  A third-order multireference perturbation theory based on the driven
similarity renormalization group approach (DSRG-MRPT3) is presented. The
DSRG-MRPT3 method has several appealing features: a) it is intruder free, b) it
is size consistent, c) it leads to a non-iterative algorithm with ${\cal
O}(N^6)$ scaling, and d) it includes reference relaxation effects. The
DSRG-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 bond
dissociation coordinates, respectively. The nonparallelism errors of DSRG-MRPT3
are consistent to those of CASPT3 and MRCISD, and show significant improvements
over those obtained from DSRG second-order multireference perturbation theory.
Our efficient implementation of the DSRG-MRPT3 based on factorized electron
repulsion integrals enables studies of medium-sized open-shell organic
compounds. This point is demonstrated with computations of the singlet-triplet
splitting ($\Delta_{\rm ST} = E_{\rm T} - E_{\rm S}$) of 9,10-anthracyne. At
the DSRG-MRPT3 level of theory, our best estimate of the adiabatic $\Delta_{\rm
ST}$ is 3.9 kcal mol$^{-1}$, a value that is within 0.1 kcal mol$^{-1}$ from
multireference coupled cluster results.

Chemical Physics