Wavelet Scattering Regression of Quantum Chemical Energies
This provides a computationally efficient alternative to DFT for quantum chemical energy estimation in organic planar molecules, though it is incremental as it builds on wavelet scattering and sparse regression techniques.
The paper tackles the problem of estimating quantum chemical energies of organic molecules by introducing multiscale invariant dictionaries, achieving regression errors comparable to density functional theory (DFT) codes but at a fraction of the computational cost.
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.