Surface hopping methods, such as fewest switches surface hopping (FSSH), are widely used to simulate ultrafast nonadiabatic phenomena. However, their accuracy in capturing long-time nonadiabatic dynamics remains largely untested. Here, we assess and compare several surface hopping approaches for describing long-timescale nonadiabatic dynamics, using the S 1 → S 0 internal conversion of the carotenoid lutein in vacuum and in solution as a test case. Our simulations show that the commonly used FSSH with energy-based decoherence-correction (FSSH-EDC) and our recently proposed semi-focused mapping approach to surface hopping (SMASH) fail to accurately describe the slow internal conversion of lutein. In contrast, two surface hopping variants introduced in this work, namely an adapted FSSH-EDC scheme (A-EDC) and a decoherence-corrected SMASH method (SMASH-DEC), effectively improve the treatment of decoherence effects, compared to their parent methods, and predict S 1 → S 0 decay times in significantly better agreement with experimental spectroscopic data and more consistent with ab initio multiple spawning (AIMS) simulations.

The mapping approach to surface hopping (MASH) is one of the most promising methods for simulating nonadiabatic dynamics in molecular systems, in a mixed quantum/classical framework. In its original formulation, MASH is limited to the treatment of two-state systems. Here, we present a generalization of MASH to multiple electronic states, which we call semi-focused MASH (SMASH). A key distinguishing aspect of our approach is that only a selected subset of electronic states, identified through an appropriate clustering procedure, is initially populated. Test simulations of the ultrafast photodynamics of three molecular systems (spiropyran, thioguanine, and azobenzene) show that SMASH gives results closely matching those of decoherence-corrected fewest-switches surface hopping, while eliminating the need for the ad hoc decoherence correction.

Light-driven rotary molecular motors convert light energy into unidirectional rotational movement. In overcrowded alkene-based molecular motors, rotary motion is accomplished through consecutive cis-trans photoisomerization reactions and thermal helix inversion steps. To date, a complete understanding of the photoisomerization reactions of overcrowded alkene motors has not been achieved yet. In this work, we use quantum chemical calculations and quantum mechanics/molecular mechanics nonadiabatic dynamics simulations to investigate the photoinduced dynamics of a push-pull alkene-based molecular motor in two different solvents: cyclohexane and methanol. We show that, while in both solvents the main photorelaxation pathway of our investigated push-pull motor involves two different excited-state minima, in polar methanol, the photorelaxation dynamics is much faster than in nonpolar cyclohexane because of two main effects: (i) a lowering of the energy barrier between the excited-state minima and (ii) a reduction in the energy gap with the ground state at the largely twisted dark minimum, where the excited-state decay takes place. Both effects can be attributed to solvent-polarity stabilization of the charge-transfer excited state along the photorelaxation pathway. In line with the experimental findings, our simulations also indicate that, in methanol, the accelerated photoinduced dynamics goes along with a faster fluorescence decay and a large reduction in the forward photoisomerization yield of our investigated motor.

Simulating the coupled electronic and nuclear response of a molecule to light excitation requires the application of nonadiabatic molecular dynamics. However, when faced with a specific photophysical or photochemical problem, selecting the most suitable theoretical approach from the wide array of available techniques is not a trivial task. The challenge is further complicated by the lack of systematic method comparisons and rigorous testing on realistic molecular systems. This absence of comprehensive molecular benchmarks remains a major obstacle to advances within the field of nonadiabatic molecular dynamics. A CECAM workshop, Standardizing Nonadiabatic Dynamics: Towards Common Benchmarks, was held in May 2024 to address this issue. This Perspective highlights the key challenges identified during the workshop in defining molecular benchmarks for nonadiabatic dynamics. Specifically, this work outlines some preliminary observations on essential components needed for simulations and proposes a roadmap aiming to establish, as an ultimate goal, a community-driven, standardized molecular benchmark set.

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.

In plants, light-harvesting complexes serve as antennas to collect and transfer the absorbed energy to reaction centers, but also regulate energy transport by dissipating the excitation energy of chlorophylls. This process, known as nonphotochemical quenching, seems to be activated by conformational changes within the light-harvesting complex, but the quenching mechanisms remain elusive. Recent spectroscopic measurements suggest the carotenoid S* dark state as the quencher of chlorophylls' excitation. By investigating lutein embedded in different conformations of CP29 (a minor antenna in plants) via nonadiabatic excited state dynamics simulations, we reveal that different conformations of the complex differently stabilize the lutein s-trans conformer with respect to the dominant s-cis one. We show that the s-trans conformer presents the spectroscopic signatures of the S* state and rationalize its ability to accept energy from the closest excited chlorophylls, providing thus a relationship between the complex's conformation and the nonphotochemical quenching.

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.

In this review, we discuss the successes and challenges of the atomistic modeling of photoreceptors. Throughout our presentation, we integrate explanations of the primary methodological approaches, ranging from quantum mechanical descriptions to classical enhanced sampling methods, all while providing illustrative examples of their practical application to specific systems. To enhance the effectiveness of our analysis, our primary focus has been directed towards the examination of applications across three distinct photoreceptors. These include an example of Blue Light-Using Flavin (BLUF) domains, a bacteriophytochrome, and the orange carotenoid protein (OCP) employed by cyanobacteria for photoprotection. Particular emphasis will be placed on the pivotal role played by the protein matrix in fine-tuning the initial photochemical event within the embedded chromophore. Furthermore, we will investigate how this localized perturbation initiates a cascade of events propagating from the binding pocket throughout the entire protein structure, thanks to the intricate network of interactions between the chromophore and the protein.

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 which 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 S2 state quickly decays (in ∼50 fs) to the dark intermediate Sx, eventually ending up in the S1 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

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.

We present two different computational approaches to design covalently bound dimers for singlet fission. Both designs aim at maximizing the effective coupling between the initial singlet excited state S* and the double triplet state TT, by tuning the interaction (mainly through-space) between the chromophore units. Design I is based on a preliminary search for the optimal relative arrangements of chromophores in a space of possible stacked pair geometries. Then, the optimized dimeric arrangements are used as targets for the covalent connection of the two chromophores. In design II, all viable ways to covalently bind the two chromophores are considered, using a given set of linkers. Next, the most promising covalent dimers for singlet fission, among our tested candidates, are identified. The application of our approaches to a locked 1,3-diphenyl-isobenzofuran chromophore and a diamino-fluoroquinone compound allowed to design several promising dimers for singlet fission, featuring large S*-TT effective couplings and favorable energetics.

We present a new geminal product wave function Ansatz where the geminals are not constrained to be strongly orthogonal or to be of seniority-zero. Instead, we introduce weaker orthogonality constraints between geminals that significantly lower the computational effort without sacrificing the indistinguishability of the electrons. That is to say, the electron pairs corresponding to the geminals are not fully distinguishable, and their product has yet to be antisymmetrized according to the Pauli principle to form a bona fide electronic wave function. Our geometrical constraints translate into simple equations involving the traces of products of our geminal matrices. In the simplest non-trivial model, a set of solutions is given by block-diagonal matrices where each block is 2 × 2 and consists of either a Pauli matrix or a normalized diagonal matrix multiplied by a complex parameter to be optimized. With this simplified Ansatz for geminals, the number of terms in the calculation of the matrix elements of quantum observables is considerably reduced. A proof of principle is reported and confirms that the Ansatz is more accurate than strongly orthogonal geminal products while remaining computationally affordable.

We present three different computational designs of potential singlet fission chromophores. In the first two cases, we propose structural modifications of two biradicaloid compounds already known with regard to singlet fission, namely 1,3-diphenyl-isobenzofuran (DPBF) and 2,3-diamino-1,4-benzoquinone (DABQ). In the former case, the introduction of methylene bridges between the phenyl rings and the isobenzofuran core of DPBF leads to an improvement of the singlet fission energetics and confers a higher degree of rigidity to the resulting molecule. In the second case, structural modifications of DABQ are proposed in order to overcome its fast nonradiative excited state decay and to improve its singlet fission energetics. The resulting diamino-fluoroquinone compounds fulfill the desired energy criteria and represent new potential chromophores for singlet fission. Finally, in the third proposed design we exploit the captodative effect to tune the energy levels of small biradicaloid molecules, leading to propose several compounds presented for the first time as suitable chromophores for singlet fission.

In this chapter we deal mainly with nonadiabatic independent trajectory approaches to the simulation of excited state dynamics. We focus on a ubiquitous shortcoming of such methods, namely overcoherence, or lack of decoherence, in the time-evolution of the electronic wavefunction and density matrix. In the mean-field approach the overcoherence affects the average potential energy surface on which the trajectory runs, yielding unphysical results, while in the surface hopping dynamics it leads to an overestimation of the couplings between electronic states. In the introduction we frame the theme of decoherence as a fundamental element of quantum theory and a real process affecting molecular dynamics. In the next section, we introduce the overcoherence problem in independent trajectory methods for nonadiabatic dynamics. In the third section, we shortly review the mean-field and surface hopping approaches, we show how decoherence can be described in the framework of Liouville-von Neumann equation, and we introduce several formulas and procedures to compute decoherence rates. In the fourth section we examine a variety of algorithms that have been proposed to correct the overcoherence in mean-field and surface hopping methods, dividing them in two classes: those based on stochastic sudden decoherence events, and those introducing smooth modifications of the (over)coherent electronic dynamics. Finally, in the last section we recall the most popular and/or promissing decoherence correction methods, and we focus on tests showing how such corrections really improve the accuracy of the nonadiabatic trajectories simulations.

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.

Surface hopping investigation of singlet fission in covalently linked dimers: impact of the mutual arrangement.

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 similar to 204%, which is larger than both the one extracted for the dimer (similar to 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.

We present a diabatization method of general applicability, based on the localization of molecular orbitals on user specified groups of atoms. The method yields orthogonal molecular orbitals similar to the canonical ones for the isolated atom groups, that are the basis to build reference spin-adapted configurations representing localized or charge transfer excitations. An orthogonal transformation from the adiabatic to the quasi-diabatic basis is defined by requiring maximum overlap with the diabatic references. We present the diabatization algorithm as implemented in the framework of semiempirical configuration interaction based on floating occupation molecular orbitals (FOMO-CI), but the same transformation can also be applied to ab initio wavefunctions, obtained for instance with state-average CASSCF. The diabatic representation so obtained and the associated hamiltonian matrix are particularly suited to assess quantitatively the interactions that account for charge and energy transfer transitions, and to analyze the results of nonadiabatic dynamics simulations involving such phenomena.

We present a computational protocol devised to test the suitability of newly proposed chromophores for singlet fission. The protocol includes two main steps: testing the basic energetic requirements by ab initio calculations and simulating the photodynamics to determine singlet fission quantum yields. We applied this protocol to 2,3-diamino-1,4-benzoquinone (DAPBQ), recently proposed as a possible chromophore for singlet fission. We determined the excitation energies of DAPBQ by second order perturbation CASPT2 and NEVPT2 calculations. Then, we optimized a possible crystal structure of DAPBQ, we identified the most favourable pair of molecules within it and we ran a simulation of the excited state dynamics for that dimer embedded in the crystal at a semiempirical QM/MM level. The results indicate that DAPBQ in the crystalline phase does not undergo singlet fission and the initially prepared singlet excited state rapidly decays to the ground state.