# Wavelet Scattering Regression of Quantum Chemical Energies

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*Article:*

"**Wavelet Scattering Regression of Quantum Chemical Energies**"

Matthew Hirn, Stephane Mallat, Nicolas Poilvert

*Multiscale Modeling and Simulation, Volume 15, Number 2, Pages 827-863, 2 May 2017*

Link: http://epubs.siam.org/doi/abs/10.1137/16M1075454

**Abstract**

In this paper we introduce multiscale invariant dictionaries to estimate quantum chemical energies of organic molecules from training databases. Molecular energies are invariant to isometric atomic displacements and are Lipschitz continuous to molecular deformations. Similarly to density functional theory (DFT), the molecule is represented by an electronic density function. A multiscale invariant dictionary is calculated with wavelet scattering invariants. It cascades a first wavelet transform which separates scales with a second wavelet transform which computes interactions across scales. Sparse scattering regressions give state-of-the-art results over two databases of organic planar molecules. On these databases, the regression error is of the order of the error produced by DFT codes, but at a fraction of the computational cost.