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Surface potential energy fundamentally arises from the configuration-dependent energetic state of atoms or molecules at an interface or boundary, reflecting how atomic positions influence the overall energy landscape of a system. This concept gains clarity when viewed through the lens of potential energy surfaces (PES), which map the total potential energy as a function of atomic coordinates. The PES is a multidimensional function \( E(\mathbf{r}) \), where \(\mathbf{r}\) represents the positions of all atoms involved, typically expressed in Cartesian coordinates or internal bond distances and angles [1].
In chemical systems, surface potential energy dictates molecular stability and reactivity by defining minima and saddle points on the PES. Minima correspond to physically stable chemical species, while saddle points correspond to transition states, the highest energy point on the reaction coordinate (the lowest energy pathway connecting a chemical reactant to a chemical product). These stationary points are identified by zero gradient conditions—the first derivative of \( E(\mathbf{r}) \) with respect to atomic positions—and characterized by curvature information from second derivatives, which determine their nature as minima or saddle points [1].
The potential energy associated with the formation and breaking of chemical bonds can be analyzed by examining changes in bond lengths during reactions. For example, consider a generic reaction:
\[
\text{A} + \text{B} - \text{C} \rightarrow \text{A} - \text{B} + \text{C}
\]
Here, the changes in bond lengths at the transition state relative to reactants and products define distinct energetic characteristics. The bond length extension for the newly formed bond A–B is given by
\[
R^*_{AB} = R_{AB} - R^0_{AB}
\]
where \(R_{AB}\) is the A–B bond length in the transition state and \(R^0_{AB}\) in the product molecule. Similarly, for the bond being broken,
\[
R^*_{BC} = R_{BC} - R^0_{BC}
\]
with \(R^0_{BC}\) referring to the reactant molecule’s bond length [1].
These parameters allow classification of PES types: attractive (or early-downhill) surfaces occur when \(R^*_{AB} > R^*_{BC}\), indicating that the transition state is reached while the reactants are approaching each other. Conversely, repulsive (or late-downhill) surfaces arise when \(R^*_{AB} < R^*_{BC}\), meaning that the transition state is reached when the products are separating [1].
In exothermic reactions exhibiting attractive PES behavior, such as the harpoon reaction
\[
\text{K} + \text{Br}_2 \rightarrow \text{K}-\text{Br} + \text{Br},
\]
the initial long-range attraction of the reactants leads to an activated complex resembling \(\mathrm{K}^+•••\mathrm{Br}^-•••\mathrm{Br}\). 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, detectable via infrared chemiluminescence [1].
In contrast, repulsive PES examples like
\[
\text{H} + \text{Cl}_2 \rightarrow \text{HCl} + \text{Cl}
\]
exhibit late-downhill dynamics where the transition state is reached when the products are separating. Because hydrogen (atom A) is lighter than chlorine atoms B and C, the reaction energy is released primarily as translational kinetic energy of the products [1].
The mass disparity among reacting atoms modulates how surface potential energy transforms into different modes post-reaction. In reactions such as
\[
\text{F} + \text{H}_2 \rightarrow \text{HF} + \text{H},
\]
where atom A (fluorine) is heavier than B and C (hydrogen nuclei), there is mixed energy release, both vibrational and translational, even though the PES is repulsive [1].
Additionally, vibrational excitation levels impact reaction rates significantly on repulsive surfaces. For instance,
\[
\mathrm{F} + \mathrm{HCl}(v=1) \rightarrow \mathrm{Cl} + \mathrm{HF}
\]
is about five times faster than \(\mathrm{F} + \mathrm{HCl}(v=0) \rightarrow \mathrm{Cl} + \mathrm{HF}\) for the same total energy of HCl, highlighting how vibrational excitation is more effective for reactions with a repulsive surface [1].
The concept of a potential energy surface for chemical reactions was first suggested by the French physicist René Marcelin in 1913. The first semi-empirical calculation of a potential energy surface was proposed for the \(\mathrm{H} + \mathrm{H}_2\) 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 [1].
While PES primarily addresses intramolecular or intermolecular interactions at atomic scales, macroscopic analogs exist in surface physics through surface energy, defined as the energy required to increase the surface area of a liquid by one unit area. It arises because molecules at the surface have higher potential energy [2].
Molecules residing at an interface experience unsaturated bonding interactions resulting in elevated potential energies relative to molecules fully surrounded by neighbors inside a phase. This excess energy per unit area manifests physically as phenomena like surface tension or capillarity forces [2].
This macroscopic concept connects directly with microscopic PES analyses since both describe energetic penalties associated with configurational constraints—be it atomic positions defining reaction pathways or molecules constrained at phase boundaries influencing wetting properties.
Direct calculation of full-dimensional PESs remains computationally prohibitive for large systems. For these systems, a possible approach is to calculate only a reduced set of points on the PES and then use a computationally cheaper interpolation method, for example Shepard interpolation, to fill in the gaps [1].
Approximate analytical potentials like the Morse/Long-range potential serve well for simplified diatomic systems, while more complex systems like the \(\mathrm{H} + \mathrm{H}_2\) reaction may use the London-Eyring-Polanyi-Sato potential [1].
Such hybrid strategies balance fidelity against computational feasibility when mapping surface potential energies for realistic molecular assemblies relevant to catalysis design, protein folding studies, or glassing models where local minima correspond to metastable low-temperature states [1].
[1] https://en.wikipedia.org/wiki/Potential_energy_surface
[2] https://flexbooks.ck12.org/cbook/ck-12-cbse-physics-class-11/secti...
Italiano: Energia potenziale di superficie: concetti e applicazioni
Español: Energía potencial de superficie en sistemas químicos
Deutsch: Oberflächenpotenzialenergie: Grundlagen und Anwendungen
Français: Comprendre l’énergie potentielle de surface en chimie
Русский: Потенциальная энергия поверхности: основы и значение
Română: Energia potențială de suprafață explicații și exemple
Português: Compreendendo a Energia Potencial de Superfície
Hrvatski: Potencijalna energija površine: važnost u kemiji
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