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

Abstract

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 -1.4eV. 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.

arXiv comment10 pages, 9 figures

References in corpus (17)

• Continuum variational and diffusion quantum Monte Carlo calculations
• Ice structures, patterns, and processes: A view across the ice-fields
• Phonon-assisted optical absorption in silicon from first principles
• {\it Ab--initio} finite temperature excitons
• Anharmonic vibrational properties in periodic systems: energy, electron-phonon coupling, and stress
• Electron Emission from Diamondoids: A Diffusion Quantum Monte Carlo Study
• On the Accuracy of van der Waals Inclusive Density-Functional Theory Exchange-Correlation Functionals for Ice at Ambient and High Pressures
• Stochastic approach to phonon-assisted optical absorption
• Decomposition and terapascal phases of water ice
• The refractive index and electronic gap of water and ice increase with increasing pressure
• Diffusion Quantum Monte Carlo Calculations of Excited States of Silicon
• Unified theory of electron-phonon renormalization and phonon-assisted optical absorption
• Giant electron-phonon interactions in molecular crystals and the importance of non-quadratic coupling
• Anharmonic nuclear motion and the relative stability of hexagonal and cubic ice
• Temperature effects in first-principles solid state calculations of the chemical shielding tensor made simple
• Configurational entropy of hydrogen-disordered ice polymorphs
• Theory of temperature dependent phonon-renormalized properties

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• Phonons and Anomalous Thermal Expansion Behaviour of H2O and D2O ice Ih