Fund Project: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)
Received Date:14 April 2021
Accepted Date:08 June 2021
Available Online:30 June 2021
Published Online:05 July 2021
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:atomic-scale two-dimensional ice I/ electronic structure/ optical properties/ theoretical simulation
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2.理论计算二维冰相I的原胞构型由12个原子组成, 分别在x方向和y方向进行3 × 3周期性扩展, 在z方向设置10 ?的真空层, 建立了具有周期性边界条件的108个原子的二维六边形结构. 互锁双层冰结构的顶视图、斜视图和侧视图如图1所示. 在DFT计算中, 使用PBE[58]和SCAN泛函来处理价电子之间的交换关联相互作用. 用rVV10非局域密度泛函和vdW-DF-ob86[59,60]泛函计算水分子间的vdW相互作用. 用超软赝势[61]来处理离子实与价电子之间的相互作用. 用模守恒赝势[62]来精确描述原子散射特性. 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 Figure1. 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.
二维冰相I是一个互锁的双层冰结构, 由两个平坦的六边形水层组成, 如图1所示. 平面中水分子之间的夹角为108.9°. 在每个水层中, 一半的水分子平行于基底, 另一半垂直于基底, 一个OH向上或向下. 一层中的垂直水与另一层中的平行水形成氢键, 从而导致完全饱和的氢键结构. 图2给出了120 K时不同泛函的二维冰相I的RDF. 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(gOO, gOH和gHH)及与冰Ih, XV相在100 K的gOO的对比. 插图显示了在0.95—1.05 ?距离范围内的gOH的曲线图 Figure2. Radial distribution functions (gOO, gOH and gHH) of two-dimensional ice I in different functionals at 120 K and the comparison with the gOO of the ice Ih and XV phase at 100 K. The insets show elaborations of the gOH plots within the 0.95–1.05 ? distance range.
而介电函数实部可以由虚部通过Kramers-Kronig关系[69]变换得到. 通过能带结构, 可以计算得到全部的光学常数. 本文给出了二维冰相I在不同泛函的光学性质, 如图5所示给出了二维冰相I的介电函数的实部和虚部$\left( {{\varepsilon ^{xx}}, {\varepsilon ^{yy}}, {\varepsilon ^{zz}}} \right)$. 此处, x和y表示平面内分量, 而z分量垂直于x-y平面. PBE和vdW-DF-ob86泛函的介电常数几乎相同, 约为1.431, 且SCAN和SCAN + rVV10泛函的介电常数也基本相同, 约为1.393, 但值小于PBE和vdW-DF-ob86泛函的介电常数. 这表明采用SCAN和SCAN + rVV10泛函, 二维冰相I具有更好的绝缘性, 这与能带图中SCAN和SCAN + rVV10具有较大的带隙一致. PBE泛函的实部约等于vdW-DF-ob86的实部, 同样SCAN泛函的实部也约等于SCAN + rVV10的实部. 与低能区域(0—10 eV)中的SCAN和SCAN + rVV10相比, 介电函数的实部在PBE和vdW-DF-ob86中具有更大的值, 这可能是由于SCAN泛函的强约束性. 对于二维冰相I, 实部和虚部中${\varepsilon ^{xx}} \ne {\varepsilon ^{yy}}$, 这是由于实部和虚部都具有二维六边形冰的各向异性晶格. 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 Figure5. 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.
分别使用DFPT和AIMD模拟对二维冰相I的IR和VDOS进行了理论研究. 基于准谐波近似得到0 K时的IR光谱. 这里给出了PBE、vdW-DF-ob86和SCAN + rVV10泛函的IR光谱如图6(a)所示. 可以看出, IR光谱具有四个主要特征峰, 在低频区和高频区PBE和vdW-DF-ob86泛函的IR光谱基本一致: 在约259 cm–1处有一个明显的峰, 以839 cm–1为中心出现宽频带, 在1638 cm–1处有一个窄峰(分子内弯曲), 分子内伸缩带的中心在3186 cm–1处. 相比之下, SCAN + rVV10泛函的IR光谱的峰的位置略有不同, 前两个峰出现蓝移, 高频区的两个峰出现红移. 这主要是因为低频峰是由分子间摆动引起, 分子间摆动模式增强, 而分子内H—O—H弯曲振动和O—H键伸缩振动减弱. 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 Figure6. (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.