Systematically improved potential energy surfaces via sinNN models and sparse grid sampling.

Area of Science:

• Computational Chemistry
• Quantum Dynamics
• Theoretical Chemistry

Background:

• Accurate global potential energy surfaces (PESs) in sum-of-products (SOP) form are crucial for efficient high-dimensional quantum dynamics simulations.
• The multi-configuration time-dependent Hartree (MCTDH) method requires robust PESs for accurate simulations.

Purpose of the Study:

• To develop a novel methodology for constructing accurate, global PESs in SOP form.
• To enable efficient high-dimensional quantum dynamics simulations using the MCTDH method.
• To address the curse of dimensionality in PES construction.

Main Methods:

• Hierarchical sparse grid sampling for unbiased configuration space discretization.
• Single-layer neural networks with sinusoidal activation functions (sinNN) for PES fitting.
• Trigonometric factorization identity for maintaining compact SOP form and numerical stability.

Main Results:

• The methodology successfully constructs global PESs with controlled accuracy and systematic improvement.
• Refitting an analytical PES for nitrous acid (HONO) reproduced vibrational transition energies with spectroscopic precision (<2.5 cm-1).
• An AIQM2-based PES for HONO reproduced experimental vibrational frequencies with a root mean square deviation of ~16 cm-1, comparable to high-level ab initio methods.

Conclusions:

• The combination of sparse grid sampling and sinNN fitting is a powerful, automated tool for generating topologically sound, spectroscopic-quality PESs.
• The approach demonstrates robustness on larger molecules like formic acid and carbamic acid.
• This methodology significantly advances the field of quantum dynamics simulations by providing accurate and efficient PES construction.