二维冰相I的电子和光学性质

王丹; 邱荣; 陈博; 包南云; 康冬冬; 戴佳钰

doi:10.7498/aps.70.20210708

摘要

二维冰是典型的原子制造技术获得的新型原子级材料, 其结构和成核生长在材料科学、摩擦学、生物学、大气科学和行星科学等众多领域具有至关重要的作用. 虽然二维冰的结构性质已被广泛研究, 但对其电学和光学性质知之甚少. 本文通过密度泛函理论和线性响应理论计算了二维冰相I在零温时的主要电学、光学、介电性质和红外光谱. 其次, 利用从头算分子动力学方法模拟得到了二维冰相I在有限温度下的声子振动态密度. 本文的结果揭示了原子级二维冰相I的电子结构, 同时展示了其独特的光吸收机理, 有助于二维冰相I的进一步实验表征和原子级操控. 由于表面上的二维冰可以促进或抑制三维冰的形成, 这对于设计和研发防结冰材料具有潜在的应用价值. 此外, 二维冰本身也可以作为一种特殊的二维材料, 为高温超导电性、深紫外探测、冷冻电镜成像等研究提供全新的标准材料.

关键词:

Abstract

Two-dimensional ice is a new type of atomic-scale material obtained by typical atomic manufacturing techniques. Its structure and nucleation growth play an essential role in many fields such as material science, tribology, biology, atmospheric science and planetary science. Although the structural properties of two-dimensional ice have been investigated extensively, little is known about its electronic and optical properties. In this paper, the main electronic, optical, dielectric properties and infrared spectra of two-dimensional ice I at zero temperature are calculated by density functional theory and linear response theory. The study reveals that the two-dimensional ice I is an indirect band gap and its optical properties show anisotropic lattice. And the absorption energy range for the two-dimensional ice I is in the ultraviolet region of the spectrum (> 3.2 eV) and the visible region of the spectrum (between 2 and 3.2 eV), respectively. Secondly, the radial distribution function and the vibrational density of states of the two-dimensional ice I at a finite temperature are simulated by ab initio molecular dynamics method. For the structure of the two-dimensional ice I, whether SCAN or PBE functional, after considering the vdW effect, there is almost no effect on the atomic distance, while by comparison, the SCAN functional and the PBE functional are quite different. Therefore, it can be seen that the main reason for affecting the distance between atoms in the structure is due to the consideration of the strong confinement effect of SCAN. In terms of the vibration characteristics of two-dimensional ice I, comparing with PBE and vdW-DF-ob86, the first two peaks of the IR spectrum of SCAN + rVV10 functional show blue shift, and the two peaks in the high frequency region present the red shift. Therefore, considering the strong confinement effect of SCAN, the intermolecular tensile vibration of two-dimensional ice I becomes stronger, while the intramolecular H—O—H bending vibration and O—H bond tensile vibration become weaker. The effect of van der Waals action on vibration properties is not obvious. Furthermore, we investigate the temperature effects on the vibration spectra of two-dimensional ice I. It is found that with the increase of temperature, the intermolecular librational mode weakens at a low frequency, the intramolecular bending and stretching bands gradually broaden, and the intramolecular O-H stretching peak presents the blue-shifts with temperature rising. The results of this paper reveal the electronic structure of atomic-scale two-dimensional ice I, and demonstrate its unique optical absorption mechanism, which is helpful in further experimentally characterizing and manipulating the two-dimensional ice on an atomic scale. Since the two-dimensional ice on the surface can promote or inhibit the formation of three-dimensional ice, it has potential applications in designing and developing the anti-icing materials. In addition, two-dimensional ice itself can also be used as a unique two-dimensional material, providing a brand-new standard material for high-temperature superconductivity, deep-ultraviolet detection, cryo-electron microscopy imaging.

Keywords:

作者及机构信息

国防科技大学物理系, 长沙　410073

通信作者: 康冬冬, ddkang@nudt.edu.cn

基金项目: 国家重点研发计划资助(批准号: 2017YFA0403200)、国家自然科学基金(批准号: 11774429, 11874424)和NSAF联合基金(批准号: U1830206)资助的课题

Authors and contacts

Department of Physics, National University of Defense Technology, Changsha 410073, China

Corresponding author: Kang Dong-Dong, ddkang@nudt.edu.cn

Funds: Project supported by the National Key R&D Program of China (Grant No. 2017YFA0403200), the National Natural Science Foundation of China (Grant Nos. 11774429, 11874424), and the NSAF (Grant No. U1830206)

文章全文 : translate this paragraph

参考文献

[1]	Hetzel R, Hampel A 2005 Nature 435 81 Google Scholar
[2]	孙贤明, 韩一平 2006 55 682 Google Scholar Sun X M, Han Y P 2006 Acta Phys. Sin. 55 682 Google Scholar
[3]	Zhu T, Li J, Jin Y, Liang Y, Ma G 2008 Int. J. Environ. Sci. Te 5 375 Google Scholar
[4]	Tao W K, Chen J P, Li Z Q, Wang C, Zhang C D 2012 Rev. Geophys. 50 Rg2001 Google Scholar
[5]	Zheng S L, Li C, Fu Q T, Hu W, Xiang T F, Wang Q, Du M P, Liu X C, Chen Z 2016 Mater. Des. 93 261 Google Scholar
[6]	刘胜兴, 李整林 2017 66 234301 Google Scholar Liu S X, Li Z L 2017 Acta Phys. Sin. 66 234301 Google Scholar
[7]	张桐鑫, 王志军, 王理林, 李俊杰, 林鑫, 王锦程 2018 67 196401 Google Scholar Zhang T X, Wang Z J, Wang L L, Li J J, Lin X, Wang J C 2018 Acta Phys. Sin. 67 196401 Google Scholar
[8]	Lee H 2019 J. Mol. Graph. Model. 87 48 Google Scholar
[9]	Bragg W H 1924 Science 60 139 Google Scholar
[10]	Bjerrum N 1952 Science 115 385 Google Scholar
[11]	Moore E B, Molinero V 2011 Phys. Chem. Chem. Phys. 13 20008 Google Scholar
[12]	Malkin T L, Murray B J, Brukhno A V, Anwar J, Salzmann C G 2012 Proc. Natl. Acad. Sci. USA 109 1041 Google Scholar
[13]	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
[14]	Li T, Donadio D, Russo G, Galli G 2011 Phys. Chem. Chem. Phys. 13 19807 Google Scholar
[15]	Radhakrishnan R, Trout B L 2003 J. Am. Chem. Soc. 125 7743 Google Scholar
[16]	Jovanović D, Zagorac D, Schön J C, Milovanović B, Zagorac J 2020 Z. Naturforsch. B. 75 125 Google Scholar
[17]	Ghosh M, Pradipkanti L, Rai V, Satapathy D K, Vayalamkuzhi P, Jaiswal M 2015 Appl. Phys. Lett. 106 241902 Google Scholar
[18]	Ma M, Tocci G, Michaelides A, Aeppli G 2016 Nat. Mater. 15 66 Google Scholar
[19]	Adachi Y, Koga K 2020 J. Chem. Phys. 153 114501 Google Scholar
[20]	Algara-Siller G, Lehtinen O, Wang F C, Nair R R, Kaiser U, Wu H A, Geim A K, Grigorieva I V 2015 Nature 519 443 Google Scholar
[21]	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
[22]	Wang F C, Wu H A, Geim A K 2015 Nature 528 16146 Google Scholar
[23]	Algara-Siller G, Lehtinen O, Kaiser U 2015 Nature 528 16149 Google Scholar
[24]	Zhu Y, Wang F, Bai J, Zeng X C, Wu H 2015 ACS Nano 9 12197 Google Scholar
[25]	Corsetti F, Matthews P, Artacho E 2016 Sci. Rep. 6 18651 Google Scholar
[26]	Zhu Y, Wang F, Wu H 2017 J. Chem. Phys. 146 134703 Google Scholar
[27]	Chen J, Zen A, Brandenburg J G, Alfe D, Michaelides A 2016 Phys. Rev. B. 94 220102 Google Scholar
[28]	Hodgson A, Haq S 2009 Surf. Sci. Rep. 64 381 Google Scholar
[29]	Corem G, Kole P R, Zhu J, Kravchuk T, Manson J R, Alexandrowicz G 2013 J. Phys. Chem. C. 117 23657 Google Scholar
[30]	Lin C, Avidor N, Corem G, Godsi O, Alexandrowicz G, Darling G R, Hodgson A 2018 Phys. Rev. Lett. 120 076101 Google Scholar
[31]	Xu K, Cao P, Heath J R 2010 Science 329 1188 Google Scholar
[32]	Peng J, Guo J, Hapala P, Cao D, Ma R, Cheng B, Xu L, Ondracek M, Jelinek P, Wang E, Jiang Y 2018 Nat. Commun. 9 122 Google Scholar
[33]	Kimmel G A, Matthiesen J, Baer M, Mundy C J, Petrik N G, Smith R S, Dohnalek Z, Kay B D 2009 J. Am. Chem. Soc. 131 12838 Google Scholar
[34]	Lupi L, Kastelowitz N, Molinero V 2014 Phys. Chem. Chem. Phys. 141 18c508 Google Scholar
[35]	Chakraborty S, Kumar H, Dasgupta C, Maiti P K 2017 Acc. Chem. Res. 50 2139 Google Scholar
[36]	Neek-Amal M, Lohrasebi A, Mousaei M, Shayeganfar F, Radha B, Peeters F M 2018 Appl. Phys. Lett. 113 083101 Google Scholar
[37]	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
[38]	刘子媛, 潘金波, 张余洋, 杜世萱 2021 70 027301 Google Scholar Liu Z Y, Pan J B, Zhang Y Y, Du S X 2021 Acta Phys. Sin. 70 027301 Google Scholar
[39]	Fukazawa H, Mae S, Ikeda S (Steffen K ed.) 2000 Annals of Glaciology (Vol. 31) 2000 pp247–251
[40]	Stefanutti E, Bove L E, Alabarse F G, Lelong G, Bruni F, Ricci M A 2019 J. Chem. Phys. 150 224504 Google Scholar
[41]	Futrelle R P, McGinty D J 1971 Chem. Phys. Lett. 12 285 Google Scholar
[42]	Heislbetz S, Rauhut G 2010 J. Chem. Phys. 132 124102 Google Scholar
[43]	Weymuth T, Haag M P, Kiewisch K, Luber S, Schenk S, Jacob C R, Herrmann C, Neugebauer J, Reiher M 2012 J. Comb. Chem. 33 2186 Google Scholar
[44]	Mathias G, Baer M D 2011 J. Chem. Theory. Comput 7 2028 Google Scholar
[45]	Kim K H, Späh A, Pathak H, Perakis F, Mariedahl D, Amann-Winkel K, Sellberg J A, Lee J H, Kim S, Park J, Nam K H, Katayama T, Nilsson A 2017 Science 358 1589 Google Scholar
[46]	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
[47]	Aragones J L, MacDowell L G, Vega C 2011 J. Phys. Chem. A. 115 5745 Google Scholar
[48]	Zangi R, Mark A E 2003 Phys. Rev. Lett. 91 025502 Google Scholar
[49]	Sobrino Fernández M, Peeters F M, Neek-Amal M 2016 Phys. Rev. B. 94 045436 Google Scholar
[50]	Chen J, Schusteritsch G, Pickard C J, Salzmann C G, Michaelides A 2016 Phys. Rev. Lett. 116 025501 Google Scholar
[51]	Ghasemi S, Alihosseini M, Peymanirad F, Jalali H, Ketabi S A, Khoeini F, Neek-Amal M 2020 Phys. Rev. B 101 184202 Google Scholar
[52]	Santra B, Klimes J, Tkatchenko A, Alfe D, Slater B, Michaelides A, Car R, Scheffler M 2013 J. Chem. Phys. 139 154702 Google Scholar
[53]	Sabatini R, Gorni T, de Gironcoli S 2013 Phys. Rev. B 87 041108 Google Scholar
[54]	Sun J, Ruzsinszky A, Perdew J P 2015 Phys. Rev. Lett. 115 036402 Google Scholar
[55]	Zheng L X, Chen M H, Sun Z R, Ko H Y, Santra B, Dhuvad P, Wu X F 2018 J. Chem. Phys. 148 164505 Google Scholar
[56]	Peng H, Yang Z-H, Perdew J P, Sun J 2016 Phys. Rev. X. 6 041005 Google Scholar
[57]	Wiktor J, Ambrosio F, Pasquarello A 2017 J. Chem. Phys. 147 2161012 Google Scholar
[58]	Perdew J P, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865 Google Scholar
[59]	Klimeš J, Bowler D R, Michaelides A 2009 J. Phys.: Condens. Matter. 22 022201 Google Scholar
[60]	Klimeš J, Bowler D R, Michaelides A 2011 Phys. Rev. B 83 195131 Google Scholar
[61]	Vanderbilt D 1990 Phys. Rev. B 41 7892 Google Scholar
[62]	Hamann D R 2013 Phys. Rev. B 88 085117 Google Scholar
[63]	Giannozzi P, Andreussi O, Brumme T, Bunau O, Buongiorno Nardelli M, Calandra M, Car R, Cavazzoni C, Ceresoli D, Cococcioni M, Colonna N, Carnimeo I, Dal Corso A, de Gironcoli S, Delugas P, DiStasio R A, Ferretti A, Floris A, Fratesi G, Fugallo G, Gebauer R, Gerstmann U, Giustino F, Gorni T, Jia J, Kawamura M, Ko H Y, Kokalj A, Küçükbenli E, Lazzeri M, Marsili M, Marzari N, Mauri F, Nguyen N L, Nguyen H V, Otero-de-la-Roza A, Paulatto L, Poncé S, Rocca D, Sabatini R, Santra B, Schlipf M, Seitsonen A P, Smogunov A, Timrov I, Thonhauser T, Umari P, Vast N, Wu X, Baroni S 2017 J. Phys.: Condens. Matter. 29 465901 Google Scholar
[64]	Rottger K, Endriss A, Ihringer J, Doyle S, Kuhs W F 1994 Acta. Crystallogr. B 50 644 Google Scholar
[65]	Moberg D R, Sharp P J, Paesani F 2018 J. Phys. Chem. B 122 10572 Google Scholar
[66]	Buch V, Sandler P, Sadlej J 1998 J. Phys. Chem. B 102 8641 Google Scholar
[67]	Fang C, Li W-F, Koster R S, Klimeš J, van Blaaderen A, van Huis M A 2015 Phys. Chem. Chem. Phys. 17 365 Google Scholar
[68]	Yoffe A D 1977 J. Franklin. I 303 105 Google Scholar
[69]	Roessler D M 1965 Br. J. Appl. Phys. 16 1119 Google Scholar
[70]	de Koning M, Fazzio A, da Silva A J R, Antonelli A 2016 Phys. Chem. Chem. Phys. 18 4652 Google Scholar
[71]	Garbuio V, Cascella M, Kupchak I, Pulci O, Seitsonen A P 2015 J. Chem. Phys. 143 084507 Google Scholar
[72]	Perakis F, Hamm P 2012 Phys. Chem. Chem. Phys. 14 6250 Google Scholar
[73]	Moberg D R, Straight S C, Knight C, Paesani F 2017 J. Phys. Chem. Lett. 8 2579 Google Scholar
[74]	Shi L, Skinner J L, Jansen T L C 2016 Phys. Chem. Chem. Phys. 18 3772 Google Scholar
[75]	Liu H, Wang Y, Bowman J M 2012 J. Phys. Chem. Lett. 3 3671 Google Scholar
[76]	Whalley E 1977 Can. J. Chem. 55 3429 Google Scholar
[77]	Hernandez J, Uras N, Devlin J P 1998 J. Chem. Phys. 108 4525 Google Scholar

施引文献

图 1 二维冰相I的结构的顶视图、斜视图和侧视图. 顶部水层的H和O原子分别用白色和红色圆球表示, 底部水层的H和O原子分别用深蓝色和浅蓝色圆球表示

Fig. 1. Top, oblique and side views of the structure of two-dimensional ice I. H and O atoms in the top water layer are denoted as white and red spheres, respectively. H and O atoms in the bottom water layer are shown by dark blue and light blue spheres, respectively.

下载: 全尺寸图片幻灯片

图 2 在120 K温度下, 二维冰相I在不同泛函的径向分布函数(g_OO, g_OH和g_HH)及与冰Ih, XV相在100 K的g_OO的对比. 插图显示了在0.95—1.05 Å距离范围内的g_OH的曲线图

Fig. 2. Radial distribution functions (g_OO, g_OH and g_HH) of two-dimensional ice I in different functionals at 120 K and the comparison with the g_OO of the ice Ih and XV phase at 100 K. The insets show elaborations of the g_OH plots within the 0.95–1.05 Å distance range.

下载: 全尺寸图片幻灯片

图 3 从头算分子动力学模拟的二维冰相I在不同温度的径向分布函数. 插图显示了在0.95—1.05 Å距离范围内的g_OH的曲线图

Fig. 3. Radial distribution functions of two-dimensional ice I at different temperatures from ab initio simulations. The insets show elaborations of the g_OH plots within the 0.95–1.05 Å distance range.

下载: 全尺寸图片幻灯片

图 4 二维冰相I在不同泛函的电子能带结构. 插图显示了相应的布里渊区

Fig. 4. The electronic band structure of the two-dimensional ice I in different functionals. The insets show the corresponding Brillouin zones.

下载: 全尺寸图片幻灯片

图 5 二维冰相I在不同泛函的介电函数的实部　(a), (c), (e)和虚部(b), (d), (f). 其中, x和y表示平面内分量, 而z分量垂直于x-y平面. 粉色虚线箭头表示能隙

Fig. 5. The real (a), (c), (e) and imaginary (b), (d), (f) part of dielectric function of the two-dimensional ice I in different functionals. Here, x and y denote the in-plane components, while z component is perpendicular to x-y plane. The pink-dashed arrows refer to the energy gap.

下载: 全尺寸图片幻灯片

图 6 (a)谐波近似下, 不同泛函PBE, vdW-DF-ob86和SCAN + rVV10的二维冰相I的IR; (b) 二维冰相I在不同泛函的振动态密度

Fig. 6. (a) IR of the two-dimensional ice I with different functionals PBE, vdW-DF-ob86 and SCAN+rVV10 under harmonic approximation; (b) the vibrational density of states of the two-dimensional ice I in different functionals.

下载: 全尺寸图片幻灯片

图 7 (a)二维冰相I和实验^[72,76]及理论的冰Ih相^[75]的分子内伸缩振动谱; (b) 二维冰相I和实验^[77]及理论的其他冰相^[75]的分子内弯曲振动谱

Fig. 7. (a) Intramolecular stretching vibration spectra of two-dimensional ice I and experimental^[72,76] and theoretical ice Ih^[75]; (b) intramolecular bending vibration spectra of two-dimensional ice I and experimental^[77] crystalline ice and theoretical hexagonal ice^[75].

下载: 全尺寸图片幻灯片

图 8 二维冰相I在不同温度下的振动态密度

Fig. 8. The vibrational density of states of the two-dimensional ice I at different temperatures.

下载: 全尺寸图片幻灯片

map

[1]	Hetzel R, Hampel A 2005 Nature 435 81 Google Scholar
[2]	孙贤明, 韩一平 2006 55 682 Google Scholar Sun X M, Han Y P 2006 Acta Phys. Sin. 55 682 Google Scholar
[3]	Zhu T, Li J, Jin Y, Liang Y, Ma G 2008 Int. J. Environ. Sci. Te 5 375 Google Scholar
[4]	Tao W K, Chen J P, Li Z Q, Wang C, Zhang C D 2012 Rev. Geophys. 50 Rg2001 Google Scholar
[5]	Zheng S L, Li C, Fu Q T, Hu W, Xiang T F, Wang Q, Du M P, Liu X C, Chen Z 2016 Mater. Des. 93 261 Google Scholar
[6]	刘胜兴, 李整林 2017 66 234301 Google Scholar Liu S X, Li Z L 2017 Acta Phys. Sin. 66 234301 Google Scholar
[7]	张桐鑫, 王志军, 王理林, 李俊杰, 林鑫, 王锦程 2018 67 196401 Google Scholar Zhang T X, Wang Z J, Wang L L, Li J J, Lin X, Wang J C 2018 Acta Phys. Sin. 67 196401 Google Scholar
[8]	Lee H 2019 J. Mol. Graph. Model. 87 48 Google Scholar
[9]	Bragg W H 1924 Science 60 139 Google Scholar
[10]	Bjerrum N 1952 Science 115 385 Google Scholar
[11]	Moore E B, Molinero V 2011 Phys. Chem. Chem. Phys. 13 20008 Google Scholar
[12]	Malkin T L, Murray B J, Brukhno A V, Anwar J, Salzmann C G 2012 Proc. Natl. Acad. Sci. USA 109 1041 Google Scholar
[13]	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
[14]	Li T, Donadio D, Russo G, Galli G 2011 Phys. Chem. Chem. Phys. 13 19807 Google Scholar
[15]	Radhakrishnan R, Trout B L 2003 J. Am. Chem. Soc. 125 7743 Google Scholar
[16]	Jovanović D, Zagorac D, Schön J C, Milovanović B, Zagorac J 2020 Z. Naturforsch. B. 75 125 Google Scholar
[17]	Ghosh M, Pradipkanti L, Rai V, Satapathy D K, Vayalamkuzhi P, Jaiswal M 2015 Appl. Phys. Lett. 106 241902 Google Scholar
[18]	Ma M, Tocci G, Michaelides A, Aeppli G 2016 Nat. Mater. 15 66 Google Scholar
[19]	Adachi Y, Koga K 2020 J. Chem. Phys. 153 114501 Google Scholar
[20]	Algara-Siller G, Lehtinen O, Wang F C, Nair R R, Kaiser U, Wu H A, Geim A K, Grigorieva I V 2015 Nature 519 443 Google Scholar
[21]	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
[22]	Wang F C, Wu H A, Geim A K 2015 Nature 528 16146 Google Scholar
[23]	Algara-Siller G, Lehtinen O, Kaiser U 2015 Nature 528 16149 Google Scholar
[24]	Zhu Y, Wang F, Bai J, Zeng X C, Wu H 2015 ACS Nano 9 12197 Google Scholar
[25]	Corsetti F, Matthews P, Artacho E 2016 Sci. Rep. 6 18651 Google Scholar
[26]	Zhu Y, Wang F, Wu H 2017 J. Chem. Phys. 146 134703 Google Scholar
[27]	Chen J, Zen A, Brandenburg J G, Alfe D, Michaelides A 2016 Phys. Rev. B. 94 220102 Google Scholar
[28]	Hodgson A, Haq S 2009 Surf. Sci. Rep. 64 381 Google Scholar
[29]	Corem G, Kole P R, Zhu J, Kravchuk T, Manson J R, Alexandrowicz G 2013 J. Phys. Chem. C. 117 23657 Google Scholar
[30]	Lin C, Avidor N, Corem G, Godsi O, Alexandrowicz G, Darling G R, Hodgson A 2018 Phys. Rev. Lett. 120 076101 Google Scholar
[31]	Xu K, Cao P, Heath J R 2010 Science 329 1188 Google Scholar
[32]	Peng J, Guo J, Hapala P, Cao D, Ma R, Cheng B, Xu L, Ondracek M, Jelinek P, Wang E, Jiang Y 2018 Nat. Commun. 9 122 Google Scholar
[33]	Kimmel G A, Matthiesen J, Baer M, Mundy C J, Petrik N G, Smith R S, Dohnalek Z, Kay B D 2009 J. Am. Chem. Soc. 131 12838 Google Scholar
[34]	Lupi L, Kastelowitz N, Molinero V 2014 Phys. Chem. Chem. Phys. 141 18c508 Google Scholar
[35]	Chakraborty S, Kumar H, Dasgupta C, Maiti P K 2017 Acc. Chem. Res. 50 2139 Google Scholar
[36]	Neek-Amal M, Lohrasebi A, Mousaei M, Shayeganfar F, Radha B, Peeters F M 2018 Appl. Phys. Lett. 113 083101 Google Scholar
[37]	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
[38]	刘子媛, 潘金波, 张余洋, 杜世萱 2021 70 027301 Google Scholar Liu Z Y, Pan J B, Zhang Y Y, Du S X 2021 Acta Phys. Sin. 70 027301 Google Scholar
[39]	Fukazawa H, Mae S, Ikeda S (Steffen K ed.) 2000 Annals of Glaciology (Vol. 31) 2000 pp247–251
[40]	Stefanutti E, Bove L E, Alabarse F G, Lelong G, Bruni F, Ricci M A 2019 J. Chem. Phys. 150 224504 Google Scholar
[41]	Futrelle R P, McGinty D J 1971 Chem. Phys. Lett. 12 285 Google Scholar
[42]	Heislbetz S, Rauhut G 2010 J. Chem. Phys. 132 124102 Google Scholar
[43]	Weymuth T, Haag M P, Kiewisch K, Luber S, Schenk S, Jacob C R, Herrmann C, Neugebauer J, Reiher M 2012 J. Comb. Chem. 33 2186 Google Scholar
[44]	Mathias G, Baer M D 2011 J. Chem. Theory. Comput 7 2028 Google Scholar
[45]	Kim K H, Späh A, Pathak H, Perakis F, Mariedahl D, Amann-Winkel K, Sellberg J A, Lee J H, Kim S, Park J, Nam K H, Katayama T, Nilsson A 2017 Science 358 1589 Google Scholar
[46]	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
[47]	Aragones J L, MacDowell L G, Vega C 2011 J. Phys. Chem. A. 115 5745 Google Scholar
[48]	Zangi R, Mark A E 2003 Phys. Rev. Lett. 91 025502 Google Scholar
[49]	Sobrino Fernández M, Peeters F M, Neek-Amal M 2016 Phys. Rev. B. 94 045436 Google Scholar
[50]	Chen J, Schusteritsch G, Pickard C J, Salzmann C G, Michaelides A 2016 Phys. Rev. Lett. 116 025501 Google Scholar
[51]	Ghasemi S, Alihosseini M, Peymanirad F, Jalali H, Ketabi S A, Khoeini F, Neek-Amal M 2020 Phys. Rev. B 101 184202 Google Scholar
[52]	Santra B, Klimes J, Tkatchenko A, Alfe D, Slater B, Michaelides A, Car R, Scheffler M 2013 J. Chem. Phys. 139 154702 Google Scholar
[53]	Sabatini R, Gorni T, de Gironcoli S 2013 Phys. Rev. B 87 041108 Google Scholar
[54]	Sun J, Ruzsinszky A, Perdew J P 2015 Phys. Rev. Lett. 115 036402 Google Scholar
[55]	Zheng L X, Chen M H, Sun Z R, Ko H Y, Santra B, Dhuvad P, Wu X F 2018 J. Chem. Phys. 148 164505 Google Scholar
[56]	Peng H, Yang Z-H, Perdew J P, Sun J 2016 Phys. Rev. X. 6 041005 Google Scholar
[57]	Wiktor J, Ambrosio F, Pasquarello A 2017 J. Chem. Phys. 147 2161012 Google Scholar
[58]	Perdew J P, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865 Google Scholar
[59]	Klimeš J, Bowler D R, Michaelides A 2009 J. Phys.: Condens. Matter. 22 022201 Google Scholar
[60]	Klimeš J, Bowler D R, Michaelides A 2011 Phys. Rev. B 83 195131 Google Scholar
[61]	Vanderbilt D 1990 Phys. Rev. B 41 7892 Google Scholar
[62]	Hamann D R 2013 Phys. Rev. B 88 085117 Google Scholar
[63]	Giannozzi P, Andreussi O, Brumme T, Bunau O, Buongiorno Nardelli M, Calandra M, Car R, Cavazzoni C, Ceresoli D, Cococcioni M, Colonna N, Carnimeo I, Dal Corso A, de Gironcoli S, Delugas P, DiStasio R A, Ferretti A, Floris A, Fratesi G, Fugallo G, Gebauer R, Gerstmann U, Giustino F, Gorni T, Jia J, Kawamura M, Ko H Y, Kokalj A, Küçükbenli E, Lazzeri M, Marsili M, Marzari N, Mauri F, Nguyen N L, Nguyen H V, Otero-de-la-Roza A, Paulatto L, Poncé S, Rocca D, Sabatini R, Santra B, Schlipf M, Seitsonen A P, Smogunov A, Timrov I, Thonhauser T, Umari P, Vast N, Wu X, Baroni S 2017 J. Phys.: Condens. Matter. 29 465901 Google Scholar
[64]	Rottger K, Endriss A, Ihringer J, Doyle S, Kuhs W F 1994 Acta. Crystallogr. B 50 644 Google Scholar
[65]	Moberg D R, Sharp P J, Paesani F 2018 J. Phys. Chem. B 122 10572 Google Scholar
[66]	Buch V, Sandler P, Sadlej J 1998 J. Phys. Chem. B 102 8641 Google Scholar
[67]	Fang C, Li W-F, Koster R S, Klimeš J, van Blaaderen A, van Huis M A 2015 Phys. Chem. Chem. Phys. 17 365 Google Scholar
[68]	Yoffe A D 1977 J. Franklin. I 303 105 Google Scholar
[69]	Roessler D M 1965 Br. J. Appl. Phys. 16 1119 Google Scholar
[70]	de Koning M, Fazzio A, da Silva A J R, Antonelli A 2016 Phys. Chem. Chem. Phys. 18 4652 Google Scholar
[71]	Garbuio V, Cascella M, Kupchak I, Pulci O, Seitsonen A P 2015 J. Chem. Phys. 143 084507 Google Scholar
[72]	Perakis F, Hamm P 2012 Phys. Chem. Chem. Phys. 14 6250 Google Scholar
[73]	Moberg D R, Straight S C, Knight C, Paesani F 2017 J. Phys. Chem. Lett. 8 2579 Google Scholar
[74]	Shi L, Skinner J L, Jansen T L C 2016 Phys. Chem. Chem. Phys. 18 3772 Google Scholar
[75]	Liu H, Wang Y, Bowman J M 2012 J. Phys. Chem. Lett. 3 3671 Google Scholar
[76]	Whalley E 1977 Can. J. Chem. 55 3429 Google Scholar
[77]	Hernandez J, Uras N, Devlin J P 1998 J. Chem. Phys. 108 4525 Google Scholar

[1]	叶建峰, 秦铭哲, 肖清泉, 王傲霜, 何安娜, 谢泉. Ti, V, Co, Ni掺杂二维CrSi₂材料的电学、磁学及光学性质的第一性原理研究. , 2021, 70(22): 227301. doi: 10.7498/aps.70.20211023
[2]	邢海英, 郑智健, 张子涵, 吴文静, 郭志英. 应力调控BlueP/X Te₂ (X = Mo, W)范德瓦耳斯异质结电子结构及光学性质理论研究. , 2021, 70(6): 067101. doi: 10.7498/aps.70.20201728
[3]	熊子谦, 张鹏程, 康文斌, 方文玉. 一种新型二维TiO₂的电子结构与光催化性质. , 2020, 69(16): 166301. doi: 10.7498/aps.69.20200631
[4]	潘凤春, 林雪玲, 曹志杰, 李小伏. Fe, Co, Ni掺杂GaSb的电子结构和光学性质. , 2019, 68(18): 184202. doi: 10.7498/aps.68.20190290
[5]	范达志, 刘贵立, 卫琳. 扭转形变对石墨烯吸附O原子电学和光学性质影响的电子理论研究. , 2017, 66(24): 246301. doi: 10.7498/aps.66.246301
[6]	胡永金, 吴云沛, 刘国营, 罗时军, 何开华. ZnTe结构相变、电子结构和光学性质的研究. , 2015, 64(22): 227802. doi: 10.7498/aps.64.227802
[7]	吴琼, 刘俊, 董前民, 刘阳, 梁培, 舒海波. 硫化锡电子结构和光学性质的量子尺寸效应. , 2014, 63(6): 067101. doi: 10.7498/aps.63.067101
[8]	余本海, 陈东. 用密度泛函理论研究氮化硅新相的电子结构、光学性质和相变. , 2014, 63(4): 047101. doi: 10.7498/aps.63.047101
[9]	李建华, 崔元顺, 曾祥华, 陈贵宾. ZnS结构相变、电子结构和光学性质的研究. , 2013, 62(7): 077102. doi: 10.7498/aps.62.077102
[10]	李倩倩, 郝秋艳, 李英, 刘国栋. 稀土元素(Ce, Pr)掺杂GaN的电子结构和光学性质的理论研究. , 2013, 62(1): 017103. doi: 10.7498/aps.62.017103
[11]	潘磊, 卢铁城, 苏锐, 王跃忠, 齐建起, 付佳, 张燚, 贺端威. -AlON晶体电子结构和光学性质研究. , 2012, 61(2): 027101. doi: 10.7498/aps.61.027101
[12]	王寅, 冯庆, 王渭华, 岳远霞. 碳-锌共掺杂锐钛矿相TiO2 电子结构与光学性质的第一性原理研究. , 2012, 61(19): 193102. doi: 10.7498/aps.61.193102
[13]	邓娇娇, 刘波, 顾牡, 刘小林, 黄世明, 倪晨. 伽马CuX(X=Cl,Br,I)的电子结构和光学性质的第一性原理计算. , 2012, 61(3): 036105. doi: 10.7498/aps.61.036105
[14]	焦照勇, 杨继飞, 张现周, 马淑红, 郭永亮. 闪锌矿GaN弹性性质、电子结构和光学性质外压力效应的理论研究. , 2011, 60(11): 117103. doi: 10.7498/aps.60.117103
[15]	李旭珍, 谢泉, 陈茜, 赵凤娟, 崔冬萌. OsSi2电子结构和光学性质的研究. , 2010, 59(3): 2016-2021. doi: 10.7498/aps.59.2016
[16]	张学军, 高攀, 柳清菊. 氮铁共掺锐钛矿相TiO2电子结构和光学性质的第一性原理研究. , 2010, 59(7): 4930-4938. doi: 10.7498/aps.59.4930
[17]	段满益, 徐明, 周海平, 陈青云, 胡志刚, 董成军. 碳掺杂ZnO的电子结构和光学性质. , 2008, 57(10): 6520-6525. doi: 10.7498/aps.57.6520
[18]	邢海英, 范广涵, 赵德刚, 何苗, 章勇, 周天明. Mn掺杂GaN电子结构和光学性质研究. , 2008, 57(10): 6513-6519. doi: 10.7498/aps.57.6513
[19]	丁迎春, 向安平, 徐明, 祝文军. 掺稀土元素(Y，La)的γ-Si3N4的电子结构和光学性质. , 2007, 56(10): 5996-6002. doi: 10.7498/aps.56.5996
[20]	潘洪哲, 徐明, 祝文军, 周海平. β-Si3N4电子结构和光学性质的第一性原理研究. , 2006, 55(7): 3585-3589. doi: 10.7498/aps.55.3585

计量

文章访问数: 6217
PDF下载量: 192
被引次数: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

搜索

留言板

二维冰相I的电子和光学性质