Chemistry of vibronic coupling. Part 1: How to maximize vibronic coupling constants in a diabatic harmonic potential model? Original Research Article

Using a simple diabatic model of two equivalent energy minima with crossing harmonic potential energy surfaces, we analyze the vibronic coupling constant λegi (e, g≡electronic states coupled, i≡coupling vibration). λegi (expressed in energy units) is a product of hegi (expressed in force units) and 〈ug|Qi|ve〉 (expressed in distance units) where hegi is the dynamic off-diagonal vibronic coupling constant, ug and ve are vibrational wave functions for normal mode i, in the g and e state respectively, and Qi is normal coordinate of ith mode. We study the way λegi depends on three parameters: the force constant (k), the reduced oscillator mass (m) and the displacement between two minima along the normal coordinate of the coupling mode Qi (ΔQ). For each k there is only one ΔQ which maximizes λegi. The maximum in λegi originates from the opposing behavior of hegi and 〈g|δH/δQi|e〉 factors in (k,ΔQ) space. A strategy for obtaining large λegis should adjust properly small ΔQs in systems with strong multiple bonds (large ks). This condition appears to be hard to fulfill in experiment. It also emerges that λegi correlates linearly with √(k/m). Hence, to maximize λegi one should build a system of light elements. The results presented here may be useful in the experimental search for high-temperature superconductivity, delimiting the space of element combinations which might be investigated.