Surface Hopping within an Exciton Picture. An Electrostatic Embedding Scheme

Efficient Excitonic Configuration Interaction for Large-Scale Multichromophoric Systems Using the Resolution-of-Identity Approximation

The calculation of electronic excited states in extended multichromophoric systems is computationally challenging. Here, we accelerate our recently introduced excitonic configuration interaction (ECI) method [T. Piteša et al. J. Chem. Theory Comput. 2024, 20, 5609] with the resolution-of-identity approximation for the two-site two-electron integrals in the calculation of the interchromophoric Coulomb and exchange terms. Additionally, a simple overlap-based scheme is introduced to prescreen the Cholesky-transformed tensor of the three-centric two-electron interchromophoric exchange integrals, significantly accelerating the expensive tensor contraction for the two-site exchange term. This reduces both cost and memory requirements, enabling large-scale calculations of systems with many chromophores. We demonstrate its efficiency and accuracy by calculating electronic excited states of chains of up to 32 BODIPY chromophores and networks of up to 100 peri-xanthenoxanthene units, with 12 320 and 43 600 basis functions, respectively. We achieve errors in the excitation energies below 30 meV, using site states calculated with time-dependent density functional theory.

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.

Non-adiabatic molecular dynamics simulations provide new insights into the exciton transfer in the Fenna-Matthews-Olson complex

A trajectory surface hopping approach, which uses machine learning to speed up the most time-consuming steps, has been adopted to investigate the exciton transfer in light-harvesting systems. The present neural networks achieve high accuracy in predicting both Coulomb couplings and excitation energies. The latter are predicted taking into account the environment of the pigments. Direct simulation of exciton dynamics through light-harvesting complexes on significant time scales is usually challenging due to the coupled motion of nuclear and electronic degrees of freedom in these rather large systems containing several relatively large pigments. In the present approach, however, we are able to evaluate a statistically significant number of non-adiabatic molecular dynamics trajectories with respect to exciton delocalization and exciton paths. The formalism is applied to the Fenna-Matthews-Olson complex of green sulfur bacteria, which transfers energy from the light-harvesting chlorosome to the reaction center with astonishing efficiency. The system has been studied experimentally and theoretically for decades. In total, we were able to simulate non-adiabatically more than 30 ns, sampling also the relevant space of parameters within their uncertainty. Our simulations show that the driving force supplied by the energy landscape resulting from electrostatic tuning is sufficient to funnel the energy towards site 3, from where it can be transferred to the reaction center. However, the high efficiency of transfer within a picosecond timescale can be attributed to the rather unusual properties of the BChl a molecules, resulting in very low inner and outer-sphere reorganization energies, not matched by any other organic molecule, e.g., used in organic electronics. A comparison with electron and exciton transfer in organic materials is particularly illuminating, suggesting a mechanism to explain the comparably high transfer efficiency.

Excitonic Configuration Interaction: Going Beyond the Frenkel Exciton Model

We present the excitonic configuration interaction (ECI) method─a fragment-based analogue of the CI method for electronic structure calculations of multichromophoric systems. It can also be viewed as a generalization of the exciton approach, with the following properties: (i) It constructs the effective Hamiltonian exclusively from monomer calculations. (ii) It employs the strong orthogonality assumption and is exact within McWeeny's group function theory, thus requiring only one-electron density matrices of the monomer states. (iii) It is agnostic of the monomer electronic structure method, allowing us to use/combine different methods. (iv) It includes an embedding point charge scheme (called excitonic Hartree-Fock, EHF) to improve the accuracy of the monomer states, but such that the effective full-system Hamiltonian is not explicitly dependent on the embedding. (v) It is systematically improvable, by expanding the set of monomer states and by including configurations where two or more monomers are excited (defining the ECIS, ECISD, etc., methods). The performance of ECI is assessed by computing the absorption spectrum of two exemplary multichromophoric systems, using CIS as the monomer electronic structure method. The accuracy of ECI significantly depends on the chosen embedding charges and the ECI expansion. The most accurate assessed combinations─ECIS or ECISD with EHF embedding─yield spectra that agree qualitatively and quantitatively with full-system direct calculations, with deviations of the excitation energies below 0.1 eV. We also show that ECISD based on CIS monomer calculations can predict states where two monomers are excited simultaneously (e.g., triplet-triplet double-local excitations) that are inaccessible in a full-system CIS calculation.

Quantification of the Ionic Character of Multiconfigurational Wave Functions: The Qat Diagnostic

The complete active space self-consistent field (CASSCF) method is a cornerstone in modern excited-state quantum chemistry providing the starting point for most common multireference computations. However, CASSCF, when used with a minimal active space, can produce significant errors (>2 eV) even for the excitation energies of simple hydrocarbons if the states of interest possess ionic character. After illustrating this problem in some detail, we present a diagnostic for ionic character, denoted as Q at, that is readily computed from the transition density. A set of 11 molecules is considered to study errors in vertical excitation energies. State-averaged CASSCF obtains a mean absolute error (MAE) of 0.87 eV for the 34 singlet states considered. We highlight a strong correlation between the obtained errors and the Q at diagnostic, illustrating its power to predict problematic cases. Conversely, using multireference configuration interaction with single and double excitations and Pople's size extensivity correction (MR-CISD+P), excellent results are obtained with an MAE of 0.11 eV. Furthermore, correlations with the Q at diagnostic disappear. In summary, we hope that the presented diagnostic will facilitate reliable and user-friendly multireference computations on conjugated organic molecules.

Surface hopping modeling of charge and energy transfer in active environments

An active environment is any atomic or molecular system changing a chromophore's nonadiabatic dynamics compared to the isolated molecule. The action of the environment on the chromophore occurs by changing the potential energy landscape and triggering new energy and charge flows unavailable in the vacuum. Surface hopping is a mixed quantum-classical approach whose extreme flexibility has made it the primary platform for implementing novel methodologies to investigate the nonadiabatic dynamics of a chromophore in active environments. This Perspective paper surveys the latest developments in the field, focusing on charge and energy transfer processes.

Detuning Effects on the Reverse Intersystem Crossing from Triplet Exciton to Lower Polariton

The lower polariton (LP) can reduce the energy barrier of the reverse intersystem crossing (rISC) process from T₁ to harvest triplet energy for fluorescence. Based on a Tavis-Cummings model including both singlet and triplet excitons, both coupled with quantized photons, we derive here a comprehensive rISC rate formalism. We found that the latter consists of three contributions: the one originated from spin-orbit coupling as first obtained by Martinez-Martinez et al. ( J. Chem. Phys. 2019, 151, 054106), the one from light-matter coupling of Ou et al. ( J. Am. Chem. Soc. 2021, 143, 17786), and the cross-term first reported here. We apply the formalism to investigate the experimentally observed barrier-free rISC (BFrISC) process in cavity devices with DABNA-2 molecular thin film. We found it can be attributed to the detuning effect. The rISC rates can be increased by orders of magnitude through changing the detuning energy to realize the BFrISC process. In addition, the BFrISC rates exhibit a maximum as a function of the incident angle and the doping concentration. The formalism provides a solid ground for molecular design toward highly efficient cavity-promoted light-emitting materials.

INAQS, a Generic Interface for Nonadiabatic QM/MM Dynamics: Design, Implementation, and Validation for GROMACS/Q-CHEM simulations

The accurate description of large molecular systems in complex environments remains an ongoing challenge for the field of computational chemistry. This problem is even more pronounced for photoinduced processes, as multiple excited electronic states and their corresponding nonadiabatic couplings must be taken into account. Multiscale approaches such as hybrid quantum mechanics/molecular mechanics (QM/MM) offer a balanced compromise between accuracy and computational burden. Here, we introduce an open-source software package (INAQS) for nonadiabatic QM/MM simulations that bridges the sampling capabilities of the GROMACS MD package and the excited-state infrastructure of the Q-CHEM electronic structure software. The interface is simple and can be adapted easily to other MD codes. The code supports a variety of different trajectory-based molecular dynamics, ranging from Born-Oppenheimer to surface hopping dynamics. To illustrate the power of this combination, we simulate electronic absorption spectra, free-energy surfaces along a reaction coordinate, and the excited-state dynamics of 1,3-cyclohexadiene in solution.

(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.

Enhanced Reverse Intersystem Crossing Promoted by Triplet Exciton-Photon Coupling

Polaritons are hybrid light-matter states formed via strong coupling between excitons and photons inside a microcavity, leading to upper and lower polariton (LP) bands splitting from the exciton. The LP has been applied to reduce the energy barrier of the reverse intersystem crossing (rISC) process from T₁, harvesting triplet energy for fluorescence through thermally activated delayed fluorescence. The spin-orbit coupling between T₁ and the excitonic part of the LP was considered as the origin for such an rISC transition. Here we propose a mechanism, namely, rISC promoted by the light-matter coupling (LMC) between T₁ and the photonic part of LP, which is originated from the ISC-induced transition dipole moment of T₁. This mechanism was excluded in previous studies. Our calculations demonstrate that the experimentally observed enhancement to the rISC process of the erythrosine B molecule can be effectively promoted by the LMC between T₁ and a photon. The proposed mechanism would substantially broaden the scope of the molecular design toward highly efficient cavity-promoted light-emitting materials and immediately benefit the illumination of related experimental phenomena.

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.

Excitonic Model for Strongly Coupled Multichromophoric Systems: The Electronic Circular Dichroism Spectra of Guanine Quadruplexes as Test Cases

We here propose a general and flexible approach, based on fragment diabatization, which incorporates charge transfer states and significantly increases the reliability of excitonic Hamiltonians for systems where the chromophores are very close. This model (FrDEx) is used to compute the electronic circular dichroism and absorption spectra of two prototype guanine-rich DNA sequences folded in quadruple helices (GQs), i.e., a fragment of the human telomeric sequence (Tel21, antiparallel), and (TGGGGT)₄ (TG4T, parallel). Calculations on different subsets of Tel21 and TG4T, from dimers to tetramers, show that FrDEx provides spectra close to the reference full quantum mechanical (QM) ones (obtained with time-dependent density functional theory), with significant improvements with respect to "standard" excitonic Hamiltonians. Furthermore, these tests enable the most cost-effective procedure for the whole GQ to be determined. FrDEx spectra of Tel21 and TG4T are also in good agreement with the QM and experimental ones and give access to interesting insights into the chemical-physical effects modulating the spectral signals. FrDEx could be profitably used to investigate many other biological and nanotechnological materials, from DNA to (opto)electronic polymers.

Molecular Photochemistry: Recent Developments in Theory

Photochemistry is a fascinating branch of chemistry that is concerned with molecules and light. However, the importance of simulating light-induced processes is reflected also in fields as diverse as biology, material science, and medicine. This Minireview highlights recent progress achieved in theoretical chemistry to calculate electronically excited states of molecules and simulate their photoinduced dynamics, with the aim of reaching experimental accuracy. We focus on emergent methods and give selected examples that illustrate the progress in recent years towards predicting complex electronic structures with strong correlation, calculations on large molecules, describing multichromophoric systems, and simulating non-adiabatic molecular dynamics over long time scales, for molecules in the gas phase or in complex biological environments.

Toward Quantitative Prediction of Fluorescence Quantum Efficiency by Combining Direct Vibrational Conversion and Surface Crossing: BODIPYs as an Example

Accurate theoretical description of the electronic structure of boron dipyrromethene (BODIPY) molecules has been a challenge, let alone the prediction of fluorescence quantum efficiency. In this Letter, we show that the electronic structures of BODIPYs can be accurately evaluated via the spin-flip time-dependent density functional theory with the B3LYP functional. With the resulting electronic structures, the experimental spectral line shapes of representative BODIPYs are successfully reproduced by our previously developed thermal vibration correlation function method. Most importantly, a two-channel scheme is proposed to describe the internal conversion of S₁ to S₀ in BODIPYs: channel I via direct vibrational relaxation within the harmonic region and channel II via a distorted S₀/S₁ minimum energy crossing point well away from the harmonic region. The fluorescence quantum yields are accurately predicted within this two-channel scheme, which can therefore serve as a generalized method for predicting the photophysical parameters of organic fluorescent compounds.

Ultrafast Spectroscopy of Photoactive Molecular Systems from First Principles: Where We Stand Today and Where We Are Going

Computational spectroscopy is becoming a mandatory tool for the interpretation of the complex, and often congested, spectral maps delivered by modern non-linear multi-pulse techniques. The fields of Electronic Structure Methods, Non-Adiabatic Molecular Dynamics, and Theoretical Spectroscopy represent the three pillars of the virtual ultrafast optical spectrometer, able to deliver transient spectra in silico from first principles. A successful simulation strategy requires a synergistic approach that balances between the three fields, each one having its very own challenges and bottlenecks. The aim of this Perspective is to demonstrate that, despite these challenges, an impressive agreement between theory and experiment is achievable now regarding the modeling of ultrafast photoinduced processes in complex molecular architectures. Beyond that, some key recent developments in the three fields are presented that we believe will have major impacts on spectroscopic simulations in the very near future. Potential directions of development, pending challenges, and rising opportunities are illustrated.

Synergistic Approach of Ultrafast Spectroscopy and Molecular Simulations in the Characterization of Intramolecular Charge Transfer in Push-Pull Molecules

The comprehensive characterization of Intramolecular Charge Transfer (ICT) stemming in push-pull molecules with a delocalized π-system of electrons is noteworthy for a bespoke design of organic materials, spanning widespread applications from photovoltaics to nanomedicine imaging devices. Photo-induced ICT is characterized by structural reorganizations, which allows the molecule to adapt to the new electronic density distribution. Herein, we discuss recent photophysical advances combined with recent progresses in the computational chemistry of photoactive molecular ensembles. We focus the discussion on femtosecond Transient Absorption Spectroscopy (TAS) enabling us to follow the transition from a Locally Excited (LE) state to the ICT and to understand how the environment polarity influences radiative and non-radiative decay mechanisms. In many cases, the charge transfer transition is accompanied by structural rearrangements, such as the twisting or molecule planarization. The possibility of an accurate prediction of the charge-transfer occurring in complex molecules and molecular materials represents an enormous advantage in guiding new molecular and materials design. We briefly report on recent advances in ultrafast multidimensional spectroscopy, in particular, Two-Dimensional Electronic Spectroscopy (2DES), in unraveling the ICT nature of push-pull molecular systems. A theoretical description at the atomistic level of photo-induced molecular transitions can predict with reasonable accuracy the properties of photoactive molecules. In this framework, the review includes a discussion on the advances from simulation and modeling, which have provided, over the years, significant information on photoexcitation, emission, charge-transport, and decay pathways. Density Functional Theory (DFT) coupled with the Time-Dependent (TD) framework can describe electronic properties and dynamics for a limited system size. More recently, Machine Learning (ML) or deep learning approaches, as well as free-energy simulations containing excited state potentials, can speed up the calculations with transferable accuracy to more complex molecules with extended system size. A perspective on combining ultrafast spectroscopy with molecular simulations is foreseen for optimizing the design of photoactive compounds with tunable properties.

Observe while it happens: catching photoactive proteins in the act with non-adiabatic molecular dynamics simulations

Organisms use photo-receptors to react to light. The first step is usually the absorption of a photon by a prosthetic group embedded inside the photo-receptor, often a conjugated chromophore. The electronic changes in the chromophore induced by photo-absorption can trigger a cascade of structural or chemical transformations that culminate into a response to light. Understanding how these proteins have evolved to mediate their activation process has remained challenging because the required time and spacial resolutions are notoriously difficult to achieve experimentally. Therefore, mechanistic insights into photoreceptor activation have been predominantly obtained with computer simulations. Here we briefly outline the challenges associated with such computations and review the progress made in this field.

Excitation energy transport in DNA modelled by multi-chromophoric field-induced surface hopping

Revealing the extended excited state lifetime due to excitation energy transport in DNA by multi-chromophoric field-induced surface-hopping (McFISH).

Polarizable embedding QM/MM: the future gold standard for complex (bio)systems?

We provide a perspective of the induced dipole formulation of polarizable QM/MM, showing how efficient implementations will enable their application to the modeling of dynamics, spectroscopy, and reactivity in complex biosystems.

Quantum Chemical Modeling of the Photoinduced Activity of Multichromophoric Biosystems

Multichromophoric biosystems represent a broad family with very diverse members, ranging from light-harvesting pigment-protein complexes to nucleic acids. The former are designed to capture, harvest, efficiently transport, and transform energy from sunlight for photosynthesis, while the latter should dissipate the absorbed radiation as quickly as possible to prevent photodamages and corruption of the carried genetic information. Because of the unique electronic and structural characteristics, the modeling of their photoinduced activity is a real challenge. Numerous approaches have been devised building on the theoretical development achieved for single chromophores and on model Hamiltonians that capture the essential features of the system. Still, a question remains: is a general strategy for the accurate modeling of multichromophoric systems possible? By using a quantum chemical point of view, here we review the advancements developed so far highlighting differences and similarities with the single chromophore treatment. Finally, we outline the important limitations and challenges that still need to be tackled to reach a complete and accurate picture of their photoinduced properties and dynamics.

Coupled Cluster Theory with Induced Dipole Polarizable Embedding for Ground and Excited States

In this work, we present the theory and implementation of the coupled cluster single and double excitations (CCSD) method combined with a classical polarizable molecular mechanics force field (MMPol) based on the induced dipole model. The method is developed to compute electronic excitation energies within the state specific (SS) and linear response (LR) formalisms for the interaction of the quantum mechanical and classical regions. Furthermore, we consider an approximate expression of the correlation energy, originally developed for CCSD with implicit solvation models, where the interaction term is linear in the coupled cluster density. This approximation allows us to include the explicit contribution of the environment to the CC equations without increasing the computational effort. The test calculations on microsolvated systems, where the CCSD/MMPol method is compared to full CCSD calculations, demonstrates the reliability of this computational protocol for all interaction schemes (errors < 2%). We also show that it is important to include induced dipoles on all atom centers of the classical region and that too diffuse functions in the basis set may be problematic due to too strong interaction with the environment.