It’s Complicated: On Relativistic Effects and Periodic Trends in the Melting and Boiling Points of the Group 11 Coinage Metals

While the color of metallic gold is a prominent and well-investigated example for the impact of relativistic effects, much less is known regarding the influence on its melting and boiling point (MP/BP). To remedy this situation, this work takes on the challenging task of exploring the phase transitions of the Group 11 coinage metals Cu, Ag, and Au through nonrelativistic (NR) and scalar/spin–orbit relativistic (SR/SOR) Gibbs energy calculations with λ-scaled density-functional theory (λDFT). At the SOR level, the calculations provide BPs in excellent agreement with experimental values (1%), while MPs exhibit more significant deviations (2–10%). Comparing SOR calculations to those conducted in the NR limit reveals some remarkably large and, at the same time, some surprisingly small relativistic shifts. Most notably, the BP of Au increases by about 800 K due to relativity, which is in line with the strong relativistic increase of the cohesive energy, whereas the MP of Au is very similar at the SOR and NR levels, defying the typically robust correlation between MP and cohesive energy. Eventually, an inspection of thermodynamic quantities traces the trend-breaking behavior of Au back to phase-specific effects in liquid Au, which render NR Au more similar to SOR Ag, in line with a half-a-century-old hypothesis of Pyykkö.