Unifying Time-Independent and Time-Dependent Franck--Condon Pictures in Quantum Mechanochemistry via the Linear Coupling Approximation

Quantum chemistry has achieved impressive results in modeling and interpreting mechanochemical transformations at the molecular level. An essential question, the time profile of force application, has however attracted less attention. Here, the Franck–Condon theory of quantum mechanochemistry, previously formulated for the sudden-force limit, is generalized to arbitrary time-dependent force profiles using the linear-coupling approximation. Solving the driven harmonic oscillator yields a closed-form, time-dependent effective Huang–Rhys factor: a natural measure of vibrational excitations upon force application. It is governed by the Fourier transform of the force derivative and recovers the sudden- and fixed-force limits. At the conceptual level, this linear coupling picture links mechanochemistry to vibronic spectroscopy and Marcus electron theory. For a shock-front force ramp, vibrational excitation is shown to be suppressed in frequency, only low-frequency modes being excited under realistic laser-shock-peening conditions.