About

Bond order quantifies the net bonding interactions between two atoms in a molecule. It is calculated from Molecular Orbital Theory (MOT) as N_b − N_a2, where N_b is the count of electrons in bonding molecular orbitals and N_a is the count in antibonding orbitals. A bond order of 0 means the molecule does not exist under normal conditions. Fractional bond orders (e.g., 1.5 in NO) are physically meaningful and correlate with intermediate bond lengths. Errors in electron counting propagate directly: misassigning one electron shifts the bond order by 0.5, which can flip a stability prediction entirely.

This calculator accepts raw electron counts or common molecule presets. It derives bond order, bond type classification, relative stability ranking, and magnetic character (paramagnetic vs. diamagnetic). The magnetic determination requires knowledge of unpaired electrons, which this tool computes from the orbital filling sequence. Note: the tool assumes ground-state configurations and does not account for excited states or relativistic effects in heavy elements.

Formulas

The bond order is defined by Molecular Orbital Theory as:

B.O. = N_b − N_a2

Where N_b = number of electrons in bonding molecular orbitals and N_a = number of electrons in antibonding molecular orbitals (σ^*, π^*).

Bond classification follows from the result:

{

B.O. = 0 → No stable bond0 < B.O. < 1 → Fractional / Partial bondB.O. = 1 → Single bondB.O. = 2 → Double bondB.O. = 3 → Triple bond

Magnetic character is determined by unpaired electrons in antibonding orbitals. If unpaired electrons > 0, the species is paramagnetic. If all electrons are paired, it is diamagnetic.

Reference Data

Molecule / Ion	Total e⁻	N_b	N_a	Bond Order	Bond Length (pm)	Bond Energy (kJ/mol)	Magnetic
H₂	2	2	0	1.0	74	436	Diamagnetic
He₂	4	2	2	0.0	-	-	Does not exist
Li₂	6	4	2	1.0	267	105	Diamagnetic
Be₂	8	4	4	0.0	-	-	Does not exist
B₂	10	6	4	1.0	159	290	Paramagnetic
C₂	12	8	4	2.0	124	602	Diamagnetic
N₂	14	10	4	3.0	110	945	Diamagnetic
O₂	16	10	6	2.0	121	498	Paramagnetic
F₂	18	10	8	1.0	142	159	Diamagnetic
Ne₂	20	10	10	0.0	-	-	Does not exist
NO	15	10	5	2.5	115	631	Paramagnetic
CO	14	10	4	3.0	113	1072	Diamagnetic
O₂⁻	17	10	7	1.5	126	395	Paramagnetic
O₂²⁻	18	10	8	1.0	149	204	Diamagnetic
O₂⁺	15	10	5	2.5	112	643	Paramagnetic
N₂⁺	13	9	4	2.5	112	841	Paramagnetic
N₂⁻	15	10	5	2.5	119	-	Paramagnetic
H₂⁺	1	1	0	0.5	106	256	Paramagnetic
H₂⁻	3	2	1	0.5	-	-	Paramagnetic
He₂⁺	3	2	1	0.5	108	230	Paramagnetic
CN⁻	14	10	4	3.0	117	887	Diamagnetic

Frequently Asked Questions

Molecular Orbital Theory places two electrons in degenerate π*₂p antibonding orbitals. By Hund's rule, these electrons occupy separate orbitals with parallel spins rather than pairing. This gives O₂ two unpaired electrons, making it paramagnetic despite having a bond order of 2.0. Lewis structures fail to predict this because they do not model degenerate antibonding orbitals.

Yes. Species like NO and O₂⁺ have bond orders of 2.5. A fractional bond order indicates intermediate character between two integer bond types. For NO, the bond length (115 pm) falls between a typical N=O double bond (120 pm) and N≡O triple bond (106 pm). Fractional values arise when the bonding-antibonding difference is odd.

Bond order correlates positively with bond dissociation energy and inversely with bond length. For the oxygen series: O₂⁺ (B.O. 2.5, 112 pm), O₂ (B.O. 2.0, 121 pm), O₂⁻ (B.O. 1.5, 126 pm), O₂²⁻ (B.O. 1.0, 149 pm). Each 0.5 decrease in bond order increases the length by roughly 5 - 23 pm.

Yes. For homonuclear diatomics up to and including N₂ (Z ≤ 7), the σ₂p orbital lies above the π₂p orbitals in energy due to s-p mixing. For O₂ and beyond (Z ≥ 8), s-p mixing diminishes and σ₂p drops below π₂p. This switch affects electron configuration and magnetic predictions. The calculator presets use the correct ordering for each molecule.

A bond order of 0 means bonding and antibonding contributions cancel exactly. The molecule has no net stabilization relative to separated atoms. Species like He₂ and Be₂ have bond order 0 and do not form stable molecules under standard conditions. He₂ has been detected only in extremely cold supersonic jets with binding energy under 0.001 kJ/mol.

For heteronuclear diatomics like CO and NO, the MO diagram is similar to homonuclear molecules of comparable total electron count. CO (14 electrons) uses the same filling as N₂. NO (15 electrons) adds one electron to a π* antibonding orbital. The key rule: any orbital with an asterisk (*) in its label is antibonding. Count electrons in starred orbitals for N_a and unstarred for N_b.