Complete basis set limit studies of conventional and R12 correlation methods: The silicon dicarbide (SiC2) barrier to linearity

Abstract

The problematic SiC2 barrier to linearity is investigated in a benchmark study of one-electron basis set convergence properties of both the conventional and linear R12/A formulations of second-order Møller–Plesset (MP2) perturbation theory. A procedure for computational molecular partial-wave expansions is constructed and applied to the T-shaped and linear forms of SiC2. The largest basis set used [Si(22s17p14d6f5g2h2i1k)/C(19s14p14d6f5g2h2i1k)] included functions of orbital angular momentum as large as l=7 (k), and systematic saturation was performed through l=6 (i). With respect to angular momentum l, correlation energy increments are found to decay in accord with analytical models that suggest (l+1/2)−6 and (l+1/2)−4 functional forms for the R12/A and conventional methods, respectively. A benchmark complete basis set (CBS) limit for the second-order correlation contribution to the SiC2 barrier to linearity, 5.66 kcal mol−1, was determined via MP2-R12/A partial-wave expansions. Conventional MP2 calculations, using both the standard cc-pV6Z and the [Si(22s17p14d6f5g2h2i1k)/C(19s14p14d6f5g2h2i1k)] basis sets, underestimate MP2 correlation energies by at least 3 kcal mol−1, while the barrier is underestimated by at least 0.1 kcal mol−1. Both X−3 cc-pVXZ extrapolations and partial-wave extrapolations greatly improve conventional correlation energies, with the cc-pVXZ extrapolated barrier in error by only 0.07 kcal mol−1. While the absolute accuracy of the conventional partial-wave extrapolations is substantially better than the cc-pVXZ extrapolated values, unbalanced errors result in an overestimation of the barrier by nearly 0.2 kcal mol−1. The CBS-limit MP2 contribution is combined via a focal-point analysis with conventional coupled cluster computations through triple excitations (CCSDT), resulting in an inferred CBS CCSDT barrier of 5.45 kcal mol−1 after accounting for core correlation and relativistic effects. The critical question of post-CCSDT corrections is approached through explicit coupled cluster computations perturbatively accounting for connected quadruple excitations [BD(TQ) and CCSD(2)], as well as shifted [2,1] Padé approximants of MPn series and continued fraction and quadratic Padé approximants of coupled-cluster series. The best available post-CCSDT correction, extracted from BD(TQ)/cc-pVTZ theory, of 0.87 kcal mol−1, results in a final prediction near 6.3 kcal mol−1 for the SiC2 barrier to linearity.