Extended Symmetry-Adapted Perturbation Theory (XSAPT): A Cubic-Scaling Platform for Computing Accurate Intermolecular Interaction Energies and ab Initio Energy Decomposition Analysis

This chapter provides an overview of some hybrid forms of symmetry-adapted perturbation theory (SAPT), developed over the past decade and known collectively as "extended" (X)SAPT. Two primary innovations are a self-consistent charge embedding scheme to capture many-body polarization (the "XPol" procedure) and the use of low-cost dispersion models as replacements for SAPT's perturbative description of dispersion. The latter modification reduces the formal complexity to O(N^3) with system size. In conjunction with a many-body dispersion model (XSAPT+MBD) or empirical dispersion potentials fitted to ab initio data (XSAPT+aiD), the hybrid procedure achieves sub-kcal/mol accuracy with respect to high-level benchmarks. XSAPT is equipped with an energy decomposition that partitions the intermolecular interaction energy into components that include electrostatics, Pauli repulsion, dispersion, and induction, the latter of which can be further separated into polarization and charge transfer. As compared to energy decomposition analyses used in density functional theory, separation of the dispersion energy in XSAPT is less ambiguous and the energy partition agrees well with accurate third-order SAPT benchmarks. Theoretical foundations of XSAPT are reviewed, and we provide a thorough discussion of its performance in terms of both accuracy and cost. Exemplary applications are presented that illustrate how XSAPT can be used to uncover the fundamental molecular physics of intermolecular interactions.