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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.
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Keywords:
- ice /
- hydrogen bond /
- vibration mode /
- density functional theory
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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.
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.
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.
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).
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).
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).
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).
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 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 -
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