Neural canonical transformations for vibrational spectra of molecules

Abstract

The behavior of polyatomic molecules around their equilibrium positions can be regarded as that of quantum-coupled anharmonic oscillators. Solving the corresponding Schrödinger equations enables the interpretation or prediction of the experimental spectra of molecules. In this study, we developed a novel approach for solving the excited states of anharmonic vibrational systems. The normal coordinates of the molecules are transformed into new coordinates through a normalizing flow parameterized by a neural network. This facilitates the construction of a set of orthogonal many-body variational wavefunctions. This methodology has been validated on an exactly solvable 64-dimensional coupled harmonic oscillator, yielding numerical results with a relative error of 10−6. The neural canonical transformations are also applied to calculate the energy levels of two specific molecules, acetonitrile (CH3CN) and ethylene oxide (C2H4O). These molecules involve 12 and 15 vibrational modes, respectively. A key advantage of this approach is its flexibility concerning the potential energy surface, as it requires no specific form. Furthermore, this method can be readily implemented on large-scale distributed computing platforms, making it easy to extend to investigating complex vibrational structures.