Machine-Learning-Based Construction of Molecular Potential and Its Application in Exploring the Deep-Lying-Orbital Effect in High-Order Harmonic Generation

TL;DR

This paper introduces a machine learning method to construct accurate soft-Coulomb molecular potentials that capture multiple orbital features, enabling detailed analysis of deep-lying orbital effects in high-order harmonic generation.

Contribution

The study develops a novel ML-based approach to create molecular potentials that reproduce multiple orbital properties, enhancing analysis of complex laser-molecule interactions.

Findings

HOMO-1 influences the second HHG plateau

HHG spectra are affected by H-C distance changes

ML approach is applicable to other molecules and processes

Abstract

Creating soft-Coulomb-type (SC) molecular potential within single-active-electron approximation (SAE) is essential since it allows solving time-dependent Schr\"odinger equations with fewer computational resources compared to other multielectron methods. The current available SC potentials can accurately reproduce the energy of the highest occupied molecular orbital (HOMO), which is sufficient for analyzing nonlinear effects in laser-molecule interactions like high-order harmonic generation (HHG). However, recent discoveries of significant effects of deep-lying molecular orbitals call for more precise potentials to analyze them. In this study, we present a fast and accurate method based on machine learning to construct SC potentials that simultaneously reproduce various molecular features, including energies, symmetries, and dipole moments of HOMO, HOMO-1, and HOMO-2. We use this ML model to create SC SAE potentials of the HCN molecule and then comprehensively analyze the fingerprints of lower-lying orbitals in HHG spectra emitted during the H-CN stretching. Our findings reveal that HOMO-1 plays a role in forming the second HHG plateau. Additionally, as the H-C distance increases, the plateau structure and the smoothness of HHG spectra are altered due to the redistribution of orbital electron density. These results are in line with other experimental and theoretical studies. Lastly, the machine learning approach using deconvolution and convolution neural networks in the present study is so general that it can be applied to construct molecular potential for other molecules and molecular dynamic processes.