Explicitly correlated, linear R12 electronic structure theory : next generation methods for subchemical accuracy
Kenny, Joseph Patrick
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Linear R12 electronic structure theories, taking advantage of explicit dependence on interelectronic coordinates, hold promise for efficiently approaching complete basis set limits for molecular correlation energies. A procedure for computational molecular partial-wave expansions has been constructed and applied, in conjunction with both the conventional and linear R12/A formulations of second-order Møller-Plesset perturbation theory (MP2), to the prototypical SiC2 and H2O barriers to linearity. With respect to angular momentum l, correlation 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. The basis set manipulations performed during the partial-wave analyses clearly demonstrate the accelerated convergence of MP2-R12/A energies in both radial and angular expansions. A benchmark complete basis set (CBS) limit MP2 contribution to the SiC2 barrier to linearity, 5.66 kcal mol-1, was determined via MP2-R12/A partial-wave extrapolations. The SiC2 CBS-limit MP2 contribution is combined via a focal-point analysis with conventional coupled cluster computations, resulting in a final prediction of 6.3 kcal mol-1 for the SiC2 barrier to linearity. Partial-wave analysis of the H2O barrier to linearity reveals complicated basis set trends for the MP2-R12/A method. A series of exploratory calculations, including a partial-wave expansion for the neon atom, provides an increased understanding of the effects of high exponent basis functions and emphasizes the care which must be taken in constructing basis sets for R12 methods. Drawing upon the strengths of the MP2- R12/A partial-wave expansions and previous large basis set MP2-R12/A calculations, an improved estimate of -353 cm-1 is advanced for the CBS limit MP2 contribution to the barrier to linearity of water. The accuracy of various computation and extrapolation procedures for conventional and linear R12 methods are evaluated and promising directions for linear R12 method development are highlighted.