OMNI-P2x universal neural network potential for excited-state simulations.

OMNI-P2x universal neural network potential for excited-state simulations - PMC Skip to main content An official website of the United States government Here's how you know Here's how you know Search Log in Primary site navigation Search Log in Search PMC Full-Text Archive Search in PMC Journal List User Guide As a library, NLM provides access to scientific literature. Inclusion in an NLM database does not imply endorsement of, or agreement with, the contents by NLM or the National Institutes of Health. Learn more: PMC Disclaimer | PMC Copyright Notice Nat Commun . 2026 Apr 7;17:4949. doi: 10.1038/s41467-026-71380-5 OMNI-P2x universal neural network potential for excited-state simulations Mikołaj Martyka 1 , Xin-Yu Tong 2 , Joanna Jankowska 1, ✉ , Pavlo O Dral 2, 3, 4, 5, ✉ Author information Article notes Copyright and License information 1 University of Warsaw, Faculty of Chemistry, Warsaw, Poland 2 State Key Laboratory of Physical Chemistry of Solid Surfaces, College of Chemistry and Chemical Engineering, and Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, Xiamen University, Xiamen, China 3 Institute of Physics, Faculty of Physics, Astronomy, and Informatics, Nicolaus Copernicus University in Toruń, Toruń, Poland 4 Institute of Advanced Studies, Nicolaus Copernicus University in Toruń, Toruń, Poland 5 Aitomistic, Shenzhen, China ✉ Corresponding author. Received 2025 Apr 16; Accepted 2026 Mar 19; Collection date 2026. © The Author(s) 2026 Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ . PMC Copyright notice PMCID: PMC13233842  PMID: 41946725 Abstract Photo-active molecular systems play an essential role in modern science and technology, finding applications in solar cells, organic light-emitting diodes, reaction catalysis, photodynamic therapy, and beyond. The rational design of photo-responsive molecules requires an understanding of the photophysical and photochemical processes underlying their operation, which can be gained via the first-principles quantum-mechanical calculations that are prohibitively expensive for high-throughput investigations. To break through this limitation, here we introduce OMNI-P2x: a universal neural network potential for molecular excited and ground electronic states. OMNI-P2x can be used, directly or after fine-tuning, to perform a wide range of photophysical and photochemical simulations. OMNI-P2x approaches the accuracy of time-dependent density functional theory methods at a fraction of the computational cost, while being more accurate and faster than established semiempirical methods for excited-state simulations. Here, we demonstrate its use in UV/Vis absorption spectroscopy, real-time photodynamical simulations, and in the rational design of visible-light-absorbing azobenzene systems. Subject terms: Photochemistry, Method development, Excited states OMNI-P2x is a universal neural network model that predicts molecular excited-state properties with near quantum-chemical accuracy at lower cost. It enables rapid screening and photodynamics simulations, accelerating the design of light-responsive molecules. Introduction Theoretical photochemistry leverages the ability of quantum-mechanical (QM) methods to accurately predict the properties of electronic excited states of molecules and to provide insights into light-molecule interactions. The QM calculations facilitate better understanding of complex processes such as photoreactivity and photostability 1 – 4 , operation of molecular machines 5 , 6 , separation of charge carriers in clean energy generation 7 , 8 , and, in turn, provide rational design principles for photomaterials such as organic light-emitting diodes (OLEDs) 9 , 10 , molecular solar thermal energy storage (MOST) systems 11 , 12 , and organic solar cells 13 , 14 . Because of the extensive development of computational methods, they can be not only used to explain and verify experimental results, but also to guide novel research in photochemistry. At the same time, the key obstacle preventing widespread use of theoretical methods for excited-state property prediction is their computational cost, with a schematic representation of their accuracy/computational cost tradeoff presented in Fig. 1 . While highly-accurate methods, such as equation-of-motion coupled clusters approaches 15 and their variants like ADC(2) 16 exist, they can only be used for medium-sized systems at best, requiring days or weeks of computational time due to their steep computational scaling. On the other hand, time-dependent density functional theory (TD-DFT) 17 , 18 provides a more affordable alternative, which typically scales up to systems containing about 100 atoms, however, at a price of decreased reliability. Finally, on the lower end of the accuracy-to-computational-cost spectrum, one finds semi-empirical QM methods (SQM), such as a wide family of Hamiltonians based on the neglect of diatomic differential overlap (NDDO) approximation 19 , such as AM1 20 , PM3 21 , OM2 22 , and ODM2 23 used in conjunction with the configuration interaction (CI) treatments, and time-dependent tight-binding DFT methods TD-DFTB 24 , 25 . While these methods are certainly more affordable for systems with hundreds and even thousands of atoms, the accuracy of their predictions can often be questionable. 26 – 28 Fig. 1. The universal OMNI-P2x neural network potential for excited-state simulation and its place among the hierarchy of quantum mechanical (QM) and machine learning (ML) methods. Open in a new tab a OMNI-P2x and its fine-tuning shown in the context of computational cost/accuracy tradeoff of commonly used QM methods for excited-state simulations: semi-empirical quantum chemical methods (SQM), time-dependent density functional theory (TD-DFT), complete active space self-consistent field method and its derivatives (CASSCF), equations-of-motion coupled-clusters methods (EOM-CC), as well as active learning. b Overview of the OMNI-P2x design, training, and its application capabilities. The situation becomes even more complex when real-time simulations of the light-induced processes are required, i.e., for predicting photoswitching quantum yields, two-photon dynamics, or excited-state lifetimes. The most popular and widespread technique for performing such simulations is trajectory surface hopping (TSH) 29 variant of nonadiabatic molecular dynamics (NAMD). In TSH, a swarm of independent, semi-classical trajectories are propagated, with the ability to switch (hop) between adiabatic potential energy surfaces (PESs). The electronic and nuclear degrees of freedom are coupled by so-called interstate couplings, which control the hopping probabilities. Running surface-hopping simulations requires using a QM method that can accurately predict multiple PESs and, ideally, properly describe the multireference character of the wavefunction in the vicinity of conical intersections. This severely limits the choice of theoretical methods, and typically, CASSCF is used, while much slower but higher-accuracy perturbational variants such as CASPT2 30 are also available. However, as driving dynamics requires calculations of energies and gradients at each time step, with a typical simulation setup of hundreds of trajectories propagated for ~1 ps with a time step of 0.1–0.5 fs require computing these quantities on the order of millions of times, which is only possible for simple, often model systems. For simulations of experimentally and technologically relevant compounds, the only available choice are, so far, semi-empirical methods. In recent years, progress in the field of machine learning (ML) has led to a significant paradigm shift in the area of computational chemistry 31 – 35 . Fitting machine learning potentials (MLPs) to reference QM data allows for accurate predictions of molecular properties, such as energies and energy gradients 36 – 40 , dipole moments 39 or electronic densities 41 , 42 at a greatly reduced cost, while retaining the accuracy of the reference method. This allows to break through the limitation of traditional QM methods, making simulations of larger, more complex systems possible at longer timescales 43 – 47 . A particularly important, emerging class of potentials is universal MLPs, which we define as models that were trained on vast datasets spanning across chemical space. In turn, they can be used to make out-of-the-box predictions for previously unseen molecules, generalizing from the training data. 48 – 53 Although training and using MLPs for predicting ground-state properties is becoming a rather routine task, using ML methods for electronic excited states is far more challenging, requiring expert human supervision. This is due to the inherent complexity of excited potential energy surfaces, often forming a strongly correlated manifold of states, interacting and mixing with each other in a non-smooth manner. At the same time, it should be noted that models capable of providing accurate predictions for excited-state properties, such as SchNarc 54 , SpaiNN 55 , or PyRAI 2 MD 44 have been developed and used successfully in the TSH simulations. However, their capabilities are limited to learning one molecule at a time, i.e., they are not transferable across chemical space. This has changed with the MS-ANI (Multi-state ANI) model 56 , demonstrated to be able to predict nonadiabatic dynamics of three distinct molecules within the same model, paving the way for universal excited-state potentials. More recently, another demonstration of a possibility to create transferable NN for excited-state predictions was shown in ref. 57 . Transferable nonadiabatic molecular dynamics simulations were also reported by Axelrod et al. 58 , however, it was limited to the class of diazobenzene photoswitches. Despite all the progress in MLPs for excited states, they have still been lagging behind the ground-state MLPs to such an extent that many experts are questioning whether universal MLPs for excited states are even possible. 59 , 60 It is generally agreed that developing such an MLP would be a major breakthrough. 31 , 59 In this work, we present OMNI-P2x: a universal neural network (NN) potential for molecular excited states (Fig. 1 ). We have built OMNI-P2x by combining the ideas of multi-state 56 , 61 and all-in-one 62 learning. OMNI-P2x approaches TD-DFT accuracy for excited-state energies and targets CCSD(T) quality for ground-state energies: it can predict the absorption UV/Vis spectra out-of-the-box with higher speed and accuracy than popular semiempirical QM methods, making ML approaches for excited-states a viable alternative to established, cost-efficient QM methods for high-throughput calculations, such as semi-empirical methods. We leverage the power of OMNI-P2x to perform a high-throughput screening of 500,000 compounds to find azobenzene derivatives featuring red-shifted, visible light absorption. These systems are particularly relevant due to their applications in nonlinear optics 63 , photoresponsive polymers 64 , and as MOST compounds 65 , 66 . The potential of OMNI-P2x in accelerating another type of extensive simulations: nonadiabatic dynamics, is also exploited via fine-tuning of this universal potential within an active learning loop. This approach reduces the computational cost and wall-clock time of production-ready ML-TSH simulations, while improving data efficiency and simulation stability. Results Model architecture and training The architecture of the OMNI-P2x model is based on the idea of multi-state learning 56 , 61 and its successful realization in the MS-ANI model designed for accurate and efficient learning of excited-state energies and forces. Multi-state learning can be used to efficiently learn an arbitrary number of electronic states while using the entire neural network to differentiate the molecular electronic states, as opposed to only the last layer used in the multi-output models. This effect is achieved by including an additional state ordering number as an input feature, along with the molecular descriptor containing information about the geometrical conformation. Here, we extend this model to learn across multiple QM levels, in the spirit of the all-in-one (AIO) learning paradigm introduced recently 62 . The all-in-one learning has been successfully used to develop the universal OMNI-P1 neural network potential capable of making predictions approaching DFT and CCSD(T) levels, however, it is limited to the ground-state energies and forces. It is worth noting that the ability of learning from multiple levels of theory gives an important advantage of leveraging different data sets of various quantities. Here, we combine both: multi-state learning and all-in-one learning, to obtain OMNI-P2x: the omnipotential-2x, all-in-One Machine-learning Neural-network Interatomic Potential 2 for eXcited states. OMNI-P2x is based on the established ANI NN potential 67 (Fig. 2 a). The input layer consists of an atomic environment vector (AEV), calculated using the TorchANI Python package 68 , and two additional features: the state ordering number, as in MS-ANI, and a one-hot encoded feature representing the QM level corresponding to all-in-one learning. The electronic state is encoded as a non-negative integer, consistent with the natural ordering of adiabatic state energies, which we find to be both physically motivated and empirically more accurate than one-hot encoding. In the present work, data at two levels of theory were included: the ground-state-only data with CCSD(T)/CBS accuracy from the ANI-1ccx dataset 67 , and TD-DFT B3LYP/6-31+G* excited- and ground-state data from the PubChemQC dataset 69 . As for all ANI-type models, a separate neural network is trained for each chemical element. In the present version, OMNI-P2x supports the following element types: H, C, N, O, F, S, and Cl. The predictions are then made atom-wise and summed up to yield the total energy of the molecule. For the energy part of the predictions, an ensemble of three NN potentials is used, with their predictions averaged to obtain the final predicted energy for all electronic states. A fragment-correction scheme is applied to non-covalently bound structures, to recover the correct, intensive character of excitation energies, for molecular fragments separated by distances greater than the descriptor cutoff radius, with details provided in the methods section, and Suppl. Note. 1 . A separate MS-ANI-type NN is trained and used to predict the oscillator strengths of interstate transitions, as shown in 2 b). Since only TD-DFT data is used for the excited-state training, this network does not include an additional input feature for the level of theory. Fig. 2. Architecture of the OMNI-P2x model. Open in a new tab a The architecture of the OMNI-P2x neural network potential for energies. b Summary of the OMNI-P2x model, consisting of separate NNs predicting the oscillator strengths and energies of the target, and datasets used to train them, labeled at time-dependent density function theory (TD-DFT), or coupled-clusters with singles and doubles with perturbative triples (CCSD(T)). The data for model training has been sourced from two datasets: 1) excited-state data in the PubChemQC project’s dataset 69 , and 2) ANI-1ccx, containing about 500,000 ground-state geometries, including out-of-equilibrium conformations, with their total energies computed at the gold-standard CCSD(T)/CBS level of theory. The PubChemQC project’s dataset consists of unique, optimized structures of molecules at the TD-B3LYP/6-31+G* level of theory, 70 , 71 with the energies and oscillator strengths of the first 10 excited states calculated using TD-DFT. We have used the entirety of the PubChemQC dataset, which meets our filtering criteria (as detailed in the Methods section), yielding 3.1 million molecules with 11 electronic states each. The inclusion of the ANI-1ccx data set provides an important additional information about the effect of out-of-equilibrium geometry changes on energies, which is important for molecular dynamics and other types of simulations. ANI-1ccx data set has been used as a basis for training multiple universal ML-based models 48 , 72 – 76 , which are successfully used in molecular dynamics, geometry optimizations, and thermochemistry calculations. In addition, combination of two different types of data set allows to cover larger chemical spaces, i.e., compare the data distribution in both data sets in Fig. 3 a: the ANI-1ccx data cover small-sized molecules, while the vast majority of the excited-state training data is comprised of medium-sized molecules containing 15 to 45 atoms, with most of their excitation energies located towards the blue end of the visible spectrum, and in the UV range (Fig. 3 b). Fig. 3. Distribution of the data used to train OMNI-P2x. Open in a new tab Panel ( a ) shows a histogram of the distribution of the number of atoms in the molecules of the training sets PubChemQC (excited-state TD-DFT) and ANI-1ccx (ground-state CCSD(T)) (bin size 1); panel ( b ) shows the distribution of first excitation energies in PubChemQC (bin size 0.1 eV). We evaluate the performance of the model using a test set of 300k unseen molecules from the PubChemQC dataset for the excitation energies, as well as a test set of almost 49k ground-state conformations from the ANI dataset. The MAE in energy predictions for the first 11 electronic states with respect to the TD-DFT data shows that the quality of the predictions increases when going to higher excited states, reaching a minimal value for S 7 (Fig. 4 b, c). An outlier here is S 0 , which has the smallest energy MAE of 1.6 kcal/mol, which we attribute to the improved data-efficiency due to the application of the all-in-one learning to the combined set with the ground-state DFT (from PubChem) and the CCSD(T) (from ANI-1ccx) data, and an overall smoother and lower-variance distribution of ground-state energies that makes them easier for the model to learn. This ground-state MAE can be compared to the similar metrics of other MLIPs: ANI-1 67 with an RMSE of 1.3 kcal/mol (OMNI-P2x 2.93 kcal/mol), UMA 77 with around 1 to 3 meV/atom (0.023 to 0.069 kcal/(mol  ⋅ atom), depending on the version (OMNI-P2x 0.11 kcal/(mol  ⋅ atom) and AIMNet2 78 reporting a MAE of around 1.25 kcal/mol for neutral compounds. Although those results are not comparable one-to-one, as each of the models was trained and tested on a different dataset, they show that the ground-state error of OMNI-P2x remains within a reasonable range from current state-of-the-art machine-learning derived models, despite not being the main focus of this study. Correlation plots showing the predicted vs true excitation energies for all transitions are available as Supplementary Fig. 4 . In all cases, the R 2 is above 0.91. For the ground-state energies in the test ANI-1ccx subset, OMNI-P2x has a higher MAE of 4.14 kcal/mol, but a high R 2 = 0.9966 for the normalized energies (0.9999 for unnormalized) (Fig. 4 a). This is anticipated, as the ANI-1ccx training data, which is only used as an auxiliary data set, is much smaller than PubChemQC, and is also featuring a different data distribution (Fig. 3 a). Fig. 4. Test performance of the OMNI-P2x model. Open in a new tab Panel ( a ): correlation plot of the reference (true) and OMNI-P2x predicted ground-state energies at the CCSD(T) level of theory, for the test part of the ANI-1ccx dataset; ( b ) Mean absolute error (MAE) of the electronic state energies. c MAE of the excitation energies. d MAE of the predicted oscillator strengths. Additionally, OMNI-P2x provides an uncertainty quantification (UQ) of all predicted energies, using the standard deviations between quantities predicted by each of the three NN potentials as the error bar. A warning is issued to the user if the UQ of any excited states exceeds a safe threshold, which is determined as the median plus three median absolute deviations of the UQs of the test set, for each electronic state. Finally, the MAE in OMNI-P2x predictions of oscillator strengths is below 0.04 for all studied electronic states (Fig. 4 d). One can note that the highest accuracy in terms of the predicted oscillator strengths is achieved for the excitations to S 1 and to higher-lying S 8 –S 10 states. UV/Vis absorption spectra OMNI-P2x is a universal model that can predict both excitation energies and oscillator strengths, i.e., which allows one to obtain the UV/Vis excitation spectra of the QM quality, yet with a much higher speed (see Methods for details). To test the OMNI-P2x performance for simulating the UV/Vis spectra, we generate the spectra for 50k test molecules from the PubChemQC database and compare them to the reference TD-DFT spectra (see Methods). Let us first examine representative spectra shown in Fig. 5 . Looking at a spectrum belonging to the first quartile (top 25% spectra with the highest similarity between the OMNI-P2x and TD-DFT based on the similarity score, see Methods and below for details), agreement is observed both: in the intensity and position of the peaks (panel a in Fig. 5 ). For the second quartile, the agreement becomes somewhat worse, which is manifested by the absorption energy red-shift of about 10 nm, however, the intensity of the peak is consistent with the reference method (panel b). This agreement becomes worse in the bottom half of the predicted spectra: while the positions of the predicted peaks are rather accurate, the intensities are different from the reference method. Inspecting the bottom quartile of the predicted spectra, the agreement is still acceptable, with the higher absorption maximum predicted quite accurately, both in terms of the absorption energy and intensity, however, the first absorption peak appears to be blue-shifted due to the incorrect prediction of S 2 as a bright state. To provide a benchmark of the predicted spectra that is unaffected by the choice of a broadening factor in the SPC construction, we also rank the spectra by a geometric mean of the excitation energy and oscillator strength MAE, which is presented in Supplementary Fig. 5 . Later, we also explore the application of OMNI-P2x for spectra calculations without relying on SPC approximation and the broadening factor. Fig. 5. Comparison between reference TD-DFT/B3LYP spectra and OMNI-P2x predicted spectra. Open in a new tab Four examples are shown, randomly chosen from the top 25% of the predicted spectra (panel a ), ranked, 25–50% (panel b ), 50–75% (panel c ) and the bottom 25% (panel d ). For the test molecules shown in Figure 5 , we tested the effect of finite-temperature distortions on the accuracy of OMNI-P2x and found that higher excited states remain close to equilibrium benchmarks, while the accuracy of the lowest excitations (S 1 –S 3 ) may decrease more sharply. Violin plots showing the error distribution on non-equlibrium structures are available in Supplementary Figs. 6 – 9 . To further probe this behavior, we performed relaxed PES scans of cyclohexanone (C=O stretch) and azobenzene (C–N=N–C torsion), shown in Suppl. Fig. 10 . These scans confirm that OMNI-P2x is accurate near equilibrium and along moderate distortions, but errors grow for strongly compressed geometries or when torsion induces a change in excited-state character. Together, these results indicate that OMNI-P2x can extrapolate PES shapes close to equilibrium, but its reliability decreases as the molecular distortion drives the system beyond the domain of the training data. To put the performance of the universal potential into perspective, we also evaluate two commonly used semiempirical QM methods: ODM2/CIS and TD-DFTB, on the same test of 50k molecules, as shown in Fig. 6 . The OMNI-P2x spectra are clearly more similar to the reference TD-DFT than the semiempirical ODM2/CIS and TD-DFTB as judged by the distribution of the Spearman correlation coefficients for this test set (Fig. 6 a). On average, the OMNI-P2x and TD-DFT spectra agree well with each other, with an average correlation coefficient of 0.86, and 80% of the predicted spectra having a correlation coefficient larger than 0.80. In comparison, both the semiempirical QM methods have a substantially worse performance, with an average SCC of 0.53 for TD-DFTB and 0.50 for ODM2/CIS. Additionally, ODM2’s parameterization is limited to molecules consisting of H, C, N, O, F atoms only (39164 out of 50k structures), i.e., OMNI-P2x has a broader element coverage than ODM2/CIS. Noteworthy, the OMNI-P2x is not just more accurate than semiempirical QM methods, but is also clearly the fastest of the available approaches, with an average calculation time of 225 ms per predicted spectrum, while the ODM2/CIS and TD-DFTB approaches take on average 827 ms and 1152 ms, respectively (Fig. 6 b). The reference TD-DFT calculations are orders of magnitude slower: more than 357.87 s per predicted spectrum. While the QM methods follow an approximately exponential scaling of cost with respect to accuracy, measured as correlation of the predicted spectra with TD-DFT/B3LYP spectra (note the logarithmic scale on the y axis), OMNI-P2x breaks this unfavorable scaling. Fig. 6. The evaluation of the quality of the UV/Vis absorption spectra predicted by OMNI-P2x model on a test set of 50k molecules, at their ground-state equlibrium structures. Open in a new tab a The histogram of the correlation coefficients, quantifying the agreement between time-dependent density functional theory (TD-DFT) and OMNI-P2x electronic spectra, as well as two other commonly used cost-effective, semiempirical QM methods: orthogonalization and dispersion corrected method with configuration interaction single excitations (ODM2/CIS) and time-dependent density functional based tight binding (TD-DFTB). b The cost to accuracy correlation of OMNI-P2x, semiempirical QM, and TD-DFT spectra, with accuracy defined as the Spearman Correlation Coefficient (SCC) with respect to TD-DFT spectra, showing how the ML model breaks the traditional cost/accuracy tradeoff. The gray dashed line guides the eye to the difference in scaling between QM and ML methods. Nuclear ensemble approach spectra A more accurate method for predicting UV/Vis absorption spectra is the nuclear ensemble approach (NEA). In this technique, vertical excitation energies and oscillator strengths are computed for an ensemble of hundreds or thousands of molecular geometries 79 , 80 . The final spectrum is constructed by summing Lorentzian or Gaussian functions centered at each geometry’s excitation energy, weighted by the corresponding oscillator strength. Compared to single-point convolution, this approach better captures vibronic effects. However, NEA simulations are computationally demanding, as they require quantum mechanical calculations for all structures in the ensemble. To address this cost, ML models offer a natural path for acceleration 81 – 83 . Since OMNI-P2x is trained on excited-state data only from equilibrium structures, it is not directly applicable to NEA simulations. Nevertheless, fine-tuning enables it to achieve high data efficiency and simulation speed in this context, requiring a mere 25–50 additional, molecule-specific, training points to reproduce reference spectra. To demonstrate this, we consider two test cases: pyrazine (with 4 excited states) and 9-dicyanomethylene derivative of acridine (9-DCMA, with 30 excited states), the latter of which was previously used to benchmark ML-NEA spectra with kernel ridge regression models 81 (see Methods for details). The NEA spectra simulated using reference TD-DFT data, as well as those predicted by the fine-tuned OMNI-P2x model—trained on just 25 data points for pyrazine and 50 for 9-DCMA—-are shown in Fig. 7 . For pyrazine (panel a), the agreement is observed across the entire spectrum. In the more complex case of 9-DCMA, the model accurately captures the intensity and position of the lower-lying excitations. Deviations start emerging below 250 nm, especially in predicted intensities, while the position of the peaks remains rather accurate. We attribute this to the model extrapolating in a regime beyond the number of excited states included in the training dataset: OMNI-P2x was pre-trained on 10 excited states, while 30 are considered in this example. Such simulations can be done on commodity hardware (Jupyter notebook using 4 CPUs), in under a minute for pyrazine, and about 40 min for 9-DCMA, excluding the labeling time of QM methods. Fig. 7. Nuclear ensemble approach spectra simulations using OMNI-P2x. Open in a new tab The comparison between the ML-simulated (red) and TD-DFT (black) spectra for a ) pyrazine and b ) 9-DCMA. Interpertability of ML predictions To provide interpretability of the ML-learned excitations, we introduce a new approach for analyzing atom-wise contributions to excitation energies. For each atom i , the fractional contribution is defined as ∣Δ E i ∣/Δ E , where Δ E is the excitation energy for a given transition, and atomic contributions are calculated as the differences between ground- and excited-state atomic energies predicted by the NN ensemble. We show that the OMNI-P2x-derived atom-wise contributions agree well with the reference TD-DFT density difference plots (Fig. 8 ). Such analysis allows us to obtain the spatial character of the excitation by identifying which atoms are most involved in the transition. This analysis is conceptually related to work by Tkatchenko et al. 84 , analyzing atom-wise contributions to ground-state energies. Fig. 8. Interpretability of OMNI-P2x excitation energies. Open in a new tab Panel ( a ) shows fractional atomic contributions to excitation energies for several different organic molecules, compared with time-dependent density functional theory (TD-DFT) density differences. Panel ( b ) shows different excited states of the same molecule, azobenzene. We demonstrate that this interpretability analysis can work well across chemical space and for different excitations of the same molecule. Panel a) of Fig. 8 shows the S 0 → S 1 ML Δ E contributions and TD-DFT density differences for several organic molecules. We begin by comparing the examples of benzene and pyrazine, two 6- π electron aromatic compounds. OMNI-P2x correctly localizes the transitions, spreading it evenly across all the benzene carbon atoms, while in pyrazine it is mostly localized on the two nitrogen atoms, reproducing the TD-DFT results. The excitations also exhibit appropriate symmetry: C 6 for benzene, and D 2 h for pyrazine. The next example, azobenzene, shows physically correct localization of the excitation on the N=N double bond, while in p -nitroaniline the partial charge-transfer character of the excited state is well reproduced. Overall, this shows an interpretable character of ML predictions, that is transferable across chemical space. Atomic contributions to different electronic transitions of the same molecule are shown in Fig. 8 b, using azobenzene as an example. OMNI-P2x correctly reproduces the S 0 → S 1 transition as localized on the central N = N bond, while the S 2 transition has larger contributions from the aromatic rings. Finally, a higher excited state (S 11 ) is shown, which is delocalized across the entire conjugated system. The means of analysis presented above do not exclude the need for dedicated analysis, either manual or using wavefunction-based tools such as TheoDORE 85 or Multiwfn 86 , which can provide additional insights beyond spatial localization of the excitations, such as the orbitals’ character. These tools are complementary, as massive-scale simulations enabled by OMNI-P2x can serve as a first step for generating enough statistical data, from where representative samples can be drawn, and post-processed further with the wavefunction-based tools. Design and screening of visible-light absorbing azobenzene compounds The speed and accuracy of OMNI-P2x lend themselves for performing efficient high-throughput screening (HTS) of photo-active molecular systems. To demonstrate an application of OMNI-P2x for such a scenario, we perform the HTS of azobenzene derivatives characterizing with low-energy absorption. Our choice is motivated by the relevance of such compounds for applications in nonlinear optics 63 , photoresponsive polymers 64 , and as MOST systems 65 , 66 . To this end, firstly, we have generated a total of half a million azobenzene derivatives (Fig. 9 ) as SMILES strings, using RDkit 87 . In this procedure, we have allowed up to five substitutions with the following functional groups: methyl, ethyl, trifluoromethyl, nitro, hydroxyl, thiol, fluoro, chloro, amine, nitrile, and carboxyl. 3D structures (Cartesian coordinates) have been generated from SMILES using MLatom 88 , 89 , and optimized using the fast and accurate AIQM3 model 76 (see Methods for details). Subsequently, we have predicted the excitation energies of the optimized structures with OMNI-P2x. To refine the quality of the OMNI-P2x predictions, 1000 random structures have been sampled from the generated set and labeled using the TD-DFT/B3LYP method (see Methods for details on the level of theory). We have then fine-tuned two copies of one of the OMNI-P2x energy models on this set, using different training/validations splits. The procedure of prediction, selection, and optimization has been repeated two more times, at each iteration adding the 1000 most uncertain molecules to the training set, with the uncertainty measured by the deviation between the two trained models. When a correlation coefficient of 0.78 and an MAE of 0.25 eV have been reached as tested on 1000 randomly sampled structures, we have stopped the first phase of the screening procedure, as this accuracy is similar to the accuracy of the target TD-DFT methods. For the 1000 lowest-energy absorbing candidates, as predicted by the fine-tuned model, TD-DFT predictions have been made again. Out of these structures, a total of 21 lead candidates with transition energies below 2.0 eV have been determined (see Supporting Material, SM). Due to the potential charge-transfer character of excitations in these molecules, which the B3LYP functional would be unable to capture correctly, we have used at this stage a higher-level electronic structure method, ADC(2) 16 , to re-evaluate the excitation energies of the 21 lead candidates. Fig. 9. Summary of the high-throughput screening process for red-shifted, visible-light absorbing azobenzene derivatives. Open in a new tab Out of the 500 k generated structures, iterative fine-tuning of the OMNI-P2x model on structures optimized with UAIQM (see “Methods”) determined 1000 candidates for which time-dependent density functional theory (TD-DFT) spectra were computed. The procedure was repeated several times. From these structures, higher-quality spectra using the second-order algebraic diagrammatic construction (ADC(2)) method were computed for the best candidates, yielding 21 compact, visible light-absorbing azobenzene derivatives, with the three most red-shifted compounds presented in the figure. The three most red-shifted derivatives identified with the described procedure are presented at the bottom of Fig. 9 , while a database containing all the structures and their computed UV/Vis spectra is available in the SM. A plot comparing the spectra predicted at the three studied levels of theory is available in Supplementary Note 3 . The predicted absorption energies of the top three derivatives are lower than the absorption energies of reported human-designed red-shifted azobenzene units with the same core structure 90 – 93 . At the same time, our top candidates determined via in silico screening show similarities to subsitution patterns of the human-designed derivatives, i.e., ortho- and para-placements of electron-donating groups 94 , 95 . Efficient ML-driven nonadiabatic dynamics As a universal model, OMNI-P2x has the potential to accelerate nonadiabatic dynamics (NAMD) simulations, similarly to how ground-state models are used to efficiently perform ground-state dynamics. However, in this respect, it should be noted that NAMD is not just much more computationally demanding than the ground-state dynamics, but also typically requires a system-specific selection of a level of theory, as the common black-box approaches, like TD-DFT, cannot properly describe the key features of excited-state PES, i.e., the first excited to ground-state PES intersection 96 . This often necessitates a suitable choice of more advanced QM methods, such as CASSCF or CASPT2, which require the active spaces specifically selected for a given system. Since our OMNI-P2x is only trained on TD-DFT data, here, instead of directly using it to propagate NAMD, we consider a more realistic scenario, in which we want to fine-tune OMNI-P2x for the specific problem, i.e., the given combination of the desired QM level and system. To perform the fine-tuning as data-efficient, as possible, we generate data to fine-tune the pre-trained universal potential OMNI-P2x by modifying our previously developed active learning procedure 56 , where we use the OMNI-P2x as a starting point in each iteration of the active learning loop. Performing direct active learning from scratch, i.e., generating data for a neural network potential with random weights, has been, so far, state of the art in terms of time- and data-efficiency for ML-driven NAMD, but it might still take several days to weeks of wall-clock time to converge, even for relatively simple systems, such as fulvene or azobenzene 56 . As our first test system, we use fulvene, popularly chosen as a prototypical molecule for benchmarking NAMD methods 97 . This choice also allows us to compare our new protocol, based on fine-tuning OMNI-P2x, to the previous state-of-the-art protocol using MS-ANI with random initial weights 56 . As the reference electronic-structure method, we use CASSCF (6,6). The NAMD is performed with the Landau–Zener–Belyaev–Lebedev (LZBL) variant of TSH 98 – 102 , which does not require the calculation of the nonadiabatic coupling vectors (see Methods). With active transfer learning employing fine-tuning of the universal potential OMNI-P2x in the active learning loop, we are able to slash the convergence time of fulvene from over three days to about 24 h, with a ca. three-fold increase in computational efficiency. Active transfer learning yielded only 3550 conformations, which is about twice fewer than the number of training points required to achieve convergence in active learning procedure performed from scratch, as can be seen in Fig. 10 a. Moreover, inspecting the time evolution of the electronic state populations, we can see a statistically significant difference in the populations predicted by the fine-tuned model and the previous MS-ANI model. Despite a smaller training set, the TL version of OMNI-P2x better captures the photophysical behavior of the system. A comparison of the dynamics predicted using different ML models and different LZBL propagation settings with reference fewest switches surface hopping dynamics is available in Supplementary Note 4 . Further analysis of the NAMD trajectories of fulvene, including comparison of the ML-predicted potential energy surfaces, minimum energy conical intersections, as well as hopping points and deactivation channels, is provided in Supplementary Note 4.1 . In all cases, agreement between the ML model and reference CASSCF calculations is noted. Fig. 10. Performance of fine-tuned OMNI-P2x in NAMD simulations. Open in a new tab Panel ( a ) shows the ground-state population evolution of fulvene, from NAMD trajectories propagated using ML models trained in an active learning loop from scratch (red line) and by fine-tuning OMNI-P2x (blue line), as well as reference complete active space self-consistent field method (CASSCF) dynamics (black line), along with shaded, 95% confidence interval error bars. Panel ( b ) shows the stability of the NAMD simulations of azobenzene photoswitching as a function of the full active learning dataset, while panel ( c ) shows the predicted photoisomerisation quantum yield by models trained on increasing fractions of the training set, with a shaded area corresponding to the prediction of the reference method, from ref. 56 . TL -- transfer learning. Error bars were estimated using the normal approximation interval for a binomial process with a confidence interval of 95%. This improvement is even more substantial when moving to more complex cases of active learning. One such example is the photoisomerization reaction of azobenzene, simulated at the AIQM1/MRCI-SD level of theory (see Methods). Due to a large volume of chemical space covered during such a process, learning photoreactions is a particularly difficult task. To assess the improvement in data-efficiency that comes from using a pre-trained universal model, we compare the performance of the OMNI-P2x fine-tuned and MS-ANI trained from scratch on fractions of the full training set required to converge an AL procedure (35071 points, as reported in ref. 56 ). Looking at the stability of the dynamics, calculated as the percentage of trajectories finishing without dissociation, shown in Fig. 10 b, the fine-tuned OMNI-P2x model can propagate stable dynamics given just 0.1% of the dataset, while dynamics propagated using the pure learning approach become consistently stable above 10% of the data. Furthermore, Fig. 10 c presents the predicted quantum yield of trans to cis photoisomerization, as a function of the training set size. For the TL potentials, all models trained on above 2% of the data predict QYs within the reference range, up to a 95% confidence interval error bar. On the other hand, the performance of the models trained from scratch is much less consistent, with outliers predicting incorrect quantum yields even at high fractions of the training set. An analysis of azobenzene S 0 and S 1 PES’, optimized MECIs, and deactivation geometries is provided in Supplementary Note 4.2 , along with a comparison to reference results, which agree with the ML models. The above findings highlight that pre-training of OMNI-P2x on a vast dataset allows it to gain knowledge on both the chemical compound space and some information about conformational space, greatly reducing the amount of data needed for its fine-tuning. This makes OMNI-P2x a method of choice for propagating ML-accelerated surface hopping dynamics after data-efficient fine-tuning. A similar phenomenon has been reported in refs. 57 , 103 , where a neural network potential pre-trained on ground-state data could achieve a lower MAE for excited-state predictions than a potential trained from scratch, in the low-data regime. Discussion We present OMNI-P2x: a universal ML potential for predicting key molecular excited-state properties, including energies, forces, and oscillator strengths. The model enables out-of-the-box predictions of electronic spectra of organic molecules, targeting the TD-DFT/B3LYP level of theory, with an accuracy of about 0.15 eV. Importantly, OMNI-P2x offers higher-quality spectra predictions than commonly used semiempirical QM methods for excited states, while having a substantially lower computational cost. This efficiency and accuracy in electronic spectra predictions enable high-throughput screening of photo-active molecular systems with required properties: we demonstrate this by screening half a million of azobenzene derivatives for red-shifted, visible light-absorbing photoswitches. The screening delivered three top candidates absorbing in longer-wavelength regions than previously reported azobenzene derivatives. As with all machine-learning interatomic potentials, OMNI-P2x can only be as accurate as the reference method on which it is trained. In our case, this is TD-DFT/B3LYP/6-31+G*, which offers a practical balance between accuracy and computational feasibility across large chemical spaces, but is known to struggle with certain excited-state properties—most notably charge-transfer and Rydberg excitations. In small molecules, the use of a modest basis set such as 6-31 + G* can further exacerbate this issue, as higher-lying excitations may correspond to poorly described Rydberg states. As such, the expected level of error of TD-DFT/B3LYP, which is usually between 0.2 and 0.4 eV with respect to experimental benchmarks 104 , 105 , or theoretical best estimates (TBE) 106 – 109 , will be retained. The same is true for the oscillator strengths, which have reported MAE of between 0.05 and 0.15, compared to TBE 106 , 110 . We supplement these benchmarks by providing a comparison between ADC(2) and TD-DFT/B3LYP vertical excitation energies in Suppl. Fig. 19 and Supplementary Table 3 . The DFT results correlate well with ADC(2), showing a systematic underestimation of excitation energies, that increases when moving to higher excited states. These limitations are intrinsic to the reference data and thus propagate into the trained model. Furthermore, the neural network model is expected to produce reliable predictions primarily for molecules whose size and chemical composition are similar to those represented in the training set; extrapolation to significantly larger or chemically distinct molecules may lead to unphysical or unexpected results. Nevertheless, OMNI-P2x is fully agnostic to the level of theory when fine-tuned on more accurate data when available; in fact, we show in this work that transfer learning from TD-DFT/B3LYP already improves performance when adapted to higher-level reference methods. Importantly, we show that the OMNI-P2x universal model can be used to accelerate and increase the robustness of the ML-driven NAMD simulations. For this, we developed a protocol using fine-tuning OMNI-P2x in the active learning loop, allowing up to a ten-fold increase in the data efficiency compared to active learning from scratch. The quality of the resulting ML-driven NAMD is retained or even improved compared to the ML-NAMD without using OMNI-P2x. The pre-trained weights in OMNI-P2x contain the knowledge of the vast chemical compound and conformational space, which imparts ML-driven NAMD greater stability compared to the ML dynamics performed with the networks trained from scratch. This advantage has already been used in the follow-up study, enabling the NAMD simulations with electronic-structure methods without analytical gradients such as QD-NEVPT2 111 . While OMNI-P2x is the first universal excited-state neural network potential, it naturally has scope for further enhancements. Expanding the training set could enable support for a wider range of element types and out-of-equilibrium structures. Future extensions of the framework will aim to predict not only for neutral molecules in the singlet manifold, but also for states of higher multiplicity and charged species. Although the present focus on singlet states already enables accurate and chemically diverse predictions for many photophysical applications, the architecture is inherently extensible, and these additional capabilities will be the subject of future work. Additionally, developing a universal potential capable of performing NAMD simulations across chemical space without the need of fine-tuning remains an arduous task due to the diversity of photochemical transformations, high variations in molecular conformations in the direct vicinity of conical intersections, many possible choices of QM levels and settings inside the QM levels (e.g., active space), and would require extensive training data and, possibly, additional modifications to the architecture. In the meantime, the protocol combining fine-tuning of the OMNI-P2x with active learning, as presented here, can substantially ameliorate this problem by providing specific solutions for the problem in hand. Methods Model training and data collection The entire PubChemQC dataset 69 was obtained from the PubChemQC Project ( https://nakatamaho.riken.jp/pubchemqc.riken.jp/b3lyp_2017.html ). The molecules in the PubChemQC dataset were optimized at the level of B3LYP 71 /6-31G* 70 , and excited-state properties were calculated with TD-B3LYP/6-31+G* 70 using GAMESS 112 . For each molecule, the first 11 electronic states were calculated, leading to 10 excitation energies and oscillator strengths. In this study, the molecules were selected from the PubChemQC dataset, which satisfied the following conditions: multiplicity of 1, net charge of 0, and TD-DFT data for 11 electronic states, and containing elements C, H, O, N, F, S, and Cl. The resulting data set contained 3.1 million molecules, which we compiled with MLatom 3.16.2 88 , 89 , 102 to MLatom’s native machine-readable database format and saved in JSON files, used for training and testing in this study. During training, the MSE loss function for energies-only was used: L = E ML − E ref 2 , 1 where E ML and E ref are the ML-predicted and reference energies, respectively. Analogously, the MSE loss for oscillator strengths was used for a model trained on oscillator strengths. UV/Vis spectra prediction The electronic, UV/Vis absorption spectra are obtained using the standard single-point convolution approximation based on the broadening function as derived in ref. 113 : L ( x ) = 0.619 ∑ i f i Γ e − ( x − x i ) 2 / Γ 2 , 2 where x i are the predicted transition energies, f i are their oscillator strengths, and Γ is a pre-defined full-width at half maximum parameter (FWHM). In this work, a broadening parameter of 0.3 eV was used, as recommended in ref. 113 . Electronic spectra predicted by different methods were compared using Spearman’s rank correlation coefficient (SCC), r SCC : r SCC = 1 − 1 n ( n 2 − 1 ) ∑ i d i 2 , 3 where d i is the difference in rank between the two spectra, and n is the total length of the spectrum. The ODM2/CIS spectra were computed using the MLatom’s interface to the MNDO package 114 , and TD-DFTB spectra were obtained using an interface to the DFTB+ program, release 24.1, 115 , with the 3ob-3-1 set of parameters 116 . To address non-covalently bound structures separated by distances larger than the molecular descriptor cutoff, we introduce a fragment correction scheme (Supplementary Fig. 1 ). The method checks for non-covalently bound fragments and compares excitation energies of the full system against those of individual fragments to determine whether the state corresponds to localized excitations or an excimer. Validation on a benzene dimer as a function of intermolecular separation shows that the corrected model agrees well with TD-DFT/B3LYP reference values, whereas the uncorrected model diverges when parts of the system fall outside the cutoff radius. Full details are provided in Supplementary Note 1 . For the nuclear ensemble approach spectra, 500 conformations of pyrazine were sampled from a 298 K Wigner distribution, as implemented in MLatom, and labeled using TD-DFT/B3LYP (6-31+G*) in Gaussian 16.0 (Revision C.01) software package 117 . Geometry optimization was performed using the geomeTRIC 118 package, and PySCF 119 was used for frequency calculations. Data for the 9-DCMA system was extracted from ref. 81 , where it was computed at the CAM-B3LYP 120 /ma-TZVP 121 level of theory. The thermally distorted structures of molecules presented in Supllementary Figs. S6–S9 were sampled from a 2-ps-long ground-state Born–Oppenheimer molecular dynamics trajectory, with the first 1 ps discarded for thermalization, performed at the GFN2-xTB level of theory 122 – 124 . All the calculations and plots were prepared with MLatom. NAMD simulations CASSCF calculations used as a reference method for TSH simulations were performed through the interface to the COLUMBUS quantum chemistry package 125 , using an active space of 6 electrons in 6 orbitals. TSH simulations were performed using the Landau–Zener–Belyaev–Lebedev formalism 98 – 102 , with hopping probabilities between states k and j, P j → k calculated using the following formula: P j → k = exp − π 2 ℏ Z j k 3 Z ¨ j k , 4 where Z j k is the energy gap between states j and k, and Z ¨ j k is its second-order time derivative. The active learning loop uses the standard settings presented in ref. 56 , with initial points sampled from a harmonic approximation Wigner distribution, for a total of 250 points. The maximum propagation time was set to 60 fs with a time step of 0.1 fs. Velocities after hopping were rescaled in the direction of the momentum vector, using a reduced kinetic energy reservoir 126 . In each iteration of the AL procedure, 50 ML-TSH trajectories were run, and 50 gapMD trajectories. 15 additional points were sampled based on hopping probability uncertainty, up to a threshold of 300 points. Testing of the model was performed using 10000 trajectories for the MS-ANI model, as well as the fine-tuned OMNI-P2x model, and 623 CASSCF(6,6) trajectories were used as reference. One model from the energy ensemble of OMNI-P2x was used for fine-tuning in all NAMD applications. For both the studied systems, inital conditions were generated by sampling from a 298K Wigner distribution, as implemented in MLatom, using the same software for optimization and frequencies as for pyrazine. The reference data for azobenzene dynamics was labeled using the AIQM1/MRCI-SD method 127 . In the semiempirical part of AIQM1, the half-electron restricted open-shell Hartree–Fock formalism 128 was used in the SCF step, with the singly-occupied HOMO and LUMO orbitals. Two additional closed-shell references were added in the MRCI procedure, a HOMO–HOMO configuration and a doubly excited, LUMO–LUMO configuration. The active space consisted of 8 electrons in 10 orbitals (four occupied orbitals, six unoccupied). Single and double excitations within a such-defined active space were allowed. 100 trajectories were ran and analyzed for both the trans → cis and cis → trans photoisomerization reaction. The same number of trajectories was used when testing the model that was trained from scratch. The simulated quantum yields Φ were calculated as the fraction of the trajectories relaxing to form the photoproduct (the other isomer), N reactive , to the total number of trajectories N traj : Φ = N reactive / N traj . Azobenzene screening All computations were performed with the XACS version of MLatom (now MLatom with Aitomic add-ons) 102 , 129 , 130 . We used the MLatom interface to the TorchANI 68 package for all models based on ANI-type networks and their modifications (i.e., MS-ANI, OMNI-P2x, and AIQM3 76 ). The AIQM3 calculations also used the MLatom interface to the s-dftd3 program 131 , providing the D3(BJ) corrections 132 and the xtb program 133 providing the GFN2-xTB* baseline (GFN2-xTB 122 – 124 without the D4 dispersion corrections, e.g., as in the AIQM2 method 75 ). The azobenzene derivatives were optimized with the AIQM3 version of the UAIQM models 72 targeting the CCSD(T)/CBS accuracy; this model is available as an add-on to MLatom provided via the Aitomic package 134 . For TD-DFT calculations, MLatom’s interface to the Gaussian 16 software package (Revision C.01) 117 was used. ADC(2)-level spectra were computed using the Turbomole 135 software package, with the Dunning correlation-consistent double- ζ basis set (cc-pVDZ) 136 . Supplementary information Supplementary Information (28.2MB, pdf) Transparent Peer Review file (10.2MB, pdf) Source data Source Data (44.7MB, zip) Acknowledgements M.M. acknowledges the Polish Ministry of Education and Science for funding this research under the program “Perły Nauki,” grant number PN/01/0064/2022, amount of funding and the total value of the project: 239 800,00 PLN, as well as gratefully acknowledge Polish high-performance computing infrastructure PLGrid (HPC Centers: ACK Cyfronet AGH) for providing computer facilities and support within computational grant no. PLG/2024/017363. P.O.D. acknowledges funding by the projects for International Senior Scientists (Project No.: W2531013) and for Outstanding Youth Scholars (Overseas, 2021) of the National Natural Science Foundation of China, via the Lab project of the State Key Laboratory of Physical Chemistry of Solid Surfaces, and by Aitomistic, Shenzhen. Part of the computations were performed on the Xiamen Atomistic Computing Suite cloud server at http://XACScloud.com (succeeded by Aitomistic Lab@XMU at https://atom.xmu.edu.cn ). The authors also thank Yuxinxin Chen for providing the AIQM3 method of better quality for optimizing geometries of the azobenzene derivatives, before this method publication. Author contributions M.M. developed the code for training the OMNI-P2x and MS-ANI models, tested the collected datasets, performed model training, benchmarking and testing, performed the fine-tuning experiments, designed the screening pipeline and performed the required calculations and model training, developed the modified active learning protocol for TSH and performed the NAMD simulations, analyzed the results, wrote the original version of the manuscript and prepared the figures. X.Y.T. performed data collection and initial evaluation of their quality via MS-ANI model training, implemented the interface to DFTB + (used for TD-DFTB calculations), and assisted in optimization of azobenzene derivatives. J.J. participated in the result analysis and interpretation, co-supervised research, and assisted in the writing of the original version of the manuscript. P.O.D. designed and conceived the project, contributed to the result analysis and interpretation, co-supervised research, wrote the initial manuscript’s outline, title and abstract, and secured funding. All authors discussed the results, contributed to the manuscript and its revisions. Peer review Peer review information Nature Communications thanks the anonymous reviewers for their contribution to the peer review of this work. A peer review file is available. Data availability The PubChemQC and ANI-1ccx datasets are publicly available at 10.1021/acs.jcim.7b00083 and 10.1038/s41597-020-0473-z, respectively. Data supporting the findings, including the screening of azobenzene derivatives and nonadiabatic molecular dynamics trajectories, are deposited on Figshare, at 10.6084/m9.figshare.28794599. Source data are provided in this paper. Code availability The code is available in the open-source MLatom under the MIT license as described at https://github.com/dralgroup/mlatom with the OMNI-P2x model weights and scripts relevant to this publication available in a dedicated repository under the MIT license at https://github.com/dralgroup/omni-p2x . The calculations can also be performed online on Aitomistic Lab@XMU ( https://atom.xmu.edu.cn ) and Aitomistic Hub ( https://aitomistic.xyz ) with convenient GUIs and Aitomia (or its successors such as Protomia) – AI agents assisting in simulations via natural language prompts 137 . Competing interests The authors declare no competing interests. Footnotes Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Contributor Information Joanna Jankowska, Email: jjankowska@chem.uw.edu.pl. Pavlo O. Dral, Email: dral@xmu.edu.cn Supplementary information The online version contains supplementary material available at 10.1038/s41467-026-71380-5. References 1. Schultz, T. et al. Efficient deactivation of a model base pair via excited-state hydrogen transfer. Science 306 , 1765–1768 (2004). [ DOI ] [ PubMed ] [ Google Scholar ] 2. Sobolewski, A. L., Domcke, W., Dedonder-Lardeux, C. & Jouvet, C. Excited-state hydrogen detachment and hydrogen transfer driven by repulsive 1 π σ * states: A new paradigm for nonradiative decay in aromatic biomolecules. Phys. Chem. Chem. Phys. 4 , 1093–1100 (2002). [ Google Scholar ] 3. Boulanger, E., Anoop, A., Nachtigallova, D., Thiel, W. & Barbatti, M. Photochemical steps in the prebiotic synthesis of purine precursors from HCN. Angew. Chem. Int. Ed. 52 , 8000–8003 (2013). [ DOI ] [ PubMed ] [ Google Scholar ] 4. Tiefel, A. F. et al. Unimolecular net heterolysis of symmetric and homopolar σ -bonds. Nature 632 , 550–556 (2024). [ DOI ] [ PMC free article ] [ PubMed ] [ Google Scholar ] 5. Sheng, J. et al. General strategy for boosting the performance of speed-tunable rotary molecular motors with visible light. Sci. Adv . 11 , 10.1126/sciadv.adr9326 (2025). [ DOI ] [ PMC free article ] [ PubMed ] 6. Jarota, A. & Pastorczak, E. Tale of three dithienylethenes: Following the photocycloreversion with ultrafast spectroscopy and quantum dynamics simulations. J. Phys. Chem. B 129 , 1605–1613 (2025). [ DOI ] [ PMC free article ] [ PubMed ] [ Google Scholar ] 7. Ghosh, A., Ball, B., Pal, S. & Sarkar, P. Ultrafast charge transfer and delayed recombination in graphitic-CN/WTe 2 van der Waals heterostructure: A time domain ab initio study. J. Phys. Chem. Lett. 13 , 7898–7905 (2022). [ DOI ] [ PubMed ] [ Google Scholar ] 8. Di Liberto, G., Cipriano, L. A., Tosoni, S. & Gianfranco, P. Rational design of semiconductor heterojunctions for photocatalysis. Chem. Eur. J. 27 , 13306–13317 (2021). [ DOI ] [ PMC free article ] [ PubMed ] [ Google Scholar ] 9. Thakur, D. et al. In search of hosts for blue OLEDs: Computational design and experimental validation. Chem. Eur. J . 29 , 10.1002/chem.202203282 (2023). [ DOI ] [ PubMed ] 10. Chen, Y.-N. et al. Theoretical design study on the origin of the improved phosphorescent efficiency of dpephos quinoline-substituted derivatives for OLEDs. Org. Electron. 97 , 106185 (2021). [ Google Scholar ] 11. Rong, Z., Ding, J., Lu, J., Wang, W. & Yan, Y. Experimental and theoretical investigation of an innovative composite nanofluid for solar energy photothermal conversion and storage. J. Energy Storage 52 , 104800 (2022). [ Google Scholar ] 12. Hernández, F. J., Cox, J. M., Li, J., Crespo-Otero, R. & Lopez, S. A. Multiconfigurational calculations and photodynamics describe norbornadiene photochemistry. J. Org. Chem. 88 , 5311–5320 (2023). [ DOI ] [ PMC free article ] [ PubMed ] [ Google Scholar ] 13. Rodríguez-Martínez, X., Pascual-San-José, E. & Campoy-Quiles, M. Accelerating organic solar cell material’s discovery: high-throughput screening and big data. Energy Environ. Sci. 14 , 3301–3322 (2021). [ DOI ] [ PMC free article ] [ PubMed ] [ Google Scholar ] 14. Asif, M., Ahmad, I. & Wang, J.-L. Machine learning and molecular dynamics simulation-assisted evolutionary design and discovery pipeline to screen efficient small molecule acceptors for ptb7-th-based organic solar cells with over 15. J. Mater. Chem. A 10 , 4170–4180 (2022). [ Google Scholar ] 15. Sneskov, K. & Christiansen, O. Excited state coupled cluster methods. WIREs Comput. Mol. Sci. 2 , 566–584 (2011). [ Google Scholar ] 16. Schirmer, J. Beyond the random-phase approximation: A new approximation scheme for the polarization propagator. Phys. Rev. A 26 , 2395–2416 (1982). [ Google Scholar ] 17. Runge, E. & Gross, E. K. U. Density-functional theory for time-dependent systems. Phys. Rev. Lett. 52 , 997–1000 (1984). [ Google Scholar ] 18. Casida, M. E. Time-Dependent Density Functional Response Theory for Molecules (1995). 19. Pople, J. A., Santry, D. P. & Segal, G. A., Approximate self-consistent molecular orbital theory. i. invariant procedures. J. Chem. Phys . 43 , S129–S135 (1965). 20. Dewar, M. J. S., Zoebisch, E. G., Eamonn, F. H. & Stewart, J. J. P. Development and use of quantum mechanical molecular models. 76. AM1: a new general purpose quantum mechanical molecular model. J. Am. Chem. Soc. 107 , 3902–3909 (1985). [ Google Scholar ] 21. Stewart, J. J. P. Optimization of parameters for semiempirical methods I. Method. J. Comput. Chem. 10 , 209–220 (1989). [ Google Scholar ] 22. Dral, P. O. et al. Semiempirical quantum-chemical orthogonalization-corrected methods: Theory, Implementation, and Parameters. J. Chem. Theory Comput. 12 , 1082–1096 (2016). [ DOI ] [ PMC free article ] [ PubMed ] [ Google Scholar ] 23. Dral, P. O., Wu, X. & Thiel, W. Semiempirical Quantum-Chemical Methods with Orthogonalization and Dispersion Corrections. J. Chem. Theory Comput. 15 , 1743–1760 (2019). [ DOI ] [ PMC free article ] [ PubMed ] [ Google Scholar ] 24. Seifert, G. & Joswig, J.-O. Density-functional tight binding-an approximate density-functional theory method. WIREs Comput. Mol. Sci. 2 , 456–465 (2012). [ Google Scholar ] 25. Kowalczyk, T., Le, K. & Irle, S. Self-consistent optimization of excited states within density-functional tight-binding. J. Chem. Theory Comput. 12 , 313–323 (2015). [ DOI ] [ PubMed ] [ Google Scholar ] 26. Thiel, W. Semiempirical quantum-chemical methods. WIREs Comput. Mol. Sci. 4 , 145–157 (2013). [ Google Scholar ] 27. Niehaus, T. A. Approximate time-dependent density functional theory. J. Mol. Struct. 914 , 38–49 (2009). [ Google Scholar ] 28. Tuna, D., Lu, Y., A.el, K. & Thiel, W. Semiempirical quantum-chemical orthogonalization-corrected methods: Benchmarks of electronically excited states. J. Chem. Theory Comput. 12 , 4400–4422 (2016). [ DOI ] [ PubMed ] [ Google Scholar ] 29. Barbatti, M. Nonadiabatic dynamics with trajectory surface hopping method. WIREs Comput. Mol. Sci. 1 , 620–633 (2011). [ Google Scholar ] 30. Andersson, K., Malmqvist, P. A., Roos, B. O., Sadlej, A. J. & Wolinski, K. Second-order perturbation theory with a CASSCF reference function. J. Phys. Chem. 94 , 5483–5488 (1990). [ Google Scholar ] 31. Dral, P. O. editor. Quantum Chemistry in the Age of Machine Learning . Elsevier, 2023. ISBN: 9780323900492. 10.1016/C2020-0-03124-5. 32. Aldossary, A. et al. In silico chemical experiments in the age of AI: From quantum chemistry to machine learning and back. Adv. Mater . 36 , 2402369 (2024). [ DOI ] [ PubMed ] 33. Zhang, J. et al. Artificial intelligence enhanced molecular simulations. J. Chem. Theory Comput. 19 , 4338–4350 (2023). [ DOI ] [ PubMed ] [ Google Scholar ] 34. Butler, K. T., Davies, D. W., Cartwright, H., Isayev, O. & Walsh, A. Machine learning for molecular and materials science. Nature 559 , 547–555 (2018). [ DOI ] [ PubMed ] [ Google Scholar ] 35. Huang, B., von Rudorff, G. F. & von Lilienfeld, O. A. The central role of density functional theory in the AI age. Science 381 , 170–175 (2023). [ DOI ] [ PubMed ] [ Google Scholar ] 36. Chmiela, S. et al. Machine learning of accurate energy-conserving molecular force fields. Sci. Adv. 3 , e1603015 (2017). [ DOI ] [ PMC free article ] [ PubMed ] [ Google Scholar ] 37. Zhang, L., Han, J., Wang, H., Car, R. & Weinan, E. Deep potential molecular dynamics: A scalable model with the accuracy of quantum mechanics. Phys. Rev. Lett. 120 , 143001 (2018). [ DOI ] [ PubMed ] [ Google Scholar ] 38. Bartók, A. P., Payne, M. C., Kondor, R. & Csányi, G. Gaussian approximation potentials: The accuracy of quantum mechanics, without the electrons. Phys. Rev. Lett. 104 , 136403 (2010). [ DOI ] [ PubMed ] [ Google Scholar ] 39. Unke, O. T. & Meuwly, M. PhysNet: A neural network for predicting energies, forces, dipole moments, and partial charges. J. Chem. Theory Comput. 15 , 3678–3693 (2019). [ DOI ] [ PubMed ] [ Google Scholar ] 40. Ilyes Batatia, David P. Kovacs, Gregor Simm, Christoph Ortner & Gabor Csanyi, Advances in Neural Information Processing Systems, 35 , 11423–11436 (2022) 41. Lewis, A. M., Grisafi, A., Ceriotti, M. & Rossi, M. Learning electron densities in the condensed phase. J. Chem. Theory Comput. 17 , 7203–7214 (2021). [ DOI ] [ PMC free article ] [ PubMed ] [ Google Scholar ] 42. Lewis, A. M., Lazzaroni, P. & Rossi, M. Predicting the electronic density response of condensed-phase systems to electric field perturbations. J. Chem. Phys. 159 , 014103 (2023). [ DOI ] [ PubMed ] [ Google Scholar ] 43. Hou, Y.-F., Zhang, Q. & Dral, P. O. Surprising dynamics phenomena in the diels-alder reaction of c 60 uncovered with ai. J. Org. Chem. 89 , 15041–15047 (2024). [ DOI ] [ PubMed ] [ Google Scholar ] 44. Li, J. et al. Automatic discovery of photoisomerization mechanisms with nanosecond machine learning photodynamics simulations. Chem. Sci. 12 , 5302–5314 (2021). [ DOI ] [ PMC free article ] [ PubMed ] [ Google Scholar ] 45. Li, J., Stein, R., Adrion, D. M. & Lopez, S. A. Machine-learning photodynamics simulations uncover the role of substituent effects on the photochemical formation of cubanes. J. Am. Chem. Soc. 143 , 20166–20175 (2021). [ DOI ] [ PubMed ] [ Google Scholar ] 46. Ang, S. hiJ. un, Wujie, W. & Simon, A. Active learning accelerates ab initio molecular dynamics on reactive energy surfaces. Chem . 7 , 738–751 (2021). [ Google Scholar ] 47. Schaub, T. A. et al. Tunable macrocyclic polyparaphenylene nanolassos via copper-free click chemistry. Chem. Eur. J . 29 , e202300668 (2023). [ DOI ] [ PubMed ] 48. Smith, J. S. et al. Approaching coupled cluster accuracy with a general-purpose neural network potential through transfer learning. Nat. Commun. 10 , 2903–2910 (2019). [ DOI ] [ PMC free article ] [ PubMed ] [ Google Scholar ] 49. Deng, B. et al. CHGNet as a pretrained universal neural network potential for charge-informed atomistic modelling. Nat. Mach. Intell. 5 , 1031–1041 (2023). [ Google Scholar ] 50. Neumann, M. et al. ORB: A fast, scalable neural network potential. Preprint at 10.48550/arXiv.2410.22570 (2024). 51. Chen, C. & Ong, S. P. A universal graph deep learning interatomic potential for the periodic table. Nat. Comput. Sci. 2 , 718–728 (2022). [ DOI ] [ PubMed ] [ Google Scholar ] 52. Batatia, I. et al. A foundation model for atomistic materials chemistry. J. Chem. Phys. 163 , 184110 (2025). [ DOI ] [ PubMed ] 53. Kovacs, D. P. et al. MACE-OFF: Short-Range Transferable Machine Learning Force Fields for Organic Molecules. J. Am. Chem. Soc. 147 , 17598–17611 (2025). [ DOI ] [ PMC free article ] [ PubMed ] 54. Westermayr, J., Gastegger, M. & Marquetand, P. Combining SchNet and SHARC: The SchNarc machine learning approach for excited-state dynamics. J. Phys. Chem. Lett. 11 , 3828–3834 (2020). [ DOI ] [ PMC free article ] [ PubMed ] [ Google Scholar ] 55. Mausenberger, S. et al. SpaiNN: equivariant message passing for excited-state nonadiabatic molecular dynamics. Chem. Sci. 15 , 15880–15890 (2024). [ DOI ] [ PMC free article ] [ PubMed ] [ Google Scholar ] 56. Martyka, M. et al. Charting electronic-state manifolds across molecules with multi-state learning and gap-driven dynamics via efficient and robust active learning. Npj Comput. Mater . 11 , 132 (2025). [ DOI ] [ PMC free article ] [ PubMed ] 57. Barrett, R., Ortner, C. & Westermayr, J. Transferable machine learning potential X-MACE for excited states using integrated DeepSets. Preprint at 10.48550/arXiv.2502.12870 (2025). 58. Axelrod, S., Shakhnovich, E. & Gómez-Bombarelli, R. Excited state non-adiabatic dynamics of large photoswitchable molecules using a chemically transferable machine learning potential. Nat. Commun . 13 , 3440 (2022). [ DOI ] [ PMC free article ] [ PubMed ] 59. Jacobs, R. et al. A practical guide to machine learning interatomic potentials - status and future. Curr. Opin. Solid State Mater. Sci. 35 , 101214 (2025). [ Google Scholar ] 60. Westermayr, J. & Marquetand, P. Machine learning for electronically excited states of molecules. Chem. Rev. 121 , 9873–9926 (2020). [ DOI ] [ PMC free article ] [ PubMed ] [ Google Scholar ] 61. Westermayr, J., Faber, F. A., Christensen, A. S., von Lilienfeld, O. A. & Marquetand, P. Neural networks and kernel ridge regression for excited states dynamics of : From single-state to multi-state representations and multi-property machine learning models. Mach. Learn. Sci. Technol. 1 , 025009 (2020). [ Google Scholar ] 62. Chen, Y. & Dral, P. O. One to Rule Them All: A Universal Interatomic Potential Learning across Quantum Chemical Levels. J. Chem. Theory Comput. 21 , 8762–8772 (2025). [ DOI ] [ PubMed ] 63. Natansohn, A. & Rochon, P. Photoinduced motions in azo-containing polymers. Chem. Rev. 102 , 4139–4176 (2002). [ DOI ] [ PubMed ] [ Google Scholar ] 64. Yesodha, S. K., Sadashiva Pillai, C. K. & Tsutsumi, N. Stable polymeric materials for nonlinear optics: a review based on azobenzene systems. Prog. Polym. Sci. 29 , 45–74 (2004). [ Google Scholar ] 65. Salthouse, R. J. & Moth-Poulsen, K. Multichromophoric photoswitches for solar energy storage: from azobenzene to norbornadiene, and most things in between. J. Mater. Chem. A 12 , 3180–3208 (2024). [ DOI ] [ PMC free article ] [ PubMed ] [ Google Scholar ] 66. Giménez-Gómez, A. et al. State-of-the-art and challenges towards a molecular solar thermal (most) energy storage device. React. Chem. Eng. 9 , 1629–1640 (2024). [ Google Scholar ] 67. Smith, J. S., Isayev, O. & Roitberg, A. E. ANI-1: an extensible neural network potential with DFT accuracy at force field computational cost. Chem. Sci. 8 , 3192–3203 (2017). [ DOI ] [ PMC free article ] [ PubMed ] [ Google Scholar ] 68. Gao, X., Ramezanghorbani, F., Isayev, O., Smith, J. S. & Roitberg, A. E. TorchANI: A free and open source pytorch-based deep learning implementation of the ANI neural network potentials. J. Chem. Inf. Model. 60 , 3408–3415 (2020). [ DOI ] [ PubMed ] [ Google Scholar ] 69. Nakata, M. & Shimazaki, T. Pubchemqc project: A large-scale first-principles electronic structure database for data-driven chemistry. J. Chem. Inf. Model. 57 , 1300–1308 (2017). [ DOI ] [ PubMed ] [ Google Scholar ] 70. Dunning Jr, T. H. Gaussian basis sets for use in correlated molecular calculations. i. the atoms boron through neon and hydrogen. J. Chem. Phys. 90 , 1007–1023 (1989). [ Google Scholar ] 71. Stephens, P. J., Devlin, F. J., Chabalowski, C. F. & Frisch, M. J. Ab initio calculation of vibrational absorption and circular dichroism spectra using density functional force fields. J. Phys. Chem. 98 , 11623–11627 (1994). [ Google Scholar ] 72. Chen, Y., Hou, Y. F., Isayev, O. & Dral, P. O. Universal and updatable artificial intelligence-enhanced quantum chemical foundational models. Preprint at 10.26434/chemrxiv-2024-604wb (2024). 73. Christian, D. et al. Extending the applicability of the ani deep learning molecular potential to sulfur and halogens. J. Chem. Theo. Comput. 16 , 4192–4202 (2020). [ DOI ] [ PubMed ] [ Google Scholar ] 74. Zheng, P., Zubatyuk, R., Wu, W., Isayev, O. & Dral, P. O. Artificial intelligence-enhanced quantum chemical method with broad applicability. Nat. Commun . 12 , 7022 (2021). [ DOI ] [ PMC free article ] [ PubMed ] 75. Chen, Y. & Dral, P. O. AIQM2: Organic reaction simulations beyond DFT. Chem. Sci. 16 , 15901–15912 (2025). [ DOI ] [ PMC free article ] [ PubMed ] [ Google Scholar ] 76. Chen, Y., Hou, Y. F., Zubatyuk, R., Isayev, O. & Dral, P. O. AIQM3: Targeting coupled-cluster accuracy with semi-empirical speed across seven main-group elements. J. Chem. Theory Comput . 22 , 2232–2242 (2026). [ DOI ] [ PubMed ] 77. Wood, B. M. et al. UMA: A family of universal models for atoms. Preprint at 10.48550/arXiv.2506.23971 (2025). 78. Dylan, M. A., Zubatyuk, R. & Isayev, O. AIMNet2: a neural network potential to meet your neutral, charged, organic, and elemental-organic needs. Chem. Sci. 16 , 10228–10244 (2025). [ DOI ] [ PMC free article ] [ PubMed ] [ Google Scholar ] 79. Bergsma, J. P., Berens, P. H., Wilson, K. R., Fredkin, D. R. & Heller, E. J. Electronic spectra from molecular dynamics: a simple approach. J. Phys. Chem. 88 , 612–619 (1984). [ Google Scholar ] 80. Crespo-Otero, R. & Barbatti, M. Spectrum simulation and decomposition with nuclear ensemble: formal derivation and application to benzene, furan and 2-phenylfuran. Theor. Chem. Acc. 131 , 1237 (2012). 81. Xue, B.-X., Barbatti, M. & Dral, P. O. Machine learning for absorption cross sections. J. Phys. Chem. A 124 , 7199–7210 (2020). [ DOI ] [ PMC free article ] [ PubMed ] [ Google Scholar ] 82. Cerdán, L. & Roca-Sanjuán, D. Reconstruction of nuclear ensemble approach electronic spectra using probabilistic machine learning. J. Chem. Theory Comput. 18 , 3052–3064 (2022). [ DOI ] [ PMC free article ] [ PubMed ] [ Google Scholar ] 83. Westermayr, J. & Marquetand, P. Deep learning for UV absorption spectra with SchNarc: First steps toward transferability in chemical compound space. J. Chem. Phys . 153 , 154112 (2020). [ DOI ] [ PubMed ] 84. Schütt, K. T., Arbabzadah, F., Chmiela, S., Müller, K. R. & Tkatchenko, A. Quantum-chemical insights from deep tensor neural networks. Nat. Commun. 8 , 13890 (2017). [ DOI ] [ PMC free article ] [ PubMed ] [ Google Scholar ] 85. Plasser, F. et al. TheoDORE: A toolbox for a detailed and automated analysis of electronic excited state computations. J. Chem. Phys . 152 , 084108 (2020). [ DOI ] [ PubMed ] 86. Lu, T. A comprehensive electron wavefunction analysis toolbox for chemists, Multiwfn. J. Chem. Phys. 161 , 082503 (2024). [ DOI ] [ PubMed ] [ Google Scholar ] 87. RDKit: Open-source cheminformatics. https://www.rdkit.org . 88. Dral, P. O. et al. MLatom 3: A platform for machine learning-enhanced computational chemistry simulations and workflows. J. Chem. Theory Comput. 20 , 1193–1213 (2024). [ DOI ] [ PMC free article ] [ PubMed ] [ Google Scholar ] 89. Dral, P. O. et al. MLatom: A package for atomistic simulations with machine learning. Development version. Xiamen University, Xiamen, China (2013–2026). Available at: http://MLatom.com . 90. Bléger, D., Schwarz, J., Brouwer, A. M. & Hecht, S. o-fluoroazobenzenes as readily synthesized photoswitches offering nearly quantitative two-way isomerization with visible light. J. Am. Chem. Soc. 134 , 20597–20600 (2012). [ DOI ] [ PubMed ] [ Google Scholar ] 91. Beharry, A. A., Sadovski, O. & Woolley, G. A. Azobenzene photoswitching without ultraviolet light. J. Am. Chem. Soc. 133 , 19684–19687 (2011). [ DOI ] [ PubMed ] [ Google Scholar ] 92. Dong, M., Amirhossein, B., Subhas, S., Beharry, A. A. & Woolley, G. A. Red-shifting azobenzene photoswitches for in vivo use. Acc. Chem. Res. 48 , 2662–2670 (2015). [ DOI ] [ PubMed ] [ Google Scholar ] 93. Konrad, D. B., Savasci, G. et al. Computational design and synthesis of a deeply red-shifted and bistable azobenzene. J. Am. Chem. Soc. 142 , 6538–6547 (2020). [ DOI ] [ PMC free article ] [ PubMed ] [ Google Scholar ] 94. Jerca, F. A., Jerca, V. V. & Hoogenboom, R. Advances and opportunities in the exciting world of azobenzenes. Nat. Rev. Chem. 6 , 51–69 (2021). [ DOI ] [ PubMed ] [ Google Scholar ] 95. Eom, T. & Khan, A. Push-pull azobenzene chromophores with negative halochromism. Dyes and Pigm. 188 , 109197 (2021). [ Google Scholar ] 96. Levine, B. G., Ko, C., Quenneville, J. & Martínez, T. J. Conical intersections and double excitations in time-dependent density functional theory. Mol. Phys. 104 , 1039–1051 (2006). [ Google Scholar ] 97. Ibele, L. M. & Curchod, B. F. E. A molecular perspective on Tully models for nonadiabatic dynamics. Phys. Chem. Chem. Phys. 22 , 15183–15196 (2020). [ DOI ] [ PubMed ] [ Google Scholar ] 98. Landau, L. D. On the theory of transfer of energy at collisions II Physikalische Zeitschrift der Sowjetunion. Sci. Res. 2 , 46–51 (1932). [ Google Scholar ] 99. Landau, L. D. On the theory of transfer of energy at collisions ii. Physikalische Zeitschrift der Sowjetunion 2 , 46 (1932). [ Google Scholar ] 100. Belyaev, A. K. & Lebedev, O. V. Nonadiabatic nuclear dynamics of atomic collisions based on branching classical trajectories. Phys. Rev. A 84 , 014701 (2011). [ Google Scholar ] 101. Zener, C. & Fowler, R. H. Non-adiabatic crossing of energy levels. Proc. R. Soc. Lond. A 137 , 696–702 (1932). [ Google Scholar ] 102. Zhang, L. et al. MLatom software ecosystem for surface hopping dynamics in Python with quantum mechanical and machine learning methods. J. Chem. Theory Comput. 20 , 5043–5057 (2024). [ DOI ] [ PubMed ] [ Google Scholar ] 103. Barrett, R., Dietschreit, J.C.B. & Westermayr, J. Incorporating long-range interactions via the multipole expansion into ground and excited-state molecular simulations. npj Comput. Mater. 12 , 135 (2026). 104. Winter, N. O. C., Graf, N. K., Leutwyler, S. & Hättig, C. Benchmarks for 0-0 transitions of aromatic organic molecules: DFT/B3LYP, ADC(2), CC2, SOS-CC2 and SCS-CC2 compared to high-resolution gas-phase data. Phys. Chem. Chem. Phys. 15 , 6623–6630 (2013). [ DOI ] [ PubMed ] [ Google Scholar ] 105. Leang, S. S., Zahariev, F. & Gordon, M. S. Benchmarking the performance of time-dependent density functional methods. J. Chem. Phys. 136 , 104101 (2012). [ DOI ] [ PubMed ] [ Google Scholar ] 106. Sarkar, R., Boggio-Pasqua, M., Loos, P.-F. & Jacquemin, D. Benchmarking TD-DFT and wave function methods for oscillator strengths and excited-state dipole moments. J. Chem. Theory Comput. 17 , 1117–1132 (2021). [ DOI ] [ PubMed ] [ Google Scholar ] 107. Silva-Junior, M. R., Schreiber, M., Sauer, S. P. A. & Thiel, W. Benchmarks for electronically excited states: Time-dependent density functional theory and density functional theory based multireference configuration interaction. J. Chem. Phys. 129 , 104103 (2008). [ DOI ] [ PubMed ] [ Google Scholar ] 108. Jacquemin, D., Wathelet, V., Perpète, E. A. & Adamo, C. Extensive TD-DFT benchmark: Singlet-excited states of organic molecules. J. Chem. Theory Comput. 5 , 2420–2435 (2009). [ DOI ] [ PubMed ] [ Google Scholar ] 109. Knysh, I. et al. Reference CC3 excitation energies for organic chromophores: Benchmarking TD-DFT, BSE/GW, and wave function methods. J. Chem. Theory Comput . 20 , 8152–8174 (2024). [ DOI ] [ PubMed ] 110. Robinson, D. Comparison of the transition dipole moments calculated by TDDFT with high-level wave function theory. J. Chem. Theory Comput. 14 , 5303–5309 (2018). [ DOI ] [ PubMed ] [ Google Scholar ] 111. Martyka, M., Jankowska, J., Lischka, H. & Dral, P. O. Gradients not needed: ML-driven propagation of nonadiabatic molecular dynamics without reference gradients. Chem. Sci. 17 , 6043–6054 (2026). [ DOI ] [ PMC free article ] [ PubMed ] 112. Schmidt, M. W. et al. General atomic and molecular electronic structure system. J. Comput. Chem. 14 , 1347–1363 (1993). [ Google Scholar ] 113. Bai, S., Mansour, R., Stojanovic, L., Toldo, J. M. & Barbatti, M. On the origin of the shift between vertical excitation and band maximum in molecular photoabsorption. J. Mol. Model . 26 , 107 (2020). [ DOI ] [ PMC free article ] [ PubMed ] 114. Dewar, M. J. S. & Thiel, W. Ground states of molecules. 38. The MNDO method. Approximations and parameters. J. Am. Chem. Soc. 99 , 4899–4907 (1977). [ Google Scholar ] 115. Hourahine, B. et al. DFTB+, a software package for efficient approximate density functional theory based atomistic simulations. J. Chem. Phys . 152 , 124101 (2020). [ DOI ] [ PubMed ] 116. Gaus, M., Goez, A. & Elstner, M. Parametrization and Benchmark of DFTB3 for Organic Molecules. J. Chem. Theory Comput. 9 , 338–354 (2013). [ DOI ] [ PubMed ] 117. Frisch, M. J. et al. Gaussian 16 Revision C.01, 2016. Gaussian Inc. Wallingford CT. (2016). 118. Wang, L. P. & Song, C. Geometry optimization made simple with translation and rotation coordinates. J. Chem. Phys. 144 , 214108 (2016). [ DOI ] [ PubMed ] 119. Sun, Q. et al. Recent developments in the PySCF program package. J. Chem. Phys. 153 , 024109 (2020). [ DOI ] [ PubMed ] 120. Takeshi, Y., Tew, D. P. & Handy, N. C. A new hybrid exchange-correlation functional using the Coulomb-attenuating method (CAM-B3LYP). Chem. Phys. Lett. 393 , 51–57 (2004). [ Google Scholar ] 121. Zheng, J., Xu, X. & Truhlar, D. G. Minimally augmented Karlsruhe basis sets. Theor. Chem. Acc. 128 , 295–305 (2010). [ Google Scholar ] 122. Grimme, S., Bannwarth, C. & Shushkov, P. A robust and accurate tight-binding quantum chemical method for structures, vibrational frequencies, and noncovalent interactions of large molecular systems parametrized for all spd-block elements (z = 1-86). J. Chem. Theory Comput. 13 , 1989–2009 (2017). [ DOI ] [ PubMed ] [ Google Scholar ] 123. Bannwarth, C., Ehlert, S. & Grimme, S. Gfn2-xtb-an accurate and broadly parametrized self-consistent tight-binding quantum chemical method with multipole electrostatics and density-dependent dispersion contributions. J. Chem. Theory Comput. 15 , 1652–1671 (2019). [ DOI ] [ PubMed ] [ Google Scholar ] 124. Pracht, P., Caldeweyher, E., Ehlert, S. & Grimme, S. A robust non-self-consistent tight-binding quantum chemistry method for large molecules. 10.26434/chemrxiv.8326202.v1 (2019). 125. Lischka, H. et al. The generality of the GUGA-MRCI approach in COLUMBUS for treating complex quantum chemistry. J. Chem. Phys. 152 , 134110–134131 (2020). [ DOI ] [ PubMed ] [ Google Scholar ] 126. Toldo, J. M., Mattos, R. S., Max Jr, P., Mukherjee, S. & Barbatti, M. Recommendations for velocity adjustment in surface hopping. J. Chem. Theory Comput. 20 , 614–624 (2024). [ DOI ] [ PubMed ] [ Google Scholar ] 127. Koslowski, A., Beck, M. E. & Thiel, W. Implementation of a general multireference configuration interaction procedure with analytic gradients in a semiempirical context using the graphical unitary group approach. J. Comput. Chem. 24 , 714–726 (2003). [ DOI ] [ PubMed ] [ Google Scholar ] 128. Michael, J. S. D., Hashmall, J. A. & Venier, C. G. Ground states of conjugated molecules. ix. hydrocarbon radicals and radical ions. J. Am. Chem. Soc. 90 , 1953–1957 (1968). [ Google Scholar ] 129. Dral, P. O. et al. MLatom 2: An integrative platform for atomistic machine learning. Top. Curr. Chem. 379 , 27 (2021). [ DOI ] [ PMC free article ] [ PubMed ] [ Google Scholar ] 130. Dral, P. O. MLatom: A program package for quantum chemical research assisted by machine learning. J. Comput. Chem. 40 , 2339–2347 (2019). [ DOI ] [ PubMed ] [ Google Scholar ] 131. Ehlert, S. Simple DFT-D3: library-first implementation of the D3 dispersion correction. J. Open Source Softw. 9 , 7169 (2024). [ Google Scholar ] 132. Grimme, S., Ehrlich, S. & Goerigk, L. Effect of the damping function in dispersion corrected density functional theory. J. Comput. Chem. 32 , 1456–1465 (2011). [ DOI ] [ PubMed ] [ Google Scholar ] 133. Bannwarth, C. et al. Extended tight-binding quantum chemistry methods. WIREs Comput. Mol. Sci. 11 , e1493 (2020). 134. Dral, P. O., Chen, Y., Martyka, M. & Li, J., Aitomic — MLatom.com. http://mlatom.com/aitomic/ (2025). 135. TURBOMOLE V7.7 2022, a development of University of Karlsruhe and Forschungszentrum Karlsruhe GmbH, 1989-2007, TURBOMOLE GmbH, since 2007. 136. Dunning, T. H. Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen. J. Chem. Phys. 90 , 1007–1023 (1989). [ Google Scholar ] 137. Hu, J. et al. Aitomia: Your intelligent assistant for ai-driven atomistic and quantum chemical simulations. Preprint at 10.48550/arXiv.2505.08195 (2025). Associated Data This section collects any data citations, data availability statements, or supplementary materials included in this article. Supplementary Materials Supplementary Information (28.2MB, pdf) Transparent Peer Review file (10.2MB, pdf) Source Data (44.7MB, zip) Data Availability Statement The PubChemQC and ANI-1ccx datasets are publicly available at 10.1021/acs.jcim.7b00083 and 10.1038/s41597-020-0473-z, respectively. Data supporting the findings, including the screening of azobenzene derivatives and nonadiabatic molecular dynamics trajectories, are deposited on Figshare, at 10.6084/m9.figshare.28794599. Source data are provided in this paper. The code is available in the open-source MLatom under the MIT license as described at https://github.com/dralgroup/mlatom with the OMNI-P2x model weights and scripts relevant to this publication available in a dedicated repository under the MIT license at https://github.com/dralgroup/omni-p2x . The calculations can also be performed online on Aitomistic Lab@XMU ( https://atom.xmu.edu.cn ) and Aitomistic Hub ( https://aitomistic.xyz ) with convenient GUIs and Aitomia (or its successors such as Protomia) – AI agents assisting in simulations via natural language prompts 137 . Articles from Nature Communications are provided here courtesy of Nature Publishing Group ACTIONS View on publisher site PDF (1.8 MB) Cite Collections Permalink RESOURCES Similar articles Cited by other articles Links to NCBI Databases Follow NCBI NCBI on X (formerly known as Twitter) NCBI on Facebook NCBI on LinkedIn NCBI on GitHub NCBI RSS feed Connect with NLM NLM on X (formerly known as Twitter) NLM on Facebook NLM on YouTube National Library of Medicine 8600 Rockville Pike Bethesda, MD 20894 Web Policies FOIA HHS Vulnerability Disclosure Help Accessibility Careers NLM NIH HHS USA.gov Back to Top

Related documents

• Autonomous Chaotic Time Series Prediction using Physical Neuromorphic Networks#973975
• Unified nonlinear modeling approach for machine learning and artificial … — Nxgen Partners Ip, Llc (US12488266B2)#607072
• The WEST code for large-scale excited-state materials simulations#1141605
• In situ local learning of dynamic network materials#973590
• Democratizing Atomistic Simulation Workflows for the AI Era with the Quantum Accelerator#1118896