Pseudo-Jahn-Teller origin of the low barrier hydrogen bond in N2H7+

Abstract

The microscopic origin and quantum effects of the low barrier hydrogen bond (LBHB) in the proton-bound ammonia dimer cation N2H7+ were studied by means of ab initio and density-functional theory(DFT) methods. These results were analyzed in the framework of vibronic theory and compared to those obtained for the Zundel cation H5O2+. All geometry optimizations carried out using wavefunction-based methods [Hartree–Fock, second and fourth order Möller–Plesset theory (MP2 and MP4), and quadratic configuration interaction with singles and doubles excitations (QCISD)] lead to an asymmetrical H3N–H+⋯NH3 conformation (C3v symmetry) with a small energy barrier (1.26kcal/mol in MP4 and QCISD calculations) between both equivalent minima. The value of this barrier is underestimated in DFT calculations particularly at the local density approximation level where geometry optimization leads to a symmetric H3N⋯H+⋯NH3 structure (D3d point group). The instability of the symmetric D3d structure is shown to originate from the pseudo-Jahn–Teller mixing of the electronic A1g1ground state with five low lying excited states of A2u symmetry through the asymmetric α2u vibrational mode. A molecular orbital study of the pseudo-Jahn–Teller coupling has allowed us to discuss the origin of the proton displacement and the LBHB formation in terms of the polarization of the NH3 molecules and the transfer of electronic charge between the proton and the NH3 units (rebonding). The parallel study of the H5O2+ cation, which presents a symmetric single-well structure, allows us to analyze why these similar molecules behave differently with respect to proton transfer. From the vibronic analysis, a unified view of the Rudle–Pimentel three-center four-electron and charge transfer models of LBHBs is given. Finally, the large difference in the N–N distance in the D3d and C3v configurations of N2H7+ indicates a large anharmonic coupling between α2u-α1g modes along the proton-transfer dynamics. This issue was explored by solving numerically the vibrational Schrödinger equation corresponding to the bidimensional E[Q(α2u),Q(α1g)] energy surface calculated at the MP4/6-311++G** level of theory.