Benchmarking Excited-State Calculations Using Exciton Properties

Photoswitching Molecules Functionalized with Optical Cycling Centers Provide a Novel Platform for Studying Chemical Transformations in Ultracold Molecules

A novel molecular structure that bridges the fields of molecular optical cycling and molecular photoswitching is presented. It is based on a photoswitching molecule azobenzene functionalized with one and two CaO- groups, which can act as optical cycling centers (OCCs). This paper characterizes the electronic structure of the resulting model systems, focusing on three questions: (1) how the electronic states of the photoswitch are impacted by a functionalization with an OCC; (2) how the states of the OCC are impacted by the scaffold of the photoswitch; and (3) whether the OCC can serve as a spectroscopic probe of isomerization. The experimental feasibility of the proposed design and the advantages that organic synthesis can offer in the further functionalization of this molecular scaffold are also discussed. This work brings into the field of molecular optical cycling a new dimension of chemical complexity intrinsic to only polyatomic molecules.

QUEST#4X: An Extension of QUEST#4 for Benchmarking Multireference Wave Function Methods

Given a number of data sets for evaluating the performance of single reference methods for the low-lying excited states of closed-shell molecules, a comprehensive data set for assessing the performance of multireference methods for the low-lying excited states of open-shell systems is still lacking. For this reason, we propose an extension (QUEST#4X) of the radical subset of QUEST#4 (J. Chem. Theory Comput. 2020, 16, 3720) to cover 110 doublet and 39 quartet excited states. Near-exact results obtained by iterative configuration interaction with selection and second-order perturbation correction (iCIPT2) are taken as benchmark to calibrate static-dynamic-static configuration interaction (SDSCI) and static-dynamic-static second-order perturbation theory (SDSPT2), which are minimal MRCI and CI-like perturbation theory, respectively. It is found that SDSCI is very close in accuracy to internally contracted multireference configuration interaction with singles and doubles (ic-MRCISD), although its computational cost is just that of one iteration of the latter. Unlike most variants of MRPT2, SDSPT2 treats single and multiple states in the same way and performs similarly to multistate n-electron valence second-order perturbation theory (MS-NEVPT2). These findings put SDSCI and SDSPT2 on a firm basis.

Resonant Auger Decay in Benzene

We present ab initio calculations of the resonant Auger spectrum of benzene. In the resonant process, Auger decay ensues following the excitation of a core-level electron to a virtual orbital. Hence, resonant Auger decay gives rise to higher-energy Auger electrons compared to nonresonant decay. We apply equation-of-motion coupled-cluster (EOM-CC) methods to compute the spectrum in order to explain the main features in the experimental spectrum and to assess the capability and limitations of the available theoretical approaches. The results indicate that participator decay can be well described with the Feshbach-Fano approach based on EOM-CC wave functions in the singles and doubles (SD) approximation, but spectator decay is more difficult to describe. This is because the target states of spectator decay are doubly excited, resulting in the need to include triple excitations in the EOM-CC wave function. Resonant Auger decay in benzene is thus a challenging test case for EOM-CC theory. We examine the performance of different noniterative triple corrections to EOM-IP-CCSD and our numerical results highlight the need to include triple excitations iteratively.

Ab initio electronic absorption spectra of para-nitroaniline in different solvents: Intramolecular charge transfer effects

Intramolecular charge transfer (ICT) effects of para-nitroaniline (pNA) in eight solvents (cyclohexane, toluene, acetic acid, dichloroethane, acetone, acetonitrile, dimethylsulfoxide, and water) are investigated extensively. The second-order algebraic diagrammatic construction, ADC(2), ab initio wave function is employed with the COSMO implicit and discrete multiscale solvation methods. We found a decreasing amine group torsion angle with increased solvent polarity and a linear correlation between the polarity and ADC(2) transition energies. The first absorption band involves π → π* transitions with ICT from the amine and the benzene ring to the nitro group, increased by 4%-11% for different solvation models of water compared to the vacuum. A second band of pNA is characterized for the first time. This band is primarily a local excitation on the nitro group, including some ICT from the amine group to the benzene ring that decreases with the solvent polarity. For cyclohexane, the COSMO implicit solvent model shows the best agreement with the experiment, while the explicit model has the best agreement for water.

Importance of Orbital Invariance in Quantifying Electron-Hole Separation and Exciton Size

A fundamental tenet of quantum mechanics is that properties should be independent of representation. In self-consistent field methods such as density functional theory, this manifests as a requirement that properties be invariant with respect to unitary transformations of the occupied molecular orbitals and (separately) the unoccupied molecular orbitals. Various ad hoc measures of excited-state charge separation that are commonly used to analyze time-dependent density-functional calculations violate this requirement, as they are based on incoherent averages of excitation amplitudes rather than expectation values involving coherent superpositions. As a result, these metrics afford markedly different values in various common representations, including canonical molecular orbitals, Boys-localized orbitals, and natural orbitals. Numerical values can be unstable with respect to basis-set expansion and may afford nonsensical results in the presence of extremely diffuse basis functions. In contrast, metrics based on well-defined expectation values are stable, representation-invariant, and physically interpretable. Use of natural transition orbitals improves the stability of the incoherent averages, but numerical values can only be interpreted as expectation value in the absence of superposition. To satisfy this condition, the particle and hole density matrices must each be dominated by a single eigenvector so that the transition density is well described by a single pair of natural transition orbitals. Counterexamples are readily found where this is not the case. Our results suggest that ad hoc charge-transfer diagnostics should be replaced by rigorous expectation values, which are no more expensive to compute.

A mountaineering strategy to excited states: Accurate vertical transition energies and benchmarks for substituted benzenes

In an effort to expand the existing QUEST database of accurate vertical transition energies [Véril et al. WIREs Comput. Mol. Sci. 2021, 11, e1517], we have modeled more than 100 electronic excited states of different natures (local, charge-transfer, Rydberg, singlet, and triplet) in a dozen of mono- and di-substituted benzenes, including aniline, benzonitrile, chlorobenzene, fluorobenzene, nitrobenzene, among others. To establish theoretical best estimates for these vertical excitation energies, we have employed advanced coupled-cluster methods including iterative triples (CC3 and CCSDT) and, when technically possible, iterative quadruples (CC4). These high-level computational approaches provide a robust foundation for benchmarking a series of popular wave function methods. The evaluated methods all include contributions from double excitations (ADC(2), CC2, CCSD, CIS(D), EOM-MP2, STEOM-CCSD), along with schemes that also incorporate perturbative or iterative triples (ADC(3), CCSDR(3), CCSD(T)(a)  ⋆ , and CCSDT-3). This systematic exploration not only broadens the scope of the QUEST database but also facilitates a rigorous assessment of different theoretical approaches in the framework of a homologous chemical series, offering valuable insights into the accuracy and reliability of these methods in such cases. We found that both ADC(2.5) and CCSDT-3 can provide very consistent estimates, whereas among less expensive methods SCS-CC2 is likely the most effective approach. Importantly, we show that some lower order methods may offer reasonable trends in the homologous series while providing quite large average errors, and vice versa. Consequently, benchmarking the accuracy of a model based solely on absolute transition energies may not be meaningful for applications involving a series of similar compounds.

Direct Estimation of Aromatization Energy from 1H NMR and UV-Vis Absorption Data of Homodesmotic Molecules

This study delves into the ring-opening reaction of two distinct diaryl-ring-pyran systems, referred to as drnp1 and drnp2, where the term 'ring' encompasses aromatic, nonaromatic, or antiaromatic motifs. These systems transform into the corresponding cis-ortho quinonoid systems, denoted as c-drnq1 and c-drnq2. Homodesmotic pairs (drnp1, drnp2) and (c-drnq1, c-drnq2) are categorized as (aromatic, nonaromatic), (aromatic, partially aromatic), (antiaromatic, nonaromatic), and (nonaromatic, nonaromatic), with their energy difference representing aromatization energy (Earoma). Using reliable density functional theory, Earoma is assessed for various aromatic and antiaromatic ring motifs, including borderline cases and nonaromatic structures. For example, benzene exhibits an Earoma of 23.4 kcal/mol, indicating 3.9 kcal/mol aromatic stabilization per CC bond, while cyclobutadiene shows -29.9 kcal/mol, indicating a 7.5 kcal/mol destabilization of the CC bond. This approach extends to evaluating global and local aromatic stabilization effects in polycyclic hydrocarbons, nonbenzenoid systems, and heterocyclic compounds. Additionally, variation in 1H NMR chemical shift (δavg) correlates with Earoma, suggesting that a -1.0 ppm shift corresponds to 24.2 kcal/mol aromatization energy. UV-vis absorption maxima difference (Δλavg) correlates linearly with Earoma, enabling direct assessment of aromatization energy from UV-vis spectra using suitable homodesmotic pairs. This comprehensive approach enhances our understanding of structural, energetic, and spectroscopic aspects of aromatic and antiaromatic systems.

Coupled-cluster treatment of complex open-shell systems: the case of single-molecule magnets

We investigate the reliability of two cost-effective coupled-cluster methods for computing spin-state energetics and spin-related properties of a set of open-shell transition-metal complexes. Specifically, we employ the second-order approximate coupled-cluster singles and doubles (CC2) method and projection-based embedding that combines equation-of-motion coupled-cluster singles and doubles (EOM-CCSD) with density functional theory (DFT). The performance of CC2 and EOM-CCSD-in-DFT is assessed against EOM-CCSD. The chosen test set includes two hexaaqua transition-metal complexes containing Fe(II) and Fe(III), and a large Co(II)-based single-molecule magnet with a non-aufbau ground state. We find that CC2 describes the excited states more accurately, reproducing EOM-CCSD excitation energies within 0.05 eV. However, EOM-CCSD-in-DFT excels in describing transition orbital angular momenta and spin-orbit couplings. Moreover, for the Co(II) molecular magnet, using EOM-CCSD-in-DFT eigenstates and spin-orbit couplings, we compute spin-reversal energy barriers, as well as temperature-dependent and field-dependent magnetizations and magnetic susceptibilities that closely match experimental values within spectroscopic accuracy. These results underscore the efficiency of CC2 in computing state energies of multi-configurational, open-shell systems and highlight the utility of the more cost-efficient EOM-CCSD-in-DFT for computing spin-orbit couplings and magnetic properties of complex and large molecular magnets.

Alternative CNDOL Fockians for fast and accurate description of molecular exciton properties

CNDOL is an a priori, approximate Fockian for molecular wave functions. In this study, we employ several modes of singly excited configuration interaction (CIS) to model molecular excitation properties by using four combinations of the one electron operator terms. Those options are compared to the experimental and theoretical data for a carefully selected set of molecules. The resulting excitons are represented by CIS wave functions that encompass all valence electrons in the system for each excited state energy. The Coulomb-exchange term associated to the calculated excitation energies is rationalized to evaluate theoretical exciton binding energies. This property is shown to be useful for discriminating the charge donation ability of molecular and supermolecular systems. Multielectronic 3D maps of exciton formal charges are showcased, demonstrating the applicability of these approximate wave functions for modeling properties of large molecules and clusters at nanoscales. This modeling proves useful in designing molecular photovoltaic devices. Our methodology holds potential applications in systematic evaluations of such systems and the development of fundamental artificial intelligence databases for predicting related properties.

Two- and one-photon absorption spectra of aqueous thiocyanate anion highlight the role of symmetry in the condensed phase

We present the two-photon absorption (2PA) spectrum of aqueous thiocyanate calculated using high-level quantum-chemistry methods. The 2PA spectrum is compared to the one-photon absorption (1PA) spectrum computed using the same computational protocol. Although the two spectra probe the same set of electronic states, the intensity patterns are different, leading to an apparent red-shift of the 2PA spectrum relative to the 1PA spectrum. The presented analysis explains the intensity patterns and attributes the differences between the 1PA and 2PA spectra to the native symmetry of isolated SCN  - , which influences the spectra in the low-symmetry solvated environment. The native symmetry also manifests itself in variations of the polarization ratio (e.g., parallel vs. perpendicular cross sections) across the spectrum. The presented results highlight the potential of 2PA spectroscopy and high-level quantum-chemistry methods in studies of condensed-phase phenomena.

Absorption spectra of p-nitroaniline derivatives: charge transfer effects and the role of substituents

CONTEXT

Push-pull compounds are model systems and have numerous applications. By changing their substituents, properties are modified and new molecules for different applications can be designed. The work investigates the gas-phase electronic absorption spectra of 15 derivatives of push-pull para-nitroaniline (pNA). This molecule has applications in pharmaceuticals, azo dyes, corrosion inhibitors, and optoelectronics. Both electron-donor and electron-withdrawing groups were investigated. Employing machine learning-derived Hammett's constants σm, σm0, σR, and σI, correlations between substituents and electronic properties were obtained. Overall, the σm0 constants presented the best correlation with HOMO and LUMO energies, whereas the σR constants best agreed with the transition energy of the first band and HOMO-LUMO energy gap. Electron-donors, which have lower σR values, redshift the absorption spectrum and reduce the HOMO-LUMO energy gap. Conversely, electron-withdrawing groups (higher σR's) blueshift the spectrum and increase the energy gap. The second band maximum energies, studied here for the first time, showed no correlation with σ but tended to increase with σ. A comprehensive charge transfer (CT) analysis of the main transition of all systems was also carried out. We found that donors (lower σ's) slightly enhance the CT character of the unsubstituted pNA, whereas acceptors (higher σ's) decrease it, leading to increased local excitations within the aromatic ring. The overall CT variation is not large, except for pNA-SO2H, which considerably decreases the total CT value. We found that the strong electron donors pNA-OH, pNA-OCH3, and pNA-NH2, which have the smallest HOMO-LUMO energy gaps and lowest σ's, have potential for optoelectronic applications. The results show that none of the studied molecules is fluorescent in the gas phase. However, pNA-NH2 and pNA-COOH in cyclohexane and water reveal fluorescence upon solvation.

METHODS

We investigated theoretically employing the second-order algebraic diagrammatic construction (ADC(2)) ab initio wave function and time-dependent density functional theory (TDDFT) the gas-phase electronic absorption spectra of 15 derivatives of p-nitroaniline (pNA). The investigated substituents include both electron-donor (C6H5, CCH, CH3, NH2, OCH3, and OH,) and electron-withdrawing (Br, CCl3, CF3, Cl, CN, COOH, F, NO2, and SO2H) substituents.

Revisiting the benzene excimer using [2,2] paracyclophane model system: Experiment and theory

We report high-level calculations of the excited states of [2,2]-paracyclophane (PCP), which was recently investigated experimentally by ultrafast pump-probe experiments on oriented single crystals [Haggag et al., ChemPhotoChem 6 e202200181 (2022)]. PCP, in which the orientation of the two benzene rings and their range of motion are constrained, serves as a model for studying benzene excimer formation. The character of the excimer state and the state responsible for the brightest transition are similar to those of the benzene dimer. The constrained structure of PCP allows one to focus on the most important degree of freedom, the inter-ring distance. The calculations explain the main features of the transient absorption spectral evolution. This brightest transition of the excimer is polarized along the inter-fragment axis. The absorption of the light polarized in the plane of the rings reveals the presence of other absorbing states of Rydberg character, with much weaker intensities. We also report new transient absorption data obtained by a broadband 8 fs pump, which time-resolve strong modulations of the excimer absorption. The combination of theory and experiment provides a detailed picture of the evolution of the electronic structure of the PCP excimer in the course of a single molecular vibration.

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.

Performance of Density Functionals for Excited-State Properties of Isolated Chromophores and Exciplexes: Emission Spectra, Solvatochromic Shifts, and Charge-Transfer Character

This study assesses the performance of various meta-generalized gradient approximation (meta-GGA), global hybrid, and range-separated hybrid (RSH) density functionals in capturing the excited-state properties of organic chromophores and their excited-state complexes (exciplexes). Motivated by their uses in solar energy harvesting and photoredox CO2 reduction, we use oligo-(p-phenylenes) and their excited-state complexes with triethylamine as model systems. We focus on the fluorescence properties of these systems, specifically emission energies. We also consider solvatochromic shifts and wave function characteristics. The latter is described by using reduced quantities such as natural transition orbitals (NTOs) and exciton descriptors. The functionals are benchmarked against the experimental fluorescence spectra and the equation-of-motion coupled-cluster method with single and double excitations. Both in isolated chromophores and in exciplexes, meta-GGA functionals drastically underestimate the emission energies and exhibit significant exciton delocalization and anticorrelation between electron and hole motion. The performance of global hybrid functionals is strongly dependent on the percentage of exact exchange. Our study identifies RSH GGAs as the best-performing functionals, with ωPBE demonstrating the best agreement with experimental results. RSH meta-GGAs often overestimate emission energies in exciplexes and yield larger hole NTOs. Their performance can be improved by optimally tuning the range-separation parameter.

Visualizing and characterizing excited states from time-dependent density functional theory

Time-dependent density functional theory (TD-DFT) is the most widely-used electronic structure method for excited states, due to a favorable combination of low cost and semi-quantitative accuracy in many contexts, even if there are well recognized limitations. This Perspective describes various ways in which excited states from TD-DFT calculations can be visualized and analyzed, both qualitatively and quantitatively. This includes not just orbitals and densities but also well-defined statistical measures of electron-hole separation and of Frenkel-type exciton delocalization. Emphasis is placed on mathematical connections between methods that have often been discussed separately. Particular attention is paid to charge-transfer diagnostics, which provide indicators of when TD-DFT may not be trustworthy due to its categorical failure to describe long-range electron transfer. Measures of exciton size and charge separation that are directly connected to the underlying transition density are recommended over more ad hoc metrics for quantifying charge-transfer character.

Eclipsed and Twisted Excimers of Pyrene and 2-Azapyrene: How Nitrogen Substitution Impacts Excimer Emission

Due to their unique photophysical and electronic properties, pyrene and its analogues have been the subject of extensive research in recent decades. The propensity of pyrene and its derivatives to form excimers has found wide application in various fields. Nitrogen-substituted pyrene derivatives display similar photophysical properties, but for them, excimer emission has not been reported to date. Here, we use time-dependent density functional theory (TD-DFT) calculations to investigate the low-lying exciton states of dimers of pyrene and 2-azapyrene. The excimer equilibrium structures are determined and the contribution of charge transfer (CT) excitations and intermolecular interactions to the exciton states is disclosed using a diabatization procedure. The study reveals that the dimers formed by the two molecules have quite similar exciton-state patterns, in which the relevant CT contributions govern the formation of excimer states, along with the La/Lb state inversion. In contrast with pyrene, the dipole-dipole interactions in 2-azapyrene stabilize the dark eclipsed excimer structure and increase the barrier for conversion into a bright twisted excimer. It is suggested that these differences in the nitrogen-substituted derivative might influence the excimer emission properties.

Quantification of the Ionic Character of Multiconfigurational Wave Functions: The Qat Diagnostic

The complete active space self-consistent field (CASSCF) method is a cornerstone in modern excited-state quantum chemistry providing the starting point for most common multireference computations. However, CASSCF, when used with a minimal active space, can produce significant errors (>2 eV) even for the excitation energies of simple hydrocarbons if the states of interest possess ionic character. After illustrating this problem in some detail, we present a diagnostic for ionic character, denoted as Q at, that is readily computed from the transition density. A set of 11 molecules is considered to study errors in vertical excitation energies. State-averaged CASSCF obtains a mean absolute error (MAE) of 0.87 eV for the 34 singlet states considered. We highlight a strong correlation between the obtained errors and the Q at diagnostic, illustrating its power to predict problematic cases. Conversely, using multireference configuration interaction with single and double excitations and Pople's size extensivity correction (MR-CISD+P), excellent results are obtained with an MAE of 0.11 eV. Furthermore, correlations with the Q at diagnostic disappear. In summary, we hope that the presented diagnostic will facilitate reliable and user-friendly multireference computations on conjugated organic molecules.

μ2 -η1 :η1 -N2 Bridged Bimetallic Dinitrogen Complexes: Geometry of the First Excited State in Connection to N2 π-Photoactivation

Bimetallic end-on μ2 -η1 :η1 -N2 bridging dinitrogen complexes have served as the platform for photochemical N2 activation, mainly for the N-N cleavage. However, the alternate N-N π-photoactivation route has remained largely unexplored. This study strengthens the notion of weakening the N-N bond through the population of π* orbital upon electronic excitation from the ground to the first excited state using four prototypical complexes based on Fe (1), Mo (2), and Ru (3,4). The complexes 1-4 possess characteristic N-N π* based LUMO (π*-π*-π*) centered on their M-N-N-M core, which was earlier postulated to play a central role in the N2 photoactivation. Vertical electronic excitation of the highest oscillator strength involves transitions to the N-N π*-based acceptor orbital (π*-π*-π*) in complexes 1-4. This induces geometry relaxation of the first excited metal-to-nitrogen (π*) charge transfer (1 MNCT) state leading to a "zigzag" M-N-N-M core in the equilibrium structure. Obtaining the equilibrium geometry in the first excited state with the full-sized complexes widens the scope of N-N π-photoactivation with μ2 -η1 :η1 -N2 bridging dinitrogen complexes. Promisingly, the elongated N-N bond and bent ∠MNN angle in the photoexcited S1 state of 1-4 resemble their radical- and di-anion forms, which lead toward thermodynamically feasible N-N protonation in the S1 excited state.

Molecular-Orbital Framework of Two-Electron Processes: Application to Auger and Intermolecular Coulomb Decay

States with core- or inner-shell vacancies, which are commonly created by absorption of high-energy photons, can decay by a two-electron process in which one electron fills the core hole and the second one is ejected. These processes accompany many X-ray spectroscopies. Depending on the nature of the initial core- or inner-shell-hole state and the decay valence-hole state, these processes are called Auger decay, intermolecular Coulomb decay, or electron-transfer-mediated decay. To connect many-body wave functions of the initial and final states with the molecular orbital picture of the decay, we introduce the concept of natural Auger orbitals (NAOs). NAOs are obtained by a two-step singular value decomposition of the two-body Dyson orbitals, reduced quantities that enter the expression of the decay rate in the Feshbach-Fano treatment. NAOs afford chemical insight and interpretation of the high-level ab initio calculations of Auger decay and related two-electron relaxation processes.

Natural orbitals and two-particle correlators as tools for the analysis of effective exchange couplings in solids

Using generalizations of spin-averaged natural orbitals and two-particle charge correlators for solids, we investigate the electronic structure of antiferromagnetic transition-metal oxides with a fully self-consistent, imaginary-time GW method. Our findings disagree with the Goodenough-Kanamori (GK) rules that are commonly used for the qualitative interpretation of such solids. First, we found a strong dependence of the natural orbital occupancies on momenta, contradicting GK assumptions. Second, along the momentum path, the character of natural orbitals changes. In particular, the contributions of oxygen 2s orbitals are important, which has not been considered in the GK rules. To analyze the influence of the electronic correlation on the values of effective exchange coupling constants, we use both natural orbitals and two-particle correlators and show that electronic screening modulates the degree of superexchange by stabilizing the charge-transfer contributions, which greatly affects these coupling constants. Finally, we give a set of predictions and recommendations regarding the use of density functional, Green's function, and wave-function methods for evaluating effective magnetic couplings in molecules and solids.

Excited states of ortho-nitrobenzaldehyde as a challenging case for single- and multi-reference electronic structure theory

We present a large set of vertical excitation calculations for the ortho-nitrobenzaldehyde (oNBA) molecule, which exhibits a very challenging excited-state electronic structure like other nitroaromatic compounds. The single-reference methods produce mostly consistent results up to about 5.5 eV. By contrast, the CAS second-order perturbation theory (CASPT2) results depend sensitively on the employed parameters. At the CAS self-consistent field level, the energies of the bright ππ * $$ {\pi \pi}^{\ast } $$ states are strongly overestimated while doubly excited states appear too low and mix with these ππ * $$ {\pi \pi}^{\ast } $$ states. This mixing hampers the CASPT2 step, leading to inconsistent results. Only by increasing the number of states in the state-averaging step to about 40-to cover all bright ππ * $$ {\pi \pi}^{\ast } $$ states embedded in the double excitations-and employing extended multistate CASPT2 could CASPT2 results consistent with experiment be obtained. We assign the four bands in the molecule's spectrum: The weakest band at 3.7 eV arises from the n NO 2 π * $$ {n}_{\mathrm{NO}2}{\pi}^{\ast } $$ states, the second one at 4.4 eV from the ππ * $$ {\pi \pi}^{\ast } $$ ( L b $$ {L}_b $$ ) state, the shoulder at 5.2 eV from the ππ * $$ {\pi \pi}^{\ast } $$ ( L a $$ {L}_a $$ ) state, and the maximum at 5.7 eV from the ππ * $$ {\pi \pi}^{\ast } $$ ( B a / B b $$ {B}_a/{B}_b $$ ) states. We also highlight the importance of modern wave function analysis techniques in elucidating the absorption spectrum of challenging molecules.

Intermolecular Interactions and Charge Resonance Contributions to Triplet and Singlet Exciton States of Oligoacene Aggregates

Intermolecular interactions modulate the electro-optical properties of molecular materials and the nature of low-lying exciton states. Molecular materials composed by oligoacenes are extensively investigated for their semiconducting and optoelectronic properties. Here, we analyze the exciton states derived from time-dependent density functional theory (TDDFT) calculations for two oligoacene model aggregates: naphthalene and anthracene dimers. To unravel the role of inter-molecular interactions, a set of diabatic states is selected, chosen to coincide with local (LE) and charge-transfer (CT) excitations within a restricted orbital space including two occupied and two unoccupied orbitals for each molecular monomer. We study energy profiles and disentangle inter-state couplings to disclose the (CT) character of singlet and triplet exciton states and assess the influence of inter-molecular orientation by displacing one molecule with respect to the other along the longitudinal translation coordinate. The analysis shows that (CT) contributions are relevant, although comparably less effective for triplet excitons, and induce a non-negligible mixed character to the low-lying exciton states for eclipsed monomers and for small translational displacements. Such (CT) contributions govern the L_a/L_b state inversion occurring for the low-lying singlet exciton states of naphthalene dimer and contribute to the switch from H- to J-aggregate type of the strongly allowed B_b transition of both oligoacene aggregates.

Cherry-Picking Resolvents: Recovering the Valence Contribution in X-ray Two-Photon Absorption within the Core-Valence-Separated Equation-of-Motion Coupled-Cluster Response Theory

Calculations of first-order response wave functions in the X-ray regime often diverge within correlated frameworks such as equation-of-motion coupled-cluster singles and doubles (EOM-CCSD), a consequence of the coupling with the valence ionization continuum. Here, we extend our strategy of introducing a hierarchy of approximations to the EOM-EE-CCSD resolvent (or, inversely, the model Hamiltonian) involved in the response equations for the calculation of X-ray two-photon absorption (X2PA) cross sections. We exploit the frozen-core core-valence separation (fc-CVS) scheme to first decouple the core and valence Fock spaces, followed by a separate approximate treatment of the valence resolvent. We demonstrate the robust convergence of X-ray response calculations within this framework and compare X2PA spectra of small benchmark molecules with the previously reported density functional theory results.

Theoretical Study of the Structural, Optoelectronic, and Reactivity Properties of N-[5′-Methyl-3′-Isoxasolyl]-N-[(E)-1-(-2-)]Methylidene] Amine and Some of Its Fe2+, Co2+, Ni2+, Cu2+, and Zn2+ Complexes for OLED and OFET Applications

Herein, we report the structural, electronic, and charge transfer properties of N-[5′-methyl-3′-isoxasolyl]-N-[(E)-1-(-2-thiophene)] methylidene] amine (L) and its Fe2+, Co2+, Ni2+, Cu2+, and Zn2+ complexes (dubbed A, B, C, D, and E, respectively) using the density functional theory (DFT). All molecules investigated were optimized at the BP86/def2-TZVP/RI level of theory. Single point energy calculations were carried out at the M06-D3ZERO/def2-TZVP/RIJCOSX level of theory. Reorganization energies of the hole and electron (λh and λe) and the charge transfer mobilities of the electron and hole (μe and μh) have been computed and reported. The λe and λh values vary in the order D > E > A > B > C > L and E > A > D > L > C > B, respectively, while μe and μh vary in the order B > C > L > A > E > D and C > B > A > L > E > D, respectively. μh of B (39.5401 cm2·V−1S−1) and C (366.4740 cm2·V−1s−1) is remarkably large, suggesting their application in organic light-emitting diode (OLED) and organic field-effect transistor (OFET) technologies. Electron excitation analysis based on time-dependent (TD)-DFT calculations revealed that charge transfer excitations may significantly affect charge transfer mobilities. Based on charge transfer mobility results, B and C are outstanding and are promising molecules for the manufacture of electron and hole-transport precursor materials for the construction of OLED and OFET devices as compared to L. The results also show that L and all its complexes interestingly have higher third-order NLO activity than those of para-nitroaniline, a prototypical NLO molecule.

Charge-Transfer Excitations within Density Functional Theory: How Accurate Are the Most Recommended Approaches?

The performance of the most recent density functionals is assessed for charge-transfer (CT) excitations using comprehensive intra- and intermolecular CT benchmark sets with high-quality reference values. For this comparison, the state-of-the-art range-separated (RS) and long-range-corrected (LC) double hybrid (DH) approaches are selected, and global DH and LC hybrid functionals are also inspected. The correct long-range behavior of the exchange-correlation (XC) energy is extensively studied, and various CT descriptors are compared as well. Our results show that the most robust performance is attained by RS-PBE-P86/SOS-ADC(2), as it is suitable to describe both types of CT excitations with outstanding accuracy. Furthermore, concerning the intramolecular transitions, unexpectedly excellent results are obtained for most of the global DHs, but their limitations are also demonstrated for bimolecular complexes. Despite the outstanding performance of the LC-DH methods for common intramolecular excitations, serious deficiencies are pointed out for intermolecular CT transitions, and the wrong long-range behavior of the XC energy is revealed. The application of LC hybrids to such transitions is not recommended in any respect.

Insight into the defluorination ability of per- and polyfluoroalkyl substances based on machine learning and quantum chemical computations

UV-generated hydrated electrons play a critical role in the defluorination reaction of poly- and perfluoroalkyl substances (PFAS). However, limited experimental data hinder insight into the effects of the structural characteristics of emerging PFAS on their defluorination abilities. Therefore, in this study, we adopted quantity structure-activity relationship models based on machine learning algorithms to develop the predictive models of the relative defluorination ability of PFAS. Five-fold cross-validations were used to perform the hyperparameter tuning of the models, which suggested that the gradient boosting algorithms with PaDEL descriptors as the best model possessed superior predictive performance (R²_test = 0.944 and RMSE_test = 0.114). The importance of the descriptor indicated that the electrostatic properties and topological structure of the compounds significantly affected the defluorination ability of the PFAS. For the emerging PFAS the best model showed that most compounds, such as potential alternatives of perfluorooctane sulfonic acid, were recalcitrant to reductive defluorination, whereas perfluoroalkyl ether carboxylic acids had relatively stronger defluorination abilities than perfluorooctanoic acid. The theoretical calculations implied that additional electrons on PFAS could cause molecular deconstruction, such as changes in the dihedral angle involved in the carbon chain, as well as C-F bond and ether C-O bond cleavages. In general, the current computational models could be useful for screening emerging PFAS to assess their defluorination ability for the molecular design of fluorochemical structures.

Influence of N-introduction in pentacene on the electronic structure and excited electronic states

N-Heteropolycyclic aromatic compounds are promising organic semiconductors for applications in field effect transistors and solar cells. Thereby the electronic structure of organic/metal interfaces and thin films is essential for the performance of organic-molecule-based devices. Here, we studied the structural and the electronic properties of 6,7,12,13-tetraazapentacene (TAP) adsorbed on Au(111) using vibrational and electronic high-resolution electron energy loss spectroscopy in combination with state-of-the-art quantum chemical calculations. In the mono- and multilayer TAP adsorbs in a planar adsorption geometry with the molecular backbone oriented parallel to the gold substrate. The energies of the lowest excited electronic singlet states (S) as well as the triplet state (T) are assigned. The optical gap (S₀ → S₁ transition) is found to be 1.6 eV and the T₁ energy 1.2 eV. In addition, thorough comparison to previously studied pentacene (PEN) and 6,13-diazapentacene (6,13-DAP) is made explaining in detail the influence of nitrogen substitution on the electronic structure and in particular on the intensity of the α-band in the UV/vis absorption spectrum. In the series PEN, 6,13-DAP, and TAP, the α-band (S₀ → S₂ transition) gains significantly in intensity due to individual effects of the introduced nitrogen atoms on the orbital energies.

Impact of Charge-Resonance Excitations on CT-Mediated J-Type Aggregation in Singlet and Triplet Exciton States of Perylene Di-Imide Aggregates: A TDDFT Investigation

The modulation of intermolecular interactions upon aggregation induces changes in excited state properties of organic molecules that can be detrimental for some optoelectronic applications but can be exploited for others. The time-dependent density functional theory (TDDFT) is a cost-effective approach to determining the exciton states of molecular aggregates, and it has been shown to provide reliable results when coupled with the appropriate choice of the functional. Here we apply a general procedure to analyze the aggregates’ exciton states derived from TDDFT calculations in terms of diabatic states chosen to coincide with local (LE) and charge-transfer (CT) excitations within a restricted orbital space. We apply the approach to study energy profiles, interstate couplings, and the charge-transfer character of singlet and triplet exciton states of perylene di-imide aggregates (PDI). We focus on the intermolecular displacement along the longitudinal translation coordinate, which mimics different amounts of slip-stacking observed in PDI crystals. The analysis, in terms of symmetry-adapted Frenkel excitations (FE) and charge-resonance (CR) states and their interactions, discloses how the interchange of the H/J character for small longitudinal shifts, previously reported for singlet exciton states, also occurs for triplet excitons.

Absorption Spectra and the Electronic Structure of Gallic Acid in Water at Different pH: Experimental Data and Theoretical Cluster Models

Gallic acid (GA) has been characterized in terms of its optical properties in aqueous solutions at varying pH in experiments and in theoretical calculations by analyzing the protonated and deprotonated forms of GA. This work is part of a series of studies of the optical properties of different carboxylic acids in aqueous media. The experimental electronic spectra of GA exhibit two strong well-separated absorption peaks (B- and C-bands), which agree with previous studies. However, in the current study, an additional well-defined low-energy shoulder band (A-band) in the optical spectra of GA was identified. It is likely that the A-band occurs for other carboxylic acids in solution, but because it can overlap with the B-band, it is difficult to discern. The theoretical calculations based on density functional theory were used to simulate the optical absorption spectra of GA in water at different pH to prove the existence of this newly found shoulder band and to describe and characterize the full experimental optical spectra of GA. Different cluster models were tested: (i) all water molecules are coordinated near the carboxy-group and (ii) additional water molecules near the hydroxy-groups of the phenyl ring were included. In this study, we found that both the polarizable continuum model (dielectric property of a medium) and neighboring water molecules (hydrogen-bonding) play significant roles in the optical spectrum. The results showed that only an extended cluster model with water molecules near carboxy- and hydroxy-groups together with the polarizable continuum model allowed us to fully reproduce the experimental data and capture all three absorption bands (A, B, and C). The oscillator strengths of the absorption bands were obtained from the experimental data and compared with theoretical results. Additionally, our work provides a detailed interpretation of the pH effects observed in the experimental absorption spectra.

Oxygen Deficiencies in Titanium Oxide Clusters as Models for Bulk Defects

TD-DFT calculations were performed on neutral Ti_nO_2n, Ti_nO_2n-1, and Ti_nO_2n-2 clusters, where n ≤ 7. Calculations show the Ti_nO_2n clusters are closed shell systems containing empty d orbitals and that the partially filled d orbitals of the suboxide clusters have a profound effect on their structural, electronic, and topological properties. The low energy photoexcitations of Ti_nO_2n clusters are all O-2p to Ti-3d transitions, while the open-shell suboxide clusters are all characterized by d-d transitions that occur at a much smaller optical gap. Upon low energy photoabsorption, the localization of the hole is accompanied by a local bond elongation, i.e., polaron formation, whereas d-electrons are generally delocalized around the cluster. The properties of the clusters, including the oxygen binding energies and structures, were calculated to account for the variation in relative populations found in experimental cluster distributions. Several Ti_nO_2n-2 clusters contain higher symmetry which is reflected in their relative stability. In particular, the tetrahedral symmetry of Ti₄O₆ inhibits charge carrier localization and therefore exhibits higher stability.

The role of excited-state character, structural relaxation, and symmetry breaking in enabling delayed fluorescence activity in push-pull chromophores

Thermally activated delayed fluorescence (TADF) is a current promising route for generating highly efficient light-emitting devices. However, the design process of new chromophores is hampered by the complicated underlying photophysics. In this work, four closely related donor-π-acceptor-π-donor systems are investigated, two of which were synthesised previously, with the aim of elucidating their varying effectiveness for TADF. We outline that the frontier orbitals are insufficient for discriminating between the molecules. Subsequently, a detailed analysis of the excited states at a correlated ab initio level highlights the presence of a number of closely spaced singlet and triplet states of varying character. Results from five density functionals are compared against this reference revealing dramatic changes in, both, excited state energies and wavefunctions following variations in the amount of Hartree-Fock exchange included. Excited-state minima are optimised in solution showing the crucial role of structural variations and symmetry breaking for producing a strongly emissive S₁ state. The adiabatic singlet-triplet gaps thus obtained depend strongly on the range separation parameter used in the hybrid density functional calculations. More generally, this work highlights intricate differences present between singlet and triplet excited state wavefunctions and the challenges in describing them accurately.

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.

Software for the frontiers of quantum chemistry: An overview of developments in the Q-Chem 5 package

This article summarizes technical advances contained in the fifth major release of the Q-Chem quantum chemistry program package, covering developments since 2015. A comprehensive library of exchange-correlation functionals, along with a suite of correlated many-body methods, continues to be a hallmark of the Q-Chem software. The many-body methods include novel variants of both coupled-cluster and configuration-interaction approaches along with methods based on the algebraic diagrammatic construction and variational reduced density-matrix methods. Methods highlighted in Q-Chem 5 include a suite of tools for modeling core-level spectroscopy, methods for describing metastable resonances, methods for computing vibronic spectra, the nuclear-electronic orbital method, and several different energy decomposition analysis techniques. High-performance capabilities including multithreaded parallelism and support for calculations on graphics processing units are described. Q-Chem boasts a community of well over 100 active academic developers, and the continuing evolution of the software is supported by an "open teamware" model and an increasingly modular design.

Equation-of-Motion Coupled-Cluster Protocol for Calculating Magnetic Properties: Theory and Applications to Single-Molecule Magnets

We present a new computational protocol for computing macroscopic magnetic properties of transition-metal complexes using the equation-of-motion coupled-cluster (EOM-CC) framework. The approach follows a two-step state-interaction scheme: we first compute zero-order states using nonrelativistic EOM-CC and then use these states to evaluate matrix elements of the spin-orbit and Zeeman operators. Diagonalization of the resulting Hamiltonian yields spin-orbit- and field-perturbed eigenstates. Temperature- and field-dependent magnetization and susceptibility are computed by numerical differentiation of the partition function. To compare with powder-sample experiments, these quantities are numerically averaged over field orientations. We applied this protocol to several single-molecule magnets (SMMs) with Fe(II) and Fe(III) in trigonal pyramidal, linear, and trigonal bipyramidal coordination environments. We described the underlying electronic structure by the electron-attachment (EOM-EA) and spin-flip (EOM-SF) variants of EOM-CC. The computed energy barriers for spin inversion, and macroscopic magnetization and susceptibility agree well with experimental data. Trends in magnetic anisotropy and spin-reversal energy barriers are explained in terms of a molecular orbital picture rigorously distilled from spinless transition density matrices between many-body states. The results illustrate excellent performances of EOM-CC in describing magnetic behavior of mononuclear transition-metal SMMs.

Geometry dependence of excitonic couplings and the consequences for configuration-space sampling

Excitonic coupling plays a key role for the understanding of excitonic energy transport (EET) in, for example, organic photovoltaics. However, the calculation of realistic systems is often beyond the applicability range of accurate wavefunction methods so that lower-scaling semi-empirical methods are used to model EET events. In the present work, the distance and angle dependence of excitonic couplings of dimers of selected organic molecules are evaluated for the semi-empirical long-range corrected density functional based tight binding (LC-DFTB) method and spin opposite scaled second order approximate coupled cluster singles and doubles (SOS-CC2). While semi-empirically scaled methods can lead to slightly increased deviations for excitation energies, the excitonic couplings and their dependence on the dimer geometry are reproduced. LC-DFTB yields a similar accuracy range as density-functional theory (DFT) employing the ωB97X functional while the computation time is reduced by several orders of magnitude. The dependence of the exchange contributions to the excitonic couplings on the dimer geometry is analyzed assessing the calculation of Coulombic excitonic couplings from monomer local excited states only, which reduces the computational effort significantly. The present work is a necessary first step toward the simulation of excitonic energy transport using semi-empirical methods.

The orbital picture of the first dipole hyperpolarizability from many-body response theory

We present an approach for obtaining a molecular orbital picture of the first dipole hyperpolarizability (β) from correlated many-body electronic structure methods. Ab initio calculations of β rely on quadratic response theory, which recasts the sum-over-all-states expression of β into a closed-form expression by calculating a handful of first- and second-order response states; for resonantly enhanced β, damped response theory is used. These response states are then used to construct second-order response reduced one-particle density matrices (1PDMs), which, upon visualization in terms of natural orbitals (NOs), facilitate a rigorous and black-box mapping of the underlying electronic structure with β. We explain the interpretation of different components of the response 1PDMs and the corresponding NOs within both the undamped and damped response theory framework. We illustrate the utility of this new tool by deconstructing β for cis-difluoroethene, para-nitroaniline, and hemibonded OH^· + H₂O complex, computed within the framework of coupled-cluster singles and doubles response theory, in terms of the underlying response 1PDMs and NOs for a range of frequencies.