Quantum chemical topology at the spin–orbit configuration interaction level: Application to astatine compounds

Abstract

We report a methodology that allows the investigation of the consequences of the spin-orbit coupling by means of the QTAIM and ELF topological analyses performed on top of relativistic and multiconfigurational wave functions. In practice, it relies on the "state-specific" natural orbitals (NOs; expressed in a Cartesian Gaussian-type orbital basis) and their occupation numbers (ONs) for the quantum state of interest, arising from a spin-orbit configuration interaction calculation. The ground states of astatine diatomic molecules (AtX with X = At F) and trihalide anions (IAtI − , BrAtBr − , and IAtBr −) are studied, at exact two-component relativistic coupled cluster geometries, revealing unusual topological properties as well as a significant role of the spinorbit coupling on these. In essence, the presented methodology can also be applied to the ground and/or excited states of any compound, with controlled validity up to including elements with active 5d, 6p, and/or 5f shells, and potential limitations starting with active 6d, 7p, and/or 6f shells bearing strong spin-orbit couplings.

Astatine Facing Janus: Halogen Bonding vs. Charge-Shift Bonding

“…We will focus more specifically on the influence of the spin–orbit interaction, at the origin of the significant effect shown by Alvarez-Thon and co-workers (i.e., perastatobenzene becoming more aromatic than benzene) [ 26 ]. The tools of QCT, and especially the QTAIM and ELF topological analyses, have previously demonstrated their benefits for such studies [ 55 , 56 , 57 , 58 , 59 ].…”

“…The elements that are prone to CS bonding are compact electronegative and/or lone-pair-rich atoms, albeit with moderate electronegativities [ 64 ]. Astatine has notably a demonstrated potential to form bonds of CS type [ 25 , 52 , 59 ], notably with carbon atoms [ 32 , 52 ].…”

“…The ability of chemical elements to form CS bonds originates in part from the compactness of their valence orbitals [ 62 ]. The SOC enhances the astatine propensity for CS bonding [ 52 , 59 ], most probably due to the dominant shrinkage of the 6p 1/2 shell upon inclusion of SOC, by ~0.2 Å with respect to the 6p z orbital [ 68 ]. It is therefore of interest to scrutinize the SOC effects on the topological descriptors in order to assess the CS character of C–At bonds in C 6 At 6 .…”

“…Indeed, the relative stability between the At C– XB and I C– XB interactions was inverted by ~0.9 kJ/mol, with respect to the sr results ( Table S2 in the Supplementary Materials ). Since SOC enhances the astatine propensity to form CS bonds [ 52 , 59 ] and C–At bonds can exhibit a significant CS character [ 32 , 52 ], it is unsurprising to notice in C 2 BAt 3 a weakening of the local electrophilicity at the astatine’s σ-hole. The ω + S,max value was reduced by 7% upon SOC ( Figure S3 in the Supplementary Materials ) and, consequently, the potential of astatine to accept charge transfers from XB acceptors.…”

“…CS bonding is a mechanism that aims to minimize Pauli repulsion between the bonding electrons and the σ lone-pair of astatine (referred to as the lone-pair bond-weakening effect, LPBWE [ 63 ]). The spin–orbit coupling (SOC) is known to enhance the astatine propensity for CS bonding [ 25 , 52 , 59 ], and the CS component of C–At bonds in C 6 At 6 is indeed increased upon inclusion of SOC in relativistic calculations. If σ electrons suffer a stronger Pauli repulsion (LPBWE), the local electrophilicity at the astatine σ-hole is also significantly decreased, by ~20% according to the ω + S,max value.…”