Are multiple proton transfers in (HCO3)2(2−) dimers in kalicinite, KHCO3, coupled to vibrations of heavy atoms? A periodic DFT and LMP2 description

For H-bonded (HCO3)2(2−) dimers in the kalicinite crystal, KHCO3, the anharmonic coupling between the high-frequency νOH and low-frequency νσOO modes was studied by calculating the double-well potentials of the multiple (collective) intradimer double proton transfers at fixed and relaxed O⋯O interatomic distances using five different one-electron Hamiltonians, viz., Hartree–Fock, gradient-corrected PW91 and PBE, hybrid B3LYP(-D*), and Möller–Plesset with the second-order contribution to the correlation energy based on localized orbitals (LMP2). The strongly anharmonic shape of the resulting double-well potential, governing the energy spacings between vibrational levels, is shown to be very sensitive to the chosen combination of the one-electron and vibrational Hamiltonians. Numerical solutions of the one- and two-dimensional vibrational problem for the OH oscillators allowed us to evaluate transitions between tunnel-split doublets of the ground and the first excited vibrational levels. The best agreement with the low-temperature inelastic neutron scattering data for KHCO3 is achieved by using the B3LYP-D* Hamiltonian for the collective proton transfer pathway, which is decoupled from the KHCO3 crystal lattice. The influence of the chosen one-electron Hamiltonian on the accuracy of the calculation of the weakly anharmonic δOH, γOH, and νσOO modes is shown to be less dramatic. The shape of the νOH vs ROO dependence, calculated for KHCO3, semi-quantitatively captures the experimentally observed trend for OHO bonds in hydroxyl-bearing solids: a non-linear red shift of the νOH band with the O⋯O distance shortening; in addition, a reversal of the trend is predicted for extremely short O⋯O contacts: νOH rises again, indicating potential well narrowing when oxygens are pushed closer than ∼2.35 Å.