In this explainer, we will learn how to explain and identify hybridization of atomic orbitals.
The atomic orbitals of atoms can merge together and form hybrid orbitals that have altogether different shapes and structures from ordinary atomic orbitals. The concept of atomic orbital hybridization has helped chemists to understand why molecules like methane have four carbon–hydrogen () covalent bonds despite carbon atoms having only two unpaired p-subshell electrons. It has also helped chemists to understand why the carbon–carbon bonds are so different in molecules like ethene and ethyne and why molecular geometries seem to be inextricably linked with the number of sigma () and pi () carbon–carbon bonds in organic compounds.
Linus Pauling pioneered much of the early work that described the hybridization and overlap of different types of bonding orbitals when he published landmark papers on the subject of valence bond theory in the first half of the 20th century. His work described how the concept of atomic and hybridized bonding orbitals could be used to accurately explain the bonding characteristics of almost all molecules including simple diatomic molecules such as hydrogen and larger organic compounds such as acetyl cyanide (). His work is incredibly interesting, but it can be complex, and it is important that we first understand the basic ideas of atomic orbitals before we try to understand how orbitals can hybridize and make bonds with other adjacent atoms.
Definition: Atomic Orbital
Atomic orbitals are mathematical functions that describe the location and wavelike behavior of an electron in an atom.
The simplest and lowest energy atomic orbital is the 1s atomic orbital and the next lowest energy atomic orbitals are the 2s and 2p atomic orbitals. The s-type atomic orbitals have a relatively simple spherical shape, and each p-type atomic orbital has an interesting dumbbell shape that is plane polarized around one of the three Cartesian coordinate axes. Carbon atoms have the  electron configuration, and it would be reasonable to assume that the 2s and 2p atomic orbitals have different interactions with covalently bonded hydrogen atoms in molecules like methane, but experimental data suggests this is not the case at all. The 2s- and 2p-subshell electrons tend to combine and form four hybrid bonding orbitals that all make equivalent bonds with the 1s orbital electrons of adjacent hydrogen atoms.
Definition: Orbital Hybridization
Orbital hybridization is the concept of mixing atomic orbitals into new and different types of hybrid orbitals.
The hybridization process occurs when one of the two 2s-subshell electrons on the bonding carbon atom is promoted (excited) into a vacant atomic orbital. The bonding carbon atom then has four unpaired electrons in four suborbitals that can merge together and form four hybrid -type bonding orbitals that all have the same energy and are all equally capable of forming covalent bonds.
Example 1: Understanding How s and p Orbitals Merge Together and Form Hybrid Orbitals
During the formation of chemical bonds, hybridization can occur. Atomic orbitals merge together mathematically to form hybrid orbitals.
What hybrid orbitals are formed when one s orbital and three p orbitals all hybridize?
- Four orbitals
- Two orbitals
- Four orbitals
- One orbital
- Three orbitals
s orbitals are spherically shaped and p orbitals are shaped like dumbbells that are plane polarized around one of the three Cartesian coordinate axes. s and p orbitals look very different but they can merge together during chemical reactions and form hybrid orbitals that have interesting bonding properties. Carbon atoms have the  electron configuration, and their s- and p-subshell electrons can merge together and form four equivalent hybrid orbitals during a chemical reaction. The hybridization process occurs when one of the 2s-subshell electrons on the bonding carbon atom is promoted (excited) into a vacant atomic orbital. The bonding carbon atom then has four unpaired electrons in four suborbitals. These suborbitals can merge together and form four hybrid -type bonding orbitals. Option C correctly summarizes this explanation by stating that one s orbital and three p orbitals can all hybridize together and produce four hybrid orbitals. We can conclude then that option C is the correct answer to this question.
It can be stated that the four hybrid orbitals look somewhat like the 2p atomic orbitals of unbonded carbon atoms because they have a similar oblong appearance. It is important to realize however, that the orbitals are not plane polarized around the three Cartesian coordinate axes. Each lobe of the four hybrid orbitals is directed toward the four corners of a tetrahedron. It is also important to appreciate that the lobes of the orbitals are much larger than the lobes of the comparative 2p atomic orbitals. The arrangement minimizes the repulsive electrostatic interactions between the four bonding orbital electrons. The carbon atoms can form structures that have low system energy when they bond other adjacent atoms.
The hybrid orbitals can overlap with the unpaired 1s atomic orbital electron of four other hydrogen atoms to make one methane molecule that has four equivalent carbon–hydrogen covalent bonds and four equivalent () bond angles. The end-to-end overlap of the four hybridized bonding orbitals with the four 1s atomic orbitals produces four sigma bonds that are cylindrically symmetric. The cross-sectional plane of the sigma bonds will always produce a circle of electron density if it is sampled at any point along the carbon–hydrogen interatomic-bond axis.
Definition: Sigma (𝜎) Bond
Sigma bonds are covalent bonds that are formed through the head-on or end-to-end overlap of different types of hybridized or unhybridized bonding orbitals.
The excited s- and p-subshell electrons of bonding carbon atoms will sometimes only form three equivalent hybridized bonding orbitals and one of the valence electrons will remain in an unhybridized atomic orbital.
The hybridized orbitals can then form some combination of cylindrically symmetric carbon–carbon and carbon–hydrogen sigma bonds as they overlap with other adjacent atoms. Ethene is the simplest monounsaturated hydrocarbon. It contains two carbon atoms and four hydrogen atoms.
There is a single sigma bond between the two carbon atoms in ethene, and each carbon atom forms another two sigma bonds with adjacent hydrogen atoms. The unhybridized atomic orbitals overlap with each other side by side, and they form a pi bond ( bond) that has a single nodal plane that coincides with the molecular plane of the hydrogen and carbon atoms.
Definition: Pi (𝜋) Bond
Pi bonds are a type of covalent bond that is formed through the sideways overlap of two adjacent p-subshell orbitals.
Example 2: Identifying the Hybridization of the Carbon Atoms in a Sheet of Graphene
By considering the shape of the individual units that make up the macromolecule in the diagram, which type of hybridization is occurring in the carbon atoms of graphene?
We can see from the diagram above that graphene is composed of a series of interconnected hexagons. The hexagons are made up of carbon atoms and they have bond angles of . Each carbon atom makes three carbon–carbon sigma bonds and they have one unhybridized electron. This arrangement and number of hybrid orbitals correspond to hybridization. We can use these statements to determine that option B is the correct answer to this question.
Example 3: Determining the Location of the Pi Bond in an Ethylene Molecule
In a molecule of ethene, all five of the bonds exist in the same plane. What region of space does the bond occupy in relation to the central bond in a molecule of ethene?
Both of the carbon atoms in a molecule of ethene are hybridized with one of the valence electrons in each atom remaining in an unhybridized atomic orbital. The side-by-side overlap of the unhybridized atomic orbitals forms a pi bond ( bond) that has a single nodal plane that coincides with the molecular plane of the hydrogen and carbon atoms. The electron density of a pi bond is split above and below this nodal plane as shown in diagram B. We can use these statements to determine that option choice B is the correct answer to this question.
The excited s- and p-subshell electrons of bonding carbon atoms can even more unusually form just two hybridized sp bonding orbitals while the other valence electrons remain in unhybridized and atomic orbitals.
Ethyne (acetylene) contains a single carbon–carbon sigma bond that is formed through the overlap of two sp hybridized orbital electrons. The other sp hybridized orbital electron on each carbon atom is used to make one carbon–hydrogen covalent bond. The pairs of unhybridized and atomic orbitals overlap and they make two separate bonds that are perpendicular to each other and parallel to the single carbon–carbon sigma bond. There is said to be a triple bond between the two adjacent carbon atoms because the carbon atoms are effectively linked with one sigma bond and another two pi bonds.
The bonding electrons of carbon atoms can form hybrid orbitals when they bond other atoms such as oxygen or nitrogen. The process of exciting one electron from the 2s atomic orbital is an effective way to optimize the bonding characteristics of any carbon atom, and sp hybridization processes are common in more complex molecules like acetyl cyanide (). Acetyl cyanide (pyruvonitrile) has one central hybridized carbon atom that is bonded on one side to an hybridized carbon atom and is bonded on its other side to an sp hybridized carbon atom. The hybridized carbon atom is bonded to four other atoms and the and sp carbon atoms are bonded to three and two other atoms. The number of bonding atoms is linked with the hybridization state of any carbon atom and it can always be determined as , where is the superscript number in the orbital hybridization term.
Valence bond theory can similarly be applied to understand the bonding characteristics of simpler systems such as diatomic hydrogen () and diatomic hydrogen fluoride () molecules. Valence bond theory assumes that most simple diatomic molecules are formed through the head-on or end-to-end overlap of two adjacent atomic orbitals. Diatomic hydrogen gas is formed when two adjacent 1s atomic orbitals overlap and make a single cylindrically symmetric sigma bond. Hydrogen fluoride is formed when the 1s orbital of one hydrogen atom overlaps with the 2p atomic orbital of another fluorine atom. The formation of a sigma bond does not have to involve the head on overlap of any s-type atomic orbitals. Some of the halogen gases are made when two p-type atomic orbitals overlap end to end. The end-to-end overlap of two half-filled atomic orbitals produces one low-energy sigma bond in fluorine () molecules and the end-to-end overlap of two half-filled atomic orbitals produces one low-energy sigma bond in chlorine () molecules.
It is important to appreciate here that sigma bonds were formed in the diatomic halogen molecules through the end-to-end or collinear overlap of two atomic orbitals and not through the sideways overlap of two atomic orbitals. Sigma bonds can be made through the combination of a few different hybridized and unhybridized bonding orbitals, but the sideways overlap of two parallel p-type atomic orbitals always produces a single pi bond. The following image shows how certain types of hybridized and unhybridized orbitals can overlap with each other and form different types of sigma bonds.
Example 4: Identifying What Is and What Is Not a Sigma (𝜎) Bond
A sigma bond is created when specific combinations of atomic orbitals overlap. Which of the following occurrences does not result in the formation of a bond?
- A hybrid sp orbital overlapping with another hybrid sp orbital
- An s orbital overlapping with a p orbital
- A p orbital overlapping with another p orbital side by side
- An s orbital overlapping with another s orbital
- A p orbital overlapping with another p orbital end to end
Sigma () bonds are covalent bonds that are formed through the head-on or end-to-end overlap of different types of hybridized or unhybridized bonding orbitals. Sigma bonds can be formed through a few different combinations of hybridized and unhybridized orbitals, but they are not formed through the sideways overlap of two adjacent p-type atomic orbitals. The sideways overlap of two adjacent p-type atomic orbitals produces a pi () bond rather than a cylindrically symmetric sigma bond. These statements are in line with option C. We can therefore conclude that C must be the correct answer to this question.
Let us summarize what has been learned in this explainer.
- Valence bond theory can be used to understand how bonding orbitals overlap with each other and form sigma () and pi () bonds.
- The bonding electrons of a carbon atom can merge together and form hybrid orbitals that can bond with other hybridized and unhybridized electrons.
- Single carbon–carbon () bonds are formed from one sigma bond, and double () or triple () bonds are formed through the combination of one sigma bond and either one or two pi bonds.
- Valence bond theory can be used to understand the bonding characteristics of almost all molecules, and this includes large organic compounds that contain multiple carbon atoms and simple diatomic molecules that contain just two atoms of the same element.