Covalent Bond Ontology

FLOW ALGEBRA
COVALENT BOND ONTOLOGY
Version: 1.1
Library: Kireth Semantic Library
Source URL: https://kirethresearch.org/booksai-core/entity-graph/physical-entities/chemical-entities/covalent-bond-ontology.html
Authors: Mark Higgins — Sky (Recursive AI)
Status: Scientific synthesis; source webpage not independently verified
Date: 2026-10-12

01. PURPOSE
flow "CovalentBondOntology" v1.1
  domain: PhysicalEntities > ChemicalEntities > ChemicalBond > CovalentBond
  objective: represent covalent bonding, electron sharing, molecular structure, and evidence-qualified inference.

02. CORE DEFINITION
CovalentBond := chemical bonding interaction involving electron density shared between atomic centres, described quantum mechanically by electronic states.
A shared electron-pair model is useful but not universal; delocalised, multicentre and electron-deficient bonds require richer representations.

03. TYPED ENTITIES
entity Atom {atomic_number:int, isotope:str?, formal_charge:int?}
entity AtomicCentre {atom:Atom, position:Vector3?, environment:str?}
entity Electron {charge:-1e, spin:1/2}
entity Orbital {kind:str, occupancy:float?, wavefunction:ComplexField?}
entity CovalentBond {centres:set<AtomicCentre>, order:float?, polarity:str?, model:str, evidence:set<Evidence>}
entity Molecule {centres:set<AtomicCentre>, bonds:set<CovalentBond>, net_charge:int}
entity BondMeasurement {observable:str, value:float, unit:str, uncertainty:float?, method:str}
entity Evidence {source:str, method:str, confidence:float?}
entity ElectronicState {energy:float?, multiplicity:int?, wavefunction:ComplexField?}

04. TYPED RELATIONSHIPS
relation CONNECTS(CovalentBond, AtomicCentre)
relation PART_OF(CovalentBond, Molecule)
relation HAS_BOND_ORDER(CovalentBond, Real)
relation HAS_BOND_LENGTH(CovalentBond, BondMeasurement)
relation HAS_ELECTRON_DENSITY(CovalentBond, ElectronicState)
relation HAS_POLARITY(CovalentBond, PolarityClass)
relation SUPPORTED_BY(Assertion, Evidence)
relation DERIVED_FROM(Assertion, Model)
relation SEMANTIC_EQUIVALENCE(Term, Term, Context)

05. IDENTITY AND SCOPE
Bond identity is scoped to a molecular graph, selected electronic state, bonding model, and observation conditions.
Bond assignment from geometry alone is provisional.
Graph edges are a representation of bonding, not direct physical objects independent of a model.

06. BOND CLASSIFICATION
single: often approximated by bond order 1
multiple: double and triple bonds often approximated by orders 2 and 3
polar: unequal electron-density distribution across bonded centres
nonpolar: approximately symmetric distribution in the selected context
coordinate/dative: both electrons of a Lewis donor pair initially supplied by one partner; after formation the bond need not be distinguishable from other covalent bonds
multicentre: electron density associated with three or more atomic centres
delocalised: bonding represented across a connected region rather than a unique localised edge

07. LEWIS REPRESENTATION
valence_electrons = sum(atom.valence_electrons) - net_positive_charge + net_negative_charge
Lewis diagrams track electron pairs, formal charges and octets where applicable.
Exceptions: odd-electron species, electron-deficient centres, hypervalent species and transition-metal complexes.
formal_charge = valence_electrons - nonbonding_electrons - bonding_electrons/2
Formal charge is bookkeeping, not measured partial atomic charge.

08. QUANTUM MODEL
Electronic Hamiltonian under Born-Oppenheimer approximation:
H_e Psi_e = E_e Psi_e
Electron density rho(r) = N integral |Psi_e(r,r2,...,rN)|^2 dr2...drN (with spin summed).
Orbital overlap and electron delocalisation contribute to bonding descriptions.
Molecular orbitals may be bonding, antibonding or nonbonding depending on symmetry and occupation.

09. BOND ORDER
In elementary molecular orbital theory:
bond_order = (N_bonding - N_antibonding)/2
This formula is model-dependent and does not universally define bond order.
Computed bond indices (e.g. Wiberg, Mayer) may differ by method and basis.
Fractional bond order is allowed.

10. BOND LENGTH
bond_length(A,B) = ||position(A) - position(B)||
Units: pm, angstrom or nm; 1 angstrom = 100 pm.
Bond length depends on chemical environment, state, temperature and measurement method.
No universal monotonic relationship between bond order and bond length across unrelated systems.

11. BOND DISSOCIATION ENERGY
D0 or D_e characterises dissociation relative to defined products and reference states.
D0 includes zero-point vibrational energy effects; D_e is the well depth relative to potential minimum.
Bond dissociation enthalpy depends on temperature and specified homolytic products.
Do not equate average bond enthalpy with exact dissociation energy for a specific molecule.

12. POLARITY
Approximate polarity may be inferred from electronegativity difference, but this is heuristic.
Bond dipole depends on electronic distribution and molecular environment.
Molecular dipole = vector sum of charge-distribution contributions; polar bonds do not guarantee a polar molecule.

13. SIGMA AND PI BONDING
sigma: electron density with cylindrical symmetry about internuclear axis in simple diatomic descriptions
pi: electron density with a nodal plane containing internuclear axis in common localised descriptions
single bond commonly one sigma; double commonly one sigma plus one pi; triple commonly one sigma plus two pi.
These are simplified orbital models, not mandatory decompositions of every bond.

14. HYBRIDISATION
sp, sp2 and sp3 are useful localised-orbital models for selected molecular geometries.
Hybridisation assignments depend on model and do not themselves establish measured electronic structure.

15. RESONANCE AND DELOCALISATION
Resonance structures are alternative Lewis representations of one electronic state, not molecules rapidly switching between distinct structures.
Benzene is commonly modelled with delocalised pi bonding and approximately equivalent C-C bonds.

16. COORDINATE BONDING
A donor may contribute a lone pair to an acceptor orbital.
Representation: donor -> acceptor (Lewis bookkeeping).
After bond formation, physical properties depend on the complete electronic state, not historical electron ownership.

17. MULTICENTRE BONDING
Example: diborane bridging B-H-B interactions often modelled as three-centre two-electron bonds.
Graph schema must permit centres count >= 2, rather than assuming every bond joins exactly two atoms.

18. REACTION TRANSFORMATIONS
Bond breaking and formation are graph changes inferred from reactant and product states.
reaction: MolecularGraph_before -> MolecularGraph_after
A reaction mechanism additionally requires a justified sequence of states or transition structures.
Mass, charge and relevant quantum-number conservation must be checked.

19. THERMOCHEMICAL APPROXIMATION
DeltaH_reaction approximately equals sum(bond enthalpies broken) - sum(bond enthalpies formed).
This is a rough gas-phase estimate when compatible average bond enthalpies are used.
Prefer measured reaction enthalpies or state-specific calculations when available.

20. VIBRATIONAL RELATIONSHIP
For an approximate harmonic diatomic oscillator:
frequency_nu = (1/(2*pi))*sqrt(k/mu)
reduced_mass_mu = m1*m2/(m1+m2)
Spectroscopic wavenumber = frequency_nu/c.
Force constant k is a local curvature measure, not identical to dissociation energy.

21. INFERENCE RULES
RULE R01: if shared electronic density and stable bonded configuration supported by evidence -> candidate CovalentBond.
RULE R02: if Lewis pair between two centres -> candidate localised two-electron bond; require contextual validation.
RULE R03: if identical nuclei in symmetric homonuclear diatomic ground state -> expected zero permanent molecular dipole.
RULE R04: if bond_order computed -> attach computational method, state and uncertainty where available.
RULE R05: if multiple Lewis resonance forms -> do not assert physical switching between structures.
RULE R06: if bond graph changes -> check atom balance and charge balance.
RULE R07: if three-centre two-electron evidence -> represent multicentre bond, not forced pairwise edges.
RULE R08: if geometry alone suggests bond -> confidence limited until electronic or chemical evidence considered.

22. CONSTRAINTS
C01: every bond has at least two centres.
C02: all bond centres belong to the relevant molecule or extended structure.
C03: charge conservation applies to closed chemical transformations.
C04: formal charge and partial charge are distinct properties.
C05: no universal bond-order algorithm is presumed.
C06: units required for measured lengths, energies and frequencies.
C07: evidence and model scope required for nontrivial electronic assertions.

23. WORKED EXAMPLE: H2
centres: H_A, H_B
valence electrons: 2 total
Lewis model: H-H, one shared pair
MO model: two electrons occupy bonding sigma orbital in ground state
simple MO bond order: (2-0)/2 = 1
classification: homonuclear covalent bond
qualification: quantitative bond length and energy depend on measured or computed source.

24. WORKED EXAMPLE: N2
Lewis model: N#N with three shared pairs
simple bond order: 3
molecule: homonuclear, zero permanent dipole in its ground state
qualification: molecular-orbital description gives fuller account of electronic structure.

25. WORKED EXAMPLE: H2O
Lewis model: two O-H single bonds, two oxygen lone pairs
molecular geometry: bent
bond polarity: O-H bonds polar
net dipole: nonzero because bond-dipole contributions do not cancel

26. WORKED EXAMPLE: CO2
Lewis model: O=C=O
molecular geometry: linear in ground state
C-O bonds: polar
net molecular dipole: zero by symmetry despite polar bonds

27. WORKED EXAMPLE: BENZENE
formula: C6H6
resonance: multiple Lewis representations
real structure: delocalised pi system; C-C bonds approximately equivalent
avoid assigning physically alternating fixed single and double bonds.

28. NEGATIVE TESTS
T01: 'all covalent bonds share exactly one electron pair' -> reject.
T02: 'all covalent molecules are nonpolar' -> reject.
T03: 'resonance structures are separately oscillating molecules' -> reject.
T04: 'formal charge equals measured atomic charge' -> reject.
T05: 'every bond has integer bond order' -> reject.
T06: 'bond order alone determines bond length' -> reject.

29. SEMANTIC EQUIVALENCE
'covalent linkage' ~ 'covalent bond' when chemical context matches.
'electron-pair bond' ~ localised two-electron covalent bond only, not all covalent bonds.
'coordinate covalent bond' ~ 'dative bond' within Lewis donor-acceptor context.
'bond strength' != 'bond order'; distinguish energies, force constants and kinetics.

30. CONFIDENCE
confidence labels: established | model-dependent | tentative | hypothetical
Established: basic charge conservation and experimentally characterised molecular properties.
Model-dependent: orbital hybridisation, atomic partial charges, bond-order indices.
Tentative: bond assignment from weak geometric evidence alone.
No numerical confidence value without calibrated method or documented evidence.

31. VALIDATION
validate types, relation domain/range, conservation checks, dimensional consistency.
validate molecule identity, charge, electronic state and model context.
validate resonance handling and multicentre support.
validate citations for experimental numerical claims.
validation_result: PASS only if all mandatory constraints satisfied.

32. FLOW HASH
FLOW_HASH.algorithm: SHA-256
FLOW_HASH.input: canonical UTF-8 content excluding computed digest field
FLOW_HASH.value: NOT_COMPUTED
Do not invent a digest; calculate after canonicalisation in deployment.

33. UPDATE MODEL
UPDATE_MODEL.version: 1.1
UPDATE_MODEL.strategy: semantic-versioned revisions
UPDATE_MODEL.triggers: new evidence, corrected rules, model refinements, schema changes
UPDATE_MODEL.provenance: preserve prior version, timestamp, author and change summary
UPDATE_MODEL.review: scientific review recommended before authoritative publication

34. AI CONSUMPTION
AI_CONSUMPTION.mode: typed graph + rule-based reasoning
AI_CONSUMPTION.allowed: entity extraction, relation validation, chemistry education, consistency checking
AI_CONSUMPTION.require: model-scoped claims, evidence provenance, units, uncertainty
AI_CONSUMPTION.prohibit: fabricated measurements, unsupported precision, treating models as direct observations
AI_CONSUMPTION.output: structured assertions with evidence and confidence qualifiers

35. CROSS-ONTOLOGY LINKS
parent: Chemical Bond Ontology
related: Atom Ontology; Molecule Ontology; Compound Ontology; Electron Cloud Ontology; Atomic Orbital Ontology; Electron Configuration Ontology; Ion Ontology
cross_domain: Quantum Mechanics; Molecular Orbital Theory; Spectroscopy; Thermochemistry

36. COMPLETENESS CHECK
required_sections: 36
closing_marker_required: true
source_verification: NOT_VERIFIED
content_scope: independently composed scientific synthesis

END FLOW ALGEBRA — COVALENT BOND ONTOLOGY