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Covalent Bonding

Friday, March 18, 2022

Features of Covalent Bonding

When atoms in a molecule share electrons, they are covalently bonding. An example would be H2\text{H}_2, which has two identical atoms of hydrogen (called homopolar or homonuclear bonding).

Features of covalent bonding include:

  1. As two atoms are brought together, the electrons interact and the separate atomic states and energy levels are transformed into molecular states
  2. The electron wave functions overlap in such a way as to give a lower energy than the separated atoms had
  3. The other molecular state has an increased energy relative to the separated atoms, and so does not lead to the formation of a stable molecule
  4. The Pauli exclusion principle applies to molecular states; each state can have two electrons (one for each spin orientation)

Dissociation energy

The dissociation energy of a molecule indicates the energy needed to break the molecule into neutral atoms.

As the atomic number increases, the ss electrons become associated with higher principle quantum numbers, nn. This leads to lower dissociation energies since the equilibrium separation increases (due to higher average radius).


Atoms with pp states can also form covalent bonds, and the three atomic pp states lead to six possible molecular pp states. The three values of mlm_l lead to the three "figure-eight" shaped distributions for pp states: for ml=0m_l=0 we see a distribution with two lobes aligned with the zz-axis. For ml=±1m_l=\pm 1, we observe a smeared out figure-eight distribution in the xyxy-plane due to the uncertainty principle. Instead of mlm_l values, we use pxp_x, pyp_y, and pzp_z to represent these distributions (even though the xx and yy ones cannot be observed, they do exist).

There are three types of covalent bonds for pp types: pppp bonds, spsp directed bonds, and spsp hybrid states.

pppp Covalent Bonds

Bringing two atoms with pp states together overlaps their probability distributions along one of the axes (assuming they approach along the xx-axis is convention). The pxp_x states overlap, producing a significant attractive force between the nuclei and electrons. The pyp_y and pzp_z states also overlap, but in such a way that their attractive forces are far less significant than those of the pxp_x states.

pp covalent bond

The bonds with a more direct overlap of pp states (such as aa in the image above) are known as sigma bonds, denoted σ\sigma. The bonds with an indirect, off-axis overlap (such as bb in the image above) are known as pi bonds, denoted π\pi. In general, σ\sigma bonds are stronger than π\pi bonds.


Consider the bonding of two atoms with filled 1s1s and 2s2s states and valence electrons in the 2p2p state. The four 1s1s electrons occupy the bonding and anti-bonding molecular states, and same with the 2s2s electrons. This leaves the pp state electrons, which begin filling the bonding (lower energy) states. Two electrons can fill each pppp covalent bond (pxp_x, pyp_y, pzp_z) before filling the antibonding states.

spsp Molecular Bonds

It is possible for a stable molecule to form with an atom with an ss-state valence electron and one with one or more pp-state valence electrons. Fluorine, for instance, has five electrons in the pp shell, so it has four paired electrons (two of the 2p2p states reached capacity), meaning one electron participates in bonding. This creates a lobe-shaped wave function where the signs are opposite on different lobes (one is positive, one is negative). Another atom, such as hydrogen, can bond to the fluorine by overlapping wave functions in such a way that increase the probability of finding an electron in between the atoms (bonding spsp state). The other overlapping direction is the antibonding spsp state.

sp bond

Directed bonds

In a water molecule (H2O\text{H}_2\text{O}), there are four pp electrons. They fill one pp state completely, leaving two half-filled with one electron each. This allows two bonds with hydrogen, forming the molecule. Water has directed bonds since the relative positions and directions of the bonds are fixed.

spsp Hybrid States

Some atoms with pp electrons behave as though they have more valence electrons than expected. Carbon, for instance, has an electron configuration of 1s2 2s2 2p21s^2~2s^2~2p^2, however it forms bonds as though it has four valence electrons. This effect is known as sp hybridization. The bonds these atoms form are identical, not as if there are two ssss bonds and two spsp bonds for instance.

spsp hybrids usually form as follows:

  1. In an atom with a configuration of 2s2 2pn2s^2~2p^n, one of the 2s2s electrons is excited to the 2p2p shell, giving a configuration of 2s1 2pn+12s^1~2p^{n+1}
  2. The hybrid states are formed by taking equal mixtures of the wave functions representing the 2s2s state and each of the 2p2p states. For instance, boron (configuration 2s2 2p12s^2~2p^1) first becomes 2s1 2p22s^1~2p^2, meaning the hybrid states are represented as different combinations of ψ2s\psi_{2s}, ψ2px\psi_{2p_x}, and ψ2py\psi_{2p_y}.

sp hybrid states


In CH4\text{CH}_4, the carbon has four sp3sp^3 hybrid states, each of which forms a bond (σ\sigma) with a hydrogen. This gives a tetrahedral structure.


Carbon can also form three sp2sp^2 hybrid states, allowing two carbon atoms to bond to two hydrogens each and double bond with each other (one σ\sigma and one π\pi).


It is even possible for two carbons to form spsp hybrids, allowing one hydrogen each with a triple bond between the two carbons.