On the nonadditivity of the second-order exchange-dispersion energy in the interaction of three helium atoms

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Abstract
Explicit formulas for the nonadditivity of the exchange‐dispersion energy in the interaction of three closed‐shell systems are derived under the assumption that the electron correlation within the noninteracting systems is neglected. The idea of applying many centered basis sets is presented and its usefulness in the investigation of nonadditive effects is discussed. Numerical calculations of the exchange‐dispersion nonadditive effect have been performed for the interaction of three ground‐state He atoms in the equilateral triangle configuration within the trimer centered basis set scheme. The nonadditivity of the exchange‐dispersion energy has been found to be positive and much smaller than that due to the first‐order exchange‐repulsion in the region under consideration. However, because of the cancellation of the first‐order and triple‐dipole nonadditive effects it becomes much more important around Re and, e.g., at R=6 a0 it accounts for ∼90% of the total nonadditive effect. In contrast to the Jansen prediction [Adv. Quantum Chem. 2, 119 (1965)], the relative second‐order three‐body interaction energy has been found to be much smaller than the first‐order one. A damping function has been proposed for evaluation of the nonexpanded triple‐dipole energy. The role of various contributions to the total nonadditivity of the interaction energy is discussed. The values of the two‐body effects are also presented.

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