Symmetry-adapted perturbation theory or SAPT is a methodology in

electronic structure Quantum chemistry, also called molecular quantum mechanics, is a branch of physical chemistry focused on the application of quantum mechanics to chemical systems, particularly towards the quantum-mechanical calculation of electronic contributions ...

theory developed to describe

non-covalent interactions In chemistry, a non-covalent interaction differs from a covalent bond in that it does not involve the sharing of electrons, but rather involves more dispersed variations of electromagnetic interactions between molecules or within a molecule. The ...

between

atoms Atoms are the basic particles of the chemical elements. An atom consists of a nucleus of protons and generally neutrons, surrounded by an electromagnetically bound swarm of electrons. The chemical elements are distinguished from each other ...

and/or

molecules A molecule is a group of two or more atoms that are held together by attractive forces known as chemical bonds; depending on context, the term may or may not include ions that satisfy this criterion. In quantum physics, organic chemistry ...

. 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_=E_-E_-E_

where

\Delta E_

is the total interaction energy obtained via subtracting isolated monomer energies

E_

and

E_

from the dimer energy

E_

. A key deficiency of the supermolecular interaction energy is that it is susceptible to

basis set superposition error In quantum chemistry, calculations using finite basis sets are susceptible to basis set superposition error (BSSE). As the atoms of interacting molecules (or of different parts of the same molecule - intramolecular BSSE) approach one another, thei ...

(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 In quantum mechanics, perturbation theory is a set of approximation schemes directly related to mathematical perturbation for describing a complicated quantum system in terms of a simpler one. The idea is to start with a simple system for which ...

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 in the intermolecular perturbation. The simplest such SAPT approach is called SAPT0 because it neglects intramolecular correlation effects (i.e., it is based on Hartree–Fock densities). SAPT0 captures the classical

electrostatic interaction Electrostatics is a branch of physics that studies slow-moving or stationary electric charges. Since classical times, it has been known that some materials, such as amber, attract lightweight particles after rubbing. The Greek word (), meani ...

of two charge densities and exchange (or

Pauli repulsion In chemistry and physics, the exchange interaction is a quantum mechanical constraint on the states of indistinguishable particles. While sometimes called an exchange force, or, in the case of fermions, Pauli repulsion, its consequences cannot alw ...

) at first-order, and at second-order the terms for

electrostatic induction Electrostatic induction, also known as "electrostatic influence" or simply "influence" in Europe and Latin America, is a redistribution of electric charge in an object that is caused by the influence of nearby charges. In the presence of a charg ...

(the polarization of the

molecular orbitals In chemistry, a molecular orbital is a mathematical function describing the location and wave-like behavior of an electron in a molecule. This function can be used to calculate chemical and physical properties such as the probability of finding ...

in the electric field of the interacting atom/molecule) and dispersion (see

London dispersion London dispersion forces (LDF, also known as dispersion forces, London forces, instantaneous dipole–induced dipole forces, fluctuating induced dipole bonds or loosely as van der Waals forces) are a type of intermolecular force acting between at ...

) appear, along with their exchange counterparts.

E_^=E_^+E_^+E_^+E_\text^+E_^+E_\text^

Higher terms in the perturbation series can be accounted for using many-body perturbation theory or coupled-cluster approaches. Alternatively, density functional theory variants of SAPT have been formulated. The higher-level SAPT methods approach supermolecular coupled-cluster singles, doubles, and perturbative triples CSD(T)in accuracy.

References

Molecular physics Quantum chemistry Physical chemistry Electronic structure methods {{quantum-stub