We investigate the possibility of reducing the complexity of multireference perturbation theory through cumulant based approximations to the high-order density matrices that appear in such theories. Our test cases show that while the cumulant approximated forms are degraded in accuracy relative to the parent theory and exhibit intruder state problems that must be carefully handled, they may provide a route to a simple estimation of dynamic correlation when the parent perturbation theory is

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... sible. Nonetheless, further work is clearly needed on better approximations to the denominators in the perturbation theory.