Electronic excitation spectra and recovery of excited states with neural network wave functions

Abstract

Accurate electronic spectra require both a flexible description of electron correlation and a tractable treatment of the many states contributing to the response. We combine neural network wave functions with the Lorentz integral transform to calculate electronic spectra directly in continuous coordinates, without truncation error from a fixed one-electron basis and with polynomial computational cost per optimization step. Instead of constructing a prescribed set of excited states, the method solves an inhomogeneous Schr\"odinger equation at a chosen complex energy. This formulation gives access, in principle, to the entire spectrum coupled to a perturbation, including bound excitations and the ionization continuum, without explicitly determining all lower-lying eigenstates. A finite imaginary energy controls the resolution and keeps the response square integrable. Near an isolated bound excitation, the normalized response also recovers the corresponding eigenstate as the width tends to zero. A helium application illustrates the extraction of an excitation energy and oscillator strength. The formulation provides a route from neural descriptions of electronic correlation to spectra beyond a small manifold of low-lying states.