SPA${}^{\mathrm{H}}$M: the Spectrum of Approximated Hamiltonian Matrices representations

Abstract

Physics-inspired molecular representations are the cornerstone of similarity-based learning applied to solve chemical problems. Despite their conceptual and mathematical diversity, this class of descriptors shares a common underlying philosophy: they all rely on the molecular information that determines the form of the electronic Schrödinger equation. Existing representations take the most varied forms, from non-linear functions of atom types and positions to atom densities and potential, up to complex quantum chemical objects directly injected into the ML architecture. In this work, we present the Spectrum of Approximated Hamiltonian Matrices (SPA${}^{\mathrm{H}}$M) as an alternative pathway to construct quantum machine learning representations through leveraging the foundation of the electronic Schrödinger equation itself: the electronic Hamiltonian. As the Hamiltonian encodes all quantum chemical information at once, SPA${}^{\mathrm{H}}$M representations not only distinguish different molecules and conformations, but also different spin, charge, and electronic states. As a proof of concept, we focus here on efficient SPA${}^{\mathrm{H}}$M representations built from the eigenvalues of a hierarchy of well-established and readily-evaluated "guess" Hamiltonians. These SPA${}^{\mathrm{H}}$M representations are particularly compact and efficient for kernel evaluation and their complexity is independent of the number of different atom types in the database.

arXiv comment9 pages + SI (8 pages)

References in corpus (26)

• Array Programming with NumPy
• On representing chemical environments
• Fast and Accurate Modeling of Molecular Atomization Energies with Machine Learning
• Deep Potential Molecular Dynamics: a scalable model with the accuracy of quantum mechanics
• Machine Learning Force Fields
• Intrinsic atomic orbitals: An unbiased bridge between quantum theory and chemical concepts
• Big Data meets Quantum Chemistry Approximations: The $\Delta$-Machine Learning Approach
• Physics-inspired structural representations for molecules and materials
• FCHL revisited: faster and more accurate quantum machine learning
• Alchemical and structural distribution based representation for improved QML
• Symmetry-Adapted Machine-Learning for Tensorial Properties of Atomistic Systems
• Equivariant message passing for the prediction of tensorial properties and molecular spectra
• Understanding molecular representations in machine learning: The role of uniqueness and target similarity
• OrbNet: Deep Learning for Quantum Chemistry Using Symmetry-Adapted Atomic-Orbital Features
• Accurate Interatomic Force Fields via Machine Learning with Covariant Kernels
• Machine Learning for Quantum Mechanical Properties of Atoms in Molecules
• Incorporating long-range physics in atomic-scale machine learning
• Learning physical descriptors for materials science by compressed sensing
• A fingerprint based metric for measuring similarities of crystalline structures
• OrbNet Denali: A machine learning potential for biological and organic chemistry with semi-empirical cost and DFT accuracy
• An assessment of initial guesses for self-consistent field calculations. Superposition of Atomic Potentials: simple yet efficient
• Recursive evaluation and iterative contraction of $N$-body equivariant features
• A new parametrizable model of molecular electronic structure
• Efficient implementation of the superposition of atomic potentials initial guess for electronic structure calculations in Gaussian basis sets
• Atomic Cluster Expansion: Completeness, Efficiency and Stability
• Atomic effective potentials for starting molecular electronic structure calculations

Cited by in corpus (7)

• Scalable Hybrid Deep Neural Networks/Polarizable Potentials Biomolecular Simulations including long-range effects
• 3DReact: Geometric deep learning for chemical reactions
• Advancing Molecular Machine Learning Representations with Stereoelectronics-Infused Molecular Graphs
• Exploring the design space of machine-learning models for quantum chemistry with a fully differentiable framework
• SPA${}^{\mathrm{H}}$M(a,b): encoding the density information from guess Hamiltonian in quantum machine learning representations
• Spectral Operator Representations
• Machine learning of electronic structure and atomistic properties from the external potential