Zurich Open Repository and Archive University of Zurich Main Library Strickhofstrasse 39 CH-8057 Zurich www.zora.uzh.ch Year: 2015 Proton disorder in cubic ice: effect on the electronic and optical properties Garbuio, Viviana ; Cascella, Michele ; Kupchak, Igor ; Pulci, Olivia ; Seitsonen, Ari Paavo Abstract: The proton disorder in ice has a key role in several properties such as the growth mode, ther- modynamical properties, and ferroelectricity. While structural phase transitions from proton disordered to proton ordered ices have been extensively studied, much less is known about their electronic and optical properties. Here, we present ab initio many body perturbation theory-based calculations of the electronic and optical properties of cubic ice at different levels of proton disorder. We compare our results with those from liquid water, that acts as an example of a fully (proton- and oxygen-)disordered system. We find that by increasing the proton disorder, a shrinking of the electronic gap occurs inice,andit is smallest in the liquid water. Simultaneously, the excitonic binding energy decreases, so that the final optical gaps result to be almost independent on the degree of proton disorder. We explain these findings as an interplay between the local dipolar disorder and the electronic correlation. DOI: https://doi.org/10.1063/1.4929468 Posted at the Zurich Open Repository and Archive, University of Zurich ZORA URL: https://doi.org/10.5167/uzh-114303 Journal Article Published Version Originally published at: Garbuio, Viviana; Cascella, Michele; Kupchak, Igor; Pulci, Olivia; Seitsonen, Ari Paavo (2015). Proton disorder in cubic ice: effect on the electronic and optical properties. Journal of Chemical Physics, 143(8):084507. DOI: https://doi.org/10.1063/1.4929468 Proton disorder in cubic ice: Effect on the electronic and optical properties Viviana Garbuio, Michele Cascella, Igor Kupchak, Olivia Pulci, and Ari Paavo Seitsonen Citation: The Journal of Chemical Physics 143, 084507 (2015); doi: 10.1063/1.4929468 View online: http://dx.doi.org/10.1063/1.4929468 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/143/8?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Electronic properties of tantalum pentoxide polymorphs from first-principles calculations Appl. Phys. Lett. 105, 202108 (2014); 10.1063/1.4901939 Quasiparticle electronic structure and optical absorption of diamond nanoparticles from ab initio many-body perturbation theory J. Chem. Phys. 140, 214315 (2014); 10.1063/1.4880695 Structural transition in II-VI nanofilms: Effect of molar ratio on structural, morphological, and optical properties J. Appl. 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Downloaded to IP: 130.60.47.22 On: Thu, 12 May 2016 10:48:13 THE JOURNAL OF CHEMICAL PHYSICS 143, 084507 (2015) Proton disorder in cubic ice: Effect on the electronic and optical properties Viviana Garbuio,1 Michele Cascella,2 Igor Kupchak,3 Olivia Pulci,1 and Ari Paavo Seitsonen4,5 1MIFP, ETSF, Physics Department of Tor Vergata University, Via della Ricerca Scientifica 1, I-00133 Rome, Italy 2Department of Chemistry and Centre for Theoretical and Computational Chemistry (CTCC), University of Oslo, Postboks 1033, Blindern, N-0315 Oslo, Norway 3MIFP, V. Lashkarev Institute of Semiconductor Physics of National Academy of Sciences of Ukraine, pr. Nauki 45, UA-03680 Kiev, Ukraine 4Institut für Chemie, Universität Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland 5Département de Chimie, École Normale Supérieure, 24 rue Lhomond, F-75005 Paris, France (Received 5 June 2015; accepted 11 August 2015; published online 27 August 2015) The proton disorder in ice has a key role in several properties such as the growth mode, thermo- dynamical properties, and ferroelectricity. While structural phase transitions from proton disordered to proton ordered ices have been extensively studied, much less is known about their electronic and optical properties. Here, we present ab initio many body perturbation theory-based calculations of the electronic and optical properties of cubic ice at different levels of proton disorder. We compare our results with those from liquid water, that acts as an example of a fully (proton- and oxygen-)disordered system. We find that by increasing the proton disorder, a shrinking of the electronic gap occurs in ice, and it is smallest in the liquid water. Simultaneously, the excitonic binding energy decreases, so that the final optical gaps result to be almost independent on the degree of proton disorder. We explain these findings as an interplay between the local dipolar disorder and the electronic correlation. C 2015 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4929468] I. INTRODUCTION ice phases depend on the eventual presence of this orientational disorder. The phase diagram of H2O is probably the richest and In this work we focus on ice Ic, investigating the electronic most intriguing in nature. The large variety of structures of and optical properties of configurations at different levels of ice, its importance in many research fields, and the still open orientational order. We chose to investigate the ice Ic because questions concerning the local structure of water and ice and it is more isotropic than ice Ih, thus simplifying the analysis its connection to their optical and X-ray spectra1–13 make this and assignment of results to electronic effects only. In these ice system extremely interesting. systems structural17–21 and electronic properties, such as band Ordinary water can solidify in 15 crystalline and several structures and dielectric constants,21 have been studied within amorphous forms.14 Among these, under mild temperature and the density functional theory (DFT) approach. Infrared spectra pressure conditions ice has a hexagonal crystal structure with of cubic ice have been recently experimentally measured the oxygen atoms laying on a hexagonal wurtzite lattice and the and calculated within DFT.22 Concerning the excited state 15 hydrogens disordered but obeying Bernal-Fowler ice rules. properties of ice Ic, these have been experimentally probed These rules state that each oxygen must be covalently bonded many years ago by Watanabe.23 From a theoretical point of to two hydrogen atoms, and hydrogen bonded to two other view, these properties have been investigated within DFT24 hydrogen atoms. Moreover, there can be only one hydrogen and tight binding methods,25–27 but neither many-body effects atom per bond. The excited state properties of the hexagonal have been included nor the effects of the proton disorder on phase of ice (ice Ih) have been experimentally studied by these properties discussed in there. 16 Kobayashi. Ice Ih is stable, at ambient pressure, down to Here, we analyze the influence of proton disorder on about 72 K; below this temperature, a proton ordered ferro- the electronic states and on the excitonic effects in ice Ic electric phase, ice XI, becomes energetically more favorable. studying the fully proton-ordered polar structure and three At ambient pressure and temperatures between 113 and other, proton-disordered ones. We also compare the properties 28–30 153 K cubic ice (Ic), a metastable form, can be found. In of ice Ic with previous and new results related to the most this case, the sublattice of the oxygen atoms has a simple “disordered” phase, liquid water. We consider the different fcc diamond structure, while the hydrogens still obey to molecular orientations that lead both to a geometrical disorder the Bernal-Fowler ice rules. Beyond fulfilling these rules, and to a dipolar electrostatic disorder. We perform calculations orientational disorder can be present and thus several different of the electronic band structures and of the excitonic effects configurations are possible. Many physical quantities such as within many-body perturbation theory (MBPT) within the thermodynamical properties or ferroelectricity of the various self-energy and Bethe-Salpeter approaches, that have already 0021-9606/2015/143(8)/084507/7/$30.00 143, 084507-1 © 2015 AIP Publishing LLC Reuse of AIP Publishing content is subject to the terms: https://publishing.aip.org/authors/rights-and-permissions. Downloaded to IP: 130.60.47.22 On: Thu, 12 May 2016 10:48:13 084507-2 Garbuio et al. J. Chem. Phys. 143, 084507 (2015) shown their strength and predictive power (for a review, see, for example, Ref. 31). Apart from realizing another step toward the complete comprehension of the H2O properties, we will also indicate a new potential way to discriminate among proton ordered and proton disordered structures with spectroscopic characteriza- tion, opposed to traditional structural diffraction. This paper is organized as follows: in Section II the theoretical methods are briefly described together with the details of the calculations. In Section III the results related to the condensed phases of ice Ic are presented, grouped into electronic and optical properties. These results are further compared with those obtained from liquid water. Conclusions are drawn in Section IV. II. THEORETICAL METHODS AND CALCULATION DETAILS In this work, we compute excited state properties in four configurations of cubic ice at different levels of proton disorder, and in liquid water. By disorder we here refer to the relative orientations of the dipole moments of the water molecules, not in the entropic or statistical sense. For ice Ic, we employ 8-molecule supercells with the hydrogens obeying the Bernal-Fowler ice rules. With 8 molecules, we can have four physically distinct configurations. These configurations have a degeneracy of 6, 12, 24, 48 and macroscopic polarization 1 1 1 17 ⟨100⟩, ⟨ 2 2 0⟩, ⟨000⟩, and ⟨ 2 00⟩, respectively.