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Constructing Molecular Orbital Diagrams for Diatomics

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Quantum Chemistry FoundationsMolecular Orbital Theory: LCAO-MO→→Bonding and Antibonding Orbitals: Sigma, Pi, and the HOMO-LUMO GapExchange Integral and Chemical Bonding+1 more
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

Understanding Zero → The Number Zero → Counting to Five → Counting to 10 → Counting to 20 → Counting a Set of Objects Up to 20 → Cardinality: The Last Number Counted → Matching Numerals to Quantities → Subitizing Small Quantities → Addition Within 10 → Number Bonds to 10 → Addition Within 20 → Doubles and Near Doubles → Doubles Facts Within 10 → Near Doubles Facts Within 20 → Mental Math Strategies for Addition → Mental Math: Adding and Subtracting Tens → Addition Within 100 → Repeated Addition as Multiplication → Multiplication as Equal Groups → Multiplication: Arrays → Basic Multiplication Facts (0s, 1s, 2s, 5s, 10s) → Multiplication Facts Within 100 → Division as Equal Sharing → Division as Grouping (Measurement Division) → Division: Grouping (Repeated Subtraction) Model → Division: Fair Sharing Model → Division as Equal Sharing → Division as Grouping → Basic Division Facts → Division Facts Within 100 → Multiplication and Division Fact Families → Relationship Between Multiplication and Division → Division Facts as Inverse of Multiplication → Remainders and Quotients in Division → Division Word Problems → Multi-Step Word Problems → Solving Multi-Step Word Problems → Multiplication Word Problems → Division Word Problems → Introduction to Long Division → Factors and Multiples → Prime and Composite Numbers → Equivalent Fractions → Relating Fractions and Decimals → Decimal Place Value → Integers and the Number Line → Comparing and Ordering Integers → Absolute Value → Adding Integers → Subtracting Integers → Multiplying Integers → Dividing Integers → Unit Rates → Proportions → Percent Concept → Converting Between Fractions, Decimals, and Percents → Operations with Rational Numbers → Two-Step Equations → Solving Multi-Step Equations → Equations with Variables on Both Sides → Angle Pairs: Complementary, Supplementary, and Vertical → Parallel Lines and Transversals → Corresponding Angles → Alternate Interior Angles → Triangle Angle Sum Theorem → Exterior Angle Theorem → Triangle Inequality Theorem → Similar Triangles: AA Similarity → Similar Triangles: SSS and SAS Similarity → Proportions in Similar Triangles → Right Triangle Trigonometry Introduction → Sine, Cosine, and Tangent Ratios → Trigonometric Ratios Review → Radian Measure → Converting Between Degrees and Radians → The Unit Circle → Graphing Sine and Cosine → Graphing Tangent and Reciprocal Trigonometric Functions → Derivatives of Trigonometric Functions → Antiderivatives → Indefinite Integrals → Basic Integration Rules → Riemann Sums → Definite Integral Definition → Double Integrals: Definition and Setup → Iterated Integrals and Fubini's Theorem → Double Integrals over Rectangular Regions → Double Integrals over General Regions → Applications of Double Integrals: Area, Mass, and Moments → Triple Integrals in Cartesian Coordinates → Triple Integrals in Cylindrical and Spherical Coordinates → Change of Variables and the Jacobian Determinant → Applications of Triple Integrals: Volume and Mass → Vector Fields and Their Representations → Line Integrals of Vector Fields → Work and Circulation → Line Integrals of Scalar and Vector Functions → Fundamental Theorem for Line Integrals → Conservative Vector Fields → Conservative Vector Fields and Potential Functions → Curl and Divergence of Vector Fields → Curl and Divergence → Divergence Theorem → Electric Flux and Divergence Theorem → Gauss's Law: Integral Form and Meaning → Solving Problems with Gauss's Law → Conductors in Electrostatic Equilibrium → Capacitance and Capacitors → Dielectrics → Dielectric Constant and Relative Permittivity → Electric Field Inside Dielectric Materials → Dielectric Materials and Polarization → Dielectric Susceptibility and Permittivity → Energy Density in Electric Fields → Electric Current and Current Density → Electrical Resistance and Resistivity → Ohm's Law and Circuit Elements → Electromotive Force (EMF) and Batteries → Kirchhoff's Circuit Laws: Voltage and Current → DC Circuit Network Analysis Methods → Transient Response in RC Circuits → RC Circuits → LC and RLC Circuits → AC Circuits: Fundamentals → Impedance and Reactance → AC Power and Resonance → Electromagnetic Waves → Postulates of Special Relativity → Time Dilation → Length Contraction → Lorentz Transformation → Relativistic Velocity Addition → Relativistic Momentum and Energy → Mass-Energy Equivalence and E=mc² → Photons as Particles with Energy and Momentum → Planck-Einstein Relation: Energy and Frequency → Photoelectric Effect → The Photon: Light as Quanta → Compton Scattering → Wave-Particle Duality → de Broglie Wavelength → The Schrödinger Equation → State Vectors and Wavefunctions → Quantum Superposition → Quantum Entanglement → Bell Theorem and Bell Inequalities → Postulates of Quantum Mechanics → Observables and Quantum Operators → Commutators and Commutation Relations → Quantum Angular Momentum → Quantum Mechanical Treatment of Hydrogen → Solving the Schrödinger Equation for Hydrogen Atom → Quantum Numbers → Electron Configuration → Atomic Orbitals → Quantum Chemistry Foundations → Hydrogen Atom Wavefunctions and Atomic Orbitals → Schrödinger Equation for Molecular Systems → The Variational Principle and Trial Wavefunctions → Molecular Orbital Theory: LCAO-MO → Constructing Molecular Orbital Diagrams for Diatomics

Longest path: 162 steps · 954 total prerequisite topics

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