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Bottom-up methods for coarse-grained (CG) molecular modeling are critically needed to establish rigorous links between atomistic reference data and reduced molecular representations. For a target molecule, the ideal reduced CG representation is a function of both the conformational ensemble of the system and the target physical observable(s) to be reproduced at the CG resolution. However, there is an absence of algorithms for selecting CG representations of molecules from which complex properties, including molecular electronic structure, can be accurately modeled. We introduce continuously gated message passing (CGMP), a graph neural network (GNN) method for atomically decomposing molecular electronic structure sampled over conformational ensembles. CGMP integrates 3D-invariant GNNs and a novel gated message passing system to continuously reduce the atomic degrees of freedom accessible for electronic predictions, resulting in a one-shot importance ranking of atoms contributing to a target molecular property. Moreover, CGMP provides the first approach by which to quantify the degeneracy of “good” CG representations conditioned on specific prediction targets, facilitating the development of more transferable CG representations. We further show how CGMP can be used to highlight multiatom correlations, illuminating a path to developing CG electronic Hamiltonians in terms of interpretable collective variables for arbitrarily complex molecules.

 

We employ deep kernel learning electronic coarse-graining (DKL-ECG) with approximate Gaussian processes as a flexible and scalable framework for learning heteroscedastic electronic property distributions as a smooth function of coarse-grained (CG) configuration. The appropriateness of the Gaussian prior on predictive CG property distributions is justified as a function of CG model resolution by examining the statistics of target distributions. The certainties of predictive CG distributions are shown to be limited by CG model resolution with DKL-ECG predictive noise converging to the intrinsic physical noise induced by the CG mapping operator for multiple chemistries. Further analysis of the resolution dependence of learned CG property distributions allows for the identification of CG mapping operators that capture CG degrees of freedom with strong electron–phonon coupling. We further demonstrate the ability to construct the exact quantum chemical valence electronic density of states (EDOS), including behavior in the tails of the EDOS, from an entirely CG model by combining iterative Boltzmann inversion and DKL-ECG. DKL-ECG provides a means of learning CG distributions of all-atom properties that are traditionally “lost” in CG model development, introducing a promising methodological alternative to backmapping algorithms commonly employed to recover all-atom property distributions from CG simulations. 

A series of molecular rotors was designed to study and measure the rate accelerating effects of an intramolecular hydrogen bond. The rotors form a weak neutral O–H/O]C hydrogen bond in the planar transition state (TS) of the bond rotation process. The rotational barrier of the hydrogen bonding rotors was dramatically lower (9.9 kcal mol
1) than control rotors which could not form hydrogen bonds. The magnitude of the stabilization was significantly larger than predicted based on the independently measured strength of a similar OH/OC hydrogen bond (1.5 kcal mol-1). The origins of the large transition state stabilization were studied via experimental substituent effect and computational perturbation analyses. Energy decomposition analysis of the hydrogen bonding interaction revealed a significant reduction in the repulsive component of the hydrogen bonding interaction. The rigid framework of the molecular rotors positions and preorganizes the interacting groups in the transition state. This study demonstrates that with proper design a single hydrogen bond can lead to a TS stabilization that is greater than the intrinsic interaction energy, which has applications in catalyst design and in the study of enzyme mechanisms.