Deduction of bond length changes of symmetric molecules from experimental vibrational progressions, including a topological mass factor

摘要

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/w1/2) (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 ΔRx must not be neglected. The spectra and bond length changes of several symmetric molecules AXn and Xn are discussed. The experimental bond length changes correctly derived with factor 1/w1/2 are verified by reliable quantum chemical calculations.