Constructing Molecular Orbital Diagrams for Diatomics

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MO-diagrams diatomics bond-order paramagnetism energy-levels

Core Idea

Molecular orbital (MO) diagrams are energy-level diagrams that show how atomic orbitals on separate atoms combine to form molecular orbitals shared across the molecule. For homonuclear diatomics, atomic orbitals of the same symmetry mix to produce bonding (lower energy) and antibonding (higher energy) MOs, and the filling order follows Aufbau, Pauli, and Hund principles. Bond order = (bonding electrons - antibonding electrons)/2 predicts bond strength and existence; the diagram also reveals magnetic properties directly, since unpaired electrons in degenerate MOs produce paramagnetism. A key subtlety is the s-p mixing (orbital ordering switch) that occurs for diatomics lighter than O2, where the sigma-2p orbital rises above the two pi-2p orbitals.

How It's Best Learned

Construct MO diagrams for the full series Li2 through Ne2, filling electrons and computing bond orders at each step. Compare predicted magnetic behavior (paramagnetic vs diamagnetic) to experimental data -- the O2 case is the classic validation.

Common Misconceptions

Explainer

From your study of quantum chemistry foundations and molecular orbital theory, you know that electrons in molecules occupy orbitals that extend over the entire molecule, not just individual atoms. A molecular orbital (MO) diagram is the visual tool for organizing these orbitals by energy and seeing how they arise from atomic orbital combinations. Building one for a homonuclear diatomic like O₂ or N₂ follows a systematic procedure that, once mastered, provides immediate predictions about bond strength, bond order, and magnetic behavior.

Start by placing the atomic orbital energy levels for each atom on the left and right sides of the diagram. For second-row diatomics, you use the 2s and 2p orbitals. Orbitals combine according to symmetry: the two 2s orbitals form a σ₂s (bonding) and σ*₂s (antibonding) pair. The 2p orbitals split by their orientation relative to the internuclear axis. The two p orbitals pointing along the axis (pz) combine to form σ₂p and σ*₂p, while the perpendicular pairs (px, py) form two degenerate π₂p (bonding) and π*₂p (antibonding) pairs. Every atomic orbital that goes in produces one bonding and one antibonding MO — orbital count is conserved.

The critical subtlety is the s-p mixing (also called s-p hybridization in the MO context). For lighter diatomics — Li₂ through N₂ — the 2s and 2p energy levels on the atoms are close enough that the σ₂s and σ₂p orbitals interact, pushing σ₂p up in energy above the π₂p orbitals. This gives the ordering: σ₂s < σ*₂s < π₂p < σ₂p < π*₂p < σ*₂p. For O₂ and F₂, the larger 2s-2p energy gap reduces this mixing, and the "normal" ordering holds: σ₂p drops below π₂p. Getting this switch right is essential — it determines whether B₂ and C₂ are paramagnetic or diamagnetic.

Once the energy levels are set, fill electrons from the bottom up following the Aufbau principle, Pauli exclusion (two electrons per orbital, opposite spins), and Hund's rule (fill degenerate orbitals singly before pairing). Then calculate bond order = (bonding electrons − antibonding electrons)/2. For O₂, you fill 12 electrons and get bond order 2 (a double bond), but the diagram also reveals two unpaired electrons in the degenerate π*₂p orbitals — correctly predicting that O₂ is paramagnetic, a fact that Lewis structures cannot explain. For N₂, bond order is 3 (a triple bond) with no unpaired electrons (diamagnetic). Ne₂ gives bond order 0 — confirming that neon does not form a stable diatomic. The MO diagram thus unifies bond strength, bond existence, and magnetic properties in a single framework.

Practice Questions 5 questions

Prerequisite Chain

Counting to 10Counting to 20Understanding ZeroThe Number ZeroCounting to FiveOne-to-One CorrespondenceCombining Small Groups Within 5Addition Within 10Addition Within 20Two-Digit Addition Without RegroupingTwo-Digit Addition with RegroupingAddition Within 100Repeated Addition as MultiplicationMultiplication Facts Within 100Division as Equal SharingDivision as Grouping (Measurement Division)Division: Grouping (Repeated Subtraction) ModelDivision: Fair Sharing ModelDivision as Equal SharingDivision as GroupingBasic Division FactsDivision Facts Within 100Two-Digit by One-Digit DivisionDivision with RemaindersRemainders and Quotients in DivisionDivision Word ProblemsIntroduction to Long DivisionFactors and MultiplesPrime and Composite NumbersEquivalent FractionsRelating Fractions and DecimalsDecimal Place ValueReading and Writing DecimalsComparing and Ordering DecimalsAdding and Subtracting DecimalsMultiplying DecimalsDividing DecimalsDividing FractionsMixed Number ArithmeticOrder of OperationsInteger Order of OperationsVariable ExpressionsCombining Like TermsOne-Step EquationsTwo-Step EquationsSolving Multi-Step EquationsEquations with Variables on Both SidesAngle Pairs: Complementary, Supplementary, and VerticalParallel Lines and TransversalsCorresponding AnglesAlternate Interior AnglesTriangle Angle Sum TheoremExterior Angle TheoremTriangle Inequality TheoremSimilar Triangles: AA SimilaritySimilar Triangles: SSS and SAS SimilarityProportions in Similar TrianglesRight Triangle Trigonometry IntroductionTrigonometric Ratios ReviewRadian MeasureConverting Between Degrees and RadiansThe Unit CircleGraphing Sine and CosineGraphing Tangent and Reciprocal Trigonometric FunctionsDerivatives of Trigonometric FunctionsAntiderivativesIterated Integrals and Fubini's TheoremDouble Integrals in Cartesian CoordinatesDouble Integrals over Rectangular RegionsDouble Integrals in Polar CoordinatesDouble Integrals: Definition and SetupIterated Integrals and Fubini's TheoremDouble Integrals over Rectangular RegionsDouble Integrals over General RegionsApplications of Double Integrals: Area, Mass, and MomentsTriple Integrals in Cartesian CoordinatesTriple Integrals in Cylindrical and Spherical CoordinatesChange of Variables and the Jacobian DeterminantApplications of Triple Integrals: Volume and MassVector Fields and Their RepresentationsLine Integrals of Vector FieldsGreen's TheoremSurface Integrals and Flux of Vector FieldsSurface Integrals and Flux of Vector FieldsDivergence Theorem: Flux and OutflowDivergence TheoremElectric FluxGauss's LawConductors in Electrostatic EquilibriumCapacitance and CapacitorsDielectricsDielectric Constant and Relative PermittivityElectric Field Inside Dielectric MaterialsDielectric Materials and PolarizationDielectric Susceptibility and PermittivityEnergy Density in Electric FieldsElectric Current and Current DensityElectrical Resistance and ResistivityOhm's Law and Circuit ElementsElectromotive Force (EMF) and BatteriesKirchhoff's Circuit Laws: Voltage and CurrentDC Circuit Network Analysis MethodsTransient Response in RC CircuitsRC CircuitsLC and RLC CircuitsAC Circuits: FundamentalsImpedance and ReactanceAC Power and ResonanceElectromagnetic WavesThe Electromagnetic SpectrumBlackbody Radiation and Planck's LawPhotoelectric EffectThe Photon: Light as QuantaCompton ScatteringWave-Particle Dualityde Broglie WavelengthHeisenberg Uncertainty PrincipleWavefunction and the Born RuleThe Schrödinger EquationState Vectors and WavefunctionsQuantum SuperpositionQuantum EntanglementBell Theorem and Bell InequalitiesPostulates of Quantum MechanicsScattering TheoryIntroduction to Scattering TheoryPartial Wave Analysis in ScatteringSpin Angular MomentumElectron Spin and Intrinsic Magnetic MomentStern-Gerlach Experiment: Spin Quantization and MeasurementElectron Diffraction and Matter Wave PropertiesDavisson-Germer Experiment: Crystal Diffraction of ElectronsElectron Diffraction and Matter Wave InterferenceWavefunctions and Probability Density InterpretationQuantum Superposition and Linear Combinations of StatesQuantum Operators and ObservablesCanonical Commutation Relations and UncertaintyHeisenberg Uncertainty Principle and Measurement LimitsTime-Independent Schrödinger Equation and EigenvaluesHydrogen Atom in Quantum MechanicsSpectral Lines and Energy TransitionsSelection Rules for Atomic TransitionsLS and jj Coupling Schemes in Multi-Electron AtomsPauli Exclusion Principle and Antisymmetric WavefunctionsElectron Configuration and the Aufbau PrincipleThe Periodic Table and Atomic Electronic StructureThe Periodic TableElectron ConfigurationQuantum Chemistry FoundationsHydrogen Atom Wavefunctions and Atomic OrbitalsThe Variational Principle and Trial WavefunctionsMolecular Orbital Theory: LCAO-MOConstructing Molecular Orbital Diagrams for Diatomics

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