Imagine an atom as a miniature solar system: electrons revolve around the nucleus, occupying specific energy regions called orbitals. These orbits, described by the powerful Schrödinger equation, direct the electron's direction. But when atoms become friends and bond to form molecules, something magical happens. Their individual orbitals merge, forming entirely new units known as molecular orbitals.
Atomic Orbital
- Atomic orbital relates to an atom. The electron cloud surrounds an atom.
- It has a simple shape like a sphere, dumbbell double dumbbell, etc.
- Atomic orbitals are designated as s.p.d or orbital.
- The electrons involved belong to a particular atom.
- There is nothing like an anti-bonding atomic orbital.
Molecular Orbital
- It relates to molecules. The electron cloud surrounds a molecule.
- It has a complicated shape.
- Molecular orbitals are designed as sigma and pi orbitals.
- The electrons involved belong not to the atom but to the molecule as a whole.
- There are bonding and anti-bonding molecular orbitals.
Equations for Atomic and Molecular Orbitals
Atomic Orbital equations
The journey in the orbital equations begins with the atom, the basic building block of matter. Electrons orbit around the Atomic nucleus, occupying specific energy levels known as orbitals. These orbitals are described by the Schrödinger equation, which is a cornerstone of quantum mechanics:
\[ĤΨ(x, y, z) = EΨ(x, y, z)\}
Where:
Ĥ is the Hamiltonian operator, representing the total energy of the electron.
Ψ(x, y, z) is the wave function, which contains information about the electron's probability of being found at a particular location.
E is the energy of the electron in its orbital.
Solving the Schrödinger equation for hydrogen gives us the wave functions for its atomic orbitals:
\[Ψ(n, l, m_l) = R_(n, l)(r) * Y_(l, m_l)(θ, φ)\]
Where:
n, l, and m_l are the quantum numbers that define the orbital (principal quantum number, angular momentum quantum number, and magnetic quantum number, respectively).
R_(n, l)(r) is the radial part of the wave function, depending on the distance from the nucleus.
Y_(l, m_l)(θ, φ) is the angular part of the wave function, depending on the angles that define the electron's position.
Molecular Orbitals: When Atoms Join Forces
When atoms bond to form molecules, their atomic orbitals merge to create new entities called molecular orbitals. These orbitals accommodate the electrons of the constituent atoms, determining the molecule's stability and properties.
The wave functions for molecular orbitals can be obtained using linear combinations of atomic orbitals (LCAO method). Imagine two atomic orbitals, ϕ_a and ϕ_b, overlapping. The resulting molecular orbitals can be expressed as:
Ψ_bonding = c_a * φ_a + c_b * φ_b
Ψ_antibonding = c_a * ϕ_a - c_b * ϕ_b
where:
c_a and c_b are coefficients determined by the overlap and energy of the atomic orbitals.
Ψ_bonding is the bonding molecular orbital, which lowers the energy of the molecule and stabilizes it.
Ψ_antibonding is the antibonding molecular orbital, which raises the energy of the molecule and destabilizes it.
