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chem: add expanded vsepr theory, fix orbital style wirting

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@ -377,7 +377,7 @@ The four types of orbitals currently known are: *s*, *p*, *d*, and *f*.
The group of orbitals of the same type in the same energy level is known as the **sublevel**. A coefficient is given to indicate the energy level of that sublevel.
!!! example
The *p* sublevel consists of 3 *p*-orbitals at a given energy level. The *p* sublevel of energy level 2 is written as **2*****p***.
The *p* sublevel consists of 3 p orbitals at a given energy level. The *p* sublevel of energy level 2 is written as **2*****p***.
| Main energy level | Types of orbitals | Number of orbitals | Maximum number of electrons |
| --- | --- | --- | --- |
@ -391,13 +391,13 @@ Orbitals of the same type but in higher energy levels are simply larger, so any
<img src="/resources/images/s-p-orbitals.png" width=700>(Source: Kognity)</img>
*s*-orbitals are spherical in shape and are centred on the nucleus. There is one on each energy level.
s orbitals are spherical in shape and are centred on the nucleus. There is one on each energy level.
*p*-orbitals are dumbbell-shaped and centred on the nucleus. Each orbital is aligned on a different axis. There are three on each energy level starting from $n=2$.
p orbitals are dumbbell-shaped and centred on the nucleus. Each orbital is aligned on a different axis. There are three on each energy level starting from $n=2$.
*d*-orbitals have complex shapes. There are 5 in each energy level starting from $n=3$.
d orbitals have complex shapes. There are 5 in each energy level starting from $n=3$.
*f*-orbitals have more complex shapes. There are 7 in each energy level starting from $n=4$.
f orbitals have more complex shapes. There are 7 in each energy level starting from $n=4$.
The **Aufbau principle** states that orbitals are filled up in order of increasing energy (closest to farthest from nucleus), which is shown in the image below.
@ -446,14 +446,14 @@ The **principal** quantum number ($n$) is the **main energy level** of the elect
The **angular momentum** quantum number ($ℓ$) is the type of orbital the electron resides in, zero-indexed:
- $ℓ=0$ means that the electron is in an *s*-orbital.
- $ℓ=1$ means that the electron is in a *p*-orbital.
- $ℓ=2$ means that the electron is in a *d*-orbital.
- $ℓ=0$ means that the electron is in an s orbital.
- $ℓ=1$ means that the electron is in a p orbital.
- $ℓ=2$ means that the electron is in a d orbital.
The **magnetic** quantum number ($m_ℓ$) is contextualised by the angular momentum quantum number and identifies the specific orbital that the electron occupies in its sublevel. The centre orbital is $m_ℓ=0$ and is listed in ascending order.
!!! example
If $ℓ=1$, $m_ℓ=-2$ indicates that the electron is located in the first *p*-orbital of the sublevel and $m_ℓ=2$ indicates that it is located on the fifth and last *p*-orbital of the sublevel.
If $ℓ=1$, $m_ℓ=-2$ indicates that the electron is located in the first p orbital of the sublevel and $m_ℓ=2$ indicates that it is located on the fifth and last p orbital of the sublevel.
The **spin** quantum number ($m_s$) can either be $\frac{1}{2}$ or $-\frac{1}{2}$ and determines if the electron has a clockwise spin/is the first electron in its orbital or not, respectively.
@ -643,24 +643,27 @@ Groups of electrons that repel other electrons together are known as **electron
!!! definition
- **Molecular shape/geometry** represents the general shape of a molecule's bonds around a central atom.
- **Electron distribution/geometry** represents the general shape of a molecule's *electrons* around a central atom. It is identical to molecular shape, but takes lone pairs into consideration.
- The **central atom** is the atom from which electron distribution is looked at from. It is typically the element with the lowest $\Delta$ EN, except for hydrogen.
- **Peripheral atoms** are atoms that are bonded to the central atom. For example, peripheral atoms in $\text{CCl}_4$ are all four chlorines.
The AXE method of electron counting represents the electron pairs around a central atom with the formula $\text{AX}_n\text{E}_m$, where $A$ is the central atom, each $X$ represents a peripheral atom, and each $E$ represents a lone pair of electrons on the **central atom**. The total number of domains is equal to $X+E$. If $E=0$, the electron distribution and the molecular shape of a molecule are the same.
| AXE | Electron distribution | Molecular shape |
| --- | --- | --- |
| $\text{AX}_4$ | tetrahedral | tetrahedral |
| $\text{AX}_3\text{E}_1$ | tetrahedral | trigonal pyramidal |
| $\text{AX}_2\text{E}_2$ | tetrahedral | bent |
| $\text{AX}_3$ | trigonal planar | trigonal planar |
| $\text{AX}_2\text{E}_1$ | trigonal planar | bent |
| $\text{AX}_2$ | linear | linear |
| AXE | Electron distribution | Molecular shape | Bond angle |
| --- | --- | --- | --- |
| $\text{AX}_4$ | tetrahedral | tetrahedral | 109.5° |
| $\text{AX}_3\text{E}$ | tetrahedral | trigonal pyramidal | 107° |
| $\text{AX}_2\text{E}_2$ | tetrahedral | bent | 104.5° |
| $\text{AXE}_3$ | trigonal planar | bent | DNE |
| $\text{AX}_3$ | trigonal planar | trigonal planar | 120° |
| $\text{AX}_2\text{E}_1$ | trigonal planar | bent | 117° |
| $\text{AX}_2$ | linear | linear | 180° |
A **3D diagram** of a molecule is drawn similarly to three-dimensional Lewis structures, except for the following added rules:
A **3D diagram** of a molecule is drawn similarly to three-dimensional Lewis structures (ions must still be enclosed in square brackets), except for the following added rules:
- Only the lone pairs of the **central atom** should be drawn.
- Bonds behind the current plane should be drawn with broken lines.
- Bonds in front of the current plane should be drawn with triangle lines.
- There should never be a 90° angle anywhere.
- 90° angles are only present in molecules with five electron domains, and should be avoided in all other scenarios.
- The angle between the peripheral atoms should be labelled once for each distinct angle.
- for $\text{AX}_n\text{E}_m$ structures, where $n+m=4$, the angle between peripheral atoms is equal to $109.5° - 2.5m$.
@ -669,7 +672,43 @@ A **3D diagram** of a molecule is drawn similarly to three-dimensional Lewis str
<img src="/resources/images/vespr-diagram.png" width=700>(Source: Kognity)</img>
####
### VSEPR theory expanded
Because of the addition of d orbitals beginning from $n=3$, elements in period 3 and beyond **with p orbitals** can make use of the space for d orbitals to form bonds such that they break the octet rule.
In molecules with 5 or 6 electron domains, their electron distribution is as follows, respectively:
<img src="/resources/images/56-domains.png" width=700>(Source: Kognity)</img>
In a trigonal bipyramid, the **equatorial** positions of domains refer to the position of the domains on the x- and z-dimensions (a trigonal plane). The domains along the y-dimension are have **axial** positions. The angle between the two is known as the **equatorial-axial** angle.
| AXE | Electron distribution | Molecular shape | Bond angle |
| --- | --- | --- | --- |
| $\text{AX}_5$ | trigonal bipyramidal | trigonal bipyramidal | equatorial=120°, equatorial-axial=90° |
| $\text{AX}_4\text{E}$ | trigonal bipyramidal | see-saw | |
| $\text{AX}_3\text{E}_2$ | trigonal bipyramidal | t-shaped | |
| $\text{AX}_2\text{E}_3$ | trigonal bipyramidal | linear | 180° |
| $\text{AX}_6$ | octahedral | octahedral | 90° |
| $\text{AX}_5\text{E}_6$ | octahedral | square pyramidal | |
| $\text{AX}_4\text{E}_2$ | octahedral | square planar | 90° |
!!! example
The following are some examples of 3D diagrams of molecules with five domains (Source: Kognity):
$\text{AX}_5$:
<img src="/resources/images/vsepr-ax5.png" width=700></img>
$\text{AX}_4\text{E}$:
<img src="/resources/images/vsepr-ax4e.png" width=700></img>
$\text{AX}_3\text{E}_2$:
<img src="/resources/images/vsepr-ax3e2.png" width=700></img>
The following are some examples of 3D diagrams of molecules with six domains (Source: Kognity):
$\text{AX}_6$:
<img src="/resources/images/vsepr-ax6.png" width=700></img>
$\text{AX}_5\text{E}$:
<img src="/resources/images/vsepr-ax5e.png" width=700></img>
$\text{AX}_4\text{E}_2$:
<img src="/resources/images/vsepr-ax4e2.png" width=700></img>
## 4.4 - Intermolecular forces