Solving the vibrational Schrödinger equation with artificial neural networks

Area of Science:

• Quantum Chemistry
• Computational Chemistry
• Machine Learning

Background:

• Artificial neural networks (ANNs) excel at approximating functions and computing electronic Schrödinger equation ground-state energies.
• However, ANNs have not been widely adopted for solving the vibrational Schrödinger equation in polyatomic molecules due to accuracy and practicality concerns.

Purpose of the Study:

• To propose an efficient neural network approach for solving the vibrational Schrödinger equation.
• To demonstrate the method's efficacy on methane and propane molecules.

Main Methods:

• Developed a novel neural network architecture for vibrational Schrödinger equation.
• Applied the method to methane for illustration and propane (11 atoms, 27 vibrational degrees of freedom) for validation.
• Compared results with diffusion Monte Carlo calculations and experimental data.

Main Results:

• Achieved ground-state energy for propane within 1 cm^-1 of diffusion Monte Carlo results using a neural network with <15,000 parameters.
• Vibrational energies for three excited states of propane agreed with experimental values within experimental uncertainties.
• The method shows high accuracy for complex molecular systems.

Conclusions:

• The proposed neural network approach offers an efficient and accurate solution for the vibrational Schrödinger equation.
• This method is expected to be highly effective for calculating vibrational energies and wavefunctions for molecules with over 20 atoms.