Excited states in variational Monte Carlo using a penalty method

Finding excited states has been a long-standing challenge in variational Monte Carlo for interacting systems. While there has been notable progress on this front, existing algorithms either do not allow for optimization of all wave function parameters, can have trouble to converging to the correct state as recently shown by Filippi and coworkers, or miss degenerate states. We present an algorithm based on orthogonalization to the ground state that resolves these difficulties in the limit as the wave function parameterization becomes complete. We show an application to the benzene molecule, in which ~10,000 parameters are optimized for the first 12 excited states.