Permutationally Invariant, Reproducing Kernel-Based Potential Energy Surfaces for Polyatomic Molecules: From Formaldehyde to Acetone

Abstract

Constructing accurate, high dimensional molecular potential energy surfaces (PESs) for polyatomic molecules is challenging. Reproducing Kernel Hilbert space (RKHS) interpolation is an efficient way to construct such PESs. However, the scheme is most effective when the input energies are available on a regular grid. Thus the number of reference energies required can become very large even for penta-atomic systems making such an approach computationally prohibitive when using high-level electronic structure calculations. Here an efficient and robust scheme is presented to overcome these limitations and is applied to constructing high dimensional PESs for systems with up to 10 atoms. Using energies as well as gradients reduces the number of input data required and thus keeps the number of coefficients at a manageable size. Correct implementation of permutational symmetry in the kernel products is tested and explicitly demonstrated for the highly symmetric CH${}_4$ molecule.

arXiv comment40 pages, 13 Figures

References in corpus (20)

• ANI-1: An extensible neural network potential with DFT accuracy at force field computational cost
• Kernel methods in machine learning
• Machine Learning of Accurate Energy-Conserving Molecular Force Fields
• PhysNet: A Neural Network for Predicting Energies, Forces, Dipole Moments and Partial Charges
• Towards Exact Molecular Dynamics Simulations with Machine-Learned Force Fields
• Machine Learning Molecular Dynamics for the Simulation of Infrared Spectra
• 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
• sGDML: Constructing Accurate and Data Efficient Molecular Force Fields Using Machine Learning
• Long-range vs. short-range effects in cold molecular ion-neutral collisions: Charge exchange of Rb with N${}_2^{+}$ and O${}_2^{+}$
• Scattering resonances in slow NH${}_3$-He collisions
• High-Dimensional Potential Energy Surfaces for Molecular Simulations
• The $\mathrm{N}{(}^{4}S)+{\mathrm{O}}_2(X^3{\Sigma }_g^{-})\leftrightarrow \mathrm{O}{(}^{3}P)+\mathrm{NO}(X^2\Pi )$ Reaction: Thermal and Vibrational Relaxation Rates for the ${}^2$A${}^{\prime }$, ${}^4$A${}^{\prime }$ and ${}^2$A${}^{\prime \prime }$ States
• Accurate Reproducing Kernel-Based Potential Energy Surfaces for the Triplet Ground States of N${}_2$O and Dynamics for the N+NO$\leftrightarrow$O+N${}_2$ and N${}_2$+O$\to$2N+O Reactions
• Near dissociation states for H${}_2^{+}$-He on MRCI and FCI potential energy surfaces
• ML Models of Vibrating H${}_2$CO: Comparing Reproducing Kernels, FCHL and PhysNet
• Isomerization and Decomposition Reactions of Acetaldehyde Relevant to Atmospheric Processes from Dynamics Simulations on Neural Network-Based Potential Energy Surfaces
• Formation and Stabilization of Ground and Excited State Singlet O${}_2$ upon Recombination of ${}^3$P Oxygen on Amorphous Solid Water
• N${}_3^{+}$: Full-Dimensional Potential Energy Surface, Vibrational Energy Levels and Ground State Dynamics

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