Deduction of Bond Length Changes of Symmetric Molecules from Experimental Vibrational Progressions, Including a Topological Mass Factor

The change ΔR x of bond length R x for atom X in a molecule upon electronic transition can be derived from the intensities I i of the vibrational stretching progression v = 0 → i of the electronic absorption or emission spectrum. In many cases, a simple model is sufficient for a reasonable estimate of ΔR x . For symmetric molecules, however, conceptual problems in the literature of many decades are evident. The breathing modes of various types of symmetric molecules X n and AX n (A at the center) are here discussed. In the simplest case of a harmonic vibration of the same mode in the initial and final electronic states, we obtain ΔR x ≈ [2S/(ωm x )]1/2/ w 1/2 (all quantities in atomic units). ω and S are respectively the observed vibrational quanta and the Huang–Rhys factor (corresponding, e.g., to the vibrational intensity ratio I 1/I 0 ≈ S), m x is the mass of vibrating atom X, and w is a topological factor for molecule X n or AX n . The factor 1/ w 1/2 in the expression for ΔR x must not be neglected. The spectra and bond length changes of several symmetric molecules AX n and X n are discussed. The experimental bond length changes correctly derived with factor 1/ w 1/2 are verified by reliable quantum chemical calculations.