Investigation of hydrogen bond vibrations of ice

Qin Xiao-Ling; Zhu Xu-Liang; Cao Jing-Wen; Wang Hao-Cheng; Zhang Peng

doi:10.7498/aps.70.20210013

Abstract

Despite its simple molecular structure, water is still a mystery to scientists. For the atomic and molecular vibrational modes of ice, as is well known, there are two kinds of vibrations: intra-molecular O—H stretching vibration and H—O—H bending vibration within the molecules and three kinds of molecular spatial rotations. However, thirty years ago, a high flux inelastic neutron scattering experiment showed that there are two distinct characteristic peaks in the far-infrared molecular translational vibration region of many ice phases. The origins of these peaks have not been determined till now. In this work, based on the CASTEP code, a first-principles density functional theory plane wave programme, the vibrational spectra as well as the vibrational normal modes of a series of ice phases are investigated. Two kinds of intrinsic hydrogen bond vibrational modes are first found in hydrogen-ordered ice Ic. Then it is found to be a general rule among ice family. Based on the ideal model, we prove that the two vibrational modes can be classified as four-bond vibration and two-bond vibration. There are many coupling modes in-between due to tetrahedral structure deformation under high pressure. Besides, there are also some optical vibrational modes with lower energy in the translational region, such as cluster vibrations and inter-plane vibrations. In Ice VII/VIII and XV/VI, each of which consists of two sublattices, there exist non-hydrogen bond vibrations. These molecular translational vibrations can explain all the far-infrared vibrational spectrum of ice phase, which makes up the last piece of the jigsaw puzzle for the molecular vibration theory of ice. The two vibrational modes do not exist in liquid water due to the collapse of the rigid tetrahedral structure. Thus, a window remains for ice resonance absorption with minimum energy loss in water. This theory is expected to be applicable to industrial deicing, food thawing, gas hydrate mining, and biomolecule frozen molding, etc.

Keywords:

Authors and contacts

School of Space Science and Physics, Shandong University, Weihai 264200, China

Corresponding author: Zhang Peng, zhangpeng@sdu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11075094)

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References

[1]	邓耿, 尉志武 2016 科学通报 61 3181 Google Scholar Deng G, Wei Z W 2016 Chin. Sci. Bull. 61 3181 Google Scholar
[2]	Pauling L 1960 The Nature of Chemical Bond (New York: Cornell University Press) pp449–504
[3]	Pople J A 1957 Proc. R. Soc. London, Ser. A 239 550 Google Scholar
[4]	Claussen W F 1951 J. Chem. Phys. 19 1425 Google Scholar
[5]	Frank H S, Wen W Y 1957 Discuss. Faraday Soc. 24 133 Google Scholar
[6]	Symons M C R 1972 Nature 239 257 Google Scholar
[7]	Wernet P, Nordlund D, Bergmann U, Cavalleri M, Odelius M, Ogasawara H, Naslund L A, Hirsch T K, Ojamae L, Glatzel P, Pettersson L G M, Nilsson A 2004 Science 304 995 Google Scholar
[8]	Smith J D, Cappa C D, Wilson K R, Messer B M, Cohen R C, Saykally R J 2004 Science 306 851 Google Scholar
[9]	Sun Q 2013 Chem. Phys. Lett. 568 90 Google Scholar
[10]	Nilsson A, Wernet Ph, Nordlund D, Bergmann U, Cavalleri M 2005 Science 308 793A Google Scholar
[11]	Smith J D, Cappa C D, Messer B M, Cappa C D 2005 Science 308 793B Google Scholar
[12]	Tokushima T, Harada Y, Takahashi O, Senba Y, Ohashi H, Pettersson L G M, Nilsson A, Shin S 2008 Chem. Phys. Lett. 460 387 Google Scholar
[13]	Raichlin Y, Millo A, Katzir A 2004 Phys. Rev. Lett. 93 185703 Google Scholar
[14]	Russo J, Tanaka H 2014 Nat. Commun. 5 3556 Google Scholar
[15]	Ktihne T D, Khaliullin R Z 2013 Nat. Commun. 4 1450 Google Scholar
[16]	Ktihne T D, Khaliullin R Z 2014 J. Am. Chem. Soc. 136 3395 Google Scholar
[17]	Bertie J E, Whalley E 1967 J. Chem. Phys. 46 1271 Google Scholar
[18]	Tammann G 1900 Ann. Phys. 307 1 Google Scholar
[19]	Demontis P, LeSar R, Klein M L 1988 Phys. Rev. Lett. 60 2284 Google Scholar
[20]	Bertie J E, Calvert L D, Whalley E 1963 J. Chem. Phys. 38 840 Google Scholar
[21]	Bridgman P W 1912 Proc. Am. Acad. Arts Sci. 47 441 Google Scholar
[22]	Bridgman P W 1937 J. Chem. Phys. 5 964 Google Scholar
[23]	Whalley E, Davidson D W 1965 J. Chem. Phys. 43 2148 Google Scholar
[24]	Whalley E, Davidson D W, Heath J B R 1966 J. Chem. Phys. 45 3976 Google Scholar
[25]	Kuhs W F, Finney J L, Vettier C, Bliss D V 1984 J. Chem. Phys. 81 3612 Google Scholar
[26]	Whalley E, Heath J B R, Davidson D W 1968 J. Chem. Phys. 48 2362 Google Scholar
[27]	Tajima Y, Matsuo T, Suga H 1982 Nature 299 810 Google Scholar
[28]	Hirsch K R, Holzapfel W B 1986 J. Chem. Phys. 84 2771 Google Scholar
[29]	Lobban C, Finney J L, Kuhs W F 1998 Nature 391 268 Google Scholar
[30]	Matsuo T, Tajima Y, Suga H 1986 J. Phys. Chem. Solids 47 165 Google Scholar
[31]	Salzmann C G, Radaelli P G, Mayer A E, Finney J L 2006 Science 311 1758 Google Scholar
[32]	Tribello G A, Slater B, Salzmann C G 2006 J. Am. Chem. Soc. 128 12594 Google Scholar
[33]	Salzmann C G, Radaelli P G, Mayer E, Finney J L 2009 Phys. Rev. Lett. 103 105701 Google Scholar
[34]	Falenty A, Hansen T C, Kuhs W F 2014 Nature 516 213 Google Scholar
[35]	del Rosso L, Celli M, Ulivi L 2016 Nat. Commun. 7 13394 Google Scholar
[36]	Millot M, Hamel S, Rygg J R, Celliers P M, Collins G W, Coppari F, Fratanduono D E, Jeanloz R, Swift D C, Eggert J H 2018 Nat. Phys. 14 297 Google Scholar
[37]	Millot M, Coppari F, Rygg J R, Barrios A C, Hamel S, Swift D C 2019 Nature 569 251 Google Scholar
[38]	Algara-Siller G, Lehtinen O, Wang F C, Nair R R, Kaiser U, Wu H A, Geim A K, Grigorieva IV 2015 Nature 519 443 Google Scholar
[39]	Zhou W, Yin K, Wang C, Zhang Y, Xu T, Borisevich A, Sun L, Idrobo J C, Chisholm M F, Pantelides S T, Klie R F, Lupini A R 2015 Nature 528 E1 Google Scholar
[40]	Koga K, Zeng X C, Tanaka H 1997 Phys. Rev. Lett. 79 5262 Google Scholar
[41]	Ma R, Cao D, Zhu C, Tian Y, Peng J, Guo J, Chen J, Li X Z, Francisco J S, Zeng X C, Xu L M, Wang E G, Jiang Y 2020 Nature 577 60 Google Scholar
[42]	Kuhs W F, Lehmann M S 1983 J. Phys. Chem. 87 4312 Google Scholar
[43]	Konig H 1943 Z. Kristallogr. 105 279 Google Scholar
[44]	Dowell L G, Rinfret A P 1960 Nature 188 1144 Google Scholar
[45]	Murray B J, Bertram A K 2006 Phys. Chem. Chem. Phys. 8 186 Google Scholar
[46]	Murray B J 2008 Environ. Res. Lett. 3 025008 Google Scholar
[47]	Malkin T L, Murray B J, Brukhno A V, Anwar J, Salzmann C G 2012 Proc. Natl. Acad. Sci. U. S. A. 109 1041 Google Scholar
[48]	Whalley E 1981 Science 211 389 Google Scholar
[49]	Mayer E, Hallbrucker A 1987 Nature 325 601 Google Scholar
[50]	Kuhs W F, Bliss D V, Finney J L 1987 J. Phys. Colloq. 48 631 Google Scholar
[51]	Kuhs W F, Sippel C, Falenty A, Hansen T C 2012 Proc. Natl. Acad. Sci. U. S. A. 109 21259 Google Scholar
[52]	Murray B, Knopf D, Bertram A 2005 Nature 434 202 Google Scholar
[53]	Falenty A, Kuhs W F 2009 J. Phys. Chem. B 113 15975 Google Scholar
[54]	Baker J M, Dore J C, Behrens P 1997 J. Phys. Chem. B 101 6226 Google Scholar
[55]	Malkin T L, Murray B J, Salzmann C G, Molinero V, Pickering S J, Whale T F 2015 Phys. Chem. Chem. Phys. 17 60 Google Scholar
[56]	del Rosso L, Celli M, Grazzi F, Catti M, Ulivi L 2020 Nat. Mater. 19 663 Google Scholar
[57]	Komatsu K, Machida S, Noritake F, Hattori T, Kagi H 2020 Nat. Commun. 11 464 Google Scholar
[58]	Lekner J 1997 Physica B 240 263 Google Scholar
[59]	黄盈盈, 苏艳, 赵纪军 2019 高压物理学报 33 010001 Google Scholar Huang Y Y, Su Y, Zhao J J 2019 Chin. J. High Pressure Phys. 33 010001 Google Scholar
[60]	Bartels-Rausch T, Bergeron V, Csrtwright J H E, Escribano R, Finney J L, Grothe H 2012 Rev. Mod. Phys. 84 885 Google Scholar
[61]	Moberg D R, Sharp P J, Paesani F 2018 J. Phys. Chem. B 122 10572 Google Scholar
[62]	Kamb B 1964 Acta Crystallogr. 17 1437 Google Scholar
[63]	Finch E D 1968 J. Chem. Phys. 49 4361 Google Scholar
[64]	Kamb B, Hamilton W C, Laplaca S J, Prakash A 1971 J. Chem. Phys. 55 1934 Google Scholar
[65]	Fortes A D, Wood I G, Brodholt J P, Vočadlo L 2003 J. Chem. Phys. 119 4567 Google Scholar
[66]	Bauer M, Elsaesser M S, Winkel K, Mayer E, Loerting T 2008 Phys. Rev. B 77 220105 Google Scholar
[67]	Scheuermann M, Geil B, Löw F, Fujara F 2009 J. Chem. Phys. 130 024506 Google Scholar
[68]	Bertie J E, Whalley E 1964 J. Chem. Phys. 40 1646 Google Scholar
[69]	Bertie J E, Labbé H J, Whalley E 1968 J. Chem. Phys. 49 775 Google Scholar
[70]	Bertie J E, Francis B F 1980 J. Chem. Phys. 72 2213 Google Scholar
[71]	Bertie J E, Francis B F 1982 J. Chem. Phys. 77 1 Google Scholar
[72]	Li J C, Londono D, Ross D K, Finney J L, Bennington S M, Taylor A D 1992 J. Phys. Condens. Matter 4 2109 Google Scholar
[73]	Kamb B 1965 Science 150 205 Google Scholar
[74]	Kuhs W F, Ahsbahs H, Londono D, Finney J L 1989 Physica B 156 684 Google Scholar
[75]	Whale T F, Clark S J, Finney J L 2013 J. Raman Spectrosc. 44 290 Google Scholar
[76]	Komatsu K, Noritake F, Machida S 2016 Sci. Rep. 6 28920 Google Scholar
[77]	Nanda K D, Beran G J O 2013 J. Phys. Chem. Lett. 4 3165 Google Scholar
[78]	Gasser T M, Thoeny A, Plaga L 2018 Chem. Sci. 9 4224 Google Scholar
[79]	Klotz S, Besson J M, Hamel G, Nelmes R J, Loveday J S, Marshall W G 1999 Nature 398 681 Google Scholar
[80]	Vaks V G, Zinenko V I 1981 Solid State Commun. 39 643 Google Scholar
[81]	Song M, Yamawaki H, Fujihisa H, Sakashita M, Aoki K 2003 Phys. Rev. B 68 014106 Google Scholar
[82]	Besson J M, Kobayashi M, Nakai T, Endo S 1997 Phys. Rev. B 55 11191 Google Scholar
[83]	Pruzan P, Chervin J C, Canny B 1993 J. Chem. Phys. 99 9842 Google Scholar
[84]	Goncharov A F, Struzhkin V V, Somayazulu M S, Hemley R J, Mao H K 1996 Science 273 218 Google Scholar
[85]	Aoki K, Yamawaki H, Sakashita M, Fujihisa H 1996 Phys. Rev. B 54 15673 Google Scholar
[86]	Klug D D, Handa Y P, Tse J S, Whalley E 1989 J. Chem. Phys. 90 2390 Google Scholar
[87]	Minceva-Sukarova B, Sherman W F, Wilkinson G R 1984 J. Phys. C: Solid State Phys. 17 5833 Google Scholar
[88]	Li J C, Londono J D, Ross D K, Finney J L, Tomkinson J, Sherman W F 1991 J. Chem. Phys. 94 6770 Google Scholar
[89]	Garg A K 1988 Phys. Status Solidi A 110 467 Google Scholar
[90]	Tse J S, Klein M L, McDonald I R 1984 J. Chem. Phys. 81 6124 Google Scholar
[91]	Holzapfel W B 1972 J. Chem. Phys. 56 712 Google Scholar
[92]	Polian A, Grimsditch M 1984 Phys. Rev. Lett. 52 1312 Google Scholar
[93]	Flores-Livas J A, Sanna A, Graužinytė M, Davydov A, Goedecker S, Marques M A L 2017 Sci. Rep. 7 6825 Google Scholar
[94]	Lu X Z, Zhang Y, Zhao P, Fang S J 2011 J. Phys. Chem. B 115 71 Google Scholar
[95]	Marqués M, Ackland G, Loveday J 2009 High Pressure Res. 29 208 Google Scholar
[96]	Putrino A, Parrinello M 2002 Phys. Rev. Lett. 88 176401 Google Scholar
[97]	Goncharov A F, Struzhkin V V, Mao H K, Hemley R J 1999 Phys. Rev. Lett. 83 1998 Google Scholar
[98]	Men Z, Fang W, Li D, Li Z, Sun C 2014 Sci. Rep. 4 4606 Google Scholar
[99]	Giauque W F, Stout J W 1936 J. Am. Chem. Soc. 58 1144 Google Scholar
[100]	Kawada S 1972 J. Phys. Soc. Jpn. 32 1442 Google Scholar
[101]	Leadbetter A J, Ward R C 1985 J. Chem. Phys. 82 424 Google Scholar
[102]	Line C M B, Whitworth R W 1996 J. Chem. Phys. 104 10008 Google Scholar
[103]	Jackson S M, Nield V M, Whitworth R W, Oguro M, Wilson C C 1997 J. Phys. Chem. B 101 6142 Google Scholar
[104]	Salzmann C G, Radaelli P G, Finney J L, Mayer E 2008 Phys. Chem. Chem. Phys. 10 6313 Google Scholar
[105]	Salzmann C G, Hallbrucker A, Finney J L, Mayer E 2006 Phys. Chem. Chem. Phys. 8 3088 Google Scholar
[106]	Zhang J, Xiao Z, Kuo J 2010 J. Chem. Phys. 132 184506 Google Scholar
[107]	Tran H, Cunha A V, Shephard J J, Shalit A, Hamm P, Jansen T L C, Salzmann C G 2017 J. Chem. Phys. 147 144501 Google Scholar
[108]	Salzmann C G, Hallbrucker A, Finney J L, Mayer E 2006 Chem. Phys. Lett. 429 469 Google Scholar
[109]	Yoshimura Y, Stewart S T, Mao H K, Hemley R J 2007 J. Chem. Phys. 126 174505 Google Scholar
[110]	Koza M M, Schober H, Tölle A, Fujara F, Hansen T 1999 Nature 397 660 Google Scholar
[111]	Koza M M, Schober H, Parker S F, Peters J 2008 Phys. Rew. B 77 104306 Google Scholar
[112]	Huang Y Y, Zhu C Q, Wang L, Cao X X, Su Y, Jiang X, Meng S, Zhao J J, Zeng X C 2016 Sci. Adv. 2 e1501010 Google Scholar
[113]	Huang Y Y, Zhu C Q, Wang L, Zhao J J and Zeng X C 2017 Chem. Phys. Lett. 671 186 Google Scholar
[114]	Matsui T, Hirata M, Yagasaki T, Matsumoto M, Tanaka H 2017 J. Chem. Phys. 147 091101 Google Scholar
[115]	Liu Y, Ojamäe L 2018 Phys. Chem. Chem. Phys. 20 8333 Google Scholar
[116]	Engel E A, Anelli A, Ceriotti M, Pickard C J, Needs R J 2018 Nat. Commun. 9 2173 Google Scholar
[117]	Matsui T, Yagasaki T, Matsumoto M, Tanaka H 2019 J. Chem. Phys. 150 041102 Google Scholar
[118]	del Rosso L, Grazzi F, Celli M, Colognesi D, Garcia-Sakai V, Ulivi L 2016 J. Phys. Chem. C 120 26955 Google Scholar
[119]	Bertie J E, Labbe H J, Whalley E 1969 J. Chem. Phys. 50 4501 Google Scholar
[120]	Wong P T T, Whalley E 1976 J. Chem. Phys. 65 829 Google Scholar
[121]	Rasetti F 1932 Nuovo Cirnento 9 72 Google Scholar
[122]	Hibben J H 1937 J. Chem. Phys. 5 166 Google Scholar
[123]	Cross P C, Burnham J, Leighton P A 1937 J. Am. Chem. Soc. 59 1134 Google Scholar
[124]	Narayanaswarny P K 1948 Proc. Indian Acad. Sci. 27 311 Google Scholar
[125]	Valkov V I, Maslenkova G L 1956 Opt. Spektrosk. 1 881
[126]	Taylor M J, Whalley E 1964 J. Chem. Phys. 40 1660 Google Scholar
[127]	Marchi M, Tse J S, Klein M L 1986 J. Chem. Phys. 85 2414 Google Scholar
[128]	Renker B 1973 International Symposium on the Physics and Chemistry of Ice Ottowa, Ont., Canada, August 14–18, 1972 p82
[129]	Li J C, Ross D K, Howe L, Hall P G, Tomkinson J 1989 Physica B 156 376 Google Scholar
[130]	Klug D D, Tse J S, Whalley E 1991 J. Chem. Phys. 95 7011 Google Scholar
[131]	Li J C 1996 J. Chem. Phys. 105 6733 Google Scholar
[132]	Li J C, Ross D K 1993 Nature 365 327 Google Scholar
[133]	Morrison I, Jenkins S 1999 Physica B 263 442 Google Scholar
[134]	Klotz S, Strässle T, Salzmann C G, Philippe J, Parker S F 2005 Europhys. Lett. 72 576 Google Scholar
[135]	Zhang P, Tian L, Zhang Z P, Shao G, Li J C 2012 J. Chem. Phys. 137 044504 Google Scholar
[136]	He X, Sode O, Xantheas S S, Hirata S 2012 J. Chem. Phys. 137 204505 Google Scholar
[137]	Zhang P, Liu Y, Yu H, Han S H, Lü Y B, Lv M S, Cong W Y 2014 Chin. Phys. B 23 026103 Google Scholar
[138]	Zhang P, Wang Z, Lü Y B, Ding Z W 2016 Sci. Rep. 6 29273 Google Scholar
[139]	Yuan Z Y, Zhang P, Yao S K, Lü Y B, Yang H Z, Luo H W, Zhao Z J 2017 RSC Adv. 7 36801 Google Scholar
[140]	Yao S K, Zhang P, Zhang Y, Lü Y B, Yang T l, Sun B G, Yuan Z Y, Luo H W 2017 RSC Adv. 7 31789 Google Scholar
[141]	Jiang L, Yao S K, Zhang K, Wang Z R, Luo H W, Zhu X L, Gu Y, Zhang P 2018 Molecules 23 2780 Google Scholar
[142]	Qin X L, Zhu X L, Cao J W, Jiang L, Gu Y, Wang X C, Zhang P 2019 Molecules 24 3115 Google Scholar
[143]	Zhao Z J, Qin X L, Cao J W, Zhu X L, Yang Y C, Wang H C, Zhang P 2019 ACS Omega 4 18936 Google Scholar
[144]	Cao J W, Chen J Y, Qin X L, Zhu X L, Jiang L, Gu Y, Yu X H, Zhang P 2019 Molecules 24 3135 Google Scholar
[145]	Zhang K, Zhang P, Wang Z R, Zhu X L, Lu Y B, Guan C B, Li Y H 2018 Molecules 23 1781 Google Scholar
[146]	Gu Y, Zhu X L, Jiang L, Cao J W, Qin X L, Yao S K, Zhang P 2019 J. Phys. Chem. C 123 14880 Google Scholar
[147]	Zhu X L, Cao J W, Qin X L, Jiang L, Gu Y, Wang H C, Liu Y, Kolesnikov A I, Zhang P 2020 J. Phys. Chem. C 124 1165 Google Scholar
[148]	Wei Z W, Zhu X L, Cao J W, Qin X L, Jiang L, Gu Y, Wang H C, Zhang P 2019 AIP Adv. 9 115118 Google Scholar
[149]	Zhu X L, Yuan Z Y, Jiang L, Zhang K, Wang Z R, Luo H W, Gu Y, Cao J W, Qin X L, Zhang P 2019 New J. Phys. 21 043054 Google Scholar
[150]	Wang Z R, Zhu X L, Jiang L, Zhang K, Luo H W, Gu Y, Zhang P 2019 Materials 12 246 Google Scholar
[151]	Matsumoto M, Yagasaki T, Tanaka H 2018 J. Comput. Chem. 39 61 Google Scholar
[152]	Wang H C, Zhu X L, Cao J W, Qin X L, Yang Y C, Niu T X, LüY B, Zhang P 2020 New J. Phys. 22 093066 Google Scholar
[153]	Hammer B, Hansen L B, Norskov J K 1999 Phys. Rev. B 59 7413 Google Scholar
[154]	Bernal J D, Fowler R H 1933 J. Chem. Phys. 1 515 Google Scholar
[155]	Li J C, Burnham C, Kolesnikov A I, Eccleston R S 1999 Phys. Rev. B 59 9088 Google Scholar
[156]	Kolesnikov A I, Li J C, Ross D K, et al. 1992 Phys. Lett. A 168 308 Google Scholar

Cited By

图 1 常态冰Ih相的声子态密度(PDOS)谱. 横轴波数的单位是cm^–1, 四个独立的振动带从左到右依次是分子间平移振动带(translation), 分子转动振动(libration)带, 分子内弯曲振动(bending)带, 分子内伸缩振动(stretching)带

Figure 1. Phonon density of states (PDOS) spectrum of ice Ih. The four independent vibration bands from left to right are translation band, libration band, bending band, and stretching band.

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图 2 K点和截断能收敛性测试. 总能量与K点间隔的关系如图(a), 与截断能的关系如图(b)^[141]

Figure 2. Diagram of the K-point and energy cutoff convergence tests. The total energy against k-point separation is shown in (a) and the cutoff convergence is shown in (b)^[141].

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图 3 氢有序的冰Ic相的INS谱和PDOS谱, 横轴单位为cm^–1(底轴)和meV(顶轴)

Figure 3. INS spectrum and PDOS spectrum of hydrogen ordered Ice Ic, the units of horizontal axis are cm^–1 (bottom axis) and MeV (top axis).

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图 4 (a)布里渊区中的声子色散曲线; (b)归一化声子态密度(PDOS). PDOS曲线的纵坐标与图(a)中的纵坐标对应

Figure 4. (a) The Phonon dispersion curves; (b) the corresponding integrated PDOS spectrum.

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图 5 氢有序的Ic相理想模型平动区的三种简正模式. 因为原胞仅含两个水分子, 为显示整体的振动情况, 使用了超胞来演示两类振动模式. 绿色箭头表示振动方向, 大小正比于振幅

Figure 5. The three normal modes in the translational region of hydrogen ordered Ice Ic. The primitive cell contains two water molecules, and in order to show the vibration of the whole, the supercell is used to demonstrate two vibration modes. The green arrow indicates the direction of the vibration, and the magnitude is proportional to the amplitude.

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图 6 氢有序冰相PDOS计算谱, 按照压强大小排列, 从上到下依次是冰X, VIII, XIII, XV, XIV, II, IX, Ic和XI. 黄色矩形区域对应两个氢键特征峰的位置

Figure 6. PDOS spectrum of hydrogen ordered Ice phases, arranged by pressure, from top to bottom are ice X, VIII, XIII, XV, XIV, II, IX, Ic and XI. The yellow rectangle region corresponds to the positions of two characteristic peaks of hydrogen bond.

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图 7 冰X相的简正振动模式, 其中450, 998, 1260和1508 cm^–1波数处的振动模式都是三重简并的, 2115 cm^–1处的振动模式是二重简并的

Figure 7. The normal modes of ice X, the vibration modes at 450, 998, 1260 and 1508 cm^–1 are triplically degenerate, and the vibration modes at 2115 cm^–1 are doubly degenerate.

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图 8 冰VIII和冰VII的PDOS谱对比图. 插图为冰VIII的INS谱和计算得到的PDOS谱, 范围在2—140 meV

Figure 8. PDOS spectrum of Ice VIII and VII. The inset shows the INS spectrum of Ice VIII and the computed PDOS spectrum (2–140 meV).

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图 9 (a)冰VIII和(b)冰VII的双键振动(红色)、四键振动(蓝色)、非氢键振动(绿色)三类模式的分布图. 插图为计算模拟得到的VIII和VII的PDOS谱, 范围0—350 cm^–1

Figure 9. Statistical distribution of two-bond vibration (red), four-bond vibration (blue) and non-hydrogen bond vibration modes (green) of Ice VIII (a) and Ice VII (b). The insertation shows the PDOS spectrum of Ice VIII and VII (0–350 cm^–1).

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图 10 从上到下依次是冰Ih相的INS实验谱和模拟的PDOS谱, 冰Ih对应的氢有序相冰XI的PDOS谱, 理想模型Ic的PDOS谱

Figure 10. The INS spectrum and PDOS spectrum of ice Ih, the PDOS spectrum of hydrogen ordered ice XI and the PDOS spectrum of ice Ic.

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图 11 (a)有序相冰XI和(b)冰Ih的双键振动、四键振动模式的统计分布图. 插图为计算模拟得到的XI, Ih的PDOS谱

Figure 11. Statistical distribution of two-bond and four-bond vibrational modes of (a) ice XI and (b) ice Ih. The illustration shows the PDOS spectrum of XI and Ih.

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图 12 冰V/XII和冰VI/XV的PDOS谱对比图. 插图为冰VI和V的INS谱, 范围2—140 meV

Figure 12. Comparisons of PDOS spectrum of Ice V/XII and Ice VI/XV. The insertation shows the INS spectrum of ice VI and V (2–140 meV).

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图 13 冰VIII平动区161 cm^–1处的简正振动和冰XV在107 cm^–1处的振动; 冰II平动区115 cm^–1处的简正振动和冰IX在116 cm^–1处的振动示意图

Figure 13. The normal mode at 161 cm^–1 in ice VIII and 107 cm^–1 in ice XV; The normal mode at 115 cm^–1 in ice II and 116 cm^–1 in ice IX.

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图 14 在直角坐标系下yz平面内展示水分子的三种转动　(a)绕z轴的扭曲转动; (b)绕y轴的面间摇摆; (c)绕x轴的面内摇摆

Figure 14. Three rotations of H₂O: (a) Twisting around the z-axis; (b) wagging around the y-axis; (c) rocking around the x-axis

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图 15 冰Ih相的INS谱和冰XVII, XVI的PDOS谱. 蓝红两条虚线标记出冰Ih相实验谱两个氢键振动峰(226和303 cm^–1)的位置

Figure 15. INS spectrum of ice Ih and PDOS spectrum of ice XVII and XVI. The blue and red dotted lines mark the positions of the two hydrogen bond vibration peaks (226 and 303 cm^–1) in ice Ih.

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图 16 水与冰Ih的红外吸收谱对比图

Figure 16. Infrared absorption spectrum of water and ice Ih.

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图 A1 氢有序冰Ic相原胞及其两类氢键振动模式

Figure A1. Two kinds of H-bond vibrational modes in ice Ic.

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图 A2 氢有序冰相IX、II和XIV中两类氢键振动模式. 波数在245, 206和194 cm^–1处的振动分别为冰IX, II和XIV的双键振动模式; 波数在307, 318和292 cm^–1处的分别为冰IX, II和XIV的四键振动模式 (冰XIV中振动明显的分子用黄色标记)

Figure A2. Two kinds of H-bond vibrational modes in ice IX, II, and XIV. The two-bond vibrational modes of Ice IX, II and XIV at 245, 206 and 194 cm^–1 are respectively; The four-bond vibrational modes of ice IX, II and XIV at 307, 318 and 292 cm^–1, respectively (The yellow moleculars vibrate obviously in ice XIV).

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图 A3 冰VII相在178 cm^–1处的双键振动模式和在255 cm^–1处的四键振动模式; 冰XVI相在160 cm^–1处的双键振动模式和在237 cm^–1处的四键振动模式 (冰VII中振幅明显的分子用黄色标记)

Figure A3. Two-bond vibrational mode at 178 cm^–1 and four-bond vibrational mode at 255 cm^–1 in Ice VII phase; two-bond vibration mode at 160 cm^–1 and four bond vibration mode at 237 cm^–1 in ice VIII (The yellow moleculars vibrate obviously).

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图 A4 冰XI相220 cm^–1处的双键振动模式和310 cm^–1处的四键振动模式; 冰Ih相244 cm^–1处的双键振动模式和327 cm^–1处的四键振动模式

Figure A4. Two-bond vibrational mode at 220 cm^–1 and four-bond vibrational mode at 310 cm^–1 in ice XI; two-bond vibrational mode at 244 cm^–1 and four-bond vibrational mode at 327 cm^–1 in ice Ih.

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图 A5 冰XIII相和冰V相在223/225 cm^–1处的双键振动模式和318/312 cm^–1处的四键振动模式; 冰XV相和冰VI相在206/231 cm^–1处的双键振动模式和285/328 cm^–1处的四键振动模式 (冰VII中振幅明显的分子用黄色原子标记)

Figure A5. Two-bond vibrational mode at 223/225 cm^–1 and four-bond vibrational mode at 318/312 cm^–1 in ice XIII/V; two-bond vibrational mode at 206/231 cm^–1 and four-bond vibrational mode at 285/328 cm^–1 of ice XV/VI (The yellow moleculars vibrate obviously).

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图 A6 冰XVII相209 cm^–1处的双键振动模式和301 cm^–1处的四键振动模式; 冰XVI相220 cm^–1处的双键振动模式和314 cm^–1处的四键振动模式 (振幅明显的原子振动用黄色标记)

Figure A6. Two-bond mode at 209 cm^–1 and four-bond mode at 301 cm^–1 in ice XVII; two-bond mode at 220 cm^–1 and four-bond mode at 314 cm^–1 of ice XVI (The yellow moleculars vibrate obviously).

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表 1 部分冰相的计算参数. 包括静水压强、截断能、K点取样网格或K点间隔

Table 1. Calculation parameters of ice phases, including calculation of pressure, cutoff energy, K-mesh or seperation.

Ice phase	Environmental pressure/GPa	Energy cutoff/eV	K-mesh or seperation
Ih	0	830	3 × 2 × 2
Ic	0	1200	7 × 7 × 8
II	0.50	750	2 × 2 × 2
V	1.00	750	2 × 2 × 1
VI	2.00	750	2 × 2 × 2
VII	2.40	830	3 × 3 × 2
VIII	2.40	1000	4 × 4 × 5
IX	0.30	750	2 × 2 × 2
X	120.00	830	0.07/Å
XI	0	750	6 × 6 × 3
XIII	1.00	830	2 × 3 × 1
XIV	0.55	750	2 × 2 × 3
XV	0.90	750	4 × 4 × 4
XVI	0	750	1 × 1 × 1
XVII	0.40	830	1 × 1 × 1

DownLoad: CSV

表 2 各冰相的氢键、氢氧共价键的长度和相邻的氧原子的距离(单位: Å), H—O—H键角, 4个振动区域的波数范围(单位: cm^–1), 结构优化密度(单位: g/cm^–3)

Table 2. Length of H-bond, OH covalent bond and distance of adjacent O atoms (in Å), H—O—H bond angle, wavenumber range of four vibration regions of ice phases (in cm^–1), structure optimization density (in g/cm^–3).

ICE	H···O	O—H	O—H···O	HOH Angle	Translation	Libration	Bending	Stretching	Density
Ice X	1.138	1.138	2.275	109.5	—	—	—	—	3.3
Ice VIII	2.038	0.976	3.013	105.1	161-254	502-1032	1589-1742	3357-3480	1.42
Ice XIII	1.786–3.173	0.980–0.987	2.751–2.874	102.7–108.1	50–318	524–982	1629–1721	3198–3441	1.18
Ice XV	1.902–1.991	0.978–0.981	2.886–2.908	101.6–107.2	73–285	477–936	1609–1709	3278–3485	1.21
Ice XIV	1.986–1.838	0.978–0.984	2.793–2.951	102.8–105.3	104–292	502–933	1647–1735	3234–3478	1.15
Ice II	1.815–2.057	0.976–0.986	2.796–3.023	102.8/105.0	142–318	522–969	1659–1723	3193–3483	1.06
Ice IX	1.829–1.849	0.984/0.985	2.802–2.824	104.2/104.7	67–307	580–1003	1639–1716	3177–3391	1.01
Ice Ic	1.799	1.000	2.798	105.6	230/321	589–1053	1631–1708	3113–3334	0.89
Ice XI	1.813/1.814	0.987/0.988	2.799/2.802	105.7/106.0	47–310	586–1063	1634–1710	3110–3353	0.89
Ice Ih	1.788–1.866	0.986–0.989	2.784–2.843	104.7–106.2	33–327	579–1030	1651–1706	3110–3363	0.88
XVII	1.806–1.840	0.986–0.988	2.791–2.826	105.0–107.9	36–301	588–1037	1635–1709	3125–3369	0.81
XVI	1.797–1.845	0.984–0.990	2.768–2.830	105.1–106.3	53–315	594–1053	1649–1715	3117–3380	0.80

DownLoad: CSV

[1]	邓耿, 尉志武 2016 科学通报 61 3181 Google Scholar Deng G, Wei Z W 2016 Chin. Sci. Bull. 61 3181 Google Scholar
[2]	Pauling L 1960 The Nature of Chemical Bond (New York: Cornell University Press) pp449–504
[3]	Pople J A 1957 Proc. R. Soc. London, Ser. A 239 550 Google Scholar
[4]	Claussen W F 1951 J. Chem. Phys. 19 1425 Google Scholar
[5]	Frank H S, Wen W Y 1957 Discuss. Faraday Soc. 24 133 Google Scholar
[6]	Symons M C R 1972 Nature 239 257 Google Scholar
[7]	Wernet P, Nordlund D, Bergmann U, Cavalleri M, Odelius M, Ogasawara H, Naslund L A, Hirsch T K, Ojamae L, Glatzel P, Pettersson L G M, Nilsson A 2004 Science 304 995 Google Scholar
[8]	Smith J D, Cappa C D, Wilson K R, Messer B M, Cohen R C, Saykally R J 2004 Science 306 851 Google Scholar
[9]	Sun Q 2013 Chem. Phys. Lett. 568 90 Google Scholar
[10]	Nilsson A, Wernet Ph, Nordlund D, Bergmann U, Cavalleri M 2005 Science 308 793A Google Scholar
[11]	Smith J D, Cappa C D, Messer B M, Cappa C D 2005 Science 308 793B Google Scholar
[12]	Tokushima T, Harada Y, Takahashi O, Senba Y, Ohashi H, Pettersson L G M, Nilsson A, Shin S 2008 Chem. Phys. Lett. 460 387 Google Scholar
[13]	Raichlin Y, Millo A, Katzir A 2004 Phys. Rev. Lett. 93 185703 Google Scholar
[14]	Russo J, Tanaka H 2014 Nat. Commun. 5 3556 Google Scholar
[15]	Ktihne T D, Khaliullin R Z 2013 Nat. Commun. 4 1450 Google Scholar
[16]	Ktihne T D, Khaliullin R Z 2014 J. Am. Chem. Soc. 136 3395 Google Scholar
[17]	Bertie J E, Whalley E 1967 J. Chem. Phys. 46 1271 Google Scholar
[18]	Tammann G 1900 Ann. Phys. 307 1 Google Scholar
[19]	Demontis P, LeSar R, Klein M L 1988 Phys. Rev. Lett. 60 2284 Google Scholar
[20]	Bertie J E, Calvert L D, Whalley E 1963 J. Chem. Phys. 38 840 Google Scholar
[21]	Bridgman P W 1912 Proc. Am. Acad. Arts Sci. 47 441 Google Scholar
[22]	Bridgman P W 1937 J. Chem. Phys. 5 964 Google Scholar
[23]	Whalley E, Davidson D W 1965 J. Chem. Phys. 43 2148 Google Scholar
[24]	Whalley E, Davidson D W, Heath J B R 1966 J. Chem. Phys. 45 3976 Google Scholar
[25]	Kuhs W F, Finney J L, Vettier C, Bliss D V 1984 J. Chem. Phys. 81 3612 Google Scholar
[26]	Whalley E, Heath J B R, Davidson D W 1968 J. Chem. Phys. 48 2362 Google Scholar
[27]	Tajima Y, Matsuo T, Suga H 1982 Nature 299 810 Google Scholar
[28]	Hirsch K R, Holzapfel W B 1986 J. Chem. Phys. 84 2771 Google Scholar
[29]	Lobban C, Finney J L, Kuhs W F 1998 Nature 391 268 Google Scholar
[30]	Matsuo T, Tajima Y, Suga H 1986 J. Phys. Chem. Solids 47 165 Google Scholar
[31]	Salzmann C G, Radaelli P G, Mayer A E, Finney J L 2006 Science 311 1758 Google Scholar
[32]	Tribello G A, Slater B, Salzmann C G 2006 J. Am. Chem. Soc. 128 12594 Google Scholar
[33]	Salzmann C G, Radaelli P G, Mayer E, Finney J L 2009 Phys. Rev. Lett. 103 105701 Google Scholar
[34]	Falenty A, Hansen T C, Kuhs W F 2014 Nature 516 213 Google Scholar
[35]	del Rosso L, Celli M, Ulivi L 2016 Nat. Commun. 7 13394 Google Scholar
[36]	Millot M, Hamel S, Rygg J R, Celliers P M, Collins G W, Coppari F, Fratanduono D E, Jeanloz R, Swift D C, Eggert J H 2018 Nat. Phys. 14 297 Google Scholar
[37]	Millot M, Coppari F, Rygg J R, Barrios A C, Hamel S, Swift D C 2019 Nature 569 251 Google Scholar
[38]	Algara-Siller G, Lehtinen O, Wang F C, Nair R R, Kaiser U, Wu H A, Geim A K, Grigorieva IV 2015 Nature 519 443 Google Scholar
[39]	Zhou W, Yin K, Wang C, Zhang Y, Xu T, Borisevich A, Sun L, Idrobo J C, Chisholm M F, Pantelides S T, Klie R F, Lupini A R 2015 Nature 528 E1 Google Scholar
[40]	Koga K, Zeng X C, Tanaka H 1997 Phys. Rev. Lett. 79 5262 Google Scholar
[41]	Ma R, Cao D, Zhu C, Tian Y, Peng J, Guo J, Chen J, Li X Z, Francisco J S, Zeng X C, Xu L M, Wang E G, Jiang Y 2020 Nature 577 60 Google Scholar
[42]	Kuhs W F, Lehmann M S 1983 J. Phys. Chem. 87 4312 Google Scholar
[43]	Konig H 1943 Z. Kristallogr. 105 279 Google Scholar
[44]	Dowell L G, Rinfret A P 1960 Nature 188 1144 Google Scholar
[45]	Murray B J, Bertram A K 2006 Phys. Chem. Chem. Phys. 8 186 Google Scholar
[46]	Murray B J 2008 Environ. Res. Lett. 3 025008 Google Scholar
[47]	Malkin T L, Murray B J, Brukhno A V, Anwar J, Salzmann C G 2012 Proc. Natl. Acad. Sci. U. S. A. 109 1041 Google Scholar
[48]	Whalley E 1981 Science 211 389 Google Scholar
[49]	Mayer E, Hallbrucker A 1987 Nature 325 601 Google Scholar
[50]	Kuhs W F, Bliss D V, Finney J L 1987 J. Phys. Colloq. 48 631 Google Scholar
[51]	Kuhs W F, Sippel C, Falenty A, Hansen T C 2012 Proc. Natl. Acad. Sci. U. S. A. 109 21259 Google Scholar
[52]	Murray B, Knopf D, Bertram A 2005 Nature 434 202 Google Scholar
[53]	Falenty A, Kuhs W F 2009 J. Phys. Chem. B 113 15975 Google Scholar
[54]	Baker J M, Dore J C, Behrens P 1997 J. Phys. Chem. B 101 6226 Google Scholar
[55]	Malkin T L, Murray B J, Salzmann C G, Molinero V, Pickering S J, Whale T F 2015 Phys. Chem. Chem. Phys. 17 60 Google Scholar
[56]	del Rosso L, Celli M, Grazzi F, Catti M, Ulivi L 2020 Nat. Mater. 19 663 Google Scholar
[57]	Komatsu K, Machida S, Noritake F, Hattori T, Kagi H 2020 Nat. Commun. 11 464 Google Scholar
[58]	Lekner J 1997 Physica B 240 263 Google Scholar
[59]	黄盈盈, 苏艳, 赵纪军 2019 高压物理学报 33 010001 Google Scholar Huang Y Y, Su Y, Zhao J J 2019 Chin. J. High Pressure Phys. 33 010001 Google Scholar
[60]	Bartels-Rausch T, Bergeron V, Csrtwright J H E, Escribano R, Finney J L, Grothe H 2012 Rev. Mod. Phys. 84 885 Google Scholar
[61]	Moberg D R, Sharp P J, Paesani F 2018 J. Phys. Chem. B 122 10572 Google Scholar
[62]	Kamb B 1964 Acta Crystallogr. 17 1437 Google Scholar
[63]	Finch E D 1968 J. Chem. Phys. 49 4361 Google Scholar
[64]	Kamb B, Hamilton W C, Laplaca S J, Prakash A 1971 J. Chem. Phys. 55 1934 Google Scholar
[65]	Fortes A D, Wood I G, Brodholt J P, Vočadlo L 2003 J. Chem. Phys. 119 4567 Google Scholar
[66]	Bauer M, Elsaesser M S, Winkel K, Mayer E, Loerting T 2008 Phys. Rev. B 77 220105 Google Scholar
[67]	Scheuermann M, Geil B, Löw F, Fujara F 2009 J. Chem. Phys. 130 024506 Google Scholar
[68]	Bertie J E, Whalley E 1964 J. Chem. Phys. 40 1646 Google Scholar
[69]	Bertie J E, Labbé H J, Whalley E 1968 J. Chem. Phys. 49 775 Google Scholar
[70]	Bertie J E, Francis B F 1980 J. Chem. Phys. 72 2213 Google Scholar
[71]	Bertie J E, Francis B F 1982 J. Chem. Phys. 77 1 Google Scholar
[72]	Li J C, Londono D, Ross D K, Finney J L, Bennington S M, Taylor A D 1992 J. Phys. Condens. Matter 4 2109 Google Scholar
[73]	Kamb B 1965 Science 150 205 Google Scholar
[74]	Kuhs W F, Ahsbahs H, Londono D, Finney J L 1989 Physica B 156 684 Google Scholar
[75]	Whale T F, Clark S J, Finney J L 2013 J. Raman Spectrosc. 44 290 Google Scholar
[76]	Komatsu K, Noritake F, Machida S 2016 Sci. Rep. 6 28920 Google Scholar
[77]	Nanda K D, Beran G J O 2013 J. Phys. Chem. Lett. 4 3165 Google Scholar
[78]	Gasser T M, Thoeny A, Plaga L 2018 Chem. Sci. 9 4224 Google Scholar
[79]	Klotz S, Besson J M, Hamel G, Nelmes R J, Loveday J S, Marshall W G 1999 Nature 398 681 Google Scholar
[80]	Vaks V G, Zinenko V I 1981 Solid State Commun. 39 643 Google Scholar
[81]	Song M, Yamawaki H, Fujihisa H, Sakashita M, Aoki K 2003 Phys. Rev. B 68 014106 Google Scholar
[82]	Besson J M, Kobayashi M, Nakai T, Endo S 1997 Phys. Rev. B 55 11191 Google Scholar
[83]	Pruzan P, Chervin J C, Canny B 1993 J. Chem. Phys. 99 9842 Google Scholar
[84]	Goncharov A F, Struzhkin V V, Somayazulu M S, Hemley R J, Mao H K 1996 Science 273 218 Google Scholar
[85]	Aoki K, Yamawaki H, Sakashita M, Fujihisa H 1996 Phys. Rev. B 54 15673 Google Scholar
[86]	Klug D D, Handa Y P, Tse J S, Whalley E 1989 J. Chem. Phys. 90 2390 Google Scholar
[87]	Minceva-Sukarova B, Sherman W F, Wilkinson G R 1984 J. Phys. C: Solid State Phys. 17 5833 Google Scholar
[88]	Li J C, Londono J D, Ross D K, Finney J L, Tomkinson J, Sherman W F 1991 J. Chem. Phys. 94 6770 Google Scholar
[89]	Garg A K 1988 Phys. Status Solidi A 110 467 Google Scholar
[90]	Tse J S, Klein M L, McDonald I R 1984 J. Chem. Phys. 81 6124 Google Scholar
[91]	Holzapfel W B 1972 J. Chem. Phys. 56 712 Google Scholar
[92]	Polian A, Grimsditch M 1984 Phys. Rev. Lett. 52 1312 Google Scholar
[93]	Flores-Livas J A, Sanna A, Graužinytė M, Davydov A, Goedecker S, Marques M A L 2017 Sci. Rep. 7 6825 Google Scholar
[94]	Lu X Z, Zhang Y, Zhao P, Fang S J 2011 J. Phys. Chem. B 115 71 Google Scholar
[95]	Marqués M, Ackland G, Loveday J 2009 High Pressure Res. 29 208 Google Scholar
[96]	Putrino A, Parrinello M 2002 Phys. Rev. Lett. 88 176401 Google Scholar
[97]	Goncharov A F, Struzhkin V V, Mao H K, Hemley R J 1999 Phys. Rev. Lett. 83 1998 Google Scholar
[98]	Men Z, Fang W, Li D, Li Z, Sun C 2014 Sci. Rep. 4 4606 Google Scholar
[99]	Giauque W F, Stout J W 1936 J. Am. Chem. Soc. 58 1144 Google Scholar
[100]	Kawada S 1972 J. Phys. Soc. Jpn. 32 1442 Google Scholar
[101]	Leadbetter A J, Ward R C 1985 J. Chem. Phys. 82 424 Google Scholar
[102]	Line C M B, Whitworth R W 1996 J. Chem. Phys. 104 10008 Google Scholar
[103]	Jackson S M, Nield V M, Whitworth R W, Oguro M, Wilson C C 1997 J. Phys. Chem. B 101 6142 Google Scholar
[104]	Salzmann C G, Radaelli P G, Finney J L, Mayer E 2008 Phys. Chem. Chem. Phys. 10 6313 Google Scholar
[105]	Salzmann C G, Hallbrucker A, Finney J L, Mayer E 2006 Phys. Chem. Chem. Phys. 8 3088 Google Scholar
[106]	Zhang J, Xiao Z, Kuo J 2010 J. Chem. Phys. 132 184506 Google Scholar
[107]	Tran H, Cunha A V, Shephard J J, Shalit A, Hamm P, Jansen T L C, Salzmann C G 2017 J. Chem. Phys. 147 144501 Google Scholar
[108]	Salzmann C G, Hallbrucker A, Finney J L, Mayer E 2006 Chem. Phys. Lett. 429 469 Google Scholar
[109]	Yoshimura Y, Stewart S T, Mao H K, Hemley R J 2007 J. Chem. Phys. 126 174505 Google Scholar
[110]	Koza M M, Schober H, Tölle A, Fujara F, Hansen T 1999 Nature 397 660 Google Scholar
[111]	Koza M M, Schober H, Parker S F, Peters J 2008 Phys. Rew. B 77 104306 Google Scholar
[112]	Huang Y Y, Zhu C Q, Wang L, Cao X X, Su Y, Jiang X, Meng S, Zhao J J, Zeng X C 2016 Sci. Adv. 2 e1501010 Google Scholar
[113]	Huang Y Y, Zhu C Q, Wang L, Zhao J J and Zeng X C 2017 Chem. Phys. Lett. 671 186 Google Scholar
[114]	Matsui T, Hirata M, Yagasaki T, Matsumoto M, Tanaka H 2017 J. Chem. Phys. 147 091101 Google Scholar
[115]	Liu Y, Ojamäe L 2018 Phys. Chem. Chem. Phys. 20 8333 Google Scholar
[116]	Engel E A, Anelli A, Ceriotti M, Pickard C J, Needs R J 2018 Nat. Commun. 9 2173 Google Scholar
[117]	Matsui T, Yagasaki T, Matsumoto M, Tanaka H 2019 J. Chem. Phys. 150 041102 Google Scholar
[118]	del Rosso L, Grazzi F, Celli M, Colognesi D, Garcia-Sakai V, Ulivi L 2016 J. Phys. Chem. C 120 26955 Google Scholar
[119]	Bertie J E, Labbe H J, Whalley E 1969 J. Chem. Phys. 50 4501 Google Scholar
[120]	Wong P T T, Whalley E 1976 J. Chem. Phys. 65 829 Google Scholar
[121]	Rasetti F 1932 Nuovo Cirnento 9 72 Google Scholar
[122]	Hibben J H 1937 J. Chem. Phys. 5 166 Google Scholar
[123]	Cross P C, Burnham J, Leighton P A 1937 J. Am. Chem. Soc. 59 1134 Google Scholar
[124]	Narayanaswarny P K 1948 Proc. Indian Acad. Sci. 27 311 Google Scholar
[125]	Valkov V I, Maslenkova G L 1956 Opt. Spektrosk. 1 881
[126]	Taylor M J, Whalley E 1964 J. Chem. Phys. 40 1660 Google Scholar
[127]	Marchi M, Tse J S, Klein M L 1986 J. Chem. Phys. 85 2414 Google Scholar
[128]	Renker B 1973 International Symposium on the Physics and Chemistry of Ice Ottowa, Ont., Canada, August 14–18, 1972 p82
[129]	Li J C, Ross D K, Howe L, Hall P G, Tomkinson J 1989 Physica B 156 376 Google Scholar
[130]	Klug D D, Tse J S, Whalley E 1991 J. Chem. Phys. 95 7011 Google Scholar
[131]	Li J C 1996 J. Chem. Phys. 105 6733 Google Scholar
[132]	Li J C, Ross D K 1993 Nature 365 327 Google Scholar
[133]	Morrison I, Jenkins S 1999 Physica B 263 442 Google Scholar
[134]	Klotz S, Strässle T, Salzmann C G, Philippe J, Parker S F 2005 Europhys. Lett. 72 576 Google Scholar
[135]	Zhang P, Tian L, Zhang Z P, Shao G, Li J C 2012 J. Chem. Phys. 137 044504 Google Scholar
[136]	He X, Sode O, Xantheas S S, Hirata S 2012 J. Chem. Phys. 137 204505 Google Scholar
[137]	Zhang P, Liu Y, Yu H, Han S H, Lü Y B, Lv M S, Cong W Y 2014 Chin. Phys. B 23 026103 Google Scholar
[138]	Zhang P, Wang Z, Lü Y B, Ding Z W 2016 Sci. Rep. 6 29273 Google Scholar
[139]	Yuan Z Y, Zhang P, Yao S K, Lü Y B, Yang H Z, Luo H W, Zhao Z J 2017 RSC Adv. 7 36801 Google Scholar
[140]	Yao S K, Zhang P, Zhang Y, Lü Y B, Yang T l, Sun B G, Yuan Z Y, Luo H W 2017 RSC Adv. 7 31789 Google Scholar
[141]	Jiang L, Yao S K, Zhang K, Wang Z R, Luo H W, Zhu X L, Gu Y, Zhang P 2018 Molecules 23 2780 Google Scholar
[142]	Qin X L, Zhu X L, Cao J W, Jiang L, Gu Y, Wang X C, Zhang P 2019 Molecules 24 3115 Google Scholar
[143]	Zhao Z J, Qin X L, Cao J W, Zhu X L, Yang Y C, Wang H C, Zhang P 2019 ACS Omega 4 18936 Google Scholar
[144]	Cao J W, Chen J Y, Qin X L, Zhu X L, Jiang L, Gu Y, Yu X H, Zhang P 2019 Molecules 24 3135 Google Scholar
[145]	Zhang K, Zhang P, Wang Z R, Zhu X L, Lu Y B, Guan C B, Li Y H 2018 Molecules 23 1781 Google Scholar
[146]	Gu Y, Zhu X L, Jiang L, Cao J W, Qin X L, Yao S K, Zhang P 2019 J. Phys. Chem. C 123 14880 Google Scholar
[147]	Zhu X L, Cao J W, Qin X L, Jiang L, Gu Y, Wang H C, Liu Y, Kolesnikov A I, Zhang P 2020 J. Phys. Chem. C 124 1165 Google Scholar
[148]	Wei Z W, Zhu X L, Cao J W, Qin X L, Jiang L, Gu Y, Wang H C, Zhang P 2019 AIP Adv. 9 115118 Google Scholar
[149]	Zhu X L, Yuan Z Y, Jiang L, Zhang K, Wang Z R, Luo H W, Gu Y, Cao J W, Qin X L, Zhang P 2019 New J. Phys. 21 043054 Google Scholar
[150]	Wang Z R, Zhu X L, Jiang L, Zhang K, Luo H W, Gu Y, Zhang P 2019 Materials 12 246 Google Scholar
[151]	Matsumoto M, Yagasaki T, Tanaka H 2018 J. Comput. Chem. 39 61 Google Scholar
[152]	Wang H C, Zhu X L, Cao J W, Qin X L, Yang Y C, Niu T X, LüY B, Zhang P 2020 New J. Phys. 22 093066 Google Scholar
[153]	Hammer B, Hansen L B, Norskov J K 1999 Phys. Rev. B 59 7413 Google Scholar
[154]	Bernal J D, Fowler R H 1933 J. Chem. Phys. 1 515 Google Scholar
[155]	Li J C, Burnham C, Kolesnikov A I, Eccleston R S 1999 Phys. Rev. B 59 9088 Google Scholar
[156]	Kolesnikov A I, Li J C, Ross D K, et al. 1992 Phys. Lett. A 168 308 Google Scholar

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Vol. 70, Issue 14 - 2021-07-20

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