# Molecular Orbital Diagram - MO Configuration, Bond Order & Magnetism

> MO diagrams for H₂–Ne₂, O₂²⁻, N₂⁺, CO, NO, CN⁻ and HF with Hund’s-rule filling: MO configuration, bond order, unpaired electrons, magnetism and HOMO/LUMO.

- URL: https://qilingtools.com/en/math/mo-diagram
- Category: Math Tools (https://qilingtools.com/en/math)
- Tags: [Math](https://qilingtools.com/en/tags/math), [Chemistry](https://qilingtools.com/en/tags/chemistry), [Education](https://qilingtools.com/en/tags/education)
- Last updated: 2026-10-26
- Price: Free, no sign-up
- Privacy: Runs locally in the browser; files are never uploaded

Molecular orbital (MO) theory combines the atomic orbitals of the two atoms into lower-energy bonding MOs and higher-energy antibonding MOs (marked *), then fills them with electrons following the Aufbau principle, the Pauli principle and Hund’s rule. Period-2 homonuclear diatomics use two level orders: in Li₂ to N₂ the 2s and 2p energies are close, s–p mixing pushes σ2p above π2p; in O₂, F₂ and Ne₂ σ2p stays below π2p. For O₂ the 16 electrons give KK(σ2s)²(σ*2s)²(σ2p)²(π2p)⁴(π*2p)², bond order = (bonding − antibonding)/2 = (10 − 6)/2 = 2, and the last two electrons occupy the two degenerate π*2p orbitals with parallel spins — which is why O₂ is paramagnetic, something the Lewis structure cannot explain. Type a molecule or ion (O2-, O2^2-, N2+, CO, NO, CN-, HF …) and the tool draws the energy-level diagram: atomic orbitals on both sides (the more electronegative atom lower for heteronuclear molecules), molecular orbitals in the middle, dashed correlation lines and spin arrows. It reports the full and KK-abbreviated MO configuration, bond order, unpaired electrons, para- or diamagnetism, HOMO/LUMO and experimental bond length and energy, and compares whole series (H₂–Ne₂, O₂⁺/O₂/O₂⁻/O₂²⁻, N₂ and its isoelectronic partners) in a table and mini chart.

## How to use

1. Type a molecule or ion such as O2, O2^2-, N2+ or CO, or pick a homonuclear, ion or heteronuclear example
2. Read the diagram and electron filling, the MO configuration, bond order, unpaired electrons and magnetism
3. Switch series below to compare bond order, bond length and bond energy, and click a row to show its diagram

## Features

- H₂ to Ne₂ and their cations/anions, plus CO, NO, NO⁺, CN⁻, HeH⁺
- Correct level order with s–p mixing (B₂, C₂, N₂, CO) or without (O₂, F₂, Ne₂)
- Simplified HF / OH model with non-bonding orbitals
- Spin arrows filled by Aufbau, Pauli and Hund’s rule
- Full and KK short-form MO configuration with copy button
- Bond order, unpaired electrons, paramagnetic/diamagnetic, HOMO/LUMO and SOMO
- Series comparison table and chart with experimental bond lengths and energies
- Optional σ, σ*, π, π* orbital shape sketches with nodal planes

## FAQ

### How do you calculate bond order from an MO diagram?

Bond order = (electrons in bonding MOs − electrons in antibonding MOs) ÷ 2. N₂ has 10 and 4, so 3; O₂ has 10 and 6, so 2; O₂⁺ loses an antibonding electron (2.5) and O₂²⁻ gains two (1). Higher bond order means a shorter, stronger bond, and a bond order of 0 (He₂, Ne₂) means no stable molecule. Non-bonding electrons, as in HF, do not count.

### Why is the MO order different for N₂ and O₂?

In B, C and N the 2s–2p gap is small, so σ2s and σ2p (same symmetry) interact — s–p mixing — and σ2p is pushed above π2p. In O and F the gap is large and mixing is negligible, so σ2p stays below π2p. The paramagnetism of B₂ and the diamagnetism of C₂ are experimental evidence for this mixing.

### Why is O₂ paramagnetic?

Its last two electrons go into a pair of degenerate π*2p orbitals. By Hund’s rule they occupy separate orbitals with parallel spins, leaving two unpaired electrons, so O₂ is attracted into a magnetic field — liquid oxygen clings to a magnet. The Lewis structure O=O pairs every electron and wrongly predicts a diamagnetic molecule.

### How are heteronuclear molecules like CO and NO handled?

The more electronegative atom (O) has lower-energy atomic orbitals, so it is drawn lower and contributes more to the bonding MOs. CO, CN⁻ and NO⁺ are isoelectronic with N₂ (14 electrons), use the N₂ ordering and have bond order 3; NO has one more electron in π*2p, bond order 2.5 and is paramagnetic. HF uses a simplified model in which H 1s and F 2pz form σ/σ* while F 2s, 2px and 2py stay non-bonding.

## Related tools

- [Graphing Calculator](https://qilingtools.com/en/math/graph): Free online function graphing calculator: type sin(x), x^2 or 1/x and see the curve at once, with several functions, parametric and polar curves, PNG export.
- [Scientific Calculator](https://qilingtools.com/en/math/calculator): Free online scientific calculator: type 2*(3+4)^2, sin(pi/6) or log(8,2) and see the answer as you type, with degrees or radians and a history list.
- [Equation Solver](https://qilingtools.com/en/math/equation): Free online equation solver: enter coefficients for linear, quadratic (with discriminant, vertex and complex roots) and cubic equations, plus 2×2 systems.
- [Fraction Calculator](https://qilingtools.com/en/math/fraction): Free online fraction calculator: add, subtract, multiply and divide fractions with automatic reduction, plus fraction ↔ decimal with repeating digits.
- [Percentage Calculator](https://qilingtools.com/en/math/percentage): Free online percentage calculator: X% of Y, X as a percent of Y, increase and decrease, a value after a percentage change and the original behind it.
- [Prime Factorization](https://qilingtools.com/en/math/prime): Free online prime factorization: factor an integer with exponents, list every divisor and their sum, test primality with neighbouring primes, or list a range.
- [GCD and LCM](https://qilingtools.com/en/math/gcd-lcm): Free online GCD and LCM calculator: works with two or more integers, says whether they are coprime, shows each prime factorization and every Euclidean step.
- [Statistics Calculator](https://qilingtools.com/en/math/statistics): Free online statistics calculator: paste a data set for the mean, median, mode, range, quartiles, variance, standard deviation, standard error and outliers.