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.

Spectroscopic parameters for silacyclopropynylidene, SiC2, from extensive astronomical observations toward CW Leo (IRC +10216) with the Herschel satellite

“…data only") are quite good for low-K a transition, but deteriorate for higher K a values, which is closer to common expectations. Both fits as well as both predictions, as well as additional fits are available in the archive section of the CDMS 7 . Overall, however, the quality of the predictions is quite similar and do not provide a reasoning which reduction should be preferred.…”

“…However, the authors attached a caveat to this value as an anharmonic force field calculation provided a much too small value for the vibrational energy of 3 = 1 and much too large anharmonicity constants. Therefore, some of the authors revisited the problem of the energy difference between the two SiC 2 structures, the last time in 2003 when very high level calculations combined with very large basis sets, basis set extrapolation to infinite size as well as additional corrections yielded a value of 26.5 kJ/mol [7].…”

The correlation consistent composite approach (ccCA): An alternative to the Gaussian-n methods

“…[6][7][8][9][10] Other composite methods have been created since the original formulation of the G1 method. Some of these, such as the complete basis set ͑CBS-n͒ model chemistries of Petersson and co-workers, [11][12][13][14] the focal point method of Allen and co-workers [15][16][17][18][19][20] and Császár et al, 21,22 the W1 and W2 methods of Parthiban and Martin 23 and Martin and de Oliveira, 24 and the High Accuracy Extrapolated ab initio Thermochemistry ͑HEAT͒ method of Stanton and co-workers, 25,26 attempt to approach the complete basis set ͑CBS͒/full-configuration interaction ͑FCI͒ limit of smaller systems, consistently obtaining accuracy better than within 0.5 kcal mol −1 of experimental data. Dixon, Feller, and co-workers [27][28][29][30][31][32][33][34][35] used large basis set coupled cluster equilibrium geometries and total energies while using smaller basis sets to perform further electron correlation and scalar relativistic corrections, in order to achieve at least chemical accuracy ͑±1 kcal mol −1 ͒ for enthalpies of formation.…”

The correlation-consistent composite approach: Application to the G3/99 test set

“…Many of these model chemistries attempt to approach the complete basis set/full-configuration interaction limit when applied to smaller systems, and report accuracies to within 0.50 kcal mol −1 of experimental data. Some notable composite methods are the complete basis set ͑CBS-n͒ theories of Petersson and co-workers, [21][22][23][24] the focal point method of Allen et al [25][26][27][28][29] and Császár et al [27][28][29][30][31][32] the W1 and W2 methods of Parthiban and Martin 33 and Martin and de Oliveira, 34 and the HEAT method of Stanton and co-workers 35,36 Lastly, the composite method of Dixon and co-workers [37][38][39][40][41][42][43][44][45] has been largely successful by computing coupled cluster equilibrium geometries and total energies with large basis sets while using more efficient levels of theory to compute spin-orbit splitting, core-valence correlation, scalar relativistic, and zero-point vibrational anharmonicity effects.…”