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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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

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

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