The DFT/MRCI method

Effect of Calcium and Phosphorus on Ammonium and Nitrate Nitrogen Adsorption onto Iron (Hydr)oxides Surfaces: CD-MUSIC Model and DFT Computation

Calcium (Ca2+) and phosphorous (PO43-) significantly influence the form and effectiveness of nitrogen (N), however, the precise mechanisms governing the adsorption of ammonium nitrogen (NH4+-N) and nitrate nitrogen (NO3--N) are still lacking. This study employed batch adsorption experiments, charge distribution and multi-site complexation (CD-MUSIC) models and density functional theory (DFT) calculations to elucidate the mechanism by which Ca2+ and PO43- affect the adsorption of NH4+-N and NO3--N on the goethite (GT) surface. The results showed that the adsorption of NH4+-N on the GT exhibited an initial increase followed by a decrease as pH increased, peaking at a pH of 8.5. Conversely, the adsorption of NO3--N decreased with rising pH. According to the CD-MUSIC model, Ca2+ minimally affected the NH4+-N adsorption on the GT but enhanced NO3--N adsorption via electrostatic interaction, promoting the adsorption of ≡FeOH-NO3- and ≡Fe3O-NO3- species. Similarly, PO43- inhibited the adsorption of ≡FeOH-NO3- and ≡Fe3O-NO3- species. However, PO43- boosted NH4+-N adsorption by facilitating the formation of ≡Fe3O-NH4+ via electrostatic interaction and site competition. DFT calculations indicates that although bidentate phosphate (BP) was beneficial to stabilize NH4+-N than monodentate phosphate (SP), SP-NH4+ was the main adsorption configuration at pH 5.5-9.5 owing the prevalence of SP on the GT surface under site competition of NH4+-N. The results of CD-MUSIC model and DFT calculation were verified mutually, and provide novel insights into the mechanisms underlying N fixation and migration in soil.

Multiexcitonic and optically bright states in subunits of pentacene crystals: A hybrid DFT/MRCI and molecular mechanics study

A hybrid quantum mechanics/molecular mechanics setup was used to model electronically excited pentacene in the crystal phase. Particularly interesting in the context of singlet fission (SF) is the energetic location of the antiferromagnetically coupled multiexcitonic singlet state, 1(TT), and the ferromagnetically coupled analog in relation to the optically bright singlet state. To provide photophysical properties of the accessible spin manifold, combined density functional theory and multi-reference configuration interaction calculations were performed on pentacene dimers and a trimer, electrostatically embedded in the crystal. The likelihood of a quintet intermediate in the SF process was estimated by computing singlet-quintet electron spin-spin couplings employing the Breit-Pauli Hamiltonian. The performance of the applied methods was assessed on the pentacene monomer. The character of the optically bright state and the energetic location of the 1(TT) state depend strongly on the relative orientation of the pentacene units. In the V-shaped dimers and in the trimer, the optically bright state is dominated by local and charge transfer (CT) excitations, with admixtures of doubly excited configurations. The CT excitations gain weight upon geometry relaxation, thus supporting a CT-mediated SF mechanism as the primary step of the SF process. For the slip-stacked dimer, the energetic order of the bright and the 1(TT) states swaps upon geometry relaxation, indicating strong nonadiabatic coupling close to the Franck-Condon region-a prerequisite for a coherent SF process. The multiexcitonic singlet, triplet, and quintet states are energetically too far apart and their spin-spin couplings are too small to bring about a noteworthy multiplicity mixing.

Investigation of the electronic and optical properties of bilayer CdS as a gas sensor: first-principles calculations

We utilised first-principles computations based on density functional theory to investigate the optical and electronic properties of bilayer CdS before and after the adsorption of gas molecules. Initially, we examined four candidate adsorption sites to determine the best site for adsorbing CO, CO2, SO2, H2S, and SO. In order to achieve the optimal adsorption configurations, we analysed the adsorption energy, distance, and total charge. Our findings reveal that the CdS bilayer forms a unique connection between the O and Cd atoms, as well as the S and Cd atoms, which renders it sensitive to SO2, H2S, and SO through chemical adsorption, and CO and CO2 through strong physical adsorption. The adsorption of gas molecules enhances the optical properties of the CdS bilayer. Consequently, the CdS bilayer proves to be a highly efficient gas sensor for SO2, H2S, and SO gases.

Structural Control of Highly Efficient Thermally Activated Delayed Fluorescence in Carbene Zinc(II) Dithiolates

Luminescent metal complexes based on earth abundant elements are a valuable target to substitute 4d/5d transition metal complexes as triplet emitters in advanced photonic applications. Whereas CuI complexes have been thoroughly investigated in the last two decades for this purpose, no structure-property-relationships for efficient luminescence involving triplet excited states from ZnII complexes are established. Herein, we report on the design of monomeric carbene zinc(II) dithiolates (CZT) featuring a donor-acceptor-motif that leads to highly efficient thermally activated delayed fluorescence (TADF) with for ZnII compounds unprecedented radiative rate constants kTADF =1.2×106  s-1 at 297 K. Our high-level DFT/MRCI calculations revealed that the relative orientation of the ligands involved in the ligand-to-ligand charge transfer (1/3 LLCT) states is paramount to control the TADF process. Specifically, a dihedral angle of 36-40° leads to very efficient reverse intersystem-crossing (rISC) on the order of 109  s-1 due to spin-orbit coupling (SOC) mediated by the sulfur atoms in combination with a small ΔES1-T1 of ca. 56 meV.

The nature of carotenoid S* state and its role in the nonphotochemical quenching of plants

In plants, light-harvesting complexes serve as antennas to collect and transfer the absorbed energy to reaction centers, but also regulate energy transport by dissipating the excitation energy of chlorophylls. This process, known as nonphotochemical quenching, seems to be activated by conformational changes within the light-harvesting complex, but the quenching mechanisms remain elusive. Recent spectroscopic measurements suggest the carotenoid S* dark state as the quencher of chlorophylls' excitation. By investigating lutein embedded in different conformations of CP29 (a minor antenna in plants) via nonadiabatic excited state dynamics simulations, we reveal that different conformations of the complex differently stabilize the lutein s-trans conformer with respect to the dominant s-cis one. We show that the s-trans conformer presents the spectroscopic signatures of the S* state and rationalize its ability to accept energy from the closest excited chlorophylls, providing thus a relationship between the complex's conformation and the nonphotochemical quenching.

Synthesis, Structural Characterization, and Phosphorescence Properties of Trigonal Zn(II) Carbene Complexes

The sterically demanding N-heterocyclic carbene ITr (N,N'-bis(triphenylmethyl)imidazolylidene) was employed for the preparation of novel trigonal zinc(II) complexes of the type [ZnX2(ITr)] [X = Cl (1), Br (2), and I (3)], for which the low coordination mode was confirmed in both solution and solid state. Because of the atypical coordination geometry, the reactivity of 1-3 was studied in detail using partial or exhaustive halide exchange and halide abstraction reactions to access [ZnLCl(ITr)] [L = carbazolate (4), 3,6-di-tert-butyl-carbazolate (5), phenoxazine (6), and phenothiazine (7)], [Zn(bdt)(ITr)] (bdt = benzene-1,2-dithiolate) (8), and cationic [Zn(μ2-X)(ITr)]2[B(C6F5)4]2 [X = Cl (9), Br (10), and I (11)], all of which were isolated and structurally characterized. Importantly, for all complexes 4-11, the trigonal coordination environment of the ZnII ion is maintained, demonstrating a highly stabilizing effect due to the steric demand of the ITr ligand, which protects the metal center from further ligand association. In addition, complexes 1-3 and 8-11 show long-lived luminescence from triplet excited states in the solid state at room temperature, according to our photophysical studies. Our quantum chemical density functional theory/multireference configuration interaction (DFT/MRCI) calculations reveal that the phosphorescence of 8 originates from a locally excited triplet state on the bdt ligand. They further suggest that the phenyl substituents of ITr are photochemically not innocent but can coordinate to the electron-deficient metal center of this trigonal complex in the excited state.

UV-VUV absorption spectra of azido-based energetic plasticizer bis(1,3-diazido prop-2-yl)malonate in gas phase

Ultraviolet and vacuum ultraviolet photo-absorption spectra of azido (-N3)-based energetic plasticizer, bis(1,3-diazido-prop-2-yl)-malonate (abbreviated as BDAzPM), in the gas phase is recorded at room temperature and in the photon energy range of 5.5-9.9 eV using a synchrotron radiation source. Complementary computational results obtained using the time-dependent density functional theory document the vertical transition energies and oscillator strengths. Comparison of the simulated spectra with the experimental absorption spectrum of BDAzPM reveals that the early part of the absorption spectrum of BDAzPM is of pure valence excitation character, whereas the later intense part of the absorption spectrum is dominated by mixed Rydberg and valence electronic excitations.

Polarity-Tunable Luminescence and Intersystem Crossing of a Zinc(II) Diimine Dithiolate Complex

Combined density functional theory and multireference configuration interaction methods including spin-orbit interactions have been employed to investigate the photophysical properties and deactivation pathways of a zinc diimine dithiolate complex involving the phenanthroline derivative bathocuproine and the dianionic dithiosquarate as chelating ligands. Zn(batho)(dtsq) is one of the few luminescent zinc complexes for which triplet emission had been reported in the solid state [Gronlund, P. Inorg. Chim. Acta 1995, 234, 13-18]. Because of the high dipole moment of the complex in the electronic ground state, ligand-to-ligand charge-transfer (LLCT) states experience strong hypsochromic shifts in polar media, while ligand-centered (LC) states are nearly unaffected. Rate constants for the thermally activated upconversion of the TLLCT population to the SLLCT state are promising due to a small singlet-triplet energy gap and the participation of the sulfur in the electronic excitation, but the TLLCT state is not the lowest-lying excited triplet state in ethanol solution. In addition to the TLLCT electronic structure, TLC(batho)' and TLC(dtsq) ππ* excitations form minima on the T1 potential energy surface. The SLLCT luminescence is expected to be quenched at the nanosecond time scale by the dark TLC(dtsq)ππ* state. Moreover, a TLC(dtsq)σπ* state has been identified, which leads to degradation of the compound. In mildly polar media, the dark triplet LC states are energetically inaccessible and the lowest excited singlet and triplet states clearly exhibit an LLCT character. However, their mutual spin-orbit coupling is reduced to the extent that reverse intersystem crossing is not very likely at room temperature. While Zn(diimine)(dithiolate) complexes continue to be perceived as an interesting substance class with potential application as emitters in electroluminescent devices, the particular Zn(batho)(dtsq) complex is not considered suitable for that purpose.

Impact of Di- and Poly-Radical Characters on the Relative Energy of the Doubly Excited and La States of Linear Acenes and Cyclacenes

Linear and cyclic acenes are polycyclic aromatic hydrocarbons that can be viewed as building blocks of graphene nanoribbons and carbon nanotubes, respectively. While short linear acenes demonstrated remarkable efficiency in several optoelectronic applications, the longer members are unstable and difficult to synthesize as their cyclic counterparts. Recent progress in on-surface synthesis, a powerful tool to prepare highly reactive species, opens promising perspectives and motivates the computational investigations of these potentially functional molecules. Owing to their di- and poly-radical character, low-lying excited states dominated by doubly excited configurations are expected to become more important for longer members of both linear and cyclic molecules. In this work, we investigate the lowest-lying La and the doubly excited (DE) state of linear acenes and cyclacenes, with different computational approaches, to assess the influence of the di-/poly-radical characters (increasing with the molecular dimensions) on their relative order. We show that DFT/MRCI calculations correctly reproduce the crossing of the two states for longer linear acenes, while TDUDFT calculations fail to predict the correct excitation energy trend of the DE state. The study suggests a similarity in the excited electronic state pattern of long linear and cyclic acenes leading ultimately to a lowest lying dark DE state for both.

R2022: A DFT/MRCI Ansatz with Improved Performance for Double Excitations

A reformulation of the combined density functional theory and multireference configuration interaction method (DFT/MRCI) is presented. Expressions for ab initio matrix elements are used to derive correction terms for a new effective Hamiltonian. On the example of diatomic carbon, the correction terms are derived, focusing on the doubly excited ¹Δ_g state, which was problematic in previous formulations of the method, as were double excitations in general. The derivation shows that a splitting of the parameters for intra- and interorbital interactions is necessary for a concise description of the underlying physics. Results for ¹L_a and ¹L_b states in polyacenes and ¹A_u and ¹A_g states in mini-β-carotenoids suggest that the presented formulation is superior to former effective Hamiltonians. Furthermore, statistical analysis reveals that all the benefits of the previous DFT/MRCI Hamiltonians are retained. Consequently, the here presented formulation should be considered as the new standard for DFT/MRCI calculations.

An Air- and Moisture-stable Zinc(II) Carbene Dithiolate Dimer Showing Fast Thermally Activated Delayed Fluorescence and Dexter Energy Transfer Catalysis

A dimeric Zn^II carbene complex featuring bridging and chelating benzene-1,2-dithiolate ligands is highly stable towards air and water. The donor-Zn-acceptor structure leads to visible light emission in the solid state, solution and polymer matrices with λ_max between 577-657 nm and, for zinc(II) complexes, unusually high radiative rate constants for triplet exciton decay of up to k_r =1.5×10⁵  s^-1 at room temperature. Variable temperature and DFT/MRCI studies show that a small energy gap between the ^1/3 LL/LMCT states of only 79 meV is responsible for efficient thermally activated delayed fluorescence (TADF). Time-resolved luminescence and transient absorption studies confirm the occurrence of long-lived, dominantly ligand-to-ligand charge transfer excited states in solution, allowing for application in Dexter energy transfer photocatalysis.

Interexcited State Photophysics I: Benchmarking Density Functionals for Computing Nonadiabatic Couplings and Internal Conversion Rate Constants

We present the first benchmarking study of nonadiabatic matrix coupling elements (NACMEs) calculated using different density functionals. Using the S₁ → S₀ transition in perylene solvated in toluene as a case study, we calculate the photophysical properties and corresponding rate constants for a variety of density functionals from each rung of Jacob's ladder. The singlet photoluminescence quantum yield (sPLQY) is taken as a measure of accuracy, measured experimentally here as 0.955. Important quantum chemical parameters such as geometries, absorption, emission, and adiabatic energies, NACMEs, Hessians, and transition dipole moments were calculated for each density functional basis set combination (data set) using density functional theory based multireference configuration interaction (DFT/MRCI) and compared to experiment where possible. We were able to derive simple relations between the TDDFT and DFT/MRCI photophysical properties; with semiempirical damping factors of ∼0.843 ± 0.017 and ∼0.954 ± 0.064 for TDDFT transition dipole moments and energies to DFT/MRCI level approximations, respectively. NACMEs were dominated by out-of-plane derivative components belonging to the center-most ring atoms with weaker contributions from perturbations along the transverse and longitudinal axes. Calculated theoretical spectra compared well to both experiment and literature, with fluorescence lifetimes between 7.1 and 12.5 ns, agreeing within a factor of 2 with experiment. Internal conversion (IC) rates were then calculated and were found to vary wildly between 10⁶-10¹⁶ s^-1 compared with an experimental rate of the order 10⁷ s^-1. Following further testing by mixing data sets, we found a strong dependence on the method used to obtain the Hessian. The 5 characterized data sets ranked in order of most promising are PBE0/def2-TZVP, ωB97XD/def2-TZVP, HCTH407/TZVP, PBE/TZVP, and PBE/def2-TZVP.

On the Cooperative Origin of Solvent-Enhanced Symmetry-Breaking Charge Transfer in a Covalently Bound Tetracene Dimer Leading to Singlet Fission

Singlet fission in covalently bound acene dimers in solution is driven by the interplay of excitonic and singlet correlated triplet ¹(TT) states with intermediate charge-transfer states, a process which depends sensitively on the solvent environment. We use high-level electronic structure methods to explore this singlet fission process in a linked tetracene dimer, with emphasis on the symmetry-breaking mechanism for the charge-transfer (CT) states induced by low-frequency antisymmetric vibrations and polar/polarizable solvents. A combination of the second-order algebraic diagrammatic construction (ADC(2)) and density functional theory/multireference configuration interaction (DFT/MRCI) methods are employed, along with a state-specific conductor-like screening model (COSMO) solvation model in the former case. This work quantifies, for the first time, an earlier mechanistic proposal [Alvertis et al., J. Am. Chem. Soc. 2019, 141, 17558] according to which solvent-induced symmetry breaking leads to a high-energy CT state which interacts with the correlated triplet state, resulting in singlet fission. An approximate assessment of the nonadiabatic interactions between the different electronic states underscores that the CT states are essential in facilitating the transition from the bright excitonic state to the ¹(TT) state leading to singlet fission. We show that several types of symmetry-breaking inter- and intra-fragment vibrations play a crucial role in a concerted mechanism with the solvent environment and with the symmetric inter-fragment torsion, which tunes the admixture of excitonic and CT states. This offers a new perspective on how solvent-induced symmetry-breaking CT can be understood and how it cooperates with intramolecular mechanisms in singlet fission.

Finding Design Principles of OLED Emitters through Theoretical Investigations of Zn(II) Carbene Complexes

In this work, Zn(II) carbene complexes carrying a dianionic 1,2-dithiolbenzene (dtb) or 1,2-diolbenzene (dob) ligand were investigated regarding their suitability as organic light-emitting diode (OLED) emitter. For the optimization of the complexes, density functional-based methods were used and frequency analyses verified the obtained structures as minima. All calculations were carried out including a polarizable continuum model to mimic solvent-solute interactions. Multireference configuration interaction methods were used to determine excitation energies, spin-orbit couplings, and luminescence properties. Rate constants of spin-allowed and spin-forbidden transitions were calculated according to a Fermi golden rule expression. Using carbene ligands with varying σ-donor and π-acceptor strengths, the luminescence is found to be tunable from yellow to orange/red to deep red/near-infrared. The calculated intersystem crossing (ISC) time constants indicate thermally activated delayed fluorescence (TADF) to be the main decay channel. In contrast to many d¹⁰ coinage metal complexes, a parallel orientation of dtb or dob and the carbene ligand is found to be highly favorable. For the complexes with a cyclic (alkyl)(amino) carbene (CAAC) or cyclic (amino)(aryl) carbene (CAArC) ligand, the S₁ and T₁ states have ligand-to-ligand charge-transfer (LLCT) character and are energetically close. The complex with a classical N-heterocyclic carbene (NHC) ligand has S₁ and T₁ states with mixed ligand-to-metal charge-transfer (LMCT)/LLCT character and is a very rare example in which the zinc ion contributes to the excitation.

Newton-X Platform: New Software Developments for Surface Hopping and Nuclear Ensembles

Newton-X is an open-source computational platform to perform nonadiabatic molecular dynamics based on surface hopping and spectrum simulations using the nuclear ensemble approach. Both are among the most common methodologies in computational chemistry for photophysical and photochemical investigations. This paper describes the main features of these methods and how they are implemented in Newton-X. It emphasizes the newest developments, including zero-point-energy leakage correction, dynamics on complex-valued potential energy surfaces, dynamics induced by incoherent light, dynamics based on machine-learning potentials, exciton dynamics of multiple chromophores, and supervised and unsupervised machine learning techniques. Newton-X is interfaced with several third-party quantum-chemistry programs, spanning a broad spectrum of electronic structure methods.

Carbon Nanodots from an In Silico Perspective

Carbon nanodots (CNDs) are the latest and most shining rising stars among photoluminescent (PL) nanomaterials. These carbon-based surface-passivated nanostructures compete with other related PL materials, including traditional semiconductor quantum dots and organic dyes, with a long list of benefits and emerging applications. Advantages of CNDs include tunable inherent optical properties and high photostability, rich possibilities for surface functionalization and doping, dispersibility, low toxicity, and viable synthesis (top-down and bottom-up) from organic materials. CNDs can be applied to biomedicine including imaging and sensing, drug-delivery, photodynamic therapy, photocatalysis but also to energy harvesting in solar cells and as LEDs. More applications are reported continuously, making this already a research field of its own. Understanding of the properties of CNDs requires one to go to the levels of electrons, atoms, molecules, and nanostructures at different scales using modern molecular modeling and to correlate it tightly with experiments. This review highlights different in silico techniques and studies, from quantum chemistry to the mesoscale, with particular reference to carbon nanodots, carbonaceous nanoparticles whose structural and photophysical properties are not fully elucidated. The role of experimental investigation is also presented. Hereby, we hope to encourage the reader to investigate CNDs and to apply virtual chemistry to obtain further insights needed to customize these amazing systems for novel prospective applications.

Ultra-Long Lived Luminescent Triplet Excited States in Cyclic (Alkyl)(amino)carbene Complexes of Zn(II) Halides

The high element abundance and d¹⁰ electron configuration make Zn^II‐based compounds attractive candidates for the development of novel photoactive molecules. Although a large library of purely fluorescent compounds exists, emission involving triplet excited states is a rare phenomenon for zinc complexes. We have investigated the photophysical and ‐chemical properties of a series of dimeric and monomeric Zn^II halide complexes bearing a cyclic (alkyl)(amino)carbene (cAAC) as chromophore unit. Specifically, [(cAAC)XZn(μ‐X)₂ZnX(cAAC)] (X=Cl (1), Br (2), I (3)) and [ZnX₂(cAAC)(NCMe)] (X=Br (4), I (5)) were isolated and fully characterized, showing intense visible light photoluminescence under UV irradiation at 297 K and fast photo‐induced transformation. At 77 K, the compounds exhibit improved stability allowing to record ultra‐long lifetimes in the millisecond regime. DFT/MRCI calculations confirm that the emission stems from ³XCT/LE_cAAC states and indicate the phototransformation to be related to asymmetric distortion of the complexes by cAAC ligand rotation. This study enhances our understanding of the excited state properties for future development and application of new classes of Zn^II phosphorescent complexes.

Low-Lying Excited States of Natural Carotenoids Viewed by Ab Initio Methods

Low-lying excited states of carotenoids (the optically dark 2A_g^- and bright 1B_u⁺) are deeply involved in energy transfer processes in photosynthetic antennas, such as light harvesting and non-photochemical quenching. Though any ab initio modeling of these phenomena has to rely on precise energies of the carotenoid electronic states, the accurate evaluation of these states remains a challenging problem due to their different natures. The paper aims to study the accuracy of the excitation energies of the low-lying excited states of certain open- and closed-chain carotenoids obtained by a state-of-the-art multireference approach for electronic structure calculation. Here, density matrix renormalization group SCF (DMRGSCF) and a perturbative approach based on driven similarity renormalization group second-order multireference perturbation theory (DSRG-MRPT2) were used to treat the static and dynamic correlation, respectively. Nuclear geometries of the electronic states were optimized with DFT-based approaches. It is demonstrated that spin-flip TD-DFT can replace multiconfigurational methods for the geometry optimization of the 2A_g^- state but not for the calculation of the excitation energy. Adiabatic excitation energies to the 1B_u⁺ state were shown to be within a margin of 1000 cm^-1 with an appropriate flow parameter value. Adiabatic excitation energies to the 2A_g^- state for the open-chain carotenoids lie within a range of experimental values (taking into account the broad range of experimental estimates); for the closed-chain ones, the error does not exceed 2000 cm^-1. Ab initio stationary (1A_g^- → 1B_u⁺) and transient (2A_g^- → 1B_u⁺) absorption spectra were modeled for violaxanthin and lycopene, and these spectra showed good agreement with the experimental ones both in terms of the vibronic structure and the transition energies.

Raman Activities of Cyano-Ester Quinoidal Oligothiophenes Reveal Their Diradical Character and the Proximity of the Low-Lying Double Exciton State

Quinoidal oligothiophenes have received considerable attention as interesting platforms with remarkable amphoteric redox behavior associated with their diradical character increasing with the conjugation lengths. In this work, we considered a family of quinoidal oligothiophenes bearing cyano-ester terminal groups and characterized them by UV-Vis-NIR absorption and Raman spectroscopy measurements at different excitation wavelengths. The experimental investigation is complemented by quantum-chemical studies to assess the quality of computed density functional theory (DFT) ground state structures and their influence on predicted Raman intensities. In addition, resonance conditions with the optically active HOMO→LUMO transition as well as with the more elusive state dominated by the doubly excited HOMO,HOMO→LUMO,LUMO configuration, are determined with DFT-MRCI calculations and their contributions to Raman activity enhancement are discussed in terms of computed vibrational Huang–Rhys (HR) factors.

Mechanistic Investigations of the Synthesis of Lactic Acid from Glycerol Catalyzed by an Iridium–NHC Complex

In the present work, the reaction pathways and the origin of catalytic activity for the production of lactic acid from glycerol catalyzed by an iridium–heterocyclic carbene (Iridium-NHC) complex at 383.15 K were investigated by DFT study at the M06-D3/6-311++G (d, p)//SDD level. Compared to the noncatalytic reaction pathway, the energy barrier sharply decreased from 75.2 kcal mol−1 to 16.8 kcal mol−1 with the introduction of the iridium–NHC complex. The catalytic reaction pathway catalyzed by the iridium–NHC complex with a coordinated hydroxide included two stages: the dehydrogenation of glycerol to 2,3-dihydroxypropanal, and the subsequent isomerization to lactic acid. Two reaction pathways, including dehydrogenation in terminal and that in C2-H, were studied. It was found that the formation of dihydroxyacetone from the H-removal in C2-H was more favorable, which might have been due to the lower energy of LUMO, whereas dihydroxyacetone could be easily transferred to 2,3-dihydroxypropanal. The analyses of electrostatic potential (ESP), hardness, and f- Fukui function also confirmed that the iridium–NHC complex acted as a hydrogen anion receptor and nucleophilic reaction center to highly promote the conversion of glycerol to lactic acid.

Thermally Activated Delayed Fluorescence Mechanism of a Bicyclic "Carbene-Metal-Amide" Copper Compound: DFT/MRCI Studies and Roles of Excited-State Structure Relaxation

Herein we investigated the luminescence mechanism of one "carbene-metal-amide" copper compound with thermally activated delayed fluorescence (TADF) using density functional theory (DFT)/multireference configuration interaction, DFT, and time-dependent DFT methods with the polarizable continuum model. The experimentally observed low-energy absorption and emission peaks are assigned to the S₁ state, which exhibits clear interligand and partial ligand-to-metal charge-transfer character. Moreover, it was found that a three-state (S₀, S₁, and T₁) model is sufficient to describe the TADF mechanism, and the T₂ state should play a negligible role. The calculated S₁-T₁ energy gap of 0.10 eV and proper spin-orbit couplings facilitate the reverse intersystem crossing (rISC) from T₁ to S₁. At 298 K, the rISC rate of T₁ → S₁ (∼10⁶ s^-1) is more than 3 orders of magnitude larger than the T₁ phosphorescence rate (∼10³ s^-1), thereby enabling TADF. However, it disappears at 77 K because of a very slow rISC rate (∼10¹ s^-1). The calculated TADF rate, lifetime, and quantum yield agree very well with the experimental data. Methodologically, the present work shows that only considering excited-state information at the Franck-Condon point is insufficient for certain emitting systems and including excited-state structure relaxation is important.

Using projection operators with maximum overlap methods to simplify challenging self-consistent field optimization

Maximum overlap methods are effective tools for optimizing challenging ground- and excited-state wave functions using self-consistent field models such as Hartree-Fock and Kohn-Sham density functional theory. Nevertheless, such models have shown significant sensitivity to the user-defined initial guess of the target wave function. In this work, a projection operator framework is defined and used to provide a metric for non-aufbau orbital selection in maximum-overlap-methods. The resulting algorithms, termed the Projection-based Maximum Overlap Method (PMOM) and Projection-based Initial Maximum Overlap Method (PIMOM), are shown to perform exceptionally well when using simple user-defined target solutions based on occupied/virtual molecular orbital permutations. This work also presents a new metric that provides a simple and conceptually convenient measure of agreement between the desired target and the current or final SCF results during a calculation employing a maximum-overlap method.

Removing the Deadwood from DFT/MRCI Wave Functions: The p-DFT/MRCI Method

The combined density functional theory and multireference configuration interaction (DFT/MRCI) method is a powerful tool for the calculation of excited electronic states of large molecules. There exists, however, a large amount of superfluous configurations in a typical DFT/MRCI wave function. We show that this deadwood may be effectively removed using a simple configuration pruning algorithm based on second-order Epstein-Nesbet perturbation theory. The resulting method, which we denote p-DFT/MRCI, is shown to result in orders of magnitude saving in computational timings, while retaining the accuracy of the original DFT/MRCI method.

Linear Carbene Pyridine Copper Complexes with Sterically Demanding N,N'-Bis(trityl)imidazolylidene: Syntheses, Molecular Structures, and Photophysical Properties

The sterically demanding carbene ITr (N,N'-bis(triphenylmethyl)imidazolylidene) was used as a ligand for the preparation of luminescent copper(I) complexes of the type [(ITr)Cu(R-pyridine/R'-quinoline)]BF₄ (R = H, 4-CN, 4-CHO, 2,6-NH₂, and R' = 8-Cl, 6-Me). The selective formation of linear, bis(coordinated) complexes was observed for a series of pyridine and quinoline derivatives. Only in the case of 4-cyanopyridine a one-dimensional coordination polymer was formed, in which the cyano group of the cyanopyridine ligand additionally binds to another Cu atom in a bridging manner, thus leading to a trigonal planar coordination environment. In contrast, employing sterically less demanding monotrityl-substituted carbene 3, no (NHC)Cu-pyridine complexes could be prepared. Instead, a bis-carbene complex [(3)₂Cu]PF₆ was obtained which showed no luminescence. All linear pyridine/quinoline coordinated complexes show weak emission in solution but intense blue to orange luminescence doped with 10% in PMMA films and in the solid state either from triplet excited states with unusually long lifetimes of up to 4.8 ms or via TADF with high radiative rate constants of up to 1.7 × 10⁵ s^-1 at room temperature. Combined density functional theory and multireference configuration interaction calculations have been performed to rationalize the involved photophysics of these complexes. They reveal a high density of low-lying electronic states with mixed MLCT, LLCT, and LC character where the electronic structures of the absorbing and emitting state are not necessarily identical.

Large Inverted Singlet-Triplet Energy Gaps Are Not Always Favorable for Triplet Harvesting: Vibronic Coupling Drives the (Reverse) Intersystem Crossing in Heptazine Derivatives

Heptazine derivatives are promising dopants for electroluminescent devices. Recent studies raised the question whether heptazines exhibit a small regular or an inverted singlet-triplet (IST) gap. It was argued that the S₁ ← T₁ reverse intersystem crossing (RISC) is a downhill process in IST emitters and therefore does not require thermal activation, thus enabling efficient harvesting of triplet excitons. Rate constants were not determined in these studies. Modeling the excited-state properties of heptazine proves challenging because fluorescence and intersystem crossing (ISC) are symmetry-forbidden in first order. In this work, we present a comprehensive theoretical study of the photophysics of heptazine and its derivative HAP-3MF. The calculations of electronic excitation energies and vibronic coupling matrix elements have been conducted at the density functional theory/multireference configuration interaction (DFT/MRCI) level of theory. We have employed a finite difference approach to determine nonadiabatic couplings and derivatives of spin-orbit coupling and electric dipole transition matrix elements with respect to normal coordinate displacements. Kinetic constants for fluorescence, phosphorescence, internal conversion (IC), ISC, and RISC have been computed in the framework of a static approach. Radiative S₁ ↔ S₀ transitions borrow intensity mainly from optically bright E' π → π* states, while S₁ ↔ T₁ (R)ISC is mediated by E″ states of n → π* character. Test calculations show that IST gaps as large as those reported in the literature are counterproductive and slow down the S₁ ← T₁ RISC process. Using the adiabatic DFT/MRCI singlet-triplet splitting of -0.02 eV, we find vibronically enhanced ISC and RISC to be fast in the heptazine core compound. Nevertheless, its photo- and electroluminescence quantum yields are predicted to be very low because S₁ → S₀ IC efficiently quenches the luminescence. In contrast, fluorescence, IC, ISC, and RISC proceed at similar time scales in HAP-3MF.

Hot exciplexes in U-shaped TADF molecules with emission from locally excited states

Fast emission and high color purity are essential characteristics of modern opto-electronic devices, such as organic light emitting diodes (OLEDs). These properties are currently not met by the latest generation of thermally activated delayed fluorescence (TADF) emitters. Here, we present an approach, called "hot exciplexes" that enables access to both attributes at the same time. Hot exciplexes are produced by coupling facing donor and acceptor moieties to an anthracene bridge, yielding an exciplex with large T1 to T2 spacing. The hot exciplex model is investigated using optical spectroscopy and quantum chemical simulations. Reverse intersystem crossing is found to occur preferentially from the T3 to the S1 state within only a few nanoseconds. Application and practicality of the model are shown by fabrication of organic light-emitting diodes with up to 32 % hot exciplex contribution and low efficiency roll-off.

On the inclusion of one double within CIS and TDDFT

We present an improved approach for generating a set of optimized frontier orbitals (HOMO and LUMO) that minimizes the energy of one double configuration. We further benchmark the effect of including such a double within a rigorous configuration interaction singles or a parameterized semi-empirical time-dependent density functional theory Hamiltonian for a set of test cases. Although we cannot quite achieve quantitative accuracy, the algorithm is quite robust and routinely delivers an enormous qualitative improvement to standard single-reference electronic structure calculations.

Theoretical Study of the Photoisomerization Mechanism of All-Trans-Retinyl Acetate

The compound 9-cis-retinyl acetate (9-cis-RAc) is a precursor to 9-cis-retinal, which has potential application in the treatment of some hereditary diseases of the retina. An attractive synthetic route to 9-cis-RAc is based on the photoisomerization reaction of the readily available all-trans-RAc. In the present study, we examine the mechanism of the photoisomerization reaction with the use of state-of-the-art electronic structure calculations for two polyenic model compounds: tEtEt-octatetraene and tEtEtEc-2,6-dimethyl-1,3,5,7,9-decapentaene. The occurrence of photoisomerization is attributed to a chain-kinking mechanism, whereby a series of S₁/S₀ conical intersections associated with kinking deformations at different positions along the polyenic chain mediate internal conversion to the S₀ state, and subsequent isomerization around one of the double bonds. Two other possible photoisomerization mechanisms are taken into account, but they are rejected as incompatible with simulation results and/or the available spectroscopic data.

Vacuum Ultraviolet Excited State Dynamics of the Smallest Ketone: Acetone

We combined tunable vacuum-ultraviolet time-resolved photoelectron spectroscopy (VUV-TRPES) with high-level quantum dynamics simulations to disentangle multistate Rydberg-valence dynamics in acetone. A femtosecond 8.09 eV pump pulse was tuned to the sharp origin of the A₁(n3d_yz) band. The ensuing dynamics were tracked with a femtosecond 6.18 eV probe pulse, permitting TRPES of multiple excited Rydberg and valence states. Quantum dynamics simulations reveal coherent multistate Rydberg-valence dynamics, precluding simple kinetic modeling of the TRPES spectrum. Unambiguous assignment of all involved Rydberg states was enabled via the simulation of their photoelectron spectra. The A₁(ππ*) state, although strongly participating, is likely undetectable with probe photon energies ≤8 eV and a key intermediate, the A₂(nπ*) state, is detected here for the first time. Our dynamics modeling rationalizes the temporal behavior of all photoelectron transients, allowing us to propose a mechanism for VUV-excited dynamics in acetone which confers a key role to the A₂(nπ*) state.

Electronic Structure Methods for the Description of Nonadiabatic Effects and Conical Intersections

Nonadiabatic effects are ubiquitous in photophysics and photochemistry, and therefore, many theoretical developments have been made to properly describe them. Conical intersections are central in nonadiabatic processes, as they promote efficient and ultrafast nonadiabatic transitions between electronic states. A proper theoretical description requires developments in electronic structure and specifically in methods that describe conical intersections between states and nonadiabatic coupling terms. This review focuses on the electronic structure aspects of nonadiabatic processes. We discuss the requirements of electronic structure methods to describe conical intersections and nonadiabatic couplings, how the most common excited state methods perform in describing these effects, and what the recent developments are in expanding the methodology and implementing nonadiabatic couplings.

Reliable TDDFT Protocol Based on a Local Hybrid Functional for the Prediction of Vibronic Phosphorescence Spectra Applied to Tris(2,2'-bipyridine)-Metal Complexes

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

H2 Evolution from Electrocatalysts with Redox-Active Ligands: Mechanistic Insights from Theory and Experiment vis-à-vis Co-Mabiq

Electrocatalytic hydrogen production via transition metal complexes offers a promising approach for chemical energy storage. Optimal platforms to effectively control the proton and electron transfer steps en route to H₂ evolution still need to be established, and redox-active ligands could play an important role in this context. In this study, we explore the role of the redox-active Mabiq (Mabiq = 2-4:6-8-bis(3,3,4,4-tetramethlyldihydropyrrolo)-10-15-(2,2-biquinazolino)-[15]-1,3,5,8,10,14-hexaene1,3,7,9,11,14-N₆) ligand in the hydrogen evolution reaction (HER). Using spectro-electrochemical studies in conjunction with quantum chemical calculations, we identified two precatalytic intermediates formed upon the addition of two electrons and one proton to [Co^II(Mabiq)(THF)](PF₆) (Co_Mbq). We further examined the acid strength effect on the generation of the intermediates. The generation of the first intermediate, Co_Mbq-H¹, involves proton addition to the bridging imine-nitrogen atom of the ligand and requires strong proton activity. The second intermediate, Co_Mbq-H², acquires a proton at the diketiminate carbon for which a weaker proton activity is sufficient. We propose two decoupled H₂ evolution pathways based on these two intermediates, which operate at different overpotentials. Our results show how the various protonation sites of the redox-active Mabiq ligand affect the energies and activities of HER intermediates.

Excited States of Xanthophylls Revisited: Toward the Simulation of Biologically Relevant Systems

Xanthophylls are a class of oxygen-containing carotenoids, which play a fundamental role in light-harvesting pigment-protein complexes and in many photoresponsive proteins. The complexity of the manifold of the electronic states and the large sensitivity to the environment still prevent a clear and coherent interpretation of their photophysics and photochemistry. In this Letter, we compare cutting-edge ab initio methods (CC3 and DMRG/NEVPT2) with time-dependent DFT and semiempirical CI (SECI) on model keto-carotenoids and show that SECI represents the right compromise between accuracy and computational cost to be applied to real xanthophylls in their biological environment. As an example, we investigate canthaxanthin in the orange carotenoid protein and show that the conical intersections between excited states and excited-ground states are mostly determined by the effective bond length alternation coordinate, which is significantly tuned by the protein through geometrical constraints and electrostatic effects.

Internal conversion of singlet and triplet states employing numerical DFT/MRCI derivative couplings: Implementation, tests, and application to xanthone

We present an efficient implementation of nonadiabatic coupling matrix elements (NACMEs) for density functional theory/multireference configuration interaction (DFT/MRCI) wave functions of singlet and triplet multiplicity and an extension of the Vibes program that allows us to determine rate constants for internal conversion (IC) in addition to intersystem crossing (ISC) nonradiative transitions. Following the suggestion of Plasser et al. [J. Chem. Theory Comput. 12, 1207 (2016)], the derivative couplings are computed as finite differences of wave function overlaps. Several measures have been taken to speed up the calculation of the NACMEs. Schur's determinant complement is employed to build up the determinant of the full matrix of spin-blocked orbital overlaps from precomputed spin factors with fixed orbital occupation. Test calculations on formaldehyde, pyrazine, and xanthone show that the mutual excitation level of the configurations at the reference and displaced geometries can be restricted to 1. In combination with a cutoff parameter of t_norm = 10^-8 for the DFT/MRCI wave function expansion, this approximation leads to substantial savings of cpu time without essential loss of precision. With regard to applications, the photoexcitation decay kinetics of xanthone in apolar media and in aqueous solution is in the focus of the present work. The results of our computational study substantiate the conjecture that S₁ T₂ reverse ISC outcompetes the T₂ ↝ T₁ IC in aqueous solution, thus explaining the occurrence of delayed fluorescence in addition to prompt fluorescence.

Perspective on Simplified Quantum Chemistry Methods for Excited States and Response Properties

We review recent developments in the framework of simplified quantum chemistry for excited state and optical response properties (sTD-DFT) and present future challenges for new method developments to improve accuracy and extend the range of application. In recent years, the scope of sTD-DFT was extended to molecular response calculations of the polarizability, optical rotation, first hyperpolarizability, two-photon absorption (2PA), and excited-state absorption for large systems with hundreds to thousands of atoms. The recently introduced spin-flip simplified time-dependent density functional theory (SF-sTD-DFT) variant enables an ultrafast treatment for diradicals and related strongly correlated systems. A few drawbacks were also identified, specifically for the computation of 2PA cross sections. We propose solutions to this problem and how to generally improve the accuracy of simplified schemes. New possible simplified schemes are also introduced for strongly correlated systems, e.g., with a second-order perturbative correlation correction. Interpretation tools that can extract chemical structure-property relationships from excited state or response calculations are also discussed. In particular, the recently introduced method-agnostic RespA approach based on natural response orbitals (NROs) as the key concept is employed.

Fluorescence Quenching in J-Aggregates through the Formation of Unusual Metastable Dimers

Molecular aggregation alters the optical properties of a system as fluorescence may be activated or quenched. This is usually described within the well-established framework of H- and J-aggregates. While H-aggregates show nonfluorescent blueshifted absorption bands with respect to the isolated monomer, J-aggregates are fluorescent displaying a redshifted peak. In this publication, we employ a combined approach of experiment and theory to study the complex aggregation features and photophysical properties of diaminodicyanoquinone derivatives, which show unusual and puzzling nonfluorescent redshifted absorption bands upon aggregation. Our theoretical analysis demonstrates that stable aggregates do not account for the experimental observations. Instead, we propose an unprecedented mechanism involving metastable dimeric species formed from stable dimers to generate nonfluorescent J-aggregates. These results represent a novel kind of aggregation-induced optical effect and may have broad implications for the photophysics of dye aggregates.

Excitonic and charge transfer interactions in tetracene stacked and T-shaped dimers

Extended quantum chemical calculations were performed for the tetracene dimer to provide benchmark results, analyze the excimer survival process, and explore the possibility of using long-range-corrected (LC) time-dependent second-order density functional tight-biding (DFTB2) for this system. Ground- and first-excited-state optimized geometries, vertical excitations at relevant minima, and intermonomer displacement potential energy curves (PECs) were calculated for these purposes. Ground-state geometries were optimized with the scaled-opposite-spin (SOS) second-order Møller-Plesset perturbation (MP2) theory and LC-DFT (density functional theory) and LC-DFTB2 levels. Excited-state geometries were optimized with SOS-ADC(2) (algebraic diagrammatic construction to second-order) and the time-dependent approaches for the latter two methods. Vertical excitations and PECs were compared to multireference configuration interaction DFT (DFT/MRCI). All methods predict the lowest-energy S₀ conformer to have monomers parallel and rotated relative to each other and the lowest S₁ conformer to be of a displaced-stacked type. LC-DFTB2, however, presents some relevant differences regarding other conformers for S₀. Despite some state-order inversions, overall good agreement between methods was observed in the spectral shape, state character, and PECs. Nevertheless, DFT/MRCI predicts that the S₁ state should acquire a doubly excited-state character relevant to the excimer survival process and, therefore, cannot be completely described by the single reference methods used in this work. PECs also revealed an interesting relation between dissociation energies and the intermonomer charge-transfer interactions for some states.

Doping Capabilities of Fluorine on the UV Absorption and Emission Spectra of Pyrene-Based Graphene Quantum Dots

Functionalization of quantum carbon dots (QCDs) and graphene quantum dots (GQDs) is a popular way to tune their optical spectra increasing their potential applicability in material science and biorelated disciplines. Based on the experimental observation, functionalization by fluorine atoms induces substantial shifts in absorption and emission spectra and an intensity increase. Understanding of the effects due to fluorine functionalization at the atomic scale level is still challenging due to the complex structure of fluorinated QCDs. In this work, the effect of covalent edge-fluorination and fluorine anion doping on absorption and emission spectra of prototypical polycyclic aromatic hydrocarbons pyrene and circum-pyrene has been investigated. The ways to achieve efficient red-shifts in the UV spectra and obtaining reasonable intensities stood in the focus of the work. High-level quantum chemical methods based on density functional theory/multireference configuration interaction (DFT/MRCI) and single-reference second-order algebraic diagrammatic construction (ADC(2)) and density functional theory (DFT) using the CAM-B3LYP functional have been used for this purpose. The calculations show that doping with the fluoride anion can have significant effects on the electronic spectrum. However, the effect of the fluoride ion is strongly dependent on its position with respect to the QCD. The localization above the GQDs causes large red-shifts to both the absorption and emission of spectra of GQDs, while in-plane localization leads to only negligible shifts and a tendency to dissociation after electronic excitation. Thus, large red-shifts, observed in complexes with F^-, are obtained due to the introduction of new excited states with large CT character not yet been considered previously in this context, although they have the potential to significantly influence the photophysics of quantum dots. Doping by edge fluorination redshifts the spectra only slightly. This study provides insights on fluorine-doped GQDs, which is conducive to promoting its rational design and controllable synthesis.

Reactivity of Undissociated Molecular Nitric Acid at the Air-Water Interface

Recent experiments and theoretical calculations have shown that HNO₃ may exist in molecular form in aqueous environments, where in principle one would expect this strong acid to be completely dissociated. Much effort has been devoted to understanding this fact, which has huge environmental relevance since nitric acid is a component of acid rain and also contributes to renoxification processes in the atmosphere. Although the importance of heterogeneous processes such as oxidation and photolysis have been evidenced by experiments, most theoretical studies on hydrated molecular HNO₃ have focused on the acid dissociation mechanism. In the present work, we carry out calculations at various levels of theory to obtain insight into the properties of molecular nitric acid at the surface of liquid water (the air-water interface). Through multi-nanosecond combined quantum-classical molecular dynamics simulations, we analyze the interface affinity of nitric acid and provide an order of magnitude for its lifetime with regard to acid dissociation, which is close to the value deduced using thermodynamic data in the literature (∼0.3 ns). Moreover, we study the electronic absorption spectrum and calculate the rate constant for the photolytic process HNO₃ + hν → NO₂ + OH, leading to 2 × 10^-6 s^-1, about twice the value in the gas phase. Finally, we describe the reaction HNO₃ + OH → NO₃ + H₂O using a cluster model containing 21 water molecules with the help of high-level ab initio calculations. A large number of reaction paths are explored, and our study leads to the conclusion that the most favorable mechanism involves the formation of a pre-reactive complex (HNO₃)(OH) from which product are obtained through a coupled proton-electron transfer mechanism that has a free-energy barrier of 6.65 kcal·mol^-1. Kinetic calculations predict a rate constant increase by ∼4 orders of magnitude relative to the gas phase, and we conclude that at the air-water interface, a lower limit for the rate constant is k = 1.2 × 10^-9 cm³·molecule^-1·s^-1. The atmospheric significance of all these results is discussed.

Vacuum-Ultraviolet Absorption Spectrum of 3-Methoxyacrylonitrile

The high-resolution absorption spectrum of 3-methoxyacrylonitrile (3MAN) was measured between 5.27 and 12.59 eV using a synchrotron-based Fourier-transform spectrometer. It was related to an absolute absorption cross-section scale. Complementary calculations at the DFT-MRCI/aug-cc-pVTZ level of theory document the vertical transition energies and oscillator strengths toward the first 19 states of both the E and Z geometrical isomers of 3MAN. Comparisons with the experimental absorption spectrum reveal the similarities and differences between 3MAN, a bifunctional molecule, with acrylonitrile and methylvinylether, where only one functional group is present. As in acrylonitrile, several broad valence transitions were observed up to the ionization limit. They are likely associated with the extended π-system induced by the nitrile group but might also involve σσ* transitions close to the ionization limit. As in methylvinylether, Rydberg series converging to the ionization limit are absent. This is attributed to a difference in neutral and cationic geometry due to a 60° rotation of the methyl group.

Molecular Photochemistry: Recent Developments in Theory

Photochemistry is a fascinating branch of chemistry that is concerned with molecules and light. However, the importance of simulating light-induced processes is reflected also in fields as diverse as biology, material science, and medicine. This Minireview highlights recent progress achieved in theoretical chemistry to calculate electronically excited states of molecules and simulate their photoinduced dynamics, with the aim of reaching experimental accuracy. We focus on emergent methods and give selected examples that illustrate the progress in recent years towards predicting complex electronic structures with strong correlation, calculations on large molecules, describing multichromophoric systems, and simulating non-adiabatic molecular dynamics over long time scales, for molecules in the gas phase or in complex biological environments.

Ultrafast Spectroscopy of Photoactive Molecular Systems from First Principles: Where We Stand Today and Where We Are Going

Computational spectroscopy is becoming a mandatory tool for the interpretation of the complex, and often congested, spectral maps delivered by modern non-linear multi-pulse techniques. The fields of Electronic Structure Methods, Non-Adiabatic Molecular Dynamics, and Theoretical Spectroscopy represent the three pillars of the virtual ultrafast optical spectrometer, able to deliver transient spectra in silico from first principles. A successful simulation strategy requires a synergistic approach that balances between the three fields, each one having its very own challenges and bottlenecks. The aim of this Perspective is to demonstrate that, despite these challenges, an impressive agreement between theory and experiment is achievable now regarding the modeling of ultrafast photoinduced processes in complex molecular architectures. Beyond that, some key recent developments in the three fields are presented that we believe will have major impacts on spectroscopic simulations in the very near future. Potential directions of development, pending challenges, and rising opportunities are illustrated.

Ab Initio Study of Low-Lying Excited States of Carotenoid-Derived Polyenes

Knowledge about excited states of carotenoids is essential for understanding photophysical processes underlying photosynthesis. However, due to the presence of a large number of optically dark states, experimental study of the excited-state manifold is limited to a significant extent. In this paper, we apply high-level ab initio quantum chemical methods to study the low-lying excited states of polyenes containing from 8 to 13 conjugated double bonds, which serve as a model for natural carotenoids. Vertical and adiabatic excitation energies from the ground 1A_g^- state to the excited 2A_g^-, 1B_u⁺, and 1B_u^- states were evaluated by means of density matrix renormalization group (DMRG) with NEVPT2 perturbative correction. The energies of all excited states are highly sensitive to nuclear geometry, especially the 2A_g^- state. Thus, the 2A_g^- and 1B_u⁺ states interchange their relative positions upon geometry relaxation, while the vertical excitation energy to the 2A_g^- state is rather high. At the same time, the 1B_u^- state energy is shown to be higher than other studied excited states at any geometry. With relaxed geometries of the excited states, absorption and transient absorption spectra were calculated within the Franck-Condon approximation bridging the gap between experimental spectroscopic data and computational results.

Hole-hole Tamm-Dancoff-approximated density functional theory: A highly efficient electronic structure method incorporating dynamic and static correlation

The study of photochemical reaction dynamics requires accurate as well as computationally efficient electronic structure methods for the ground and excited states. While time-dependent density functional theory (TDDFT) is not able to capture static correlation, complete active space self-consistent field methods neglect much of the dynamic correlation. Hence, inexpensive methods that encompass both static and dynamic electron correlation effects are of high interest. Here, we revisit hole-hole Tamm-Dancoff approximated (hh-TDA) density functional theory for this purpose. The hh-TDA method is the hole-hole counterpart to the more established particle-particle TDA (pp-TDA) method, both of which are derived from the particle-particle random phase approximation (pp-RPA). In hh-TDA, the N-electron electronic states are obtained through double annihilations starting from a doubly anionic (N+2 electron) reference state. In this way, hh-TDA treats ground and excited states on equal footing, thus allowing for conical intersections to be correctly described. The treatment of dynamic correlation is introduced through the use of commonly employed density functional approximations to the exchange-correlation potential. We show that hh-TDA is a promising candidate to efficiently treat the photochemistry of organic and biochemical systems that involve several low-lying excited states-particularly those with both low-lying ππ^* and nπ^* states where inclusion of dynamic correlation is essential to describe the relative energetics. In contrast to the existing literature on pp-TDA and pp-RPA, we employ a functional-dependent choice for the response kernel in pp- and hh-TDA, which closely resembles the response kernels occurring in linear response and collinear spin-flip TDDFT.

Substituent Effect in the First Excited Triplet State of Monosubstituted Benzenes

The structure of 30 monosubstituted benzenes in the first excited triplet T₁ state was optimized with both unrestricted (U) and restricted open shell (RO) approximations combined with the ωB97XD/aug-cc-pVTZ basis method. The substituents exhibited diverse σ- and π-electron-donating and/or -withdrawing groups. Two different positions of the substituents are observed in the studied compounds in the T₁ state: one distorted from the plane and the other coplanar with a quinoidal ring. The majority of the substituents are π-electron donating in the first group while π-electron withdrawing in the second one. Basically, U- and RO-ωB97XD approximations yield concordant results except for the B-substituents and a few of the planar groups. In the T₁ state, the studied molecules are not aromatic, yet aromaticity estimated using the HOMA (harmonic oscillator model of aromaticity) index increases from ca. -0.2 to ca. 0.4 with substituent distortion, while in the S₁ state, they are only slightly less aromatic than in the ground state (HOMA ≈0.8 vs ≈1.0, respectively). Unexpectedly, the sEDA(T₁) and pEDA(T₁) substituent effect descriptors do not correlate with analogous parameters for the ground and first excited singlet states. This is because in the T₁ state, the geometry of the ring changes dramatically and the sEDA(T₁) and pEDA(T₁) descriptors do not characterize only the functional group but the entire molecule. Thus, they cannot provide useful scales for the substituents in the T₁ states. We found that the spin density in the T₁ states is accumulated at the C_ipso and C_p atoms, and with the substituent deformation angle, it nonlinearly increases at the former while decreases at the latter. It appeared that the gap between singly unoccupied molecular orbital and singly occupied molecular orbital (SUMO-SOMO) is determined by the change of the SOMO energy because the former is essentially constant. For the nonplanar structures, SOMO correlates with the torsion angle of the substituent and the ground-state pEDA(S₀) descriptor of the π-electron-donating substituents ranging from 0.02 to 0.2 e. Finally, shapes of the SOMO-1 instead of SOMO frontier orbitals in the T₁ state somehow resemble the highest occupied molecular orbital ones of the S₀ and S₁ states. For several planar systems, the shape of the U- and RO-density functional theory-calculated SOMO-1 orbitals differs substantially.