Exclusively Relativistic: Periodic Trends in the Melting and Boiling Points of Group 12

Abstract

First‐principles simulations can advance our understanding of phase transitions but are often too costly for the heavier elements, which require a relativistic treatment. Addressing this challenge, we recently composed an indirect approach: A precise incremental calculation of absolute Gibbs energies for the solid and liquid with a relativistic Hamiltonian that enables an accurate determination of melting and boiling points (MPs and BPs). Here, we apply this approach to the Group 12 elements Zn, Cd, Hg, and Cn, whose MPs and BPs we calculate with a mean absolute deviation of only 5 % and 1 %, respectively, while we confirm the previously predicted liquid aggregate state of Cn. At a non‐relativistic level of theory, we obtain surprisingly similar MPs and BPs of 650±30 K and 1250±20 K, suggesting that periodic trends in this group are exclusively relativistic in nature. Ultimately, we discuss these results and their implication for Groups 11 and 14.

Relativity as a Synthesis Design Principle: A Comparative Study of [3 + 2] Cycloaddition of Technetium(VII) and Rhenium(VII) Trioxo Complexes with Olefins

“… 25 , 26 Today the importance of relativistic effects is well recognized for the static properties of sixth- and seventh-period elements. 27 Relativity thus accounts for such well-known effects as the liquid state of Hg 28 and the yellow color of elemental Au 29 and Cs as well as a host of less well-known effects in heavy-element chemistry. 30 − 33 …”

“…Indeed, in 1929, Paul Dirac asserted that the only imperfections remaining in quantum mechanics “give rise to difficulties only when high-speed particles are involved, and are therefore of no importance in the consideration of atomic and molecular structure and ordinary chemical reactions in which it is, indeed, usually sufficiently accurate if one neglects relativity variation of mass and velocity and assumes only Coulomb forces between the various electrons and atomic nuclei.” This view started changing only in the 1970s. , Today the importance of relativistic effects is well recognized for the static properties of sixth- and seventh-period elements . Relativity thus accounts for such well-known effects as the liquid state of Hg and the yellow color of elemental Au and Cs as well as a host of less well-known effects in heavy-element chemistry. − …”

Are the chemical families still there? exploration of similarity among elements

“…The calculations of neighbors, similarity relations and so on, were based on the field 'Element Counts'. For time analyses, we used a smaller set of compounds (20,649,870) associated with reactions with reported publication year. The earliest date of publication was taken as their date of discovery.…”

“…Nowadays, the PSCE is a subject of great interest in the scientific community. Topics of interest cover ontology 8,9 , epistemology 10,11 , history [12][13][14] , discussions about its graphical representation [15][16][17] , classification of super-heavy elements [18][19][20] , and many others 21 . Some authors have discussed the quantum-mechanical foundations of the system [22][23][24] , pointing out that several periodic trends may have a relativistic nature, and the quantum origin of some "irregularities" of the heavy elements 25 .…”

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

“…This approach includes both scalar and spin–orbit relativistic contributions to the Gibbs (free) energy by combining molecular dynamics simulations (MD), thermodynamic integration (TI), and perturbation theory (TPT) as well as an empirical scaling of the Hamiltonian to mitigate systematic errors. This TI-MD-λDFT approach can pin down melting and boiling points (MPs and BPs) by locating the intersection between the Gibbs energies of the respective phases. − Previous applications have demonstrated that the approach produces phase transition temperatures, and in particular BPs, with only a few percent deviation from the experimental values, − clearing out previous uncertainties concerning the relativistic shift of the MP of Hg. , …”