Choosing an atomic basis set for TD-DFT, SOPPA, ADC(2), CIS(D), CC2 and EOM-CCSD calculations of low-lying excited states of organic dyes

Excited-State Proton Transfer in Luminescent Dyes: From Theoretical Insight to Experimental Evidence

The effective utilization of luminescent dyes often relies on a comprehensive understanding of their excitation and relaxation pathways. One such pathway, Excited-State Proton Transfer (ESPT), involves the tautomerization of the dye in its excited state, resulting in a new structure that exhibits distinct emission properties, such as a very large Stokes' shift or dual-emission. Although the ESPT phenomenon is well-explained theoretically, its experimental demonstration can be challenging due to the presence of numerous other phenomena that can yield similar experimental observations. In this review, we propose that an all-encompassing methodology, integrating experimental findings, computational analyses, and a thorough evaluation of diverse mechanisms, is essential for verifying the occurrence of ESPT in luminescent dyes. Investigations have offered significant understanding of the elements impacting the ESPT process and the array of approaches that can be used to validate the existence of ESPT. These discoveries hold crucial ramifications for the advancement of molecular probes, sensors, and other applications that depend on ESPT as a detection mechanism.

Deciphering the Spectral Tuning Mechanism in Proteorhodopsin: The Dominant Role of Electrostatics Instead of Chromophore Geometry

Proteorhodopsin (PR) is a photoactive proton pump found in marine bacteria. There are two phenotypes of PR exhibiting an environmental adaptation to the ocean's depth which tunes their maximum absorption: blue‐absorbing proteorhodopsin (BPR) and green‐absorbing proteorhodopsin (GPR). This blue/green color‐shift is controlled by a glutamine to leucine substitution at position 105 which accounts for a 20 nm shift. Typically, spectral tuning in rhodopsins is rationalized by the external point charge model but the Q105L mutation is charge neutral. To study this tuning mechanism, we employed the hybrid QM/MM method with sampling from molecular dynamics. Our results reveal that the positive partial charge of glutamine near the C₁₄−C₁₅ bond of retinal shortens the effective conjugation length of the chromophore compared to the leucine residue. The derived mechanism can be applied to explain the color regulation in other retinal proteins and can serve as a guideline for rational design of spectral shifts.

Coherent Control of Molecular Dissociation by Selective Excitation of Nuclear Wave Packets

We report on pump-probe control schemes to manipulate fragmentation product yields in p-nitrotoluene (PNT) cation. Strong field ionization of PNT prepares the parent cation in the ground electronic state, with coherent vibrational excitation along two normal modes: the C–C–N–O torsional mode at 80 cm⁻¹ and the in-plane ring-stretching mode at 650 cm⁻¹. Both vibrational wave packets are observed as oscillations in parent and fragment ion yields in the mass spectrum upon optical excitation. Excitation with 650 nm selectively fragments the PNT cation into C7H7+, whereas excitation with 400 nm selectively produces C5H5+ and C3H3+. In both cases the ion yield oscillations result from torsional wave packet excitation, but 650 and 400 nm excitation produce oscillations with opposite phases. Ab initio calculations of the ground and excited electronic potential energy surfaces of PNT cation along the C–C–N–O dihedral angle reveal that 400 nm excitation accesses an allowed transition from D₀ to D₆ at 0° dihedral angle, whereas 650 nm excitation accesses a strongly allowed transition from D₀ to D₄ at a dihedral angle of 90°. This ability to access different electronic excited states at different locations along the potential energy surface accounts for the selective fragmentation observed with different probe wavelengths. The ring-stretching mode, only observed using 800 nm excitation, is attributed to a D₀ to D₂ transition at a geometry with 90° dihedral angle and elongated C–N bond length. Collectively, these results demonstrate that strong field ionization induces multimode coherent excitation and that the vibrational wave packets can be excited with specific photon energies at different points on their potential energy surfaces to induce selective fragmentation.

Modern Theoretical Approaches to Modeling the Excited-State Intramolecular Proton Transfer: An Overview

The excited-state intramolecular proton transfer (ESIPT) phenomenon is nowadays widely acknowledged to play a crucial role in many photobiological and photochemical processes. It is an extremely fast transformation, often taking place at sub-100 fs timescales. While its experimental characterization can be highly challenging, a rich manifold of theoretical approaches at different levels is nowadays available to support and guide experimental investigations. In this perspective, we summarize the state-of-the-art quantum-chemical methods, as well as molecular- and quantum-dynamics tools successfully applied in ESIPT process studies, focusing on a critical comparison of their specific properties.

The TDDFT Excitation Energies of the BODIPYs; The DFT and TDDFT Challenge Continues

The derivatives of 4,4-difluoro-4-bora-3a,4a-diaza-s-indacene (BODIPY) are pivotal ingredients for a large number of functional, stimuli-responsive materials and therapeutic molecules based on their photophysical properties, and there is a urgent need to understand and predict their optical traits prior to investing a large amount of resources in preparing them. Density functional theory (DFT) and time-dependent DFT (TDDFT) computations were performed to calculate the excitation energies of the lowest-energy singlet excited state of a large series of common BODIPY derivatives employing various functional aiming at the best possible combination providing the least deviations from the experimental values. Using the common "fudge" correction, a series of combinations was investigated, and a methodology is proposed offering equal or better performances than what is reported in the literature.

A Simple Range-Separated Double-Hybrid Density Functional Theory for Excited States

A simple and robust range-separated (RS) double-hybrid (DH) time-dependent density functional approach is presented for the accurate calculation of excitation energies of molecules within the Tamm-Dancoff approximation. The scheme can be considered as an excited-state extension of the ansatz proposed by Toulouse and co-workers [J. Chem. Phys. 2018, 148, 164105], which is based on the two-parameter decomposition of the Coulomb potential, for which both the exchange and correlation contributions are range-separated. A flexible and efficient implementation of the new scheme is also presented, which facilitates its extension to any combination of exchange and correlation functionals. The performance of the new approximation is tested for singlet excitations on several benchmark compilations and thoroughly compared to that of representative DH, RS hybrid, and RS DH functionals. The one-electron basis set dependence and computation times are also assessed. Our results show that the new approach improves on standard DHs in most cases, and it can provide a more robust and accurate alternative. In addition, on average, it noticeably surpasses the existing RS hybrid and RS DH functionals.

Computational Study of the Influence of Nitrogen-Containing Unsaturated Heterocyclic Substituents on Electronic and Spectroscopic Properties of Squaraine Derivatives

A comprehensive understanding of the influence of the different structural elements for the molecular properties is crucial for improving the material design procedures in the field of photosensitive dyes. The present study provides a detailed analysis of the influence of the number of heteroatoms (nitrogens) and the lengths of the π-electron skeleton on the one- and two-photon absorption of the symmetric squaraine dyes. Extended computational study covers the conventional vertical excitation calculations within the TD-DFT formalisms as well as several advanced single-reference methods including double excitations such as CIS(D), SAC-CI, and ADC(2). Additionally, the weaknesses of the vertical approach are investigated by including the geometry relaxation upon excitation via adiabatic and 0-0 treatment.

Exciplex Stabilization in Asymmetric Acene Dimers

Excimers play an important role in photochemical processes ranging from singlet fission to DNA damage, and the characteristic red-shift in fluorescence spectra associated with excimer formation can provide information about aggregate formation and the orientation of chromophores. When a mixture of chromophores is present, exciplex formation may lead to spectral characteristics distinct from those of either monomer or the corresponding excimers. To predict the effects of aggregation in a system containing a mixture of small acenes, binding energies and minimum-energy geometries have been calculated for three mixed S₁ exciplexes. Benchmark CASSCF/NEVPT2 multireference binding energies of 18.2, 27.7, and 49.3 kJ/mol are reported for the benzene-naphthalene, benzene-anthracene, and naphthalene-anthracene exciplexes, respectively. TDDFT calculations have been performed using a range of exchange-correlation functionals, showing that many functionals perform inconsistently, and the error in binding energy often depends on the character of the monomer excitation from which the exciplex state is derived. Moderate exciplex stabilization observed for the benzene-naphthalene and naphthalene-anthracene exciplexes results from a mixture of charge transfer and exciton delocalization.

Predicting aromatic exciplex fluorescence emission energies

Analysis of PAH exciplex TDDFT fluorescence energies shows a linear relationship between the mean monomer HOMO–LUMO gap and complex fluorescence.

Assessment of Functionals for TDDFT Calculations of One- and Two-Photon Absorption Properties of Neutral and Anionic Fluorescent Proteins Chromophores

Performance of DFT functionals with different percentages of exact Hartree-Fock exchange energy (EX) is assessed for recovery of the CC2 reference one- (OPA) and two-photon absorption (TPA) spectra of fluorescent proteins chromophores in vacuo. The investigated DFT functionals, together with their EX contributions are BLYP (0%), B3LYP (20%), B1LYP (25%), BHandHLYP (50%), and CAM-B3LYP (19% at short range and 65% at long range). Our test set consists of anionic and neutral chromophores as naturally occurring in the fluorescent proteins. For the first time, we compare TDDFT and CC2 methods for higher excited states than the S₁ state, exhibiting relatively large TPA intensity. Our TDDFT results for neutral chromophores reveal an increase in excitation energies as well as TPA and OPA intensities errors, compared to CC2-derived results, as the DFT functional contains less exact exchange. The long-range-corrected CAM-B3LYP functional performs the best, closely followed by BHandHLYP, while BLYP usually significantly underestimates all investigated spectral properties, hence being the worst in reproducing the reference CC2 results. The hybrid B3LYP and B1LYP functionals can be roughly placed in between. We propose that TDDFT may underestimate the TPA intensities for neutral chromophores of fluorescent proteins due to underestimated oscillator strengths between some excited states. In the case of anionic chromophores, we find that B3LYP and B1LYP functionals overcome others in terms of reproducing CC2 excitation energies. On the other hand, however, TPA intensity is usually significantly underestimated, and in this respect, CAM-B3LYP functional seems to be again superior. In contrast to the case of neutral chromophores, it seems that a large magnitude of excited-state dipole moments or changes in dipole moments upon excitation may be the driving force behind high TPA transition moments.

Modeling Chemical Reactions by QM/MM Calculations: The Case of the Tautomerization in Fireflies Bioluminescent Systems

In less than half a century, the hybrid QM/MM method has become one of the most used technique to model molecules embedded in a complex environment. A well-known application of the QM/MM method is for biological systems. Nowadays, one can understand how enzymatic reactions work or compute spectroscopic properties, like the wavelength of emission. Here, we have tackled the issue of modeling chemical reactions inside proteins. We have studied a bioluminescent system, fireflies, and deciphered if a keto-enol tautomerization is possible inside the protein. The two tautomers are candidates to be the emissive molecule of the bioluminescence but no outcome has been reached. One hypothesis is to consider a possible keto-enol tautomerization to treat this issue, as it has been already observed in water. A joint approach combining extensive MD simulations as well as computation of key intermediates like TS using QM/MM calculations is presented in this publication. We also emphasize the procedure and difficulties met during this approach in order to give a guide for this kind of chemical reactions using QM/MM methods.

The Bethe–Salpeter equation in chemistry: relations with TD-DFT, applications and challenges

We review the Bethe–Salpeter formalism and analyze its performances for the calculation of the excited state properties of molecular systems.

An EOM-CCSD-PCM Benchmark for Electronic Excitation Energies of Solvated Molecules

In this work, we benchmark the equation of motion coupled cluster with single and double excitations (EOM-CCSD) method combined with the polarizable continuum model (PCM) for the calculation of electronic excitation energies of solvated molecules. EOM-CCSD is one of the most accurate methods for computing one-electron excitation energies, and accounting for the solvent effect on this property is a key challenge. PCM is one of the most widely employed solvation models due to its adaptability to virtually any solute and its efficient implementation with density functional theory methods (DFT). Our goal in this work is to evaluate the reliability of EOM-CCSD-PCM, especially compared to time-dependent DFT-PCM (TDDFT-PCM). Comparisons between calculated and experimental excitation energies show that EOM-CCSD-PCM consistently overestimates experimental results by 0.4-0.5 eV, which is larger than the expected EOM-CCSD error in vacuo. We attribute this decrease in accuracy to the approximated solvation model. Thus, we investigate a particularly important source of error: the lack of H-bonding interactions in PCM. We show that this issue can be addressed by computing an energy shift, Δ_HB, from bare-PCM to microsolvation + PCM at DFT level. Our results show that such a shift is independent of the functional used, contrary to the absolute value of the excitation energy. Hence, we suggest an efficient protocol where the EOM-CCSD-PCM transition energy is corrected by Δ_HB(DFT), which consistently improves the agreement with the experimental measurements.

Onset of the Electronic Absorption Spectra of Isolated and π-Stacked Oligomers of 5,6-Dihydroxyindole: An Ab Initio Study of the Building Blocks of Eumelanin

Eumelanin is a naturally occurring skin pigment which is responsible for developing a suntan. The complex structure of eumelanin consists of π-stacked oligomers of various indole derivatives, such as the monomeric building block 5,6-dihydroxyindole (DHI). In this work, we present an ab initio wave-function study of the absorption behavior of DHI oligomers and of doubly and triply π-stacked species of these oligomers. We have simulated the onset of the electronic absorption spectra by employing the MP2 and the linear-response CC2 methods. Our results demonstrate the effect of an increasing degree of oligomerization of DHI and of an increasing degree of π-stacking of DHI oligomers on the onset of the absorption spectra and on the degree of red-shift toward the visible region of the spectrum. We find that π-stacking of DHI and its oligomers substantially red-shifts the onset of the absorption spectra. Our results also suggest that the optical properties of biological eumelanin cannot be simulated by considering the DHI building blocks alone, but instead the building blocks indole-semiquinone and indole-quinone have to be considered as well. This study contributes to advancing the understanding of the complex photophysics of the eumelanin biopolymer.

Exciton Splitting of Adsorbed and Free 4-Nitroazobenzene Dimers: A Quantum Chemical Study

Molecular photoswitches such as azobenzenes, which undergo photochemical trans ↔ cis isomerizations, are often mounted for possible applications on a surface and/or surrounded by other switches, for example, in self-assembled monolayers. This may suppress the isomerization cross section due to possible steric reasons, or, as recently speculated, by exciton coupling to neighboring switches, leading to ultrafast electronic quenching (Gahl et al., J. Am. Chem. Soc. 2010, 132, 1831). The presence of exciton coupling has been anticipated from a blue shift of the optical absorption band, compared to molecules in solution. From the theory side the need arises to properly analyze and quantify the change of absorption spectra of interacting and adsorbed switches. In particular, suitable methods should be identified, and effects of intermolecule and molecule-surface interactions on spectra should be disentangled. In this paper by means of time-dependent Hartree-Fock (TD-HF), various flavors of time-dependent density functional theory (TD-DFT), and the correlated wave function based coupled-cluster (CC2) method we investigated the 4-nitroazobenzene molecule as an example: The low-lying singlet excited states in the isolated trans monomer and dimer as well as their composites with a silicon pentamantane nanocluster, which serves also as a crude model for a silicon surface, were determined. As most important results we found that (i) HF, CC2, range-separated density functionals, or global hybrids with large amount of exact exchange are able to describe exciton (Davydov) splitting properly, while hybrids with small amount of exact exchange fail producing spurious charge transfer. (ii) The exciton splitting in a free dimer would lead to a blue shift of the absorption signal; however, this effect is almost nullified or even overcompensated by the shift arising from van der Waals interactions between the two molecules. (iii) Adsorption on the Si "surface" leads to a further, strong red shift for the present system. (iv) At a next-nearest neighbor distance (of ∼3.6 Å), the exciton splitting is ∼0.3 eV, with or without "surface", suggesting a rapid quenching of the molecular π → π* excitation. At larger distances, exciton splitting decreases rapidly.

QM/MM calculations on a newly synthesised oxyluciferin substrate: new insights into the conformational effect

QM/MM calculations and MD give insights into the light emission of firefly oxyluciferin and into a modified red analogue.

Assessment of Approximate Coupled-Cluster and Algebraic-Diagrammatic-Construction Methods for Ground- and Excited-State Reaction Paths and the Conical-Intersection Seam of a Retinal-Chromophore Model

As a minimal model of the chromophore of rhodopsin proteins, the penta-2,4-dieniminium cation (PSB3) poses a challenging test system for the assessment of electronic-structure methods for the exploration of ground- and excited-state potential-energy surfaces, the topography of conical intersections, and the dimensionality (topology) of the branching space. Herein, we report on the performance of the approximate linear-response coupled-cluster method of second order (CC2) and the algebraic-diagrammatic-construction scheme of the polarization propagator of second and third orders (ADC(2) and ADC(3)). For the ADC(2) method, we considered both the strict and extended variants (ADC(2)-s and ADC(2)-x). For both CC2 and ADC methods, we also tested the spin-component-scaled (SCS) and spin-opposite-scaled (SOS) variants. We have explored several ground- and excited-state reaction paths, a circular path centered around the S1/S0 surface crossing, and a 2D scan of the potential-energy surfaces along the branching space. We find that the CC2 and ADC methods yield a different dimensionality of the intersection space. While the ADC methods yield a linear intersection topology, we find a conical intersection topology for the CC2 method. We present computational evidence showing that the linear-response CC2 method yields a surface crossing between the reference state and the first response state featuring characteristics that are expected for a true conical intersection. Finally, we test the performance of these methods for the approximate geometry optimization of the S1/S0 minimum-energy conical intersection and compare the geometries with available data from multireference methods. The present study provides new insight into the performance of linear-response CC2 and polarization-propagator ADC methods for molecular electronic spectroscopy and applications in computational photochemistry.

0-0 Energies Using Hybrid Schemes: Benchmarks of TD-DFT, CIS(D), ADC(2), CC2, and BSE/GW formalisms for 80 Real-Life Compounds

The 0-0 energies of 80 medium and large molecules have been computed with a large panel of theoretical formalisms. We have used an approach computationally tractable for large molecules, that is, the structural and vibrational parameters are obtained with TD-DFT, the solvent effects are accounted for with the PCM model, whereas the total and transition energies have been determined with TD-DFT and with five wave function approaches accounting for contributions from double excitations, namely, CIS(D), ADC(2), CC2, SCS-CC2, and SOS-CC2, as well as Green's function based BSE/GW approach. Atomic basis sets including diffuse functions have been systematically applied, and several variations of the PCM have been evaluated. Using solvent corrections obtained with corrected linear-response approach, we found that three schemes, namely, ADC(2), CC2, and BSE/GW allow one to reach a mean absolute deviation smaller than 0.15 eV compared to the measurements, the two former yielding slightly better correlation with experiments than the latter. CIS(D), SCS-CC2, and SOS-CC2 provide significantly larger deviations, though the latter approach delivers highly consistent transition energies. In addition, we show that (i) ADC(2) and CC2 values are extremely close to each other but for systems absorbing at low energies; (ii) the linear-response PCM scheme tends to overestimate solvation effects; and that (iii) the average impact of nonequilibrium correction on 0-0 energies is negligible.