Molecular geometry can be defined as the arrangement of atoms of molecules in a 3-dimensional space. This gives a proper shape to molecules. There are some advanced techniques that help to understand the molecular geometry of molecules. For example, x-ray diffraction and spectroscopy. These techniques give data with great accuracy.

Basic knowledge about bonding in molecules helps to understand their geometries such as Lewis theory, VSEPR theory, and hybridization theory. These theories about bonding though give incomplete knowledge but are still very useful. They explain the electronic structure of molecules. The bonding sense is really important to figure out the reactivity, polarity, and physical properties of molecules.

**Localized Bonds**

The localized bond approach is a simple and sophisticated bond that is easy to draw on paper. Covalent bonds are explained with a combination of theories of bonding. To determine the molecular shapes or geometry, three theories are to be understood and are to be somehow simultaneously applied.

**Lewis’s Concept of molecular geometry**

G.N Lewis was an American chemist. He first recognized that bonding between two atoms is due to sharing of electrons. According to him, two electrons shared by each atom to form a bond form a bonding pair, while the electron pair on each atom not involved in bonding is called a lone pair. He was the first-ever scientist who presented the electronic structure of a molecule or a polyatomic ion.

Electron and molecular geometry provide a complete framework of molecular geometries.

**Example: Lewis diagram of (NF**_{3}) molecule

_{3}) molecule

The lewis diagram of a molecule (NH_{3}) can be drawn by following the step below;

**Count the total number of valence electrons in a molecule.**

The valence electrons of nitrogen and the fluorine atoms are added and the number comes out is 26.

N + H + H + H

Valence electrons = 5 + 7 + 7 + 7 = 26

**Choose the central atom**

It is a crucial step to draw the best lewis structure. The central atom should be the least electronegative one. Oxygen and hydrogen are generally peripheral atoms. Hence, nitrogen in NF_{3} is the central atom here.

**Connect the central atom with surrounding atoms to draw the structure**

The central atom is connected with other atoms through lines called bonds to give a skeleton to the molecule.

**Complete the outermost electrons of peripheral atoms**

Now complete the octet of all peripheral atoms.

**Place the remaining electrons on the central atom**

After the connection and distribution of electrons, 2 electrons are left behind (from 26) which are placed on the central atom.

**Calculate the formal charge on each atom**

Formal charge = Valence electrons – (Bonded electrons + Non-bonded electrons)

Formal charge on nitrogen = 5 – 3 – 2 = 0

Formal charge on fluorine-(1) =7- 6 -1 = 0

Formal charge on flourine-(2) =7- 6 -1 = 0

Formal charge on flourine-(3) = 7- 6 -1 = 0

It may be noted that the best lewis diagram is the one with the least formal charge.

**Lewis structure of the resonating structures**

Some molecular compounds have more than one lewis diagram. These possible structures are known as their canonical forms and are best described as hybrids of all the resonance forms.

For example, NO_{3}^{2-}

The combined or hybrid structure deduced from the possible lewis structures is given below:

**Hybridization Theory**

In a localized bond approach after drawing a lewis diagram of a molecule, hybridization or VSEPR model is applied to understand its best representation. Hybrid means a mixture of two which in molecular geometry states that two or more atomic orbitals of a central atom are mixed to form new and degenerate (same energy) hybridized orbitals.

For example, in a methane molecule, carbon is bonded with 4 hydrogen atoms which means that carbon has four atomic orbitals involved in bonding. All four bonds of this molecule are sigma bonds and constitute sam lengths due to hybridization.

Carbon has one (s) and three (p) orbitals which are hybridized to form four new degenerate orbitals. Thus an atom that has s and p orbitals in its valence shell can form 3 types of hybrid orbitals

hybridization give a linear molecule. For example, Ethyne CH≡CH**sp**hybridization has a triangular planner geometry. For example, Ethene CH**sp**^{2}_{2}=CH_{2}hybridization gives a tetrahedral molecular geometry. For example, methane CH**sp**^{3}_{4}

Note that, If d orbitals are also present in its valence shell, it may rise to the following hybrids and their corresponding shape.

** d^{2}sp^{3} hybridization: **When two d orbitals d

_{x2-y2}and d

_{z2}are mixed with one “s” px, py, and p

_{z}orbitals, a set of 6 equivalent hybridized orbitals is formed. It gives octahedral geometry to a molecule or polyatomic ion. For example, SF

_{6}.

** dsp^{3} hybridization:** A d

_{xy}orbital, one s orbital, and p

_{x}and p

_{y}and p

_{z}orbitals combine to give five slightly different energy orbitals of dsp

^{3}. It has the shape of a trigonal bipyramidal vertex. For example, ClF

_{4}

^{+}.

** sd^{3} hybridization:** An s and d

_{xy}, d

_{yz}, d

_{zx}are combined to give rise to sd

^{3}hybrid orbitals. It has tetrahedral vertices. For example, TeCl

_{4}.

** dsp^{2} Hybridization: **d

_{x2-y2}orbital, one s orbital, p

_{x,}and p

_{y}orbitals combine to give four degenerate energy orbitals. It provides square planner geometry. For example, XeCl

_{4}.

**VSEPR Model**

The VSEPR theory provides a model to assign a shape to a molecule. It is the most simple and easiest approach to predicting the electron and molecular geometry of a molecule. This was first presented by Sidgwick and Powell and then further elaborated by Nyholm and Gillespie in the 1940s. This theory explains how the shape or geometry is controlled by repulsion between valence electrons of central and peripheral atoms. Its main postulates are summarized below:

**All EX**_{n}bonds are significant

In a molecule, each bond pair, when bonded or not is stereochemically unique. The repulsion between electron pairs actually determines the shape.

**The sequence of repulsion of electron pairs**

Electronic pair repulsions follow the trend given below;

Lone pair – Lone pair > Lone pair – Bond pair > Bond pair – Bond pair

**Double and Triple bonds**

Multi bonds such as double or triple bods are considered as one-electron density. The VSEPR model is best applied on the p-orbital as a valence shell e.g Halides, etc.

**ABE notations and occupancy (x +y)**

In this model, the central atom is represented by ‘A’, and bond pairs and lone pairs are shown with ‘B’ and ‘E’ respectively. For a given structure, AB_{x}E_{y}, ‘x’ is the number of bond pairs while ‘y’ is the number of lone pairs, surrounding the central atom. If the molecular model has no lone pairs its structure is AB_{x}E_{0} type. The geometry that shows all electron pairs, whether lone pairs or bond pairs is called its prototype or electronic geometry.

It is to be noted that electron pairs around a central atom arrange themselves in such a way that they are at the maximum possible distance. Hence they experience minimum electrostatic repulsions.

## AB_{x}E_{y} type geometries

There are two possible types of AB_{x}E_{y} geometries based on the availability of electron pairs. If the central atom has no lone pair it must have regular geometry. Whereas, in the presence of both bond pairs and lone pairs the electronic geometry deviates from the regular ones. This can be explained by the relatively greater repulsion of lone pairs.

### Regular polyhedral geometries

** **If a molecule has no lone pairs the geometry of the molecule is regular polyhedra. Regular polyhedra are classified as follows;

**AB**_{2}

_{2}

** **It is a regular prototype geometry. If the central atom is surrounded by 2 atoms, its bond pairs may experience an electrostatic repulsion. These pairs should be at 180° to minimize the repulsion.

**Example:**Carbon dioxide

**AB**AB_{X}E_{y}:_{2}**Bond angle(s):**180°**Molecular geometry:**Linear

**AB**_{3}

_{3}

In this arrangement, central atom A is surrounded by three other atoms. The placement best suited for its minimum repulsions is 120 degrees. As they are in the same plane, the geometry is named trigonal planer geometry. Hence, a ceiling fan-like shape is observed.

**Example**: Boron trifluoride (BF_{3})

**AB**AB_{X}E_{y}:_{3}**Bond angle(s):**120°**Molecular geometry:**Trigonal planar

**AB**_{4}

_{4}

It has four atoms that encapsulated the central atom ‘A’. As the number of outer atoms or bond pairs are four, the two of the bonded pair are forced to go outside the plane. It gives a tetrahedral geometry.

**Example: Dichloromethane (CH**_{2}Cl_{2})

**AB**AB_{X}E_{y}:_{4}**Bond angle(s):**109°**Molecular geometry:**Tetrahedron

**AB**_{5 }

_{5 }

Here A is surrounded by five bonded pairs. The bonded pairs have two groups. Three of them are present in the same plane while the other two are perpendicular to them.

**Example:**Phosphorus Pentachloride

**AB**AB_{X}E_{y}:_{5}**Bond angle(s): 180°, 117°****Molecular geometry:**Trigonal bipyramid

**AB**_{6}

_{6}

When an atom is surrounded by 6 atoms or bond pairs, each of them is adjusted at a position to form an octahedron.

**Example:**Sulphur Hexafluoride**AB**AB_{X}E_{y}:_{6}**Bond angle(s):**180°, 90°**Molecular geometry:**Octahedron

**Irregular Geometries **

When any of the bond pairs are replaced by a lone pair, the geometry formed is known as irregular polyhedra. Lone pairs are under the influence of one nucleus hence have more energy and occupy more space.

**AB**_{1}E_{1}

_{1}E

_{1}

This type of geometry has and bond pair and lone pair. It’s still a linear geometry.

**Example:**Carbon monoxide

**AB**ABE_{X}E_{y}:**Bond angle(s):**180°**Molecular geometry:**Linear

**AB**_{2}E

_{2}E

If two bonded pairs and one lone pair are present in a molecule its geometry is V or bent shape and its angle is less than120° (the expected angle of occupancy for 3). It is because one of the electron pairs is lone pair hence, occupies more space.

**Example:**Nitrogen dioxide NO_{2}

**AB**AB_{X}E_{y}:_{3}E**Bond angle:**117°**Molecular geometry:**Bent or V-shaped

**AB**_{3}E

_{3}E

This prototype or electron geometry is near tetrahedral but is actually pyramidal with less the 109°angle between atoms. In case of ammonia, the bond angle is 107°, while for phosphorus trichloride, it is 104°. This decrease in the bond angle for PCl_{3} is due to the electronegative chlorine atoms that attract each other.

**Example:**Phosphorus trichloride

**AB**AB_{X}E_{y}:_{3}E**Bond angle:**104°**Molecular geometry:**Pyramid

**AB**_{2}E_{2}

_{2}E

_{2}

The central atom is surrounded by 2 boned pairs as well 2 lone pairs. It also has V or bent-shaped geometry. The bond angle for this geometry is less than 107°.

**Example:** Water H_{2}O

**AB**AB_{X}E_{y}:_{2}E_{2}**Bond angle:**104°**Molecular geometry:**Bent or V-shaped

**AB**_{4}E

_{4}E

It has 4 bonded pairs and one lone pair having a sea-saw like geometry.

**AB**AB_{X}E_{y}:_{4}E_{1}**Bond angle:**184°**Molecular geometry:**See-saw

**AB**_{4}E_{2}

_{4}E

_{2}

It has 4 bond pairs and 2 lone pairs that have a square planer geometry.

**Example:** Xenon tetrafluoride (XeF_{4})

**AB**AB_{X}E_{y}:_{4}E_{2}**Bond angle(s):**90°, 180°**Molecular geometry:**Square Planar

## How to determine the molecular geometry

Molecular geometry is best elucidated by using all three theories discussed above. The unison of these three approaches is utilized to deduce and predict the best possible geometry. Some common examples are given below in which Lewis, VSEPR, and hybridization theories have been used to explain molecular geometry.

### 1. Molecular geometry of CLF_{4}^{+}

**Step 1: Lewis structure**

**Step 2: Electron Geometry**

- Bond angle(s): 90°, 180°
- Electron geometry: Square pyramid
- Hybridization: dsp
^{3}

**Step 3: Molecular geometry**

- AB
_{X}E_{y}: AB_{4}E_{1} - Occupancy: 4+1 =5
- Bond angle(s): 184°
- Molecular geometry: See-saw

### 2. Molecular geometry of XeCl_{4}

**Step 1: Lewis structure**

**Step 2: Electron Geometry**

- Bond angle(s): 90°, 180°
- Electron geometry: Octahedron
- Hybridization: dsp
^{2}

**Step 3: Molecular Geometry**

- AB
_{X}E_{y}: AB_{4}E_{2} - Occupancy: 4+2 =6
- Bond angle(s): 90°, 180°
- Molecular geometry: Square Planar

### 3. Molecular geometry of SF_{5}^{–}

**Step 1: Lewis structure**

**Step 2: Electron Geometry**

- Bond angle(s): 90°, 180°
- Electron geometry: Octahedron
- Hybridization:
*dsp*^{3}

**Step 3: Molecular Geometry**

- AB
_{X}E_{y}: AB_{4}E_{2} - Occupancy (x+y): 5 + 1 =6
- Bond angle(s): 90°, 180°
- Molecular geometry: Square pyramid

### 4. Molecular geometry of POF_{3}

**Step 1: Lewis diagram**

**Step 2: Electron Geometry**

- Bond angle(s): 107°
- Electron geometry: Octahedron
- Hybridization:
*sp*^{3}

**Step 3: Molecular Geometry**

- AB
_{X}E_{y}: AB_{4}E_{2} - Occupancy (x+y): 4+0 =4
- Bond angle(s): 108°, 35°
- Molecular geometry: Tetrahedron

## Key Takeaways

**Concepts Berg**

**What is the molecular geometry of BF _{3} boron trifluoride?**

Boron trifluoride has a trigonal planar molecular geometry with a 120° bond angle.

**How to determine, how many dots are on an element’s lewis dot structure?**

The dots on Lewis structures of elements can be determined by the group number. The valence electrons are the dots on the symbol.

**How do you find the molecular geometry?**

Molecular geometry can be determined by applying bonding theories such as Lewis, VSEPR, and hybridization. Moreover, the predicted geometry by these theories can be verified by using instrumental techniques.

**How does molecular geometry affect properties?**

The molecular geometry can be related to physical and chemical properties. If the molecular attain the shape with the minimum torsional and angular strain it is considered most stable and therefore less reactive.

**What is the molecular geometry of CH _{3}NH_{2}?**

The molecular geometry of methylamine is a pyramid. ABE type is AB_{3}E, and occupancy is 3 + 1= 4.

**What is the molecular geometry of SeF _{6}?**

It has the shape of an octahedron, with bond angles of 90° and 180°.

**What is the molecular geometry of NCl _{3}?**

The geometry of NCl_{3} is pyramidal in shape.

**What is the molecular geometry of ethanol?**

Ethanol has oxygen as the central atom with two lone pairs and two bond pairs present on it. The ethanol molecule is bent or v-shaped.

**Do double bonds matter when trying to predict molecular geometry?**

According to VSEPR theory, double bond is considered a one-electron density equivalent. However, the predicted angle of molecular geometry may be affected by two bond pairs.

**References**

**Basic Inorganic Chemistry**By**Cotton**and**Wilkinson****Inorganic Chemistry**fifth edition By**Shriver**and**Atkins**- The shape of molecules (sydney.edu.au)