Accurate Prediction of Three-Body Intermolecular Interactions via Electron Deformation Density-Based Machine Learning

Abstract

This work extends the electron deformation densitybased descriptor, originally developed in the electron deformation density-based interaction energy machine learning (EDDIE-ML) algorithm to predict dimer interaction energies, to the prediction of three-body interactions in trimers. Using a sequential learning process to select the training data, the resulting Gaussian process regression (GPR) model predicts the three-body interaction energy within 0.2 kcal mol −1 of the SRS-MP2/cc-pVTZ reference values for the 3B69 and S22-3 trimer data sets. A hybrid kernel function is introduced, which combines contributions from the average and individual atomic environments, allowing the total trimer interaction energy to be predicted in addition to the three-body contribution using the same descriptor. To extend the range and diversity of trimer interaction energies available in the literature, a new data set based on a protein−ligand crystal structure is introduced, consisting of 509 structures of a central ligand with two protein fragments. Benchmark calculations are provided for the new data set, which contains significantly larger molecular interactions than current databases in the literature in addition to charged fragments. Compared to density funtional theory (DFT)-and wavefunction-based methods for calculating the three-body interaction energy, our model makes predictions in a significantly shorter time frame by reducing the number of required SCF calculations from 7 to 4 performed at the PBE0 level of theory, showcasing the utility and efficiency of our Δ-ML method particularly when applied to larger systems.

Repurposing quantum chemical descriptor datasets for on-the-fly generation of informative reaction representations: application to hydrogen atom transfer reactions

“…One potential approach to improve the data efficiency of machine learning models is introducing domain knowledge about the underlying physics/quantum chemistry into the model. Models starting from physically meaningful input representations, i.e., representations based on quantum mechanical (QM) reactivity descriptors, have been demonstrated to reach reasonable accuracy for datasets consisting of only a couple hundred or a few thousand data points, [9][10][11][12][13][14][15][16][17][18] and they have been reported to be signicantly more generalizable, i.e., they are signicantly more accurate in out-of-sample predictions, than conventional, structure/graph-based, analogs. 11,12,19 Unfortunately, QM descriptors tend to be computationally expensivesince they typically involve an elaborate workow consisting of conformer generation, geometry optimization and nally a single-point density functional theory (DFT) calculation for each unique moleculelimiting their applicability in broad virtual screening campaigns.…”

“…Models starting from physically meaningful input representations, i.e. , representations based on quantum mechanical (QM) reactivity descriptors, have been demonstrated to reach reasonable accuracy for datasets consisting of only a couple hundred or a few thousand data points, 9–18 and they have been reported to be significantly more generalizable, i.e. , they are significantly more accurate in out-of-sample predictions, than conventional, structure/graph-based, analogs.…”

Can we quantitatively evaluate the mutual impacts of intramolecular metal–ligand bonds the same as intermolecular noncovalent bonds?

“…1 There are some well-known methodologies for the evaluation of the cooperativity of noncovalent bonds and the calculation of related cooperative energies. The following equations have been frequently used for the evaluation of the cooperativity of coinage-metal bonds with other types of interactions 2–13 and also that of intermolecular noncovalent bonds, especially those including hydrogen bonds, 14–25 dihydrogen bonds, 26–28 beryllium bonds, 29,30 lithium bonds, 31–34 lithium–π, 35 halogen bonds, 36–48 chalcogen bonds, 49–51 pnicogen bonds, 52–56 cation–π interactions, 57–60 anion–π interactions, 61–63 π⋯π interactions, 64 σ -hole 65,66 and π -hole 67–70 interactions in ternary systems. Δ ABC = IE total ABC − (IE ABC A–B + IE ABC B–C + IE ABC A–C ) E coop = SE ABC − (SE AB + SE BC + SE ABC AC ) E coop = SE ABC − (SE AB + SE BC )In the above equations, Δ ABC and E coop correspond to the three-body term 71–77 and cooperative energy, respectively. The term IE total ABC is used for the value of the total interaction energy of the ABC system, and the terms IE ABC AB , IE ABC BC and IE ABC AC are used for pairwise interaction energies in the structure of the ABC system.…”

“…In the above equations, D ABC and E coop correspond to the threebody term [71][72][73][74][75][76][77] and cooperative energy, respectively. The term IE total ABC is used for the value of the total interaction energy of the ABC system, and the terms IE ABC AB , IE ABC BC and IE ABC AC are used for pairwise interaction energies in the structure of the ABC system.…”

Accurate three-body noncovalent interactions: the insights from energy decomposition

“…Their study focuses on investigating and quantitatively estimating the many-body dispersion effects for different bonding motifs in molecular clusters, and the trimers have 1-2 types of nonequivalent monomers (thus, they are of either the AAA or AAB type). More recently, Low et al 27 combined the 3B-69 and S22(3) datasets with a larger, 509-trimer collection extracted from an enzyme-inhibitor complex to develop a machine learning approach to predict three-body interaction energies. This new collection involves trimers that are heteromolecular and also larger (up to 77 atoms), but the reference interaction energies were only computed with a tailored version of the spin-component-scaled MP2 approach 28 and it is not entirely clear if they all are of benchmark CCSD(T) quality.…”