Unveiling the Mechanism of Plasmon Photocatalysis via Multiquantum Vibrational Excitation

Plasmon photocatalysis reactions are thought to occur through vibrationally activated reactants, driven by nonthermal energy transfer from plasmon-induced hot carriers. However, a detailed quantum-state-level understanding and quantification of the activation have been lacking. Using anti-Stokes surface-enhanced Raman scattering (SERS) spectroscopy, we mapped the vibrational population distributions of reactants on plasmon-excited nanostructures. Our results reveal a highly nonthermal distribution with an anomalously enhanced population of multiquantum excited states  (v ≥ 2). The shape of the distribution and its dependence on local field intensity and excitation wavelength cannot be explained by photothermal heating or vibronic optical transitions of the metal-molecule complex. Instead, it can be modeled by hot electron-molecule energy transfer mediated by the transient negative ions, establishing direct links among nonthermal reactant activation, plasmon-induced hot electrons, and negative ion resonances. Moreover, the presence of multiquantum excited reactants, which are far more reactive than those in the ground state or first excited state, presents opportunities for vibrationally controlling chemical selectivities.

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.

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.

Femtosecond to Microsecond Observation of Photochemical Pathways in Nitroaromatic Phototriggers Using Transient Absorption Spectroscopy

The synthetic accessibility and tolerance to structural modification of phototriggered compounds (PTs) based on the ortho- nitrobenzene (ONB) protecting group have encouraged a myriad of applications including optimization of biological activity, and supramolecular polymerization. Here, a combination of ultrafast transient absorption spectroscopy techniques is used to study the multistep photochemistry of two nitroaromatic phototriggers based on the ONB chromophore, O-(4,5-dimethoxy-2-nitrobenzyl)-l-serine (DMNB-Ser) and O-[(2-nitrophenyl)methyl]-l-tyrosine hydrochloride (NB-Tyr), in DMSO solutions on femtosecond to microsecond time scales following the absorption of UV light. From a common nitro-S1 excited state, the PTs can either undergo excited state intramolecular hydrogen transfer (ESIHT) to an aci-S1 isomer within the singlet state manifold, leading to direct S1 → S0 internal conversion through a conical intersection, or competitive intersystem crossing (ISC) to access the triplet state manifold on time scales of (1.93 ± 0.03) ps and (13.9 ± 1.2) ps for DMNB-Ser and NB-Tyr, respectively. Deprotonation of aci-T1 species to yield triplet anions is proposed to occur in both PTs, with an illustrative time constant of (9.4 ± 0.7) ns for DMNB-Ser. More than 75% of the photoexcited molecules return to their electronic ground states within 8 μs, either by direct S1 → S0 relaxation or anion reprotonation. Hence, upper limits to the quantum yields of photoproduct formation are estimated to be in the range of 13-25%. Mixed DMSO/H2O solvents show the influence of the environment on the observed photochemistry, for example, revealing two nitro-S1 lifetimes for DMNB-Ser in a 10:1 DMSO/H2O mixture of 1.95 ps and (10.1 ± 1.2) ps, which are attributed to different microsolvation environments.

Mechanistic variances in NO release: ortho vs. meta isomers of nitrophenol and nitroaniline

The NO release following 266 nm photolysis of ortho and meta isomers of nitrophenol and nitroaniline shows a bimodal translational energy distribution, wherein the slow and fast components originate from dynamics in the S0 and T1 states, respectively. The translational energy distribution profiles for any NO product state show a higher slow-to-fast (s/f) branching ratio for the ortho isomer in comparison with the meta isomer. The observed variation in the s/f branching ratio vis-à-vis the ortho and meta isomers is attributed to the presence of intramolecular hydrogen bonding between the ortho substituent and NO2 moiety, which favours the roaming mechanism.

Orbital-Optimized Versus Time-Dependent Density Functional Calculations of Intramolecular Charge Transfer Excited States

The performance of time-independent, orbital-optimized calculations of excited states is assessed with respect to charge transfer excitations in organic molecules in comparison to the linear-response time-dependent density functional theory (TD-DFT) approach. A direct optimization method to converge on saddle points of the electronic energy surface is used to carry out calculations with the local density approximation (LDA) and the generalized gradient approximation (GGA) functionals PBE and BLYP for a set of 27 excitations in 15 molecules. The time-independent approach is fully variational and provides a relaxed excited state electron density from which the extent of charge transfer is quantified. The TD-DFT calculations are generally found to provide larger charge transfer distances compared to the orbital-optimized calculations, even when including orbital relaxation effects with the Z-vector method. While the error on the excitation energy relative to theoretical best estimates is found to increase with the extent of charge transfer up to ca. -2 eV for TD-DFT, no correlation is observed for the orbital-optimized approach. The orbital-optimized calculations with the LDA and the GGA functionals provide a mean absolute error of ∼0.7 eV, outperforming TD-DFT with both local and global hybrid functionals for excitations with a long-range charge transfer character. Orbital-optimized calculations with the global hybrid functional B3LYP and the range-separated hybrid functional CAM-B3LYP on a selection of states with short- and long-range charge transfer indicate that inclusion of exact exchange has a small effect on the charge transfer distance, while it significantly improves the excitation energy, with the best-performing functional CAM-B3LYP providing an absolute error typically around 0.15 eV.

Unraveling the Ultrafast Photochemical Dynamics of Nitrobenzene in Aqueous Solution

Nitroaromatic compounds are major constituents of the brown carbon aerosol particles in the troposphere that absorb near-ultraviolet (UV) and visible solar radiation and have a profound effect on the Earth's climate. The primary sources of brown carbon include biomass burning, forest fires, and residential burning of biofuels, and an important secondary source is photochemistry in aqueous cloud and fog droplets. Nitrobenzene is the smallest nitroaromatic molecule and a model for the photochemical behavior of larger nitroaromatic compounds. Despite the obvious importance of its droplet photochemistry to the atmospheric environment, there have not been any detailed studies of the ultrafast photochemical dynamics of nitrobenzene in aqueous solution. Here, we combine femtosecond transient absorption spectroscopy, time-resolved infrared spectroscopy, and quantum chemistry calculations to investigate the primary steps following the near-UV (λ ≥ 340 nm) photoexcitation of aqueous nitrobenzene. To understand the role of the surrounding water molecules in the photochemical dynamics of nitrobenzene, we compare the results of these investigations with analogous measurements in solutions of methanol, acetonitrile, and cyclohexane. We find that vibrational energy transfer to the aqueous environment quenches internal excitation, and therefore, unlike the gas phase, we do not observe any evidence for formation of photoproducts on timescales up to 500 ns. We also find that hydrogen bonding between nitrobenzene and surrounding water molecules slows the S1/S0 internal conversion process.

Two determinant distinguishable cluster

A two reference determinant version of the distinguishable cluster with singles and doubles (DCSD) has been developed. We have implemented the two determinant distinguishable cluster (2D-DCSD) and the corresponding traditional 2D-CCSD method in a new open-source package written in Julia called ElemCo.jl. The methods were benchmarked on singlet and triplet excited states of valence and Rydberg character, as well as for singlet-triplet gaps of diradicals. It is demonstrated that the distinguishable cluster approximation improves the accuracy of 2D-CCSD.

A First Proposal on the Nitrobenzene Photorelease Mechanism of NO2 and Its Relation to NO Formation through a Roaming Mechanism

Despite the fact that NO2 is considered to be the main photoproduct of nitrobenzene photochemistry, no mechanism has ever been proposed to rationalize its formation. NO photorelease is instead a more studied process, probably due to its application in the drug delivery sector and the study of roaming mechanisms. In this contribution, a photoinduced mechanism accounting for the formation of NO2 in nitrobenzene is theorized based on CASPT2, CASSCF, and DFT electronic structure calculations and CASSCF classical dynamics. A triplet nπ* state is shown to evolve toward C-NO2 dissociation, being, in fact, the only low-lying excited state favoring such a deformation. Along the triplet dissociation path, the possibility to decay to the singlet ground state results in the frustration of the dissociation and in the recombination of the fragments, either back to the nitro or the nitrite isomer. The thermal decomposition of the latter to NO constitutes globally a roaming mechanism of NO formation.

Photodegradation of Flutamide and Halogen Derivatives of Nitrobenzotrifluoride: The NO Release Channel

The photodegradation of the nonsteroidal antiandrogen drug flutamide has been long linked to the photoisomerization involving the nitro group. In this work, the dynamics of NO photoelimination upon photolysis at 266 nm of flutamide, nitrobenzotrifluoride, and its halogen derivatives were investigated. Similar to nitrobenzene and its derivatives, a bimodal translational energy distribution was observed for the NO photofragment indicating the presence of two distinct elimination channels resulting in slow and fast components. The trends in the slow/fast branching ratio show that halogen substitution at the para position increases the triplet state yield due to the internal heavy-atom effect leading to enhancement of the fast component. Furthermore, the topology of the triplet state potential energy surface showed that the minimum energy path favors the oxaziridine ring-type intermediate over the NO2 roaming mechanism in all five molecules investigated. The steric interaction between the NO2 group and the CF3 group, which are placed in the ortho position, lowers the barrier for the formation of the oxaziridine transition state compared to that of nitrobenzene.

The Value of Different Experimental Observables: A Transient Absorption Study of the Ultraviolet Excitation Dynamics Operating in Nitrobenzene

Excess energy redistribution dynamics operating in nitrobenzene under hexane and isopropanol solvation were investigated using ultrafast transient absorption spectroscopy (TAS) with a 267 nm pump and a 340-750 nm white light continuum probe. The use of a nonpolar hexane solvent provides a proxy to the gas-phase environment, and the findings are directly compared with a recent time-resolved photoelectron imaging (TRPEI) study on nitrobenzene using the same excitation wavelength [L. Saalbach et al., J. Phys. Chem. A 2021, 125, 7174-7184]. Of note is the observation of a 1/e lifetime of 3.5-6.7 ps in the TAS data that was absent in the TRPEI measurements. This is interpreted as a dynamical signature of the T2 state in nitrobenzene─analogous to observations in the related nitronaphthalene system, and additionally supported by previous quantum chemistry calculations. The discrepancy between the TAS and TRPEI measurements is discussed, with the overall findings providing an example of how different spectroscopic techniques can exhibit varying sensitivity to specific steps along the overall reaction coordinate connecting reactants to photoproducts.

Role of Ultrafast Internal Conversion and Intersystem Crossing in the Nonadiabatic Relaxation Dynamics of ortho-Nitrobenzaldehyde

ortho-Nitrobenzaldehyde (oNBA) is a well-known photoactivated acid and a prototypical photolabile nitro-aromatic compound. Despite extensive investigations, the ultrafast relaxation dynamics of oNBA is still not properly understood, especially concerning the role of the triplet states. In this work, we provide an in-depth picture of this dynamics by combining single- and multireference electronic structure methods with potential energy surface exploration and nonadiabatic dynamics simulations using the Surface Hopping including ARbitary Couplings (SHARC) approach. Our results reveal that the initial decay from the bright ππ* state to the S₁ minimum is barrierless. It involves three changes in electronic structure from ππ* (ring) to nπ* (nitro group), to nπ* (aldehyde group), and then to another nπ* (nitro group). The decay of the ππ* takes 60-80 fs and can be tracked with time-resolved luminescence spectroscopy, where we predict for the first time a short-lived coherence of the luminescence energy with a 25 fs period. Intersystem crossing can occur already during the S₄ → S₁ deactivation cascade but also from S₁, with a time constant of about 2.4 ps and such that first a triplet ππ* state localized on the nitro group is populated. The triplet population first evolves into an nπ* and then quickly undergoes hydrogen transfer to form a biradical intermediate, from where the ketene is eventually produced. The majority of the excited population decays from S₁ through two conical intersections of equal utilization, a previously unreported one involving a scissoring motion of the nitro group that leads back to the oNBA ground state and the one involving hydrogen transfer that leads to the ketene intermediate.

Vibrationally Hot Reactants in a Plasmon-Assisted Chemical Reaction

Recent studies on plasmon-assisted chemical reactions postulate that the hot electrons of plasmon-excited nanostructures may induce a non-thermal vibrational activation of metal-bound reactants. However, the postulate has not been fully validated at the level of molecular quantum states. We directly and quantitatively prove that such activation occurs on plasmon-excited nanostructures: The anti-Stokes Raman spectra of reactants undergoing a plasmon-assisted reaction reveal that a particular vibrational mode of the reactant is selectively excited, such that the reactants possess >10 times more energy in the mode than is expected from the fully thermalized molecules at the given local temperature. Furthermore, a significant portion (∼20%) of the excited reactant is in vibrational overtone states with energies exceeding 0.5 eV. Such mode-selective multi-quantum excitation could be fully modeled by the resonant electron-molecule scattering theory. Such observations suggest that the vibrationally hot reactants are created by non-thermal hot electrons, not by thermally heated electrons or phonons of metals. The result validates the mechanism of plasmon-assisted chemical reactions and further offers a new method to explore the vibrational reaction control on metal surfaces.

Modulating the Roaming Dynamics for the NO Release in ortho-Nitrobenzenes

The dynamics of NO release upon photodissociation of nitroaromatic compounds is dependent on the nature of the interaction between the NO₂ group and substituent in the ortho position. A bimodal (slow and fast) translational energy distribution of the NO photofragment indicates the presence of two distinct NO elimination channels. The slow-to-fast branching ratio for the NO release is regulated by the hydrogen bonding ability of the ortho substituent and follows the order [OH > NH₂ > CH₃ > OCH₃], indicating that the intramolecular hydrogen bonding plays a pivotal role in NO release dynamics. Further, the topology of the triplet state potential energy surface acts as a doorway to the dissociation pathway switching between the roaming and nonroaming mechanisms, with hydrogen bonding substituents (OH and NH₂) favoring the roaming mechanism.

Amino-Terephthalonitrile-Based Single Benzene Fluorophores with Large Stokes Shifts and Solvatochromic Behavior

We have synthesized a small library of blue-to-green emissive single benzene-based fluorophores (SBFs) in a short synthetic sequence. The molecules exhibit good Stokes shift in the range of 60-110 nm and select examples also possess very high fluorescence quantum yields of up to 87%. Theoretical investigations into the ground state and excited state geometries of many of these compounds reveal that good degree of planarization between the electron donor secondary amines and electron accepting benzodinitrile units can be achieved under certain solvatochromic conditions, giving rise to the strongly fluorescent behavior. On the other hand, the excited state geometry which lacks co-planarity of the donor amine and the single benzene moiety can open up a non-fluorescent channel. Additionally, in molecules with a dinitrobenzene acceptor, the perpendicular nitro moieties render the molecules completely non-emissive.

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.

On the photorelease of nitric oxide by nitrobenzene derivatives: A CASPT2//CASSCF model

Nitroaromatic compounds can photorelease nitric oxide after UV absorption. The efficiency of the photoreaction depends on the molecular structure, and two features have been pointed out as particularly important for the yield of the process: the presence of methyl groups at the ortho position with respect to the nitro group and the degree of conjugation of the molecule. In this paper, we provide a theoretical characterization at the CASPT2//CASSCF (complete active space second-order perturbation theory//complete active space self-consistent field) level of theory of the photorelease of NO for four molecules derived from nitrobenzene through the addition of ortho methyl groups and/or the elongation of the conjugation. Our previously described mechanism obtained for the photorelease of NO in nitrobenzene has been adopted as a model for the process. According to this model, the process proceeds through a reactive singlet-triplet crossing (STC) region that the system can reach from the triplet 3(πOπ*) minimum. The energy barrier that must be surmounted in order to populate the reactive STC can be associated with the efficiency of the photoreaction. Here, the obtained results display clear differences in the efficiency of the photoreaction in the studied systems and can be correlated with experimental results. Thus, the model proves its ability to highlight the differences in the photoreaction efficiency for the nitroaromatic compounds studied here.

Electronic Structure of Nitrobenzene: A Benchmark Example of the Accuracy of the Multi-State CASPT2 Theory

The electronic structure of nitrobenzene (C₆H₅NO₂) has been studied by means of the complete active space self-consistent field (CASSCF) and multi-state second-order perturbation (MS-CASPT2) methods. To this end, an active space of 20 electrons distributed in 17 orbitals has been selected to construct the reference wave function. In this work, we have calculated the vertical excitation energies and the energy barrier for the dissociation of the molecule on the ground state into phenyl and nitrogen dioxide. After applying the corresponding vibrational corrections to the electronic energies, it is demonstrated that the MS-CASPT2//CASSCF values obtained in this work yield an excellent agreement between calculated and experimental data. In addition, other active spaces of lower size have been applied to the system in order to check the active space dependence in the results.

Potent strategy towards strongly emissive nitroaromatics through a weakly electron-deficient core

Nitroaromatics seldom fluoresce. The importance of electron-deficient (n-type) conjugates, however, has inspired a number of strategies for suppressing the emission-quenching effects of the strongly electron-withdrawing nitro group. Here, we demonstrate how such strategies yield fluorescent nitroaryl derivatives of dipyrrolonaphthyridinedione (DPND). Nitro groups near the DPND core quench its fluorescence. Conversely, nitro groups placed farther from the core allow some of the highest fluorescence quantum yields ever recorded for nitroaromatics. This strategy of preventing the known processes that compete with photoemission, however, leads to the emergence of unprecedented alternative mechanisms for fluorescence quenching, involving transitions to dark nπ* singlet states and aborted photochemistry. Forming nπ* triplet states from ππ* singlets is a classical pathway for fluorescence quenching. In nitro-DPNDs, however, these ππ* and nπ* excited states are both singlets, and they are common for nitroaryl conjugates. Understanding the excited-state dynamics of such nitroaromatics is crucial for designing strongly fluorescent electron-deficient conjugates.

Making Nitronaphthalene Fluoresce

Nitroaromatic compounds are inherently nonfluorescent, and the subpicosecond lifetimes of the singlet excited states of many small nitrated polycyclic aromatic hydrocarbons, such as nitronaphthalenes, render them unfeasible for photosensitizers and photo-oxidants, despite their immensely beneficial reduction potentials. This article reports up to a 7000-fold increase in the singlet-excited-state lifetime of 1-nitronaphthalene upon attaching an amine or an N-amide to the ring lacking the nitro group. Varying the charge-transfer (CT) character of the excited states and the medium polarity balances the decay rates along the radiative and the two nonradiative pathways and can make these nitronaphthalene derivatives fluoresce. The strong electron-donating amine suppresses intersystem crossing (ISC) but accommodates CT pathways of nonradiate deactivation. Conversely, the N-amide does not induce a pronounced CT character but slows down ISC enough to achieve relatively long lifetimes of the singlet excited state. These paradigms are key for the pursuit of electron-deficient (n-type) organic conjugates with promising optical characteristics.

Ultraviolet Excitation Dynamics of Nitrobenzenes

Time-resolved photoelectron imaging was used to investigate nonadiabatic processes operating in the excited electronic states of nitrobenzene and three methyl-substituted derivatives: 3,5-, 2,6-, and 2,4-dimethylnitrobenzene. The primary goal was evaluating the dynamical impact of the torsional angle between the NO₂ group and the benzene ring plane-something previously implicated in mediating the propensity for branching into different photodissociation pathways (NO vs NO₂ elimination). Targeted, photoinitiated release of NO radicals is of interest for clinical medicine applications, and there is a need to establish basic structure-dynamics-function principles in systematically varied model systems following photoexcitation. Within our 200 ps experimental detection window, we observed no significant differences in the excited-state lifetimes exhibited by all species under study using a 267 nm pump and ionization with an intense 400 nm probe. In agreement with previous theoretical predictions, this suggests that the initial energy redistribution dynamics within the singlet and triplet manifolds are driven by motions localized predominantly on the NO₂ group. Our findings also imply that both NO and NO₂ elimination occur from a vibrationally hot ground state on extended (nanosecond) timescales, and any variations in NO vs NO₂ branching upon site-selective methylation are due to steric effects influencing isomerization prior to dissociation.

Method for Calculating Excited Electronic States Using Density Functionals and Direct Orbital Optimization with Real Space Grid or Plane-Wave Basis Set

A direct orbital optimization method is presented for density functional calculations of excited electronic states using either a real space grid or a plane-wave basis set. The method is variational, provides atomic forces in the excited states, and can be applied to Kohn-Sham (KS) functionals as well as orbital-density-dependent (ODD) functionals including explicit self-interaction correction. The implementation for KS functionals involves two nested loops: (1) An inner loop for finding a stationary point in a subspace spanned by the occupied and a few virtual orbitals corresponding to the excited state; (2) an outer loop for minimizing the energy in a tangential direction in the space of the orbitals. For ODD functionals, a third loop is used to find the unitary transformation that minimizes the energy functional among occupied orbitals only. Combined with the maximum overlap method, the algorithm converges in challenging cases where conventional self-consistent field algorithms tend to fail. The benchmark tests presented include two charge-transfer excitations in nitrobenzene and an excitation of CO to degenerate π* orbitals where the importance of complex orbitals is illustrated. The application of this method to several metal-to-ligand charge-transfer and metal-centered excited states of an Fe^II photosensitizer complex is described, and the results are compared to reported experimental estimates. This method is also used to study the effect of the Perdew-Zunger self-interaction correction on valence and Rydberg excited states of several molecules, both singlet and triplet states, and the performance compared to semilocal and hybrid functionals.

Orbital Optimized Density Functional Theory for Electronic Excited States

Density functional theory (DFT) based modeling of electronic excited states is of importance for investigation of the photophysical/photochemical properties and spectroscopic characterization of large systems. The widely used linear response time-dependent DFT (TDDFT) approach is, however, not effective at modeling many types of excited states, including (but not limited to) charge-transfer states, doubly excited states, and core-level excitations. In this perspective, we discuss state-specific orbital optimized (OO) DFT approaches as an alterative to TDDFT for electronic excited states. We motivate the use of OO-DFT methods and discuss reasons behind their relatively restricted historical usage (vs TDDFT). We subsequently highlight modern developments that address these factors and allow efficient and reliable OO-DFT computations. Several successful applications of OO-DFT for challenging electronic excitations are also presented, indicating their practical efficacy. OO-DFT approaches are thus increasingly becoming a useful route for computing excited states of large chemical systems. We conclude by discussing the limitations and challenges still facing OO-DFT methods, as well as some potential avenues for addressing them.

Fluorescent Chromophores Containing the Nitro Group: Relatively Unexplored Emissive Properties

Apart from numerous applications, for example in azo dye precursors, explosives, and industrial processes, the nitro group (-NO₂ ) appears on countless molecules in photochemical research owing to its unique characteristics such as a strong electron-withdrawing ability and facile conversion to the reduced substituent. Although it is well known as a fluorescence quencher, fluorescent chromophores that contain the nitro group have also emerged, with 3-nitrophenothiazine being recently reported to have 100 % emission quantum yield in nonpolar solvents. The diverse characters of nitro-containing chromophores motivated us to systematically review those chromophores with nitro substituents, their associated photophysical properties, and applications. In this Review, we succinctly elaborate the advance of the fluorescent nitro chromophores in fields of intramolecular charge transfer, fluorescent probes and nonlinear properties. Special attention is paid to the rationalization of the associated emission spectroscopy, so that the readers can gain insights into the structure-photophysics relationship and hence gain insights for the strategic design of nitro chromophores.

Time-resolved ultrafast transient polarization spectroscopy to investigate nonlinear processes and dynamics in electronically excited molecules on the femtosecond time scale

We report a novel experimental technique to investigate ultrafast dynamics in photoexcited molecules by probing the 3rd-order nonlinear optical susceptibility. A non-collinear 3-pulse scheme is developed to probe the ultrafast dynamics of excited electronic states using the optical Kerr effect. Optical homodyne and optical heterodyne detections are demonstrated to measure the 3rd-order nonlinear optical response for the S₁ excited state of liquid nitrobenzene, which is populated by 2-photon absorption of a 780 nm 40 fs excitation pulse.

Excited State Orbital Optimization via Minimizing the Square of the Gradient: General Approach and Application to Singly and Doubly Excited States via Density Functional Theory

We present a general approach to converge excited state solutions to any quantum chemistry orbital optimization process, without the risk of variational collapse. The resulting square gradient minimization (SGM) approach only requires analytic energy/Lagrangian orbital gradients and merely costs 3 times as much as ground state orbital optimization (per iteration), when implemented via a finite difference approach. SGM is applied to both single determinant ΔSCF and spin-purified restricted open-shell Kohn-Sham (ROKS) approaches to study the accuracy of orbital optimized DFT excited states. It is found that SGM can converge challenging states where the maximum overlap method (MOM) or analogues either collapse to the ground state or fail to converge. We also report that ΔSCF/ROKS predict highly accurate excitation energies for doubly excited states (which are inaccessible via TDDFT). Singly excited states obtained via ROKS are also found to be quite accurate, especially for Rydberg states that frustrate (semi)local TDDFT. Our results suggest that orbital optimized excited state DFT methods can be used to push past the limitations of TDDFT to doubly excited, charge-transfer, or Rydberg states, making them a useful tool for the practical quantum chemist's toolbox for studying excited states in large systems.

How important is roaming in the photodegradation of nitrobenzene?

Three pathways have been found for the formation of NO from nitrobenzene photodegradation that lead to either low or high translational energy, with a roaming mechanism involved at high excitation energies.

Variational calculations of excited states via direct optimization of the orbitals in DFT

A direct optimization method for obtaining excited electronic states using density functionals is presented.

Nonadiabatic Dynamics Simulation Predict Intersystem Crossing in Nitroaromatic Molecules on a Picosecond Time Scale

Previous time-resolved spectroscopic experiments and static quantum-chemical calculations attributed nitronaphthalene derivatives one of the fastest time scales for intersystem crossing within organic molecules, reaching the 100 fs mark. Nonadiabatic dynamics simulations on three nitronaphthalene derivatives challenge this view, showing that the experimentally observed ∼100 fs process corresponds to internal conversion in the singlet manifolds. Intersystem crossing, instead, takes place on a longer time scale of ∼1 ps. The dynamics simulations further reveal that the spin transitions occur via two distinct pathways with different contribution for the three systems, which are determined by electronic factors and the torsion of the nitro group. This study, therefore, indicates that the existence of sub-picosecond intersystem crossing in other nitroaromatic molecules should be questioned.

Density-based descriptors and exciton analyses for visualizing and understanding the electronic structure of excited states

Analysis and interpretation of the electronic structure of excited electronic states are prerequisites for developing a fundamental understanding of photochemistry and optical properties of molecular systems and an everyday task for a computational photochemist. Hence, wavefunction-based and density-based analysis tools have been devised over the last decades, and most recently also a family of quantitative exciton-wavefunction based descriptors has been developed. While the latter represent the main focus of this perspective, they are also discussed in the context of other existing analysis methods. Exciton analysis bridges the gap between the physically intuitive exciton picture and complex quantum-chemical wavefunctions by yielding insightful quantitative descriptors like exciton size, hole and electron size, electron-hole distance and exciton correlation. Thereby, not only a comprehensive characterization of the electronic structure is provided, but moreover, the formalism is automatizable and thus also optimally suited for benchmarking excited-state electronic structure methods.

Similar chemical structures, dissimilar triplet quantum yields: a CASPT2 model rationalizing the trend of triplet quantum yields in nitroaromatic systems

S₁/S₀ accessibility strongly influences the triplet quantum yields of nitronaphthalenes.

A Photophysical Deactivation Channel of Laser-Excited TATB Based on Semiclassical Dynamics Simulation and TD-DFT Calculation

A deactivation channel for laser-excited 1,3,5-triamino-2,4,6-trinitrobenzene (TATB) was studied by semiclassical dynamics. Results indicate that the excited state resulting from an electronic transition from the highest occupied molecular orbital (HOMO) to the lowest unoccupied molecular mrbital (LUMO) is deactivated via pyramidalization of the activated N atom in a nitro group, with a lifetime of 2.4 ps. An approximately 0.5-electron transfer from the aromatic ring to the activated nitro group led to a significant increase of the C–NO₂ bond length, which suggests that C–NO₂ bond breaking could be a trigger for an explosive reaction. The time-dependent density functional theory (TD-DFT) method was used to calculate the energies of the ground and S₁ excited states for each configuration in the simulated trajectory. The S₁←S₀ energy gap at the instance of non-adiabatic decay was found to be 0.096 eV, suggesting that the decay geometry is close to the conical intersection.

Intersystem Crossing Drives Photoisomerization in o-Nitrotoluene, a Model for Photolabile Caged Compounds

o-Nitrobenzyl (oNB) derivatives are widely used photolabile caged compounds in chemical and biological applications. The primary step in the photoinduced deprotection is an excited state intramolecular hydrogen transfer (ESIHT) leading to tautomerization of the oNB compound and subsequent release of the protecting group. The prototype molecule for studying such ESIHT is o-nitrotoluene (oNT), where hydrogen transfers from the methyl to the nitro group. Using the complete active space self-consistent field (CASSCF) method with second-order perturbative energy corrections (CASPT2), we have comprehensively investigated the photoisomerization and photo decay mechanisms in oNT. We have obtained the minimum energy crossing points (MECPs) between relevant electronic states and identified the singlet and triplet pathways. There is a barrierless path for oNT to relax to the lowest triplet state. In this T₁ state, the ESIHT products are more stable than T₁ oNT. Hydrogen-transfer occurs on the T₁ state followed by relaxation to the ground state to give the isomerized product. A biradical intermediate proposed by previous studies is characterized to be the hydrogen-transferred T₁ product. On the singlet pathway, in contrast to the triplet, the ground state tautomer is formed from the S₁ oNT through a geometrically distant and energetically higher S₁/S₀ conical intersection. Although nonadiabatic dynamical studies are essential for determining branching ratios, our study, which considers the accessibility of different MECPs based on geometry and energy, and the magnitude of spin-orbit coupling at singlet-triplet MECPs, suggests that a significant fraction of the isomerization yield is due to the triplet channel.

Modeling TADF in organic emitters requires a careful consideration of the environment and going beyond the Franck-Condon approximation

The origin of the thermally-activated delayed fluorescence (TADF) of three organic emitters is investigated, focusing on the nature of the lowest excited states, their transition properties, as well as the role of the environment. For this purpose, the algebraic-diagrammatic construction for the polarization propagator at second order of perturbation theory [ADC(2)], time-dependent density-functional theory in the Tamm-Dancoff approximation (TDA) and unrestricted Kohn-Sham DFT in combination with the maximum-overlap method (ΔDFT) are employed. The influence of the dielectric environment is rigorously included using different variants of the polarizable continuum model. The calculations reveal the lowest excited singlet and triplet states of all studied emitters to be dominated by charge-transfer (CT) character already in the most apolar environment corresponding to cyclo-hexane. The dielectric stabilization entails a drastic reduction of the singlet-triplet gaps, increasing the calculated TADF rates by several orders of magnitude. Another ingredient for accurate TADF rates is hidden in the excited-state potential-energy surfaces along the donor-acceptor twisting angle. A presence of large, shallow plateaus in apolar environments causes the transition properties to be governed by thermal fluctuations rather than the minimum-energy geometries. This leads to a large increase of the oscillator strengths, as well as a breakdown of the Franck-Condon approximation. The last ingredient is a small but significant spin-orbit coupling (SOC) between the singlet and triplet CT states, which is traced back to a delocalization of the excitation hole or excited electron of the triplet CT state. Taking into account all of these effects, a reasonable agreement with experimental TADF and fluorescence lifetimes is obtained. For this, it proves to be sufficient to consider only the lowest lying singlet and triplet excited states.

Substituent Effect in the First Excited Singlet State of Monosubstituted Benzenes

sEDA, pEDA, and cSAR descriptors of the substituent effect were determined for >30 monosubstituted benzenes in the first excited singlet S₁ state at the LC-ωB97XD/aug-cc-pVTZ level. It was found that in the S₁ state, the σ- and π-valence electrons are a bit less and a bit more affected, respectively, than in the S₀ state, but basically, the effect in both states remains the same. In the S₀ and S₁ states, the d(C-X) distances to the substituent's first atom and the ring perimeter correlate with the sEDA and pEDA in the appropriate states, respectively. The energies and the gap of the frontier orbitals in the two states are linearly correlated and for the HOMO(S₁), LUMO(S₁), and HOMO(S₁)-LUMO(S₁) gap correlate also with the pEDA(S₁) and cSAR(S₁) descriptors. In all studied correlations, three similar groups of substituents can be distinguished, for which correlations (i) are very good, (ii) deviate slightly, and (iii) deviate significantly. Comparison of the shape of the HOMO(S₀) and HOMO(S₁) orbitals shows that for case (i) HOMO orbitals exhibit almost perfect antisymmetry against the benzene plane, for case (ii) the antisymmetry of HOMO in one of the states is either perturbed or changed, and for case (iii) one HOMO state has σ-character.

Ultrafast stimulated emission of nitrophenolates in organic and aqueous solutions

Early-time dynamics of nitroaromatics and its coressponding bases can give valuable insights into photo-induced reactions relevant to atmospheric and environmental processes. In this work, femtosecond broadband absorption spectroscopy between 350 and 700 nm has been applied to explore the ultrafast dynamics of o-, p- and m-nitrophenol anions (NP-) in basic organic and aqueous solution. Excitation at 400 nm promotes these compounds into the first bright electronic singlet state, which is a charge-transfer state. A surprising finding for all nitrophenolates was a characteristic, spectrally broad stimulated emission (SE) from the electronically excited state into the ground state. The corresponding lifetime was on the order of a few hundred femtoseconds for o- and p-NP- while it was roughly ten times larger for m-NP-. In line with earlier observations, the SE is governed by an out-of-plane torsional motion of the nitro group, leading to a close energetic approach of the relevant electronically excited singlet and ground states. Subsequent dynamics can be assigned to excited state absorption and ground state relaxation due to energy dissipation of the vibrational modes to the solvent that occur for up to several tens of picoseconds. No longer-lasting transient absorption (TA) was found; instead, a complete recovery of the ground state bleaching was observed indicating that triplet state relaxation is either not significantly involved in this spectral part or shifted to other regions. In the aqueous system, time constants for all processes are much smaller than in organic solution, a fact that can be explained by the larger dipole moment of the solvent and the correspondingly stronger intermolecular coupling between NP- and the aqueous solvent.

Mechanism of Ultrafast Intersystem Crossing in 2-Nitronaphthalene

Nitronaphthalene derivatives efficiently populate their electronically excited triplet states upon photoexcitation through ultrafast intersystem crossing (ISC). Despite having been studied extensively by time-resolved spectroscopy, the reasons behind their ultrafast ISC remain unknown. Herein, we present the first ab initio nonadiabatic molecular dynamics study of a nitronaphthalene derivative, 2-nitronaphthalene, including singlet and triplet states. We find that there are two distinct ISC reaction pathways involving different electronic states at distinct nuclear configurations. The high ISC efficiency is explained by the very small electronic and nuclear alterations that the chromophore needs to undergo during the singlet-triplet transition in the dominating ISC pathway after initial dynamics in the singlet manifold. The insights gained in this work are expected to shed new light on the photochemistry of other nitro polycyclic aromatic hydrocarbons that exhibit ultrafast intersystem crossing.