Deduction of bond length changes of symmetric molecules from experimental vibrational progressions, including a...

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.