An improved formulation of pair natural orbital (PNO)–based explicitly correlated Møller–Plesset second-order perturbation theory is presented. Increased efficiency has been achieved by modifying the representation of the strong orthogonality projector used in the evaluation of the F12 intermediates. We demonstrate two simple relationships between the truncation errors arising from PNOs in the virtual space and those arising from the PNOs in the strong orthogonality operators. This permits robust error control through a single parameter.
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