W1X-1 and W1X-2: W1-Quality Accuracy with an Order of Magnitude Reduction in Computational Cost.

We have examined a number of approaches for reducing the computational requirements of the W1w and W1-F12 procedures, while maintaining the accuracy. A key finding is that MP2/cc-pCVTZ provides a reliable means for the evaluation of core-correlation effects at a cost that is negligible in the context of W1-type procedures. This greatly reduces the overall computational cost, since calculations for core-correlation represent the most time-consuming steps for both W1w and W1-F12. For the evaluation of valence CCSD(T)/CBS, we find that truncation of the sets of diffuse functions leads to a significant savings in time, with only a minor deterioration in the performance. In order to eliminate the need to carry out CCSD calculations with a quadruple-ζ basis set, we have maintained the approach employed in W1-F12, namely the use of explicitly correlated procedures. Our resulting procedures are termed W1X-1 and W1X-2 (where the X refers to the eXplicitly correlated procedures). Of these, the W1X-1 protocol requires two CCSD-F12b plus two CCSD(T) calculations to obtain the valence CCSD(T)/CBS energy component, as with W1-F12. The W1X-2 procedure, on the other hand, requires only two CCSD(T)-F12b calculations for the evaluation of CCSD(T)/CBS and is therefore less expensive than W1X-1. Indeed, the W1X-2 protocol is an order of magnitude less computationally demanding than W1w and ∼80% less costly than W1-F12. Extensive assessment of the W1X-1 and W1X-2 procedures shows that W1X-1 performs well and comparably to W1w and W1-F12 in virtually all cases. The W1X-2 method gives equivalently good results for most thermochemical properties, but the heats of formation of fluorocarbons and complexation energies of hydrogen fluoride clusters represent notable exceptions.