Relativity–Induced Bonding Pattern Change in Coinage Metal Dimers M₂ (M = Cu, Ag, Au, Rg)

Abstract

The periodic table provides a fundamental protocol for qualitatively classifying and predicting chemical properties based on periodicity. While the periodic law of chemical elements had already been rationalized within the framework of the nonrelativistic description of chemistry with quantum mechanics, this law was later known to be affected significantly by relativity. We here report a systematic theoretical study on the chemical bonding pattern change in the coinage metal dimers (Cu, Ag, Au, Rg) due to the relativistic effect on the superheavy elements. Unlike the lighter congeners basically demonstrating ns- ns bonding character and a 0 ground state, Rg shows unique 6d-6d bonding induced by strong relativity. Because of relativistic spin-orbit (SO) coupling effect in Rg, two nearly degenerate SO states, 0 and 2, exist as candidate of the ground state. This relativity-induced change of bonding mechanism gives rise to various unique alteration of chemical properties compared with the lighter dimers, including higher intrinsic bond energy, force constant, and nuclear shielding. Our work thus provides a rather simple but clear-cut example, where the chemical bonding picture is significantly changed by relativistic effect, demonstrating the modified periodic law in heavy-element chemistry.

Spectroscopic/Bond Property Relationship in Group 11 Dihydrides via Relativistic Four-Component Methods

“…By comparing our results with those we find in the literature, we see that this dissociation energy trend is well-known and somehow expected for these complexes. A similar trend is also displayed for group 11 dimers and an analogous trend with the Ag–H showing the lowest value of D e is also reported for group 11 monohydrides …”

“…Moreover, the trend found here for dihydrides is very similar to that observed both previously and in the current study for monohydrides (Table S3 in the SI) and also resembles the trend observed for atomic radii , of group 11 metals, which suggests the strong relativistic stabilization of 6s and 7s orbitals to be responsible for the very short Au–H and Rg–H distances, respectively. The same trend has also been observed in a recent work for the M–M distances in group 11 dimers M 2 (M = Cu, Ag, Au, Rg) (Cu < Rg < Au < Ag), where correlated approaches have been used to investigate their spectroscopic constants . The differences between DFT and 4c-CCSD­(T) results point out that a very accurate treatment of electron correlation and relativistic effects is a particularly important ingredient when dealing with these properties …”

“…The trend displayed for both stretching frequencies and M–H force constants appears, with no surprises, to be the same trend as that observed for dissociation energies, with the Ag–H bond showing the lowest force constant (and stretching frequencies) and Rg–H the highest. The same trend has been observed in the case of the group 11 dimers, where the sharp increase of both dissociation energies and force constants in Au 2 and Rg 2 has been ascribed to the relativistic increase of the extent of sd z 2 hybridization, which should cause the bond to be shortened and strengthened. We will return to this point later.…”

Understanding Periodic and Non-periodic Chemistry in Periodic Tables

“…In the case of the coinage metal dimers M 2 from group 11 (Cu 2 , Ag 2 , Au 2 ), the M-M single bond is due to interaction of σ (n−1)d,ns valence-hybrids between the polarized M-(n−1)d 10 closed shell cores. In Rg 2 however, the upper antibonding σ * u−6d 2 orbital has changed its character due to the relativistic 6d 5 / 2 destabilization and 7s½ stabilization to dominantly σ * u,7s 2 type, with remarkable changes of force constant, bond energy and charge and pair density distributions (Li et al, 2018).…”

Artificial relativistic molecules

“…The direct and real space observation of relativistic molecular orbitals is exceptional, since most of previous experiments for very few heavy element molecules relied on spectroscopy techniques [28][29][30][31] and, thus, the relativistic effects were mainly discussed in theoretical aspects [32,33]. Although a Pb dimer has a much longer bond length (7 Å) than other relativistic molecules [33][34][35] and there is a substantial adatom-substrate interaction, the molecular splitting mainly arises from the direct overlap of relativistic p orbitals. This is distinguished from the substrate-mediated long-range interaction of other metal clusters on metal surfaces [36,37].…”