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We propose using sum-over-states calculations with the compact wavefunctionsof Monte Carlo configuration interaction to approach accurate values forhigher-order dipole properties up to second hyperpolarizabilities in acontrolled way. We apply the approach to small systems that can generally becompared with full configuration interaction (FCI) results. We considerhydrogen fluoride with a 6-31g basis and then look at results, includingfrequency dependent properties, in an aug-cc-pVDZ basis. We extend onecalculation beyond FCI by using an aug-cc-pVTZ basis. The properties of anH$_{4}$ molecule with multireference character are calculated in an aug-cc-pVDZbasis. We then investigate this method on a strongly multireference system witha larger FCI space by modelling the properties of carbon monoxide with astretched geometry. The behavior of the approach with increasing basis size isconsidered by calculating results for the neon atom using aug-cc-pVDZ toaug-cc-pVQZ. We finally test if the unusual change in polarizability betweenthe first two states of molecular oxygen can be reproduced by this method in a6-31g basis.

Approaching exact hyperpolarizabilities via sum-over-states Monte Carlo configuration interaction