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.

Vibrations and hydrogen bonding in porphycene

“…In conclusion, the low, if not undetectable, intensity of the N-H stretching vibration in the experimental IR spectra results from the broadening caused by other modes. Coupling of the asymmetric 30 BU mode to the low frequency 7 AG mode was discussed previously by many authors 18,27,35,36 and our results confirm nicely their findings. The extended analysis presented here reveals other additional modes that contribute significantly to the broadening of the IR N-H stretching vibration (Fig.…”

“…Analysis based on this observation has been performed for porphycene using a limited number of modes. 35,36 Consequently the perturbation of the PES along one normal mode vector would affect the force constants, and thus vibrational frequencies associated with the remaining normal modes. In the following we apply the quantitative approach that takes into account couplings of all normal modes to the asymmetric N-H stretching mode 30 BU in porphycene (see inset in Fig.…”

“…These findings point to the important role of tunneling and indicate a multidimensional character of tautomerization in porphycene, confirmed by theoretical studies. 18,24,27,[34][35][36] In a work devoted to identifying vibrational modes relevant for the proper description of the potential governing the motion of the inner protons, Ku¨hn and co-workers used four-dimensional and six-dimensional nuclear wavefunctions, the latter for a singly deuterated isotopologue. 35 Naturally, the key to understanding the complex mechanism of tautomerization in Pc is the knowledge of the intramolecular hydrogen bond (HB) parameters.…”

Geometric H/D Isotope Effects and Cooperativity of the Hydrogen Bonds in Porphycene

“…In a preliminary investigation [26] we identified a strongly coupled low-frequency mode (Q HH=DD 4 ) for the HH and DD case by displacing the molecular geometry along Q and calculating the force exerted on all other normal modes. The displacement vector of this strongly coupled mode is shown in Figure 4 d. Apparently, this promoting-type mode causes a symmetric contraction of the two HBs, that is, it is strongly related to the secondary GIE.…”

“…For molecules of the size of porphycene further approximations are required, degrading the quality of the quantum chemistry. [26] Herein, we present multidimensional nuclear wavefunction calculations of the HH/HD/DD primary and secondary GIE in porphycene. In the following section we extend our previous study of the HH/DD GIE in porphycene [26] and derive reduceddimensionality Born-Oppenheimer PES based on explicit twodimensional quantum chemical calculations supplemented by third-order anharmonic couplings for the different isotopom- [18] and 1528.…”