Driven similarity renormalization group: Third-order multireference perturbation theory

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.