Massive Assessment of the Binding Energies of Atmospheric Molecular Clusters

Abstract

Quantum chemical studies of the formation and growth of atmospheric molecular clusters are important for understanding aerosol particle formation. However, the search for the lowest free-energy cluster configuration is extremely time consuming. This makes high-level benchmark data sets extremely valuable in the quest for the global minimum as it allows the identification of costefficient computational methodologies, as well as the development of high-level machine learning (ML) models. Herein, we present a highly versatile quantum chemical data set comprising a total of 11 749 (acid) 1−2 (base) 1−2 cluster configurations, containing up to 44 atoms. Utilizing the LUMI supercomputer, we calculated highly accurate PNO-CCSD(F12*)(T)/cc-pVDZ-F12 binding energies of the full set of cluster configurations leading to an unprecedented data set both in regard to sheer size and with respect to the level of theory. We employ the constructed benchmark set to assess the performance of various semiempirical and density functional theory methods. In particular, we find that the r 2 -SCAN-3c method shows excellent performance across the data set related to both accuracy and CPU time, making it a promising method to employ during cluster configurational sampling. Furthermore, applying the data sets, we construct ML models based on Δ-learning and provide recommendations for future application of ML in cluster configurational sampling.

Clusterome: A Comprehensive Data Set of Atmospheric Molecular Clusters for Machine Learning Applications

“…MD Simulation Method. The AM1 and PM3 methods do not accurately describe the interaction for simple systems such as the (SA) 1 (AM) 1 cluster (see also the results in Jensen et al 33 ) and MD simulations with these methods lead to dissociation within a few nanoseconds for these clusters (see Figure S1). Hence, we discarded the AM1 and PM3 methods from further examination.…”

“…Although r 2 SCAN-3c is extremely fast compared to other DFT methods, using it for MD simulations for all clusters, which contain up to 42 atoms, is still computationally expensive and slow. Therefore, in this work, we use GFN1-xTB for further MD simulations, and we define the r 2 SCAN-3c method as the high level of theory, as suggested by Jensen et al 33 We performed MD simulations, at the GFN1-xTB level, around each (SA) 1 (AM/DMA) 1 and (SA) 2 (AM/DMA) 2 equilibrium structure to generate up to 30 out-of-equilibrium structures for each cluster. For technical details, see Section S4.…”

“…In this work, we use the KRR method and the FCHL19 molecular representation, which showed excellent results for water clusters and atmospherically relevant clusters. ,, All mathematical scripts can be found within the quantum machine learning (QML) program, which we interfaced with our own Jammy Key for Machine Learning (JKML [part of JKCS] ) scripts that handle file management and automatizes the procedure. For kernel ridge regression with a local representation, it is assumed that a molecular property scriptM ( i ) (energy in our case) of a molecular system target i can be written as a sum of atomic contributions. scriptM ( i ) = prefix∑ B ∈ i scriptM local ( q B ) = prefix∑ B ∈ i ∑ j ∑ A ∈ j scriptK ( q A , q B ) α j where A and B are atoms in the target i and the trained system j , respectively, q is the molecular representation of the system, α j is the regression coefficients for the training system j , and scriptK ( q A , q B ) are the pairwise kernels between the atoms in the two molecules.…”

“…Using ML models, one can train a property of interest, such as electronic energy, on a training set of molecular representations and then predict the same properties for a new structure. − However, several studies showed that the performance of Δ-ML models where the training and prediction are done on the difference between two methods consistently outperforms the ‘direct-ML’ models in predicting the property of interest. − For instance, Kubečka et al used Δ-ML between the GFN1-xTB and ωB97X-D/6-31++G­(d,p) methods to predict sulfuric acid–water cluster binding energies with mean absolute errors down to 0.5 kcal/mol. To train a proper ML model, a representative database is required.…”

Limited Role of Malonic Acid in Sulfuric Acid–Dimethylamine New Particle Formation

“…The evaporation probabilities are calculated from the balance equation and cluster binding free energies obtained from quantum chemical calculations . The structures and energies of the SA–DMA clusters were taken from Kubečka et al The remaining clusters containing one MaA were constructed through the same configurational sampling protocol, and the binding free energies were evaluated at the same level of theory (i.e., DLPNO–CCSD­(T) − /aug-cc-pVTZ//ωB97X-D/6-31++G­(d,p)) and using the same computational software (i.e., ABCluster, , XTB, , Gaussian, and ORCA. , The DLPNO–CCSD­(T)/aug-cc-pVTZ//ωB97X-D/6-31++G­(d,p) level of theory has been thoroughly benchmarked both with regards to the structures , and binding energies. , This methodology is generally recommended for atmospheric cluster formation studies by our group and others . More technical details are given in Kubečka et al The identified structure coordinates and binding free energies of all clusters are presented in SI-4.…”