In this series, I will introduce and discuss the latest computational approaches for first-principle electrocatalysis (FPEC), which is the foundation for understanding electrochemical reactions at the electrified interface. This is episode 1, which is the general discussion of the question.

## Master question of electrocatalysis

The structure of the electrochemical interface is shown in the following figure:

As computational electrochemist, we are interested in the thermodynamic and dynamic properties of the interfacial region under certaion pH, temperature and applied potential (can be mathematically represented as \( U_{\text{app}}=\phi_M-\phi_S \)).

Generally speaking, we want to get both thermodynamic and dynamic properties of the interface from our simulation under certain pH, temperature and applied potential:

**Thermodynamic**: The interfacial pourbaix diagram**Dynamic**: The activation barrier of certain reaction step

In the next section, we will see how difficult these two pursuits really are.

## Difficulties of FPEC

Constructing a model slab consisting surface facet, explicit water molecules and ions is relatively easy. The hard part is how do we calculate its energy and reaction pathway under certain external conditions (e.g. pH, temperature and applied potential)

**Difficulty 1**: Let's first look at pH (\( c_{\text{H}^+} = 10^{-\text{pH}} \)), which is related to the concentration of proton in the solution, which is a macroscopic property. How can it be related to the atomistic model that we use?

**Difficulty 2**: What's the effect of temperature? The answer: the thermal distributions (e.g. Boltzmann distribution: \( f_i=e^{-\beta\epsilon_i} \), where \(f_i\) is the probability of finding the state i with energy \(\epsilon_i\)). In order to get the high-quality distribution, we need large samples, which means long trajectories. This will drastically increase the computational cost.

**Difficulty 3**: How do we keep the applied potential constant to a certain value? Usually in DFT code, we could vary the number of electrons in the system to change the applied potential, but how we know the exact number? And how can we determine it during simulation self-consistently? During the NEB simulation, how can we keep all the structures under the same applied potential? Those questions we will discuss in detail in the following episodes.

By maintaining the applied potential, we will change the number of electrons in our system, and this will cause the imbalance between the number of cations and anions near the surface. Meanwhile, the interfacial region should remain neutral. How do we calculate the distribution of ions? This is also a key questions in FPEC.

## The next episode

In the next episode, we will discuss the development of FPEC, from the simplest computational hydrogen electrode (CHE) to the **state-of-the-art** simulation which combines ab-initio molecular dynamics (AIMD) and constant-potential control scheme.

Thanks for your time. See you in the next post.

Best,

Zhengda