Session D60: Machine Learning of Molecules and Materials: Chemical Space and Dynamics

Quantum Machine Learning

Many of the most relevant observables of matter depend explicitly on atomistic and electronic structure, rendering physics based approaches to chemistry and materials necessary. Unfortunately, due to the combinatorial scaling of the number of chemicals and potential reaction settings, gaining a holistic and rigorous understanding through exhaustive quantum and statistical mechanics based sampling is prohibitive --- even when using high-performance computers. Accounting for explicit and implicit dependencies and correlations, however, will not only deepen our fundamental understanding but also benefit exploration campaigns (computational and experimental). I will discuss recently gained insights from my labs elucidating such relationships thanks to alchemical perturbation density functional theory and supervised machine learning.   

Machine learning and many-body molecular interactions

Machine learning (ML) potentials, particularly those based on deep neural networks (DNNs), have emerged as powerful tools for simulating molecular systems with a broad spectrum of applications, spanning liquids to materials. In our work, we aim at combining the computational prowess of the DeePMD framework with the proven accuracy of MB-pol, a data-driven many-body potential, to develop a DNN potential for large-scale simulations of water across various phases. Our findings underscore that while the DNN potential reliably reproduces the MB-pol results for liquid water, it falters in accurately describing the vapor-liquid equilibrium properties—a shortcoming rooted in the DNN potential's inability to correctly "learn" many-body interactions. Our attemp at encoding explicit many-body effects information leads to a new DNN potential, which albeit accurately rendering the MB-pol vapor-liquid equilibrium properties, stumbled in capturing liquid properties. Nevertheless, the computational efficiency of DeePMD holds promise for training DNN potentials on data-driven many-body potentials, thereby unlocking the potential for large-scale, chemically accurate simulations of water and aqueous solutions. This promise comes with a caveat—the targeted state points must be well-represented in the training phase by the reference data-driven many-body potential to ensure an accurate portrayal of the associated properties.   

Thermodynamic and electronic properties of water and ice: joining machine learning and manybody perturbation theory

Water and ice are fundamental substances for life on Earth: the relations among water's molecular structure, electronic structure, and anomalous thermodynamic properties have been extensively investigated.

Modeling through accurate computer simulations is essential to connect experimental observation with the molecular-level picture of water and ice. It is by now established that nuclear quantum effects (NQEs) play a crucial role in determining the structural and thermodynamic properties of water. However, to date the understanding of how NQEs influence the electronic structure of water systems is limited, in particular in bulk ice, and in interfacial and confined water and ice systems.

Here, we conducted a systematic comparison of both the structural and electronic properties for various

water systems, including water clusters, liquid water, and hexagonal ice simulated at the level of classical molecular dynamics (MD) and quantum path-integral MD. These simulations leverage the efficiency and accuracy of machine learning potentials fitted to state-of-the-art density functional theory calculations. Electronic structure calculations using GW manybody perturbation theory provide a detailed insight of the distinct impact that NQEs have on different aqueous systems.    

Accurate thermodynamic tables for solids using Machine Learning Interaction Potentials and Covariance of Atomic Positions

Finite-temperature thermodynamic properties such as entropy and free energies of solids are notoriously difficult to compute accurately despite their importance in many standard calculations. Experimental data only exists at easy to operate conditions for specific phases, limiting the ability to predict phase and thermodymic behavior at extreme conditions such as high pressure. The difficulty in calculating thermodynamic properties comes from the very high cost of more accurate methods such as Density Functional Theory as well as the long simulation times needed for methods such as thermodynic integration. To overcome these issues, we use Machine Learning Interaction Potentials (MLIPs) to allow fast but still accurate calculations and calculate entropy from the covariance of atomic positions. The combination of these two methods allows the accurate parallelized computing of thermodynamic properties for arbitrary phases at arbitrary pressure and temperature. We perform these calculations for alkali metal systems and find excellent agreement with experimental measurements.   

AI-enhanced chemical physics simulations

I will present our methods and software tools enabling practical AI-enhanced chemical physics simulations and demonstrate their applications. The methods include the general-purpose, artificial intelligence-enhanced quantum mechanical method 1 (AIQM1), [2] which for many properties approaches the accuracy of golden-standard, traditional CCSD(T)/CBS approach while being orders of magnitude faster than DFT. Other methods focus on novel approaches for learning dynamics such as our AI-quantum dynamics [3] and 4D-spacetime atomistic AI [4] approaches which predict dynamics properties such as nuclear coordinates as the function of time and do not require iterative trajectory propagation as in classical MD. AIQM1 and AI-QD along with many other methods such as a host of ML interatomic potentials are implemented in our MLatom program package and Python library for user-friendly atomistic machine learning simulations which can be run online using our MLatom@XACS cloud-based service. [5]   

Learning polarization using equivariant neural networks

Polarization is key to the understanding of dielectrics and ferroelectrics, and recent advances, such as the modern theory of polarization [1] and electric enthalpy functionals [2], have opened the path to computational studies of polarization in crystals. However, the high computational cost associated with these simulation techniques remains a challenging problem of electronic structure calculations. Here, we introduce an equivariant neural network approach to efficiently learn and predict the polarization for each atomic configuration, building on and extending state-of-the-art machine learning force field architectures. This allows for the study of the polarization autocorrelation function over a molecular dynamics simulation at first-principles accuracy, thereby enabling the simulation of infrared spectrum, frequency-dependent dielectric constant, and Raman cross section from first principles. Our scheme is implemented within the E(3)-equivariant NequIP/Allegro framework [3], and is interfaced with the LAMMPS code.

[1] R. Resta, Macroscopic polarization in crystalline dielectrics: the geometric phase approach, Rev. Mod. Phys. 66, 899 (1994).

[2] P. Umari and A. Pasquarello, Ab initio molecular dynamics in a finite homogeneous electric field, Phys. Rev. Lett. 89, 157602 (2002).

[3] A. Musaelian, S. Batzner, A. Johansson, L. Sun, C. Owen, M. Kornbluth, and B. Kozinsky, Learning local equivariant representations for large-scale atomistic dynamics, Nat. Commun. 14, 579 (2023).   

Efficient ensemble averaging methods to study electronic structure at finite temperature from first principles calculations using neural network

Calculating electronic and lattice properties of materials at finite temperature in the presence of disorder and defects is important for data-driven design and discovery of materials. One of the current methods for calculating temperature dependent electronic structure of materials, within first principles calculations, is the use of perturbative Feynman diagram method which involves calculation of electron-phonon matrix elements and electronic self-energy corrections. An alternative non-perturbative approach which avoids the calculation of the electron-phonon matrix elements altogether is to perform configurational averaging over many nuclear supercell configurations. While easy to implement in first-principles code and possibly advantageous to explore effects beyond the harmonic regime, these methods require sampling over many extremely large supercells to get accurate results. In this work, we propose a rigorous group theory-based supervised machine learning (ML) method which can reduce the computational cost of such finite temperature calculations. We demonstrate that our Density functional theory+ML based approach, after appropriate training and neural network optimization, can i) reduce the number of DFT calculations necessary to perform ensemble average for a given temperature and ii) efficiently predict the temperature dependence of electronic band gap thereby making finite temperature electronic structure calculations computationally tractable.   

Predicting electron dynamics in proton-irradiated small molecules by recurrent neural networks

We demonstrate the application of recurrent neural networks toward learning the real-time electron dynamics of small organic molecules irradiated by fast protons. Real-time time-dependent density functional (RT-TDDFT) theory is a powerful method to capture full time dependence of electronic excitations due to motion of fast H+ ions (at the order of 1.0 Bohr velocity). However, the computational costs becomes prohibitively expensive with the combinatorial space of molecular targets, proton trajectories, and range of speeds. We show that the required number of RT-TDDFT simulations can be minimized by incrementally adding more speed-trajectory combinations selected by an active learning loop. Once trained, recurrent neural networks (RNNs) are able to predict the time dependent change in orbital occupation number with mean absolute errors of 0.04 electrons for speed-trajectory combinations not used in model training. The RNNs show a limited ability to extrapolate to molecular targets not included in the training set. Our approach developed in this work shows potential to vastly accelerate the study of time dependent electronic excitations by using RNN models to reduce the number of RT-TDDFT calculations required to fully examine irradiation processes. Furthermore, our approach opens the opportunity for future multi-scale simulations of electron-ion dynamics in molecules irradiated by ion beams.   

Efficient mapping of CO2RR intermediates adsorption energies on Cu1-xMx bimetallic alloys via Machine Learning

Electrochemical CO₂ reduction (CO₂RR) may decrease greenhouse effect while producing valuable C₂ chemicals like ethylene and ethanol, nevertheless achieving high selectivity remains challenging due to complex competing reactions occurring at the catalyst surface. Crucial to the formation of these molecules are the adsorption energies of CO and other reaction intermediates like H, O and OH. In this work, we used Machine Learning algorithms trained with Density Functional Theory data to predict the CO adsorption energies on Cu-based surfaces containing metal atom impurities. Classification algorithms were used to evaluate binding site stability, while regression models were employed to predict CO adsorption energies. Accuracy of the predictions was confirmed by F1 scores exceeding 98% in classification and MSE below 0.05 eV² in regression. This two-step analysis appeared to be robust also when employed to predict CO binding energies on Cu surfaces containing impurity concentrations up to six times higher than that used during the training phase. We are currently applying a similar approach to develop ML models to predict the binding of other adsorbates relevant to electrocatalysis such as H, O and OH. In this way, we aim at obtaining an in-depth understanding of the CO₂RR, enabling rapid evaluation of promising candidates for effective CO₂ reduction.   

Machine Learning with Semi-Empirical Quantum Mechanical Methods for Band Gap Prediction

Band gap predicted from the use of typical Density Functional Theory (DFT) functional are generally smaller than the true experimental gaps. Thus, there is a search for computational methods which can give accurate band gap predictions. There have been different studies which employed Machine Learning (ML) methods to predict the correct band gaps, or DFT combined with ML. In our work, we propose combining Machine Learning (ML) methods with semi-empirical quantum mechanical (SEQM) methods to predict the band gap of materials. Results using two SEQM parameterizations with ML will be presented. SEQM methods are usually computationally cheaper than DFT and, thus, our approach can achieve reasonable accuracy at only a fraction of the cost of DFT, DFT with ML, or DFT with hybrid functionals.