Implicitly perturbed Hamiltonian as a class of versatile and general-purpose molecular representations for machine learning

Abstract

Unraveling challenging problems by machine learning has recently become a hot topic in many scientific disciplines. For developing rigorous machine-learning models to study problems of interest in molecular sciences, translating molecular structures to quantitative representations as suitable machine-learning inputs play a central role. Many different molecular representations and the state-of-the-art ones, although efficient in studying numerous molecular features, still are suboptimal in many challenging cases, as discussed in the context of the present research. The main aim of the present study is to introduce the Implicitly Perturbed Hamiltonian (ImPerHam) as a class of versatile representations for more efficient machine learning of challenging problems in molecular sciences. ImPerHam representations are defined as energy attributes of the molecular Hamiltonian, implicitly perturbed by a number of hypothetic or real arbitrary solvents based on continuum solvation models. We demonstrate the outstanding performance of machine-learning models based on ImPerHam representations for three diverse and challenging cases of predicting inhibition of the CYP450 enzyme, high precision, and transferrable evaluation of non-covalent interaction energy of molecular systems, and accurately reproducing solvation free energies for large benchmark sets.

Theoretical Evaluation of Radii of Atoms in Molecules and their Dependence on Atomic Partial Charge

“…They range from the classical example of Lennard-Jones interactions suggesting van der Waals (vdW) attraction and Pauli repulsion interactions to be proportional to 6 th and 12 th power of atomic radii [5], respectively, to a more recent theoretical demonstration of a linear relationship between atomic polarizability and the seventh power of atomic radii [6]. Similarly, the successful advancements in the theoretical treatment of solvation effects in molecular systems via continuum solvation models strongly rely on defining a solute cavity occupied by the solute molecule constructed via tailored atomic radii [7][8][9][10].…”

On the Theoretical Quantification of Radii of Atoms in Molecules

“…These include inter- and intramolecular interaction energies ranging from van der Waals (vdW) interactions, as evident in the classical example of Lennard-Jones potentials suggesting dispersion attraction and exchange repulsion to be proportional to 6th and 12th power of atomic radii, respectively, to a more recent theoretical work showing that the atomic polarizability is proportional to the 7th power of the atomic radius . The advancements in the theoretical treatment of solvation effects via continuum solvation models strongly rely on a proper definition of a solute cavity constructed with tailored atomic radii. − Molecular bonding, reactivity, and stability are other quantities strongly influenced by atomic radii. − …”

Comparison of Implicit and Explicit Solvent Approaches in Ab Initio Evaluation of Thermochemistry in Solution: Application in Studying Boron Isotope Fractionation in Water

“…When solvent effects need to be included in theoretical studies of the solution phase, the two major approaches in computational chemistry are the explicit and implicit one. Based on the explicit solvent approaches, the solute molecule is placed in a cluster of explicitly defined solvent molecules, while according to the implicit solvent approaches, the solute is placed in a cavity of a continuous medium that models the solvent allowing to achieve reasonable accuracy for remarkably reduced computational costs compared to explicit solvent approaches. − Each one of these approaches has its own pros and cons.…”