We describe a machine learning approach to approximate reaction energy barriers (E), requiring as input only estimates of geometry and energies of reactants and products. Using the dataset of Grambow, Pattanaik, and Green [Sci. Data 7 (1 3 7) (2020)] for reactions involving seven or fewer non-hydrogen atoms, 300 reaction features are computed, and an estimate of E is obtained by fitting a Kernel Ridge Regression (KRR) model with Laplacian kernel to a subset of Density Functional Theory reaction barriers. Our main interest is small energy barriers with the goal of modeling reactions in the interstellar medium and circumstellar envelope. We omitted reactions with E > 40 kcal mol−1 to obtain a subset of 5,276 reactions for 5-fold cross-validation. For this set, the KRR model predicts E with a mean absolute error of 4.13 kcal mol−1 and a root-mean square error of 6.02 kcal mol−1.
Melting Transitions in Small Aluminum Clusters Simulated with Energies Approaching DFT Accuracy.
(2025)
We describe a computational framework for modelling melting-like transitions in atomic clusters that combines first-principles energy calculations, global optimization, and machine-learned interatomic potentials. A diverse set of configurations is generated by global optimization, and energies are calculated by Density Functional Theory. The energies are fitted to an accuracy of 10 meV/atom or better with an Allegro E(3)-equivariant neural network potential. The model allows efficient parallel tempering Monte Carlo simulations with near DFT-level accuracy. This methodology was validated by simulating Na_20 and comparing it to earlier experimental and computational results. We used it to study melting-like transitions in Al_n+ clusters (n=9 to 16), and Al_n and Al_n^- (n=12, 13,14). The simulated heat capacity of these clusters, in particular Al_16+, are in qualitative agreement with experiments.
The melting point of Al_n+ clusters with n=11-16 are well above the bulk melting point (934 K). The closed-shell Al_13- species has an exceptionally high melting point, close to 2100 K.
Melting-like transitions in clusters are normally identified by a peak in the heat capacity curve C(T ) at T = Tc. Computing C(T ) requires costly simulations with millions of steps. We discuss four easily calculated functions of temperature that help detect and characterize melting-like transitions. The first, f1 (or WU ), is the width of the potential energy distribution which shows an abrupt increase near Tc. The other three are statistics of the ordered set of N(N − 1)/2
interatomic distances rij: (i) f2 is a measure of dissimilarity to the lowest energy configuration, or global minimum; (ii) f3 is the effective number of rij’s found in a small interval centered around (r1 + r2)/2 where r1, r2 are the positions of the first two peaks in the pair distribution function; and (iii) f4 is a measure of non-uniformity in the distribution of the
ri j’s. Numerical tests with empirical potentials that model three types of bonding (van der Waals, covalent, and metallic) show that f1, f2, f3, and f4 produce estimates for the middle of the melting region in general agreement with Tc. An Artificial Neural Network (ANN) classifier that takes, as inputs, f2, f3, and many variants of f4, is used to calculate the solid fraction FS(T) and find the solid-liquid coexistence region between freezing and melting temperatures, [Tf , Tm]. Inflection points in f3(T ) and FS(T ) are very sensitive indicators of phase transitions. Estimates of Tc obtained from them converge one to three orders of magnitude faster, in simulation time, than those obtained with C(T ).
Life as we know it is the result of billions of years of evolution; yet, understanding how the very first organisms came into existence is a challenge that has yet to be solved. One theory states that components of the first biotic molecules may not have formed on Earth. Rather, they may have initially formed in the interstellar medium (ISM) and been transported to Earth, as supported by recorded instances of organic molecules detected in space. The ISM, with its low temperatures and specific collision processes, allows for molecular stability and the formation of biotic precursors that would otherwise be unlikely in Earth's prebiotic conditions. Understanding how these molecules formed in the ISM may be the key to determining how life began.
The goal of this research is to develop a new model for solving astrobiophysical problems by studying the formation mechanisms of biomolecules found in the ISM. Although such pathways have been studied individually, there has not yet been a comprehensive method to understand all the formation reactions that can occur in ISM. Several quantum chemical and numerical methods are available for finding transition states (TS) and energy barriers (E) of chemical reactions but are time-consuming and can hardly be applied to systems with more than a few atoms. Our main interest is to develop a a machine learning approach to approximate TS, and E, requiring as input only estimates of geometry and energies of reactants and products. Using a complete dataset 300 reaction features are computed, and an estimate of E is obtained by fitting a Kernel Ridge Regression (KRR) model with Laplacian kernel, and a fully connected Artificial Neural Network (ANN) to estimate reaction energy barriers.
Understanding the Origins of Life - A Machine learning approach to estimate reaction mechanisms of biotic precursors. Life as we know it is the result of billions of years of evolution; however, understanding how the very first organisms came into existence is a challenge that has yet to be solved. One theory states that components of these molecules may have formed in the interstellar medium (ISM) and been transported to Earth. The ISM, with its specific conditions, allows for molecular stability and the formation of biotic precursors that would otherwise be unlikely in Earth's prebiotic conditions. Understanding how these molecules formed in the ISM may be the key to determining how life began. The goal of this research is to develop a model for solving astrobiophysical problems by studying the formation mechanisms of biomolecules found in the ISM. Although such pathways have been studied individually, there has not yet been a comprehensive method to understand the complete reactions mechanisms. Several QM methods are available for finding transition states (TS) and energy barriers (E) of chemical reactions but are time-consuming and can hardly be applied to more complex systems. Our interest is to develop a machine learning approach to approximate TS, and E, requiring as input only estimates of geometry and energies of reactants and products.
The discovery of molecules in the interstellar medium (ISM) plays a key role in understanding prebiotic chemistry. Relatively few (∼250) molecules have been confirmed in the ISM, and detecting additional species is crucial for expanding our knowledge of astrochemical processes. We present a strategy for predicting possible prebiotic molecules in the ISM that combines machine learning and high-accuracy quantum chemistry calculations. Using a reaction dataset of over 153,000 possible combinations of known interstellar molecules, we applied a machine learning model to estimate reaction energy barriers and identify those with low or zero barriers that are most likely to occur in the ISM. From this screening process, 24 molecules were identified, five of which have already been observed in interstellar space. For the remaining 19 molecules, we conducted density functional theory (DFT) and coupled cluster theory calculations to determine the most stable conformers, spectroscopic parameters, and predict their detectability through spectroscopy. We present data to guide future observational searches for new interstellar species, contributing to the ongoing exploration of complex organic molecules in space and their potential role in prebiotic chemistry.
We present a computational approach for screening reaction mechanisms with machine learning estimates of energy barriers. A comprehensive screening of thousands of reactions identified the CH2 reactions with HCNO and HNCO as possible sources of relatively complex organic molecules in space. We report detailed reaction mechanisms, including TS, intermediate, and product energies, calculated with density functional theory and coupled cluster theory. Singlet CH2, located 9 kcal/mol above the triplet ground state, reacts with HCNO or HNCO without a barrier, producing four prod11 ucts: CH2NCHO, N-methyleneformamide, the thermodynamically favored product; NHCHCHO, imine acetaldehyde; NHCHOCH; and (CH2OC)NH, oxiran-2-ylazanide. The lowest energy pathway for CH2 + HCNO, involving a triplet-to-singlet crossing,
has a barrier of 8 kcal/mol and leads to N -methyleneformamide, imine acetaldehyde, and NHCHOCH. The reaction of triplet CH2 with HNCO has a lowest energy pathway with a barrier of 11 kcal/mol, yielding CH2(CO)NH.