Isotope Effect and Structure of the B2O3 and B4O6 Molecules

Abstract

A systematic application of the Teller‐Redlich product rule to the isotope effect has been carried out for several of the most likely structures of the B₂O₃ molecule, and tetrahedral B₄O₆. It is pointed out that an isotope effect of the magnitude reported by Dows and Porter in the infrared emission (2013 and 2114 cm^—1 for B₂¹¹O₃ and B₂¹⁰O₃, respectively) is incompatible with the bipyramidal (D_3h) model they consider, as well as with the linear (D_∞h) structure. Less symmetrical structures of B₂O₃ (C₂, C_2v, and C_3v symmetries) are not excluded; neither is the tetrahedral B₄O₆ structure. These conclusions are reached by using in conjunction with the product rule the theorem that the frequency of each and every vibrational mode of a molecule is a monotonic function of each atomic mass. This makes it possible to set bounds on the isotope effect of individual modes of each symmetry type, and this procedure should be generally useful. A proof of the theorem stated is given in the Appendix.