Van der Waals energy of a 1-dimensional lattice

Van der Waals dispersion forces are examined for an infinite one-dimensional (1D) chain of atoms. Building on the work of Bade and Kirkwood (J. Chem. Phys. 27, 1284, 1957), dipolar fluctuations of the 1D chain are analyzed in terms of polarization waves. The van der Waals energy of the chain is evaluated from the zero-point energy of these waves. Several results are found. (1) A critical value exists for the dimensionless coupling parameter v = α0/a³, for large polarizabilities (α0) or small lattice spacings (a). When v > 0.208, the 1D line has divergences in both the dispersion relation of the waves and the effective site polarizability. The resulting instability is analogous to 1D ferroelectricity. (2) The sum of higher order (than three-body) interactions are shown to be more important than three-body interactions (which are small); when v approaches 0.208, the higher order terms are comparable to the two-body term. (3) Finite 1D chains of N atoms behave like infinite chains when N exceeds 100. (4) 1D surface tensions deviate from two-body predictions for large values of the coupling parameter (v > 0.10).