 105 corresponding triplet vertical excitation energies from the QUEST database. The overall lowest mean absolute error is obtained with the local hybrid (LH) functional LH12ct-SsirPW92 with individual errors of 0.11 eV (0.11 eV) for singlet (triplet) n → π* excitations and 0.29 eV (0.17 eV) for π → π* excitations. This is slightly better than with the overall best performing global hybrid M06-2X [n → π*: 0.13 eV (0.17 eV), π → π*: 0.30 eV (0.20 eV)], while most other global and range-separated hybrids and some LHs suffer from the "triplet problem" of time-dependent density functional theory. This is exemplified by correlating the errors for singlet and triplet excitations on a state-by-state basis. The excellent performance of LHs based on a common local mixing function, i.e., an LMF constructed from the spin-summed rather than the spin-resolved semilocal quantities, is systematically investigated by the introduction of a spin-channel interpolation scheme that allows us to continuously modulate the fraction of opposite-spin terms used in the LMF. The correlation of triplet and singlet errors is systematically improved for the n → π* excitations when larger fractions of the opposite-spin-channel are used in the LMF, whereas this effect is limited for the π → π* excitations. This strongly supports a previously made hypothesis that attributes the excellent performance of LHs based on a common LMF to cross-spin-channel nondynamical correlation terms.

Photophysical properties of a boron analogue of coumarin

In this report, we present a study into the structure and electronic properties of difluoroboronsalicylaldoxime (DFBS), a boron-based structural analog of coumarin. The modification of the heterocyclic ring of coumarin with boron results in a compound with similar structural parameters and molecular orbitals to coumarin. DFT and TDDFT calculations reveal a significant stabilization of the LUMO in DFBS; this is supported by a ∼40 nm red shift of the lowest electronic transition in the absorption spectrum. Interestingly, DFBS is emissive, while unmodified coumarin is effectively non-radiative. Comparisons between DFBS, emissive coumarin variants, and unmodified coumarin suggest that the charge transfer character of the transition contributes to the fluorescence.

Efficient Open-Source Implementations of Linear-Scaling Polarizable Embedding: Use Octrees to Save the Trees

We present open-source implementations of the linear-scaling fast multipole method (FMM) within the polarizable embedding (PE) model for efficient treatment of large polarizable environments in computational spectroscopy simulations. The implementations are tested for accuracy, efficiency, and usability on model systems as well as more realistic biomolecular systems. We explain how FMM parameters affect the calculation of molecular properties and show that PE calculations employing FMM can be carried out in a black-box manner. The efficiency of the linear-scaling approach is demonstrated by simulating the UV/vis spectrum of a chromophore in an environment of more than 1 million polarizable sites. Our implementations are interfaced to several open-source quantum chemistry programs, making computational spectroscopy simulations within the PE model and FMM available to a large variety of methods and a broad user base.

Assessing the Accuracy of Local Hybrid Density Functional Approximations for Molecular Response Properties

A comprehensive overview of the performance of local hybrid functionals for molecular properties like excited states, ionization potentials within the GW framework, polarizabilities, magnetizabilities, NMR chemical shifts, and NMR spin-spin coupling constants is presented. We apply the generalization of the kinetic energy, τ, with the paramagnetic current density to all magnetic properties and the excitation energies from time-dependent density functional theory. This restores gauge invariance for these properties. Different ansätze for local mixing functions such as the iso-orbital indicator, the correlation length, the Görling-Levy second-order limit, and the spin polarization are compared. For the latter, we propose a modified version of the corresponding hyper-generalized gradient approximation functional of Perdew, Staroverov, Tao, and Scuseria (PSTS) [Phys. Rev. A 2008, 78, 052513] to allow for a numerically stable evaluation of the exchange-correlation kernel and hyperkernel. The PSTS functional leads to a very consistent improvement compared to the related TPSSh functional. It is further shown that the "best" choice of the local mixing function depends on the studied property and molecular class. While functionals based on the iso-orbital indicator lead to rather accurate excitation energies and ionization energies, the results are less impressive for NMR properties, for which a considerable dependence on the considered molecular test set and nuclei is observed. Johnson's local hybrid functional based on the correlation length yields remarkable results for NMR shifts of compounds featuring heavy elements and also for the excitation energies of organic compounds.

BODIPY dimers: structure, interaction, and absorption spectrum

The object of the present study are BODIPY molecules obtained previously by Piskorz et al. (Dyes Pigm. 178:108322, 2020) for their antimicrobial activity. Structural analysis of the BODIPY dimers is presented in context of the aggregation influence on the photophysical properties. The thorough investigation of the nature of intermolecular interaction in the representative BODIPY dimers is provided together with the decomposition of the interaction energy into the components of well-defined origin according to SAPT procedure. For the model BODIPY systems the careful examination of the interaction nature for the dimer structure based on experimental crystal study as well as fully optimized is given. The tendencies observed in the model dimers are further on investigated for two pairs of BODIPY systems designed for biomedical application. The analyzed molecules are shown to maximize the mutual interaction by the optimization of the stacking dispersion contacts between the aromatic rings of the molecules, therefore producing stable dimers. The estimation of SAPT0 interaction energy components confirms the dominating dispersion character arising from mutual BODIPY core contacts. The influence of the dimerization process on the photophysical properties of the systems studied theoretically depends to the high extend on the dimerization mode and is significant for parallel and antiparallel dispersion-governed dimers.

Assessing challenging intra- and inter-molecular charge-transfer excitations energies with double-hybrid density functionals

We investigate the performance of a set of recently introduced range-separated double-hybrid functionals, namely ωB2-PLYP, ωB2GP-PLYP, RSX-0DH, and RSX-QIDH models for hard-to-calculate excitation energies. We compare with the parent (B2-PLYP, B2GP-PLYP, PBE0-DH, and PBE-QIDH) and other (DSD-PBEP86) double-hybrid models as well as with some of the most widely employed hybrid functionals (B3LYP, PBE0, M06-2X, and ωB97X). For this purpose, we select a number of medium-sized intra- and inter-molecular charge-transfer excitations, which are known to be challenging to calculate using time-dependent density-functional theory (TD-DFT) and for which accurate reference values are available. We assess whether the high accuracy shown by the newest double-hybrid models is also confirmed for those cases too. We find that asymptotically corrected double-hybrid models yield a superior performance, especially for the inter-molecular charge-transfer excitation energies, as compared to standard double-hybrid models. Overall, the PBE-QIDH and its corresponding range-separated RSX-QIDH functional are recommended for general-purpose TD-DFT applications, depending on whether long-range effects are expected to play a significant role.

Evaluation of charge-transfer rates in fullerene-based donor-acceptor dyads with different density functional approximations

The shift towards renewable energy is one of the main challenges of this generation. Dye-sensitized solar cells (DSSCs), based on donor-acceptor architectures, can help in this transition as they present excellent photovoltaic efficiencies yet cheap and simple manufacturing. For molecular heterojunction DSSCs, donor-acceptor pairs are linked in a covalent manner, which facilitates their tailoring and rational design. Nevertheless, reliable computational characterization of charge transfer rate constants (kCT) is needed to speed this development process up. In this context, the performance of time-dependent density functional theory for the calculation of kCT values in donor-acceptor fullerene-based dyads has not been benchmarked yet. Herein, we present a detailed analysis on the performance of seven well-known density functional approximations (DFAs) for this type of system, focusing on several parameters such as the reorganization energies (λ), electronic couplings (VDA), and Gibbs energies (ΔG0CT), as well as the final rate constants. The amount of exact exchange at short range (SR) and long range (LR) electron-electron distances (and the transition from the SR to LR) turned out to be key for the success of the prediction. The tuning of these parameters improves significantly the performance of current DFAs.

Accurate Molecular Geometries in Complex Excited-State Potential Energy Surfaces from Time-Dependent Density Functional Theory

The interplay of electronic excitations and structural changes in molecules impacts nonradiative decay and charge transfer in the excited state, thus influencing excited-state lifetimes and photocatalytic reaction rates in optoelectronic and energy devices. To capture such effects requires computational methods providing an accurate description of excited-state potential energy surfaces and geometries. We suggest time-dependent density functional theory using optimally tuned range-separated hybrid (OT-RSH) functionals as an accurate approach to obtain excited-state molecular geometries. We show that OT-RSH provides accurate molecular geometries in excited-state potential energy surfaces that are complex and involve an interplay of local and charge-transfer excitations, for which conventional semilocal and hybrid functionals fail. At the same time, the nonempirical OT-RSH approach maintains the high accuracy of parametrized functionals (e.g., B3LYP) for predicting excited-state geometries of small organic molecules showing valence excited states.

The Trip to the Density Functional Theory Zoo Continues: Making a Case for Time-Dependent Double Hybrids for Excited-State Problems

This account is written for general users of time-dependent density functional theory (TD-DFT) methods as well as chemists who are unfamiliar with the field. It includes a brief overview of conventional TD-DFT approaches and recommendations for applications to organic molecules based on our own experience. The main emphasis of this work, however, lies in providing the first in-depth review of time-dependent double-hybrid density functionals. They were first established in 2007 with very promising follow-up studies in the subsequent four years before developments or applications became scarce. The topic has regained more interest since 2017, and this account reviews those latest developments led by our group. These developments have shown unprecedented robustness for a variety of different types of electronic excitations when compared to more conventional TD-DFT methods. In particular, time-dependent double hybrids do not suffer from artificial ghost states and are able to reproduce exciton-coupled absorption spectra. Our latest methods include range separation and belong to the currently best TD-DFT methods for singlet-singlet excitations in organic molecules. While there is still room for improvement and further development in this space, we hope that this account encourages users to adjust their computational protocols to such new methods to provide more real-life testing and scenarios.

Dipole Moment Variation Clears Up Electronic Excitations in the π-Stacked Complexes of Fluorescent Protein Chromophores

We propose a quantitative structure-property relationship (QSPR) model for prediction of spectral tuning in cyan, green, orange, and red fluorescent proteins, which are engineered by motifs of the green fluorescent protein. Protein variants, in which their chromophores are involved in the π-stacking interaction with amino acid residues tyrosine, phenylalanine, and histidine, are prospective markers useful in bioimaging and super-resolution microscopy. In this work, we constructed training sets of the π-stacked complexes of four fluorescent protein chromophores (of the green, orange, red, and cyan series) with various substituted benzenes and imidazoles and tested the use of dipole moment variation upon excitation (DMV) as a descriptor to evaluate the vertical excitation energies in these systems. To validate this approach, we computed and analyzed electron density distributions of the π-stacked complexes and correlated the QSPR predictions with the reference values of the transition energies obtained using the high-level ab initio quantum chemistry methods. According to our results, the use of the DMV descriptor allows one to predict excitation energies in the π-stacked complexes with errors not exceeding 0.1 eV, which makes this model a practically useful tool in the development of efficient fluorescent markers for in vivo imaging.

Approximately Self-Consistent Ensemble Density Functional Theory: Toward Inclusion of All Correlations

Recent theory developments in ensemble density functional theory (EDFT) promise to bring decades of work for ground states to the practical resolution of excited states, provided newly discovered "density-driven correlations" can be dealt with and adequate effective potentials can be found. This Letter introduces simple theories for both and shows that EDFT using these theories outperforms ΔSCF DFT and time-dependent DFT for low-lying gaps in most of the small atoms and molecules tested, even when all use the same density functional approximations. It thus establishes EDFT as a promising tool for low-cost studies of low-lying excited states and provides a clear route to practical EDFT implementation of arbitrary functional approximations.

The Quest for Highly Accurate Excitation Energies: A Computational Perspective

We provide an overview of the successive steps that made it possible to obtain increasingly accurate excitation energies with computational chemistry tools, eventually leading to chemically accurate vertical transition energies for small- and medium-size molecules. First, we describe the evolution of ab initio methods employed to define benchmark values, with the original Roos CASPT2 method, then the CC3 method as in the renowned Thiel set, and more recently the resurgence of selected configuration interaction methods. The latter method has been able to deliver consistently, for both single and double excitations, highly accurate excitation energies for small molecules, as well as medium-size molecules with compact basis sets. Second, we describe how these high-level methods and the creation of representative benchmark sets of excitation energies have allowed the fair and accurate assessment of the performance of computationally lighter methods. We conclude by discussing possible future theoretical and technological developments in the field.

Reduction of 1,2,3-trichloropropane (TCP): pathways and mechanisms from computational chemistry calculations

The characteristic pathway for degradation of halogenated aliphatic compounds in groundwater or other environments with relatively anoxic and/or reducing conditions is reductive dechlorination. For 1,2-dihalocarbons, reductive dechlorination can include hydrogenolysis and dehydrohalogenation, the relative significance of which depends on various structural and energetic factors. To better understand how these factors influence the degradation rates and products of the lesser halogenated hydrocarbons (in contrast to the widely studied per-halogenated hydrocarbons, like trichloroethylene and carbon tetrachloride), density functional theory calculations were performed to compare all of the possible pathways for reduction and elimination of 1,2,3-trichloropropane (TCP). The results showed that free energies of each species and reaction step are similar for all levels of theory, although B3LYP differed from the others. In all cases, the reaction coordinate diagrams suggest that β-elimination of TCP to allyl chloride followed by hydrogenolysis to propene is the thermodynamically favored pathway. This result is consistent with experimental results obtained using TCP, 1,2-dichloropropane, and 1,3-dichloropropane in batch experiments with zerovalent zinc (Zn⁰, ZVI) as a reductant.

A Mountaineering Strategy to Excited States: Highly Accurate Energies and Benchmarks for Medium Sized Molecules

Following our previous work focusing on compounds containing up to 3 non-hydrogen atoms [J. Chem. Theory Comput. 2018, 14, 4360-4379], we present here highly accurate vertical transition energies obtained for 27 molecules encompassing 4, 5, and 6 non-hydrogen atoms: acetone, acrolein, benzene, butadiene, cyanoacetylene, cyanoformaldehyde, cyanogen, cyclopentadiene, cyclopropenone, cyclopropenethione, diacetylene, furan, glyoxal, imidazole, isobutene, methylenecyclopropene, propynal, pyrazine, pyridazine, pyridine, pyrimidine, pyrrole, tetrazine, thioacetone, thiophene, thiopropynal, and triazine. To obtain these energies, we use equation-of-motion/linear-response coupled cluster theory up to the highest technically possible excitation order for these systems (CC3, EOM-CCSDT, and EOM-CCSDTQ) and selected configuration interaction (SCI) calculations (with tens of millions of determinants in the reference space), as well as the multiconfigurational n-electron valence state perturbation theory (NEVPT2) method. All these approaches are applied in combination with diffuse-containing atomic basis sets. For all transitions, we report at least CC3/aug-cc-pVQZ vertical excitation energies as well as CC3/aug-cc-pVTZ oscillator strengths for each dipole-allowed transition. We show that CC3 almost systematically delivers transition energies in agreement with higher-level methods with a typical deviation of ±0.04 eV, except for transitions with a dominant double excitation character where the error is much larger. The present contribution gathers a large, diverse, and accurate set of more than 200 highly accurate transition energies for states of various natures (valence, Rydberg, singlet, triplet, n → π*, π → π*, ...). We use this series of theoretical best estimates to benchmark a series of popular methods for excited state calculations: CIS(D), ADC(2), CC2, STEOM-CCSD, EOM-CCSD, CCSDR(3), CCSDT-3, CC3, and NEVPT2. The results of these benchmarks are compared to the available literature data.

Is ADC(3) as Accurate as CC3 for Valence and Rydberg Transition Energies?

The search for new models rapidly delivering accurate excited-state energies and properties is one of the most active research lines of theoretical chemistry. Along with these developments, the performance of known methods is constantly reassessed on the basis of new benchmark values. In this Letter, we show that the third-order algebraic diagrammatic construction, ADC(3), does not yield transition energies of the same quality as the third-order coupled cluster method, CC3. This is demonstrated by extensive comparisons with several hundred high-quality vertical transition energies obtained with FCI, CCSDTQ, and CCSDT. Direct comparisons with experimental 0-0 energies of small- and medium-size molecules support the same conclusion, which holds for both valence and Rydberg transitions. Considering these results, we introduce a composite approach, ADC(2.5), which consists of averaging the ADC(2) and ADC(3) excitation energies. Although ADC(2.5) does not match the CC3 accuracy, it significantly improves the ADC(3) results, especially for vertical energies.

TD-DFT benchmark for UV-visible spectra of fused-ring electron acceptors using global and range-separated hybrids

The accuracy of Time-Dependent Density Functional Theory in predicting the vertical absorption wavelength of 50 widely-used fused-ring electron acceptors (FREAs) has been investigated by considering the solvent effects.