# Negative thermal expansion and metallophilicity in Cu$_3$[Co(CN)$_6$]

## TL;DR

This study synthesizes and characterizes Cu$_3$[Co(CN)$_6$], revealing its unique thermal expansion properties and weaker metallophilic interactions compared to similar materials, providing insights into designing highly responsive frameworks.

## Contribution

It provides the first detailed analysis of Cu$_3$[Co(CN)$_6$]'s thermal expansion and metallophilic interactions using experimental and computational methods, highlighting the counterintuitive effects of interaction strength.

## Key findings

- Cu$_3$[Co(CN)$_6$] exhibits anisotropic thermal expansion with opposing signs.
- Weaker Cu...Cu interactions lead to moderate structural flexibility.
- Strong interactions can be used to design ultra-responsive materials.

## Abstract

We report the synthesis and structural characterisation of the molecular framework copper(I) hexacyanocobaltate(III), Cu$_3$[Co(CN)$_6$], which we find to be isostructural to H$_3$[Co(CN)$_6$] and the colossal negative thermal expansion material Ag$_3$[Co(CN)$_6$]. Using synchrotron X-ray powder diffraction measurements, we find strong positive and negative thermal expansion behaviour respectively perpendicular and parallel to the trigonal crystal axis: $\alpha_a$ = 25.4(5)\,MK$^{-1}$ and $\alpha_c$ = $-$43.5(8)\,MK$^{-1}$. These opposing effects collectively result in a volume expansivity $\alpha_V$ = 7.4(11)\,MK$^{-1}$ that is remarkably small for an anisotropic molecular framework. This thermal response is discussed in the context of the behaviour of the analogous H- and Ag-containing systems. We make use of density-functional theory with many-body dispersion interactions (DFT+MBD) to demonstrate that Cu$\ldots$Cu metallophilic (`cuprophilic') interactions are significantly weaker in Cu$_3$[Co(CN)$_6$] than Ag$\ldots$Ag interactions in Ag$_3$[Co(CN)$_6$], but that this lowering of energy scale counterintuitively translates to a more moderate---rather than enhanced---degree of structural flexibility. The same conclusion is drawn from consideration of a simple lattice dynamical model, which we also present here. Our results demonstrate that strong interactions can actually be exploited in the design of ultra-responsive materials if those interactions are set up to act in tension.