Non-adiabatic transition probability dependence on conical intersection topography

Excited State Dynamics in Unidirectional Photochemical Molecular Motors

Unidirectional photochemically driven molecular motors (PMMs) convert the energy of absorbed light into continuous rotational motion. As such they are key components in the design of molecular machines. The prototypical and most widely employed class of PMMs is the overcrowded alkenes, where rotational motion is driven by successive photoisomerization and thermal helix inversion steps. The efficiency of such PMMs depends upon the speed of rotation, determined by the rate of ground state thermal helix inversion, and the quantum yield of photoisomerization, which is dependent on the excited state energy landscape. The former has been optimized by synthetic modification across three generations of overcrowded alkene PMMs. These improvements have often been at the expense of photoisomerization yield, where there remains room for improvement. In this perspective we review the application of ultrafast spectroscopy to characterize the excited state dynamics in PMMs. These measurements lead to a general mechanism for all generations of PMMs, involving subpicosecond decay of a Franck-Condon excited state to populate a dark excited state which decays within picoseconds via conical intersections with the electronic ground state. The model is discussed in the context of excited state dynamics calculations. Studies of PMM photochemical dynamics as a function of solvent suggest exploitation of intramolecular charge transfer and solvent polarity as a route to controlling photoisomerization yield. A test of these ideas for a first generation motor reveals a high degree of solvent control over isomerization yield. These results suggest a pathway to fine control over the performance of future PMMs.

CREST-A program for the exploration of low-energy molecular chemical space

Conformer-rotamer sampling tool (CREST) is an open-source program for the efficient and automated exploration of molecular chemical space. Originally developed in Pracht et al. [Phys. Chem. Chem. Phys. 22, 7169 (2020)] as an automated driver for calculations at the extended tight-binding level (xTB), it offers a variety of molecular- and metadynamics simulations, geometry optimization, and molecular structure analysis capabilities. Implemented algorithms include automated procedures for conformational sampling, explicit solvation studies, the calculation of absolute molecular entropy, and the identification of molecular protonation and deprotonation sites. Calculations are set up to run concurrently, providing efficient single-node parallelization. CREST is designed to require minimal user input and comes with an implementation of the GFNn-xTB Hamiltonians and the GFN-FF force-field. Furthermore, interfaces to any quantum chemistry and force-field software can easily be created. In this article, we present recent developments in the CREST code and show a selection of applications for the most important features of the program. An important novelty is the refactored calculation backend, which provides significant speed-up for sampling of small or medium-sized drug molecules and allows for more sophisticated setups, for example, quantum mechanics/molecular mechanics and minimum energy crossing point calculations.

Chemical control of excited-state reactivity of the anionic green fluorescent protein chromophore

Controlling excited-state reactivity is a long-standing challenge in photochemistry, as a desired pathway may be inaccessible or compete with other unwanted channels. An important example is internal conversion of the anionic green fluorescent protein (GFP) chromophore where non-selective progress along two competing torsional modes (P: phenolate and I: imidazolinone) impairs and enables Z-to-E photoisomerization, respectively. Developing strategies to promote photoisomerization could drive new areas of applications of GFP-like proteins. Motivated by the charge-transfer dichotomy of the torsional modes, we explore chemical substitution on the P-ring of the chromophore as a way to control excited-state pathways and improve photoisomerization. As demonstrated by methoxylation, selective P-twisting appears difficult to achieve because the electron-donating potential effects of the substituents are counteracted by inertial effects that directly retard the motion. Conversely, these effects act in concert to promote I-twisting when introducing electron-withdrawing groups. Specifically, 2,3,5-trifluorination leads to both pathway selectivity and a more direct approach to the I-twisted intersection which, in turn, doubles the photoisomerization quantum yield. Our results suggest P-ring engineering as an effective approach to boost photoisomerization of the anionic GFP chromophore.

A Local Diabatisation Method for Two-State Adiabatic Conical Intersections

A methodology to locally characterize conical intersections (CIs) between two adiabatic electronic states for which no nonadiabatic coupling (NAC) vectors are available is presented. Based on the Hessian and gradient at the CI, the branching space coordinates are identified. The potential energy surface around the CI in the branching space is expressed in the diabatic representation, from which the NAC vectors can be calculated in a wave-function-free, energy-based approach. To demonstrate the universality of the developed methodology, the minimum-energy CI (MECI) between the first (S1) and second (S2) singlet excited states of formamide is investigated at the state-averaged complete active space self-consistent field (SA-CASSCF) and extended multistate complete active space second-order perturbation theory (XMS-CASPT2) levels of theory. In addition, the asymmetrical MECI between the ground state (S0) and S1 of cyclopropanone is evaluated using SA-CASSCF, as well as (ME)CIs between the S1 and S2 states of benzene using SA-CASSCF and time-dependent density functional theory (TDDFT). Finally, a CI between the S1 and S2 excited states of thiophene was analyzed using TDDFT.

Control of Photoconversion Yield in Unidirectional Photomolecular Motors by Push-Pull Substituents

Molecular motors based on the overcrowded alkene motif convert light energy into unidirectional mechanical motion through an excited state isomerization reaction. The realization of experimental control over conversion efficiency in these molecular motors is an important goal. Here, we combine the synthesis of a novel "push-pull" overcrowded alkene motor with photophysical characterization by steady state and ultrafast time-resolved electronic spectroscopy. We show that tuning of the charge transfer character in the excited state has a dramatic effect on the photoisomerization yield, enhancing it to near unity in nonpolar solvents while largely suppressing it in polar solvents. This behavior is explained through reference to solvent- and substituent-dependent potential energy surfaces and their effect on conical intersections to the ground state. These observations offer new routes to the fine control of motor efficiency and introduce additional degrees of freedom in the synthesis and exploitation of light-driven molecular motors.

From a one-mode to a multi-mode understanding of conical intersection mediated ultrafast organic photochemical reactions

This review discusses how ultrafast organic photochemical reactions are controlled by conical intersections, highlighting that decay to the ground-state at multiple points of the intersection space results in their multi-mode character.

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.

Role of conical intersection seam topography in the chemiexcitation of 1,2-dioxetanes

Chemiexcitation, the generation of electronic excited states by a thermal reaction initiated on the ground state, is an essential step in chemiluminescence, and it is mediated by the presence of a conical intersection that allows a nonadiabatic transition from ground state to excited state. Conical intersections classified as sloped favor chemiexcitation over ground state relaxation. The chemiexcitation yield of 1,2-dioxetanes is known to increase upon methylation. In this work we explore to which extent this trend can be attributed to changes in the conical intersection topography or accessibility. Since conical intersections are not isolated points, but continuous seams, we locate regions of the conical intersection seams that are close to the configuration space traversed by the molecules as they react on the ground state. We find that conical intersections are energetically and geometrically accessible from the reaction trajectory, and that topographies favorable to chemiexcitation are found in all three molecules studied. Nevertheless, the results suggest that dynamic effects are more important for explaining the different yields than the static features of the potential energy surfaces.

Internal conversion of the anionic GFP chromophore: in and out of the I-twisted S1/S0 conical intersection seam

The functional diversity of the green fluorescent protein (GFP) family is intimately connected to the interplay between competing photo-induced transformations of the chromophore motif, anionic p-hydroxybenzylidene-2,3-dimethylimidazolinone (HBDI^-). Its ability to undergo Z/E-isomerization is of particular importance for super-resolution microscopy and emerging opportunities in optogenetics. Yet, key dynamical features of the underlying internal conversion process in the native HBDI^- chromophore remain largely elusive. We investigate the intrinsic excited-state behavior of isolated HBDI^- to resolve competing decay pathways and map out the factors governing efficiency and the stereochemical outcome of photoisomerization. Based on non-adiabatic dynamics simulations, we demonstrate that non-selective progress along the two bridge-torsional (i.e., phenolate, P, or imidazolinone, I) pathways accounts for the three decay constants reported experimentally, leading to competing ultrafast relaxation primarily along the I-twisted pathway and S₁ trapping along the P-torsion. The majority of the population (∼70%) is transferred to S₀ in the vicinity of two approximately enantiomeric minima on the I-twisted intersection seam (MECI-Is). Despite their sloped, reactant-biased topographies (suggesting low photoproduct yields), we find that decay through these intersections leads to products with a surprisingly high quantum yield of ∼30%. This demonstrates that E-isomer generation results at least in part from direct isomerization on the excited state. A photoisomerization committor analysis reveals a difference in intrinsic photoreactivity of the two MECI-Is and that the observed photoisomerization is the combined result of two effects: early, non-statistical dynamics around the less reactive intersection followed by later, near-statistical behavior around the more reactive MECI-I. Our work offers new insight into internal conversion of HBDI^- that both establishes the intrinsic properties of the chromophore and enlightens principles for the design of chromophore derivatives and protein variants with improved photoswitching properties.

Resolving the ultrafast dynamics of the anionic green fluorescent protein chromophore in water

The chromophore of the green fluorescent protein (GFP) is critical for probing environmental influences on fluorescent protein behavior. Using the aqueous system as a bridge between the unconfined vacuum system and a constricting protein scaffold, we investigate the steric and electronic effects of the environment on the photodynamical behavior of the chromophore. Specifically, we apply ab initio multiple spawning to simulate five picoseconds of nonadiabatic dynamics after photoexcitation, resolving the excited-state pathways responsible for internal conversion in the aqueous chromophore. We identify an ultrafast pathway that proceeds through a short-lived (sub-picosecond) imidazolinone-twisted (I-twisted) species and a slower (several picoseconds) channel that proceeds through a long-lived phenolate-twisted (P-twisted) intermediate. The molecule navigates the non-equilibrium energy landscape via an aborted hula-twist-like motion toward the one-bond-flip dominated conical intersection seams, as opposed to following the pure one-bond-flip paths proposed by the excited-state equilibrium picture. We interpret our simulations in the context of time-resolved fluorescence experiments, which use short- and long-time components to describe the fluorescence decay of the aqueous GFP chromophore. Our results suggest that the longer time component is caused by an energetically uphill approach to the P-twisted intersection seam rather than an excited-state barrier to reach the twisted intramolecular charge-transfer species. Irrespective of the location of the nonadiabatic population events, the twisted intersection seams are inefficient at facilitating isomerization in aqueous solution. The disordered and homogeneous nature of the aqueous solvent environment facilitates non-selective stabilization with respect to I- and P-twisted species, offering an important foundation for understanding the consequences of selective stabilization in heterogeneous and rigid protein environments.

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.

The non-adiabatic nanoreactor: towards the automated discovery of photochemistry

The ab initio nanoreactor has previously been introduced to automate reaction discovery for ground state chemistry. In this work, we present the nonadiabatic nanoreactor, an analogous framework for excited state reaction discovery. We automate the study of nonadiabatic decay mechanisms of molecules by probing the intersection seam between adiabatic electronic states with hyper-real metadynamics, sampling the branching plane for relevant conical intersections, and performing seam-constrained path searches. We illustrate the effectiveness of the nonadiabatic nanoreactor by applying it to benzene, a molecule with rich photochemistry and a wide array of photochemical products. Our study confirms the existence of several types of S₀/S₁ and S₁/S₂ conical intersections which mediate access to a variety of ground state stationary points. We elucidate the connections between conical intersection energy/topography and the resulting photoproduct distribution, which changes smoothly along seam space segments. The exploration is performed with minimal user input, and the protocol requires no previous knowledge of the photochemical behavior of a target molecule. We demonstrate that the nonadiabatic nanoreactor is a valuable tool for the automated exploration of photochemical reactions and their mechanisms.

A systematic model study quantifying how conical intersection topography modulates photochemical reactions

Despite their important role in photochemistry and expected presence in most polyatomic molecules, conical intersections have been thoroughly characterized in a comparatively small number of systems. Conical intersections can confer molecular photoreactivity or photostability, often with remarkable efficacy, due to their unique structure: at a conical intersection, the adiabatic potential energy surfaces of two or more electronic states are degenerate, enabling ultrafast decay from an excited state without radiative emission, known as nonadiabatic transfer. Furthermore, the precise conical intersection topography determines fundamental properties of photochemical processes, including excited-state decay rate, efficacy, and molecular products that are formed. However, these relationships have yet to be defined comprehensively. In this article, we use an adaptable computational model to investigate a variety of conical intersection topographies, simulate resulting nonadiabatic dynamics, and calculate key photochemical observables. We varied the vibrational mode frequencies to modify conical intersection topography systematically in four primary classes of conical intersections and quantified the resulting rate, total yield, and product yield of nonadiabatic decay. The results reveal that higher vibrational mode frequencies reduce nonadiabatic transfer, but increase the transfer rate and resulting photoproduct formation. These trends can inform progress toward experimental control of photochemical reactions or tuning of molecules' photochemical properties based on conical intersections and their topography.

Discovery of conical intersection mediated photochemistry with growing string methods

Conical intersections (CIs) are important features of photochemistry that determine yields and selectivity. Traditional CI optimizers require significant human effort and chemical intuition, which typically restricts searching to only a small region of the CI space. Herein, a systematic approach utilizing the growing string method is introduced to locate multiple CIs. Unintuitive MECI are found using driving coordinates that can be generated using a combinatorial search, and subsequent optimization allows reaction pathways, transition states, products, and seam-space pathways to be located. These capabilities are demonstrated by application to two prototypical photoisomerization reactions and the dimerization of butadiene. In total, many reaction pathways were uncovered, including the elusive stilbene hula-twist mechanism, and a previously unidentified product in butadiene dimerization. Overall, these results suggest that growing string methods provide a predictive strategy for exploring photochemistry.

Relationship between Excited State Lifetime and Isomerization Quantum Yield in Animal Rhodopsins: Beyond the One-Dimensional Landau-Zener Model

We show that the speed of the chromophore photoisomerization of animal rhodopsins is not a relevant control knob for their light sensitivity. This result is at odds with the momentum-driven tunnelling rationale (i.e., assuming a one-dimensional Landau-Zener model for the decay: Zener, C. Non-Adiabatic Crossing of Energy Levels. Proc. R. Soc. London, Ser. A 1932, 137 (833), 696-702) holding that a faster nuclear motion through the conical intersection translates into a higher quantum yield and, thus, light sensitivity. Instead, a model based on the phase-matching of specific excited state vibrational modes should be considered. Using extensive semiclassical hybrid quantum mechanics/molecular mechanics trajectory computations to simulate the photoisomerization of three animal rhodopsin models (visual rhodopsin, squid rhodopsin and human melanopsin), we also demonstrate that phase-matching between three different modes (the reactive carbon and hydrogen twisting coordinates and the bond length alternation mode) is required to achieve high quantum yields. In fact, such "phase-matching" mechanism explains the computational results and provides a tool for the prediction of the photoisomerization outcome in retinal proteins.