Molecular Orbital
Free molecular orbital calculator for diatomic molecules H₂ to Ne₂. Compute MO electron configuration, bond order, unpaired electrons, and magnetic properties using molecular orbital theory instantly.
About This Calculator
The Molecular Orbital Calculator analyzes the molecular orbital (MO) configuration of homonuclear diatomic molecules from hydrogen (H₂) through neon (Ne₂). Molecular orbital theory is a fundamental concept in quantum chemistry that describes how atomic orbitals combine to form molecular orbitals, determining the bonding characteristics, stability, and magnetic properties of molecules. This calculator visualizes the electron filling across all molecular orbitals and computes the key properties that emerge from the electron configuration.
The calculator uses two distinct MO filling orders depending on the molecule's atomic number. For molecules with atomic numbers up to 7 (B₂, C₂, N₂), the π(2p) orbitals are lower in energy than σ(2pz), following the order: σ(1s) → σ*(1s) → σ(2s) → σ*(2s) → π(2px) = π(2py) → σ(2pz) → π*(2px) = π*(2py) → σ*(2pz). For molecules with atomic numbers greater than 7 (O₂, F₂, Ne₂), σ(2pz) is lower than π(2p), following: σ(1s) → σ*(1s) → σ(2s) → σ*(2s) → σ(2pz) → π(2px) = π(2py) → π*(2px) = π*(2py) → σ*(2pz). The calculator applies Hund's rule when filling degenerate π orbitals, maximizing unpaired electrons for accurate magnetic property determination.
About Molecular Orbital Theory
Molecular orbital theory explains chemical bonding through the linear combination of atomic orbitals (LCAO). When two atomic orbitals combine, they form two molecular orbitals: a lower-energy bonding orbital and a higher-energy antibonding orbital (marked with an asterisk). Bonding orbitals concentrate electron density between nuclei, strengthening the bond, while antibonding orbitals create nodes that weaken it. The balance between bonding and antibonding electrons determines the bond order — a measure of bond strength and stability.
This tool is essential for chemistry students learning molecular orbital diagrams, instructors demonstrating MO theory concepts, and researchers analyzing bonding characteristics. Select a molecule from the dropdown to instantly see its MO configuration, bond order, and magnetic properties, with visual charts showing electron distribution across all molecular orbitals.
Frequently Asked Questions
What is a molecular orbital diagram?
A molecular orbital diagram shows the energy levels of molecular orbitals formed when atomic orbitals combine. Bonding orbitals are lower in energy and stabilize the molecule, while antibonding orbitals are higher in energy and destabilize it. The diagram helps determine bond order, bond strength, and magnetic properties of diatomic molecules.
How do you calculate bond order from molecular orbital configuration?
Bond order is calculated as half the difference between bonding and antibonding electrons: Bond Order = (Bonding Electrons - Antibonding Electrons) / 2. For example, N₂ has 10 bonding and 4 antibonding electrons giving a bond order of 3 (triple bond), while O₂ has 10 bonding and 6 antibonding electrons giving a bond order of 2 (double bond).
What determines whether a molecule is paramagnetic or diamagnetic?
A molecule is paramagnetic if it has unpaired electrons, making it attracted to magnetic fields. It is diamagnetic if all electrons are paired, making it weakly repelled by magnetic fields. For example, O₂ has two unpaired electrons in its π* antibonding orbitals, making it paramagnetic, while N₂ has all electrons paired, making it diamagnetic.
What is the difference between bonding and antibonding molecular orbitals?
Bonding molecular orbitals form when atomic orbitals combine constructively, concentrating electron density between nuclei and lowering energy. Antibonding molecular orbitals (marked with an asterisk *) form when atomic orbitals combine destructively, creating a node between nuclei and raising energy. Bonding orbitals stabilize molecules while antibonding orbitals destabilize them.
Why does O₂ have unpaired electrons but N₂ does not?
O₂ has 16 electrons total. After filling σ(1s), σ*(1s), σ(2s), σ*(2s), σ(2pz), and π(2p) orbitals, the remaining 2 electrons go into π* antibonding orbitals. According to Hund's rule, they occupy separate π* orbitals with parallel spins, giving two unpaired electrons. N₂ with 14 electrons fills completely through σ(2pz), leaving the π* orbitals empty, so all electrons are paired.
What is Hund's rule and how does it apply to molecular orbitals?
Hund's rule states that electrons fill degenerate (equal-energy) orbitals singly before pairing up, and all unpaired electrons have parallel spins. In molecular orbital theory, this applies to the π(2px) and π(2py) orbitals (and their antibonding counterparts), which are degenerate. When filling these orbitals, electrons occupy each orbital singly first, maximizing the number of unpaired electrons.
What is the molecular orbital electron configuration of N₂?
The molecular orbital electron configuration of N₂ is σ(1s)² σ*(1s)² σ(2s)² σ*(2s)² π(2px)² π(2py)² σ(2pz)². This gives 10 bonding and 4 antibonding electrons, a bond order of 3 (triple bond), and no unpaired electrons (diamagnetic). N₂ is one of the most stable diatomic molecules due to its triple bond.
Is this molecular orbital calculator free to use?
Yes, this molecular orbital calculator is completely free to use with no registration or hidden charges. You can select from common diatomic molecules or enter a custom electron count. The URL with your inputs can be shared for study groups or classroom use, making it ideal for chemistry students learning molecular orbital theory.