Electronic and optical properties of two-dimensional ice I

Wang Dan; Qiu Rong; Chen Bo; Bao Nan-Yun; Kang Dong-Dong; Dai Jia-Yu

doi:10.7498/aps.70.20210708

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:

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)

FullText HTML : translate this paragraph

References

[1]	Hetzel R, Hampel A 2005 Nature 435 81 Google Scholar
[2]	孙贤明, 韩一平 2006 物理学报 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 物理学报 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 物理学报 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 物理学报 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

Cited By

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

Figure 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.

DownLoad: Full-Size Img PowerPoint

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

Figure 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.

DownLoad: Full-Size Img PowerPoint

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

Figure 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.

DownLoad: Full-Size Img PowerPoint

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

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

DownLoad: Full-Size Img PowerPoint

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

Figure 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.

DownLoad: Full-Size Img PowerPoint

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

Figure 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.

DownLoad: Full-Size Img PowerPoint

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

Figure 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].

DownLoad: Full-Size Img PowerPoint

图 8 二维冰相I在不同温度下的振动态密度

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

DownLoad: Full-Size Img PowerPoint

[1]	Hetzel R, Hampel A 2005 Nature 435 81 Google Scholar
[2]	孙贤明, 韩一平 2006 物理学报 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 物理学报 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 物理学报 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 物理学报 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]	Ye Jian-Feng, Qing Ming-Zhe, Xiao Qing-Quan, Wang Ao-Shuang, He An-Na, Xie Quan. First-principles study of electronic structure , magnetic and optical properties of Ti, V, Co and Ni doped two-dimensional CrSi₂ materials. Acta Physica Sinica, 2021, 70(22): 227301. doi: 10.7498/aps.70.20211023
[2]	Xing Hai-Ying, Zheng Zhi-Jian, Zhang Zi-Han, Wu Wen-Jing, Guo Zhi-Ying. Tunable electronic structure and optical properties of BlueP/X Te₂ (X = Mo, W) van der Waals heterostructures by strain. Acta Physica Sinica, 2021, 70(6): 067101. doi: 10.7498/aps.70.20201728
[3]	Xiong Zi-Qian, Zhang Peng-Cheng, Kang Wen-Bin, Fang Wen-Yu. Study on the electronic structure and photocatalytic properties of a novel monolayer TiO₂. Acta Physica Sinica, 2020, 69(16): 166301. doi: 10.7498/aps.69.20200631
[4]	Pan Feng-Chun, Lin Xue-Ling, Cao Zhi-Jie, Li Xiao-Fu. Electronic structures and optical properties of Fe, Co, and Ni doped GaSb. Acta Physica Sinica, 2019, 68(18): 184202. doi: 10.7498/aps.68.20190290
[5]	Fan Da-Zhi, Liu Gui-Li, Wei Lin. Electron-theoretical study on the influences of torsional deformation on electrical and optical properties of O atom absorbed graphene. Acta Physica Sinica, 2017, 66(24): 246301. doi: 10.7498/aps.66.246301
[6]	Hu Yong-Jin, Wu Yun-Pei, Liu Guo-Ying, Luo Shi-Jun, He Kai-Hua. Structural phase transition, electronic structures and optical properties of ZnTe. Acta Physica Sinica, 2015, 64(22): 227802. doi: 10.7498/aps.64.227802
[7]	Wu Qiong, Liu Jun, Dong Qian-Min, Liu Yang, Liang Pei, Shu Hai-Bo. Quantum confinement effect on electronic and optical properties of SnS. Acta Physica Sinica, 2014, 63(6): 067101. doi: 10.7498/aps.63.067101
[8]	Yu Ben-Hai, Chen Dong. Phase transition, electronic and optical properties of Si3N4 new phases at high pressure with density functional theory. Acta Physica Sinica, 2014, 63(4): 047101. doi: 10.7498/aps.63.047101
[9]	Li Jian-Hua, Cui Yuan-Shun, Zeng Xiang-Hua, Chen Gui-Bin. Investigations of structural phase transition, electronic structures and optical properties in ZnS. Acta Physica Sinica, 2013, 62(7): 077102. doi: 10.7498/aps.62.077102
[10]	Li Qian-Qian, Hao Qiu-Yan, Li Ying, Liu Guo-Dong. Theory study of rare earth (Ce, Pr) doped GaN in electronic structrue and optical property. Acta Physica Sinica, 2013, 62(1): 017103. doi: 10.7498/aps.62.017103
[11]	Pan Lei, Lu Tie-Cheng, Su Rui, Wang Yue-Zhong, Qi Jian-Qi, Fu Jia, Zhang Yi, He Duan-Wei. Study of electronic structure and optical propertise of -AlON crystal. Acta Physica Sinica, 2012, 61(2): 027101. doi: 10.7498/aps.61.027101
[12]	Wang Yin, Feng Qing, Wang Wei-Hua, Yue Yuan-Xia. First-principles study on the electronic and optical property of C-Zn co-doped anatase TiO2. Acta Physica Sinica, 2012, 61(19): 193102. doi: 10.7498/aps.61.193102
[13]	Deng Jiao-Jiao, Liu Bo, Gu Mu, Liu Xiao-Lin, Huang Shi-Ming, Ni Chen. First principles calculation of electronic structures and optical properties for -CuX(X = Cl, Br, I). Acta Physica Sinica, 2012, 61(3): 036105. doi: 10.7498/aps.61.036105
[14]	Jiao Zhao-Yong, Yang Ji-Fei, Zhang Xian-Zhou, Ma Shu-Hong, Guo Yong-Liang. Theoretical investigation of elastic, electronic, and optical properties of zinc-blende structure GaN under high pressure. Acta Physica Sinica, 2011, 60(11): 117103. doi: 10.7498/aps.60.117103
[15]	Li Xu-Zhen, Xie Quan, Chen Qian, Zhao Feng-Juan, Cui Dong-Meng. The study on the electronic structure and optical properties of OsSi2. Acta Physica Sinica, 2010, 59(3): 2016-2021. doi: 10.7498/aps.59.2016
[16]	Zhang Xue-Jun, Gao Pan, Liu Qing-Ju. First-principles study on electronic structure and optical properties of anatase TiO2 codoped with nitrogen and iron. Acta Physica Sinica, 2010, 59(7): 4930-4938. doi: 10.7498/aps.59.4930
[17]	Duan Man-Yi, Xu Ming, Zhou Hai-Ping, Chen Qing-Yun, Hu Zhi-Gang, Dong Cheng-Jun. Electronic structure and optical properties of ZnO doped with carbon. Acta Physica Sinica, 2008, 57(10): 6520-6525. doi: 10.7498/aps.57.6520
[18]	Xing Hai-Ying, Fan Guang-Han, Zhao De-Gang, He Miao, Zhang Yong, Zhou Tian-Ming. Electronic structure and optical properties of GaN with Mn-doping. Acta Physica Sinica, 2008, 57(10): 6513-6519. doi: 10.7498/aps.57.6513
[19]	Ding Ying-Chun, Xiang An-Ping, Xu Ming, Zhu Wen-Jun. Electrical structures and optical properties of doped earth element (Y，La) in γ-Si3N4. Acta Physica Sinica, 2007, 56(10): 5996-6002. doi: 10.7498/aps.56.5996
[20]	Pan Hong-Zhe, Xu Ming, Zhu Wen-Jun, Zhou Hai-Ping. First-principles study on the electrical structures and optical properties of β-Si3N4. Acta Physica Sinica, 2006, 55(7): 3585-3589. doi: 10.7498/aps.55.3585

Catalog

Vol. 70, Issue 13 - 2021-07-05

Metrics

Abstract views: 6347
PDF Downloads: 193
Cited By: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

Search

Article

留言板