Diabatization by Localization in the Framework of Configuration Interaction Based on Floating Occupation Molecular Orbitals (FOMO−CI)

Learning Multiple Potential Energy Surfaces by Automated Discovery of a Compatible Representation

Creating analytic representations of multiple potential energy surfaces for modeling electronically nonadiabatic processes is a major challenge being addressed in various ways by the chemical dynamics community. In this work, we introduce a new method that can achieve convenient learning of multiple potential energy surfaces (PESs) and their gradients (negatives of the forces) for a polyatomic system. This new method, called compatibilization by deep neural network (CDNN), is demonstrated to be accurate and, even more importantly, to be automatic. The only required input is a database with geometries and potential energies. The method produces a matrix, called the compatible potential energy matrix (CPEM), that may be interpreted as the electronic Hamiltonian in an implicit nonadiabatic basis, and the analytic adiabatic potential energy surfaces and their gradients are obtained by diagonalization and automatic differentiation. We show that the CPEM, which is neither adiabatic nor necessarily diabatic, can be discovered automatically during the learning procedure by the special design of a CDNN architecture. We believe that the CDNN method will be very useful in practice for learning coupled PESs for polyatomic systems because it is accurate and fully automatic.

Quantum-Classical Simulations Reveal the Photoisomerization Mechanism of a Prototypical First-Generation Molecular Motor

Light-driven molecular rotary motors convert the energy of absorbed light into unidirectional rotational motion and are key components in the design of molecular machines. The archetypal class of light-driven rotary motors is chiral overcrowded alkenes, where the rotational movement is achieved through consecutive cis-trans photoisomerization reactions and thermal helix inversion steps. While the thermal steps have been rather well understood by now, our understanding of the photoisomerization reactions of overcrowded alkene-based motors still misses key points that would explain the striking differences in operation efficiency of the known systems. Here, we employ quantum-chemical calculations and nonadiabatic molecular dynamics simulations to investigate the excited-state decay and photoisomerization mechanism in a prototypical alkene-based first-generation rotary motor. We show that the initially excited bright state undergoes an ultrafast relaxation to multiple excited-state minima separated by low energy barriers and reveal a slow picosecond-timescale decay to the ground state, which only occurs from a largely twisted dark excited-state minimum, far from any conical-intersection point. Additionally, we attribute the origin of the high yields of forward photoisomerization in our investigated motor to the favorable topography of the ground-state potential energy surface, which is controlled by the conformation of the central cyclopentene rings.

Excitonic Approach for Nonadiabatic Dynamics: Extending Beyond the Frenkel Exciton Model

We report the formulation and implementation of an extended Frenkel exciton model (EFEM) designed for simulating the dynamics of multichromophoric systems, taking into account the possible presence of interchromophore charge transfer states, as well as other states in which two chromophores are simultaneously excited. Our approach involves constructing a Hamiltonian based on calculations performed on monomers and selected dimers within the multichromophoric aggregate. Nonadiabatic molecular dynamics is addressed using a surface hopping approach, while the electronic wave functions and energies required for constructing the EFEM are computed utilizing the semiempirical floating occupation molecular orbitals-configuration interaction (FOMO-CI) electronic structure method. To validate our approach, we simulate the singlet fission process in a trimer of 2,5-bis(fluorene-9-ylidene)-2,5-dihydrothiophene (ThBF) molecules, embedded in their crystal environment, comparing the results of the EFEM to the standard "supermolecule" approach.

Predicting Solvatochromism of Chromophores in Proteins through QM/MM and Machine Learning

Solvatochromism occurs in both homogeneous solvents and more complex biological environments, such as proteins. While in both cases the solvatochromic effects report on the surroundings of the chromophore, their interpretation in proteins becomes more complicated not only because of structural effects induced by the protein pocket but also because the protein environment is highly anisotropic. This is particularly evident for highly conjugated and flexible molecules such as carotenoids, whose excitation energy is strongly dependent on both the geometry and the electrostatics of the environment. Here, we introduce a machine learning (ML) strategy trained on quantum mechanics/molecular mechanics calculations of geometrical and electrochromic contributions to carotenoids' excitation energies. We employ this strategy to compare solvatochromism in protein and solvent environments. Despite the important specifities of the protein, ML models trained on solvents can faithfully predict excitation energies in the protein environment, demonstrating the robustness of the chosen descriptors.

Ultrafast excited-state dynamics of Luteins in the major light-harvesting complex LHCII

Carotenoid pigments are known to present a functional versatility when bound to light-harvesting complexes. This versatility originates from a strong correlation between a complex electronic structure and a flexible geometry that is easily tunable by the surrounding protein environment. Here, we investigated how the different L1 and L2 sites of the major trimeric light-harvesting complex (LHCII) of green plants tune the electronic structure of the two embedded luteins, and how this reflects on their ultrafast dynamics upon excitation. By combining molecular dynamics and quantum mechanics/molecular mechanics calculations, we found that the two luteins feature a different conformation around the second dihedral angle in the lumenal side. The s-cis preference of the lutein in site L2 allows for a more planar geometry of the π -conjugated backbone, which results in an increased degree of delocalization and a reduced excitation energy, explaining the experimentally observed red shift. Despite these remarkable differences, according to surface hopping simulations the two luteins present analogous ultrafast dynamics upon excitation: the bright S 2 state quickly decays (in ∼ 50 fs) to the dark intermediate S x , eventually ending up in the S 1 state. Furthermore, by employing two different theoretical approaches (i.e., Förster theory and an excitonic version of surface hopping), we investigated the experimentally debated energy transfer between the two luteins. With both approaches, no evident energy transfer was observed in the ultrafast timescale.

Eclipsed and Twisted Excimers of Pyrene and 2-Azapyrene: How Nitrogen Substitution Impacts Excimer Emission

Due to their unique photophysical and electronic properties, pyrene and its analogues have been the subject of extensive research in recent decades. The propensity of pyrene and its derivatives to form excimers has found wide application in various fields. Nitrogen-substituted pyrene derivatives display similar photophysical properties, but for them, excimer emission has not been reported to date. Here, we use time-dependent density functional theory (TD-DFT) calculations to investigate the low-lying exciton states of dimers of pyrene and 2-azapyrene. The excimer equilibrium structures are determined and the contribution of charge transfer (CT) excitations and intermolecular interactions to the exciton states is disclosed using a diabatization procedure. The study reveals that the dimers formed by the two molecules have quite similar exciton-state patterns, in which the relevant CT contributions govern the formation of excimer states, along with the La/Lb state inversion. In contrast with pyrene, the dipole-dipole interactions in 2-azapyrene stabilize the dark eclipsed excimer structure and increase the barrier for conversion into a bright twisted excimer. It is suggested that these differences in the nitrogen-substituted derivative might influence the excimer emission properties.

How orange carotenoid protein controls the excited state dynamics of canthaxanthin

Orange Carotenoid Protein (OCP) is a ketocarotenoid-binding protein essential for photoprotection in cyanobacteria. The main steps of the photoactivated conversion which converts OCP from its resting state to the active one have been extensively investigated. However, the initial photochemical event in the ketocarotenoid which triggers the large structural changes finally leading to the active state is still not understood. Here we employ QM/MM surface hopping nonadiabatic dynamics to investigate the excited-state decay of canthaxanthin in OCP, both in the ultrafast S2 to S1 internal conversion and the slower decay leading back to the ground state. For the former step we show the involvement of an additional excited state, which in the literature has been often named the SX state, and we characterize its nature. For the latter step, we reveal an excited state decay characterized by multiple timescales, which are related to the ground-state conformational heterogeneity of the ketocarotenoid. We assigned the slowly decaying population to the so-called S* state. Finally, we identify a minor decay pathway involving double-bond photoisomerization, which could be the initial trigger to photoactivation of OCP.

Electronic Couplings for Singlet Fission Processes Based on the Fragment Particle-Hole Densities

A new diabatization scheme is proposed to calculate the electronic couplings for the singlet fission process in multichromophoric systems. In this approach, a robust descriptor that treats single and multiple excitations on an equal footing is adopted to quantify the localization degree of the particle and hole densities of the electronic states. By maximally localizing the particles and holes in terms of predefined molecular fragments, quasi-diabatic states with well-defined characters (locally excited, charge transfer, correlated triplet pair, etc.) can be automatically constructed as the linear combinations of the adiabatic ones, and the electronic couplings can be directly obtained. This approach is very general in that it applies to electronic states with various spin multiplicities and can be combined with various kinds of preliminary electronic structure calculations. Due to the high numerical efficiency, it is able to manipulate more than 100 electronic states in diabatization. The applications to the tetracene dimer and trimer reveal that high-lying multiply excited charge transfer states have significant influences on both the formation and separation of the correlated triplet pair and can even enlarge the coupling for the latter process by 1 order of magnitude.

Characterization of excited states in time-dependent density functional theory using localized molecular orbitals

Localized molecular orbitals are often used for the analysis of chemical bonds, but they can also serve to efficiently and comprehensibly compute linear response properties. While conventional canonical molecular orbitals provide an adequate basis for the treatment of excited states, a chemically meaningful identification of the different excited-state processes is difficult within such a delocalized orbital basis. In this work, starting from an initial set of supermolecular canonical molecular orbitals, we provide a simple one-step top-down embedding procedure for generating a set of orbitals, which are localized in terms of the supermolecule but delocalized over each subsystem composing the supermolecule. Using an orbital partitioning scheme based on such sets of localized orbitals, we further present a procedure for the construction of local excitations and charge-transfer states within the linear response framework of time-dependent density functional theory (TDDFT). This procedure provides direct access to approximate diabatic excitation energies and, under the Tamm-Dancoff approximation, also their corresponding electronic couplings-quantities that are of primary importance in modeling energy transfer processes in complex biological systems. Our approach is compared with a recently developed diabatization procedure based on subsystem TDDFT using projection operators, which leads to a similar set of working equations. Although both of these methods differ in the general localization strategies adopted and the type of basis functions (Slaters vs Gaussians) employed, an overall decent agreement is obtained.

Intermolecular Interactions and Charge Resonance Contributions to Triplet and Singlet Exciton States of Oligoacene Aggregates

Intermolecular interactions modulate the electro-optical properties of molecular materials and the nature of low-lying exciton states. Molecular materials composed by oligoacenes are extensively investigated for their semiconducting and optoelectronic properties. Here, we analyze the exciton states derived from time-dependent density functional theory (TDDFT) calculations for two oligoacene model aggregates: naphthalene and anthracene dimers. To unravel the role of inter-molecular interactions, a set of diabatic states is selected, chosen to coincide with local (LE) and charge-transfer (CT) excitations within a restricted orbital space including two occupied and two unoccupied orbitals for each molecular monomer. We study energy profiles and disentangle inter-state couplings to disclose the (CT) character of singlet and triplet exciton states and assess the influence of inter-molecular orientation by displacing one molecule with respect to the other along the longitudinal translation coordinate. The analysis shows that (CT) contributions are relevant, although comparably less effective for triplet excitons, and induce a non-negligible mixed character to the low-lying exciton states for eclipsed monomers and for small translational displacements. Such (CT) contributions govern the L_a/L_b state inversion occurring for the low-lying singlet exciton states of naphthalene dimer and contribute to the switch from H- to J-aggregate type of the strongly allowed B_b transition of both oligoacene aggregates.

Ultrafast Excited-State Dynamics of Carotenoids and the Role of the SX State

Carotenoids are natural pigments with multiple roles in photosynthesis. They act as accessory pigments by absorbing light where chlorophyll absorption is low, and they quench the excitation energy of neighboring chlorophylls under high-light conditions. The function of carotenoids depends on their polyene-like structure, which controls their excited-state properties. After light absorption to their bright S2 state, carotenoids rapidly decay to the optically dark S1 state. However, ultrafast spectroscopy experiments have shown the signatures of another dark state, termed SX. Here we shed light on the ultrafast photophysics of lutein, a xanthophyll carotenoid, by explicitly simulating its nonadiabatic excited-state dynamics in solution. Our simulations confirm the involvement of SX in the relaxation toward S1 and reveal that it is formed through a change in the nature of the S2 state driven by the decrease in the bond length alternation coordinate of the carotenoid conjugated chain.

Impact of Charge-Resonance Excitations on CT-Mediated J-Type Aggregation in Singlet and Triplet Exciton States of Perylene Di-Imide Aggregates: A TDDFT Investigation

The modulation of intermolecular interactions upon aggregation induces changes in excited state properties of organic molecules that can be detrimental for some optoelectronic applications but can be exploited for others. The time-dependent density functional theory (TDDFT) is a cost-effective approach to determining the exciton states of molecular aggregates, and it has been shown to provide reliable results when coupled with the appropriate choice of the functional. Here we apply a general procedure to analyze the aggregates’ exciton states derived from TDDFT calculations in terms of diabatic states chosen to coincide with local (LE) and charge-transfer (CT) excitations within a restricted orbital space. We apply the approach to study energy profiles, interstate couplings, and the charge-transfer character of singlet and triplet exciton states of perylene di-imide aggregates (PDI). We focus on the intermolecular displacement along the longitudinal translation coordinate, which mimics different amounts of slip-stacking observed in PDI crystals. The analysis, in terms of symmetry-adapted Frenkel excitations (FE) and charge-resonance (CR) states and their interactions, discloses how the interchange of the H/J character for small longitudinal shifts, previously reported for singlet exciton states, also occurs for triplet excitons.

(De)localization dynamics of molecular excitons: comparison of mixed quantum–classical and fully quantum treatments

Molecular excitons play a central role in processes of solar energy conversion, both natural and artificial. It is therefore no wonder that numerous experimental and theoretical investigations in the last...

Surface Hopping Dynamics with the Frenkel Exciton Model in a Semiempirical Framework

We present an implementation of the Frenkel exciton model in the framework of the semiempirical floating occupation molecular orbitals-configuration interaction (FOMO-CI) electronic structure method, aimed at simulating the dynamics of multichromophoric systems, in which excitation energy transfer can occur, by a very efficient approach. The nonadiabatic molecular dynamics is here dealt with by the surface hopping method, but the implementation we proposed is compatible with other dynamical approaches. The exciton coupling is computed either exactly, within the semiempirical approximation considered, or by resorting to transition atomic charges. The validation of our implementation is carried out on the trans-azobenzeno-2S-phane (2S-TTABP), formed by two azobenzene units held together by sulfur bridges, taken as a minimal model of multichromophoric systems, in which both strong and weak exciton couplings are present.

Excimer formation dynamics in the isolated tetracene dimer

The understanding of excimer formation and its interplay with the singlet-correlated triplet pair state ¹(TT) is of high significance for the development of efficient organic electronics. Here, we study the photoinduced dynamics of the tetracene dimer in the gas phase by time-resolved photoionisation and photoion imaging experiments as well as nonadiabatic dynamics simulations in order to obtain mechanistic insight into the excimer formation dynamics. The experiments are performed using a picosecond laser system for excitation into the S₂ state and reveal a biexponential time dependence. The time constants, obtained as a function of excess energy, lie in the range between ≈10 ps and 100 ps and are assigned to the relaxation of the excimer on the S₁ surface and to its deactivation to the ground state. Simulations of the quantum-classical photodynamics are carried out in the frame of the semi-empirical CISD and TD-lc-DFTB methods. Both theoretical approaches reveal a dominating relaxation pathway that is characterised by the formation of a perfectly stacked excimer. TD-lc-DFTB simulations have also uncovered a second relaxation channel into a less stable dimer conformation in the S₁ state. Both methods have consistently shown that the electronic and geometric relaxation to the excimer state is completed in less than 10 ps. The inclusion of doubly excited states in the CISD dynamics and their diabatisation further allowed to observe a transient population of the ¹(TT) state, which, however, gets depopulated on a timescale of 8 ps, leading finally to the trapping in the excimer minimum.

The understanding of excimer formation and its interplay with the singlet-correlated triplet pair state ¹(TT) is of high significance for the development of efficient organic electronics.

Machine Learning for Electronically Excited States of Molecules

Electronically excited states of molecules are at the heart of photochemistry, photophysics, as well as photobiology and also play a role in material science. Their theoretical description requires highly accurate quantum chemical calculations, which are computationally expensive. In this review, we focus on not only how machine learning is employed to speed up such excited-state simulations but also how this branch of artificial intelligence can be used to advance this exciting research field in all its aspects. Discussed applications of machine learning for excited states include excited-state dynamics simulations, static calculations of absorption spectra, as well as many others. In order to put these studies into context, we discuss the promises and pitfalls of the involved machine learning techniques. Since the latter are mostly based on quantum chemistry calculations, we also provide a short introduction into excited-state electronic structure methods and approaches for nonadiabatic dynamics simulations and describe tricks and problems when using them in machine learning for excited states of molecules.

Machine Learning for Electronically Excited States of Molecules

Electronically excited states of molecules are at the heart of photochemistry, photophysics, as well as photobiology and also play a role in material science. Their theoretical description requires highly accurate quantum chemical calculations, which are computationally expensive. In this review, we focus on not only how machine learning is employed to speed up such excited-state simulations but also how this branch of artificial intelligence can be used to advance this exciting research field in all its aspects. Discussed applications of machine learning for excited states include excited-state dynamics simulations, static calculations of absorption spectra, as well as many others. In order to put these studies into context, we discuss the promises and pitfalls of the involved machine learning techniques. Since the latter are mostly based on quantum chemistry calculations, we also provide a short introduction into excited-state electronic structure methods and approaches for nonadiabatic dynamics simulations and describe tricks and problems when using them in machine learning for excited states of molecules.

Addressing the Frenkel and charge transfer character of exciton states with a model Hamiltonian based on dimer calculations: Application to large aggregates of perylene bisimide

To understand the influence of interchromophoric arrangements on photo-induced processes and optical properties of aggregates, it is fundamental to assess the contribution of local excitations [charge transfer (CT) and Frenkel (FE)] to exciton states. Here, we apply a general procedure to analyze the adiabatic exciton states derived from time-dependent density functional theory calculations, in terms of diabatic states chosen to coincide with local excitations within a restricted orbital space. In parallel, motivated by the need of cost-effective approaches to afford the study of larger aggregates, we propose to build a model Hamiltonian based on calculations carried out on dimers composing the aggregate. Both approaches are applied to study excitation energy profiles and CT character modulation induced by interchromophore rearrangements in perylene bisimide aggregates up to a tetramer. The dimer-based approach closely reproduces the results of full-aggregate calculations, and an analysis in terms of symmetry-adapted diabatic states discloses the effects of CT/FE interactions on the interchange of the H-/J-character for small longitudinal shifts of the chromophores.

Delocalization effects in singlet fission: Comparing models with two and three interacting molecules

We present surface hopping simulations of singlet fission in 2,5-bis(fluorene-9-ylidene)-2,5-dihydrothiophene (ThBF). In particular, we performed simulations based on quantum mechanics/molecular mechanics (QM/MM) schemes in which either two or three ThBF molecules are inserted in the QM region and embedded in their MM crystal environment. Our aim was to investigate the changes in the photodynamics that are brought about by extending the delocalization of the excited states beyond the minimal model of a dimer. In the simulations based on the trimer model, compared to the dimer-based ones, we observed a faster time evolution of the state populations, with the largest differences associated with both the rise and decay times for the intermediate charge transfer states. Moreover, for the trimer, we predicted a singlet fission quantum yield of ∼204%, which is larger than both the one extracted for the dimer (∼179%) and the theoretical upper limit of 200% for the dimer-based model of singlet fission. Although our study cannot account for the effects of extending the delocalization beyond three molecules, our findings clearly indicate how and why the singlet fission dynamics can be affected.