Excited state gradients for a state-specific continuum solvation approach: The vertical excitation model within a Lagrangian TDDFT formulation

In silico strategy to design an efficient organic photoswitch based on excited-state cation transfer

A new class of photoswitches and the corresponding elementary photoinduced reaction, the so-called Excited-State Cation Transfer (ESCT), are investigated. This reaction relies on an intramolecular photo-release/photo-complexation of cation: after irradiation, the cation is translocated from a complexation site 1 to a site 2 during the excited state lifetime. Our purpose is thus to develop a computational strategy based on Density Functional theory (DFT) and its time-dependent counterpart (TD-DFT) to improve the different properties of the ESCT photoswitches, namely (i) the ground state complexation constant K, (ii) the excited state complexation constant K*, (iii) the photoejection properties and (iv) the population of the triplet states from a singlet state via intersystem crossing to increase the lifetime of the excited state. In this work, we are interested in optimizing the ESCT properties of a betaine pyridinium chromophore substituted by a 15-aza-5-crown, that was previously shown to efficiently photoeject a Ca2+ cation from the site 1 but no photo-recapture was observed in the site 2 [Aloïse et al., Phys. Chem. Chem. Phys., 2016, 22, 15384]. To this purpose, we have investigated the impact of the modification of the site 1 on the ESCT properties by introducing different substituents (EDG groups, halogen atoms) at different positions. So far, promising systems have been identified but a simultaneous improvement of all the ESCT photoswitches properties has yet not been achieved.

A Theoretical Study of Solvent Effects on the Structure and UV-vis Spectroscopy of 3-Hydroxyflavone (3-HF) and Some Simplified Molecular Models

Solvent effects on the UV-vis spectra of 3-hydroxyflavone and other structurally related molecules (3-hydroxychromen-4-one, 3-hydroxy-4-pyrone, and 4-pyrone) have been studied by combining time-dependent density functional theory (TDDFT) and the polarizable continuum method (PCM). Among the first five excited states of the four considered molecules, electronic states of n → π* and π → π* nature appear. In general, the stability of the n → π* states decreases as the π space becomes larger in such a way that only for 4-pyrone and 3-hydroxy-4-pyrone are they the first excited states. In addition, they become less stabilized in ethanol solution than the ground state, and this causes blueshift transitions in solution. The opposite trend is found for the π → π* excited states. They are less energetic with the π-system size and when passing from gas phase to solution. The solvent shift also depends strongly on the size of the π systems and on the formation of an intramolecular hydrogen bond; thus, it decreases when going from 4-pyrone to 3-hydroxyflavone. The performance of the three versions (cLR, cLR², and IBSF) of the specific-state PCM method in predicting transition energies are compared.

Analytical derivative couplings within the framework of time-dependent density functional theory coupled with conductor-like polarizable continuum model: Formalism, implementation, and applications

The nonadiabatic phenomena, which are characterized by a strong coupling between electronic and nuclear motions, are ubiquitous. The nonadiabatic effect of the studied system can be significantly affected by the surrounding environment, such as solvents, in which such nonadiabatic process takes place. It is essential to develop the theoretical models to simulate these processes while accurately modeling the solvent environment. The time-dependent density functional theory (TDDFT) is currently the most efficient approach to describe the electronic structures and dynamics of complex systems, while the polarizable continuum model (PCM) represents one of the most successful examples among continuum solvation models. Here, we formulate the first-order derivative couplings (DCs) between the ground and excited states as well as between two excited states by utilizing time-independent equation of motion formalism within the framework of both linear response and spin flip formulations of TDDFT/CPCM (the conductor-like PCM), and implement the analytical DCs into the Q-CHEM electronic structure software package. The analytic implementation is validated by the comparison of the analytical and finite-difference results, and reproducing geometric phase effect in the protonated formaldimine test case. Taking 4-(N,N-dimethylamino)benzonitrile and uracil in the gas phase and solution as an example, we demonstrate that the solvent effect is essential not only for the excitation energies of the low-lying excited-states but also for the DCs between these states. Finally, we calculate the internal conversion rate of benzophenone in a solvent with DC being used. The current implementation of analytical DCs together with the existing analytical gradient and Hessian of TDDFT/PCM excited states allows one to study the nonadiabatic effects of relatively large systems in solutions with low computational cost.

Evaluation of molecular photophysical and photochemical properties using linear response time-dependent density functional theory with classical embedding: Successes and challenges

Time-dependent density functional theory (TDDFT) based approaches have been developed in recent years to model the excited-state properties and transition processes of the molecules in the gas-phase and in a condensed medium, such as in a solution and protein microenvironment or near semiconductor and metal surfaces. In the latter case, usually, classical embedding models have been adopted to account for the molecular environmental effects, leading to the multi-scale approaches of TDDFT/polarizable continuum model (PCM) and TDDFT/molecular mechanics (MM), where a molecular system of interest is designated as the quantum mechanical region and treated with TDDFT, while the environment is usually described using either a PCM or (non-polarizable or polarizable) MM force fields. In this Perspective, we briefly review these TDDFT-related multi-scale models with a specific emphasis on the implementation of analytical energy derivatives, such as the energy gradient and Hessian, the nonadiabatic coupling, the spin-orbit coupling, and the transition dipole moment as well as their nuclear derivatives for various radiative and radiativeless transition processes among electronic states. Three variations of the TDDFT method, the Tamm-Dancoff approximation to TDDFT, spin-flip DFT, and spin-adiabatic TDDFT, are discussed. Moreover, using a model system (pyridine-Ag20 complex), we emphasize that caution is needed to properly account for system-environment interactions within the TDDFT/MM models. Specifically, one should appropriately damp the electrostatic embedding potential from MM atoms and carefully tune the van der Waals interaction potential between the system and the environment. We also highlight the lack of proper treatment of charge transfer between the quantum mechanics and MM regions as well as the need for accelerated TDDFT modelings and interpretability, which calls for new method developments.

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.

Simple Protocol for Capturing Both Linear-Response and State-Specific Effects in Excited-State Calculations with Continuum Solvation Models

We present an effective computational protocol (cLR²) to describe both solvatochromism and fluorosolvatochromism. This protocol, which couples the polarizable continuum model to time-dependent density functional theory, simultaneously accounts for both linear-response and state-specific solvation effects. A series of test cases, including solvatochromic and fluorosolvatochromic compounds and excited-state intramolecular proton transfers, are used to highlight that cLR² is especially beneficial for modeling bright excitations possessing a significant charge-transfer character, as well as cases in which an accurate balance between states of various polarities should be restored.

Hybrid theoretical models for molecular nanoplasmonics

The multidisciplinary nature of the research in molecular nanoplasmonics, i.e., the use of plasmonic nanostructures to enhance, control, or suppress properties of molecules interacting with light, led to contributions from different theory communities over the years, with the aim of understanding, interpreting, and predicting the physical and chemical phenomena occurring at molecular- and nano-scale in the presence of light. Multiscale hybrid techniques, using a different level of description for the molecule and the plasmonic nanosystems, permit a reliable representation of the atomistic details and of collective features, such as plasmons, in such complex systems. Here, we focus on a selected set of topics of current interest in molecular plasmonics (control of electronic excitations in light-harvesting systems, polaritonic chemistry, hot-carrier generation, and plasmon-enhanced catalysis). We discuss how their description may benefit from a hybrid modeling approach and what are the main challenges for the application of such models. In doing so, we also provide an introduction to such models and to the selected topics, as well as general discussions on their theoretical descriptions.

Electronic transitions for a fully polarizable QM/MM approach based on fluctuating charges and fluctuating dipoles: Linear and corrected linear response regimes

The fully polarizable Quantum Mechanics/Molecular Mechanics (QM/MM) approach based on fluctuating charges and fluctuating dipoles, named QM/FQFμ [T. Giovannini et al., J. Chem. Theory Comput. 15, 2233 (2019)], is extended to the calculation of vertical excitation energies of solvated molecular systems. Excitation energies are defined within two different solvation regimes, i.e., linear response (LR), where the response of the MM portion is adjusted to the QM transition density, and corrected-Linear Response (cLR) in which the MM response is adjusted to the relaxed QM density, thus being able to account for charge equilibration in the excited state. The model, which is specified in terms of three physical parameters (electronegativity, chemical hardness, and polarizability) is applied to vacuo-to-water solvatochromic shifts of aqueous solutions of para-nitroaniline, pyridine, and pyrimidine. The results show a good agreement with their experimental counterparts, thus highlighting the potentialities of this approach.

First-principles investigation of the double ESIPT process in a thiophene-based dye

Explanation of the experimental triple emission with theoretical tools requires advanced solvent models.

The Bethe-Salpeter formalism with polarisable continuum embedding: reconciling linear-response and state-specific features

The Bethe-Salpeter equation (BSE) formalism has been recently shown to be a valuable alternative to time-dependent density functional theory (TD-DFT) with the same computing time scaling with system size. In particular, problematic transitions for TD-DFT such as charge-transfer, Rydberg and cyanine-like excitations were shown to be accurately described with BSE. We demonstrate here that combining the BSE formalism with the polarisable continuum model (PCM) allows us to include simultaneously linear-response and state-specific contributions to solvatochromism. This is confirmed by exploring transitions of various natures (local, charge-transfer, etc.) in a series of solvated molecules (acrolein, indigo, p-nitro-aniline, donor-acceptor complexes, etc.) for which we compare BSE solvatochromic shifts to those obtained by linear-response and state-specific TD-DFT implementations. Such a remarkable and unique feature is particularly valuable for the study of solvent effects on excitations presenting a hybrid localised/charge-transfer character.

Solvent effects for vertical absorption and emission processes in solution using a self-consistent state specific method based on constrained equilibrium thermodynamics

A self-consistent state specific (SS) method in the framework of TDDFT is presented to account for solvent effects on absorption and emission processes for molecules in solution. In these processes, the initial state is an equilibrium state, while the polarization of the solvent is in nonequilibrium with the electron density of the solute in the final state. Nonequilibrium solvation free energy is calculated based on a novel nonequilibrium solvation model with constrained equilibrium manipulation. The bulk solvent effects are considered using the polarizable continuum method (PCM), where the solvent-solute interaction is described with a reaction field. Molecular orbitals and orbital energies in the presence of the reaction field corresponding to the excited state are employed and the response of the solvent is not included in the TDDFT calculations. A self-consistent procedure is designed to obtain the excited state reaction field. The equations based on this new nonequilibrium solvation model in the framework of the self-consistent SS-PCM/TDDFT method for calculation of vertical absorption and emission energies are presented and implemented in the Q-Chem package. Vertical absorption and emission energies for several small molecules in solution using the newly developed code are calculated and compared with available experimental data and the results of other theoretical studies. Solvent shifts of absorption and emission energies are reasonably reproduced with this approach. The new model is a promising approach to study nonequilibrium absorption and emission processes in solution.

The effects of bromine atoms on the photophysical and photochemical properties of 3-cinnamoylcoumarin derivatives

Coumarin derivatives modified using bromine atoms linked onto the right benzene ring (mainly in the HOMO) could enhance singlet oxygen generation capability.

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.

Solvent effects on excitation energies obtained using the state-specific TD-DFT method with a polarizable continuum model based on constrained equilibrium thermodynamics

Nonequilibrium solvation effects need to be treated properly in the study of electronic absorption processes of solutes since solvent polarization is not in equilibrium with the excited-state charge density of the solute. In this work, we developed a state specific (SS) method based on the novel nonequilibrium solvation model with constrained equilibrium manipulation to account for solvation effects in electronic absorption processes. Time-dependent density functional theory (TD-DFT) is adopted to calculate electronic excitation energies and a polarizable continuum model is employed in the treatment of bulk solvent effects on both the ground and excited electronic states. The equations based on this novel nonequilibrium solvation model in the framework of TDDFT to calculate vertical excitation energy are presented and implemented in the Q-Chem package. The implementation is validated by comparing reorganization energies for charge transfer excitations between two atoms obtained from Q-Chem and those obtained using a two-sphere model. Solvent effects on electronic transitions of coumarin 153 (C153), acetone, pyridine, (2E)-3-(3,4-dimethoxyphenyl)-1-(2-hydroxyphenyl)prop-2-en-1-one (DMHP), and uracil in different solvents are investigated using the newly developed code. Our results show that the obtained vertical excitation energies as well as spectral shifts generally agree better with the available experimental values than those obtained using the traditional nonequlibrium solvation model. This new model is thus appropriate to study nonequilibrium excitation processes in solution.