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维基百科，自由的百科全书

势能面，表示某一微观体系的势能和相关参数（通常为原子坐标）之间的函数关系，是势能函数的图像。势能面用一个或更多的坐标去表示，当用一个坐标去表示时，势能面通常被称为“势能曲线”。

势能面概念被用在物理以及化学领域, 尤其是它们的理论研究分支。 势能面可以被用来从理论层面理解由原子组成的物质的性质, 例如：搜寻分子的最低能量构形或者计算化学反应速率。

势能面类似于对地形的描述：对于一个有两个自由度的体系（例如：一个键长、一个键角），体系的势能可以类比为地形的高度，两个自由度可以类比为描述某位置的坐标。通过这样的描述，体系势能随坐标的变化可以很直观地被表示出来。

水分子势能面: 势能最低点对应优化后的水分子结构， O-H 键长 0.0958nm， H-O-H尖角为 104.5°

A potential energy surface (PES) describes the energy of a system, especially a collection of atoms, in terms of certain parameters, normally the positions of the atoms. The surface might define the energy as a function of one or more coordinates; if there is only one coordinate, the surface is called a potential energy curve or energy profile. An example is the Morse/Long-range potential.

It is helpful to use the analogy of a landscape: for a system with two degrees of freedom (e.g. two bond lengths), the value of the energy (analogy: the height of the land) is a function of two bond lengths (analogy: the coordinates of the position on the ground).[1]


The PES concept finds application in fields such as chemistry and physics, especially in the theoretical sub-branches of these subjects. It can be used to theoretically explore properties of structures composed of atoms, for example, finding the minimum energy shape of a molecule or computing the rates of a chemical reaction.

Mathematical definition and computation

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原子的空间位置通过向量 r来表示，向量的元素代表某一个原子的坐标。 向量 r可以是原子 笛卡尔坐标的集合， 也可以是原子间距离、键角以及二面角等.

给定一个 r，得到能量 E(r)， E(r) 是 r的函数。类比地形的描述, E 是"能量地形"的高度， 所以 E 被称为一个面。

利用势能面作为原子位置的函数研究化学反应时，需要计算每一个关注的分子构象能量。计算特定原子排布能量可以采用计算化学方法，本节将讨论 E(r)的近似表达 。

对于一些非常简单的化学体系或者原子间相互作用简化处理后了的体系，给出原子坐标与能量直接函数的解析形式是可能的。一个简单的例子是用 London-Eyring-Polanyi-Sato 势函数[2][3][4] 描述双氢体系中的H-H距离。

对于更复杂的系统，计算较大范围的势能面十分耗时。为解决上述问题，计算过程中通常选取部分结构来计算势能面，并用计算得到的数据点插值获得更大的势能面。机器学习方法也可以用来构建势能面。

应用

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势能面是概念工具协助分析分子结构与进行化学反应动力学模拟。势能面上的点可以根据能量的一阶和二阶导数进行区分，驻点（梯度为0的点）对应着一个稳定的化学结构。鞍点对应着过渡态，是反应路径上的最高点，反应路径是连接产物与生成物的最低能量路径。

A PES is a conceptual tool for aiding the analysis of molecular geometry and chemical reaction dynamics. Once the necessary points are evaluated on a PES, the points can be classified according to the first and second derivatives of the energy with respect to position, which respectively are the gradient and the curvature. Stationary points (or points with a zero gradient) have physical meaning: energy minima correspond to physically stable chemical species and saddle points correspond to transition states, the highest energy point on the reaction coordinate (which is the lowest energy pathway connecting a chemical reactant to a chemical product).

Attractive and repulsive surfaces

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Potential energy surfaces for chemical reactions can be classified as attractive or repulsive by comparing the extensions of the bond lengths in the activated complex relative to those of the reactants and products.[5][6] For a reaction of type A + B—C → A—B + C, the bond length extension for the newly formed A—B bond is defined as R*AB = RAB − R0AB, where RAB is the A—B bond length in the transition state and R0AB in the product molecule. Similarly for the bond which is broken in the reaction, R*BC = RBC − R0BC, where R0BC refers to the reactant molecule.[7]

For exothermic reactions, a PES is classified as attractive (or early-downhill) if R*AB > R*BC, so that the transition state is reached while the reactants are approaching each other. After the transition state, the A—B bond length continues to decrease, so that much of the liberated reaction energy is converted into vibrational energy of the A—B bond.[7][8] An example is the harpoon reaction K + Br2 → K—Br + Br, in which the initial long-range attraction of the reactants leads to an activated complex resembling K+•••Br−•••Br.[7] The vibrationally excited populations of product molecules can be detected by infrared chemiluminescence.[9][10]

In contrast the PES for the reaction H + Cl2 → HCl + Cl is repulsive (or late-downhill) because R*HCl < R*ClCl and the transition state is reached when the products are separating.[7][8] For this reaction in which the atom A (here H) is lighter than B and C, the reaction energy is released primarily as translational kinetic energy of the products.[7] For a reaction such as F + H2 → HF + H in which atom A is heavier than B and C, there is mixed energy release, both vibrational and translational, even though the PES is repulsive.[7]

For endothermic reactions, the type of surface determines the type of energy which is most effective in bringing about reaction. Translational energy of the reactants is most effective at inducing reactions with an attractive surface, while vibrational excitation is more effective for reactions with a repulsive surface.[7] As an example of the latter case, the reaction F + HCl(v=1)[11] → Cl + HF is about five times faster than F + HCl(v=0) → Cl + HF for the same total energy of HCl.[12]

History

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The concept of a potential energy surface for chemical reactions was first suggested by the French physicist René Marcelin in 1913.[13] The first semi-empirical calculation of a potential energy surface was proposed for the H + H2 reaction by Henry Eyring and Michael Polanyi in 1931. Eyring used potential energy surfaces to calculate reaction rate constants in the transition state theory in 1935.

See also

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References

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  1. ^ Potential-energy (reaction) surface in Compendium of Chemical Terminology, 2nd ed. (the "Gold Book"). Compiled by A. D. McNaught and A. Wilkinson. Blackwell Scientific Publications, Oxford (1997)
  2. ^ Sato, S. A New Method of Drawing the Potential Energy Surface. Bulletin of the Chemical Society of Japan. 1955, 28 (7): 450. doi:10.1246/bcsj.28.450. On a New Method of Drawing the Potential Energy Surface. The Journal of Chemical Physics. 1955, 23 (3): 592. Bibcode:1955JChPh..23..592S. doi:10.1063/1.1742043. 
  3. ^ Keith J. Laidler, Chemical Kinetics (3rd ed., Harper & Row 1987) p.68-70 ISBN 0-06-043862-2
  4. ^ Steinfeld J.I., Francisco J.S. and Hase W.L. Chemical Kinetics and Dynamics (2nd ed., Prentice-Hall 1998) p.201-2 ISBN 0-13-737123-3
  5. ^ Attractive potential-energy surface in Compendium of Chemical Terminology, 2nd ed. (the "Gold Book"). Compiled by A. D. McNaught and A. Wilkinson. Blackwell Scientific Publications, Oxford (1997)
  6. ^ Repulsive potential-energy surface in Compendium of Chemical Terminology, 2nd ed. (the "Gold Book"). Compiled by A. D. McNaught and A. Wilkinson. Blackwell Scientific Publications, Oxford (1997)
  7. ^ 7.0 7.1 7.2 7.3 7.4 7.5 7.6 Keith J. Laidler, Chemical Kinetics (3rd ed., Harper & Row 1987) p.461-8 ISBN 0-06-043862-2
  8. ^ 8.0 8.1 Steinfeld J.I., Francisco J.S. and Hase W.L. Chemical Kinetics and Dynamics (2nd ed., Prentice-Hall 1998) p.272-4 ISBN 0-13-737123-3
  9. ^ Steinfeld J.I., Francisco J.S. and Hase W.L. Chemical Kinetics and Dynamics (2nd ed., Prentice-Hall 1998) p.263 ISBN 0-13-737123-3
  10. ^ Atkins P. and de Paula J. Physical Chemistry (8th ed., W.H.Freeman 2006) p.886 ISBN 0-7167-8759-8
  11. ^ Here v is the vibratonal quantum number.
  12. ^ Atkins P. and de Paula J. Physical Chemistry (8th ed., W.H.Freeman 2006) p.889-890 ISBN 0-7167-8759-8
  13. ^ Computational Chemistry: Introduction to the Theory and Applications of Molecular and Quantum Mechanics Errol G. Lewars, 2nd ed. (Springer 2011) p.21 ISBN 978-9048138616
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