Ultra-long-ranged dispersion interaction between degenerate molecules

It is known (see e.g. [1]) that extended nano-systems with zero electronic gaps can exhibit dispersion interactions that fall off with unexpected powers of distance $D$. We seek to find a similar phenomenon between finite molecules that have a strictly degenerate many-electron groundstate (zero gap). As a toy model we take H$_{\mathrm{3}}$ with the atoms constrained to lie on an equilateral triangle of side $a$, using a minimal (s) basis set, and with spin-orbit coupling omitted. Rotational symmetry at fixed spins guarantees a degenerate time-reversed pair of three-electron states. For sufficiently small atomic spacing $a$ where inter-atomic hopping kinetic energy dominates the electron-electron repulsion, these degenerate time-reversed pairs of states are many-electron groundstates. We confirm this groundstate degeneracy via limited-basis CI calculations. We show that the resulting dispersion energy between two such constrained H$_{\mathrm{3}}$ molecules falls off as $D$**(-3)instead of the usual \textit{D**(-6)}. Within the classification scheme proposed in ref [2], this effect can be interpreted as a ``type C non-additivity'' of the dispersion interaction. This model may be relevant to metal atom clusters. \\[4pt] [1] John F. Dobson, Angela White and Angel Rubio, Phys. Rev. Lett. \textbf{96} (2006) 073201.\\[0pt] [2] John F. Dobson, Int. J. Quantum Chem. 114, 1157 (2014).