QTAIM Atomic Charge and Polarization Parameters and Their Machine-Learning Transference among Boron-Halide Molecules

Atomic charges are invariant for out-of-plane distortions, making their molecular vibrations enticing for electronic structure studies. Of planar molecules, the boron trihalides contain some of the most polar bonds known to chemistry, although their out-of-plane bending intensities are very small contrary to expectations from atomic charge models. Here, the out-of-plane infrared intensities of the BX₍₂₎X₍₃₎X₍₄₎ (X₍₂₎, X₍₃₎, X₍₄₎ = H, F, Cl, Br) molecules are investigated using quantum theory of atoms in molecules atomic charges and atomic dipoles within the formulism of the charge, charge transfer, dipolar polarization model at the QCISD/aug-cc-pVTZ quantum level. Dipole moments induced by equilibrium charge displacement of atoms perpendicular to the molecular plane are almost completely cancelled by their electronic density polarizations. The calculated boron trihalide intensities are small for molecules with such polar bonds ranging from 0.6 to 106.1 km mol^–1. Even though the Cl atomic charge of −0.72 e in BCl₃ is more negative than the hydrogen values of −0.67 e in BH₃, the hydride out-of-plane intensity of 82.0 km mol^–1 is an order of magnitude larger than that of the trichloride, 6.3 km mol^–1. Owing to their diverse electronic structures, transference of atomic charges and dipole parameters among the boron trihalides is extremely challenging and does not result in accurate intensity values. For this reason, a machine-learning decision-tree algorithm was used to perform the transference procedure. Decision trees were optimized using quantum-level intensity values. Atomic charge and dipole parameters were estimated for a set of 12 test set molecules. These parameters provided intensity estimates with a root-mean-square error of 2.1 km mol^–1 compared with QCISD/aug-cc-pVTZ reference values.