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.

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.

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.

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.

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.

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.

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.

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.

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.

The role of the low-lying dark nπ* states in the photophysics of pyrazine: a quantum dynamics study.

The excited state dynamics of pyrazine has attracted considerable attention in the last three decades. It has long been recognized that after UV excitation, the dynamics of the molecule is impacted by strong non-adiabatic effects due to the existence of a conical intersection between the B2u(ππ*) and B3u(nπ*) electronic states. However, a recent study based on trajectory surface hopping dynamics simulations suggested the participation of the Au(nπ*) and B2g(nπ*) low-lying dark electronic states in the ultrafast radiationless decay of the molecule after excitation to the B2u(ππ*) state. The purpose of this work was to pursue the investigation of the role of the Au(nπ*) and B2g(nπ*) states in the photophysics of pyrazine. A linear vibronic coupling model hamiltonian including the four lowest excited electronic states and the sixteen most relevant vibrational degrees of freedom was constructed using high level XMCQDPT2 electronic structure calculations. Wavepacket propagations using the MCTDH method were then performed and used to simulate the absorption spectrum and the electronic state population dynamics of the system. Our results show that the Au(nπ*) state plays an important role in the photophysics of pyrazine.

New insights into the by-product fatigue mechanism of the photo-induced ring-opening in diarylethenes.

The photochromic properties of diarylethenes, some of the most studied class of molecular switches, are known to be controlled by non-adiabatic decay at a conical intersection seam. Nevertheless, as their fatigue-reaction mechanism - leading to non-photochromic products - is yet to be understood, we investigate the photo-chemical formation of the so-called by-product isomer using three complementary computational methods (MMVB, CASSCF and CASPT2) on three model systems of increasing complexity. We show that for the ring-opening reaction a transition state on S1(2A) involving bond breaking of the penta-ring leads to a low energy S1(2A)/S0(1A) conical intersection seam, which lies above one of the transition states leading to the by-product isomer on the ground state. Therefore, radiationless decay and subsequent side-product formation can take place explaining the photo-degradation responsible for the by-product generation in diarylethene-type molecules. The effect of dynamic electron correlation and the possible role of inter-system crossing along the penta-ring opening coordinate are discussed as well.

Monitoring the birth of an electronic wavepacket in a molecule with attosecond time-resolved photoelectron spectroscopy.

Numerical simulations are presented to validate the possible use of cutting-edge attosecond time-resolved photoelectron spectroscopy to observe in real time the creation of an electronic wavepacket and subsequent electronic motion in a neutral molecule photoexcited by a UV pump pulse within a few femtoseconds.

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.

A generalised vibronic-coupling Hamiltonian model for benzopyran.

A new general model for describing intersecting multidimensional potential energy surfaces when motions of large amplitude are involved is presented. This model can be seen as an extension of the vibronic coupling models of Köppel et al. ["Multimode molecular dynamics beyond the Born-Oppenheimer approximation," Adv. Chem. Phys. 57, 59 (1984)]. In contrast to the original vibronic coupling models, here the number of diabatic states is larger than the number of adiabatic states and curvilinear coordinates are used in a systematic way. Following general considerations, the approach is applied to the fitting of the potential energy surfaces for the very complex nonadiabatic photodynamics of benzopyran. Preliminary results are presented at the complete active space self-consistent field level of theory and with up to 12 active degrees of freedom. Special emphasis is placed on the physical interpretation of the diabatic states and on the influence of the various degrees of freedom on the fit.

Laser control of the radiationless decay in pyrazine using the dynamic Stark effect.

The laser control of the radiationless decay between the B(3u)(nπ*) and B(2u)(ππ*) states of pyrazine using the dynamic Stark effect has been investigated. A vibronic coupling model Hamiltonian in diabatic representation, including potential energy, transition dipole, and static polarizability surfaces as a function of the four most important vibrational modes of the molecule has been parametrized using multi-reference electronic structure calculations. The interaction of the molecule with a strong non-resonant laser pulse has been analyzed in terms of dressed potential energy surfaces. Because of the large polarizability difference between the vibronically coupled B(3u)(nπ*) and B(2u)(ππ*) states, the Stark effect induced by the non-resonant laser pulse shifts the conical intersection away from the Franck-Condon region. We have shown, by solving the time-dependent Schrödinger equation for the molecule interacting with a relatively weak pump pulse driving the electronic excitation from the ground state to the B(2u)(ππ*) state, and a strong non-resonant control pulse, that this control mechanism can be used to trap the wavepacket on the B(2u)(ππ*) potential energy surface for a much longer time than the natural B(2u)(ππ*) lifetime.

Towards converging non-adiabatic direct dynamics calculations using frozen-width variational gaussian product basis functions.

In this article, we investigate the convergence of quantum dynamics calculations with coupled variationally optimized gaussian product basis functions, describing wavepacket motion on regions of molecular potential energy surfaces calculated on the fly. As a benchmark system, we model the radiationless decay of fulvene from its first electronic excited state through an extended S(1)∕S(0) conical intersection seam and monitor two associated properties: the spatial extent to which the conical intersection seam is sampled and the timescale and stepwise nature of the population transfer. We suggest that the fully variational description reviewed here (direct dynamics-variational multi-configuration gaussian) provides a way to balance accuracy against computational cost for molecules of comparable sizes by choosing the number of coupled gaussian product basis functions and a middle way forward between grid based and trajectory surface hopping approaches to non-adiabatic molecular quantum dynamics calculations.

A generalised 17-state vibronic-coupling Hamiltonian model for ethylene.

In a previous work [B. Lasorne, M. A. Robb, H.-D. Meyer, and F. Gatti, "The electronic excited states of ethylene with large-amplitude deformations: A dynamical symmetry group investigation," Chem. Phys. 377, 30-45 (2010); and ibid. 382, 132 (2011) (Erratum)], we investigated the electronic structure of ethylene (ethene, C(2)H(4)) in terms of 17 dominant configurations selected at the multiconfiguration self-consistent field level of theory. These were shown to be sufficient to recover most of the static electron correlation among the first valence and Rydberg states at all geometries. We also devised a strategy to build a 17-quasidiabatic-state matrix representation of the electronic Hamiltonian for curvilinear coordinates using dynamical symmetry. Here, we present fitted surfaces in the form of a generalised vibronic-coupling Hamiltonian model for two nuclear coordinates, CC bond stretching and torsion. Dynamic electron correlation is included into the electronic structure to improve the energetics of the Rydberg states at the multireference configuration interaction level of theory. The chemical interpretation of the adiabatic states of interest does not change qualitatively, which validates our choice of underlying quasidiabatic states in the model. The absorption spectrum is calculated with quantum dynamics and partially assigned. This first two-dimensional model shows a surprisingly good agreement with the experimental spectrum.

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.