Quantitative Assessment of Tetrel Bonding Utilizing Vibrational Spectroscopy

Abstract

A set of 35 representative neutral and charged tetrel complexes was investigated with the objective of finding the factors that influence the strength of tetrel bonding involving single bonded C, Si, and Ge donors and double bonded C or Si donors. For the first time, we introduced an intrinsic bond strength measure for tetrel bonding, derived from calculated vibrational spectroscopy data obtained at the CCSD(T)/aug-cc-pVTZ level of theory and used this measure to rationalize and order the tetrel bonds. Our study revealed that the strength of tetrel bonds is affected by several factors, such as the magnitude of the σ-hole in the tetrel atom, the negative electrostatic potential at the lone pair of the tetrel-acceptor, the positive charge at the peripheral hydrogen of the tetrel-donor, the exchange-repulsion between the lone pair orbitals of the peripheral atoms of the tetrel-donor and the heteroatom of the tetrel-acceptor, and the stabilization brought about by electron delocalization. Thus, focusing on just one or two of these factors, in particular, the σ-hole description can only lead to an incomplete picture. Tetrel bonding covers a range of -1.4 to -26 kcal/mol, which can be strengthened by substituting the peripheral ligands with electron-withdrawing substituents and by positively charged tetrel-donors or negatively charged tetrel-acceptors.

Keywords: CCSD(T); intrinsic bond strength; local stretching force constant; noncovalent interactions; tetrel bonding; weak interactions.

Figure 1

Schematic representation of tetrel complexes between the electron-deficient tetrel atom of a Lewis acid (tetrel donor, T-donor, T = C, Si, Ge) and the electron-rich tetrel atom of a Lewis base (tetrel acceptor, T-acceptor, A = FH, OH₂, NH₃, Cl⁻).

Figure 2

Schematic representation of complexes 1-35 with atomic charges (in me) from the natural population analysis calculated at the CCSD(T)/aug-cc-pVTZ level of theory. Colors are used to correlate charges to specific atoms.

Figure 3

Molecular electrostatic potential of neutral tetrel-donors mapped onto the 0.001 a.u electron density surface. Blue and red correspond, respectively, to the positive and negative potential. The extreme values are ±1.9 eV. The ${\mathrm{V}}_{s_{max}}$ at the tetrel $\sigma$ or $\pi$-hole are given in bold blue, while the ${\mathrm{V}}_{s_{max}}$ at the H (36, 37, 38) and at the chalcogen atoms (55, 57) are shown in black. Calculated at the CCSD(T)/aug-cc-pVTZ level of theory.

Figure 4

Power relationship between the relative bond strength order (BSO) n and the local stretching force constants $k^a$ of the TA interaction of complexes 1–35. C donors are gray, Si donors are blue, Ge donors are purple, double bonded donors are green, and charge-assisted TBs are orange. Complex 28 is not shown. Calculated at the CCSD(T)/aug-cc-pVTZ level of theory.

Figure 5

Comparison of the relative bond strength order (BSO) n and the energy density at the bond critical point ${\mathrm{H}}_b$ of the tetrel bond of complexes. C tetrel bonds are gray, Si tetrel bonds are blue, Ge tetrel bonds are purple, double bonded tetrel bonds are green, and anionic tetrel bonds are orange. Complexes 26b–28 and 35 are not shown. Calculated at the CCSD(T)/aug-cc-pVTZ level of theory.

Figure 6

Relationship between the binding energy and interactomic distance computed at the CCSD(T)/aug-cc-pVTZ level of theory. All geometric parameters were optimized at each point of the curves for fixed r(TA) values. The blue dots represent the binding energy at the minima of complex 26 and the minimum of 35; the black lines connecting points were used to improve interpretation.