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 分子催化  2019, Vol. 33 Issue (5): 399-411 0

### 引用本文

YOU Jun-han, LIU Dang-bo, GAO Hai-xiang. The Chemical Activity of an Interstitial Hydrogen on the Solid Surface Arises from Pauli Repulsion[J]. Journal of Molecular Catalysis (China), 2019, 33(5): 399-411.

### 文章历史

1. 上海交通大学 物理与天文学院天文系, 上海 200240;
2. 上海交通大学 上海粒子物理和宇宙学重点实验室, 上海 200240;
3. 上海交通大学 致远学院, 上海 200240

The Chemical Activity of an Interstitial Hydrogen on the Solid Surface Arises from Pauli Repulsion
YOU Jun-han1 , LIU Dang-bo1,2 , GAO Hai-xiang3
1. Department of Astronomy, School of Physics and Astronomy, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai 200240, China;
2. Shanghai Key Laboratory for Particle Physics and Cosmology, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai 200240, China;
3. Zhiyuan College, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai 200240, China
Abstract: The surface of various solids often exerts a Pauli repulsive force on the adsorbed atoms/ions, interstitial and/or substitutional, which markedly changes the physical properties of foreign surface atoms/ions. We first demonstrate that Pauli repulsion widely exists at the surface of various solids. We introduce a concept of 'Pauli hole' to describe a depression on solid surface, where a foreign interstitial/substitutional atom sited in, and suffers from the Pauli repulsive force of the surrounding substrate atoms/ions. Then a quantitative estimation of the changes of atom properties under Pauli repulsion is obtained by this way. We pay more attention to the special Pauli hole on the surface of transition metals, the most important materials in heterogeneous catalysis. In order to easy to read this paper, we briefly introduce the work we have published, with regard to the schrodinger equation of an interstitial hydrogen in Pauli hole and its solution. Accordingly, both the obtained wave function and the energy of ground state of the interstitial hydrogen atom are compared to that of a free hydrogen, which indeed shows a change of properties of surface hydrogen. The marked change results a significant increase of chemical activity. By using these results, we further explain that, the increase of chemical activity mainly depends on two factors:the marked reduction of ionization energy (electronic affinity) and the effect of induced electric dipole of the interstitial hydrogen. We refer this kind of excitation as 'Pauli excitation of interstitial hydrogen', and emphasize its significant contribution to the hydrogenation. To date, there is a long ongoing question in the catalysis study. Experiments show that, the most active component in the hydrogenation reaction is the 'subsurface hydrogen atoms', located under the surface of transition metals, rather than the 'surface hydrogen'. The latter has little contribution to reaction. In this paper, we argue that, the 'subsurface hydrogen' is just the Pauli-excited interstitial hydrogen.Limited to discuss the heterogeneous catalysis (catalysis of interstitial hydrogen at solid surface). But in principle, the Pauli excitation can be extended to the homogeneous catalysis, where exists analogous Pauli hole too. Besides, we limited ourself to discuss the catalysis of interstitial hydrogen. But, it is easy to apply to other interstitial atoms. For example, it can be used to study the Pauli excitation of interstitial Li atom at surface of graphene.Astronomical observations in recent years show that, in many molecular clouds (e.g., H2O, CH4, C2H2, C2H4, et al.), there are plenty of dusts with size 0.001~10 μm (e.g., C or SiO2 particles) coexist with molecules. The coexistence of both the molecules and the dust particles could imply that the dusts, including some nano-particles, are just the necessary heterogeneous catalyzers, which have the Pauli hole structures at its surface.
Key words: heterogeneous catalysis mechanism    Pauli repulsion    Pauli hole    subsurface H atom    hydrogenation

1 “泡利穴”(Pauli hole)

1.1 离子晶体

 图 1 NaCl晶体结构 Fig.1 The simple cubic structure of crystal NaCl (The green and yellow balls represent Cl- and Na+ ions with full shell structure, respectively. A smaller red ball, sited in central depression of a hole, formed by four adjacent Na+ and Cl- ions, represents a foreign interstitial H, which suffers a Pauli repulsive force from the surface of Na+ and Cl- ions. We simply call the square hole surrounded by adjacent Na+ and Cl- ions 'Pauli hole'.)

1.2 共价键晶体

 图 2 金刚石, 石墨以及C60的晶体结构 Fig.2 Examples of covalent monocrystals composed of a single element a. The structure of crystaldiamond(likewise for monocrystaline silicon; b. The graphene structure; c. The C60 nano-particle

 图 3 a. SiO2(石英)单晶体结构; b.非晶态SiO2表面的各种泡利穴 Fig.3 a. The structure of crystal SiO2; b. Morphology of amorphous SiO2 (Note there are many Pauli holes with various shapes, e.g., triangles, squares, pentagonals, etc. All of them are surrounded by the adjacent Si and O atoms with full shell.)

1.3 金属晶体

1.4 化学吸附H覆盖层“表面下的泡利穴”

 图 4 d电子(l=2)各态的电子云角分布示意图 Fig.4 Angular distribution of the electronic cloud of quantum states of different ml values in d shell The Z axis is perpendicular to the surface of metals.

1) 电子波函数在核处(r=0)不是节点, 此处电子云密度ρe|r≠0.说明dz2态下, 原子核被高密度的电子云充分包围.在人们的一般印象中, 只有s态在核处才有不为零电子云密度, 其他态电子波函数在核处皆为零点. dz2态显然违反了这条规则, 使它明显不同于其他d态(见图 4).

2) 电子波函数只沿垂直表面方向(即图 4中的z轴方向)细细延伸.而其他d态波函数都在金属表面方向(水平方向), 或在靠近表面的方向延展(图 4).

 图 5 单晶钯Pd的(110)面 Fig.5 The (110) crystal plane of metal Pd (Fig. 5 a. The front view of Pd (110) plane. Both the dark and the bright green balls represent the Pd ions. But they are not in the same plane, the dark green Pd ion is lower than the bright one ~0.137 nm. Note that in Fig. 5 a, every four adjacent Pd ions with different heights surround a rhomboid depression, suitable to arrange a foreign interstitial H(the smaller black ball). The smaller red balls in Fig. 5 a represent the chemisorbed H above (110) plane. If chemisorption reaches saturation, i.e., almost every Pd ion binds a adsorbed H, then there will be a H cover filled with chemisorbed H on (110) plane.Fig. 5 b. The side view of Pd (110) plane, where the relative positions of surface Pd ions to up chemisorbed H are clearer and obvious. The chemisorbed H (red ball) is higher than Pd ion(green ball) for about a H-Pd bond-length. The distance between dark green Pd ion and dark red H is the same. The black ball, sited in center of a rhomboid hole, represent interstitial H, with lower position than the chemisorbed H(the red and dark red ball)).
 图 6 钯单晶(110)面上的单个菱形泡利穴 Fig.6 The single rhomboid Pauli hole at Pd (110) plane (Fig. 6 a is front view of a single rhomboid hole. These four Pd ions, represented by green balls, are not in the same plane. The bright green ball is higher than dark one ~0.137 nm. Fig. 6 b is side view, which shows more obviously that, under the saturation adsorption, the rhomboid can be regard as a hole composed of 4 Pd ions and 4 chemisorbed H).

2 泡利穴中填隙H原子 2.1 Schrödinger方程和边条件

 图 7 固体表面“泡利穴”的简化模型 Fig.7 The simplified model of the Pauli hole at surface of solids (The Pauli hole is represented by a paraboloid of revolution around Z axis. The regularly arranged black spots represent the substrate atoms/ions sited at lattice points of the crystal. the X-Y coordinate plane is arranged on the surface of solids. Z-axis is perpendicular to solid surface. The focus F of paraboloid of revolution around Z-axis is put at this surface. The nucleus of H atom is put at F point. The section of paraboloid with solid surface is a circle with radius ξ0 (ξ0 is in the unit of Bohr radius a0). The center of circle is at focus F. PF= ξ0/2 is the focal length of paraboloid, represents the depth of Pauli hole. The electronic cloud of interstitial H can not penetrate into the solid through the paraboloidal wall due to the Pauli repulsion. This fact can be expressed by a boundary condition which the electronic wave function Φ of H has to satisfy. Namely, at the paraboloidal wall ξ=ξ0 (the surface of Pauli hole), Φ(ξ0, η, z)=0).
 $x=\sqrt{\xi, \eta} \cos \varphi, y=\sqrt{\xi, \eta} \sin \varphi, z=(\eta-\xi) / 2$ (1)

ξη取值范围是(0, ∞), φ为(0, 2 π).由(1)式不难看出, 当ξ为常数时(即(ξ=ξ0), 且ξ0>0), 就得到一个绕Z轴向上开放的旋转抛物面.

 $\hat{H} \varPhi=E \varPhi, \varPhi\left(\xi_{0}, \eta, z\right)=0\\ \left.\Phi\left(\xi_{0}, \eta, z\right)\right|_{\eta \rightarrow \infty}=0, (自然边界条件)$ (2)

 $\hat{H}=\frac{\hbar^{2}}{2 m_{0}} \nabla^{2}-\frac{e^{2}}{r}$ (3)
2.2 填隙H的基态波函数, 电离能, 诱导电矩和催化

 图 8 自由H原子基态1s的球对称电子云分布 Fig.8 The spherically symmetric distribution of electronic cloud of ground state 1s of a free H (Fig. 8 b. The contours of probability density(|Ф|2) of the ground state of interstitial H(taken from [4]), confined in a Pauli hole with a simplified Pauli wall of paraboloid of revolution. The black point represents the nuclear of H, the hollow circle represents the substrate atoms with closed shell. The electronic cloud of confined H atom no longer has a distribution of spherical symmetry. The deformation of wave function is obvious, which is elongated along the direction perpendicular to the solid surface, thus induced an electric dipole p, vertically points to the interior of solid.)

 图 9 填隙H的诱导电矩p (单位是ea0)和基态能量E(eV)随泡利穴半径ξ0 Fig.9 The variations of induced dipole p (in unit ea0) and energy of ground state E(in unit eV) with the radius of Pauli hole, p ~ ξ0 and E ~ ξ0 (quoted from [4]). ξ0 is a dimensionless radius in unit a0, the Bohr radius. From Figure 9 we see, both the dipole p and the energy E(E < 0) are monotonically increased with decreased radius ξ0. In fact, ξ0 scales the strength of Pauli repulsion.
Table 1 Numerical relations of the ionization potential I (I>0) (induced dipole p of gound state of confined H with Pauli radius ξ0 (quoted from [4]). Table 1 is the numerical representation of Fig. 9.)

1.它保证填隙H原子稳定地黏贴在“泡利穴”中.如上所述, 电矩PH垂直表面并指向固体内部.它必然在晶体表面感应一个带负电的面电荷分布(对金属, 是自由电子面电荷分布, 对固体介质, 为极化面电荷), 感应面电荷与电矩PH之间的静电吸引使外来填隙H原子“瞬时地粘黏”于表面.所以, 我们讨论的填隙H原子, 是物理吸附于固体表面的稳定的物理存在, 而不是一个假想的模型考虑.

2.电矩PH的偶极电场对周边环境中的正离子(如N++, O+等)的静电吸引和对中性原子分子的范德瓦斯吸力, 会使外来原子(离子)有沿PH的电场线移动的倾向, 造成对填隙H原子的靶向轰击.填隙H成为靶原子.显然相比气体中的随机碰撞而言, 这种靶向轰击增大了外来原子对H的碰撞概率, 对加氢反应更为有利.

3. 表 1中, 电矩PH足够大, 其电场会使周边气体中的靠近填隙H的原子或离子发生明显拉伸形变, 自然造成这些外来原子电离能IX减小(以下, 外来原子一概用X来标记).它们在向填隙H原子接近并最终碰撞的过程中, 伴随原子拉伸形变而逐渐减小的电离能IX会不断与填隙H电离能IH趋同, 即IX→IH(注意IH已经很小.只要ξ0取较小值, 就有IH ≪ 13.6 eV, 见表 1).最终近似相等, IX≈IH (也可以等价地表示为基态能量EX≈EH).限于篇幅, 我们将在另文中对趋同, 近似相等的必然性做更深入的, 半定量的物理论证.顺便指出, 在此过程中, 填隙H的电离能几乎不变, IH ≈Const(同样在另文中证明).显然, 两个原子接近时的’能量趋同’效应, 有利于共价键形成.只当不断靠近的外来原子和填隙H原子的两个原子波函数Ψ1和Ψ2最终成了’同一能级’上的’简并态’, 交叠的原子波函数才可以通过线性组合, 成为分子波函数Ψ12=C1Φ1+C2Φ2 (即分子轨道[28]).所以, 能级趋同, 产生简并, 是形成分子波函数应该满足的前提条件.这也符合人们的物理直观:能量趋同保证了两个原子的价电子可以在原子间无能量障碍地自由迁移, 成为共用电子, 从而形成共价键.

4.填隙H强的非零电矩PH造成外来原子X形变，也诱导出一个非零电矩PX.电矩PX沿PH的电场EH取向, 即PX‖EH.最终, 发生碰撞时, PX将与填隙H电矩PH平行, PX‖PH(因为在填隙H处必有EHPH. PX‖PH对成键至关重要:在很多情况下, 它使得两个交叠原子波函数固有的空间对称性(这种对称性在量子力学中称为’宇称’)彼此适配.只有这样, 才不会出现两个原子碰撞时, 相互叠加的原子驻波态Ψ1和Ψ2产生干涉相消的情况.以此保证共价键得以形成. PXPH通常就是理想的’最佳碰撞方位’.限于篇幅, 我们将在另文中对“宇称匹配”, 避免干涉相消对形成共价键的重要意义给与详细的说明.

3 结论和讨论

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