  This study explores the application of neural network variational Monte Carlo
(NN-VMC) for the computation of low-lying excited states in molecular systems.
Our focus lies on the implementation and evaluation of two distinct
methodologies, the penalty method and a novel modification of the auxiliary
wave function (AW) method, within the framework of the FermiNet-based NN-VMC
package. Importantly, this specific application has not been previously
reported.Our investigation advocates for the efficacy of the modified AW
method, emphasizing its superior robustness when compared to the penalty
method. This methodological advancement introduces a valuable tool for the
scientific community, offering a distinctive approach to target low-lying
excited states. We anticipate that the modified AW method will garner interest
within the research community, serving as a complementary and robust
alternative to existing techniques. Moreover, this contribution enriches the
ongoing development of various neural network ansatz, further expanding the
toolkit available for the accurate exploration of excited states in molecular
systems.
