{
  "id": "bond-order",
  "version": "3dd2e502a805",
  "status": "published",
  "name": "Bond Order Calculator",
  "question": "What is the bond order?",
  "summary": "Finds the bond order of a diatomic molecule or ion from H₂ to Ne₂ by filling its molecular orbitals, with its configuration and magnetism, or from counts of bonding and antibonding electrons.",
  "category": "chemistry",
  "subcategory": "atoms",
  "url": "https://www.acalculator.org/chemistry/bond-order-calculator",
  "markdown": "https://www.acalculator.org/chemistry/bond-order-calculator.md",
  "kind": "function",
  "method": "Bond order = (electrons in bonding orbitals − electrons in antibonding orbitals) ÷ 2. A diatomic molecule fills σ1s, σ*1s, σ2s, σ*2s, then π2p before σ2p for Li to N (σ2p before π2p for O, F, Ne), then π*2p and σ*2p.",
  "assumptions": [
    "Homonuclear diatomic molecules and ions from H₂ to Ne₂ with a charge from −2 to +2, in their ground state; 1 to 20 electrons.",
    "The two π2p orbitals and the two π*2p orbitals each fill one electron per orbital before pairing (Hund’s rule).",
    "A bond order above 0 means a stable bond is expected; 0 means none."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "from": {
        "title": "From",
        "description": "A diatomic molecule or ion of one element, or your own counts of bonding and antibonding electrons.",
        "type": "string",
        "enum": [
          "molecule",
          "counts"
        ]
      },
      "atom": {
        "title": "Molecule",
        "description": "The two-atom molecule of one element, from H₂ to Ne₂.",
        "type": "string",
        "enum": [
          "H",
          "He",
          "Li",
          "Be",
          "B",
          "C",
          "N",
          "O",
          "F",
          "Ne"
        ]
      },
      "q": {
        "title": "Charge",
        "description": "The charge of the molecule: 0, or from −2 to +2 for an ion such as O₂⁻ or N₂⁺.",
        "type": "integer",
        "minimum": -2,
        "maximum": 2
      },
      "nb": {
        "title": "Bonding electrons",
        "description": "Electrons in bonding molecular orbitals.",
        "type": "integer",
        "minimum": 0,
        "maximum": 40
      },
      "na": {
        "title": "Antibonding electrons",
        "description": "Electrons in antibonding (starred) molecular orbitals.",
        "type": "integer",
        "minimum": 0,
        "maximum": 40
      }
    }
  },
  "outputs": {
    "result": {
      "label": "Bond order",
      "description": "Half the difference between bonding and antibonding electrons.",
      "format": "text"
    },
    "order": {
      "label": "Bond order (number)",
      "description": "The bond order as a number.",
      "format": "number"
    },
    "bondingCount": {
      "label": "Bonding electrons",
      "description": "Electrons in bonding orbitals.",
      "format": "integer"
    },
    "antibondingCount": {
      "label": "Antibonding electrons",
      "description": "Electrons in antibonding orbitals.",
      "format": "integer"
    },
    "stability": {
      "label": "Stability",
      "description": "A bond order above 0 means a stable bond is expected; 0 means none.",
      "format": "text"
    },
    "configuration": {
      "label": "Molecular orbital configuration",
      "description": "The filled molecular orbitals and their electrons, lowest energy first.",
      "format": "text"
    },
    "unpaired": {
      "label": "Unpaired electrons",
      "description": "Electrons alone in a molecular orbital, by Hund’s rule.",
      "format": "integer"
    },
    "magnetism": {
      "label": "Magnetism",
      "description": "Paramagnetic with any unpaired electron, diamagnetic with none.",
      "format": "text"
    },
    "subject": {
      "label": "For",
      "description": "The molecule, or the electron counts the bond order is for.",
      "format": "text"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "from": "molecule",
      "atom": "O",
      "q": 0,
      "nb": 8,
      "na": 2
    },
    "outputs": {
      "result": "Bond order = 2",
      "order": 2,
      "bondingCount": 10,
      "antibondingCount": 6,
      "stability": "Above 0: a stable bond is expected; a higher bond order means a stronger bond.",
      "configuration": "(σ1s)² (σ*1s)² (σ2s)² (σ*2s)² (σ2p)² (π2p)⁴ (π*2p)²",
      "unpaired": 2,
      "magnetism": "Paramagnetic (2 unpaired electrons)",
      "subject": "O₂"
    },
    "text": "Bond order = 2 for O₂."
  },
  "examples": [
    {
      "given": {
        "from": "molecule",
        "atom": "O",
        "q": 0
      },
      "expect": {
        "order": 2,
        "unpaired": 2,
        "magnetism": "Paramagnetic (2 unpaired electrons)"
      },
      "source": "OpenStax, Chemistry 2e, §8.4 Molecular Orbital Theory (bond order = (bonding − antibonding electrons) ÷ 2), https://openstax.org/books/chemistry-2e/pages/8-4-molecular-orbital-theory, Example 8.6 (O₂): bond order 2, two unpaired electrons, paramagnetic"
    },
    {
      "given": {
        "from": "molecule",
        "atom": "N",
        "q": 0
      },
      "expect": {
        "order": 3,
        "unpaired": 0,
        "magnetism": "Diamagnetic (all electrons paired)"
      },
      "source": "OpenStax, Chemistry 2e, §8.4 Molecular Orbital Theory (bond order = (bonding − antibonding electrons) ÷ 2), https://openstax.org/books/chemistry-2e/pages/8-4-molecular-orbital-theory, Check Your Learning after Example 8.6 (N₂): bond order 3, diamagnetic"
    },
    {
      "given": {
        "from": "molecule",
        "atom": "C",
        "q": -2
      },
      "expect": {
        "order": 3,
        "bondingCount": 10,
        "antibondingCount": 4
      },
      "source": "OpenStax, Chemistry 2e, §8.4 Molecular Orbital Theory (bond order = (bonding − antibonding electrons) ÷ 2), https://openstax.org/books/chemistry-2e/pages/8-4-molecular-orbital-theory, Example 8.7 (C₂²⁻): bond order 3, six more bonding than antibonding electrons"
    },
    {
      "given": {
        "from": "molecule",
        "atom": "Be",
        "q": -2
      },
      "expect": {
        "unpaired": 2,
        "order": 1,
        "configuration": "(σ1s)² (σ*1s)² (σ2s)² (σ*2s)² (π2p)²"
      },
      "source": "OpenStax, Chemistry 2e, §8.4 Molecular Orbital Theory (bond order = (bonding − antibonding electrons) ÷ 2), https://openstax.org/books/chemistry-2e/pages/8-4-molecular-orbital-theory, Check Your Learning after Example 8.7 (Be₂²⁻): two unpaired electrons, paramagnetic; hand calculation in content.mdx: bond order (6 − 4) ÷ 2 = 1"
    },
    {
      "given": {
        "from": "molecule",
        "atom": "Be",
        "q": 0
      },
      "expect": {
        "order": 0,
        "stability": "Bond order 0: no stable bond is expected."
      },
      "source": "OpenStax, Chemistry 2e, §8.4 Molecular Orbital Theory (bond order = (bonding − antibonding electrons) ÷ 2), https://openstax.org/books/chemistry-2e/pages/8-4-molecular-orbital-theory, Table 8.3: Be₂ bond order 0, unstable"
    },
    {
      "given": {
        "from": "molecule",
        "atom": "F",
        "q": 0
      },
      "expect": {
        "order": 1,
        "unpaired": 0
      },
      "source": "OpenStax, Chemistry 2e, §8.4 Molecular Orbital Theory (bond order = (bonding − antibonding electrons) ÷ 2), https://openstax.org/books/chemistry-2e/pages/8-4-molecular-orbital-theory, Table 8.3: F₂ bond order 1"
    },
    {
      "given": {
        "from": "molecule",
        "atom": "H",
        "q": 1
      },
      "expect": {
        "order": 0.5,
        "result": "Bond order = 0.5",
        "unpaired": 1
      },
      "source": "OpenStax, Chemistry 2e, §8.4 Molecular Orbital Theory (bond order = (bonding − antibonding electrons) ÷ 2), https://openstax.org/books/chemistry-2e/pages/8-4-molecular-orbital-theory (bond order formula); hand calculation in content.mdx: (1 − 0) ÷ 2 = 0.5"
    },
    {
      "given": {
        "from": "counts",
        "nb": 8,
        "na": 2
      },
      "expect": {
        "order": 3,
        "result": "Bond order = 3"
      },
      "source": "OpenStax, Chemistry 2e, §8.4 Molecular Orbital Theory (bond order = (bonding − antibonding electrons) ÷ 2), https://openstax.org/books/chemistry-2e/pages/8-4-molecular-orbital-theory (bond order formula); hand calculation in content.mdx: (8 − 2) ÷ 2 = 3"
    }
  ],
  "sources": [
    "OpenStax, Chemistry 2e, §8.4 Molecular Orbital Theory: bond order = (bonding − antibonding electrons) ÷ 2, the molecular orbital energy order for second-period diatomics with s-p mixing for Li₂ to N₂ and none for O₂, F₂ and Ne₂, Table 8.3 (bond orders Li₂ 1, Be₂ 0, B₂ 1, C₂ 2, N₂ 3, O₂ 2, F₂ 1, Ne₂ 0), Example 8.6 (O₂: bond order 2, paramagnetic) and its Check Your Learning (N₂: 3, diamagnetic), Example 8.7 (C₂²⁻: 3) and its Check Your Learning (Be₂²⁻: 2 unpaired electrons). https://openstax.org/books/chemistry-2e/pages/8-4-molecular-orbital-theory (retrieved 2026-10-19)"
  ],
  "related": [
    "electron-configuration",
    "formal-charge",
    "valence-electrons",
    "electronegativity"
  ],
  "changelog": []
}