Fast Near Ab Initio Potential Energy Surfaces Using Machine Learning

Abstract

A machine-learning based approach for evaluating potential energies for quantum mechanical studies of properties of the ground and excited vibrational states of small molecules is developed. This approach uses the molecular-orbital-based machine learning (MOB-ML) method to generate electronic energies with the accuracy of CCSD­(T) calculations at the same cost as a Hartree–Fock calculation. To further reduce the computational cost of the potential energy evaluations without sacrificing the CCSD­(T) level accuracy, GPU-accelerated Neural Network Potential Energy Surfaces (NN-PES) are trained to geometries and energies that are collected from small-scale Diffusion Monte Carlo (DMC) simulations, which are run using energies evaluated using the MOB-ML model. The combined NN+(MOB-ML) approach is used in variational calculations of the ground and low-lying vibrational excited states of water and in DMC calculations of the ground states of water, CH5 +, and its deuterated analogues. For both of these molecules, comparisons are made to the results obtained using potentials that were fit to much larger sets of electronic energies than were required to train the MOB-ML models. The NN+(MOB-ML) approach is also used to obtain a potential surface for C2H5 +, which is a carbocation with a nonclassical equilibrium structure for which there is currently no available potential surface. This potential is used to explore the CH stretching vibrations, focusing on those of the bridging hydrogen atom. For both CH5 + and C2H5 + the MOB-ML model is trained using geometries that were sampled from an AIMD trajectory, which was run at 350 K. By comparison, the structures sampled in the ground state calculations can have energies that are as much as ten times larger than those used to train the MOB-ML model. For water a higher temperature AIMD trajectory is needed to obtain accurate results due to the smaller thermal energy. A second MOB-ML model for C2H5 + was developed with additional higher energy structures in the training set. The two models are found to provide nearly identical descriptions of the ground state of C2H5 +.

Isotope Effects on Ground and Excited States of Ethyl Cation, H+(C2H4)

“…All of these spectral assignments and calculations relied on the premise that the ground state of the ethyl cation is localized in a single minimum on the potential surface. This is supported by our recently reported ground state diffusion Monte Carlo study of this ion, which employed a potential surface that was based on electronic energies evaluated at the CCSD­(T)/aug-cc-pVTZ level of theory/basis . On the basis of that work, the ground state wave function is localized in the minimum that corresponds to the nonclassical structure shown in Figure , and there is no evidence of proton scrambling in the ground state.…”

Trendbericht Theoretische Chemie 2023 (2/3): Berechnungen von Molekülschwingungen in der Thermodynamik

“…Abgesehen von Deskriptoren basierend auf der Kerngeometrie lässt sich zudem die Elektronenstruktur in den Trainingsdatensatz einbeziehen, zum Beispiel die Elektronendichte 7) oder die Molekülorbitale. 11) Auch können die Zielgrößen des maschinellen Lernens variiert werden, zum Beispiel können Frequenzen direkt -oder deren Abweichung vom Experiment 12) oder Verschiebung 7) -modelliert werden. Auch die Größen Energie, Kraft und Dipolmoment als Grundlage für die Spektrenberechnung von protonierten Wasserclustern wurden modelliert.…”

Topical Review: Extracting molecular frame photoionization dynamics from experimental data

“…Some recent use of ML/AI in the AMO context has proved successful, e.g. [117,118] tackle specific data-analysis and reconstruction type problems; [119,120] examine ML for ab initio computation of potential energy surfaces; [115] provides a broad review of ML in the physical sciences, including quantum state reconstruction, as well as particle physics, cosmology and materials science.…”