Relevance of effective bond orders in heterodiatomic molecules and role of the spin-orbit coupling in theAtX(X=At–F)series

Abstract

Scalar and spin-dependent relativistic effects can influence the geometries and wave functions of the ground and excited states of molecular systems in a way that is not always trivial. However, it is still common for researchers, in particular within the quantum chemistry community, to neglect the spin-dependent effects while discussing the binding between atoms in heavy-element systems. Within multiconfigurational self-consistent field frameworks, the binding in diatomic molecules can be derived from the occupation of the natural orbitals, which by definition form a basis that diagonalizes the one-body density matrix. This does not fully prevent arbitrariness, and the first objective of the present paper will be to review the concept of effective bond order, in particular with respect to the rounding up rule. Then, the respective roles of the scalar and the spin-dependent relativistic effects on the bond lengths are investigated by means of state-of-the-art nonrelativistic, scalar-relativistic, and exact two-component coupled-cluster calculations, providing reference molecular geometries for the whole $\mathrm{At}X$ ($X$ = At -- F) series. A diagnostic of relevance for defining effective bond orders in heterodiatomic molecules is introduced and applied to this series, showing that the more dissymmetric the system, the less defined the effective bond order is. Finally, the role of the spin-orbit coupling on the effective bond orders is discussed. AtI appears as a key intermediate in the series in terms of the ground-state $\ensuremath{\pi}$ bonding or antibonding character. Although emphasis will be put on ground states, the present methodology is readily applicable to the description of excited states.