Orbitals Chemistry

In chemistry, the concept of orbitals is pivotal to understanding how atoms bond together to form molecules. Orbitals explain not only where electrons are likely to be found but also how electrons in different atoms interact to create bonds.

1.0What are Atomic Orbitals

Atomic orbitals are a core concept in quantum chemistry, fundamentally describing where an electron is likely to be found around an atom's nucleus. 

Atomic orbitals are mathematical functions derived from solutions to the Schrödinger equation, representing the probable locations of electrons in atoms. Unlike a fixed path, an orbital indicates regions in space where there is a high likelihood of finding an electron. Each orbital is characterized by specific energy levels and is associated with quantum numbers that define its shape, size, and orientation.

2.0Difference between Atomic Orbits and Atomic Orbitals

3.0Types of Orbitals

Orbitals are classified into several types based on their shape and energy characteristics:

1. s-orbitals:

s-orbitals are the simplest type of orbital with a spherical shape centered around the nucleus. The probability of finding an electron is uniform in all directions at a certain distance from the nucleus. Each principal energy level from n=1 upwards contains one s-orbital.

2. p-orbitals:

p-orbitals have a dumbbell shape and are oriented along the x, y, or z axis, leading to three distinct p-orbitals (p_x, p_y, p_z) per energy level, starting from n=2 upwards. These orbitals have a nodal plane through the nucleus where the probability of finding an electron is zero.

3. d-orbitals:

d-orbitals begin to appear at the third energy level (n=3). There are five d-orbitals (dxy, dyz, dxz, dx²-y², dz²) per level, each with more complex shapes involving four lobes or a donut shape around the nucleus. These orbitals also contain more nodal planes compared to p-orbitals.

4. f-orbitals:

f-orbitals are present from the fourth energy level (n=4) and onwards. There are seven distinct f-orbitals, each with intricate, multi-lobed shapes. These orbitals have even more complex nodal structures and are less commonly encountered in basic chemistry due to their higher energy and complexity.

4.0Quantum numbers

Quantum numbers are important for understanding the electronic structure of atoms. They provide a set of four integers that not only specify the properties of atomic orbitals but also the properties of electrons in these orbitals. Each quantum number provides different information about the electron’s behavior and its location within the atom.

1. Principal Quantum Number (n)

• The principal quantum number, n, is the first and perhaps the most fundamental of the quantum numbers, which indicates the main energy level occupied by the electron.
• The value of n determines the overall size and energy of the orbital. As n increases, the orbital becomes larger, the electron is further from the nucleus, and the electron has higher energy.
• Allowed Values: n can be any positive integer starting from 1 (i.e., n=1,2,3,…).

2. Angular Momentum Quantum Number (ℓ)

• This quantum number describes the shape of the orbital. It is sometimes referred to as the azimuthal or orbital quantum number.
• Different values of ℓ correspond to different orbital shapes (s, p, d, f, etc.). For a given n, ℓ defines the subshells or sublevels that exist within that main energy level.
• Allowed Values: ℓ ranges from 0 to n−1 for each principal quantum number n. Each value of ℓ corresponds to a specific type of orbital:
• • ℓ=0 (s-orbital)
  • ℓ=1 (p-orbital)
  • ℓ=2 (d-orbital)
  • ℓ=3 (f-orbital), and so on.

3. Magnetic Quantum Number (m_ℓ)

• The magnetic quantum number specifies the orientation of the orbital in space relative to the other orbitals within the same subshell.
• This number determines the orientation of the electron cloud of an orbital within a particular subshell around the nucleus.
•  m_ℓ​ can range from −ℓ, including zero. This means for each orbital shape designated by ℓ, there are 2ℓ+1 possible orientations.

4. Spin Quantum Number (m_s​)

• The spin quantum number describes the direction of the intrinsic angular momentum (spin) of the electron.
• The spin can be thought of as the electron spinning on its own axis, either clockwise or counterclockwise.
• m_s can be either +1/2 or -1/2, representing the two possible directions of spin. 

Here is a summarized form of Quantum numbers:

5.0Orbital Chemistry in Bonding

1. Hybridization: 

Hybridization is a process where atomic orbitals mix to form new hybrid orbitals that are equivalent in energy. Common types of hybrid orbitals include:

• sp³: Forms four equivalent orbitals arranged tetrahedrally, typical in methane (CH₄).
• sp²: Forms three planar orbitals with 120° separation, common in benzene (C₆H₆).
• sp: Forms two linear orbitals, seen in acetylene (C₂H₂).

2. Molecular Orbitals: 

• Beyond individual atoms, atomic orbitals can combine when atoms bond, forming molecular orbitals that are distributed over multiple atoms, influencing molecular stability and properties.

Molecular orbitals formed from the linear combination of atomic orbitals can be bonding or antibonding:

• Bonding Orbitals: Lower in energy, they increase molecular stability by allowing electrons to be shared between atoms.
• Antibonding Orbitals: Higher in energy, potentially destabilizing if occupied.

3. Types of Chemical Bonds:

• Sigma Bonds (σ\sigma): Formed by the head-on overlap of orbitals, typically stronger and found in single bonds.
• Pi Bonds (π\pi): Formed by the side-to-side overlap of p-orbitals, generally found in double and triple bonds alongside sigma bonds.