12.10.1 Introduction

The “XSAPT” method, which may be regarded either as an acronym for “XPol+SAPT” or for “extended” symmetry adapted perturbation theory (SAPT), was originally introduced by Jacobson and Herbert ⁵⁸⁴ Jacobson L. D., Herbert J. M.
J. Chem. Phys.
(2011), 134, pp. 094118. Link ^{, 521} Herbert J. M. et al.
Phys. Chem. Chem. Phys.
(2012), 14, pp. 7679. Link as a low-scaling, systematically-improvable method for intermolecular interactions that could be applicable to large systems. The idea was to replace the need for empirical parameters in the XPol method with on-the-fly evaluation of exchange-repulsion and dispersion interactions via pairwise-additive SAPT. Stated differently, XSAPT uses XPol to evaluate many-body (non-pairwise-additive) polarization effects, but then assumes that dispersion and exchange-repulsion interactions are pairwise additive, and evaluates them via pairwise SAPT0 or SAPT0(KS) calculations. The method was significantly extended by Lao, Herbert, and co-workers, ⁷¹⁹ Lao K. U., Herbert J. M.
J. Phys. Chem. Lett.
(2012), 3, pp. 3241. Link ^{, 720} Lao K. U., Herbert J. M.
J. Chem. Phys.
(2013), 139, pp. 034107. Link ^{, 722} Lao K. U., Herbert J. M.
J. Phys. Chem. A
(2015), 119, pp. 235. Link ^{, 724} Lao K. U., Herbert J. M.
J. Chem. Theory Comput.
(2018), 14, pp. 2955. Link ^{, 725} Lao K. U., Herbert J. M.
J. Chem. Theory Comput.
(2018), 14, pp. 5128. Link ^{, 183} Carter-Fenk K. et al.
J. Phys. Chem. Lett.
(2019), 10, pp. 2706. Link ^{, 799} Liu K.-Y., Carter-Fenk K., Herbert J. M.
J. Chem. Phys.
(2019), 151, pp. 031102. Link ^{, 445} Gray M., Herbert J. M.
J. Chem. Phys.
(2021), 155, pp. 034103. Link with various approximations applied in place of the SAPT0 or SAPT0(KS) dispersion terms, ¹⁸² Carter-Fenk K., Lao K. U., Herbert J. M.
Acc. Chem. Res.
(2021), 54, pp. 3679. Link which are both the least accurate and most expensive contributions to second-order SAPT. Overviews of of XSAPT-based methods can be found in Refs.  722 Lao K. U., Herbert J. M.
J. Phys. Chem. A
(2015), 119, pp. 235. Link and 182 Carter-Fenk K., Lao K. U., Herbert J. M.
Acc. Chem. Res.
(2021), 54, pp. 3679. Link and implementation details can be found in Refs.  521 Herbert J. M. et al.
Phys. Chem. Chem. Phys.
(2012), 14, pp. 7679. Link , 724 Lao K. U., Herbert J. M.
J. Chem. Theory Comput.
(2018), 14, pp. 2955. Link , and 799 Liu K.-Y., Carter-Fenk K., Herbert J. M.
J. Chem. Phys.
(2019), 151, pp. 031102. Link . In particular, the XSAPT+MBD method ¹⁸³ Carter-Fenk K. et al.
J. Phys. Chem. Lett.
(2019), 10, pp. 2706. Link stands out as a way to obtain qualitative insight about noncovalent interactions in large systems, backed by quantitative energetics calculations. ¹⁸² Carter-Fenk K., Lao K. U., Herbert J. M.
Acc. Chem. Res.
(2021), 54, pp. 3679. Link In many cases, this type of analysis has upended textbook “conventional wisdom", as reviewed in Ref.  530 Herbert J. M.
J. Phys. Chem. A
(2021), 125, pp. 7125. Link .