On the origin of univalent Mg$^+$ ions in solution and their role in anomalous anodic hydrogen evolution

This study utilizes advanced \emph{ab initio} simulations to reveal that the anomalous anodic hydrogen evolution and violent dissolution of magnesium are caused by the formation of a solvated [Mg$^{2+}$(OH)$^-$]$^+$ complex, which explains the previously elusive presence of univalent Mg$^+$ ions and the failure of protective oxide layers.

The Gist

The Mystery: The "Impossible" Magnesium

Imagine you have a piece of magnesium metal. You put it in water and try to make it dissolve by applying an electrical push (an "anodic" charge).

According to the rules of chemistry we learned in school, this should be a calm process. The metal should slowly dissolve, and the water should stay relatively quiet.

But magnesium is a rebel.
When you push it, it doesn't just dissolve; it explodes with bubbles of hydrogen gas. It dissolves faster than physics says it should, and it creates more hydrogen gas than the math predicts. Scientists have been baffled by this "Anomalous Hydrogen Evolution" for over 150 years. It's like trying to push a car uphill, but instead of slowing down, the car suddenly speeds up and starts shooting sparks everywhere.

The Old Theory vs. The New Discovery

For decades, scientists had two main theories:

1. The "Impurity" Theory: Maybe dirty spots on the metal are acting like tiny catalysts to speed things up.
2. The "Magic Ion" Theory: Maybe magnesium dissolves as a weird, one-time-charged ion ($Mg^+$) instead of the usual two-time-charged ion ($Mg^{2+}$). But no one could ever catch this "magic ion" in the act. It was like trying to photograph a ghost; everyone claimed to see it, but no camera could capture it.

The Breakthrough:
The researchers in this paper used super-powerful computer simulations (like a microscopic movie camera) to watch exactly what happens when a magnesium atom leaves the metal surface and enters the water.

They found that the "ghost" was real, but it wasn't what anyone expected.

The "Backpack" Analogy

Here is the core discovery, explained simply:

The Old Picture:
Imagine a magnesium atom ($Mg$) trying to leave a crowded party (the metal surface). It usually sheds its "coat" (electrons) and runs out the door alone as a heavy, two-charged ion ($Mg^{2+}$). This is slow and difficult because the door is guarded by a layer of "security" (a hydroxide film) that tries to stop it.

The New Picture (The Discovery):
The researchers found that the magnesium atom doesn't leave alone. Instead, it grabs a hydroxide molecule ($OH^-$) from the water before it leaves.

Think of it like this:

• The magnesium atom is a heavy backpacker.
• The hydroxide molecule is a backpack.
• Normally, the backpacker tries to run out of the building alone, but the security guard (the surface film) stops them.
• The Trick: The backpacker grabs the backpack, straps it on, and suddenly, they look like a completely different person. To the security guard, this new package looks like a one-charged person ($Mg^+$) instead of a two-charged one.

Because the "backpack" (the hydroxide) is attached, the magnesium atom can slip past the security guard much easier. It dissolves quickly, carrying the backpack with it into the water.

Why This Solves the Mystery

This "Backpack Strategy" explains everything that was confusing:

1. Why it dissolves so fast: The "backpack" (the $[Mg^{2+}(OH)^-]^+$ complex) bypasses the protective layer that usually stops corrosion. It's like having a VIP pass that lets you skip the line.
2. Why there is so much hydrogen gas: Because the magnesium leaves the surface with the hydroxide attached, the surface is left empty and ready for more water to crash in. This constant crashing of water molecules splits them apart, creating a massive amount of hydrogen gas bubbles.
3. The "Ghost" Ion: The "unipositive" $Mg^+$ ion scientists were looking for isn't a naked magnesium atom. It's actually this magnesium-hydroxide backpack. It acts like a single-charged ion, which is why it behaves so strangely and can travel far in the water before finally dropping its backpack and becoming a normal magnesium ion.

The Big Picture

This paper is a game-changer because it shows that water isn't just a passive liquid that metal sits in. Water is an active participant. It hands the magnesium a "backpack" (the hydroxide group) that allows it to escape the metal surface in a way we never thought possible.

In summary:
Magnesium isn't breaking the laws of physics; it's just using a clever loophole. By teaming up with a water molecule to form a "backpack" complex, it escapes corrosion faster than anyone expected, causing the violent bubbling that has puzzled scientists for a century. This discovery helps us understand how to stop this corrosion, which is crucial for making better batteries and lighter, safer cars.

Technical Summary

1. Problem Statement

The paper addresses the long-standing scientific mystery of anomalous hydrogen evolution (AHE) and the negative difference effect (NDE) in magnesium (Mg) corrosion.

• The Phenomenon: Under anodic polarization (where Mg should dissolve and hydrogen evolution should decrease according to the Butler-Volmer equation), Mg exhibits violent dissolution accompanied by increased rates of hydrogen evolution (HE).
• The Discrepancy: Experimental observations show that the amount of Mg dissolved exceeds the amount predicted by Faraday's law if Mg oxidizes solely to the divalent state ($Mg^{2+}$). This suggests the existence of a unipositive $Mg^+$ ion intermediate.
• The Controversy: While indirect evidence for $Mg^+$ exists, direct experimental observation has been elusive. Conventional chemistry suggests $Mg^+$ should be extremely unstable and short-lived in aqueous solutions. Furthermore, standard models fail to explain why the protective oxide/hydroxide layer (which usually passivates the surface) does not form under these specific anodic conditions, allowing continuous dissolution.

2. Methodology

The authors utilized ab initio thermopotentiostat molecular dynamics (AIMD) simulations to model the Mg-water interface under controlled electrochemical potential.

• System Setup: A 6-layer Mg slab oriented in the (1 2 $\bar{3}$ 15) direction with a "kink" site (created by a miscut) to simulate high-energy dissolution sites. The system included 64 explicit water molecules.
• Electrochemical Control: The simulations employed a recently developed thermopotentiostat to maintain a constant electrode potential ($\langle\Phi\rangle = -2$ V) and control surface charge, mimicking anodic polarization conditions.
• Simulation Process:
  1. Equilibration under open-circuit conditions to observe initial water adsorption.
  2. Application of anodic potential to drive dissolution.
  3. Analysis of reaction pathways, specifically focusing on proton transfer mechanisms and the breaking of surface bonds.

3. Key Contributions and Findings

A. Identification of the "Unipositive" Species

The study reveals that the elusive "univalent $Mg^+$" is not a bare atomic ion, but a solvated ion complex: $[Mg^{2+}(OH)^-]^+$.

• Mechanism: During anodic dissolution, a surface Mg atom at a kink site dissociates from the lattice. Instead of releasing a bare $Mg^{2+}$ ion, it remains tethered to the surface via a hydroxyl bridge ($OH^-$) formed from dissociated water.
• Charge State: The complex consists of a divalent $Mg^{2+}$ core and a monovalent $OH^-$ ligand, resulting in a net charge of +1. This explains the experimental observation of a "unipositive" species without violating chemical stability rules regarding bare $Mg^+$.

B. Two Competing Dissolution Pathways

The simulations identified two distinct pathways for the detachment of the solvated Mg species, which determine whether anomalous hydrogen evolution occurs:

1. Passivation Pathway (Double Proton Transfer):

   • A concerted double proton transfer from a neighboring water molecule to the hydroxyl bridge releases the $Mg^{2+}$ ion into the solution.
   • Result: The $OH^-$ group remains on the surface. The surface becomes hydroxylated and electrochemically passive, blocking further dissociative water adsorption. This pathway does not lead to anomalous HE.

2. Anomalous HE Pathway (Intra-Solvation Shell Proton Transfer):

   • A single proton transfers from a water molecule within the solvation shell directly to the hydroxyl bridge.
   • Result: The entire $[Mg^{2+}(OH)^-]^+$ complex detaches from the surface and enters the solution as a unit.
   • Consequence: The surface site is cleared of the hydroxyl group, leaving the next kink site exposed. This allows for continuous dissociative water adsorption, which generates hydrogen ($H_2$) and sustains the anomalous hydrogen evolution.

C. Stability and Longevity

The paper explains why the $[Mg^{2+}(OH)^-]^+$ complex is stable enough to be observed experimentally (lifetimes of several minutes):

• Coulomb Barrier: The complex is positively charged. To oxidize it further to $Mg^{2+}$, it must react with a proton ($H^+$). The electrostatic repulsion (Coulomb barrier) between the positive complex and the positive proton creates a kinetic barrier, slowing down the reaction and extending the ion's lifetime.
• Thermodynamics: The complex is thermodynamically favored at high local pH (pH > 11.44), which is consistent with the alkaline environment created by the hydrolysis of Mg.

4. Proposed Reaction Model

The authors propose a unified reaction model balancing the total charge and mass:

• Step 1 (Dissolution): $Mg + H_2O \rightleftharpoons [Mg^{2+}(OH)^-]^+ + \frac{1}{2}H_2 + e^-$ (Anodic step generating the complex).
• Step 2 (Oxidation in Solution): $[Mg^{2+}(OH)^-]^+ + H^+ \rightleftharpoons Mg^{2+} + H_2O$ (The complex reduces $H^+$ to $H_2$ elsewhere, explaining the "extra" hydrogen evolution).
• Net Result: The sum of these steps yields the standard corrosion equation ($Mg + 2H^+ \rightarrow Mg^{2+} + H_2$), but the mechanism involves a transient unipositive intermediate that bypasses surface passivation.

5. Significance

• Resolution of a 150-Year Mystery: The paper provides the first atomistic explanation for the "negative difference effect" and the existence of unipositive Mg ions, resolving a debate that has persisted since the 19th century.
• Role of Water: It demonstrates that water is not merely a spectator solvent but an active reactant that facilitates a low-barrier pathway for dissolution via proton transfer, circumventing the formation of passivating films.
• Technological Impact: Understanding this mechanism is crucial for developing corrosion-resistant Mg alloys for lightweight structural applications and batteries. It suggests that preventing the formation of the $[Mg^{2+}(OH)^-]^+$ complex or stabilizing the surface hydroxide layer could be key strategies for corrosion prevention.
• Methodological Advance: The study validates the power of ab initio thermopotentiostat simulations in describing complex solid-liquid electrochemical interfaces, a capability previously difficult to achieve with experimental techniques alone.