AxilrodTellerMutoterm

The Axilrod–Teller–Muto term, often abbreviated as ATM term, is a three-body contribution to the long-range dispersion energy between three atoms or molecules. It represents the leading non-additive correction to the pairwise van der Waals (London) interactions and arises from correlated instantaneous dipole fluctuations among the three bodies. The term is a standard component of high-accuracy potential energy surfaces and is used in quantum chemistry and molecular simulations to improve predictions of binding energies and structures in weakly bound systems.

Mathematically, the ATM energy for three atoms with interatomic distances r12, r23, and r31 and interior angles θ1, θ2, θ3 is typically written as E_ATM = -C9 × [1 + 3 cos θ1 cos θ2 cos θ3] / (r12^3 r23^3 r31^3), where C9 is a positive coefficient depending on the atomic species. The expression shows the energy decays with the ninth power of the characteristic separations and depends sensitively on the triangle geometry. In common conventions, the overall sign yields an attractive correction for typical geometries, though the precise sign can vary with the chosen definition of C9.

Applications and context: The ATM term is especially relevant for noble-gas clusters, molecular crystals, and condensed-phase systems where non-additive dispersion effects influence properties such as binding energies and structures. Modern computational methods incorporate ATM-like three-body dispersion corrections in force fields and in density functional theory corrections (for example, certain D3/D4 schemes), providing improved accuracy over purely pairwise-additive models. Limitations include its validity primarily in the asymptotic long-range regime and the omission of higher-order many-body terms.