Benchmarking TD-DFT and Wave Function Methods for Oscillator Strengths and Excited-State Dipole Moments

Comparative Study of Vibrational Raman Optical Activity with Different Time-Dependent Density Functional Approximations: The VROA36 Database

A new database, VROA36, is introduced to investigate the performance of computational approaches for vibrational Raman optical activity (VROA) calculations. The database is composed of 36 molecules with known experimental VROA spectra. It includes 93 conformers. Normal modes calculated with B3LYP-D3(BJ)/def2-TZVP are used to compute the VROA spectra with four functionals, B3LYP-D3(BJ), ωB97X-D, M11, and optimally tuned LC-PBE, as well as several basis sets. SimROA indices and frequency scaling factors are used to compare calculated spectra with each other and with experimental data. The four functionals perform equally well independently of the basis set and usually achieve good agreement with the experimental data. For molecules in near- or at-resonance conditions, the inclusion of a complex (damped) linear response approach is important to obtain physically meaningful VROA intensities. The use of any of the tested functional approximations with the def2-SVPD Gaussian-type basis set, or a basis of similar flexibility, can be recommended for efficient and reliable theoretical VROA studies.

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.

Exploring the accuracy and usefulness of semi-empirically scaled ADC schemes by blending second and third order terms

Different approaches to mixed-order algebraic-diagrammatic construction (ADC) schemes are investigated. The performance of two different strategies for scaling third-order contributions to the ADC secular matrix is evaluated. Both considered schemes employ a single tuning parameter and conserve general properties inherent to all ADC methods such as hermiticity and size-consistency.The first approach, scaled-matrix ADC[(2)+x(3)], scales all contributions first occurring in ADC(3) equally and leads to an improvement of the accuracy of excitation energies compared to ADC(3) for x=0.4-0.5. However, with respect to excited state dipole moments this method provides lower accuracy than ADC(3). The second scaling approach, MP[(1)+x(2)]-ISR(3), scales the second order contributions of the ground-state wavefunction and derives a rigorous ADC scheme via the intermediate state representation (ISR) formalism. Although the error in excitation energies is not improved, this method provides insight into the relevance of the individual terms of the ADC(3) matrix and indicates, that the MP(2) wavefunction is indeed the optimal reference wavefunction for deriving a third-order single-reference ADC scheme.

Rationalizing the Fluorescence Behavior of Core-Substituted Naphthalene Diimides

We study the internal conversion (IC) and intersystem crossing (ISC) pathways of low-lying excited electronic states of three core-substituted naphthalene diimides (bNDI, yNDI, and gNDI) using wavepacket simulations within the linear vibronic coupling method. Our wavepacket simulations reproduce the experimental electronic absorption spectra very well. All molecules decay rapidly to S₂ upon populating a higher dipole-allowed singlet excited-state. The S₂ → S₁ IC dynamics and singlet-triplet energy gap, spin-orbit coupling strength trends suggest a favorable S₂ → T₄ ISC in gNDI. The efficient ultrafast T₄ formation and its decay to lower triplet states make gNDI nonfluorescent. Such triplet formation pathways are not operative in both bNDI and yNDI; hence, these molecules emit fluorescence from S₁ after a slower S₂ → S₁ IC.

Computational discoveries of reaction mechanisms: recent highlights and emerging challenges

This review examines some of the notable advances and trends that have shaped the field of computational elucidation of organic reaction mechanisms over the last 10-15 years. It highlights the types of mechanistic problems that have recently become possible to study and summarizes the methodological developments that have permitted these new advances. Case studies are taken from three representative areas of organic chemistry-asymmetric catalysis, glycosylation reactions, and single electron transfer reactions-which illustrate themes common to the broader field. These include the trend towards modelling systems that are increasingly complex (both structurally and mechanistically), the growing appreciation of the mechanistic roles of non-covalent interactions, and the increasing ability to explore dynamical features of reaction mechanisms. Some interesting new challenges that have emerged in the field are identified.

Basis sets dependency in constructing spectroscopy-accuracy Ab Initio global electric dipole moment functions

Recently, more attention have been paid on the construction of dipole moment functions (DMF) using theoretical methods. However, the computational methods to construct DMFs are not validated as much as those for potential energy surfaces do. In this letter, using Ar ⋯ He as an example, we tested how spectroscopy-accuracy DMFs can be constructed using ab initio methods. We especially focused on the basis set dependency in this scenario, i.e., the convergence of DMF with the sizes of basis sets, basis set superposition error, and mid-bond functions. We also tested the explicitly correlated method, which converges with smaller basis sets than the conventional methods do. This work can serve as a pictorial sample of all these computational technologies behaving in the context of constructing DMFs.

OS100: A Benchmark Set of 100 Digitized UV-Visible Spectra and Derived Experimental Oscillator Strengths

Excited-state quantum chemical calculations usually report excitation energies and oscillator strengths, f, for each electronic transition. On the other hand, UV-visible spectrophotometric experiments measure energy-dependent molar extinction/attenuation coefficients, ε(v), that give absorption band line shapes when plotted. ε(v) and f are related, but this relation is complicated by broadening and solvation effects. We fitted and integrated 100 experimental UV-visible spectra to obtain 164 f_exp values for absorption bands appearing in these spectra. The 100 UV-visible spectra belong to solvated organic molecules ranging in size from 6-34 atoms. We estimated uncertainties in the fitting to indicate confidence level in the reported f_exp values. The corresponding computed oscillator strengths (f_comp) were obtained with time-dependent density functional theory and a polarizable continuum solvent model. By expressing experimental and computed absorption strengths using a common quantity, we directly compared f_comp and f_exp. Although f_comp and f_exp are well correlated (linear regression R² = 0.921), f_comp in most cases overestimated f_exp (regression slope = 1.34). The agreement between absolute f_comp and f_exp values was substantially improved by accounting for a solvent refractive index factor, as suggested in some derivations in the literature. The 100 digitized UV-visible spectra are included as plain text files in the Supporting Information to aid in benchmarking computational or machine learning methods that aim to simulate realistic UV-visible absorption spectra.

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.

Double and Charge-Transfer Excitations in Time-Dependent Density Functional Theory

Time-dependent density functional theory has emerged as a method of choice for calculations of spectra and response properties in physics, chemistry, and biology, with its system-size scaling enabling computations on systems much larger than otherwise possible. While increasingly complex and interesting systems have been successfully tackled with relatively simple functional approximations, there has also been increasing awareness that these functionals tend to fail for certain classes of approximations. Here I review the fundamental challenges the approximate functionals have in describing double excitations and charge-transfer excitations, which are two of the most common impediments for the theory to be applied in a black-box way. At the same time, I describe the progress made in recent decades in developing functional approximations that give useful predictions for these excitations. Expected final online publication date for the Annual Review of Physical Chemistry, Volume 73 is April 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

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).

High-throughput virtual screening for organic electronics: a comparative study of alternative strategies

We present a review of the field of high-throughput virtual screening for organic electronics materials focusing on the sequence of methodological choices that determine each virtual screening protocol. These choices are present in all high-throughput virtual screenings and addressing them systematically will lead to optimised workflows and improve their applicability. We consider the range of properties that can be computed and illustrate how their accuracy can be determined depending on the quality and size of the experimental datasets. The approaches to generate candidates for virtual screening are also extremely varied and their relative strengths and weaknesses are discussed. The analysis of high-throughput virtual screening is almost never limited to the identification of top candidates and often new patterns and structure-property relations are the most interesting findings of such searches. The review reveals a very dynamic field constantly adapting to match an evolving landscape of applications, methodologies and datasets.

Accurate full configuration interaction correlation energy estimates for five- and six-membered rings

Following our recent work on the benzene molecule [P.-F. Loos, Y. Damour, and A. Scemama, J. Chem. Phys. 153, 176101 (2020)], motivated by the blind challenge of Eriksen et al. [J. Phys. Chem. Lett. 11, 8922 (2020)] on the same system, we report accurate full configuration interaction (FCI) frozen-core correlation energy estimates for 12 five- and six-membered ring molecules (cyclopentadiene, furan, imidazole, pyrrole, thiophene, benzene, pyrazine, pyridazine, pyridine, pyrimidine, s-tetrazine, and s-triazine) in the standard correlation-consistent double-ζ Dunning basis set (cc-pVDZ). Our FCI correlation energy estimates, with an estimated error smaller than 1 millihartree, are based on energetically optimized-orbital selected configuration interaction calculations performed with the configuration interaction using a perturbative selection made iteratively algorithm. Having at our disposal these accurate reference energies, the respective performance and convergence properties of several popular and widely used families of single-reference quantum chemistry methods are investigated. In particular, we study the convergence properties of (i) the Møller-Plesset perturbation series up to fifth-order (MP2, MP3, MP4, and MP5), (ii) the iterative approximate coupled-cluster series CC2, CC3, and CC4, and (iii) the coupled-cluster series CCSD, CCSDT, and CCSDTQ. The performance of the ground-state gold standard CCSD(T) as well as the completely renormalized CC model, CR-CC(2,3), is also investigated. We show that MP4 provides an interesting accuracy/cost ratio, while MP5 systematically worsens the correlation energy estimates. In addition, CC3 outperforms CCSD(T) and CR-CC(2,3), as well as its more expensive parent CCSDT. A similar trend is observed for the methods including quadruple excitations, where the CC4 model is shown to be slightly more accurate than CCSDTQ, both methods providing correlation energies within 2 millihartree of the FCI limit.

Accurate Modeling of Excitonic Coupling in Cyanine Dye Cy3

Accurate modeling of excitonic coupling in molecules is of great importance for inferring the structures and dynamics of coupled systems. Cy3 is a cyanine dye that is widely used in molecular spectroscopy. Its well-separated excitation bands, high sensitivity to the surroundings, and the high energy transfer efficiency make it a perfect choice for excitonic coupling experiments. Many methods have been used to model the excitonic coupling in molecules with varying degrees of accuracy. The atomic transition charge model offers a high-accuracy and cost-effective way to calculating the excitonic coupling. The main focus of this work is to generate high-quality atomic transition charges that can accurately model the Cy3 dye's transition density. The transition density of the excitation of the ground to first excited state is calculated using configuration-interaction singles and time-dependent density functional theory and is benchmarked against the algebraic diagrammatic construction method. Using the transition density we derived the atomic transition charges using two approaches: Mulliken population analysis and charges fitted to the transition electrostatic potential. The quality of the charges is examined, and their ability to accurately calculate the excitonic coupling is assessed via comparison to experimental data of an artificial biscyanine construct. Theoretical comparisons to the supermolecule ab initio couplings and the widely used point-dipole approximation are also made. Results show that using the transition electrostatic potential is a reliable approach for generating the transition atomic charges. A high-quality set of charges, that can be used to model the Cy3 dye dimer excitonic coupling with high-accuracy and a reasonable computational cost, is obtained.

The importance of finite temperature and vibrational sampling in the absorption spectrum of a nitro-functionalized Ru(ii) water oxidation catalyst

Consideration of finite temperature and vibrational motion can be an essential component for accurate simulations of absorption spectra. Here we use finite-temperature Wigner phase-space sampling to investigate the intense absorption of the water oxidation catalyst Ru(dppip-NO2) in the visible (vis) region. The influence of vibrational and torsional motions as well as temperature effects are addressed for the different protonation forms of the pH-sensitive dppip-NO2 ligand of the catalyst. Excitations to the nitrophenyl group and π-system of dppip-NO2, which characterize the absorption band in the equilibrium spectra, experience energy shifts and a significant decrease in oscillator strength when nuclear motion is considered. The importance of excitations to the nitrophenyl group for the vis band is reduced in the spectra computed from the 300 K ensembles, which feature broad distributions of the corresponding dihedral angles. The effects of vibrational sampling on the absorption spectra may be attributed to nitrophenyl and, in particular, to NO2 torsional motions. We expect finite temperature and vibrational sampling to be important for simulating the absorption spectra of other transition metal complexes with flexible ligands or nitro-aromatic motifs.

The Quest to Simulate Excited-State Dynamics of Transition Metal Complexes

This Perspective describes current computational efforts in the field of simulating photodynamics of transition metal complexes. We present the typical workflows and feature the strengths and limitations of the different contemporary approaches. From electronic structure methods suitable to describe transition metal complexes to approaches able to simulate their nuclear dynamics under the effect of light, we give particular attention to build a bridge between theory and experiment by critically discussing the different models commonly adopted in the interpretation of spectroscopic experiments and the simulation of particular observables. Thereby, we review all the studies of excited-state dynamics on transition metal complexes, both in gas phase and in solution from reduced to full dimensionality.

Assessment of the performance of DFT functionals in the fulfillment of off-diagonal hypervirial relationships

Off-diagonal hypervirial relationships, combined with quantum mechanical sum rules of charge-current conservation, offer a way to test electronic excited-state transition energies and moments, which does not need any external reference. A number of fundamental relationships were recast into absolute deviations from zero, which have been used to assess the performance of some popular DFT functionals. Extended TD-DFT calculations have been carried out for a pool of molecules chosen for this purpose, adopting a large basis set to ensure high quality results. A partial agreement with previous benchmarks is observed.

Elucidating an Atmospheric Brown Carbon Species-Toward Supplanting Chemical Intuition with Exhaustive Enumeration and Machine Learning

Brown carbon (BrC) is involved in atmospheric light absorption and climate forcing and can cause adverse health effects. Understanding the formation mechanisms and molecular structure of BrC is of key importance in developing strategies to control its environment and health impact. Structure determination of BrC is challenging, due to the lack of experiments providing molecular fingerprints and the sheer number of molecular candidates with identical mass. Suggestions based on chemical intuition are prone to errors due to the inherent bias. We present an unbiased algorithm, using graph-based molecule generation and machine learning, which can identify all molecular structures of compounds involved in biomass burning and the composition of BrC. We apply this algorithm to C₁₂H₁₂O₇, a light-absorbing "test case" molecule identified in chamber experiments on the aqueous photo-oxidation of syringol, a prevalent marker in wood smoke. Of the 260 million molecular graphs, the algorithm leaves only 36,518 (0.01%) as viable candidates matching the spectrum. Although no unique molecular structure is obtained from only a chemical formula and a UV/vis absorption spectrum, we discuss further reduction strategies and their efficacy. With additional data, the method can potentially more rapidly identify isomers extracted from lab and field aerosol particles without introducing human bias.

A Machine-Learning Protocol for Ultraviolet Protein-Backbone Absorption Spectroscopy under Environmental Fluctuations

Ultraviolet (UV) absorption spectra are commonly used for characterizing the global structure of proteins. However, the theoretical interpretation of UV spectra is hindered by the large number of required expensive ab initio calculations of excited states spanning a huge conformation space. We present a machine-learning (ML) protocol for far-UV (FUV) spectra of proteins, which can predict FUV spectra of proteins with comparable accuracy to density functional theory (DFT) calculations but with 3-4 orders of magnitude reduced computational cost. It further shows excellent predictive power and transferability that can be used to probe structural mutations and protein folding pathways.

Spin-Conserved and Spin-Flip Optical Excitations from the Bethe-Salpeter Equation Formalism

Like adiabatic time-dependent density-functional theory (TD-DFT), the Bethe–Salpeter equation (BSE) formalism of many-body perturbation theory, in its static approximation, is “blind” to double (and higher) excitations, which are ubiquitous, for example, in conjugated molecules like polyenes. Here, we apply the spin-flip ansatz (which considers the lowest triplet state as the reference configuration instead of the singlet ground state) to the BSE formalism in order to access, in particular, double excitations. The present scheme is based on a spin-unrestricted version of the GW approximation employed to compute the charged excitations and screened Coulomb potential required for the BSE calculations. Dynamical corrections to the static BSE optical excitations are taken into account via an unrestricted generalization of our recently developed (renormalized) perturbative treatment. The performance of the present spin-flip BSE formalism is illustrated by computing excited-state energies of the beryllium atom, the hydrogen molecule at various bond lengths, and cyclobutadiene in its rectangular and square-planar geometries.