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In this paper we discuss the performance of the non-iterative state-specific multireference coupled cluster (SS-MRCC) methods accounting for the effect of triply excited cluster amplitudes. The corrections to the Brillouin-Wigner and Mukherjee's MRCC models based on the manifold of singly and doubly excited cluster amplitudes (BW-MRCCSD and Mk-MRCCSD, respectively) are tested and compared with exact full configuration interaction results for small systems (H2O, N2, and Be3). For the larger systems (naphthyne isomers) the BW-MRCC and Mk-MRCC methods with iterative singles, doubles, and non-iterative triples (BW-MRCCSD(T) and Mk-MRCCSD(T)) are compared against the results obtained with single reference coupled cluster methods. We also report on the parallel performance of the non-iterative implementations based on the use of processor groups. [ABSTRACT FROM AUTHOR]