Edgar Engel

Giant electron-phonon interactions in molecular crystals and the importance of non-quadratic coupling

B.M. acknowledges Robinson College, Cambridge, and the Cambridge Philosophical Society for a Henslow Research Fellowship. E.A.E. and R.J.N. acknowledge financial support from the Engineering and Physical Sciences Research Council (EPSRC) of the UK [EP/K013688/1]. The calculations were performed on the Cambridge High Performance Computing Service facility and the Archer facility of the UKs national high-performance computing service (for which access was obtained via the UKCP consortium [EP/K013564/1]).

Vibrational renormalisation of the electronic band gap in hexagonal and cubic ice

Electron-phonon coupling in hexagonal and cubic water ice is studied using first-principles quantum mechanical methods. We consider 29 distinct hexagonal and cubic ice proton-orderings with up to 192 molecules in the simulation cell to account for proton-disorder. We find quantum zero-point vibrational corrections to the minimum electronic band gaps ranging from -1.5 to -1.7 eV, which leads to improved agreement between calculated and experimental band gaps. Anharmonic nuclear vibrations play a negligible role in determining the gaps. Deuterated ice has a smaller band-gap correction at zero-temperature of -1.2 to -1.4 eV. Vibrations reduce the differences between the electronic band gaps of different proton-orderings from around 0.17 eV to less than 0.05 eV, so that the electronic band gaps of hexagonal and cubic ice are almost independent of the proton-ordering when quantum nuclear vibrations are taken into account. The comparatively small reduction in the band gap over the temperature range 0 - 240 K of around 0.1 eV does not depend on the proton ordering, or whether the ice is protiated or deuterated, or hexagonal, or cubic. We explain this in terms of the atomistic origin of the strong electron-phonon coupling in ice.

Anharmonic nuclear motion and the relative stability of hexagonal and cubic ice

We use extensive first-principles quantum mechanical calculations to show that, although the static lattice and harmonic vibrational energies are almost identical, the anharmonic vibrational energy of hexagonal ice is significantly lower than that of cubic ice. This difference in anharmonicity is crucial, stabilising hexagonal ice compared with cubic ice by at least 1.4 meV/H2O, in agreement with experimental estimates. The difference in anharmonicity arises predominantly from molecular O-H bond stretching vibrational modes and is related to the different stacking of atomic layers.

Vibrational effects on surface energies and band gaps in hexagonal and cubic ice

Surface energies of hexagonal and cubic water ice are calculated using first-principles quantum mechanical methods, including an accurate description of anharmonic nuclear vibrations. We consider two proton-orderings of the hexagonal and cubic ice basal surfaces and three proton-orderings of hexagonal ice prism surfaces, finding that vibrations reduce the surface energies by more than 10%. We compare our vibrational densities of states to recent sum frequency generation absorption measurements and identify surface proton-orderings of experimental ice samples and the origins of characteristic absorption peaks. We also calculate zero point quantum vibrational corrections to the surface electronic band gaps, which range from -1.2 eV for the cubic ice basal surface up to -1.4 eV for the hexagonal ice prism surface. The vibrational corrections to the surface band gaps are up to 12% smaller than for bulk ice.

Spatially resolved proton momentum distributions in KDP from first-principles

The ferroelectric to paraelectric (PE) phase transition of KH2PO4 (KDP) is investigated as a stringent test of the first-principles, normal modes framework proposed for calculating anharmonic quantum nuclear motion. Accurate spatially resolved momentum distribution functions (MDFs) are directly calculated from the nuclear wavefunction, overcoming the limitations of path-integral molecular dynamics methods. They indicate coherent, correlated tunneling of protons across hydrogen bonds in the PE phase in agreement with neutron Compton scattering data and reproduces the key features of the experimental MDF. It further highlights the role of Slaters lateral configurations in the PE phase. The analysis in terms of normal modes demonstrates the importance of collective, correlated proton motion and underlines the value of the employed framework in interpreting experimental data. This also makes the framework very attractive for application to deuterated KDP to further elucidate the nature of the PE transition and to systems exhibiting strong quantum nuclear effects in general.