A third-order multireference perturbation theory based on the drivensimilarity renormalization group approach (DSRG-MRPT3) is presented. TheDSRG-MRPT3 method has several appealing features: a) it is intruder free, b) itis size consistent, c) it leads to a non-iterative algorithm with ${\calO}(N^6)$ scaling, and d) it includes reference relaxation effects. TheDSRG-MRPT3 scheme is benchmarked on the potential energy curves of F$_2$,H$_2$O$_2$, C$_2$H$_6$, and N$_2$ along the F-F, O-O, C-C, and N-N bonddissociation coordinates, respectively. The nonparallelism errors of DSRG-MRPT3are consistent to those of CASPT3 and MRCISD, and show significant improvementsover those obtained from DSRG second-order multireference perturbation theory.Our efficient implementation of the DSRG-MRPT3 based on factorized electronrepulsion integrals enables studies of medium-sized open-shell organiccompounds. This point is demonstrated with computations of the singlet-tripletsplitting ($\Delta_{\rm ST} = E_{\rm T} - E_{\rm S}$) of 9,10-anthracyne. Atthe DSRG-MRPT3 level of theory, our best estimate of the adiabatic $\Delta_{\rmST}$ is 3.9 kcal mol$^{-1}$, a value that is within 0.1 kcal mol$^{-1}$ frommultireference coupled cluster results.
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