Molecular Orbitals
How atomic orbitals combine into bonding and antibonding molecular orbitals, and how sigma/pi bond composition drives bond strength and length.
When atomic orbitals from separate atoms interact as those atoms come together, they combine to form molecular orbitals. This article covers how that combination happens, why it produces both stabilizing and destabilizing orbitals, the two geometric patterns atomic orbitals can overlap in to form covalent bonds — sigma and pi bonds — and how those patterns explain why single, double, and triple bonds differ in strength and length. This builds directly on the quantum numbers and atomic orbital picture from the previous subtopic, and sets up the next subtopic's coverage of hybridization.
Key Takeaways
Molecular orbitals form when atomic orbitals interact as atoms bond, through constructive or destructive interference of their wave functions.
Constructive interference (same-sign wave functions) produces a bonding molecular orbital — lower energy, more stable. Destructive interference (opposite-sign wave functions) produces an antibonding molecular orbital — higher energy, destabilizing.
Only electrons in bonding orbitals stabilize a molecule; electrons in antibonding orbitals weaken or prevent bonding. MO diagrams can show bond order and magnetic properties from this, but aren't typically MCAT-tested.
A sigma (σ) bond forms from head-to-head overlap along the internuclear axis and is the strongest type of covalent bond. It can form via s-s, s-p, p-p, or hybrid orbital overlap.
A pi (π) bond forms from sideways overlap of parallel p orbitals, is weaker than a sigma bond, and cannot exist without an accompanying sigma bond.
Bond composition: a single bond = 1σ; a double bond = 1σ + 1π; a triple bond = 1σ + 2π.
Bond strength and length trend: single bonds are longest and weakest, double bonds are shorter and stronger, and triple bonds are shortest and strongest — driven by the added pi bond(s) alongside the sigma bond.
From Atomic to Molecular Orbitals: Bonding and Antibonding Orbitals
Every atom has its own set of atomic orbitals defining the electron density around its nucleus. When two atoms approach each other, though, their atomic orbitals start to interact, and quantum mechanics treats that interaction as wave interference — the atomic orbitals' wave functions can add together (constructive interference) or cancel each other out (destructive interference).
Constructive interference occurs when the two wave functions have the same sign. This produces a bonding molecular orbital — an orbital lower in energy and more stable than the original atomic orbitals.
Destructive interference occurs when the two wave functions have opposite signs. This produces an antibonding molecular orbital — an orbital higher in energy and destabilizing.
In other words, molecular orbitals come from mathematically adding or subtracting the atomic orbitals' wave functions. Only electrons that occupy bonding orbitals actually contribute to a molecule's stability; electrons in antibonding orbitals weaken a bond or can prevent it from forming at all. This is the underlying reason some molecular structures are stable while others simply don't exist under normal conditions.
From this bonding/antibonding picture, chemists can build molecular orbital (MO) diagrams to determine whether two atoms will bond, what the resulting bond order is, and even a molecule's magnetic properties. MO diagrams themselves, though, are not typically required at MCAT depth — what matters for the exam is the underlying bonding/antibonding concept covered above, not constructing or reading a full MO diagram.
Sigma Bonds and Patterns of Orbital Overlap
Chemical bonds form through the overlap of atomic orbitals, and the specific way that overlap happens determines the bond's strength and properties. There are two primary types of covalent bonds: sigma (σ) bonds and pi (π) bonds.
A sigma bond forms through direct, head-to-head (or tail-to-tail) overlap of atomic orbitals along the internuclear axis — the straight line connecting the nuclei of the two bonded atoms. Because this overlap puts the highest electron density directly between the two nuclei, sigma bonds are the strongest type of covalent bond.
Sigma bonds can form through several different types of orbital overlap:
s-s overlap — two s orbitals from different atoms overlap directly, as in the hydrogen molecule (H₂).
s-p overlap — an s orbital from one atom overlaps with a p orbital from another.
p-p overlap — two p orbitals interact head-on.
Hybrid orbital overlap — hybridized orbitals, such as sp³, sp², or sp, participate in the bond. Hybridization itself is covered in the next subtopic.
Regardless of how it forms, every single bond in a molecule consists of exactly one sigma bond. Even in double and triple bonds, one of the bonds is always a sigma bond, with any remaining bonds being pi bonds.
Pi Bonds
A pi bond arises from the sideways overlap of two parallel p orbitals, which puts the resulting electron density above and below the bond axis rather than directly between the nuclei. Because this type of overlap is less direct than sigma bonding, a pi bond is weaker than a sigma bond and more susceptible to breaking in chemical reactions.
A pi bond cannot exist without a sigma bond. Pi bonding requires a stable internuclear framework to form along, and that framework is always provided by an initial sigma bond. As a result:
A single bond contains one sigma bond.
A double bond contains one sigma bond and one pi bond.
A triple bond contains one sigma bond and two pi bonds.
Bond Composition, Strength, and Length
Because sigma and pi bonds form differently, bond strength and bond length follow a predictable pattern across single, double, and triple bonds.
Sigma bonds, being the strongest type of bond, hold atoms together most effectively on their own. Adding pi bonds on top of that sigma bond — as happens in double and triple bonds — pulls the bonded atoms closer together and adds further strength. In summary:
Single bonds (C–C): longest and weakest — only one sigma bond.
Double bonds (C=C): shorter and stronger — one sigma bond and one pi bond.
Triple bonds (C≡C): shortest and strongest — one sigma bond and two pi bonds.
Common MCAT Mistakes
Mixing up bonding/antibonding with sigma/pi. These are two separate classification systems. Bonding vs. antibonding is about interference type and orbital energy (stabilizing vs. destabilizing); sigma vs. pi is about overlap geometry (head-to-head vs. sideways). A bond can be sigma or pi and still occupy a bonding molecular orbital.
Treating a triple bond as three identical bonds. A triple bond is not three equivalent bonds — it's one sigma bond plus two pi bonds, and the pi bonds form differently (sideways p-orbital overlap) and are individually weaker than the sigma bond.
Forgetting a pi bond needs a sigma bond first. Pi bonds can't form or exist on their own — they require the internuclear framework a sigma bond provides. There's no such thing as a molecule with a pi bond but no sigma bond between the same two atoms.
Assuming any orbital overlap stabilizes a molecule. Only electrons in bonding orbitals add stability. Electrons occupying antibonding orbitals destabilize the interaction, regardless of how much orbital overlap occurs.
MCAT-Style Concept Check
Question: A carbon-carbon triple bond (C≡C), such as the one found in acetylene, consists of which combination of sigma and pi bonds?
A) Three sigma bonds
B) One sigma bond and one pi bond
C) One sigma bond and two pi bonds
D) Two sigma bonds and one pi bond
Answer: C
Explanation: Every bond—single, double, or triple—contains exactly one sigma bond, since a pi bond cannot form without the internuclear framework a sigma bond provides. A triple bond adds two pi bonds on top of that one sigma bond, giving one sigma and two pi bonds total. (A ignores that pi bonds require sideways p-orbital overlap, not head-to-head overlap; B describes a double bond; D isn't a bond composition that occurs, since only one sigma bond forms per bonded pair of atoms.)
FAQ
What's the difference between a bonding and an antibonding molecular orbital?
A bonding molecular orbital forms from constructive interference (same-sign wave functions) of two atomic orbitals and is lower in energy and more stable. An antibonding molecular orbital forms from destructive interference (opposite-sign wave functions) and is higher in energy and destabilizing.
What's the difference between a sigma bond and a pi bond?
A sigma bond forms from direct, head-to-head overlap of orbitals along the internuclear axis and is the strongest type of covalent bond. A pi bond forms from sideways overlap of two parallel p orbitals, is weaker than a sigma bond, and cannot exist without an accompanying sigma bond.
How many sigma and pi bonds are in a double bond versus a triple bond?
A double bond has one sigma bond and one pi bond. A triple bond has one sigma bond and two pi bonds. A single bond has only one sigma bond and no pi bonds.
Why are triple bonds shorter and stronger than single bonds?
A triple bond has the same one sigma bond as a single bond, plus two additional pi bonds. Each added pi bond pulls the bonded atoms closer together and adds bond strength, which is why bond order correlates directly with both shorter bond length and greater bond strength.
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