Symmetry-adapted perturbation theory

Symmetry-Adapted Perturbation Theory or SAPT^[1]^[2] is a methodology in electronic structure theory developed to describe non-covalent interactions between atoms and/or molecules. SAPT is a member of the family of methods known as Energy Decomposition Analysis (EDA). Most EDA methods decompose a total interaction energy that is computed via a supermolecular approach, such that:

\Delta E_{int}=E_{AB}-E_{A}-E_{B}

where ${\textstyle \Delta E_{int}}$ is the total interaction energy obtained via subtracting isolated monomer energies ${\textstyle E_{X}}$ from the dimer energy ${\textstyle E_{AB}}$ . A key deficiency of the supermolecular interaction energy is that it is susceptible to basis set superposition error (BSSE).

The major difference between SAPT and supermolecular EDA methods is that, as the name suggests, SAPT computes the interaction energy directly via a perturbative approach. One consequence of capturing the total interaction energy as a perturbation to the total system energy rather than using the subtractive supermolecular method outlined above, is that the interaction energy is made free of BSSE in a natural way.

Being a perturbation expansion, SAPT also provides insight into the contributing components to the interaction energy. The lowest-order expansion at which all interaction energy components are obtained is second-order. The second-order, or SAPT0, expansion captures the classical electrostatic interaction of two charge densities and exchange (or Pauli repulsion) at first-order. At second-order the terms for electrostatic induction (the polarization of the molecular orbitals in the electric field of the interacting atom/molecule) and dispersion (see London dispersion) appear, along with their exchange counterparts.

E_{int}^{SAPT0}=E_{elst}^{(1)}+E_{exch}^{(1)}+E_{ind}^{(2)}+E_{exch-ind}^{(2)}+E_{disp}^{(2)}+E_{exch-disp}^{(2)}

References

↑ Szalewicz, Krzysztof (March 1, 2012). "Symmetry-adapted perturbation theory of intermolecular forces". WIREs Comput Mol Sci. 2 (2): 254–272. doi:10.1002/wcms.86.
↑ Jeziorski, Bogumil; Moszynski, Robert; Szalewicz, Krzysztof (1994). "Perturbation Theory Approach to Intermolecular Potential Energy Surfaces of van der Waals Complexes". Chem. Rev. 94 (7): 1887–1930. doi:10.1021/cr00031a008.

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[1] Szalewicz, Krzysztof (March 1, 2012). "Symmetry-adapted perturbation theory of intermolecular forces". WIREs Comput Mol Sci. 2 (2): 254–272. doi:10.1002/wcms.86.

[2] Jeziorski, Bogumil; Moszynski, Robert; Szalewicz, Krzysztof (1994). "Perturbation Theory Approach to Intermolecular Potential Energy Surfaces of van der Waals Complexes". Chem. Rev. 94 (7): 1887–1930. doi:10.1021/cr00031a008.