Abstract
We introduce a representation of any atom in any chemical environment for the automatized generation of universal kernel ridge regression-based quantum machine learning (QML) models of electronic properties, trained throughout chemical compound space. The representation is based on Gaussian distribution functions, scaled by power laws and explicitly accounting for structural as well as elemental degrees of freedom. The elemental components help us to lower the QML model's learning curve, and, through interpolation across the periodic table, even enable "alchemical extrapolation" to covalent bonding between elements not part of training. This point is demonstrated for the prediction of covalent binding in single, double, and triple bonds among main-group elements as well as for atomization energies in organic molecules. We present numerical evidence that resulting QML energy models, after training on a few thousand random training instances, reach chemical accuracy for out-of-sample compounds. Compound datasets studied include thousands of structurally and compositionally diverse organic molecules, non-covalently bonded protein side-chains, (H2O)40-clusters, and crystalline solids. Learning curves for QML models also indicate competitive predictive power for various other electronic ground state properties of organic molecules, calculated with hybrid density functional theory, including polarizability, heat-capacity, HOMO-LUMO eigenvalues and gap, zero point vibrational energy, dipole moment, and highest vibrational fundamental frequency.
Highlights
Ground-state properties of chemical compounds can generally be estimated with acceptable accuracy using methods such as ab initio quantum chemistry or density functional theory (DFT).1 these can be computationally expensive and have a limited applicability, especially for larger systems
Using learning curves, we first present numerical results which indicate the predictive power of our quantum machine learning (QML) model for atomization and formation energies in various datasets
We have introduced a universal representation of an atom in a chemical compound for use in QML models
Summary
Ground-state properties of chemical compounds can generally be estimated with acceptable accuracy using methods such as ab initio quantum chemistry or density functional theory (DFT). these can be computationally expensive and have a limited applicability, especially for larger systems. Ground-state properties of chemical compounds can generally be estimated with acceptable accuracy using methods such as ab initio quantum chemistry or density functional theory (DFT).. Ground-state properties of chemical compounds can generally be estimated with acceptable accuracy using methods such as ab initio quantum chemistry or density functional theory (DFT).1 These can be computationally expensive and have a limited applicability, especially for larger systems. We can represent a compound as a list of interatomic potentials.7–9 Another approach consists of creating a fingerprint of the compound, transforming internal coordinates into a fixed set of numbers. Distributions of internal coordinates represent another systematic approach, shown to yield well performing QML models applicable throughout chemical space.. Compositional information is encoded directly into the distributions This allows measuring structural differences and “alchemical” differences between elements in the atomic environments. This particular combination combines similarity to the potential energy target function and compliance with many known (translational, rotational, permutational) invariances
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