The geometric (H/D) isotope effect in porphycene: grid-based Born–Oppenheimer vibrational wavefunctions vs. multi-component molecular orbital theory

Abstract

Two approaches for the determination of the primary and secondary geometric isotope effect are compared for the exemplary porphyrinoid system porphycene, which has two intramolecular hydrogen bonds. A three-dimensional Born–Oppenheimer potential energy surface is calculated in terms of the symmetric and antisymmetric N–H stretching as well as a low-frequency hydrogen bond vibrational normal mode coordinate. From the respective ground-state nuclear wavefunction the quantum correction to the classical equilibrium geometry is determined. Further, geometry optimization within a full-dimensional multi-component molecular orbital (MC_MO) type calculation, which treats both the electrons and the hydrogen-bonded protons quantum mechanically, is performed. Both approaches yield geometric isotope effects, that is, upon H/D double substitution the hydrogen bonds are weakened and the respective N–N distances increase. In addition the MC_MO calculation gives a H/D isotope effect on the electronic structure, that is, the electronic wavefunction becomes more localized at the deuterium nucleus as compared with the proton case.