Machine learning of two-dimensional spectroscopic data

Artificial-Intelligence-Enhanced On-the-Fly Simulation of Nonlinear Time-Resolved Spectra

Time-resolved spectroscopy is an important tool for unraveling the minute details of structural changes in molecules of biological and technological significance. The nonlinear femtosecond signals detected for such systems must be interpreted, but it is a challenging task for which theoretical simulations are often indispensable. Accurate simulations of transient absorption or two-dimensional electronic spectra are, however, computationally very expensive, prohibiting the wider adoption of existing first-principles methods. Here, we report an artificial-intelligence-enhanced protocol to drastically reduce the computational cost of simulating nonlinear time-resolved electronic spectra, which makes such simulations affordable for polyatomic molecules of increasing size. The protocol is based on the doorway-window approach for the on-the-fly surface-hopping simulations. We show its applicability for the prototypical molecule of pyrazine for which it produces spectra with high precision with respect to ab initio reference while cutting the computational cost by at least 95% compared to pure first-principles simulations.

Higher-Order Multidimensional and Pump-Probe Spectroscopies

Transient absorption and coherent two-dimensional spectroscopy are widely established methods for the investigation of ultrafast dynamics in quantum systems. Conventionally, they are interpreted in the framework of perturbation theory at the third order of interaction. Here, we discuss the potential of higher-(than-third-)order pump-probe and multidimensional spectroscopy to provide insight into excited multiparticle states and their dynamics. We focus on recent developments from our group. In particular, we demonstrate how phase cycling can be used in fluorescence-detected two-dimensional spectroscopy to isolate higher-order spectra that provide information about highly excited states such as the correlation of multiexciton states. We discuss coherently detected fifth-order 2D spectroscopy and its power to track exciton diffusion. Finally, we show how to extract higher-order signals even from ordinary pump-probe experiments, providing annihilation-free signals at high excitation densities and insight into multiexciton interactions.

Mapping Simulated Two-Dimensional Spectra to Molecular Models Using Machine Learning

Two-dimensional (2D) spectroscopy encodes molecular properties and dynamics into expansive spectral data sets. Translating these data into meaningful chemical insights is challenging because of the many ways chemical properties can influence the spectra. To address the task of extracting chemical information from 2D spectroscopy, we study the capacity of simple feedforward neural networks (NNs) to map simulated 2D electronic spectra to underlying physical Hamiltonians. We examined hundreds of simulated 2D spectra corresponding to monomers and dimers with varied Franck-Condon active vibrations and monomer-monomer electronic couplings. We find the NNs are able to correctly characterize most Hamiltonian parameters in this study with an accuracy above 90%. Our results demonstrate that NNs can aid in interpreting 2D spectra, leading from spectroscopic features to underlying effective Hamiltonians.

Computational spectroscopy of complex systems

Numerous linear and non-linear spectroscopic techniques have been developed to elucidate structural and functional information of complex systems ranging from natural systems, such as proteins and light-harvesting systems, to synthetic systems, such as solar cell materials and light-emitting diodes. The obtained experimental data can be challenging to interpret due to the complexity and potential overlapping spectral signatures. Therefore, computational spectroscopy plays a crucial role in the interpretation and understanding of spectral observables of complex systems. Computational modeling of various spectroscopic techniques has seen significant developments in the past decade, when it comes to the systems that can be addressed, the size and complexity of the sample types, the accuracy of the methods, and the spectroscopic techniques that can be addressed. In this Perspective, I will review the computational spectroscopy methods that have been developed and applied for infrared and visible spectroscopies in the condensed phase. I will discuss some of the questions that this has allowed answering. Finally, I will discuss current and future challenges and how these may be addressed.

Molecular excited states through a machine learning lens

Theoretical simulations of electronic excitations and associated processes in molecules are indispensable for fundamental research and technological innovations. However, such simulations are notoriously challenging to perform with quantum mechanical methods. Advances in machine learning open many new avenues for assisting molecular excited-state simulations. In this Review, we track such progress, assess the current state of the art and highlight the critical issues to solve in the future. We overview a broad range of machine learning applications in excited-state research, which include the prediction of molecular properties, improvements of quantum mechanical methods for the calculations of excited-state properties and the search for new materials. Machine learning approaches can help us understand hidden factors that influence photo-processes, leading to a better control of such processes and new rules for the design of materials for optoelectronic applications.

Modeling and Simulating the Excited-State Dynamics of a System with Condensed Phases: A Machine Learning Approach

Simulating the irreversible quantum dynamics of exciton- and electron-transfer problems poses a nontrivial challenge. Because the irreversibility of the system dynamics is a result of quantum thermal activation and dissipation caused by the surrounding environment, it is necessary to include infinite environmental degrees of freedom in the simulation. Because the capabilities of full quantum dynamics simulations that include the surrounding molecular degrees of freedom are limited, employing a system-bath model is a practical approach. In such a model, the dynamics of excitons or electrons are described by a system Hamiltonian, while the other degrees of freedom that arise from the environmental molecules are described by a harmonic oscillator bath (HOB) and system-bath interaction parameters. By extending on a previous study of molecular liquids [ J. Chem. Theory Comput. 2020, 16, 2099], here, we construct a system-bath model for exciton- and electron-transfer problems by means of a machine learning approach. We determine both the system and system-bath interaction parameters, including the spectral distribution of the bath, using the electronic excitation energies obtained from a quantum mechanics/molecular mechanics (QM/MM) simulation that is conducted as a function of time. Using the analytical expressions of optical response functions, we calculate linear and two-dimensional electronic spectra (2DES) for indocarbocyanine dimers in methanol. From these results, we demonstrate the capability of our approach to elucidate the nonequilibrium exciton dynamics of a quantum system in a nonintuitive manner.

Exploiting Machine Learning to Efficiently Predict Multidimensional Optical Spectra in Complex Environments

The excited-state dynamics of chromophores in complex environments determine a range of vital biological and energy capture processes. Time-resolved, multidimensional optical spectroscopies provide a key tool to investigate these processes. Although theory has the potential to decode these spectra in terms of the electronic and atomistic dynamics, the need for large numbers of excited-state electronic structure calculations severely limits first-principles predictions of multidimensional optical spectra for chromophores in the condensed phase. Here, we leverage the locality of chromophore excitations to develop machine learning models to predict the excited-state energy gap of chromophores in complex environments for efficiently constructing linear and multidimensional optical spectra. By analyzing the performance of these models, which span a hierarchy of physical approximations, across a range of chromophore-environment interaction strengths, we provide strategies for the construction of machine learning models that greatly accelerate the calculation of multidimensional optical spectra from first principles.

Unravelling the Kinetic Model of Photochemical Reactions via Deep Learning

Time-resolved spectroscopies have been playing an essential role in the elucidation of the fundamental mechanisms of light-driven processes, particularly in exploring relaxation models for electronically excited molecules. However, the determination of such models from experimentally obtained time-resolved and spectrally resolved data still demands a high degree of intuition, frequently poses numerical challenges, and is often not free from ambiguities. Here, we demonstrate the analysis of time-resolved laser spectroscopy data via a deep learning network to obtain the correct relaxation kinetic model. In its current design, the presented Deep Spectroscopy Kinetic Analysis Network (DeepSKAN) can predict kinetic models (involved states and relaxation pathways) consisting of up to five states, which results in 103 possible different classes, by estimating the probability of occurrence of a given kinetic model class. DeepSKAN was trained with synthetic time-resolved spectra spanning over 4 orders of magnitude in time with a unitless time axis, thereby demonstrating its potential as a universal approach for analyzing data from various time-resolved spectroscopy techniques in different time ranges. By adding the probabilities of each pathway of the top-k models normalized by the total probability, we can determine the relaxation pathways for a given data set with high certainty (up to 99%). Due to its architecture and training, DeepSKAN is robust against experimental noise and typical preanalysis errors like time-zero corrections. Application of DeepSKAN to experimental data is successfully demonstrated for three different photoinduced processes: transient absorption of the retinal isomerization, transient IR spectroscopy of the relaxation of the photoactivated DRONPA, and transient absorption of the dynamics in lycopene. This approach delivers kinetic models and could be a unifying asset in several areas of spectroscopy.

Effect of disorder and polarization sequences on two-dimensional spectra of light-harvesting complexes

Two-dimensional electronic spectra (2DES) provide unique ways to track the energy transfer dynamics in light-harvesting complexes. The interpretation of the peaks and structures found in experimentally recorded 2DES is often not straightforward, since several processes are imaged simultaneously. The choice of specific pulse polarization sequences helps to disentangle the sometimes convoluted spectra, but brings along other disturbances. We show by detailed theoretical calculations how 2DES of the Fenna-Matthews-Olson complex are affected by rotational and conformational disorder of the chromophores.

Excitonic Wave Function Reconstruction from Near-Field Spectra Using Machine Learning Techniques

A general problem in quantum mechanics is the reconstruction of eigenstate wave functions from measured data. In the case of molecular aggregates, information about excitonic eigenstates is vitally important to understand their optical and transport properties. Here we show that from spatially resolved near field spectra it is possible to reconstruct the underlying delocalized aggregate eigenfunctions. Although this high-dimensional nonlinear problem defies standard numerical or analytical approaches, we have found that it can be solved using a convolutional neural network. For both one-dimensional and two-dimensional aggregates we find that the reconstruction is robust to various types of disorder and noise.

Insights into the mechanisms and dynamics of energy transfer in plant light-harvesting complexes from two-dimensional electronic spectroscopy

During the past two decades, two-dimensional electronic spectroscopy (2DES) and related techniques have emerged as a potent experimental toolset to study the ultrafast elementary steps of photosynthesis. Apart from the highly engaging albeit controversial analysis of the role of quantum coherences in the photosynthetic processes, 2DES has been applied to resolve the dynamics and pathways of energy and electron transport in various light-harvesting antenna systems and reaction centres, providing unsurpassed level of detail. In this paper we discuss the main technical approaches and their applicability for solving specific problems in photosynthesis. We then recount applications of 2DES to study the exciton dynamics in plant and photosynthetic light-harvesting complexes, especially light-harvesting complex II (LHCII) and the fucoxanthin-chlorophyll proteins of diatoms, with emphasis on the types of unique information about such systems that 2DES is capable to deliver. This article is part of a Special Issue entitled Light harvesting, edited by Dr. Roberta Croce.