Ultrafast dynamics of water system under photoexcitation

Jia Yun-Zhe; Meng Sheng

doi:10.7498/aps.73.20240047

Abstract

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1. 引　言
2. 水分子和水团簇的光激发行为
2.1 光电离中的迟滞
2.2 Feshbach共振的探究
3. 水体系辐照解离的重要动力学过程
3.1 水合电子的动力学
3.2 空穴定域化的动力学
3.3 ${{\mathbf{H}}_{2}\mathbf{O}}^{+}$ 的寿命探测
3.4 热电子诱导的O—H键断裂
4. 水的等离子体化
5. 结　论

References

Abstract

Experimental techniques and theoretical calculations have made significant breakthroughs recently in realizing the ultrafast time resolution and the understanding of microscopic details on an atomic scale, which has brought new insights into the ultrafast microscopic dynamics of water system and aqueous system. Here we focus on the dynamic processes of ionization, dissociation, as well as plasmonization of water molecules, water clusters, and liquid water under different intensities of light excitation.The pump-probe technique allows one to extract the information about the orbital-dependent phase shift during photoionization, corresponding to delays on a time scale from tens to hundreds of attoseconds. Delay time in photoionization is found to be proportional to the delocalization of molecular/cluster orbitals. In addition, the information related to the Feshbach resonance is also of interest. By solving the scattering equations, the detailed information about the scattering cross section, the β-parameter, and the involved Rydberg orbitals during valence electron ionization of water is obtained.For liquid water undergoing irradiation by an optical field, the tunneling electrons are unable to move away and recombine with the parent molecule on a time scale of 100 fs if the external field is not strong enough (e.g. ~100 kV/cm). For terahertz fields as high as 250 kV/cm, electrons will move away from the parent molecule after tunnelling and undergo decoherence on a 10-fs time scale. At the beginning of tunneling the electrons will be more delocalized and will collapse to a certain position on a time scale of ~1 ps, and then slowly diffuse or recombine with holes on a longer time scale. For the strong excitation case, hot electrons may also be formed. When a hot electron is located on a particular water molecule, the O—H bond will be broken.When an electron ionizes away, a hole will be created. The hole will be located on a water molecule within 10 fs, and will trigger off subsequent processes such as proton transfer and coherent oscillations. In particular, after the hole is localized and before the proton is transferred, there is a brief appearance of the metastable

${{{\mathrm{H}}}_{2}{\mathrm{O}}}^{+}$ ion, whose lifetime is experimentally captured and is predicted to be (46±10) fs. The nuclear quantum effect in this process plays a key role.Using the methods such as real time-time dependent density functional theory (rt-TDDFT), it is found that the water undergoes plasmonization under intense laser pulses corresponding to a field strength amplitude larger than 2.4 V/Å. The effective electron temperature in this period reaches over 20000 K. Strongly excited water in this state exhibits the behaviors of a liquid metal, and extremely strong nonthermal effect and nonadiabatic effect. In the process of plasmonization, a large fraction of chemical bonds in water molecules are broken and reorganize themselves, and many chemical species such as hydrogen molecules may appear, which also implies that laser-induced plasmonization can be used to synthesize new substances.Although the previous researches have brought about a very rich understanding, we have also found some details that still need to be explored: i) the influence of nuclear quantum effects has not been taken into account in most of theoretical calculations, which may result in the inadequate description and inaccurate prediction; ii) some of the microscopic details observed in simulations do not yet have a direct counterpart in experimental measurements; iii) the current simulation of water plasmonization is for the local behavior under the spatially uniform external field, while in the real situation there are spatial inhomogeneity and energy flow, which urgently need larger-scale excited state dynamics simulations.With the development of laser technology, the integration of water science and ultrafast technologies will be increasingly strong, so we believe that such a systematic understanding will play a key role in the future. It is expected that new research efforts will continue to contribute to a better understanding and the generation of new technologies in this exciting research field.

Keywords:

PACS:

42.65.Re	(Ultrafast processes; optical pulse generation and pulse compression)
33.20.Xx	(Spectra induced by strong-field or attosecond laser irradiation)
92.40.Bc	(Chemistry of fresh water)
71.15.Qe	(Excited states: methodology)

Authors and contacts

1.
Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
2.
School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
3.
Songshan Lake Materials Laboratory, Dongguan 523808, China

Corresponding author: Meng Sheng, smeng@iphy.ac.cn

Funds: Project supported by the National Key Research and Development Program of China (Grant Nos. 2021YFA1400201, 2021YFA1400503), the National Natural Science Foundation of China (Grant Nos. 11934003, 12025407, 11974400), and the Chinese Academy of Sciences (Grant Nos. YSBR-047, XDB330301).

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1. 引　言

水科学是一个备受多学科关注的特殊领域, 这是因为水在自然界中普遍存在, 在生命过程中举足轻重, 以及在物理化学性质上尤为特殊. 从所属的学科背景出发, 可以将水科学的研究大体分为以下几个部分: 星际水科学^[1]、大气与环境水科学^[2]、生命水科学^[3,4]、水的物相与物性认知^[5–7]、表面与界面水科学^[8–10]、限域水科学^[11]与含水分散体系^[12–14]的研究. 当然, 这些部分之间有着诸多的关联与交叉, 比如水-磷脂界面^[10]虽然可以归属于界面水科学, 但也是理解细胞膜相关生命化学行为的重要模型. 对于准一维纳米孔道中的限域水行为^[11]的认识, 也正是跨膜水通道蛋白功能研究的重要模型系统. 而深刻地理解水在不同温度、压力下的物相与性质, 甚至在强场激发下、特殊表界面处的新奇行为, 对于揭示自然界中水参与的诸多过程的机制、设计以含水电解液为代表的新一代能源与化工产品都有着重要意义.

一直以来, 水体系都备受科研人员关注, 但是对于水的性质的认识似乎远未到达尽头. 其中重要的限制便是实验上对于空间与时间分辨能力带来的, 这使得我们无法十分清晰地捕捉相关体系的行为细节. 随着以飞秒甚至阿秒激光脉冲为代表的全新实验技术的发展, 一系列对于水体系超快动力学行为的研究涌现出来, 包括但不限于对于水体系光谱细节的全新认识^[15,16]、对于水体系辐照解离动力学过程的细致解析^[17–19]、对于含水界面的行为研究^{[8–10,20–22]}, 以及对于极端条件下金属态及等离子态水的行为研究^[23].

与此同时, 计算技术的发展带来的强大算力以及含时密度泛函(time-dependent density functional theory, TDDFT)理论等方法的不断发展使得我们可以对于水体系进行更加精确的建模, 并使得在亚飞秒时间尺度追踪电子与原子核的演化成为可能^[24–26]. 这种技术手段上的进步不仅可以与实验结果相互印证, 而且可以给出当前实验仍无法完整给出的动力学演化细节, 为认识水科学以及指导进一步的实验工作提供支持.

本文将从水分子和团簇的光激发行为、水的辐照解离过程、以及水的等离子体化等视角出发, 介绍近些年应用前沿的实验技术与理论计算方法所带来的对于水体系超快动力学行为的认识. 这一总结将不仅让读者看到水科学的前沿进展, 还有助于将分散在各个领域的诸多工作中相关的内容关联起来, 并产生对于未来工作的合理展望. 当然, 本文由于篇幅限制无法涉及有关限域水、表界面水等更多领域的相关工作, 这些只能寄望于未来其他的论文予以总结提炼.

2. 水分子和水团簇的光激发行为

2.1 光电离中的迟滞

对于光电离等散射问题, 人们往往将远离散射中心的波函数写作一个入射平面波与出射球面波的和, 即写作:

$\underset{\boldsymbol{r}\to \mathbf{\infty }}{{\mathrm{lim}}}\psi \left(\boldsymbol{r}\right)={{\mathrm{e}}}^{{\mathrm{i}}kz}+f\left(\theta ,\phi \right)\frac{{{\mathrm{e}}}^{{\mathrm{i}}kr}}{r}.$

(1)

在分波展开的方法中, 将总波函数写作一系列分波的和:

$\psi \left(\boldsymbol{r}\right)=\sum _{l=0}^{{\mathrm{\infty }}}{R}_{l}\left(k,r\right){P}_{l}\left({\mathrm{c}}{\mathrm{o}}{\mathrm{s}}\theta \right).$

(2)

经过求解, 可以得到散射振幅以及总散射截面的表达式:

$f\left(\theta \right)=\frac{1}{k}\sum _{l=0}^{{\mathrm{\infty }}}\left(2l+1\right){{\mathrm{e}}}^{{\mathrm{i}}{\delta }_{l}}\cdot{\mathrm{s}}{\mathrm{i}}{\mathrm{n}}{\delta }_{l}\cdot{P}_{l}\left({\mathrm{c}}{\mathrm{o}}{\mathrm{s}}\theta \right),$

(3)

${\sigma }_{t}=\frac{4{\mathrm{\pi }}}{{k}^{2}}\sum _{l=0}^{{\mathrm{\infty }}}\left(2l+1\right){{\mathrm{s}}{\mathrm{i}}{\mathrm{n}}}^{2}{\delta }_{l},$

(4)

其中 ${\delta }_{l}$ 便是重要的分波相移, 曾有前人的工作^[27]指出它与光电子角分布行为息息相关. 然而, 在实验中往往只能测得散射截面的信息, 而无法获悉分波相移的信号. 基于Pazourek等^[28]的阿秒光电离理论基础, Huppert及其所在团队^[16]首次尝试通过实验手段获得了包括水分子在内的最外层两个价电子轨道之间的能量依赖的光电离延迟.

该实验中, 共有两束电磁波作用到被测定的分子上, 其中一束是近红外(near-infrared, NIR)光, 而另一束则是由该红外光照射氩气导致的极紫外(extreme ultraviolet, XUV)波段的高次谐波产生(higher harmonic generation, HHG), 后者的谐波光子能量为前者的奇数倍. 在实验上, 通过调节光路可以控制这两束光照射到分子的时间延迟, 且在任意延迟下, 由于近红外光会与高次谐波中的任意阶次的谐波产生双光子电离或者受激拉曼散射的过程, 于是会在偶数倍的能量处诱导出干涉边带. 对于 $2 n$ 阶次的边带, 其强度是由 $2 n-1$ 阶次的谐波与红外光子产生的双光子电离以及 $2 n+1$ 阶次的谐波与红外光子产生的受激拉曼散射这两种不同量子路径之间干涉后的强度决定的, 而这种干涉振幅就会受到两个光束之间的时间延迟信息的影响.

对于一个特定的边带, 如第 $q$ 个边带, 可以认为其振幅变化满足如下关系:

${A}_{q}={A}_{2\omega ,q}{\mathrm{cos}}\left[2\omega \left(\tau -{\tau }_{q}^{{\mathrm{X}}{\mathrm{U}}{\mathrm{V}}}-{\tau }_{q}^{{\mathrm{s}}{\mathrm{y}}{\mathrm{s}}}\right)\right]+{B}_{q},$

(5)

其中 $\tau$ 便是IR-XUV延迟, 即图1(b)中的纵轴. B_q对应着上文提及的两种量子路径共存时非干涉项对边带强度的贡献, 表现为一个与延迟无关的净数值. 而 ${\tau }_{q}^{{\mathrm{X}}{\mathrm{U}}{\mathrm{V}}}$ 和 ${\tau }_{q}^{{\mathrm{s}}{\mathrm{y}}{\mathrm{s}}}$ 分别是XUV发射延迟和从分子中电离造成的延迟. 其中后者又可以分为两项:

$图 1 (a) H2O分子的光电子能谱[16]; (b) IR-XUV延迟的差谱[16]\r\nFig. 1. (a) Photoelectron spectrum of H2O[16]; (b) difference spectrum as a function of the IR-XUV delay[16].$

图 1 (a) H₂O分子的光电子能谱^[16]; (b) IR-XUV延迟的差谱^[16]

Fig. 1. (a) Photoelectron spectrum of H₂O^[16]; (b) difference spectrum as a function of the IR-XUV delay^[16].

下载: 全尺寸图片幻灯片

${\tau }_{q}^{{\mathrm{s}}{\mathrm{y}}{\mathrm{s}}}={\tau }_{{\mathrm{c}}{\mathrm{c}}}+{\tau }_{{\mathrm{m}}{\mathrm{o}}{\mathrm{l}}}.$

(6)

${\tau }_{{\mathrm{c}}{\mathrm{c}}}$ 代表着光电子在连续态传播过程中, 受近红外光驱动及母核分子库仑势影响, 产生的光电离延迟. 而 ${\tau }_{{\mathrm{m}}{\mathrm{o}}{\mathrm{l}}}$ 则是一个与真实分子非球对称形状相关的延迟. 在分子电离过程中, 高轨道角动量的光电子会被分子外层的离心势垒部分俘获, 这意味着它在平均意义上必须几次穿过才能真正逃离分子的束缚, 这种现象称为形状共振, 且表现为一种在出射时间上的延迟^[29]. 很显然, 分子外围离心势垒与分子轨道形状息息相关, 这直接影响了 ${\tau }_{{\mathrm{m}}{\mathrm{o}}{\mathrm{l}}}$ , 而该工作的一个重点正是解析了分子形状共振带来的延迟行为.

Huppert等^[16]发现, 在20—40 eV的光子能量范围内, N₂O分子中分子形状共振带来的延迟可以达到160 as, 且这一延迟随着光子能量的变化有较为显著的差异, 如图2(a)所示. 而相比之下, H₂O分子中的相应延迟信息不超过50 as, 且随着光子能量变化没有显著的延迟变化, 见图2(b). 这说明水分子的连续能级形状共振的行为较弱, 且没有库珀极小值^[30]等其他连续能级结构.

$图 2 (a) 计算和测量得到的光电子从N2O+的$ {\widetilde{{\mathrm{A}}}}^{+} $和$ {\widetilde{{\mathrm{X}}}}^{+} $态离开的时间延迟[16]; (b) 与图(a)相同, 针对H2O分子[16]; (c), (d) 对于两个物种计算得到的分子延迟[16]\r\nFig. 2. (a) Measured and calculated delays between photo electrons leaving N2O+ in its $ {\widetilde{{\mathrm{A}}}}^{+} $ or $ {\widetilde{{\mathrm{X}}}}^{+} $ states[16], (b) same as Figure (a) for H2O[16]; (c), (d) calculated molecular delays for the two species[16].$

图 2 (a) 计算和测量得到的光电子从N₂O⁺的

${\widetilde{{\mathrm{A}}}}^{+}$

和

${\widetilde{{\mathrm{X}}}}^{+}$

态离开的时间延迟^[16]; (b) 与图(a)相同, 针对H₂O分子^[16]; (c), (d) 对于两个物种计算得到的分子延迟^[16]

Fig. 2. (a) Measured and calculated delays between photo electrons leaving N₂O⁺ in its

${\widetilde{{\mathrm{A}}}}^{+}$

${\widetilde{{\mathrm{X}}}}^{+}$

states^[16], (b) same as Figure (a) for H₂O^[16]; (c), (d) calculated molecular delays for the two species^[16].

下载: 全尺寸图片幻灯片

利用类似的方法, Gong等^[15]探究了不同大小水团簇上的电离延迟行为, 主要结果如所示. 结果表明, 团簇中水分子数小于5时, 相对电离延迟的数值会随着团簇的增大而增大, 其中小于3个水分子时这种趋势尤为明显. 但是对于更大的团簇, 这种增大趋势就不再显著. 其中, 作者考虑了多分子团簇构象的非唯一性. 进一步地, 作者尝试从轨道的离域性角度去理解这样的结果, 他们定义了如下的对应轨道 $i$ 的一阶矩:

$图 3 水团簇的尺寸分辨光电离时间延迟　(a) 相对于H2O (或 D2O), 在SB12中测得的水团簇1b1分波的光电离时间延迟(空心圆圈). 误差条代表95%的置信区间. 计算的延迟(实心符号)是在6.0 eV的动能下得到的[15]. (b) 与图(a)相同, 但对应于边带SB14, 其中计算值是在9.1 eV的动能下得到的. 单光子(1hν)和双光子(2hν)延迟计算结果分别以实心圆圈和星形表示[15]. (c), (d) 不同尺寸水团簇1b1轨道1—3 HOMO (记作HOMO-i)的电子密度图和计算的绝对光电离延迟. 在图(c)中以黄色背景表示了电子基本在整个团簇上离域, 而图(d)中紫色背景表示只定域在部分水分子上的情况[15]\r\nFig. 3. Size-resolved photoionization time delays of water clusters. (a) Time delays for photoionization out of the 1b1 band of water clusters, relative to H2O (or D2O), measured in SB12 (empty circles). The error bars represent 95% confidence intervals. The calculated delays (filled symbols) were obtained for a kinetic energy of 6.0 eV[15]. (b) Same as Figure (a), but measured for SB14, or calculated with kinetic energy (eKE) of 9.1 eV, the one-photon (1hν) and two-photon (2hν) delay calculations are presented as filled circles and stars, respectively[15]. (c), (d) Electron density map and calculated absolute photoionization delays of the 1–3 HOMO of the 1b1 band of water clusters (designated HOMO-i), highlighting the effect of delocalization (yellow shading), followed by partial localization (Figure (d), violet shading)[15].$

图 3 水团簇的尺寸分辨光电离时间延迟　(a) 相对于H₂O (或 D₂O), 在SB12中测得的水团簇1b₁分波的光电离时间延迟(空心圆圈). 误差条代表95%的置信区间. 计算的延迟(实心符号)是在6.0 eV的动能下得到的^[15]. (b) 与图(a)相同, 但对应于边带SB14, 其中计算值是在9.1 eV的动能下得到的. 单光子(1hν)和双光子(2hν)延迟计算结果分别以实心圆圈和星形表示^[15]. (c), (d) 不同尺寸水团簇1b₁轨道1—3 HOMO (记作HOMO-i)的电子密度图和计算的绝对光电离延迟. 在图(c)中以黄色背景表示了电子基本在整个团簇上离域, 而图(d)中紫色背景表示只定域在部分水分子上的情况^[15]

Fig. 3. Size-resolved photoionization time delays of water clusters. (a) Time delays for photoionization out of the 1b₁ band of water clusters, relative to H₂O (or D₂O), measured in SB12 (empty circles). The error bars represent 95% confidence intervals. The calculated delays (filled symbols) were obtained for a kinetic energy of 6.0 eV^[15]. (b) Same as Figure (a), but measured for SB14, or calculated with kinetic energy (eKE) of 9.1 eV, the one-photon (1hν) and two-photon (2hν) delay calculations are presented as filled circles and stars, respectively^[15]. (c), (d) Electron density map and calculated absolute photoionization delays of the 1–3 HOMO of the 1b₁ band of water clusters (designated HOMO-i), highlighting the effect of delocalization (yellow shading), followed by partial localization (Figure (d), violet shading)^[15].

下载: 全尺寸图片幻灯片

${M}_{i}=\frac{\displaystyle\int {\rho }_{i}\left(\boldsymbol{r}-{\boldsymbol{r}}_{i}\right)\left|\boldsymbol{r}-{\boldsymbol{r}}_{i}\right|{{\mathrm{d}}}^{3}r}{\displaystyle\int {\rho }_{i}\left(\boldsymbol{r}\right){{\mathrm{d}}}^{3}r},$

(7)

其中 ${\rho }_{i}\left(\boldsymbol{r}\right)$ 是某一个轨道的电荷密度, ${\boldsymbol{r}}_{i}$ 是该轨道的电荷中心.

Gong等^[15]发现, 电离延迟时间的长度与一阶矩所反映的轨道离域性有比较明显的正相关, 且可以较好地解释一些趋势上的细节(图4). 比如对于小团簇, 其最高占据轨道基本离域在整个团簇上, 所以随着团簇的增大, 这一轨道的整体离域性必然有明显的增强. 然而对于较大的团簇, 比如对于(H₂O)₆, 其部分靠近最高占据分子轨道(highest occupied molecular orbital, HOMO)的轨道会部分定域在3个、2个甚至1个水分子上, 与之对应的电离延迟就低至345 as, 292 as甚至接近50 as, 这个数值低于s4构型的(H₂O)₄团簇的HOMO-1轨道的电离延迟数值424 as, 因为该轨道是离域在全部4个水分子上的. 这一工作不仅让我们认识到水团簇的超快尺度的电离行为的细节, 还有助于我们理解从单一水分子向凝聚态水行为的渐变趋势.

$图 4 轨道离域性对水团簇光电离延迟的影响　(a) 动能(eKE)为6.0 eV时对应水团簇1b1轨道的光电离延迟, 与SB12中的实验测量结果一致[15]; (b) 与图(a)相同, 对水簇的O-1s波段使用相同的动能但是调整了光子能量[15]; (c) 光离子化时间延迟与对应水团簇1b1带的电子-空穴密度的一阶矩之间的相关性. 误差条代表 95% 的置信区间[15]\r\nFig. 4. Effect of orbital delocalization on photoionization delays of water clusters: (a) Photoionization delays for the 1b1 band of water clusters for a kinetic energy of eKE = 6.0 eV, corresponding to the experimental measurements in SB12[15]; (b) same as Figure (a), but for the O-1s band of water clusters using the same kinetic energy, and a correspondingly adjusted photon energy[15]; (c) correlation between the photoionization time delays and the first moment of the electron-hole density of the 1b1 band of water clusters (eKE = 6.0 eV). The error bars represent 95% confidence intervals[15].$

图 4 轨道离域性对水团簇光电离延迟的影响　(a) 动能(eKE)为6.0 eV时对应水团簇1b₁轨道的光电离延迟, 与SB12中的实验测量结果一致^[15]; (b) 与图(a)相同, 对水簇的O-1s波段使用相同的动能但是调整了光子能量^[15]; (c) 光离子化时间延迟与对应水团簇1b₁带的电子-空穴密度的一阶矩之间的相关性. 误差条代表 95% 的置信区间^[15]

Fig. 4. Effect of orbital delocalization on photoionization delays of water clusters: (a) Photoionization delays for the 1b₁ band of water clusters for a kinetic energy of eKE = 6.0 eV, corresponding to the experimental measurements in SB12^[15]; (b) same as Figure (a), but for the O-1s band of water clusters using the same kinetic energy, and a correspondingly adjusted photon energy^[15]; (c) correlation between the photoionization time delays and the first moment of the electron-hole density of the 1b₁ band of water clusters (eKE = 6.0 eV). The error bars represent 95% confidence intervals^[15].

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2.2 Feshbach共振的探究

除了通过XUV-IR方法对于形状共振以及电离延迟的探测, 还有一些前沿的工作尝试解析分子电离时Feshbach共振相关的信息. 虽然这些理论工作并没有给出某种时间上的动力学行为信息, 但却是共同揭示水分子电离行为以及光谱细节必不可少的一环. 前人的工作表明, Feshbach共振以及伴生的俄歇衰变等过程可能与高分辨光电子能谱中的卫星线和振荡线等有关, 然而真正从微观上理解这一过程需要考虑在电离时的电子关联效应, 并测得分子框架的光电子角分布(molecular frame photoelectron angular distributions, MFPADs). XCHEM方法正是求解方案中的一个, 其中轨道基分为了两个部分, 分别是反应分子束缚能级的多中心高斯基和描述强振荡连续能级的b样条函数. 该方法通过在紧密耦合方法中求解散射方程从而给出正确的渐进边界条件, 曾被用于给出He, Ne, N₂, O₂和CO等分子共振区域的精确光电离能谱^[31].

最近, Fernández-Milán等^[32]将这一方法应用在水分子光电离行为的解析上. 在图5中, 作者示意性画出从水分子1b₁、3a₁及1b₂三个态电离一个电子得到的 $\widetilde{{\mathrm{X}}}{}^{2}{{\mathrm{B}}}_{1}$ , $\widetilde{{\mathrm{A}}}{}^{2}{{\mathrm{A}}}_{1}$ 和 $\widetilde{{\mathrm{B}}}{}^{2}{{\mathrm{B}}}_{2}$ 三个离子态, 同时, 这也代表三个电离的可能末态. 忽略 $\widetilde{{\mathrm{B}}}{}^{2}{{\mathrm{B}}}_{2}$ 以上的阳离子状态, 作者将注意力集中在12.2—18.7 eV这一能量区域, 因为在这个能量区域, 从 $\widetilde{{\mathrm{X}}}{}^{2}{{\mathrm{B}}}_{1}$ 和 $\widetilde{{\mathrm{A}}}{}^{2}{{\mathrm{A}}}_{1}$ 电离阈值开始的连续能级区域充满Feshbach共振, 如图6所示. 在文中, 作者计算了分别对应3个不同末态的光电离截面和β参数, 并与前人的实验和理论进行对比, 发现在多数情况下实验值较好地落在XCHEM方法在速度和长度规范下给出的值之间, 并且, 虽然该模型是在相对低能(<20 eV)条件下构建的, 但是可以与高达40 eV的部分结果有较好的一致性.

$图 5 H2O的分子轨道示意图以及移除相应电子产生的阳离子态$ \widetilde{{\mathrm{X}}}{}^{2}{{\mathrm{B}}}_{1} $, $ \widetilde{{\mathrm{A}}}{}^{2}{{\mathrm{A}}}_{1} $和$ \widetilde{{\mathrm{B}}}{}^{2}{{\mathrm{B}}}_{2} $. 不同的轨道对称性以不同的颜色显示: (蓝色) a1, (红色) b1 和(黑色) b2. 灰色背景包含活性空间中的轨道. 插图还显示了水分子的方向, 其中z轴与C2旋转轴重合[32]\r\nFig. 5. Schematic molecular orbital diagram of H2O and the corresponding electron removals that give rise to the cation states $ \widetilde{{\mathrm{X}}}{}^{2}{{\mathrm{B}}}_{1} $, $ \widetilde{{\mathrm{A}}}{}^{2}{{\mathrm{A}}}_{1} $, and $ \widetilde{{\mathrm{B}}}{}^{2}{{\mathrm{B}}}_{2} $. Different orbital symmetries appear with different colors: (blue) a1, (red) b1, and (black) b2. The gray background contains the orbitals included in the active space. The orientation of the water molecule is also shown, with the z axis coinciding with the C2 rotation axis[32].$

图 5 H₂O的分子轨道示意图以及移除相应电子产生的阳离子态

$\widetilde{{\mathrm{X}}}{}^{2}{{\mathrm{B}}}_{1}$

$\widetilde{{\mathrm{A}}}{}^{2}{{\mathrm{A}}}_{1}$

和

$\widetilde{{\mathrm{B}}}{}^{2}{{\mathrm{B}}}_{2}$

. 不同的轨道对称性以不同的颜色显示: (蓝色) a₁, (红色) b₁ 和(黑色) b₂. 灰色背景包含活性空间中的轨道. 插图还显示了水分子的方向, 其中z轴与C2旋转轴重合^[32]

Fig. 5. Schematic molecular orbital diagram of H₂O and the corresponding electron removals that give rise to the cation states

$\widetilde{{\mathrm{X}}}{}^{2}{{\mathrm{B}}}_{1}$

$\widetilde{{\mathrm{A}}}{}^{2}{{\mathrm{A}}}_{1}$

, and

$\widetilde{{\mathrm{B}}}{}^{2}{{\mathrm{B}}}_{2}$

. Different orbital symmetries appear with different colors: (blue) a₁, (red) b₁, and (black) b₂. The gray background contains the orbitals included in the active space. The orientation of the water molecule is also shown, with the z axis coinciding with the C2 rotation axis^[32].

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$图 6 在两组不同角动量截断下用XCHEM计算获得的H2O单光子电离的方向平均部分截面. 计算考虑了12至19 eV之间的能量区域　(a) 离开$ \widetilde{{\mathrm{X}}}{}^{2}{{\mathrm{B}}}_{1} $态离子的部分电离截面[32]; (b) 离开$ \widetilde{{\mathrm{A}}}{}^{2}{{\mathrm{A}}}_{1} $态离子的部分电离截面. 蓝色和绿色分别对应长度规范(L)和速度规范(V). 实线和点线分别对应最大角量子数$ {l}_{{\mathrm{m}}{\mathrm{a}}{\mathrm{x}}} $为4和6 [32]\r\nFig. 6. Orientation-averaged partial cross sections for single-photon ionization of H2O obtained from two XCHEM calculations with different angular momentum bases in the energy region between 12 and 19 eV: (a) Partial ionization cross section for leaving the ion in the $ \widetilde{{\mathrm{X}}}{}^{2}{{\mathrm{B}}}_{1} $ state[32]; (b) same for the $ \widetilde{{\mathrm{A}}}{}^{2}{{\mathrm{A}}}_{1} $ state. Blue: length gauge. Green: velocity gauge. Solid line: $ {l}_{{\mathrm{m}}{\mathrm{a}}{\mathrm{x}}}= 4 $. Dots: $ {l}_{{\mathrm{m}}{\mathrm{a}}{\mathrm{x}}}= 6 $[32].$

图 6 在两组不同角动量截断下用XCHEM计算获得的H₂O单光子电离的方向平均部分截面. 计算考虑了12至19 eV之间的能量区域　(a) 离开

$\widetilde{{\mathrm{X}}}{}^{2}{{\mathrm{B}}}_{1}$

态离子的部分电离截面^[32]; (b) 离开

$\widetilde{{\mathrm{A}}}{}^{2}{{\mathrm{A}}}_{1}$

态离子的部分电离截面. 蓝色和绿色分别对应长度规范(L)和速度规范(V). 实线和点线分别对应最大角量子数

${l}_{{\mathrm{m}}{\mathrm{a}}{\mathrm{x}}}$

为4和6^[32]

Fig. 6. Orientation-averaged partial cross sections for single-photon ionization of H₂O obtained from two XCHEM calculations with different angular momentum bases in the energy region between 12 and 19 eV: (a) Partial ionization cross section for leaving the ion in the

$\widetilde{{\mathrm{X}}}{}^{2}{{\mathrm{B}}}_{1}$

state^[32]; (b) same for the

$\widetilde{{\mathrm{A}}}{}^{2}{{\mathrm{A}}}_{1}$

state. Blue: length gauge. Green: velocity gauge. Solid line:

${l}_{{\mathrm{m}}{\mathrm{a}}{\mathrm{x}}}= 4$

. Dots:

${l}_{{\mathrm{m}}{\mathrm{a}}{\mathrm{x}}}= 6$

^[32].

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利用下面的公式对于所考察能量范围内的散射截面进行拟合, 可以得到一系列共振能级(也称自电离态或者Rydberg轨道)的位置以及对应的宽度,

$\delta \left(E\right)={\delta }_{{\mathrm{b}}}\left(E\right)+\arctan\frac{{\varGamma }_{n}}{2\left(E-{E}_{n}\right)}.$

(8)

这里, 到 $\widetilde{{\mathrm{X}}}{}^{2}{{\mathrm{B}}}_{1}$ 和 $\widetilde{{\mathrm{A}}}{}^{2}{{\mathrm{A}}}_{1}$ 阈值的自电离态分别以橙色和蓝色标注在图7中.

$图 7 对应于$ \widetilde{{\mathrm{X}}}{}^{2}{{\mathrm{B}}}_{1}({\mathrm{紫}}{\mathrm{色}}{\mathrm{线}}) $和$ \widetilde{{\mathrm{A}}}{}^{2}{{\mathrm{A}}}_{1}({\mathrm{绿}}{\mathrm{线}}) $电离通道的部分截面. 结果考虑了12—19 eV的能量区间, 且利用XCHEM方法在长度规范下完成　(a) 沿着X方向极化的部分截面[32]; (b) 沿着Y方向极化的部分截面[32]; (c) 沿着Z方向极化的部分截面. 收敛到$ \widetilde{{\mathrm{A}}}{}^{2}{{\mathrm{A}}}_{1} $和$ \widetilde{{\mathrm{B}}}{}^{2}{{\mathrm{B}}}_{2} $阈值的自电离态分别用橙色和蓝色标注在图中[32]\r\nFig. 7. Partial cross sections for (purple line) $ \widetilde{{\mathrm{X}}}{}^{2}{{\mathrm{B}}}_{1} $ and (green line) $ \widetilde{{\mathrm{A}}}{}^{2}{{\mathrm{A}}}_{1} $ ionization channels in the energy region 12–19 eV, calculated with XCHEM in the length gauge: (a) Partial cross sections for polarization along the X directions[32]; (b) partial cross sections for polarization along the Y directions[32]; (c) partial cross sections for polarization along the Z directions. Labels of autoionizing states converging to the $ \widetilde{{\mathrm{A}}}{}^{2}{{\mathrm{A}}}_{1} $ threshold are indicated in orange and those converging to $ \widetilde{{\mathrm{B}}}{}^{2}{{\mathrm{B}}}_{2} $ in blue[32].$

图 7 对应于

$\widetilde{{\mathrm{X}}}{}^{2}{{\mathrm{B}}}_{1}({\mathrm{紫}}{\mathrm{色}}{\mathrm{线}})$

和

$\widetilde{{\mathrm{A}}}{}^{2}{{\mathrm{A}}}_{1}({\mathrm{绿}}{\mathrm{线}})$

电离通道的部分截面. 结果考虑了12—19 eV的能量区间, 且利用XCHEM方法在长度规范下完成　(a) 沿着X方向极化的部分截面^[32]; (b) 沿着Y方向极化的部分截面^[32]; (c) 沿着Z方向极化的部分截面. 收敛到

$\widetilde{{\mathrm{A}}}{}^{2}{{\mathrm{A}}}_{1}$

和

$\widetilde{{\mathrm{B}}}{}^{2}{{\mathrm{B}}}_{2}$

阈值的自电离态分别用橙色和蓝色标注在图中^[32]

Fig. 7. Partial cross sections for (purple line)

$\widetilde{{\mathrm{X}}}{}^{2}{{\mathrm{B}}}_{1}$

and (green line)

$\widetilde{{\mathrm{A}}}{}^{2}{{\mathrm{A}}}_{1}$

ionization channels in the energy region 12–19 eV, calculated with XCHEM in the length gauge: (a) Partial cross sections for polarization along the X directions^[32]; (b) partial cross sections for polarization along the Y directions^[32]; (c) partial cross sections for polarization along the Z directions. Labels of autoionizing states converging to the

$\widetilde{{\mathrm{A}}}{}^{2}{{\mathrm{A}}}_{1}$

threshold are indicated in orange and those converging to

$\widetilde{{\mathrm{B}}}{}^{2}{{\mathrm{B}}}_{2}$

in blue^[32].

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表1和表2中画出了图7中各个里德伯轨道的能量和宽度信息, 以及高斯函数部分的轨道形状. 表格中也列出了Diercksen等计算得到的能量的对比, 可见一致性比较好.

表 1 拟合得到的收敛到

$\widetilde{{\mathrm{A}}}{}^{2}{{\mathrm{A}}}_{1}$

阈值的里德伯轨道的能量、宽度以及在X, Y和Z方向的轨道形状示意^[32]

Table 1. Energy positions, autoionization widths and views along the X, Y, and Z axes of the Rydberg orbitals for Feshbach resonances converging to the

$\widetilde{{\mathrm{A}}}{}^{2}{{\mathrm{A}}}_{1}$

threshold obtained by fitting^[32].

Resonance	Energy/eV	Widths/meV	Diercksen/eV	X view	Y view	Z view
4sa₁5sa₁6sa₁	12.71713.54313.910	11.333.831.63	12.7713.6714.07
3db₂	12.886	2.81	13.13
3da₁	12.941	1.41	13.14
3db₁	13.020	2.60	13.25
4db₁5db₁	13.67913.979	0.900.48	13.8814.18
3da₁	13.030	2.71	13.23
4pb₂	13.208	3.07	13.35
4pb₁5pb₁6pb₁	13.29713.79614.039	3.291.360.74	13.4513.9713.97
4pa₁5pa₁6pa₁	13.31713.80414.044	13.726.153.24	13.5113.9914.30

下载: 导出CSV

| 显示表格

表 2 拟合得到的收敛到

$\widetilde{{\mathrm{B}}}{}^{2}{{\mathrm{B}}}_{2}$

阈值的里德伯轨道的能量、宽度以及在X, Y和Z方向的轨道形状示意^[32]

Table 2. Energy positions, autoionization widths and views along the X, Y, and Z axes of the Rydberg orbitals for Feshbach resonances converging to the

$\widetilde{{\mathrm{B}}}{}^{2}{{\mathrm{B}}}_{2}$

threshold obtained by fitting^[32].

Resonance	Energy/eV	Widths/meV	Diercksen/eV	X view	Y view	Z view
3pb₂	15.888	219.45	15.77
3pb₂	15.888	219.45	15.77
3pa₁	16.212	3.14	15.97
4sa₁	16.885	7.63	16.47
3db₂	17.112	29.38	17.04
3da₂	17.180	2.12	17.03
4da₂5da₂	17.85418.170	0.880.46	17.7018.01

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| 显示表格

值得一提的是, 标签为3pb₂的自电离态的宽度达到0.2 eV, 最有可能在实验中被实际观察到.

进一步地, 作者也得到了分子框架下角度分辨的辐射相对强度信息. 方位角积分后, 对于两个末态的角分辨光电子能谱被绘制在图8中, 其中Z轴与分子对称轴重合, X轴与水分子平面垂直. 由图8可以看到, 在共振能级附近, MFPAD随着光子能量迅速变化, 作者将这一现象解读为直接电离与自电离过程之间的干扰结果. 相比于直接电离的情况, 这种干扰使得最大辐射方向发生了显著的变化.

$图 8 对应x (a), y (b)和z (c)方向极化的对于方位角ϕ积分后得到的不同光子能量和电子发射角θ的光电子谱[32]\r\nFig. 8. Photoelectron spectra as a function of photon energy and the electron emission angle θ obtained after integrating over the azimuthal angle ϕ panels: (a) x polarization[32]; (b) y polarization[32]; (c) z polarization. The corresponding θ and ϕ integrated partial cross sections are shown on top of each panel[32].$

图 8 对应x (a), y (b)和z (c)方向极化的对于方位角ϕ积分后得到的不同光子能量和电子发射角θ的光电子谱^[32]

Fig. 8. Photoelectron spectra as a function of photon energy and the electron emission angle θ obtained after integrating over the azimuthal angle ϕ panels: (a) x polarization^[32]; (b) y polarization^[32]; (c) z polarization. The corresponding θ and ϕ integrated partial cross sections are shown on top of each panel^[32].

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3. 水体系辐照解离的重要动力学过程

对于光电离等以激光脉冲技术为代表的光学技术的发展不仅带来更加先进的探测手段, 使我们能拥有在时间尺度或能量尺度上前所未有的分辨能力, 同时还使得水在接受辐照后的解离等行为成为不容忽视的过程. 这种涉及激发甚至解离的过程可能是人们主动去诱发的, 比如我们即将提及的等离子体化过程^[26], 还有可能是被动的、且需要避免的, 比如水合电子的出现对于DNA等生物大分子结构的破坏^[33]. 同样是在探究水的行为, 不仅能够揭示一些星际空间、大气环境或者生命体系中自然存在的过程, 而且能为一些新兴的甚至尚处襁褓阶段的技术提供素材与依据. 这种看似不可思议的关联正是水分子这种无处不在的特殊属性造就的.

在此前的综述中, Herbert和Coons^[17]较为全面地展示了水体系在受到辐照后可能出现的电离或者激发的后续过程, 见图9. 其中关于辐照电离, 有两个至关重要的动力学过程: 一个是电离出的电子被周围水分子的氢键网络俘获形成水合电子; 另一个是剩余空穴在体系中定域化并诱导O—H键断裂等后续的反应过程.

$图 9 水的辐射分解示意图. 电离辐射会产生自由基中间体 $ {{\mathrm{e}}}^{-} $(aq), H· 和HO·. 图的下部显示了体相水中 $ {{\mathrm{e}}}^{-} $(aq)的能级图[17]\r\nFig. 9. Schematic overview of water radiolysis, wherein ionizing radiation generates radical intermediates $ {{\mathrm{e}}}^{-} $(aq), H·, and HO·. An energy-level diagram of $ {{\mathrm{e}}}^{-} $(aq) in bulk water is depicted in the lower part of the figure[17].$

图 9 水的辐射分解示意图. 电离辐射会产生自由基中间体

${{\mathrm{e}}}^{-}$

(aq), H· 和HO·. 图的下部显示了体相水中

${{\mathrm{e}}}^{-}$

(aq)的能级图^[17]

Fig. 9. Schematic overview of water radiolysis, wherein ionizing radiation generates radical intermediates

${{\mathrm{e}}}^{-}$

(aq), H·, and HO·. An energy-level diagram of

${{\mathrm{e}}}^{-}$

(aq) in bulk water is depicted in the lower part of the figure^[17].

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3.1 水合电子的动力学

Savolainen等^[18]的工作为我们展现了液态水中光激发产生自由电子并最终溶解在水中的动力学过程. 展现了在不同泵浦-探测时延 ${t}_{{\mathrm{p}}{\mathrm{p}}}$ 的情况下, 三种波长脉冲在纯水中产生的太赫兹响应信号. 不同于在266和400 nm脉冲激发过程中的多光子吸收效应, 800 nm的脉冲作用下主要体现为强场激发. 通过单指数函数拟合, 得到了一个约200 fs的衰减信号, 对应着被电离的电子在约200 fs的时间尺度内, 其光吸收频段逐渐离开太赫兹区域. 近红外探测表明, 经过皮秒(ps)量级的时间延迟后, 光吸收频段最终落在近红外波段.

$图 10 纯水光电离的太赫兹响应　(a) 800 nm泵浦(红色三角形)与单指数拟合结果(200 fs, 红线)、400 nm泵浦(蓝色填充方形)和266 nm泵浦(黑色开口圆圈)的结果. 400和266 nm波长的泵浦轨迹以800 nm波长泵浦的水合电子($ {{\mathrm{e}}}_{{\mathrm{a}}{\mathrm{q}}}^{-} $)浓度进行了缩放. 插图: 通过二维扫描推导出的 800 nm泵浦时过量电子的光谱特征. 该初始光谱在约1.5 THz处达到峰值[18]. (b) 使用 800 nm泵浦(红色, 按 11 倍缩放)的长时间太赫兹响应保持不变, 而在近红外条件下探测到的响应则清楚地显示了成对重组的动力学[18]\r\nFig. 10. Terahertz response to photoionization of neat water. (a) The 800 nm pump (red triangles) with a single exponential fit (200 fs, redline), 400 nm pump (blue filled squares) and 266 nm pump (open black circles). The 400 and 266 nm pump traces are scaled to the $ {{\mathrm{e}}}_{{\mathrm{a}}{\mathrm{q}}}^{-} $ concentration in the 800 nm pump measurement. Inset: spectral signature of the excess electron upon 800 nm pumping deduced from a two-dimensional scan. This initial spectrum peaks at ~1.5 THz[18]. (b) The long-time terahertz response with the 800 nm pump (red, scaled by factor of 11) remains constant, whereas the response probed at NIR shows clearly the geminate recombination kinetics (green) [18].$

图 10 纯水光电离的太赫兹响应　(a) 800 nm泵浦(红色三角形)与单指数拟合结果(200 fs, 红线)、400 nm泵浦(蓝色填充方形)和266 nm泵浦(黑色开口圆圈)的结果. 400和266 nm波长的泵浦轨迹以800 nm波长泵浦的水合电子(

${{\mathrm{e}}}_{{\mathrm{a}}{\mathrm{q}}}^{-}$

)浓度进行了缩放. 插图: 通过二维扫描推导出的 800 nm泵浦时过量电子的光谱特征. 该初始光谱在约1.5 THz处达到峰值^[18]. (b) 使用 800 nm泵浦(红色, 按 11 倍缩放)的长时间太赫兹响应保持不变, 而在近红外条件下探测到的响应则清楚地显示了成对重组的动力学^[18]

Fig. 10. Terahertz response to photoionization of neat water. (a) The 800 nm pump (red triangles) with a single exponential fit (200 fs, redline), 400 nm pump (blue filled squares) and 266 nm pump (open black circles). The 400 and 266 nm pump traces are scaled to the

${{\mathrm{e}}}_{{\mathrm{a}}{\mathrm{q}}}^{-}$

concentration in the 800 nm pump measurement. Inset: spectral signature of the excess electron upon 800 nm pumping deduced from a two-dimensional scan. This initial spectrum peaks at ~1.5 THz^[18]. (b) The long-time terahertz response with the 800 nm pump (red, scaled by factor of 11) remains constant, whereas the response probed at NIR shows clearly the geminate recombination kinetics (green)^[18].

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结合理论计算, Savolainen等^[18]在定量的水平确定了水合电子的产生过程. 在光激发后最初产生的电子离域半径至少达到40 Å的量级, 且电子基本处在被电离的水分子周围, 如图11(a)所示. 然而, 该离域电子的波函数将在约1 ps的时间尺度上坍缩, 同时伴随着吸收波段从太赫兹波段滑向近红外波段. 当实现完全溶剂化时, 该电子的吸收波段将基本落在近红外区域. 同时, 如果这一坍缩的最终位置与初始电子密度成正相关, 则溶剂化电子位置与初始中心位置的平均距离约等于初始的回转半径, 如图11(b)所示. 最终, 该溶剂化电子可能经历更长时间尺度的缓慢扩散或复合, 见图11(c).

$图 11 过剩电子在水中的形成和定域过程示意图　(a) 辐射出的局部过剩电子(灰色), 半径为rg[18]; (b) 电子波函数的坍缩, 这将导致平均迁移长度为rg[18]; (c) 扩散性成对重组[18]\r\nFig. 11. Schematic depiction of excess electron formation and localization process in water: (a) Ejected delocalized excess electron (in grey) with radius rg[18]; (b) collapse of the electron wavefunction, which will result in an average ejection length rg[18]; (c) diffusive geminate recombination[18].$

图 11 过剩电子在水中的形成和定域过程示意图　(a) 辐射出的局部过剩电子(灰色), 半径为r_g^[18]; (b) 电子波函数的坍缩, 这将导致平均迁移长度为r_g^[18]; (c) 扩散性成对重组^[18]

Fig. 11. Schematic depiction of excess electron formation and localization process in water: (a) Ejected delocalized excess electron (in grey) with radius r_g^[18]; (b) collapse of the electron wavefunction, which will result in an average ejection length r_g^[18]; (c) diffusive geminate recombination^[18].

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进一步地, Ghalgaoui等^[19]在工作中指出了太赫兹场在诱导电子隧穿电离过程中的作用, 即促进了被激发电子与母体分子的空间分离, 从而有效地抑制了在原处的复合. 在该工作中, 作者采用了pump-probe的技术, 其中A脉冲为泵浦光, B脉冲为探测光, 后者相对于前者有一个正的时间延迟τ, 如图12(f)所示. 这两束光先后通过了一个厚度为50 μm的水膜, 即图12(f)中蓝色区域. 通过对比探测光透射光强随着波长的变化以及水合电子的吸收谱, 作者印证了水合电子在体系中的产生, 如图12(d)所示. 作者还发现溶剂化电子的存在会明显影响水的折射率的实部和虚部.

$图 12 水的场致电子动力学和非线性二维太赫兹(2D-THz)光谱　(a), (b) 分子动力学模拟计算出的液态水中电子在两个最高占位轨道1b1 (HOMO)和3a1 (HOMO-1)位置的波动电场[19]; (c) 场致电子隧道示意图[19]; (d) 电子传播和定域化示意图[19]; (e) 水样品在与峰值场EA,P = 1.9 MV/cm太赫兹泵浦脉冲相互作用后, 在延迟时间τ = 300 ps 时的近红外吸收变化ΔA = –ln(T/T0), 蓝线: 溶解电子的缩放吸收光谱[19]; (f) 采用锁相太赫兹技术的二维太赫兹实验示意图. 水射流(蓝色)的形状, 以及通向电光采样(EOS)的路径[19]\r\nFig. 12. Two-dimensional terahertz (2D-THz) spectroscopy: (a), (b) Fluctuating electric fields in liquid water as calculated from a molecular dynamics simulation for electrons at the position of the two highest occupied orbitals 1b1 (HOMO) and 3a1 (HOMO-1) [19]; (c) schematic diagram of field-induced electron tunneling[19]; (d) schematic of electron propagation and localization[19]; (e) near-infrared absorption change ΔA = –ln(T/T0) of the water sample at a delay time of τ = 300 ps after interaction with a THz pump pulse of a peak field EA,P = 1.9 MV/cm transmitted through the sample (symbols, T, T0: sample transmission with and without excitation, blue line: Scaled absorption spectrum of solvated electrons)[19]; (f) schematic of the 2D-THz experiment with phase-locked THz pulses A and B of delay τ, the water jet (blue) in transmission geometry, and the path toward the electrooptic sampling (EOS) detector[19].$

图 12 水的场致电子动力学和非线性二维太赫兹(2D-THz)光谱　(a), (b) 分子动力学模拟计算出的液态水中电子在两个最高占位轨道1b₁(HOMO)和3a₁(HOMO-1)位置的波动电场^[19]; (c) 场致电子隧道示意图^[19]; (d) 电子传播和定域化示意图^[19]; (e) 水样品在与峰值场E_A,P = 1.9 MV/cm太赫兹泵浦脉冲相互作用后, 在延迟时间τ = 300 ps 时的近红外吸收变化ΔA = –ln(T/T₀), 蓝线: 溶解电子的缩放吸收光谱^[19]; (f) 采用锁相太赫兹技术的二维太赫兹实验示意图. 水射流(蓝色)的形状, 以及通向电光采样(EOS)的路径^[19]

Fig. 12. Two-dimensional terahertz (2D-THz) spectroscopy: (a), (b) Fluctuating electric fields in liquid water as calculated from a molecular dynamics simulation for electrons at the position of the two highest occupied orbitals 1b₁ (HOMO) and 3a₁ (HOMO-1)^[19]; (c) schematic diagram of field-induced electron tunneling^[19]; (d) schematic of electron propagation and localization^[19]; (e) near-infrared absorption change ΔA = –ln(T/T₀) of the water sample at a delay time of τ = 300 ps after interaction with a THz pump pulse of a peak field E_A,P = 1.9 MV/cm transmitted through the sample (symbols, T, T₀: sample transmission with and without excitation, blue line: Scaled absorption spectrum of solvated electrons)^[19]; (f) schematic of the 2D-THz experiment with phase-locked THz pulses A and B of delay τ, the water jet (blue) in transmission geometry, and the path toward the electrooptic sampling (EOS) detector^[19].

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Ghalgaoui等^[19]利用非线性响应的信号E_NL来捕捉泵浦光诱导出的体系的动力学过程, 如图13所示. 随着时间延迟的增加, 作者发现体系中存在一个约持续2 ps的快过程和一个持续长达10 ps以上的慢过程. 而在7 ps左右, 基本达到了可以一直稳定到近40 ps的水平, 于是该延迟被用来作为判定体系中是否形成水合电子的标准. Ghalgaoui等^[19]发现, 在无外场情况下, 水分子所处环境可产生强度为100 kV/cm量级的电场波动, 如图12(a)和图12(b)所示, 这一数值足以让价电子通过隧穿效应电离. 然而水合电子的出现需要达到更大场强的太赫兹场, 约为250 kV/cm. 这是因为电子如果仅仅在环境的诱导下隧穿, 并不能远离母分子, 而是会在100 fs内的时间尺度与母分子复合. 只有当电子在交变的外场的半个周期内获得足够能量才能真正挣脱母分子的束缚, 从而稳定地溶解, 这在量子力学的框架下对应着一个10 fs时间尺度的退相干过程.

$图 13 时间分辨非线性太赫兹响应　(a), (b) 延迟时间为 τ = 7 ps时的非线性信号场ENL(t, τ = 7 ps)(蓝线)、探测场 EB(t)(橙色线)以及二者的和EB,T(t, τ = 7 ps) = EB(t) + ENL(t, τ = 7 ps)(黑色虚线)都是入射脉冲A峰值振幅为EA,P = 500, 200 kV/cm时真实时间t的函数. 场EB,T(t, τ = 7 ps)代表通过激发样品传输的总THz探针场. 图(a)中的红色虚线表示传输的泵浦场EA(t) [19]. (c) 非线性信号场ENL(t = ±0.2 ps, τ)作为在泵浦电场峰值振幅EA,P = 500 kV/cm下, t = –0.2 ps (图(a)中的红色实线, 信号最小值)和t = +0.2 ps (图(a)中的蓝色实线, 信号最大值)时的延迟时间 τ 的函数. 虚线来自通过稍微改变泵浦场条件, 进行的符合实验精度范围(误差条)且有更长的延迟时间τ的轨迹[19]\r\nFig. 13. Time-resolved nonlinear THz response. (a), (b) Nonlinear signal field ENL(t, τ = 7 ps) (blue line) for a delay time of τ = 7 ps together with the probe field EB(t) (orange line) and the sum EB, T(t, τ = 7 ps) = EB(t)+ENL(t, τ = 7 ps) (black dashed line) as a function of real time t for peak amplitudes EA, P = 500, 200 kV/cm of incoming pump pulse A. Field EB, T(t, τ = 7 ps) represents the total THz probe field transmitted through the excited sample. The dotted red line in panel (a) shows the transmitted pump field EA(t) [19]. (c) Nonlinear signal field ENL(t = ±0.2 ps, τ) as a function of delay time τ for t = –0.2 ps (red solid line, signal minimum in panel (a)) and t = +0.2 ps (blue solid line, signal maximum in panel (a)) for a pump field amplitude EA, P = 500 kV/cm. The dashed lines from an independent measurement with a slightly different pump field agree with the experimental accuracy (error bars) and extend to longer delay times τ [19].$

图 13 时间分辨非线性太赫兹响应　(a), (b) 延迟时间为 τ = 7 ps时的非线性信号场E_NL(t, τ = 7 ps)(蓝线)、探测场 E_B(t)(橙色线)以及二者的和E_B,T(t, τ = 7 ps) = E_B(t) + E_NL(t, τ = 7 ps)(黑色虚线)都是入射脉冲A峰值振幅为E_A,P = 500, 200 kV/cm时真实时间t的函数. 场E_B,T(t, τ = 7 ps)代表通过激发样品传输的总THz探针场. 图(a)中的红色虚线表示传输的泵浦场E_A(t)^[19]. (c) 非线性信号场E_NL(t = ±0.2 ps, τ)作为在泵浦电场峰值振幅E_A,P = 500 kV/cm下, t = –0.2 ps (图(a)中的红色实线, 信号最小值)和t = +0.2 ps (图(a)中的蓝色实线, 信号最大值)时的延迟时间 τ 的函数. 虚线来自通过稍微改变泵浦场条件, 进行的符合实验精度范围(误差条)且有更长的延迟时间τ的轨迹^[19]

Fig. 13. Time-resolved nonlinear THz response. (a), (b) Nonlinear signal field E_NL(t, τ = 7 ps) (blue line) for a delay time of τ = 7 ps together with the probe field E_B(t) (orange line) and the sum E_{B, T}(t, τ = 7 ps) = E_B(t)+E_NL(t, τ = 7 ps) (black dashed line) as a function of real time t for peak amplitudes E_{A, P} = 500, 200 kV/cm of incoming pump pulse A. Field E_{B, T}(t, τ = 7 ps) represents the total THz probe field transmitted through the excited sample. The dotted red line in panel (a) shows the transmitted pump field E_A(t)^[19]. (c) Nonlinear signal field E_NL(t = ±0.2 ps, τ) as a function of delay time τ for t = –0.2 ps (red solid line, signal minimum in panel (a)) and t = +0.2 ps (blue solid line, signal maximum in panel (a)) for a pump field amplitude E_{A, P} = 500 kV/cm. The dashed lines from an independent measurement with a slightly different pump field agree with the experimental accuracy (error bars) and extend to longer delay times τ ^[19].

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通过模拟初始展宽为0.15 nm的波包在高斯型势场(图14(b)中黑线)中的行为, 作者发现了在亚飞秒时间尺度波包的迅速展宽. 这在一定程度上反映了束缚轨道上的电子波包在隧穿后瞬间的动力学行为, 即补足了图11(a)状态前的超快时间尺度的图像. 同时, 模拟的结果也进一步印证了隧穿概率随场强增强的结论.

$图 14 (a)—(c) 场诱导电子隧穿的分析[19]; (d) 电子隧穿概率PT与10 fs高斯驱动脉冲峰值电场的函数关系(参见图(b))[19]\r\nFig. 14. (a)–(c) Spatio-temporal aspects of field-induced electron tunneling[19]; (d) electron tunneling probability PT as a function of the peak electric field of a 10-fs Gaussian driving pulse (cf. panel (b)) [19].$

图 14 (a)—(c) 场诱导电子隧穿的分析^[19]; (d) 电子隧穿概率P_T与10 fs高斯驱动脉冲峰值电场的函数关系(参见图(b))^[19]

Fig. 14. (a)–(c) Spatio-temporal aspects of field-induced electron tunneling^[19]; (d) electron tunneling probability P_T as a function of the peak electric field of a 10-fs Gaussian driving pulse (cf. panel (b))^[19].

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值得一提的是, Lan等^[25]通过机器学习的办法, 建立了可以准确描述多余电子影响的力场模型, 这使得对于水合电子直接动力学模拟以及进一步加入核量子效应的贡献成为可能. 通过该方法, 作者观察到了水合电子的两种扩散机制.

其中第一种机制是经典的非瞬态机制, 如图15(a)—(d)所示. 符合该机制的图示事件中水分子A和B中的悬挂氢键与水合电子结合, 取代了原先与水合电子结合的C分子. 而最终B和C分子也因为与周边分子成氢键而脱离与水合电子的键合. 这样的机制与水合电子在溶剂中定域化的机制是类似的. 在定域过程中一个断裂的氢键释放出一个O—H片段从而俘获水合电子^[34,35]. 而第二种机制则是仅在包含核量子效应后才能被观察到的瞬态机制, 如图15(e)—(h)所示. 在这种机制下, 可能同时存在两个腔. 随着自旋密度从一个腔转移到另一个腔, 这两个腔的体积会发生变化. 这种机制中会伴随着初始水合电子腔周围的几个氢键的同时断裂.

$图 15 非瞬态(上)和瞬态(下)扩散机制. 自旋密度用蓝色(正)和黄色(负)表示. 非瞬态机理是由形成空腔的分子与其相邻的无键水分子之间形成氢键(HBs)而引发的(在图(a)—(d)中以A和B表示). 随后A, B的悬空氢氧根与空腔中的水合电子结合, 取代了第三个分子C(图(c)). 分子B和C与它们的邻居形成HBs, 并从空腔中脱离(图(d)). 瞬态扩散(图(e)至(h))为特点是存在双腔(图(f))[25]\r\nFig. 15. Non-transient (top) and transient (bottom) diffusion mechanisms. Spin densities are shown in blue (positive) and yellow (negative). Non-transient mechanism is initiated by the formation of the hydrogen bonds (HBs) between a cavity-forming molecule and its unbonded neighboring water molecules (indicated as A and B in panels (a)–(d)). The dangling OH of A, B subsequently binds to the hydrated electron in the cavity, replacing that of a third molecule, C (panel (c)). Molecules B and C form HBs with their neighbors, and unbind from the cavity (panel (d)). Transient diffusion (panels (e) to (h)) is characterized by the existence of the double-cavity (panel (f))[25].$

图 15 非瞬态(上)和瞬态(下)扩散机制. 自旋密度用蓝色(正)和黄色(负)表示. 非瞬态机理是由形成空腔的分子与其相邻的无键水分子之间形成氢键(HBs)而引发的(在图(a)—(d)中以A和B表示). 随后A, B的悬空氢氧根与空腔中的水合电子结合, 取代了第三个分子C(图(c)). 分子B和C与它们的邻居形成HBs, 并从空腔中脱离(图(d)). 瞬态扩散(图(e)至(h))为特点是存在双腔(图(f))^[25]

Fig. 15. Non-transient (top) and transient (bottom) diffusion mechanisms. Spin densities are shown in blue (positive) and yellow (negative). Non-transient mechanism is initiated by the formation of the hydrogen bonds (HBs) between a cavity-forming molecule and its unbonded neighboring water molecules (indicated as A and B in panels (a)–(d)). The dangling OH of A, B subsequently binds to the hydrated electron in the cavity, replacing that of a third molecule, C (panel (c)). Molecules B and C form HBs with their neighbors, and unbind from the cavity (panel (d)). Transient diffusion (panels (e) to (h)) is characterized by the existence of the double-cavity (panel (f))^[25].

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随着理论和实验手段的不断进步, 还将从更多更细节的侧面认识水合电子的动力学过程, 并更加深入地了解相关的物理学机制.

3.2 空穴定域化的动力学

除了对于水合电子的探究, 还有一些工作将焦点落在空穴的行为上. Lu等^[24]的工作通过Ehrenfest动力学的方法提供了对于电子电离后约70 fs内超快时间尺度上的空穴行为的认识. 在该工作中电离是通过在HOMO轨道上直接移除电子实现的.

首先, Lu等^[24]通过运行多条轨迹模拟捕捉到了空穴在经历5 fs相干过程后定域在初始密度较高的水分子上(图16(a))或者转移到初始密度较低水分子上(图16(b))的行为, 两者的可能性占比分别约为70%和20%. 由图16(b)可以看到, 无论是定域还是转移, 时间尺度都在10 fs左右. 通过与固定原子核位置的模拟(图16(c)和图16(d))相比, Lu等^[24]发现核的动力学是不可忽略的. 从5—10 fs这段极短的时间内, 电子结构的变化开始引起原子核的运动, 这种原子核体系的、远小于常见电声耦合时间尺度的超快响应与固体中位移型声子激发的物理图像是一致的.

$图 16 (a), (b)采用从头算Ehrenfest动力学的选择模拟的时间分辨空穴密度图[16]; (c), (d)固定核实时电子动力学, 初始条件分别与子图(a)和图(b)相同. 空穴密度是用在氧原子上的Mulliken自旋密度来计算的, 绘制的是两个最大的空穴密度[16]\r\nFig. 16. (a), (b) Time-resolved hole density plots of selected simulations using ab initio Ehrenfest dynamics[16]; (c), (d) fixed-nucleus real-time electronic dynamics using the same initial conditions as in panels (a) and (b), respectively. Hole densities are computed as Mulliken spin densities projected on oxygen atoms. The two largest hole densities are plotted[16].$

图 16 (a), (b)采用从头算Ehrenfest动力学的选择模拟的时间分辨空穴密度图^[16]; (c), (d)固定核实时电子动力学, 初始条件分别与子图(a)和图(b)相同. 空穴密度是用在氧原子上的Mulliken自旋密度来计算的, 绘制的是两个最大的空穴密度^[16]

Fig. 16. (a), (b) Time-resolved hole density plots of selected simulations using ab initio Ehrenfest dynamics^[16]; (c), (d) fixed-nucleus real-time electronic dynamics using the same initial conditions as in panels (a) and (b), respectively. Hole densities are computed as Mulliken spin densities projected on oxygen atoms. The two largest hole densities are plotted^[16].

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接下来, Lu等^[16]捕捉到了空穴引发的质子动力学行为. 在图17(a)中所示的轨迹中, 质子在跨过了相邻两个水分子氧的中心位置后, 并没有直接与新的分子中氧原子成键, 而是在近40 fs内在两个分子的氧原子间往复振荡, 直到40 fs后才开始稳定地与新分子成键. 统计发现, 约24%的质子并未在模拟时间内完成转移, 而有76%左右的质子在30—40 fs左右完成了转移. 这一转移的时间尺度与Loh等^[36]在实验中测得的(46±10) fs是吻合的, 该实验细节将在下文介绍. 此外, 作者还发现质子转移可能会诱发新的水分子上的质子的二次转移, 且前后两个质子的转移事件有10—20 fs的延迟. 这意味着, 在两次转移间, 会有寿命为10—20 fs 的H(H₂O) ${}_2^+$ 阳离子团簇的形成.

$图 17 (a)电离后轨迹b (和图16(b)中的轨迹一致)的从头算Ehrenfest动力学比图, 表示第一(蓝色, 实线)和第二(红色, 虚线)质子转移过程[16]; (b)第一和第二质子转移示意图[16]\r\nFig. 17. (a) Ratio plots of ab initio Ehrenfest dynamics for trajectory b (same as that in Fig. 16(b)) after the ionization, indicating the first (blue, solid) and second (red, dashed) proton transfer processes[16]; (b) illustrations of the first and second proton transfers[16]$

图 17 (a)电离后轨迹b (和图16(b)中的轨迹一致)的从头算Ehrenfest动力学比图, 表示第一(蓝色, 实线)和第二(红色, 虚线)质子转移过程^[16]; (b)第一和第二质子转移示意图^[16]

Fig. 17. (a) Ratio plots of ab initio Ehrenfest dynamics for trajectory b (same as that in Fig. 16(b)) after the ionization, indicating the first (blue, solid) and second (red, dashed) proton transfer processes^[16]; (b) illustrations of the first and second proton transfers^[16]

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最后, 部分轨迹还捕捉到了空穴在30 fs内离域在三个水分子之间发生相干振荡(如图18所示), 随后转移至少持续到70 fs的在两个水分子之间发生相干振荡的状态. 虽然Ehrenfest动力学本身可能高估了相干行为的强度, 但是Lu等^[16]的工作预言在低温下的冰中, 很可能有同等强度甚至更高强度的长寿命相干空穴动力学行为.

$图 18 三个不同水分子的时间分辨自旋密度图[16]\r\nFig. 18. Time-resolved spin density plots of three different water molecules[16].$

图 18 三个不同水分子的时间分辨自旋密度图^[16]

Fig. 18. Time-resolved spin density plots of three different water molecules^[16].

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当然, 空穴产生的机制不局限于光子的辐照, 还可能来源于质子等带电粒子的碰撞. 比如Shepard与Kanai^[37]就通过第一性原理计算的方法对于辐照质子路径周围的激发以及空穴的动力学行为进行了探究, 发现了在质子路径周围产生的空穴在约6 fs的时间内有显著比例的衰减, 并在远离辐照质子路径的空间区域产生二次激发.

3.3 ${{\mathbf{H}}_{2}\mathbf{O}}^{+}$ 的寿命探测

如图9所示, 在水分子发生电离后会产生自由电子的水合过程以及空穴的定域化过程, 后者将产生一个H₂O⁺离子. 然而在水环境中, H₂O⁺会向邻近水转移一个质子, 发生较为迅速的 ${{{\mathrm{H}}}_{2}{\mathrm{O}}}^{+}+{{\mathrm{H}}}_{2}{\mathrm{O}}\to {{{\mathrm{H}}}_{3}{\mathrm{O}}}^{+}+{\mathrm{H}}{\mathrm{O}}\cdot$ 反应, 因此在较长一段时间内H₂O⁺并没有被实验有效地观测到.

为了实现对于H₂O⁺以及相应动力学过程的捕捉, Loh等^[36]采用了pump-probe技术探测了不同时间延迟下的光电子能谱. 由于HO·与H₂O⁺是等电子体, 其对应吸收峰的位置与H₂O⁺相近, 而H₃O⁺的吸收谱线则被液态水的吸收所掩盖, 所以我们很难通过某一个峰的强度直接捕捉到 ${{{\mathrm{H}}}_{2}{\mathrm{O}}}^{+}+{{\mathrm{H}}}_{2}{\mathrm{O}}\to {{{\mathrm{H}}}_{3}{\mathrm{O}}}^{+}+{\mathrm{H}}{\mathrm{O}}\cdot$ 反应发生的时间尺度. 比如在图19(a)中展示的, 只能在526 eV附近发现一个属于H₂O⁺/HO·的价电子激发的峰, 却无法分辨.

$图 19 (a) 通过分散荧光通道分别对于Δt < 0和Δt > 100 fs进行探测[36]; (b) 价空穴(H2O+/OH)区微分吸收ΔA. 在1.5和5.8 ps之间的216个时间延迟中收集的光谱被平均以产生共振剖面, 该共振剖面可以用两个洛伦兹函数的和来拟合[36]; (c) 525.43, 525.93和526.73 eV三种X射线探针能量下的按极化方向平均后的时间轨迹[36]; (d) 电荷-空穴距离(CHD)(蓝色)和质子完全转移百分比(橙色)的时间演化[36]\r\nFig. 19. (a) Absorption for Δt < 0 and Δt > 100 fs monitored through the dispersed fluorescence channel[36]; (b) differential absorption ΔA in the valence hole (H2O+/OH) region. Spectra collected at 216 time delays between 1.5 and 5.8 ps are averaged to produce the resonance profile, which is fit to a sum of two Lorentzians[36]; (c) polarization averaged time traces at three X-ray probe energies: 525.43, 525.93, and 526.73 eV[36]; (d) charge-hole distance (CHD) (blue) and completed proton transfer percentage (orange)[36]$

图 19 (a) 通过分散荧光通道分别对于Δt < 0和Δt > 100 fs进行探测^[36]; (b) 价空穴(H₂O⁺/OH)区微分吸收ΔA. 在1.5和5.8 ps之间的216个时间延迟中收集的光谱被平均以产生共振剖面, 该共振剖面可以用两个洛伦兹函数的和来拟合^[36]; (c) 525.43, 525.93和526.73 eV三种X射线探针能量下的按极化方向平均后的时间轨迹^[36]; (d) 电荷-空穴距离(CHD)(蓝色)和质子完全转移百分比(橙色)的时间演化^[36]

Fig. 19. (a) Absorption for Δt < 0 and Δt > 100 fs monitored through the dispersed fluorescence channel^[36]; (b) differential absorption ΔA in the valence hole (H₂O⁺/OH) region. Spectra collected at 216 time delays between 1.5 and 5.8 ps are averaged to produce the resonance profile, which is fit to a sum of two Lorentzians^[36]; (c) polarization averaged time traces at three X-ray probe energies: 525.43, 525.93, and 526.73 eV^[36]; (d) charge-hole distance (CHD) (blue) and completed proton transfer percentage (orange)^[36]

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于是Loh等^[36]进一步给出了包含不同时间延迟Δt下的二维光电子能谱图, 如所示, 其中微分吸收强度被定义为 $\Delta A = A(\Delta t) - A(\Delta t < 0)$ . 图19(b)中显示, 在0时刻出现了迅速的增加, 对应着电离产物H₂O⁺的出现. 在1 ps内, 吸收强度较快衰减, 而随后进入缓慢的衰减阶段. Loh等^[36]将该过程对应的物理图像理解为, 电离产物H₂O⁺在产生后的1 ps内以寿命τ₁衰减, 产生寿命为τ₂的中间产物HO·. 对图19(b)中数据进行拟合, Loh等^[36]得到τ₁ = (0.18 ± 0.02) ps, τ₂ = (14.2 ± 0.4) ps. 其中τ₂作为HO·自由基的衰减函数被解释为HO·自由基与水合电子复合形成OH^–的过程, 而τ₁可以对应于H₂O⁺的衰减或振动的热HO·自由基的冷却.

在图19(c)中呈现了三个选定的光子能量为525.43, 525.93和526.73 eV时, 各向同性信号ΔA_iso = (ΔA_// + 2ΔA_⊥)/3的时间演化. 对比可以发现, 525.93 eV的曲线相较其他两种情况的衰减明显迟缓, 这暗示着一个额外的超快过程. 通过对ΔA_iso进行全局拟合, Loh等^[36]得到了时间常数的一个新分量(46 ± 10) fs, 其余两个分别为(0.16 ±0.03) ps 和 (9.2 ± 1.3) ps, 对应于前面对于图19(b)分析中的τ₁和τ₂. 这一新的46 fs时间常数分量在525.93 eV表现为一个增长分量, 即在羟基自由基吸收峰值525.97 eV的附近, 这表明其反映了羟基自由基形成的时间尺度. 如果接受羟基自由基是由H₂O⁺衰减得到, 这说明H₂O⁺阳离子的寿命为46 fs.

随后, Loh等^[36]又利用QM/MM方法对于强场电离后的水进行了模拟, 发现了电子-空穴距离(charge-hole distance, CHD)与质子转移完成度较好地符合, 如图19(d)所示. 这印证了前人Marsalek等^[38]此前研究的结论: H₂O⁺形成后电子与空穴在阳离子处重叠, 当质子转移发生, 空穴继续留在HO·处, 而电子被H₃O⁺携带离开. 通过模拟, 作者也得到了与前人工作^[38]符合较好的质子转移时间尺度, 即60 fs, 这也与实验结果的(46 ± 10) fs基本相符.

值得强调的是, Zhao等^[39]基于环状聚合物分子动力学模拟(ring polymer molecular dynamics, RPMD)的探究表明, 核量子效应(nuclear quantum effect, NQE)在数十飞秒超快时间尺度内水分子质子转移的发生过程中起到了不可忽视的作用. 图20中对比了考虑和忽略NQE的情况下双水分子体系经历的动力学过程, 其中只有前者在符合Loh等^[36]实验结果的时间尺度内发生了质子转移.

$图 20 (a)氢原子(H)和离它最近的两个氧原子(O1, O2)的距离差. 阴影表示所有珠子的量子涨落. 右侧是过程的示意图[39]. (b) 激发态动力学中0和47 fs的快照. 在RPMD-IB仿真中, 给出了所有珠子的构型. 在47 fs时, 劈裂的氢原子的完整核波包接近第一个水分子的氧原子(O1), 表明水合氢离子(H3O+)和OH·自由基的形成[39]\r\nFig. 20. (a) The distance difference of the hydrogen atom (H) and its two nearest oxygen atoms (O1, O2). Shadows indicate the quantum fluctuation of all beads. Schematic setting is shown in the right panel[39]. (b) The snapshots at 0 and 47 fs in the excited state dynamics. In the RPMD-IB simulation, the configurations of all beads are presented. At 47 fs, the whole nuclear wave packet of split hydrogen atom approaches the oxygen atom (O1) of the first water molecule, indicating the formation of hydronium (H3O+) and OH· radical[39].$

图 20 (a)氢原子(H)和离它最近的两个氧原子(O1, O2)的距离差. 阴影表示所有珠子的量子涨落. 右侧是过程的示意图^[39]. (b) 激发态动力学中0和47 fs的快照. 在RPMD-IB仿真中, 给出了所有珠子的构型. 在47 fs时, 劈裂的氢原子的完整核波包接近第一个水分子的氧原子(O1), 表明水合氢离子(H₃O⁺)和OH·自由基的形成^[39]

Fig. 20. (a) The distance difference of the hydrogen atom (H) and its two nearest oxygen atoms (O1, O2). Shadows indicate the quantum fluctuation of all beads. Schematic setting is shown in the right panel^[39]. (b) The snapshots at 0 and 47 fs in the excited state dynamics. In the RPMD-IB simulation, the configurations of all beads are presented. At 47 fs, the whole nuclear wave packet of split hydrogen atom approaches the oxygen atom (O1) of the first water molecule, indicating the formation of hydronium (H₃O⁺) and OH· radical^[39].

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3.4 热电子诱导的O—H键断裂

在图9所列举的过程中, 前文已经涉及了水合电子的形成以及H₂O⁺阳离子启动的O—H键断裂过程. 然而热电子除了可以稳定为水合电子, 还可以在相对高能的状态下令临近水分子的O—H键失稳断裂从而形成OH^–, 称为水的解离电子附着(dissociative electron attachment, DEA). Jones和Schatz^[40]的工作采用了最小面间跳跃(fewest switches surface hopping, FSSH)的方法, 并结合基于Tamm-Dancoff近似(Tamm-Dancoff approximation, TDA)的密度泛函理论(density functional theory, DFT)方法进行了动力学模拟, 细致探究了在(H₂O)₅团簇中的解离电子附着过程以及在不同团簇大小下通过添加高能电子启动氢原子解离过程所需要的能量阈值.

其中, 对于5个水分子组成的团簇进行了三次动力学的演化, 附加电子在最初被放置在第10激发态(D10)上, 随后分别经历了30 fs以及约10 fs后该电子从D10态回到了D1态, 如图21(a)—(c)所示. 对于图26(a)所示的第一条轨迹, 在约30 fs时发生了迅速的由D4向D1的跳跃(如图21(d)), 这正对应着氢原子解离的瞬间. 不难看出, 当解离发生后, D1和D2的能量相距较近, 且都显著低于D3的能量. D1和D2对应着OH^–的两个π*轨道, 这意味着最终电子趋向于定域在剩余的OH^–骨架上, 而解离后的HOMO轨道(如图22(d))清晰地印证了这一结论.

$图 21 FSSH的激发态表面和活性表面分别为第1—3次轨迹(分别对应(a)—(c)), 作为时间的函数, 对于五个水分子簇和一个初始激发态被选为第10激发态的电子. 青色粗曲线表示FSSH计算中任何时刻的“活化”状态. D1, D2和更高能级之间的能量分离表明电子在OH上的状态与电子在H上的状态(对于相同的结构)是相关的[40]. (d)活性激发态表面轮廓随反应时间的变化[40]\r\nFig. 21. Excited state surfaces and active surface of FSSH runs 1–3 ((a)–(c), respectively) as a function of time for a cluster of five water molecules and an electron for an initial excited state chosen to be the 10 th excited state. The thick cyan curve labels the “active” state in the FSSH calculation at any time. Note that the separation in energy among D1, D2, and the higher states indicates states where the electron is on the OH are involved vs. states where the electron is on the H (for the same structure)[40]. (d) Active excited state surface profile as a function of reaction time[40].$

图 21 FSSH的激发态表面和活性表面分别为第1—3次轨迹(分别对应(a)—(c)), 作为时间的函数, 对于五个水分子簇和一个初始激发态被选为第10激发态的电子. 青色粗曲线表示FSSH计算中任何时刻的“活化”状态. D1, D2和更高能级之间的能量分离表明电子在OH上的状态与电子在H上的状态(对于相同的结构)是相关的^[40]. (d)活性激发态表面轮廓随反应时间的变化^[40]

Fig. 21. Excited state surfaces and active surface of FSSH runs 1–3 ((a)–(c), respectively) as a function of time for a cluster of five water molecules and an electron for an initial excited state chosen to be the 10 th excited state. The thick cyan curve labels the “active” state in the FSSH calculation at any time. Note that the separation in energy among D1, D2, and the higher states indicates states where the electron is on the OH are involved vs. states where the electron is on the H (for the same structure)^[40]. (d) Active excited state surface profile as a function of reaction time^[40].

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$图 26 液态水的离子动力学　(a) 各氢原子平均δ随电场的时间演化. δ的定义如插图所示[26]; (b) 平均δ值和最终δ值随激光脉冲电场的变化[26]; (c) 平均δ随第一阶段离子温度的升高而降低[26]; (d) 随激光脉冲电场变化的氧-氧径向分布函数. 对每个电场进行了长达500 fs的模拟, 计算了径向分布函数. 插图显示了与参考文献[44]中的数据的比较\r\nFig. 26. Ionic dynamics of liquid water: (a) Temporal evolutions of average δ of all hydrogen atoms with electric field, the definition of δ is shown in the inset[26]; (b) minimum of average δ and the final δ with electric fields of laser pulses[26]; (c) decrease of average δ vs. the first-stage ionic temperature increase[26]; (d) oxygen–oxygen radial distribution functions with the electric field of laser pulses. The radial distribution functions are calculated with the whole 500 fs long simulations for each electric field[26]. The inset shows the comparison with the data from ref. [44].$

图 26 液态水的离子动力学　(a) 各氢原子平均δ随电场的时间演化. δ的定义如插图所示^[26]; (b) 平均δ值和最终δ值随激光脉冲电场的变化^[26]; (c) 平均δ随第一阶段离子温度的升高而降低^[26]; (d) 随激光脉冲电场变化的氧-氧径向分布函数. 对每个电场进行了长达500 fs的模拟, 计算了径向分布函数. 插图显示了与参考文献[44]中的数据的比较

Fig. 26. Ionic dynamics of liquid water: (a) Temporal evolutions of average δ of all hydrogen atoms with electric field, the definition of δ is shown in the inset^[26]; (b) minimum of average δ and the final δ with electric fields of laser pulses^[26]; (c) decrease of average δ vs. the first-stage ionic temperature increase^[26]; (d) oxygen–oxygen radial distribution functions with the electric field of laser pulses. The radial distribution functions are calculated with the whole 500 fs long simulations for each electric field^[26]. The inset shows the comparison with the data from ref. [44].

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$图 22 加入一个热电子的五分子水团簇的超快激发态动力学中HOMO波函数的快照. 在D2→D1表面跳前后的选定时间帧拍摄快照　(a) 跳前5 fs[40]; (b) 跳时[40]; (c) 跳后5 fs[40]; (d) 跳后20 fs[40]\r\nFig. 22. Snapshots of the HOMO wave function during ultrafast excited state dynamics of a water cluster of five molecules with the addition of a hot electron. The snapshots are taken at selected time frames around the D2 → D1 surface hop: (a) 5 fs before the hop[40]; (b) at the hop[40]; (c) 5 fs after the hop[40]; (d) 20 fs after the hop[40].$

图 22 加入一个热电子的五分子水团簇的超快激发态动力学中HOMO波函数的快照. 在D2→D1表面跳前后的选定时间帧拍摄快照　(a) 跳前5 fs^[40]; (b) 跳时^[40]; (c) 跳后5 fs^[40]; (d) 跳后20 fs^[40]

Fig. 22. Snapshots of the HOMO wave function during ultrafast excited state dynamics of a water cluster of five molecules with the addition of a hot electron. The snapshots are taken at selected time frames around the D2 → D1 surface hop: (a) 5 fs before the hop^[40]; (b) at the hop^[40]; (c) 5 fs after the hop^[40]; (d) 20 fs after the hop^[40].

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作者通过对2—12个水分子组成的团簇的对比探究发现, 对于越大的团簇, 需要更高初始占据的激发态才能最终导致H解离的过程. 然而启动反应所需的热电子的能量阈值只相差约0.7 eV (图23). 此外, 最终电子定域在O—H骨架上, 从而形成H原子以及OH^–的行为似乎对于各个尺寸的团簇都是成立的, 这与单个水分子的情形截然相反. 这样的趋势似乎预示着对于液态水而言形成H + OH^–依然是更有利的, 但是直接的证据仍需要未来更加有针对性的工作给出.

$图 23 不同大小的水团簇中加入热电子的能量阈值[40]\r\nFig. 23. Energy threshold for addition for hot electrons to water clusters of various sizes[40].$

图 23 不同大小的水团簇中加入热电子的能量阈值^[40]

Fig. 23. Energy threshold for addition for hot electrons to water clusters of various sizes^[40].

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4. 水的等离子体化

液体水的等离子体化并不是一个新出现的概念, 自2002年起就已经有围绕这一话题开展的实验工作^[41–43], 它们展示了水的液滴或者液柱等在强激光脉冲辐照后的行为. 由于这些文章主要围绕水在等离子化过程中宏观上的行为进行讨论, 而并没有涉及超快尺度分子级别的动力学过程, 因此在本文中不做详述.

利用含时密度泛函(rt-TDDFT)方法, Xu等^[26]给出了液态水的激光诱导等离子体化过程的微观图像. 非绝热动力学模拟表明, 被强激光脉冲辐射后的液态水经历了在脉冲下加热加压和无脉冲的迟豫两个过程. 脉冲辐射对应的电场可以写作 $E(t) = E_0\cos[2\text{\pi}(c/\lambda)t] \exp[- (t - t_0)^2/2\sigma^2]$ , 其中λ = 800 nm, σ = 5 fs, t₀ = 24 fs, 最大场强E₀的值在0.7—2.4 V/Å范围, 对应的峰值强度为10¹³ W/cm².

从趋势上来看, 随着最大场强E₀的增大, 水体系得到的升温和加压的程度都在明显地增强(如图24(b), (d)); 从结果上来看, 只有强度达到一定阈值, 如2.4 V/Å, 体系才会在100 fs量级的时间尺度上发生显著的等离子体化而产生氢氧自由基、游离氧、游离氢等诸多解离产物(如图25(c)所示), 这与图9中所列举的各种反应路径的终产物有较好的对应. 从100—500 fs, 动力学模拟还捕捉到了自由氧原子组合成为氧气分子等过程, 图26(d)中径向分布函数上新的氧-氧峰的出现也印证了这一点. 这也暗示着激光诱导等离子体产生可以被视为产生一些由氢或氧组成的重要产物的全新手段.

$图 24 液态水的光致动力学　(a) 800 nm激光脉冲照射液态水的示意图[26]; (b) 离子温度随体系压力的增加而增加, 色条表示脉冲的电场, 单位为V/Å[26]; (c) 离子温度随激光脉冲电场的时间演变, 光场包络线如插图所示, 这条竖线标志着第一阶段和第二阶段的分离[26]; (d) 液态水的两步离子加热[26]\r\nFig. 24. Photoinduced dynamics of liquid water: (a) Schematic diagram shows the liquid water irradiated with the 800 nm laser pulses[26]. (b) Increase of ionic temperature versus the increase of system pressure. The colorbar shows the electric field of the pulses, and the units are V/Å[26]. (c) Temporal evolutions of ionic temperatures with the electric field of laser pulses. The light envelope is shown in the inset. The vertical line marks the separation of the first and second stage[26]. (d) Two-step ionic heating of liquid water[26]$

图 24 液态水的光致动力学　(a) 800 nm激光脉冲照射液态水的示意图^[26]; (b) 离子温度随体系压力的增加而增加, 色条表示脉冲的电场, 单位为V/Å^[26]; (c) 离子温度随激光脉冲电场的时间演变, 光场包络线如插图所示, 这条竖线标志着第一阶段和第二阶段的分离^[26]; (d) 液态水的两步离子加热^[26]

Fig. 24. Photoinduced dynamics of liquid water: (a) Schematic diagram shows the liquid water irradiated with the 800 nm laser pulses^[26]. (b) Increase of ionic temperature versus the increase of system pressure. The colorbar shows the electric field of the pulses, and the units are V/Å^[26]. (c) Temporal evolutions of ionic temperatures with the electric field of laser pulses. The light envelope is shown in the inset. The vertical line marks the separation of the first and second stage^[26]. (d) Two-step ionic heating of liquid water^[26]

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$图 25 (a)—(d) 非绝热从头算分子动力学模拟构型. 激光脉冲的电场和时间如图所示. 水分子、水合离子、羟基、自由质子和氧原子、瞬态氢分子和氧分子分别显示为白色、红色、橙色、绿色、紫色、粉红色和深蓝色[26]\r\nFig. 25. (a)–(d) Configurations of the nonadiabatic ab initio molecular dynamics simulations. The electric field of laser pulses and the time are shown in the inset. The water molecules, hydroniums, hydroxyls, free protons and oxygens, transient hydrogen molecules, and oxygen molecules are shown in white, red, orange, green, purple, pink, and dark blue colors, respectively[26].$

图 25 (a)—(d) 非绝热从头算分子动力学模拟构型. 激光脉冲的电场和时间如图所示. 水分子、水合离子、羟基、自由质子和氧原子、瞬态氢分子和氧分子分别显示为白色、红色、橙色、绿色、紫色、粉红色和深蓝色^[26]

Fig. 25. (a)–(d) Configurations of the nonadiabatic ab initio molecular dynamics simulations. The electric field of laser pulses and the time are shown in the inset. The water molecules, hydroniums, hydroxyls, free protons and oxygens, transient hydrogen molecules, and oxygen molecules are shown in white, red, orange, green, purple, pink, and dark blue colors, respectively^[26].

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对于水体系而言, 质子转移是开启分子解离等诸多反应的开端, 因此Xu等^[26]设计了结构参数δ = |d_HO1–d_HO2|, 即某一个氢原子与邻近的两个氧原子的距离差. 随着场强幅值的增加, 体系平均的δ受到电场的扰动明显增大. 对于2.4 V/Å的情况, 体系平均的δ在30 fs内降低至0.5 Å以下, 这意味着已经有相当比例的氢氧键已经失去稳定性, 且发生了质子转移过程. 从时间演化上来看, 2.4 V/Å下体系平均的δ在几百飞秒内恒小于1, 这也说明体系出现了剧烈的反应过程. 作者还发现了第一阶段温度升高与结构参数改变之间近似线性的关系(如图26).

除了离子的动力学行为, Xu等^[26]的工作还关注了电子的超快过程. 将t = 100 fs时激发电子的价电子数比例定义为有效电子激发, 其随着电场的增强呈现的非线性变化如所示. 这种非线性体现了从多光子电离到强场电离的转变, 阈值在 $E_0 \approx 1.9$ V/Å的位置. 电子激发不仅增强了液态水的内部压力(如图12(c)), 还在快速平衡的过程中促进了质子转移和水的解离. 如图27(a)所示, 受激发的电子数在达到最大值后随时间减少, 而这种复合过程的强度被发现与第二阶段温度升高成正比. 这说明图24(c)中后半段温度的升高主要来自于激发电子与空穴的重组.

$图 27 液态水电子动力学　(a) 受激价电子随激光脉冲电场的时间演化[26]. (b) 激光脉冲电场下的有效电子激发和电子复合. 箭头显示了从多光子到强场电离过程的转变[26]. (c) 电子复合与离子子系统第二阶段升温的关系[26]. (d) 模拟中电场为2.4 V/Å时t = 100 fs时的电子占据, 给出了态的瞬时电子密度[26]\r\nFig. 27. Electronic dynamics of liquid water. (a) Temporal evolutions of excited valence electrons with the electric field of laser pulses[26]. (b) Effective electron excitation and electron recombination with electric fields of laser pulses. The arrow shows the transition from multiphoton to strong-field ionization processes[26]. (c) Electron recombination vs. the second-stage temperature increase of ionic subsystems[26]. (d) Electronic occupation at t = 100 fs in the simulation with an electric field of 2.4 V/Å. The instantaneous electronic density of states is also shown[26].$

图 27 液态水电子动力学　(a) 受激价电子随激光脉冲电场的时间演化^[26]. (b) 激光脉冲电场下的有效电子激发和电子复合. 箭头显示了从多光子到强场电离过程的转变^[26]. (c) 电子复合与离子子系统第二阶段升温的关系^[26]. (d) 模拟中电场为2.4 V/Å时t = 100 fs时的电子占据, 给出了态的瞬时电子密度^[26]

Fig. 27. Electronic dynamics of liquid water. (a) Temporal evolutions of excited valence electrons with the electric field of laser pulses^[26]. (b) Effective electron excitation and electron recombination with electric fields of laser pulses. The arrow shows the transition from multiphoton to strong-field ionization processes^[26]. (c) Electron recombination vs. the second-stage temperature increase of ionic subsystems^[26]. (d) Electronic occupation at t = 100 fs in the simulation with an electric field of 2.4 V/Å. The instantaneous electronic density of states is also shown^[26].

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值得注意的是, 对于2.4 V/Å的情况, 强烈的电子激发导致体系已经从半导体转变为近似金属的特殊状态, 有效电子温度约40000 K, 电子占据数情况见图27(d). Chen等^[23]的工作也发现了在超过15000 K电子温度下, 强激发水呈现出与Ziman理论相符的液态金属的行为, 比如体现出极低的折射率和极高的载流子密度. 借助密度泛函动力学方法, Medvedev等^[45]在2.5 eV (约29000 K)的电子温度下捕捉到了约380 fs时出现的导带底能级的显著降低, 该能级跨越带隙, 最终与价带顶轨道相交(如图28(a)). 随着温度继续升高至3.5 eV(约35000 K), 导带与价带轨道合并的时间尺度可以缩短至约50 fs. 这种带隙的坍缩与金属态的形成被解释为非热和非绝热效应, 这与Xu等^[26]的工作在图像上具有充分的一致性.

$图 28 (a)第一性原理计算得到的1.6 eV/原子, (b) 2 eV/原子和(c) 2.5 eV/原子情况下超快能量沉积中水的电子能级演化[45]\r\nFig. 28. Electronic energy levels evolution of water under ultrafast energy deposition with the dose to the electronic system of (a) 1.6 eV/atom, (b) 2 eV/atom, and (c) 2.5 eV/atom calculated by ab initio method[45].$

图 28 (a)第一性原理计算得到的1.6 eV/原子, (b) 2 eV/原子和(c) 2.5 eV/原子情况下超快能量沉积中水的电子能级演化^[45]

Fig. 28. Electronic energy levels evolution of water under ultrafast energy deposition with the dose to the electronic system of (a) 1.6 eV/atom, (b) 2 eV/atom, and (c) 2.5 eV/atom calculated by ab initio method^[45].

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综合离子和电子行为, 作者给出了等离子体化的相对清晰的微观图像: 第一阶段电子受到激发, 由于电声耦合作用电子子系统在第二阶段的弛豫过程中也会把部分能量传递给离子子系统, 造成离子子系统的加热和变形. 第二阶段离子运动仍带来压力的升高, 然而电子的迟豫过程带来的压力释放更显著, 造成整体压力轻微地下降.

5. 结　论

通过双光子延迟技术, 人们可以提取在光电离过程中的分波相移信息, 对应于几十到几百阿秒时间尺度的延迟, 且水分子连续能级相对较弱的形状共振被发现. 对于小团簇而言, 随着团簇尺寸的增大电离过程中经历的延迟不断增大. 但是对于大于5个水分子数的团簇, 这种延迟不再有明显的增加, 这是由于团簇轨道的离域性并不明显增加, 而是仅涉及几个相邻的水分子. 此外, Feshbach共振相关的信息也得到了关注. 通过在紧密耦合方法中求解散射方程, 得到了水分子价电子轨道电离的散射截面、β参数以及里德堡轨道等细节信息.

对于经历光场辐照的液态水, 如果外场不够强(如100 kV/cm量级), 隧穿的电子无法远离母分子并在100 fs内的时间尺度与母分子复合; 对于高达250 kV/cm的太赫兹场, 电子会在隧穿后远离母分子, 且经历10 fs时间尺度的退相干过程. 在40 fs左右的隧穿初期, 电子会有较大的离域性, 且会在约1 ps的时间尺度内坍缩到平均距离原中心初始离域半径尺寸的位置. 且在更长的时间尺度缓慢扩散或者复合. 在扩散过程中, 核量子效应的引入在理论上预测了一种双中心的水合电子状态, 揭示了该效应在动力学上的体现. 对于强激发情况, 也可能形成高能的自由电子, 即热电子. 当热电子定域到某一个水分子上, 会引发其O—H键断裂, 从而形成H原子以及OH^–.

电离的电子离开后, 会留下一个空穴. 该空穴会在10 fs内在初始密度最高或者邻近的水分子上定域, 并引发质子转移、相干振荡等后续过程. 其中, 在空穴完成定域化后、质子转移前会短暂出现亚稳态的 ${{{\mathrm{H}}}_{2}{\mathrm{O}}}^{+}$ 离子, 该离子的寿命被实验捕捉到, 预计为(46±10) fs. 该过程中的核量子效应起到不可忽视的作用.

利用含时密度泛函(rt-TDDFT)等方法, 人们发现在对应2.4 V/Å场强幅值的强激光脉冲下, 水体系可能会经历等离子体化的过程. 期间有效电子温度会达到20000 K以上, 甚至40000 K. 这种状态下强激发水呈现出与Ziman理论相符的液态金属的行为, 导带与价带间的带隙关闭, 出现了极强的非热效应和非绝热效应. 在等离子体化的过程中, 水分子中大量的化学键断裂, 且出现重组, 可能出现氢原子、氧原子、氢分子、氧分子等诸多物种, 这也暗示着激光诱导等离子体化可能在未来作为一种合成物质如氢气的特殊途径.

通过梳理实验和理论计算给出的光激发下水体系的超快动力学行为, 使我们对于单个水分子、水团簇以及液态水与光的相互作用有了更加完整和清晰的认识, 如图29所示. 由于这些工作原本分散在水科学的各个子领域, 很容易被从事部分子领域的科研工作者所忽略. 因此本文有助于指导未来的工作, 使其更加高效准确地选择恰当的实验技术与建模方案, 或者在数据分析时持有更加清晰的物理图像.

$图 29 水体系受到不同强度光激发后主要动力学过程的时间尺度示意\r\nFig. 29. Schematic diagram of the time scale of the main dynamic processes of water system excited by different intensities of light.$

图 29 水体系受到不同强度光激发后主要动力学过程的时间尺度示意

Fig. 29. Schematic diagram of the time scale of the main dynamic processes of water system excited by different intensities of light.

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同时, 也发现了一些仍待探索或者完善的细节: 1)在多数理论计算的工作中, 并未考虑核量子效应的影响, 而这很可能导致部分模拟结果的失真; 2)部分在模拟中观测到的微观细节还没有与之直接对应的实验证据, 这意味着一些动力学的细节并未定论; 3)当前进行的对于等离子体化现象的模拟是针对空间均匀外场下的局部行为, 而真实情况下激光辐照区域与周围区域之间的能量扩散过程可能带来更加丰富的物理信息, 这亟需更大尺度下的激发态动力学模拟技术的出现; 4)以形状共振为代表的电离延迟的动力学细节尚无细致的探究, 以及在这个过程中原子核体系的运动有无影响尚未被阐明.

随着激光技术的发展, 水科学与相关技术的融合将会日趋密切, 因此相信这样的系统性的认识必然会在越来越多的实际探索中发挥作用. 也期待更多科研工作者能贡献出与本文互补的或者更进一步的认识, 以及去完善尚待填补的空白.

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图 1 (a) H₂O分子的光电子能谱^[16]; (b) IR-XUV延迟的差谱^[16]

Figure 1. (a) Photoelectron spectrum of H₂O^[16]; (b) difference spectrum as a function of the IR-XUV delay^[16].

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图 2 (a) 计算和测量得到的光电子从N₂O⁺的 ${\widetilde{{\mathrm{A}}}}^{+}$ 和 ${\widetilde{{\mathrm{X}}}}^{+}$ 态离开的时间延迟^[16]; (b) 与图(a)相同, 针对H₂O分子^[16]; (c), (d) 对于两个物种计算得到的分子延迟^[16]

Figure 2. (a) Measured and calculated delays between photo electrons leaving N₂O⁺ in its ${\widetilde{{\mathrm{A}}}}^{+}$ or ${\widetilde{{\mathrm{X}}}}^{+}$ states^[16], (b) same as Figure (a) for H₂O^[16]; (c), (d) calculated molecular delays for the two species^[16].

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Figure 3. Size-resolved photoionization time delays of water clusters. (a) Time delays for photoionization out of the 1b₁ band of water clusters, relative to H₂O (or D₂O), measured in SB12 (empty circles). The error bars represent 95% confidence intervals. The calculated delays (filled symbols) were obtained for a kinetic energy of 6.0 eV^[15]. (b) Same as Figure (a), but measured for SB14, or calculated with kinetic energy (eKE) of 9.1 eV, the one-photon (1hν) and two-photon (2hν) delay calculations are presented as filled circles and stars, respectively^[15]. (c), (d) Electron density map and calculated absolute photoionization delays of the 1–3 HOMO of the 1b₁ band of water clusters (designated HOMO-i), highlighting the effect of delocalization (yellow shading), followed by partial localization (Figure (d), violet shading)^[15].

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Figure 4. Effect of orbital delocalization on photoionization delays of water clusters: (a) Photoionization delays for the 1b₁ band of water clusters for a kinetic energy of eKE = 6.0 eV, corresponding to the experimental measurements in SB12^[15]; (b) same as Figure (a), but for the O-1s band of water clusters using the same kinetic energy, and a correspondingly adjusted photon energy^[15]; (c) correlation between the photoionization time delays and the first moment of the electron-hole density of the 1b₁ band of water clusters (eKE = 6.0 eV). The error bars represent 95% confidence intervals^[15].

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H₂O的分子轨道示意图以及移除相应电子产生的阳离子态 $\widetilde{{\mathrm{X}}}{}^{2}{{\mathrm{B}}}_{1}$ , $\widetilde{{\mathrm{A}}}{}^{2}{{\mathrm{A}}}_{1}$ 和 $\widetilde{{\mathrm{B}}}{}^{2}{{\mathrm{B}}}_{2}$ . 不同的轨道对称性以不同的颜色显示: (蓝色) a₁, (红色) b₁ 和(黑色) b₂. 灰色背景包含活性空间中的轨道. 插图还显示了水分子的方向, 其中z轴与C2旋转轴重合^[32]

Schematic molecular orbital diagram of H₂O and the corresponding electron removals that give rise to the cation states $\widetilde{{\mathrm{X}}}{}^{2}{{\mathrm{B}}}_{1}$ , $\widetilde{{\mathrm{A}}}{}^{2}{{\mathrm{A}}}_{1}$ , and $\widetilde{{\mathrm{B}}}{}^{2}{{\mathrm{B}}}_{2}$ . Different orbital symmetries appear with different colors: (blue) a₁, (red) b₁, and (black) b₂. The gray background contains the orbitals included in the active space. The orientation of the water molecule is also shown, with the z axis coinciding with the C2 rotation axis^[32].

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在两组不同角动量截断下用XCHEM计算获得的H₂O单光子电离的方向平均部分截面. 计算考虑了12至19 eV之间的能量区域　(a) 离开 $\widetilde{{\mathrm{X}}}{}^{2}{{\mathrm{B}}}_{1}$ 态离子的部分电离截面^[32]; (b) 离开 $\widetilde{{\mathrm{A}}}{}^{2}{{\mathrm{A}}}_{1}$ 态离子的部分电离截面. 蓝色和绿色分别对应长度规范(L)和速度规范(V). 实线和点线分别对应最大角量子数 ${l}_{{\mathrm{m}}{\mathrm{a}}{\mathrm{x}}}$ 为4和6^[32]

Orientation-averaged partial cross sections for single-photon ionization of H₂O obtained from two XCHEM calculations with different angular momentum bases in the energy region between 12 and 19 eV: (a) Partial ionization cross section for leaving the ion in the $\widetilde{{\mathrm{X}}}{}^{2}{{\mathrm{B}}}_{1}$ state^[32]; (b) same for the $\widetilde{{\mathrm{A}}}{}^{2}{{\mathrm{A}}}_{1}$ state. Blue: length gauge. Green: velocity gauge. Solid line: ${l}_{{\mathrm{m}}{\mathrm{a}}{\mathrm{x}}}= 4$ . Dots: ${l}_{{\mathrm{m}}{\mathrm{a}}{\mathrm{x}}}= 6$ ^[32].

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对应于 $\widetilde{{\mathrm{X}}}{}^{2}{{\mathrm{B}}}_{1}({\mathrm{紫}}{\mathrm{色}}{\mathrm{线}})$ 和 $\widetilde{{\mathrm{A}}}{}^{2}{{\mathrm{A}}}_{1}({\mathrm{绿}}{\mathrm{线}})$ 电离通道的部分截面. 结果考虑了12—19 eV的能量区间, 且利用XCHEM方法在长度规范下完成　(a) 沿着X方向极化的部分截面^[32]; (b) 沿着Y方向极化的部分截面^[32]; (c) 沿着Z方向极化的部分截面. 收敛到 $\widetilde{{\mathrm{A}}}{}^{2}{{\mathrm{A}}}_{1}$ 和 $\widetilde{{\mathrm{B}}}{}^{2}{{\mathrm{B}}}_{2}$ 阈值的自电离态分别用橙色和蓝色标注在图中^[32]

Partial cross sections for (purple line) $\widetilde{{\mathrm{X}}}{}^{2}{{\mathrm{B}}}_{1}$ and (green line) $\widetilde{{\mathrm{A}}}{}^{2}{{\mathrm{A}}}_{1}$ ionization channels in the energy region 12–19 eV, calculated with XCHEM in the length gauge: (a) Partial cross sections for polarization along the X directions^[32]; (b) partial cross sections for polarization along the Y directions^[32]; (c) partial cross sections for polarization along the Z directions. Labels of autoionizing states converging to the $\widetilde{{\mathrm{A}}}{}^{2}{{\mathrm{A}}}_{1}$ threshold are indicated in orange and those converging to $\widetilde{{\mathrm{B}}}{}^{2}{{\mathrm{B}}}_{2}$ in blue^[32].

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图 8 对应x (a), y (b)和z (c)方向极化的对于方位角ϕ积分后得到的不同光子能量和电子发射角θ的光电子谱^[32]

Figure 8. Photoelectron spectra as a function of photon energy and the electron emission angle θ obtained after integrating over the azimuthal angle ϕ panels: (a) x polarization^[32]; (b) y polarization^[32]; (c) z polarization. The corresponding θ and ϕ integrated partial cross sections are shown on top of each panel^[32].

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水的辐射分解示意图. 电离辐射会产生自由基中间体 ${{\mathrm{e}}}^{-}$ (aq), H· 和HO·. 图的下部显示了体相水中 ${{\mathrm{e}}}^{-}$ (aq)的能级图^[17]

Schematic overview of water radiolysis, wherein ionizing radiation generates radical intermediates ${{\mathrm{e}}}^{-}$ (aq), H·, and HO·. An energy-level diagram of ${{\mathrm{e}}}^{-}$ (aq) in bulk water is depicted in the lower part of the figure^[17].

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纯水光电离的太赫兹响应　(a) 800 nm泵浦(红色三角形)与单指数拟合结果(200 fs, 红线)、400 nm泵浦(蓝色填充方形)和266 nm泵浦(黑色开口圆圈)的结果. 400和266 nm波长的泵浦轨迹以800 nm波长泵浦的水合电子( ${{\mathrm{e}}}_{{\mathrm{a}}{\mathrm{q}}}^{-}$ )浓度进行了缩放. 插图: 通过二维扫描推导出的 800 nm泵浦时过量电子的光谱特征. 该初始光谱在约1.5 THz处达到峰值^[18]. (b) 使用 800 nm泵浦(红色, 按 11 倍缩放)的长时间太赫兹响应保持不变, 而在近红外条件下探测到的响应则清楚地显示了成对重组的动力学^[18]

Terahertz response to photoionization of neat water. (a) The 800 nm pump (red triangles) with a single exponential fit (200 fs, redline), 400 nm pump (blue filled squares) and 266 nm pump (open black circles). The 400 and 266 nm pump traces are scaled to the ${{\mathrm{e}}}_{{\mathrm{a}}{\mathrm{q}}}^{-}$ concentration in the 800 nm pump measurement. Inset: spectral signature of the excess electron upon 800 nm pumping deduced from a two-dimensional scan. This initial spectrum peaks at ~1.5 THz^[18]. (b) The long-time terahertz response with the 800 nm pump (red, scaled by factor of 11) remains constant, whereas the response probed at NIR shows clearly the geminate recombination kinetics (green)^[18].

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Figure 11. Schematic depiction of excess electron formation and localization process in water: (a) Ejected delocalized excess electron (in grey) with radius r_g^[18]; (b) collapse of the electron wavefunction, which will result in an average ejection length r_g^[18]; (c) diffusive geminate recombination^[18].

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Figure 12. Two-dimensional terahertz (2D-THz) spectroscopy: (a), (b) Fluctuating electric fields in liquid water as calculated from a molecular dynamics simulation for electrons at the position of the two highest occupied orbitals 1b₁ (HOMO) and 3a₁ (HOMO-1)^[19]; (c) schematic diagram of field-induced electron tunneling^[19]; (d) schematic of electron propagation and localization^[19]; (e) near-infrared absorption change ΔA = –ln(T/T₀) of the water sample at a delay time of τ = 300 ps after interaction with a THz pump pulse of a peak field E_A,P = 1.9 MV/cm transmitted through the sample (symbols, T, T₀: sample transmission with and without excitation, blue line: Scaled absorption spectrum of solvated electrons)^[19]; (f) schematic of the 2D-THz experiment with phase-locked THz pulses A and B of delay τ, the water jet (blue) in transmission geometry, and the path toward the electrooptic sampling (EOS) detector^[19].

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Figure 13. Time-resolved nonlinear THz response. (a), (b) Nonlinear signal field E_NL(t, τ = 7 ps) (blue line) for a delay time of τ = 7 ps together with the probe field E_B(t) (orange line) and the sum E_{B, T}(t, τ = 7 ps) = E_B(t)+E_NL(t, τ = 7 ps) (black dashed line) as a function of real time t for peak amplitudes E_{A, P} = 500, 200 kV/cm of incoming pump pulse A. Field E_{B, T}(t, τ = 7 ps) represents the total THz probe field transmitted through the excited sample. The dotted red line in panel (a) shows the transmitted pump field E_A(t)^[19]. (c) Nonlinear signal field E_NL(t = ±0.2 ps, τ) as a function of delay time τ for t = –0.2 ps (red solid line, signal minimum in panel (a)) and t = +0.2 ps (blue solid line, signal maximum in panel (a)) for a pump field amplitude E_{A, P} = 500 kV/cm. The dashed lines from an independent measurement with a slightly different pump field agree with the experimental accuracy (error bars) and extend to longer delay times τ ^[19].

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图 14 (a)—(c) 场诱导电子隧穿的分析^[19]; (d) 电子隧穿概率P_T与10 fs高斯驱动脉冲峰值电场的函数关系(参见图(b))^[19]

Figure 14. (a)–(c) Spatio-temporal aspects of field-induced electron tunneling^[19]; (d) electron tunneling probability P_T as a function of the peak electric field of a 10-fs Gaussian driving pulse (cf. panel (b))^[19].

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Figure 15. Non-transient (top) and transient (bottom) diffusion mechanisms. Spin densities are shown in blue (positive) and yellow (negative). Non-transient mechanism is initiated by the formation of the hydrogen bonds (HBs) between a cavity-forming molecule and its unbonded neighboring water molecules (indicated as A and B in panels (a)–(d)). The dangling OH of A, B subsequently binds to the hydrated electron in the cavity, replacing that of a third molecule, C (panel (c)). Molecules B and C form HBs with their neighbors, and unbind from the cavity (panel (d)). Transient diffusion (panels (e) to (h)) is characterized by the existence of the double-cavity (panel (f))^[25].

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Figure 16. (a), (b) Time-resolved hole density plots of selected simulations using ab initio Ehrenfest dynamics^[16]; (c), (d) fixed-nucleus real-time electronic dynamics using the same initial conditions as in panels (a) and (b), respectively. Hole densities are computed as Mulliken spin densities projected on oxygen atoms. The two largest hole densities are plotted^[16].

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Figure 17. (a) Ratio plots of ab initio Ehrenfest dynamics for trajectory b (same as that in Fig. 16(b)) after the ionization, indicating the first (blue, solid) and second (red, dashed) proton transfer processes^[16]; (b) illustrations of the first and second proton transfers^[16]

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图 18 三个不同水分子的时间分辨自旋密度图^[16]

Figure 18. Time-resolved spin density plots of three different water molecules^[16].

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Figure 19. (a) Absorption for Δt < 0 and Δt > 100 fs monitored through the dispersed fluorescence channel^[36]; (b) differential absorption ΔA in the valence hole (H₂O⁺/OH) region. Spectra collected at 216 time delays between 1.5 and 5.8 ps are averaged to produce the resonance profile, which is fit to a sum of two Lorentzians^[36]; (c) polarization averaged time traces at three X-ray probe energies: 525.43, 525.93, and 526.73 eV^[36]; (d) charge-hole distance (CHD) (blue) and completed proton transfer percentage (orange)^[36]

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Figure 20. (a) The distance difference of the hydrogen atom (H) and its two nearest oxygen atoms (O1, O2). Shadows indicate the quantum fluctuation of all beads. Schematic setting is shown in the right panel^[39]. (b) The snapshots at 0 and 47 fs in the excited state dynamics. In the RPMD-IB simulation, the configurations of all beads are presented. At 47 fs, the whole nuclear wave packet of split hydrogen atom approaches the oxygen atom (O1) of the first water molecule, indicating the formation of hydronium (H₃O⁺) and OH· radical^[39].

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Figure 21. Excited state surfaces and active surface of FSSH runs 1–3 ((a)–(c), respectively) as a function of time for a cluster of five water molecules and an electron for an initial excited state chosen to be the 10 th excited state. The thick cyan curve labels the “active” state in the FSSH calculation at any time. Note that the separation in energy among D1, D2, and the higher states indicates states where the electron is on the OH are involved vs. states where the electron is on the H (for the same structure)^[40]. (d) Active excited state surface profile as a function of reaction time^[40].

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Figure 26. Ionic dynamics of liquid water: (a) Temporal evolutions of average δ of all hydrogen atoms with electric field, the definition of δ is shown in the inset^[26]; (b) minimum of average δ and the final δ with electric fields of laser pulses^[26]; (c) decrease of average δ vs. the first-stage ionic temperature increase^[26]; (d) oxygen–oxygen radial distribution functions with the electric field of laser pulses. The radial distribution functions are calculated with the whole 500 fs long simulations for each electric field^[26]. The inset shows the comparison with the data from ref. [44].

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Figure 22. Snapshots of the HOMO wave function during ultrafast excited state dynamics of a water cluster of five molecules with the addition of a hot electron. The snapshots are taken at selected time frames around the D2 → D1 surface hop: (a) 5 fs before the hop^[40]; (b) at the hop^[40]; (c) 5 fs after the hop^[40]; (d) 20 fs after the hop^[40].

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图 23 不同大小的水团簇中加入热电子的能量阈值^[40]

Figure 23. Energy threshold for addition for hot electrons to water clusters of various sizes^[40].

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Figure 24. Photoinduced dynamics of liquid water: (a) Schematic diagram shows the liquid water irradiated with the 800 nm laser pulses^[26]. (b) Increase of ionic temperature versus the increase of system pressure. The colorbar shows the electric field of the pulses, and the units are V/Å^[26]. (c) Temporal evolutions of ionic temperatures with the electric field of laser pulses. The light envelope is shown in the inset. The vertical line marks the separation of the first and second stage^[26]. (d) Two-step ionic heating of liquid water^[26]

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Figure 25. (a)–(d) Configurations of the nonadiabatic ab initio molecular dynamics simulations. The electric field of laser pulses and the time are shown in the inset. The water molecules, hydroniums, hydroxyls, free protons and oxygens, transient hydrogen molecules, and oxygen molecules are shown in white, red, orange, green, purple, pink, and dark blue colors, respectively^[26].

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Figure 27. Electronic dynamics of liquid water. (a) Temporal evolutions of excited valence electrons with the electric field of laser pulses^[26]. (b) Effective electron excitation and electron recombination with electric fields of laser pulses. The arrow shows the transition from multiphoton to strong-field ionization processes^[26]. (c) Electron recombination vs. the second-stage temperature increase of ionic subsystems^[26]. (d) Electronic occupation at t = 100 fs in the simulation with an electric field of 2.4 V/Å. The instantaneous electronic density of states is also shown^[26].

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图 28 (a)第一性原理计算得到的1.6 eV/原子, (b) 2 eV/原子和(c) 2.5 eV/原子情况下超快能量沉积中水的电子能级演化^[45]

Figure 28. Electronic energy levels evolution of water under ultrafast energy deposition with the dose to the electronic system of (a) 1.6 eV/atom, (b) 2 eV/atom, and (c) 2.5 eV/atom calculated by ab initio method^[45].

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图 29 水体系受到不同强度光激发后主要动力学过程的时间尺度示意

Figure 29. Schematic diagram of the time scale of the main dynamic processes of water system excited by different intensities of light.

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拟合得到的收敛到 $\widetilde{{\mathrm{A}}}{}^{2}{{\mathrm{A}}}_{1}$ 阈值的里德伯轨道的能量、宽度以及在X, Y和Z方向的轨道形状示意^[32]

Table 1. Energy positions, autoionization widths and views along the X, Y, and Z axes of the Rydberg orbitals for Feshbach resonances converging to the $\widetilde{{\mathrm{A}}}{}^{2}{{\mathrm{A}}}_{1}$ threshold obtained by fitting^[32].

Resonance	Energy/eV	Widths/meV	Diercksen/eV	X view	Y view	Z view
4sa₁5sa₁6sa₁	12.71713.54313.910	11.333.831.63	12.7713.6714.07
3db₂	12.886	2.81	13.13
3da₁	12.941	1.41	13.14
3db₁	13.020	2.60	13.25
4db₁5db₁	13.67913.979	0.900.48	13.8814.18
3da₁	13.030	2.71	13.23
4pb₂	13.208	3.07	13.35
4pb₁5pb₁6pb₁	13.29713.79614.039	3.291.360.74	13.4513.9713.97
4pa₁5pa₁6pa₁	13.31713.80414.044	13.726.153.24	13.5113.9914.30

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拟合得到的收敛到 $\widetilde{{\mathrm{B}}}{}^{2}{{\mathrm{B}}}_{2}$ 阈值的里德伯轨道的能量、宽度以及在X, Y和Z方向的轨道形状示意^[32]

Table 2. Energy positions, autoionization widths and views along the X, Y, and Z axes of the Rydberg orbitals for Feshbach resonances converging to the $\widetilde{{\mathrm{B}}}{}^{2}{{\mathrm{B}}}_{2}$ threshold obtained by fitting^[32].

Resonance	Energy/eV	Widths/meV	Diercksen/eV	X view	Y view	Z view
3pb₂	15.888	219.45	15.77
3pb₂	15.888	219.45	15.77
3pa₁	16.212	3.14	15.97
4sa₁	16.885	7.63	16.47
3db₂	17.112	29.38	17.04
3da₂	17.180	2.12	17.03
4da₂5da₂	17.85418.170	0.880.46	17.7018.01

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Vol. 73, Issue 8 - 2024-04-20

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