The bonding in molecules was understood in a new way with the new theories presented by Schrodinger, Heisenberg and Paul Diarc. The quantum mechanics came into the picture with their findings. They found that an electron has both particle and wave properties. With this, Schrodinger developed equations to find the wave nature of an electron, and came up with the wave equation and wave function. Wave function (Ψ) corresponds to different states for the electron.
Atomic Orbital
Max Born points out a physical meaning to the square of wave function (Ψ^{2}), after Schrodinger put forward his theory. According to Born, Ψ^{2 }expresses the probability of finding an electron in a particular location. So, if Ψ^{2 }is a large value, then the probability of finding the electron in that space is higher. Therefore, in the space, electron probability density is large. On the contrary, if the Ψ^{2 }is low, then the electron probability density is low. The plots of Ψ^{2 }in x, y and z axes show these probabilities, and they take the shape of s, p, d and f orbitals. These are known as atomic orbitals. An atomic orbital can be defined as a region of space where the probability of finding an electron is large in an atom. Atomic orbitals are characterized by quantum numbers, and each atomic orbital can accommodate two electrons with opposite spins. For example, when we write the electron configuration, we write as 1s^{2}, 2s^{2}, 2p^{6}, 3s^{2}. 1, 2, 3….n integer values are the quantum numbers. The superscript number after the orbital name shows the number of electrons in that orbital. s orbitals are sphere shaped, and small. P orbitals are dumbbell shaped with two lobes. One lobe is said to be positive, and the other lobe is negative. The place where two lobes touch each other is known as a node. There are 3 p orbitals as x, y and z. They are arranged in space so that their axes are perpendicular to each other. There are five d orbitals and 7 f orbitals with different shapes. So collectively, following are the total number of electrons that can be resided in an orbital.
s orbital2 electrons
P orbitals 6 electrons
d orbitals 10 electrons
f orbitals 14 electrons
Molecular Orbital
Atoms join to form molecules. When two atoms move closer together to form a molecule, atomic orbitals overlap and combine to become molecular orbitals. The number of newly formed molecular orbitals is equal to the number of combined atomic orbitals. The molecular orbital surrounds the two nuclei of the atoms, and electrons can move around both nuclei. Similar to atomic orbitals, molecular orbitals maximally contain 2 electrons, which have opposite spins. Molecular orbitals are of two types, bonding molecular orbitals and antibonding molecular orbitals. Bonding molecular orbitals contain electrons in the ground state and antibonding molecular orbitals contain no electrons in the ground state. Electrons may occupy in the antibonding orbitals if the molecule is in the excited state.
What is the difference between atomic orbital and molecular orbital? ¤ Atomic orbitals are seen in atoms, and molecular orbitals are seen in molecules. When atomic orbitals join together, molecular orbitals are form. ¤ Atomic orbitals describe the locations where probability of finding the electrons is high in an atom. Molecular orbitals describe the probable locations of electrons in a molecule. ¤ Atomic orbitals are named as s,p,d, and f. There are two types of molecular orbitals as bonding and antibonding molecular orbitals.

Janalius Murugu says
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