Visible-light Organic Photosensitizers Based on 2-(2-Aminophenyl)benzothiazoles for Photocycloaddition Reactions.

We have studied 2-(2-aminophenyl)benzothiazole and related derivatives for their photophysical properties in view of employing them as new and readily tunable organic photocatalysts. Their triplet energies were estimated by DFT calculations to be in the range of 52-57 kcal·mol-1 suggesting their suitability for the [2+2] photocycloaddition of unsaturated acyl imidazoles with styrene derivatives. Experimental studies have shown that 2­(2­aminophenyl)benzothiazoles comprising alkylamino groups (NHMe, NHiPr) or the native amino group provide the best photocatalytic results in these visible-light mediated [2+2] reactions without the need of any additives yielding a range of cyclobutane derivatives. A combined experimental and theoretical approach has provided insights into the underlying triplet-triplet energy transfer process.

Excitation energy transfer and vibronic relaxation through light-harvesting dendrimer building blocks: A nonadiabatic perspective.

The light-harvesting excitonic properties of poly(phenylene ethynylene) (PPE) extended dendrimers (tree-like π-conjugated macromolecules) involve a directional cascade of local excitation energy transfer (EET) processes occurring from the "leaves" (shortest branches) to the "trunk" (longest branch), which can be viewed from a vibronic perspective as a sequence of internal conversions occurring among a connected graph of nonadiabatically coupled locally excited electronic states via conical intersections. The smallest PPE building block that is able to exhibit EET, the asymmetrically meta-substituted PPE oligomer with one acetylenic bond on one side and two parallel ones on the other side (hence, 2-ring and 3-ring para-substituted pseudo-fragments), is a prototype and the focus of the present work. From linear-response time-dependent density functional theory electronic-structure calculations of the molecule as regards its first two nonadiabatically coupled, optically active, singlet excited states, we built a (1 + 2)-state-8-dimensional vibronic-coupling Hamiltonian model for running subsequent multiconfiguration time-dependent Hartree wavepacket relaxations and propagations, yielding both steady-state absorption and emission spectra as well as real-time dynamics. The EET process from the shortest branch to the longest one occurs quite efficiently (about 80% quantum yield) within the first 25 fs after light excitation and is mediated vibrationally through acetylenic and quinoidal bond-stretching modes together with a particular role given to the central-ring anti-quinoidal rock-bending mode. Electronic and vibrational energy relaxations, together with redistributions of quantum populations and coherences, are interpreted herein through the lens of a nonadiabatic perspective, showing some interesting segregation among the foremost photoactive degrees of freedom as regards spectroscopy and reactivity.

On the unusual Stokes shift in the smallest PPE dendrimer building block: Role of the vibronic symmetry on the band origin?

1,3-Bis(phenylethynyl)benzene is the primary chromophore of the light-harvesting polyphenylene ethynylene (PPE) dendrimers. It is experimentally known to share the same absorption spectrum as its pair of diphenylacetylene (aka. tolane) meta-substituted branches yet exhibits an unusual Stokes shift of about 2000 cm-1 with respect to its band origin (corresponding to the loss of one vibrational quantum within the antisymmetric acetylenic stretching) in its emission spectrum. We suggest, in the present work, the unusual but plausible involvement of molecular symmetry selection rules in a situation where the Born-Oppenheimer approximation is far to be valid. Our hypothesis is comforted with quantum dynamics simulations of absorption and emission UV-visible spectra based on the quantum chemistry data and a diabatic vibronic coupling Hamiltonian model.

Analytical Nonadiabatic Couplings and Gradients within the State-Averaged Orbital-Optimized Variational Quantum Eigensolver.

We introduce several technical and analytical extensions to our recent state-averaged orbital-optimized variational quantum eigensolver (SA-OO-VQE) algorithm (see Yalouz et al. Quantum Sci. Technol. 2021, 6, 024004). Motivated by the limitations of current quantum computers, the first extension consists of an efficient state-resolution procedure to find the SA-OO-VQE eigenstates, and not just the subspace spanned by them, while remaining in the equi-ensemble framework. This approach avoids expensive intermediate resolutions of the eigenstates by postponing this problem to the very end of the full algorithm. The second extension allows for the estimation of analytical gradients and nonadiabatic couplings, which are crucial in many practical situations ranging from the search of conical intersections to the simulation of quantum dynamics, in, for example, photoisomerization reactions. The accuracy of our new implementations is demonstrated on the formaldimine molecule CH2NH (a minimal Schiff base model relevant for the study of photoisomerization in larger biomolecules), for which we also perform a geometry optimization to locate a conical intersection between the ground and first-excited electronic states of the molecule.

Funneling dynamics in a phenylacetylene trimer: Coherent excitation of donor excitonic states and their superposition.

Funneling dynamics in conjugated dendrimers has raised great interest in the context of artificial light-harvesting processes. Photoinduced relaxation has been explored by time-resolved spectroscopy and simulations, mainly by semiclassical approaches or referring to open quantum systems methods, within the Redfield approximation. Here, we take the benefit of an ab initio investigation of a phenylacetylene trimer, and in the spirit of a divide-and-conquer approach, we focus on the early dynamics of the hierarchy of interactions. We build a simplified but realistic model by retaining only bright electronic states and selecting the vibrational domain expected to play the dominant role for timescales shorter than 500 fs. We specifically analyze the role of the in-plane high-frequency skeletal vibrational modes involving the triple bonds. Open quantum system non-adiabatic dynamics involving conical intersections is conducted by separating the electronic subsystem from the high-frequency tuning and coupling vibrational baths. This partition is implemented within a robust non-perturbative and non-Markovian method, here the hierarchical equations of motion. We will more precisely analyze the coherent preparation of donor states or of their superposition by short laser pulses with different polarizations. In particular, we extend the π-pulse strategy for the creation of a superposition to a V-type system. We study the relaxation induced by the high-frequency vibrational collective modes and the transitory dissymmetry, which results from the creation of a superposition of electronic donor states.

Diabatization around Conical Intersections with a New Phase-Corrected Valence-Bond-Based Compression Approach.

In the present work, the valence-bond-based compression approach for diabatization (VBCAD), previously presented in the literature [J. Phys. Chem. Lett. 2020, 11, 5295-5301] in the case of avoided crossings, is extended to the more general situation of conical intersections and their vicinity. A pointwise phase-correction scheme for diabatic states is proposed, based on the explicit use of the peculiarities of the nonorthogonality of ab initio valence bond (VB) theory. Rather than fitting or propagating nonadiabatic couplings, it allows us to determine the phase of diabatic states consistently and automatically at each geometry point. Moreover, it is shown that the undetermination of degenerate states around a conical intersection can be fixed naturally from a straightforward classical VB picture. These are illustrated with two prototypical symmetry-induced (Jahn-Teller) conical intersection models.

Quantum light-induced nonadiabatic phenomena in the absorption spectrum of formaldehyde: Full- and reduced-dimensionality studies.

The coupling of a molecule to a cavity can induce conical intersections of the arising polaritonic potential energy surfaces. Such intersections give rise to the strongest possible nonadiabatic effects. By choosing an example that does not possess nonadiabatic effects in the absence of the cavity, we can study, for the first time, the emergence of these effects in a polyatomic molecule due to its coupling with the cavity taking into account all vibrational degrees of freedom. The results are compared with those of reduced-dimensionality models, and the shortcomings and merits of the latter are analyzed.

A Novel Valence-Bond-Based Automatic Diabatization Method by Compression.

A novel valence-bond-based automatic diabatization method by compression, called valence-bond-based compression approach for dibatization (VBCAD), is presented in this Letter. It is a "black-box" type method that provides an automatic diabatization from a classical valence bond (VB) perspective. In VBCAD, a model space projection is performed by an eigenvalue decomposition algorithm followed by dimensional reduction based on a sequence of Householder transformations. Our diabaticity criterion is implemented in a way that maximizes the diversity of VB structure weights between different diabatic states. Owing to the rigorous Householder transformations employed in this entire procedure, the invariance of the target eigensubspace is preserved. This is illustrated on two prototypical examples.

Striking Generic Impact of Light-Induced Non-Adiabaticity in Polyatomic Molecules.

Non-adiabaticity, i.e., the effect of mixing electronic states by nuclear motion, is a central phenomenon in molecular science. The strongest nonadiabatic effects arise due to the presence of conical intersections of electronic energy surfaces. These intersections are abundant in polyatomic molecules. Laser light can induce in a controlled manner new conical intersections, called light-induced conical intersections, which lead to strong nonadiabatic effects similar to those of the natural conical intersections. These effects are, however, controllable and may even compete with those of the natural intersections. In this work we show that the standard low-energy vibrational spectrum of the electronic ground state can change dramatically by inducing non-adiabaticity via a light-induced conical intersection. This generic effect is demonstrated for an explicit example by full-dimensional high-level quantum calculations using a pump-probe scheme with a moderate-intensity pump laser and a weak probe laser.

A generalized vibronic-coupling Hamiltonian for molecules without symmetry: Application to the photoisomerization of benzopyran.

We present a model for the lowest two potential energy surfaces (PESs) that describe the photoinduced ring-opening reaction of benzopyran taken as a model compound to study the photochromic ring-opening reaction of indolinobenzospiropyran and its evolution toward its open-chain analog. The PESs are expressed in terms of three effective rectilinear coordinates. One corresponds to the direction between the equilibrium geometry in the electronic ground state, referred to as the Franck-Condon geometry, and the minimum of conical intersection (CI), while the other two span the two-dimensional branching space at the CI. The model correctly reproduces the topography of the PESs. The ab initio calculations are performed with the extended multiconfiguration quasidegenerate perturbation theory at second order method. We demonstrate that accounting for electron dynamic correlation drastically changes the global energy landscape since some zwitterionic states become strongly stabilized. Quantum dynamics calculations using this PES model produce an absorption spectrum that matches the experimental one to a good accuracy.

Statistical distributions of the tuning and coupling collective modes at a conical intersection using the hierarchical equations of motion.

We investigate the possibility of extracting the probability distribution of the effective environmental tuning and coupling modes during the nonadiabatic relaxation through a conical intersection. Dynamics are dealt with an open quantum system master equation by partitioning a multistate electronic subsystem out of all the nuclear vibrators. This is an alternative to the more usual partition retaining the tuning and coupling modes of a conical intersection in the active subsystem coupled to a residual bath. The minimal partition of the electronic system generally leads to highly structured spectral densities for both vibrational baths and requires a strongly nonperturbative non-Markovian master equation, treated here by the hierarchical equations of motion (HEOMs). We extend-for a two-bath situation-the procedure proposed by Shi et al. [J. Chem. Phys. 140, 134106 (2014)], whereby the information contained in the auxiliary HEOM matrices is exploited in order to derive the nuclear dissipative wave packet, i.e., the statistical distribution of the displacement of the two tuning and coupling collective coordinates in each electronic state and the coherence. This allows us to visualize the distribution, all along the nonadiabatic decay. We explore a large parameter space for a symmetrical conical intersection model and a symmetrical initial Franck-Condon preparation. Some parameters could be controlled by external fields, while others are molecule dependent and could be designed by molecular engineering. We illustrate the relation between the strongly coupled electronic and bath dynamics together with a geometric measure of non-Markovianity.

On the applicability of a wavefunction-free, energy-based procedure for generating first-order non-adiabatic couplings around conical intersections.

The primal definition of first-order non-adiabatic couplings among electronic states relies on the knowledge of how electronic wavefunctions vary with nuclear coordinates. However, the non-adiabatic coupling between two electronic states can be obtained in the vicinity of a conical intersection from energies only, as this vector spans the branching plane along which degeneracy is lifted to first order. The gradient difference and derivative coupling are responsible of the two-dimensional cusp of a conical intersection between both potential-energy surfaces and can be identified to the non-trivial eigenvectors of the second derivative of the square energy difference, as first pointed out in Köppel and Schubert [Mol. Phys. 104(5-7), 1069 (2006)]. Such quantities can always be computed in principle for the cost of two numerical Hessians in the worst-case scenario. Analytic-derivative techniques may help in terms of accuracy and efficiency but also raise potential traps due to singularities and ill-defined derivatives at degeneracies. We compare here two approaches, one fully numerical, the other semianalytic, where analytic gradients are available but Hessians are not, and investigate their respective conditions of applicability. Benzene and 3-hydroxychromone are used as illustrative application cases. It is shown that non-adiabatic couplings can thus be estimated with decent accuracy in regions of significant size around conical intersections. This procedure is robust and could be useful in the context of on-the-fly non-adiabatic dynamics or be used for producing model representations of intersecting potential energy surfaces with complete obviation of the electronic wavefunctions.

Vibronic properties of para-polyphenylene ethynylenes: TD-DFT insights.

The first singlet excited states of a series of para-polyphenylene ethynylenes (PPEs) are investigated using time-dependent density functional theory (TD-DFT). Vibronic absorption spectra are calculated and show excellent agreement with the experiments, thus validating the adequacy of TD-DFT for such systems. The vibronic structure is assigned to the excitation of a few typical stretching and bending modes. The significant discrepancy between the simulated vertical-transition energies and the experimental absorption maxima in PPEs is underlined and explained. The evolution of the spectroscopic properties and of the electronic structure with the chain length is discussed and characterized.

Fast and slow excited-state intramolecular proton transfer in 3-hydroxychromone: a two-state story?

The photodynamics of 3-hydroxychromone in its first-excited singlet electronic state (bright state of ππ* character) is investigated with special emphasis given to two types of reaction pathways: the excited-state intramolecular-proton-transfer coordinate and the hydrogen-torsion coordinate linking the excited cis and trans isomers. A newly-found conical intersection with the second-excited singlet electronic state (dark state of nπ* character) is suspected to be, to some extent, the reason for the slower rate constant. This hypothesis based on quantum-chemistry calculations is supported by quantum-dynamics simulations in full dimensionality. They show significant transfer of electronic population and provide consistently a vibronic interpretation for the forbidden band in the UV absorption spectrum.

Accidental degeneracy in the spiropyran radical cation: charge transfer between two orthogonal rings inducing ultra-efficient reactivity.

Photochromism of the spiropyran radical cation to the corresponding merocyanine form is investigated by a combination of electrochemical oxidation, UV/vis absorption spectroscopy, spectroelectrochemistry and first-principles calculations (TD-DFT, CAS-SCF and CAS-PT2). First, we demonstrate that the ring-opening of mono-spiropyrans occurs upon one-electron oxidation and that it can be driven photochemically as well as thermally, with trapping of the merocyanine by protonation. Second, in order to explain this experimentally observed spectroelectrochemical behaviour we suggest a theoretical mechanism based on the reactivity of the two lowest electronic excited-states, which promotes effective electron transfer from the indoline (nitrogen-ring) to the pyran (oxygen-ring) moieties (and vice versa) through a conical intersection seam of degeneracy. Characterisation of the minimum energy conical intersection on this crossing revealed that it presents a rare diabatic trapping topology. The excited state molecule cannot escape from crossing the intersection seam due to the presence of only one degeneracy-lifting coordinate that efficiently channels into the formation of the merocyanine photoproduct, so giving rise to a "kitchen sink" funnel-like effect. Therefore, assuming rapid relaxation after vertical excitation to a higher electronic state, photoconversion cannot be avoided in the D1 electronic state, which rationalises the remarkably efficient visible light driven excited-state reactivity observed experimentally.

Attosecond electronic and nuclear quantum photodynamics of ozone monitored with time and angle resolved photoelectron spectra.

Recently we reported a series of numerical simulations proving that it is possible in principle to create an electronic wave packet and subsequent electronic motion in a neutral molecule photoexcited by a UV pump pulse within a few femtoseconds. We considered the ozone molecule: for this system the electronic wave packet leads to a dissociation process. In the present work, we investigate more specifically the time-resolved photoelectron angular distribution of the ozone molecule that provides a much more detailed description of the evolution of the electronic wave packet. We thus show that this experimental technique should be able to give access to observing in real time the creation of an electronic wave packet in a neutral molecule and its impact on a chemical process.

Intramolecular Charge Transfer in 4-Aminobenzonitrile Does Not Need the Twist and May Not Need the Bend.

A study combining accurate quantum chemistry and full-dimensional quantum dynamics is presented to confirm the existence of an ultrafast radiationless decay channel from the charge-transfer state to the locally excited state in 4-aminobenzonitrile. This intramolecular charge-transfer pathway proceeds through a newly found planar conical intersection, and it is shown to be more efficient in the presence of acetonitrile than in the gas phase. Our results are consistent with recent experimental observations.

A curve-crossing model to rationalize and optimize diarylethene dyads.

Going from photochromic compounds presenting a single switchable function to multi-addressable photochromic multimers remains an extremely difficult task notably because the interactions of several photochromic units through a linker generally result in a substantial loss of photoactivity. Due to their size and the intrinsic complexity of their electronic structure, coupled photochromes also constitute a fundamental challenge for theoretical chemistry. We present here an effective curve-crossing model that, used in connection with easily accessible ab initio data, allows a first understanding of the difficulty to obtain efficient multiphotochromes. Indeed, we demonstrate that extra crossing points, specific to multiphotochromes, have to be passed to ensure reactivity. In addition, the proposed approach allows the definition of an intuitive tilt criterion that can be used to screen a large number of substitution patterns and hence help in the design of new compounds, an aspect that is also developed here. The compatibility of this tilt criterion with previously proposed static Franck-Condon parameters is discussed as well.

Full-dimensional control of the radiationless decay in pyrazine using the dynamic Stark effect.

We present a full quantum-mechanical study of the laser control of the radiationless decay between the B3u(nπ(*)) and B2u(ππ(*)) states of pyrazine using the dynamic Stark effect. In contrast to our previous study [Sala et al., J. Chem. Phys. 140, 194309 (2014)], where a four-dimensional model was used, all the 24 degrees of freedom are now included in order to test the robustness of the strategy of control. Using a vibronic coupling Hamiltonian model in a diabatic representation, the multi-layer version of the multi-configuration time-dependent Hartree method is exploited to propagate the corresponding wave packets. We still observe a trapping of the wavepacket on the B2u(ππ(*)) potential energy surface due to the Stark effect for a longer time than the "non-resonant field-free" B2u(ππ(*)) lifetime.