  We introduce several improvements to the penalty-based variational quantum
Monte Carlo (VMC) algorithm for computing electronic excited states, and
demonstrate that the accuracy of the updated method is competitive with other
available excited-state VMC approaches. A theoretical comparison of the
computational aspects of these algorithms is presented, where several benefits
of the penalty-based method are identified. Our main contributions include an
automatic mechanism for tuning the scale of the penalty terms, an updated form
of the overlap penalty with proven convergence properties, and a new term that
penalizes the spin of the wave function, enabling the selective computation of
states with a given spin. With these improvements, along with the use of the
latest self-attention-based ansatz, the penalty-based method achieves a mean
absolute error below 1 kcal/mol for the vertical excitation energies of a set
of 26 atoms and molecules, without relying on variance matching schemes.
Considering excited states along the dissociation of the carbon dimer, the
accuracy of the penalty-based method is on par with that of
natural-excited-state (NES) VMC, while also providing results for larger
sections of the potential energy surface. Additionally, the accuracy of the
original penalty-based method is improved for a conical intersection of
ethylene, with the predicted angle of the intersection agreeing well with both
NES-VMC and multi-reference configuration interaction.
