# # The Grotthuss mechanism

The Grotthuss machanism (also known as proton jumping) is the process by which an 'excess' proton or proton defect diffuses through the hydrogen bond network of water molecules or other hydrogen-bonded liquids through the formation and concomitant cleavage of covalent bonds involving neighboring molecules.[0]

Isomer & Isomerizations

Isomer: each of two or more atomic nuclei that have the same atomic number and the same mass number but different energy states. Isomerization: In chemistry, isomerization or isomerisation is the process in which a molecule, ion or molecular fragment is transformed into an isomer with a different chemical structure.

At room temperature its limiting ionic conductance is about seven times that of a sodium cation, or approximately five times that of K+. The usual explanation is in terms of a sequence of proton-transfer reactions (proton hops) between water molecules ('prototropic mobility', 'Grotthuss mechanism').

WARNING

The combination of rotation, H-bond rearrangement, and proton transfor makes the unique properties of liquid water.

[0] https://en.wikipedia.org/wiki/Grotthuss_mechanism

[1] https://en.wikipedia.org/wiki/Isomerization

[1] Noam Agmon, The Grotthuss mechanism, Chemical Physics Letters 244 (1995) 456-462

## # Ab Initio Molecular Dynamics Simulations of Methylammonium Lead Iodide Perovskite Degradation by Water

Ab Initio Molecular Dynamics Simulations of Methylammonium /methy-lammo-nium/ Lead Iodide /ai-uh-dine/ Perovskite /peh·ruhv·skite/ (MaPbI3) Degradation (退化) by Water

To increase the stability of this class of materials, recent studies have been devoted to protect the perovskite /peh·ruhv·skite/ layer from moisture, to avoid water-induced degradation processes which are regarded as a main loss channel.

Perovskite

Calcium titanate is an inorgamic compound with the chemical formula CaTiO_3. As a mineral, it is called perovskite (钙钛矿), named afer Russian mineralogist, L. A. Perovski. (钛酸钙，三氧化钛钙) [1]

Methylammonium lead iodide MAPbI_3

Methylammonium halides (opens new window) /methy-lammo-nium/ are organic halides (鹵化物) with formula [CH3NH3]$^{+}$X${^-}$, where X can be Cl, Br(溴), I.

Pb(鉛) (opens new window): Lead is a chemical element with the symbol Pb and atomic number 82. It is a heavy metal that is denser than most common materials.

I(碘) (opens new window): Iodine /ai-uh-dine/ is a chemical element with the symbol I and atomic number 53. The heaviest of the stable halogens(鹵素元素).

This material is related to the solar cells. Although MAPbI3 is considered as a prominent light harvester, it suffers from a disturbing tetragonal–cubic phase transition at approximately 56 °C while the operating temperature of solar cells is considered up to 85 °C. This phase transition affect band structure and band gap of MAPbI3 due to Shockley-Queisser theory and cause negative impacts on photovoltaic behavior This issue has diverted attentions to FAPbI3 as the most feasible materials free of this phase transition. [2]

MAI-terminated vs PbI2 terminated surfaces

What do these terms mean?

Band gap

In solid-state physics, a band gap, also called an energy gap, is an energy range in a solid where no electronic states can exist. Therefore, the band gap is a major factor determining the electrical conductivity of a solid. [3]

Degradation pathway

From the perspective of a polymer engineer, the term "degradation" is most often used to describe processes that lead to a decline of polymer properties. Environmental chemists, however, are interested in the chemical reactions that cause the breakdown of polymers, and the properties and potential hazards associated with chemicals liberated by degradation of the polymers.[4]

The PbI2- terminated surface, characterized by shorter Pb−I bonds compared to the bulk, is found to be **less sensitive** to the presence of interfacial water, suggesting that the PbI2-terminated surface could act as a protective layer.

WARNING

How to measure the sensitivity of interfacial water? The speed of water motion?

TIP

H2O 在 organic-inorganic perovskite 里面的材料生长或者性能的影响机制。

Miller Indices

Ry: Rydberg unit of energy

The Rydberg /ˈridˌbərg/ **unit of energy** is equivalent to joules and electronvolts in the following manner:

$1 \mathrm{Ry} \equiv h c R_{\infty}=\frac{m_{\mathrm{e}} e^{4}}{8 \varepsilon_{0}^{2} h^{2}}=\frac{e^{2}}{8 \pi \varepsilon_{0} a_{0}}=2.1798723611035(42) \times 10^{-18} \mathrm{~J}=13.605693122994(26) \mathrm{eV}$

where

$R_{\infty}=\frac{m_{\mathrm{e}} e^{4}}{8 \varepsilon_{0}^{2} h^{3} c}=10973731.568160(21) \mathrm{m}^{-1}$

is constant.

$$

Atomic unit (au or a.u.) of time

- 1 atomic unit of time = $2.418884326509 \times 10^{-17}$ second
- 1 femtosecond = $10^{-15}$ of a second

Todo

- Bulk tetragonal /teˈtraɡənl/ MAPbI3 crystal structure simulation
- Cut 2x2 slabs from bulk system
- Add water around it

[1] https://en.wikipedia.org/wiki/Calcium_titanate

[2] Farhad Fouladi Targhi, Yousef Seyed Jalili, Faramarz Kanjouri,
MAPbI3 and FAPbI3 perovskites as solar cells: Case study on structural, electrical and optical properties, Results in Physics, Volume 10, 2018,616-627

[3] https://en.wikipedia.org/wiki/Band_gap

[4] Berit Gewert, Merle M. Plassmanna and Matthew MacLeod, Pathways for degradation of plastic polymers floating in the marine environment

## # Connection between water’s dynamical and structural properties: Insights from ab initio simulations

Stokes–Einstein relation

How to simulate supercooled water?

Cooled below its melting point, liquid water is thermo-dynamically less stable than ice but typically remains liquid (in a metastable state) for a few degree below 0 °C. [1]

As with most liquids, it is possible to supercool water; this generally involves cooling the liquid below its melting tempera- ture (avoiding crystallization) until it eventually forms a glass. [2]

How to define system is liquid or solid from the micro level? (How to decide the state of the simulation system?)

What happens on the instant when liquid water change to ice?

New idea

- Supercool water and air interfaces.[3]
- What is the thickness of supercool water interface?
- I want to do a project that can help me understand physics more.

Functional

One of the fundamental things we would like to know about these atoms is their energy and, more importantly, how their energy changes if we move atoms around. A key observation in applying quantum mechanics to atoms is that atomic nuclei are much heavier than individual electrons; each proton or neutron in a nucleus has more than 1800 times the mass of an electron.

First, we solve, for fixed positions of the atomic nuclei, the equations that describe the elctron motion. For a given set of electrons moving in the field of a set of neclei, we find the lowest energy configuration, or **state**, of the electrons. The lowest energy state is known as the **ground state** of the electrons, and the separation of the nuclei and electrons into separate mathematical problems is the **Born-Oppenheimer approximation**. If we have M nuclei at positions $\bold{R}_1, ..., \bold{R}_M$, then we can express the ground-state energy, E, as a function of the positions of these nuclei, E$(\bold{R}_1, ..., \bold{R}_M)$. This function is known as the **adiabatic potential energy surface** of the atoms.

Once we are able to calculate this potential energy surface we can tackle this problem: How does the energy of the material change as we move its atoms around?

If we were interested in a single molecule of CO2, the full wave function is a 66-dimensional function (3 demensions for each of the 22 electrons). If we were interested in a nanocluster of 100 Pt atoms, the full wave function requires more than 23,000 dimensions!

The form of this contribution means that the individual electron wave functionwe defined above, $\psi_i({\bold{r}})$, cannot be found without simultaneously considering the individual electron wave functions associated with all the other electrons. In other words, **the Schrödinger equation is a many-body problem**.

The quantity that can (in principle be measured is the probability that the $N$ electrons are at a particular set of coordinates, $\bold{r}_1, ..., \bold{r}_N$. This is the probability of the configuration of the electrons, and is equal to $\psi^*(\bold{r}_1,..., \bold{r}_N )$. In experiments we do not care which electron in the material is labeled electron 1, electron 2, and so on. The quantity of physical interest is really the probability that a set of N electrons in any order have coordinates $\bold{r}_1,..., \bold{r}_N$. A closely related quantity is the **density of electrons** at a particular position in space, $n(\bold{r})$.

$n_{\bold{r}} = 2\sum_i \psi_{i}^*(\bold{r}) \psi_{i}(\bold{r})$

The **factor 2** appears because electrons have spin and the Pauli exclusion principle states that each indicudual electron wave function can be occupied by two separate electrons provided they have different spins.

The first theorem:

*The ground-state energy from Schrödinger's equation is a unique functional of the of the electron density.*

A simple example of a function dependent on a single variable is $f(x) = x^2 + 1$. A **functional** is similar, but it takes a function and defines a single number from the function. For example,

$F[f] = \int_{-1}^1 f(x) dx$

is a functional of the function $f(x)$. If we evaluate this functional using $f(x) = x^2 +1$, we get $F[f] = \frac{8}{3}$. So we can restate Hohenberg and Kohn's result by saying that the ground-state energy $E$ can be expressed as $E[n(\bold{r})]$. **This is why this field is known as density functional theory**.

Unfortunately, although the first Hohenberg-Kohn theorem rigorously proves that a functional of the electron density exists that can be used to slove the Schrödinger equation, the theorem says nothing about what the functional actually is.

The second Hohenberg-Kohn theorem defines an important property of the functional: **The electron density that minimizes the energy of the overall functional is the true electron density correspoonding to the full solution of the Schrödinger equation.**

If the "ture" functional form were known, then we could vary the electron density until the energy from the functional is minimized, giving us a prescription for finding the relevant electron density.

Thinking: This is kind of like NN?

How to get the positions of nuclei?

The solutions of Schrödinger equations are used to determine the minimum energy, so that we can find the electron density of our system. But how can I know the postion of the nuclei in my system?

[1] https://water.lsbu.ac.uk/water/supercooled_water.html

[2] Bergman, R., Swenson, J. Dynamics of supercooled water in confined geometry. Nature 403, 283–286 (2000). https://doi.org/10.1038/35002027

[3] Sellberg, J., Huang, C., McQueen, T. et al. Ultrafast X-ray probing of water structure below the homogeneous ice nucleation temperature. Nature 510, 381–384 (2014). https://doi.org/10.1038/nature13266

## # Advances in the study of supercooled water

# # Group Meeting Notes

### # Thermoelectric effect

The **thermoelectric effect** is the **direct conversion of temperature differences to electric voltage and vice versa** via a thermocouple. A thermoelectric device creates a voltage when there is a different temperature on each side. Conversely, when a voltage is applied to it, heat is transferred from one side to the other, creating a temperature difference. At the atomic scale, an applied temperature gradient causes charge carriers in the material to diffuse from the hot side to the cold side. To know more about thermoelectric material, clik here (opens new window).

### # Curie temperature

In physics and materials science, the **Curie temperature** ($T_{C}$), or **Curie point**, is the **temperature above which certain materials lose their permanent magnetic properties**, which can (in most cases) be replaced by induced magnetism. The Curie temperature is named after Pierre Curie, who showed that magnetism was lost at a critical temperature.[1]

We can design the curie temperature of the magnetic material to make rice cooker. Check this link (opens new window).

### # Phase-field simulation

**Phase-field models** are usually constructed in order to reproduce a given **interfacial dynamics**.

### # Monte Carlo Simulation

### # Spherical harmonics

[1] https://en.wikipedia.org/wiki/Curie_temperature