  The authors present a technique using variational Monte Carlo to solve for
excited states of electronic systems. The technique is based on enforcing
orthogonality to lower energy states, which results in a simple variational
principle for the excited states. Energy optimization is then used to solve for
the excited states. This technique is applied to the well-characterized benzene
molecule, in which $\sim$10,000 parameters are optimized for the first 12
excited states. Agreement within approximately 0.2 eV is obtained with higher
scaling coupled cluster methods; small disagreements with experiment are likely
due to vibrational effects.
