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Machine learning has emerged as a promising paradigm to study the quantum dissipative dynamics of open quantum systems. To facilitate the use of our recently published ML-based approaches for quantum dissipative dynamics, here we present an open-source Python package MLQD (https://github.com/Arif-PhyChem/MLQD), which currently supports the three ML-based quantum dynamics approaches: (1) the recursive dynamics with kernel ridge regression (KRR) method, (2) the non-recursive artificial-intelligence-based quantum dynamics (AIQD) approach and (3) the blazingly fast one-shot trajectory learning (OSTL) approach, where both AIQD and OSTL use the convolutional neural networks (CNN). This paper describes the features of the MLQD package, the technical details, optimization of hyperparameters, visualization of results, and the demonstration of the MLQD's applicability for two widely studied systems, namely the spin-boson model and the Fenna--Matthews--Olson (FMO) complex. To make MLQD more user-friendly and accessible, we have made it available on the Python Package Index (PyPi) platform and it can be installed via pip install mlqd. In addition, it is also available on the XACS cloud computing platform (https://XACScloud.com) via the interface to the MLATOM package (http://MLatom.com)

Semi-empirical quantum chemical approaches are known to compromise accuracy for the feasibility of calculations on huge molecules. However, the need for ultrafast calculations in interactive quantum mechanical studies, high-throughput virtual screening, and data-driven machine learning has shifted the emphasis toward calculation runtimes recently. This comes with new constraints for the software implementation as many fast calculations would suffer from a large overhead of the manual setup and other procedures that are comparatively fast when studying a single molecular structure, but which become prohibitively slow for high-throughput demands. In this work, we discuss the effect of various well-established semi-empirical approximations on calculation speed and relate this to data transfer rates from the raw-data source computer to the results of the visualization front end. For the former, we consider desktop computers, local high performance computing, and remote cloud services in order to elucidate the effect on interactive calculations, for web and cloud interfaces in local applications, and in world-wide interactive virtual sessions. The models discussed in this work have been implemented into our open-source software SCINE SPARROW., The Journal of Chemical Physics, 158 (5), ISSN:0021-9606, ISSN:1089-7690

Simulations of the dynamics of dissipative quantum systems utilize many methods such as physics-based quantum, semiclassical, and quantum-classical as well as machine learning-based approximations, development and testing of which requires diverse data sets. Here we present a new database QD3SET-1 containing eight data sets of quantum dynamical data for two systems of broad interest, spin-boson (SB) model and the Fenna--Matthews--Olson (FMO) complex, generated with two different methods solving the dynamics, approximate local thermalizing Lindblad master equation (LTLME) and highly accurate hierarchy equations of motion (HEOM). One data set was generated with the SB model which is a two-level quantum system coupled to a harmonic environment using HEOM for 1,000 model parameters. Seven data sets were collected for the FMO complex of different sizes(7- and 8-site monomer and 24-site trimer with LTLME and 8-site monomer with HEOM) for 500--879 model parameters. Our QD3SET-1 database contains both population and coherence dynamics data and part of it has been already used for machine learning-based quantum dynamics studies., 14 pages, 3 figures

High-level quantum mechanical (QM) calculations are indispensable for accurate explanation of natural phenomena on the atomistic level. Their staggering computational cost, however, poses great limitations, which luckily can be lifted to a great extent by exploiting advances in artificial intelligence (AI). Here we introduce the general-purpose, highly transferable artificial intelligence–quantum mechanical method 1 (AIQM1). It approaches the accuracy of the gold-standard coupled cluster QM method with high computational speed of the approximate low-level semiempirical QM methods for the neutral, closed-shell species in the ground state. AIQM1 can provide accurate ground-state energies for diverse organic compounds as well as geometries for even challenging systems such as large conjugated compounds (fullerene C60) close to experiment. This opens an opportunity to investigate chemical compounds with previously unattainable speed and accuracy as we demonstrate by determining geometries of polyyne molecules—the task difficult for both experiment and theory. Noteworthy, our method’s accuracy is also good for ions and excited-state properties, although the neural network part of AIQM1 was never fitted to these properties., Artificial intelligence is combined with quantum mechanics to break the limitations of traditional methods and create a new general-purpose method for computational chemistry simulations with high accuracy, speed and transferability.

The KREG and pKREG models were proven to enable accurate learning of multidimensional single-molecule surfaces of quantum chemical properties such as ground-state potential energies, excitation energies, and oscillator strengths. These models are based on kernel ridge regression (KRR) with the Gaussian kernel function and employ relative-to-equilibrium (RE) global molecular descriptor, while pKREG is designed to enforce invariance under atom permutations with a permutationally invariant kernel. Here we extend these two models to also explicitly include the derivative information from the training data into the model which greatly improves their accuracy. We demonstrate on the example of learning potential energies and energy gradients that KREG and pKREG models are better or on par with state-of-the-art machine learning models. We also found that in challenging cases both energy and energy gradient labels should be learned to properly model potential energy surfaces and learning only energies or gradients is insufficient. The models’ open-source implementation is freely available in the MLatom package for general-purpose atomistic machine learning simulations which can be also performed on the MLatom@XACS cloud computing service.

Newton-X is an open-source computational platform to perform nonadiabatic molecular dynamics based on surface hopping and spectrum simulations using the nuclear ensemble approach. Both are among the most common methodologies in computational chemistry for photophysical and photochemical investigations. This paper describes the main features of these methods and how they are implemented in Newton-X. It emphasizes the newest developments, including zero-point-energy leakage correction, dynamics on complex-valued potential energy surfaces, dynamics induced by incoherent light, dynamics based on machine-learning potentials, exciton dynamics of multiple chromophores, and supervised and unsupervised machine learning techniques. Newton-X is interfaced with several third-party quantum-chemistry programs, spanning a broad spectrum of electronic structure methods.

Multidimensional surfaces of quantum chemical properties such as potential energies and dipole moments are common targets for machine learning, requiring the development of robust and diverse databases extensively exploring molecular configurational spaces. Here we composed the WS22 database covering several quantum mechanical (QM) properties (including potential energies, forces, dipole moments, polarizabilities, HOMO, and LUMO energies) for ten flexible organic molecules of increasing complexity and with up to 22 atoms. This database consists of 1.18~million equilibrium and non-equilibrium geometries carefully sampled from Wigner distributions centered at different equilibrium conformations (either at the ground or excited electronic states) and further augmented with interpolated structures. The diversity of our data sets is demonstrated by visualizing the geometries distribution with dimensionality reduction as well as via comparison of statistical features of the QM properties with those available in existing data sets. Our sampling targets broader quantum mechanical distribution of the configurational space than provided by commonly used sampling through classical molecular dynamics, upping the challenge for machine learning models.

International audience; This chapter will briefly introduce how machine learning can assist excited-state dynamics. We start with an overview of two traditional excited-state dynamics, a two-state system-bath approach in full quantum dynamics and the trajectory surface hopping approach in mixed quantum-classical dynamics. Then, we introduce a combination of machine learning with each of these two approaches. Finally, we present case studies in a tutorial format, enabling readers to perform simple dynamics simulations on model systems and realistic molecules.

Molecules with strong two-photon absorption (TPA) are important in many advanced applications such as upconverted laser and photodynamic therapy, but their design is hampered by the high cost of experimental screening and accurate quantum chemical (QC) calculations. Here we perform a systematic study by collecting and analyzing with interpretable machine learning (ML) experimental TPA database with ca. 900 molecules. We uncovered that only very few molecular features are sufficient to explain the TPA magnitudes. The most important feature is conjugation length (rather than area as believed before) followed by features reflecting effects of donor and acceptor substitution and coplanarity. These features are used to create a very fast ML model with prediction errors of similar magnitude compared to experimental and affordable QC meth-ods errors. Our ML model has the potential for high-throughput screening as additionally validated with our new experimental measurements.

Two-photon absorption has wide applications in bioimaging, photodynamic therapy, and three-dimensional printing. De-signing molecules with a large two-photon absorption cross section (TPACS) is thus highly desirable for advancing these technologies. Here we used machine learning to analyze a TPACS dataset of ca. one thousand molecules collected from literature reports. We found that the length of the conjugated structure is the most important feature to determine the TPACS in a power law of ~1.8 order. The effect of donor and acceptor substitutions and structural coplanarity on the TPACS can be adequately addressed by another three features obtained by empirical rules. Combining these four molecular features with the experimental wavelength and solvent used in the measurement, we derived an interpretable model to predict molecular TPACS with an accuracy comparable to that of experimental measurements and common theoretical calculations. Our approach not only provides insight into the factors that are critical to TPACS but, as we demonstrate, also allows high-throughput screening of new TPA molecules.

It has been recently shown that supervised machine learning (ML) algorithms can accurately and efficiently predict the long-time populations dynamics of dissipative quantum systems given only short-time population dynamics. In the present article we benchmaked 22 ML models on their ability to predict long-time dynamics of a two-level quantum system linearly coupled to harmonic bath. The models include uni- and bidirectional recurrent, convolutional, and fully-connected feed-forward artificial neural networks (ANNs) and kernel ridge regression (KRR) with linear and most commonly used nonlinear kernels. Our results suggest that KRR with nonlinear kernels can serve as inexpensive yet accurate way to simulate long-time dynamics in cases where the constant length of input trajectories is appropriate. Convolutional Gated Recurrent Unit model is found to be the most efficient ANN model., 22 pages, 6 figures

Quantum-chemistry simulations based on potential energy surfaces of molecules provide invaluable insight into the physicochemical processes at the atomistic level and yield such important observables as reaction rates and spectra. Machine learning potentials promise to significantly reduce the computational cost and hence enable otherwise unfeasible simulations. However, the surging number of such potentials begs the question of which one to choose or whether we still need to develop yet another one. Here, we address this question by evaluating the performance of popular machine learning potentials in terms of accuracy and computational cost. In addition, we deliver structured information for non-specialists in machine learning to guide them through the maze of acronyms, recognize each potential's main features, and judge what they could expect from each one., This article provides a lifeline for those lost in the sea of the molecular machine learning potentials by providing a balanced overview and evaluation of popular potentials.

Enthalpies of formation and reaction are important thermodynamic properties that have a crucial impact on the outcome of chemical transformations. Here we implement the calculation of enthalpies of formation with a general-purpose ANI-1ccx neural network atomistic potential. We demonstrate on a wide range of benchmark sets that both ANI-1ccx and our other general-purpose data-driven method AIQM1 approach the coveted chemical accuracy of 1 kcal/mol with the speed of semiempirical quantum mechanical methods (AIQM1) or faster (ANI-1ccx). It is remarkably achieved without specifically training the machine learning parts of ANI-1ccx or AIQM1 on formation enthalpies. Importantly, we show that these data-driven methods provide statistical means for uncertainty quantification of their predictions, which we use to detect and eliminate outliers and revise reference experimental data. Uncertainty quantification may also help in the systematic improvement of such data-driven methods.

We demonstrate that artificial intelligence (AI) can learn four-dimensional (4D) atomistic systems in the spacetime continuum. Given the initial conditions – nuclear positions and velocities at time zero – the proposed 4D-atomistic AI (4D-A2I) models can predict nuclear positions at any time in the future or past for the simplest systems as we show for H2. For larger polyatomic molecules, AI is capable of learning distant but finite future as we demonstrate for an ethanol molecule. 4D-A2I models provide direct access to a multitude of properties at a given time such as geometries, velocities, forces, and energies which can be used in simulating physicochemical transformations and spectra. Our approach can be used as a cost-efficient alternative to traditional molecular dynamics. We show an example of a 4D-A2I model describing the dynamical behavior of ethanol at the coupled-cluster level with the speed of one nanosecond simulation time per one hour wall-clock time on a single GPU card – a previously unachievable feat with traditional Born–Oppenheimer molecular dynamics. 4D-A2I model is also demonstrated to provide direct access to atomistic time-resolved details of physicochemical transformations.

We report the synthesis of 5,7,12,14-tetraphenyl-substituted 6,13-dihydro-6,13-diazapentacene and its fully aromatic 6,13-diazapentacene congener. Both arylated diazapentacenes were characterized by X-ray crystallography to investigate their solid-state structures and by UV–vis spectroscopy and cyclic voltammetry to unveil their electronic properties. The experimental results are complemented with theoretical investigations. The semiconductor properties of both diazapentacene derivatives were assessed in organic field-effect transistors, whereby the fully aromatized compound showed comparably less abundant n-type behavior.

Nonadiabatic quantum dynamics are important for understanding light-harvesting processes, but their propagation with traditional methods can be rather expensive. Here we present a one-shot trajectory learning approach that allows to directly make ultra-fast prediction of the entire trajectory of the reduced density matrix for a new set of such simulation parameters as temperature and reorganization energy. The whole 10ps long propagation takes 70 milliseconds as we demonstrate on the comparatively large quantum system, the Fenna–Matthews–Olsen (FMO) complex. Our approach also significantly reduces time and memory requirements for training.

Atomistic machine learning (AML) simulations are used in chemistry at an everincreasing pace. A large number of AML models has been developed, but their implementations are scattered among different packages, each with its own conventions for input and output. Thus, here we give an overview of our MLatom 2 software package, which provides an integrative platform for a wide variety of AML simulations by implementing from scratch and interfacing existing software for a range of state-of-the-art models. These include kernel method-based model types such as KREG (native implementation), sGDML, and GAP-SOAP as well as neuralnetwork- based model types such as ANI, DeepPot-SE, and PhysNet. The theoretical foundations behind these methods are overviewed too. The modular structure of MLatom allows for easy extension to more AML model types. MLatom 2 also has many other capabilities useful for AML simulations, such as the support of custom descriptors, farthest-point and structure-based sampling, hyperparameter optimization, model evaluation, and automatic learning curve generation. It can also be used for such multi-step tasks as Δ-learning, self-correction approaches, and absorption spectrum simulation within the machine-learning nuclear-ensemble approach. Several of these MLatom 2 capabilities are showcased in application examples.

Artificial intelligence-enhanced quantum mechanical method 1 (AIQM1) is a general-purpose method that was shown to achieve high accuracy for many applications with a speed close to its baseline semiempirical quantum mechanical (SQM) method ODM2*. Here, we evaluate the hitherto unknown performance of out-of-the-box AIQM1 without any refitting for reaction barrier heights on eight datasets, including a total of ∼24 thousand reactions. This evaluation shows that AIQM1’s accuracy strongly depends on the type of transition state and ranges from excellent for rotation barriers to poor for, e.g., pericyclic reactions. AIQM1 clearly outperforms its baseline ODM2* method and, even more so, a popular universal potential, ANI-1ccx. Overall, however, AIQM1 accuracy largely remains similar to SQM methods (and B3LYP/6-31G* for most reaction types) suggesting that it is desirable to focus on improving AIQM1 performance for barrier heights in the future. We also show that the built-in uncertainty quantification helps in identifying confident predictions. The accuracy of confident AIQM1 predictions is approaching the level of popular density functional theory methods for most reaction types. Encouragingly, AIQM1 is rather robust for transition state optimizations, even for the type of reactions it struggles with the most. Single-point calculations with high-level methods on AIQM1-optimized geometries can be used to significantly improve barrier heights, which cannot be said for its baseline ODM2* method.

Exploring excitation energy transfer (EET) in light-harvesting complexes (LHCs) is essential for understanding the natural processes and design of highly-efficient photovoltaic devices. LHCs are open systems, where quantum effects may play a crucial role for almost perfect utilization of solar energy. Simulation of energy transfer with inclusion of quantum effects can be done within the framework of dissipative quantum dynamics (QD), which are computationally expensive. Thus, artificial intelligence (AI) offers itself as a tool for reducing the computational cost. Here we suggest AI-QD approach using AI to directly predict QD as a function of time and other parameters such as temperature, reorganization energy, etc., completely circumventing the need of recursive step-wise dynamics propagation in contrast to the traditional QD and alternative, recursive AI-based QD approaches. Our trajectory-learning AI-QD approach is able to predict the correct asymptotic behavior of QD at infinite time. We demonstrate AI-QD on seven-sites Fenna-Matthews-Olson (FMO) complex.

Atomistic machine learning (AML) simulations are used in chemistry at an ever-increasing pace. A large number of AML models has been developed, but their implementations are scattered among different packages, each with its own conventions for input and output. Thus, here we give an overview of our MLatom 2 software package, which provides an integrative platform for a wide variety of AML simulations by implementing from scratch and interfacing existing software for a range of state-of-the-art models. These include kernel method-based model types such as KREG (native implementation), sGDML, and GAP-SOAP as well as neural-network-based model types such as ANI, DeepPot-SE, and PhysNet. The theoretical foundations behind these methods are overviewed too. The modular structure of MLatom allows for easy extension to more AML model types. MLatom 2 also has many other capabilities useful for AML simulations, such as the support of custom descriptors, farthest-point and structure-based sampling, hyperparameter optimization, model evaluation, and automatic learning curve generation. It can also be used for such multi-step tasks as Δ-learning, self-correction approaches, and absorption spectrum simulation within the machine-learning nuclear-ensemble approach. Several of these MLatom 2 capabilities are showcased in application examples.

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. Machine learning is starting to reshape our approaches to excited-state simulations by accelerating and improving or even completely bypassing traditional theoretical methods. It holds big promises for taking the optoelectronic materials design to a new level.

We present hierarchical machine learning (hML) of highly accurate potential energy surfaces (PESs). Our scheme is based on adding predictions of multiple Δ-machine learning models trained on energies and energy corrections calculated with a hierarchy of quantum chemical methods. Our (semi-)automatic procedure determines the optimal training set size and composition of each constituent machine learning model, simultaneously minimizing the computational effort necessary to achieve the required accuracy of the hML PES. Machine learning models are built using kernel ridge regression, and training points are selected with structure-based sampling. As an illustrative example, hML is applied to a high-level ab initio CH3Cl PES and is shown to significantly reduce the computational cost of generating the PES by a factor of 100 while retaining similar levels of accuracy (errors of ∼1 cm-1).

International audience; We report on the impact of the central heteroatom on structural, electronic, and spectroscopic properties of a series of spirofluorene‐bridged heterotriangulenes and provide a detailed study on their aggregates. The in‐depth analysis of their molecular structure by NMR spectroscopy and X‐ray crystallography was further complemented by density functional theory calculations. With the aid of extensive photophysical analysis the complex fluorescence spectra were deconvoluted showing contributions from the peripheral fluorenes and the heteroaromatic cores. Beyond the molecular scale, we examined the aggregation behavior of these heterotriangulenes in THF/H2O mixtures and analyzed the aggregates by static and dynamic light scattering. The excited‐state interactions within the aggregates were found to be similar to those found in the solid state. A plethora of morphologies and superstructures were observed by scanning electron microscopy of drop‐casted dispersions.

As the quantum chemistry (QC) community embraces machine learning (ML), the number of new methods and applications based on the combination of QC and ML is surging. In this Perspective, a view of the current state of affairs in this new and exciting research field is offered, challenges of using machine learning in quantum chemistry applications are described, and potential future developments are outlined. Specifically, examples of how machine learning is used to improve the accuracy and accelerate quantum chemical research are shown. Generalization and classification of existing techniques are provided to ease the navigation in the sea of literature and to guide researchers entering the field. The emphasis of this Perspective is on supervised machine learning.

In this chapter we illustrate in a tutorial way how machine learning can be used to assist quantum chemical research. Pitfalls of machine learning are highlighted and ways to avoid them are suggested. We show how machine learning can be used to improve relatively low-cost, approximated quantum chemical methods in two conceptually different ways. The first way is to improve the low-cost quantum chemical predictions a posteriori, e.g., as in Δ-machine learning. The second way is to improve the low-cost quantum chemical method itself and then use this improved method to make predictions, e.g., as in semiempirical parameter learning. Then we show how pure machine learning can be used to build very accurate potential energy surfaces with spectroscopic accuracy. Here we also discuss the importance of sampling to reduce the number of training points and eliminate many unphysical outliers, e.g., as in structure-based and farthest-point sampling. Then we demonstrate how machine learning can be used for nonadiabatic excited-state dynamics and discuss the associated challenges. In all examples, kernel ridge regression approach to machine learning is used. This approach and its advantages and disadvantages are discussed too.

International audience; We present a machine learning (ML) method to accelerate the nuclear ensemble approach (NEA) for computing absorption cross sections. ML-NEA is used to calculate cross sections on vast ensembles of nuclear geometries to reduce the error due to insufficient statistical sampling. The electronic propertiesexcitation energies and oscillator strengthsare calculated with a reference electronic structure method only for a relatively few points in the ensemble. The KREG model (kernel-ridge-regression-based ML combined with the RE descriptor) as implemented in MLatom is used to predict these properties for the remaining tens of thousands of points in the ensemble without incurring much of additional computational cost. We demonstrate for two examples, benzene and a 9-dicyanomethylene derivative of acridine, that ML-NEA can produce statistically converged cross sections even for very challenging cases and even with as few as several hundreds of training points.

In this work we show that deep learning (DL) can be used for exploring complex and highly nonlinear multistate potential energy surfaces of polyatomic molecules and related nonadiabatic dynamics. Our DL is based on deep neural networks (DNNs), which are used as accurate representations of the CASSCF ground- and excited-state potential energy surfaces (PESs) of CH2NH. After geometries near conical intersection are included in the training set, the DNN models accurately reproduce excited-state topological structures; photoisomerization paths; and, importantly, conical intersections. We have also demonstrated that the results from nonadiabatic dynamics run with the DNN models are very close to those from the dynamics run with the pure ab initio method. The present work should encourage further studies of using machine learning methods to explore excited-state potential energy surfaces and nonadiabatic dynamics of polyatomic molecules.

International audience; We show that machine learning (ML) can be used to accurately reproduce nonadiabatic excited-state dynamics with decoherence-corrected fewest switches surface hopping in a one-dimensional model system. We propose to use ML to significantly reduce the simulation time of realistic, high-dimensional systems with good reproduction of observables obtained from reference simulations. Our approach is based on creating approximate ML potentials for each adiabatic state using a small number of training points. We investigate the feasibility of this approach by using adiabatic spin-boson Hamiltonian models of various dimensions as reference methods.