Machine learning of molecular electronic properties in chemical compound space

Montavon, Grégoire; Rupp, Matthias; Gobre, Vivekanand V.; Vázquez‐Mayagoitia, Álvaro; Hansen, Katja; Tkatchenko, Alexandre; Müller, Klaus‐Robert; Lilienfeld, O. Anatole von

doi:10.1088/1367-2630/15/9/095003

Cited by 632 publications

(731 citation statements)

References 62 publications

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“…[128] Although 10 kcal/mol is still far from ' 'chemical accuracy' ' (% 1 kcal/mol), more recent efforts have not only led to atomization errors with less than 3 kcal/mol accuracy, [129] but also include other electronic properties, such as frontier eigenvalues, polarizability, and excitation energies. [130] An appealing advantage of analytical models, independent if obtained from physical insight or statistical regression, is their amenability to analysis and interpretation. For example, otherwise ill-defined concepts in electronic structure theory, such as distance/neighborhood/similarity in CCS, can now be quantified within the ' 'world' ' of the ML model.…”

Section: Machine Learning In Ccs: the Quantum Machine Meets Schr€ Odimentioning

confidence: 99%

First principles view on chemical compound space: Gaining rigorous atomistic control of molecular properties

Lilienfeld

2013

Int J of Quantum Chemistry

139

160

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A well‐defined notion of chemical compound space (CCS) is essential for gaining rigorous control of properties through variation of elemental composition and atomic configurations. Here, we give an introduction to an atomistic first principles perspective on CCS. First, CCS is discussed in terms of variational nuclear charges in the context of conceptual density functional and molecular grand‐canonical ensemble theory. Thereafter, we revisit the notion of compound pairs, related to each other via “alchemical” interpolations involving fractional nuclear charges in the electronic Hamiltonian. We address Taylor expansions in CCS, property nonlinearity, improved predictions using reference compound pairs, and the ounce‐of‐gold prize challenge to linearize CCS. Finally, we turn to machine learning of analytical structure property relationships in CCS. These relationships correspond to inferred, rather than derived through variational principle, solutions of the electronic Schrödinger equation. © 2013 Wiley Periodicals, Inc.

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Section: Machine Learning In Ccs: the Quantum Machine Meets Schr€ Odimentioning

confidence: 99%

First principles view on chemical compound space: Gaining rigorous atomistic control of molecular properties

Lilienfeld

2013

Int J of Quantum Chemistry

139

160

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“…1 Alternatively, Kernel-Ridge-Regression (KRR) based machine learning (ML) models 2 can also infer the observable in terms of a linear expansion in chemical compound space. [3][4][5][6] More specifically, any observable can be estimated using O inf (M) =  N i α i k(d(M, M i )), where k is the kernel function (e.g., Laplacian with training set dependent width), M is the molecular representation (typically in matrix or vector format), 7,8 and d is a metric (often the L 1 -norm). The sum runs over all reference molecules i used for training to obtain regression weights {α i }.…”

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confidence: 99%

“…Panels (a) and (b) illustrate learning curves for ML models obtained for representations of varying target similarity applied to (a) modeling a 1-D Gaussian target function or (b) enthalpy of atomization for QM7b dataset. 8 Lines in (a) correspond to models resulting from linear, quadratic, and various exponential (e −x n with n = {1, 1.25, 1.75, 2, and 2.25}) representations. The inset shows the target function (red) as well as the representations.…”

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confidence: 99%

“…Finally, to place BAML into a broader perspective, we compare out-of-sample errors to Coulomb, London, and literature representation results all obtained for the same molecular data set, QM7b. 8 Table I displays MAEs and RMSEs of the M T based BAML model trained on 5k molecules, as well as London Matrix (LM), Coulomb Matrix (CM), BoB (bag of Coulomb matrix elements), bag of London (BoL) matrix elements, SOAP, 21 and randomized CM based neural network model. 8 The SOAP numbers correspond to a recently introduced sophisticated convolution of kernel, metric, and representation.…”

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confidence: 99%

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Communication: Understanding molecular representations in machine learning: The role of uniqueness and target similarity

Huang¹,

Lilienfeld²

2016

The Journal of Chemical Physics

306

342

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The predictive accuracy of Machine Learning (ML) models of molecular properties depends on the choice of the molecular representation. Based on the postulates of quantum mechanics, we introduce a hierarchy of representations which meet uniqueness and target similarity criteria. To systematically control target similarity, we rely on interatomic many body expansions, as implemented in universal force-fields, including Bonding, Angular, and higher order terms (BA). Addition of higher order contributions systematically increases similarity to the true potential energy and predictive accuracy of the resulting ML models. We report numerical evidence for the performance of BAML models trained on molecular properties pre-calculated at electron-correlated and density functional theory level of theory for thousands of small organic molecules. Properties studied include enthalpies and free energies of atomization, heatcapacity, zero-point vibrational energies, dipole-moment, polarizability, HOMO/LUMO energies and gap, ionization potential, electron affinity, and electronic excitations. After training, BAML predicts energies or electronic properties of out-of-sample molecules with unprecedented accuracy and speed.

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“…[11] Trained to reference datasets, ML models can predict energies, forces, and other molecular properties. [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27] They have been 3 used to discover materials [28][29][30][31][32][33][34][35][36][37] and study dynamical processes such as charge and exciton transfer. [38][39][40][41] Most related to this work are ML models of existing charge models, [9,[42][43][44] which are orders of magnitude faster than ab initio calculation.…”

mentioning

confidence: 99%

Discovering a Transferable Charge Assignment Model Using Machine Learning

Sifain¹,

Lubbers²,

Nebgen³

et al. 2018

Preprint

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Partial atomic charge assignment is of immense practical value to force field parametrization, molecular docking, and cheminformatics. Machine learning has emerged as a powerful tool for modeling chemistry at unprecedented computational speeds given ground-truth values, but for the task of charge assignment, the choice of ground-truth may not be obvious. In this letter, we use machine learning to discover a charge model by training a neural network to molecular dipole moments using a large, diverse set of CHNO molecular conformations. The new model, called Affordable Charge Assignment (ACA), is computationally inexpensive and predicts dipoles of out-of-sample molecules accurately. Furthermore, dipole-inferred ACA charges are transferable to dipole and even quadrupole moments of much larger molecules than those used for training. We apply ACA to long dynamical trajectories of biomolecules and successfully produce their infrared spectra. Additionally, we compare ACA with existing charge models and find that ACA assigns similar charges to Charge Model 5, but with a greatly reduced computational cost. Graphical TOC Entry Extensibility Tests Molecular Size Training DatasetKeywords machine learning, neural networks, quantum chemisty 2 Electrostatic interactions contribute strongly to the forces within and between molecules.These interactions depend on the charge density field ⇢(r), which is computationally demanding to compute. Simplified models of the charge density, such as atom-centered monopoles, are commonly employed. These partial atomic charges result in faster computation as well as provide a qualitative understanding of the underlying chemistry. [1][2][3][4] However, the decomposition of charge density into atomic charges is, by itself, an ambiguous task. Additional principles are necessary to make the charge assignment task well-defined. Here we show that a Machine Learning model, trained only on the dipole moments of small molecules, discovers a charge model that is transferable to quadrupole predictions and extensible to much larger molecules.Existing popular charge models have also been designed to reproduce observables of the electrostatic potential. The Merz-Singh-Kollman (MSK) [5,6] charge model exactly replicates the dipole moment and approximates the electrostatic potential on many points surrounding the molecule, resulting in high-quality electrostatic properties exterior to the molecule. However, MSK suffers from basis set sensitivity, particularly for "buried atoms" located inside large molecules. [7][8][9] Charge model 5 (CM5) [8] is an extension of Hirshfeld analysis, [10] with additional parametrization in order to approximately reproduce ab initio and experimental dipoles of 614 gas-phase dipoles. Unlike MSK, Hirshfeld and CM5 are nearly independent of basis set. [9] This insensitivity allows CM5 to use a single set of model parameters. The corresponding tradeoff is that its charges do not reproduce electrostatic fields as well as MSK.A limitation of these conventional charge models is...

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Machine learning of molecular electronic properties in chemical compound space

Cited by 632 publications

References 62 publications

First principles view on chemical compound space: Gaining rigorous atomistic control of molecular properties

First principles view on chemical compound space: Gaining rigorous atomistic control of molecular properties

Communication: Understanding molecular representations in machine learning: The role of uniqueness and target similarity

Discovering a Transferable Charge Assignment Model Using Machine Learning

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