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

Aug 5, 2026

Constructing soft-Coulomb-type molecular potentials within the single-active-electron approximation enables efficient time-dependent Schrödinger equation simulations, provided the highest occupied molecular orbital (HOMO) is reproduced. Yet newly observed deep-lying orbital effects require potentials that also capture additional electronic features. This study develops a fast machine-learning approach to build SC SAE potentials that reproduce energies, symmetries, and dipole moments for HOMO, HOMO-1, and HOMO-2. Applied to HCN, it analyzes how lower-orbital fingerprints shape high-order harmonic generation spectra during H–C stretching, identifying HOMO-1 as important for the second HHG plateau and revealing plateau evolution with internuclear distance via electron-density redistribution. The method uses convolution and deconvolution neural networks and is designed to generalize to other molecules and dynamical processes.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages18

Reading Time45 min

AccessFree to download

Introduction

Laser–molecule strong-field phenomena and motivation

Role of lower-lying molecular orbitals in HHG

Need for reliable potential models beyond HOMO

Limitations of traditional optimization for molecules

arXiv :2408 . 12627v3 [physics .chem-ph] 14 Sep 2024 Machine-Learning-Based Construction of Molecular Potential ... Machine-Learning-Based Construction of Molecular Potential and Its Application in Exploring the Deep-Lying-Orbital Effect in High-Order Harmonic Generation Duong D. Hoang-Trong, 1 Khang Tran,2 Doan-An Trieu,1 Quan-Hao Truong,1 Ngoc-Hung Phan,1 Ngoc-Loan Phan,1 and Van-Hoang Le1 1) Computational Physics Key Laboratory K002, Department of Physics, Ho Chi Minh City University of Education, 280 An Duong Vuong Street, Ward 4, District 5, Ho Chi Minh City 72711, Vietnam 2) Department of Informatics, New Jersey Institute of Technology, Newark, NJ 07102, USA (Dated: September 17, 2024) Creating soft-Coulomb-type (SC) molecular potential within single-active-electron approximation (SAE) is essential since it allows solving time-dependent Schrödinger 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. I. INTRODUCTION Recent decades with advanced laser technologies have witnessed an enduring endeavor of strong-field physics, focusing on the interaction of matter and intense laser field1–3. It has led to the discovery and celebration of various highly nonlinear phenomena, including high-order harmonic generation (HHG), above-threshold ionization (ATI), high-energy ATI (HATI), and non-sequential double ionization (NSDI)4–8. These nonlinear phenomena have sparked great interest due to their potential applications in generating extraordinary coherent XUV and even soft X-ray radiations, producing single attosecond pulses or attosecond pulse trains, as well as enabling time-resolved imaging and probing of dynamics inside atoms and molecules1–3,9–13 . Given their promising applications, it is crucial to accurately interpret experimental observations and understand the underlying physics, that necessitates precise theoretical descriptions of these nonlinear phenomena. One common approach is directly solving the time-dependent Schrödinger equation (TDSE) of a specific atomic or molecular potential model, ensuring the asymptotic behavior of the wave functions14–18. The potential model is often parameterized as an analytical expression of the soft-Coulomb-type (SC) potential with one or a few parameters16–21. Constructing a potential that matches experimental observations or fully quantum ab initio simulations is a challenging but not trivial task due to its high coherence and nonlin- earity19,22–24 . Most atomic or molecular potential models require the energy of the highest occupied molecule orbital (HOMO) to mimic that of a

FAQs

Why is constructing soft-Coulomb-type molecular potentials important in single-active-electron simulations?

It allows time-dependent Schrödinger equation calculations with fewer computational resources. Accurate soft-Coulomb-type potentials enable modeling nonlinear laser–molecule interactions such as high-order harmonic generation.

What does the proposed machine-learning method reproduce for multiple orbitals?

The method constructs potentials that simultaneously match energies, symmetries, and dipole moments for HOMO, HOMO-1, and HOMO-2.

What key effect is found for HCN in high-order harmonic generation spectra during H–C stretching?

The results show that HOMO-1 contributes to forming the second HHG plateau, and increasing the H–C distance changes the plateau structure and spectral smoothness due to redistribution of orbital electron density.

Aug 5, 2026

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