Materials Science and Engineering B79 (2001) 98 – 112 First principles study of isotope effect in hydrogen-bonded K 3 H(SO 4 ) 2 : II — Zero-point oscillation effect 2 Yuji Suwa a, *, Jun Yamauchi b , Hiroyuki Kageshima c,1 , Shinji Tsuneyuki d a Department of Applied Physics, Faculty of Science, Science Uniersity of Tokyo, Shinjuku -ku, Tokyo 162 -0825, Japan b Corporate Research and Deelopment Center, Toshiba Corporation, 1 Komukai Toshiba -cho, Saiwai -ku, Kawasaki 212 -8582, Japan c Department of Physics, Faculty of Science, Uniersity of Tokyo, Bunkyo -ku, Tokyo 113 -0033, Japan d Institute for Solid State Physics, Uniersity of Tokyo, Kashiwanoha 5 -1 -5, Kashiwa -shi, Chiba 277 -8581, Japan Received 14 April 2000; received in revised form 7 August 2000 Abstract First principles calculation is performed to find the difference between K 3 H(SO 4 ) 2 (KHS) and K 3 D(SO 4 ) 2 (DKHS) by taking account of the zero-point oscillation effects of the proton and the deuteron. First, we calculate the potential surface for the proton in the crystal. The ground-state energies and the wavefunctions of the proton and the deuteron in that potential are calculated. Then, the stable positions of the proton and the deuteron are calculated taking account of zero-point energy, and the electric charge distributions are calculated taking account of the spread wavefunctions of the proton and the deuteron. As a result, we find that the anharmonicity of the proton potential surface makes the position of the hydrogen closer to the center of the hydrogen bond than that of the deuterium. We also find that the zero-point oscillation effect diminishes the dipole moments, and that the shrinkage of the dipole moment in the hydrogen system is larger than that of the deuteron. These two effects play significant roles in the mechanism of the isotope effect in KHS. © 2001 Elsevier Science B.V. All rights reserved. Keywords: Hydrogen bond; K 3 H(SO 4 ) 2 ; KHS; K 3 D(SO 4 ) 2 ; DKHS; Isotope effect; Proton; Deuteron www.elsevier.com/locate/mseb 1. Introduction Phase transition temperatures in hydrogen bonded ferroelectric or antiferroelectric materials are known to be raised significantly by substituting deuterium for hydrogen. In the case of K 3 H(SO 4 ) 2 (called KHS), fully substituted K 3 D(SO 4 ) 2 (called DKHS) has antifer- roelectric phase transition at 84 K while the sample with lower concentration of deuterium K 3 H 0.7 D 0.3 - (SO 4 ) 2 has no transition [1,2]. In order to explain these large isotope effects, ‘tun- neling model’ [3–5] has been proposed. In this model, the potential surface for a hydrogen atom located be- tween the two oxygen atoms is assumed to be a double- well type, and the origin of the isotope effect is ascribed to the difference between the tunneling amplitudes of the proton and the deuteron in the double-well type potential. Since the magnitude of the electric dipole moment associated with the saturated electric polariza- tion P, can not be explained only by the displacement of a proton, the original tunneling model has been modified into the coupled proton – phonon model [5,6]. According to the latter model, the transition is of a displacive type and is accompanied by softening of an optical mode due to the displacement of surrounding atoms such as a PO 4 tetrahedron in KDP crystal. Since this conclusion seems to be supported by many experi- ments, including observations of the soft mode, this model has been long accepted as the mechanism of the phase transition of hydrogen-bonded materials. For example, as regards KHS (DKHS), which we focus on in this paper, Moritomo et al. [7] successfully explained * Corresponding author. Present address: Advanced Research Lab- oratory, Hitachi, Ltd., Hatoyama, Saitama 350-0395, Japan. Fax: +81-492-965999. E-mail address: suwa@harl.hitachi.co.jp (Y. Suwa). 1 Present address: NTT Basic Research Laboratories, 3-1 Mori- nosato-Wakamiya, Atsugi, Kanagawa 243-01, Japan. 2 Part I of this paper can be found in Materials Science & Engi- neering B, Volume 79, issue 1 pages 31–44. 0921-5107/01/$ - see front matter © 2001 Elsevier Science B.V. All rights reserved. PII:S0921-5107(00)00540-7