Nonadiabatic Excited-State Dynamics with Hybrid ab Initio Quantum-Mechanical/Molecular-Mechanical Methods: Solvation of the Pentadieniminium Cation in Apolar Media

Ultrafast Electronic Relaxation in Aqueous [Fe(bpy)3]2+: A Surface Hopping Study

Trajectory surface hopping simulations are performed to better understand the electronic relaxation dynamics of [Fe(bpy)₃]²⁺ in aqueous solution. Specifically, the ultrafast relaxation from the photoexcited singlet metal-to-ligand charge-transfer (MLCT) to the metastable quintet metal-centered (MC) states is simulated through the surface hopping method, where the MLCT and MC states of [Fe(bpy)₃]²⁺ in aqueous solution are computed by using a model electronic Hamiltonian developed previously. As a result, most of the trajectories are interpreted to show the sequential relaxation pathways via the triplet MC states, though some are the direct pathway from MLCT to the quintet MC states. Even though the triplet MC states are involved in the relaxation, the population transfer to the singlet MC ground state is very small, and the population of the quintet MC states reaches more than ∼96%, reasonably consistent with the unity quantum efficiency discussed experimentally.

Conical Intersection in Chemiluminescence of Cyclic Peroxides

Chemiluminescence (CL) utilizing chemiexcitation for energy transformation is one of the most highly sensitive and useful analytical techniques. The chemiexcitation is a chemical process of a ground-state reactant producing an excited-state product, in which a nonadiabatic event is facilitated by conical intersections (CIs), the specific molecular geometries where electronic states are degenerated. Cyclic peroxides, especially 1,2-dioxetane/dioxetanone derivatives, are the iconic chemiluminescent substances. In this Perspective, we concentrated on the CIs in the CL of cyclic peroxides. We first present a computational overview on the role of CIs between the ground (S₀) state and the lowest singlet excited (S₁) state in the thermolysis of cyclic peroxides. Subsequently, we discuss the role of the S₀/S₁ CI in the CL efficiency and point out misunderstandings in some theoretical studies on the singlet chemiexcitations of cyclic peroxides. Finally, we address the challenges and future prospects in theoretically calculating S₀/S₁ CIs and simulating the dynamics and chemiexcitation efficiency in the CL of cyclic peroxides.

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.

INAQS, a Generic Interface for Nonadiabatic QM/MM Dynamics: Design, Implementation, and Validation for GROMACS/Q-CHEM simulations

The accurate description of large molecular systems in complex environments remains an ongoing challenge for the field of computational chemistry. This problem is even more pronounced for photoinduced processes, as multiple excited electronic states and their corresponding nonadiabatic couplings must be taken into account. Multiscale approaches such as hybrid quantum mechanics/molecular mechanics (QM/MM) offer a balanced compromise between accuracy and computational burden. Here, we introduce an open-source software package (INAQS) for nonadiabatic QM/MM simulations that bridges the sampling capabilities of the GROMACS MD package and the excited-state infrastructure of the Q-CHEM electronic structure software. The interface is simple and can be adapted easily to other MD codes. The code supports a variety of different trajectory-based molecular dynamics, ranging from Born-Oppenheimer to surface hopping dynamics. To illustrate the power of this combination, we simulate electronic absorption spectra, free-energy surfaces along a reaction coordinate, and the excited-state dynamics of 1,3-cyclohexadiene in solution.

The ΔSCF method for non-adiabatic dynamics of systems in the liquid phase

Computational studies of ultrafast photoinduced processes give valuable insights into the photochemical mechanisms of a broad range of compounds. In order to accurately reproduce, interpret, and predict experimental results, which are typically obtained in a condensed phase, it is indispensable to include the condensed phase environment in the computational model. However, most studies are still performed in vacuum due to the high computational cost of state-of-the-art non-adiabatic molecular dynamics (NAMD) simulations. The quantum mechanical/molecular mechanical (QM/MM) solvation method has been a popular model to perform photodynamics in the liquid phase. Nevertheless, the currently used QM/MM embedding techniques cannot sufficiently capture all solute-solvent interactions. In this Perspective, we will discuss the efficient ΔSCF electronic structure method and its applications with respect to the NAMD of solvated compounds, with a particular focus on explicit quantum mechanical solvation. As more research is required for this method to reach its full potential, some challenges and possible directions for future research are presented as well.

do Casal M, Pinheiro M, Toldo JM, Barbatti M. Modeling the heating and cooling of a chromophore after photoexcitation

The heating of a chromophore due to internal conversion and its cooling down due to energy dissipation to the solvent are crucial phenomena to characterize molecular photoprocesses. In this work, we simulated the ab initio nonadiabatic dynamics of cytosine, a prototypical chromophore undergoing ultrafast internal conversion, in three solvents—argon matrix, benzene, and water—spanning an extensive range of interactions. We implemented an analytical energy-transfer model to analyze these data and extract heating and cooling times. The model accounts for nonadiabatic effects, and excited- and ground-state energy transfer, and can analyze data from any dataset containing kinetic energy as a function of time. Cytosine heats up in the subpicosecond scale and cools down within 25, 4, and 1.3 ps in argon, benzene, and water, respectively. The time constants reveal that a significant fraction of the benzene and water heating occurs while cytosine is still electronically excited.

An analytical energy-transfer model is implemented to obtain a chromophore's heating and cooling times in a given solvent by using quantities available in nonadiabatic dynamics simulations.

The Quest to Simulate Excited-State Dynamics of Transition Metal Complexes

This Perspective describes current computational efforts in the field of simulating photodynamics of transition metal complexes. We present the typical workflows and feature the strengths and limitations of the different contemporary approaches. From electronic structure methods suitable to describe transition metal complexes to approaches able to simulate their nuclear dynamics under the effect of light, we give particular attention to build a bridge between theory and experiment by critically discussing the different models commonly adopted in the interpretation of spectroscopic experiments and the simulation of particular observables. Thereby, we review all the studies of excited-state dynamics on transition metal complexes, both in gas phase and in solution from reduced to full dimensionality.

Multiconfigurational Quantum Chemistry Determinations of Absorption Cross Sections (σ) in the Gas Phase and Molar Extinction Coefficients (ε) in Aqueous Solution and Air-Water Interface

Theoretical determinations of absorption cross sections (σ) in the gas phase and molar extinction coefficients (ε) in condensed phases (water solution, interfaces or surfaces, protein or nucleic acids embeddings, etc.) are of interest when rates of photochemical processes, J = ∫ ϕ(λ) σ(λ) I(λ) dλ, are needed, where ϕ(λ) and I(λ) are the quantum yield of the process and the irradiance of the light source, respectively, as functions of the wavelength λ. Efficient computational strategies based on single-reference quantum-chemistry methods have been developed enabling determinations of line shapes or, in some cases, achieving rovibrational resolution. Developments are however lacking for strongly correlated problems, with many excited states, high-order excitations, and/or near degeneracies between states of the same and different spin multiplicities. In this work, we define and compare the performance of distinct computational strategies using multiconfigurational quantum chemistry, nuclear sampling of the chromophore (by means of molecular dynamics, ab initio molecular dynamics, or Wigner sampling), and conformational and statistical sampling of the environment (by means of molecular dynamics). A new mathematical approach revisiting previous absolute orientation algorithms is also developed to improve alignments of geometries. These approaches are benchmarked through the nπ* band of acrolein not only in the gas phase and water solution but also in a gas-phase/water interface, a common situation for instance in atmospheric chemistry. Subsequently, the best strategy is used to compute the absorption band for the adduct formed upon addition of an OH radical to the C6 position of uracil and compared with the available experimental data. Overall, quantum Wigner sampling of the chromophore with molecular dynamics sampling of the environment with CASPT2 electronic-structure determinations arise as a powerful methodology to predict meaningful σ(λ) and ε(λ) band line shapes with accurate absolute intensities.

First-Principles Nonadiabatic Dynamics Simulation of Azobenzene Photodynamics in Solutions

The photoisomerization of azobenzene is a prototypical reaction of various light-activated processes in material and biomedical sciences. However, its reaction mechanism has been under debate for decades, partly due to the challenges in computational simulations to accurately describe the molecule's photodynamics. A recent study (J. Am. Chem. Soc. 2020, 142 (49), 20,680-20,690) addressed the challenges by combining the hole-hole Tamm-Dancoff Approximated (hh-TDA) density functional theory (DFT) method with the ab initio multiple spawning (AIMS) algorithm. The hh-TDA-DFT/AIMS method was applied to first-principles nonadiabatic dynamics simulation of azobenzene's photodynamics in the vacuum. However, it remains necessary to benchmark this new method in realistic molecular environments against experimental data. In the current work, the hh-TDA-DFT/AIMS method was employed in a quantum mechanics/molecular mechanics setting to characterize the trans azobenzene's photodynamics in explicit methanol and n-hexane solvents, following both the S₁ (nπ*) and S₂ (ππ*) excitations. The simulated absorption and fluorescence spectra following the S₂ excitation quantitatively agree with the experiments. However, the hh-TDA-DFT method overestimates the torsional barrier on the S₁ state, leading to an overestimation of the S₁ state lifetime. The excited-state population decays to the ground state through two competing channels. The reactive channel partially yields the cis azobenzene photoproduct, and the unreactive channel exclusively leads to the reactant. The S₂ excitation increases the decay through the unreactive channel and thus decreases the isomerization quantum yield compared to the S₁ excitation. The solvent slows down the azobenzene's torsional dynamics on the S₁ state, but its polarity minimally affects the reaction kinetics and quantum yields. Interestingly, the dynamics of the central torsion and angles of azobenzene play a critical role in determining the final isomer of the azobenzene. This benchmark study validates the hh-TDA-DFT/AIMS method's accuracy for simulating the azobenzene's photodynamics in realistic molecular environments.

Quantum and semiclassical dynamical studies of nonadiabatic processes in solution: achievements and perspectives

We concisely review the main methodological approaches to model nonadiabatic dynamics in isotropic solutions and their applications. Three general classes of models are identified as the most used to include solvent effects in the simulations. The first model describes the solvent as a set of harmonic collective modes coupled to the solute degrees of freedom, and the second as a continuum, while the third explicitly includes solvent molecules in the calculations. The issues related to the use of these models in semiclassical and quantum dynamical simulations are discussed, as well as the main limitations and perspectives of each approach.

Machine Learning for Absorption Cross Sections

We present a machine learning (ML) method to accelerate the nuclear ensemble approach (NEA) for computing absorption cross sections. ML-NEA is used to calculate cross sections on vast ensembles of nuclear geometries to reduce the error due to insufficient statistical sampling. The electronic properties-excitation energies and oscillator strengths-are calculated with a reference electronic structure method only for a relatively few points in the ensemble. The KREG model (kernel-ridge-regression-based ML combined with the RE descriptor) as implemented in MLatom is used to predict these properties for the remaining tens of thousands of points in the ensemble without incurring much of additional computational cost. We demonstrate for two examples, benzene and a 9-dicyanomethylene derivative of acridine, that ML-NEA can produce statistically converged cross sections even for very challenging cases and even with as few as several hundreds of training points.

Non-adiabatic Excited-State Molecular Dynamics: Theory and Applications for Modeling Photophysics in Extended Molecular Materials

Optically active molecular materials, such as organic conjugated polymers and biological systems, are characterized by strong coupling between electronic and vibrational degrees of freedom. Typically, simulations must go beyond the Born-Oppenheimer approximation to account for non-adiabatic coupling between excited states. Indeed, non-adiabatic dynamics is commonly associated with exciton dynamics and photophysics involving charge and energy transfer, as well as exciton dissociation and charge recombination. Understanding the photoinduced dynamics in such materials is vital to providing an accurate description of exciton formation, evolution, and decay. This interdisciplinary field has matured significantly over the past decades. Formulation of new theoretical frameworks, development of more efficient and accurate computational algorithms, and evolution of high-performance computer hardware has extended these simulations to very large molecular systems with hundreds of atoms, including numerous studies of organic semiconductors and biomolecules. In this Review, we will describe recent theoretical advances including treatment of electronic decoherence in surface-hopping methods, the role of solvent effects, trivial unavoided crossings, analysis of data based on transition densities, and efficient computational implementations of these numerical methods. We also emphasize newly developed semiclassical approaches, based on the Gaussian approximation, which retain phase and width information to account for significant decoherence and interference effects while maintaining the high efficiency of surface-hopping approaches. The above developments have been employed to successfully describe photophysics in a variety of molecular materials.

Polarizable embedding QM/MM: the future gold standard for complex (bio)systems?

We provide a perspective of the induced dipole formulation of polarizable QM/MM, showing how efficient implementations will enable their application to the modeling of dynamics, spectroscopy, and reactivity in complex biosystems.

Mechanisms of fluorescence quenching in prototypical aggregation-induced emission systems: excited state dynamics with TD-DFTB

A recent implementation of time-dependent tight-binding density functional theory is employed in excited state molecular dynamics for the investigation of the fluorescence quenching mechanism in 3 prototypical aggregation-induced emission systems.

Novel Molecular-Dynamics-Based Protocols for Phase Space Sampling in Complex Systems

The adequate exploration of the phase space of a chromophore is a fundamental necessity for the simulation of their optical and photophysical properties, taking into account the effects of vibrational motion and, most importantly, the coupling with a (non-homogeneous) molecular environment. A representative set of conformational snapshots around the Franck-Condon region is also required to perform non-adiabatic molecular dynamics, for instance in the framework of surface hopping. Indeed, in the latter case one needs to prepare a set of initial conditions providing a meaningful and complete statistical base for the subsequent trajectory propagation. In this contribution, we propose two new protocols for molecular dynamics-based phase space sampling, called "local temperature adjustment" and "individual QM/MM-based relaxation." These protocols are intended for situations in which the popular Wigner distribution sampling procedure is not applicable-as it is the case when anharmonic or nonlinear vibrations are present-and where regular molecular dynamics sampling might suffer from an inaccurate distribution of internal energy or from inaccurate force fields. The new protocols are applied to the case of phase space sampling of [Re(CO)3(Im)(Phen)]+ (im, imidazole; phen, phenanthroline) in aqueous solution, showing the advantages and limitations of regular Wigner and molecular dynamics sampling as well as the strengths of the new protocols.

Vibrational Sampling and Solvent Effects on the Electronic Structure of the Absorption Spectrum of 2-Nitronaphthalene

The influence of vibrational motion on electronic excited state properties is investigated for the organic chromophore 2-nitronaphtalene in methanol. Specifically, the performance of two vibrational sampling techniques - Wigner sampling and sampling from an ab initio molecular dynamics trajectory- is assessed, in combination with implicit and explicit solvent models. The effects of the different sampling/solvent combinations on the energy and electronic character of the absorption bands are analyzed in terms of charge transfer and exciton size, computed from the electronic transition density. The absorption spectra obtained using sampling techniques and its underlying properties are compared to those of the electronic excited states calculated at the Franck-Condon equilibrium geometry. It is found that the absorption bands of the vibrational ensembles are red-shifted compared to the Franck-Condon bright states, and this red-shift scales with the displacement from the equilibrium geometry. Such displacements are found larger and better described when using ensembles from the harmonic Wigner distribution than snapshots from the molecular dynamics trajectory. Particularly relevant is the torsional motion of the nitro group that quenches the charge transfer character of some of the absorption bands. This motion, however, is better described in the molecular dynamics trajectory. Thus, none of the vibrational sampling approaches can satisfactorily capture all important aspects of the nuclear motion. The inclusion of solvent also red-shifts the absorption bands with respect to the gas phase. This red-shift scales with the charge-transfer character of the bands and is found larger for the implicit than for the explicit solvent model. The advantages and drawbacks of the different sampling and solvent models are discussed to guide future research on the calculation of UV-vis spectra of nitroaromatic compounds.

On the importance of initial conditions for excited-state dynamics

The vast majority of ab initio excited-state simulations are performed within semiclassical, trajectory-based approaches. Apart from the underlying electronic-structure theory, the reliability of the simulations is controlled by a selection of initial conditions for the classical trajectories. We discuss appropriate choices of initial conditions for simulations of different experimental arrangements: dynamics initiated by continuum-wave (CW) laser fields or triggered by ultrashort laser pulses.

Mechanism of ultrafast non-reactive deactivation of the retinal chromophore in non-polar solvents

Counterion sensitive photodynamics of the retinal chromophore in solution.

Generalized trajectory surface-hopping method for internal conversion and intersystem crossing

Trajectory-based fewest-switches surface-hopping (FSSH) dynamics simulations have become a popular and reliable theoretical tool to simulate nonadiabatic photophysical and photochemical processes. Most available FSSH methods model internal conversion. We present a generalized trajectory surface-hopping (GTSH) method for simulating both internal conversion and intersystem crossing processes on an equal footing. We consider hops between adiabatic eigenstates of the non-relativistic electronic Hamiltonian (pure spin states), which is appropriate for sufficiently small spin-orbit coupling. This choice allows us to make maximum use of existing electronic structure programs and to minimize the changes to available implementations of the traditional FSSH method. The GTSH method is formulated within the quantum mechanics (QM)/molecular mechanics framework, but can of course also be applied at the pure QM level. The algorithm implemented in the GTSH code is specified step by step. As an initial GTSH application, we report simulations of the nonadiabatic processes in the lowest four electronic states (S0, S1, T1, and T2) of acrolein both in vacuo and in acetonitrile solution, in which the acrolein molecule is treated at the ab initio complete-active-space self-consistent-field level. These dynamics simulations provide detailed mechanistic insight by identifying and characterizing two nonadiabatic routes to the lowest triplet state, namely, direct S1 → T1 hopping as major pathway and sequential S1 → T2 → T1 hopping as minor pathway, with the T2 state acting as a relay state. They illustrate the potential of the GTSH approach to explore photoinduced processes in complex systems, in which intersystem crossing plays an important role.

Photodynamic behavior of electronic coupling in a N-methylformamide dimer

The role of the bridging water molecules has been studied during the excited state photodynamics of a N-methylformamide dimer in complex with water molecules employing the complete active space self-consistent field (CASSCF) and CAS perturbation theory (CASPT2) methods.

Electronic excitation and structural relaxation of the adenine dinucleotide in gas phase and solution

The excited states and potential surfaces of the adenine dinucleotide are analyzed in gas phase and in solution using a correlated ab initio methodology in a QM/MM framework. In agreement with previous studies, a rather flat S1 surface with a number of minima of different character is found. Specifically, our results suggest that exciplexes with remarkably short intermolecular separation down to ~2.0 Å are formed. A detailed analysis shows that due to strong orbital interactions their character differs significantly from any states present in the Franck-Condon region. The lowest S1 energy minimum is a ππ* exciplex with only a small amount of charge transfer. It possesses appreciable oscillator strength with a polarization almost perpendicular to the planes of the two adenine molecules.

A QM/MM MD insight into photodynamics of hypoxanthine: distinct nonadiabatic decay behaviors between keto-N7H and keto-N9H tautomers in aqueous solution

QM/MM MD simulations reveal different H-bonding networks around DNA base analogues, and the π-electron H-bond in the solvated keto-N7H may facilitate its S₁ → S₀ nonadiabatic decay.

Modelling retinal chromophores photoisomerization: from minimal models in vacuo to ultimate bidimensional spectroscopy in rhodopsins

Modelling of retinal photoisomerization in different environments is reviewed and ultimate ultrafast electronic spectroscopy is proposed for obtaining new insights.

Nonadiabatic photodynamics of a retinal model in polar and nonpolar environment

The nonadiabatic photodynamics of the all-trans-2,4-pentadiene-iminium cation (protonated Schiff base 3, PSB3) and the all-trans-3-methyl-2,4-pentadiene-iminium cation (MePSB3) were investigated in the gas phase and in polar (aqueous) and nonpolar (n-hexane) solutions by means of surface hopping using a multireference configuration-interaction (MRCI) quantum mechanical/molecular mechanics (QM/MM) level. Spectra, lifetimes for radiationless deactivation to the ground state, and structural and electronic parameters are compared. A strong influence of the polar solvent on the location of the crossing seam, in particular in the bond length alternation (BLA) coordinate, is found. Additionally, inclusion of the polar solvent changes the orientation of the intersection cone from sloped in the gas phase to peaked, thus enhancing considerably its efficiency for deactivation of the molecular system to the ground state. These factors cause, especially for MePSB3, a substantial decrease in the lifetime of the excited state despite the steric inhibition by the solvent.