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Molecular Orbital Diagrams and Bond Order

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Molecular Orbital Theory: LCAO-MOOrbital Shapes and the Principal Quantum Number+2 more→→Configuration Interaction and Wavefunction ExpansionSelection Rules for Electronic Transitions
quantum bonding orbitals structure

Core Idea

Molecular orbital diagrams show how atomic orbitals combine to form bonding, antibonding, and nonbonding molecular orbitals in polyatomic molecules. Bond order—calculated as (bonding electrons − antibonding electrons) / 2—quantitatively relates orbital occupancy to bond strength and length. These diagrams provide a visual framework for understanding reactivity and spectroscopic properties.

How It's Best Learned

Construct MO diagrams for small molecules (O₂, NO, F₂) by starting with atomic orbital energy levels, applying orbital overlap principles, and comparing predictions to experimental bond lengths and magnetic properties (paramagnetism). Verify bond orders using photoelectron spectroscopy data.

Common Misconceptions

Explainer

From molecular orbital theory, you know that when atoms combine to form molecules, their atomic orbitals mix to produce new orbitals that belong to the molecule as a whole. A molecular orbital diagram is the visual tool that organizes this information: atomic orbital energy levels are drawn on the left and right sides, and the molecular orbitals that form from their combination are drawn in the center, with lines connecting each MO to its parent atomic orbitals. The vertical axis represents energy, and electrons are filled into the molecular orbitals from lowest to highest energy, following the Aufbau principle and Hund's rule — exactly as you do for atomic electron configurations.

When two atomic orbitals of similar energy and compatible symmetry overlap, they produce two molecular orbitals: one lower in energy than either parent (bonding) and one higher (antibonding). The bonding MO has constructive interference of the wavefunctions — electron density builds up between the nuclei, pulling them together. The antibonding MO has destructive interference — a node between the nuclei depletes electron density there, and electrons in this orbital actively weaken the bond. Some atomic orbitals may lack a symmetry-compatible partner and pass through unchanged as nonbonding orbitals, contributing neither to bond strength nor weakness.

The bond order — calculated as (number of bonding electrons − number of antibonding electrons) / 2 — quantifies the net bonding effect. For O₂, the diagram predicts a bond order of 2 (a double bond), consistent with its bond length and strength. But the diagram reveals something Lewis structures cannot: O₂ has two unpaired electrons in its degenerate π* antibonding orbitals, making it paramagnetic. This is one of the great triumphs of MO theory — it explains O₂'s magnetism, which Lewis dot structures incorrectly predict as a non-issue. Similarly, the MO diagram for NO shows an odd electron in a π* orbital, giving a bond order of 2.5 and explaining its radical character.

Building diagrams for second-row diatomics requires knowing one important detail: for Li₂ through N₂, the σ₂p orbital lies above the π₂p orbitals (due to s-p mixing), while for O₂ and F₂, the σ₂p drops below the π₂p. Getting this ordering right is essential for correct electron configurations and magnetic predictions. Beyond diatomics, MO diagrams extend to polyatomic molecules through group theory and symmetry-adapted linear combinations of atomic orbitals, but the core logic remains the same: identify the symmetry-compatible orbital interactions, rank the resulting MOs by energy, fill electrons, and read off bond orders and electronic properties. The diagram is not just a bookkeeping device — it is a map of molecular electronic structure that predicts stability, reactivity, and spectroscopic behavior.

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 → Molecular Orbital Diagrams for Polyatomic Molecules → Molecular Orbital Diagrams and Bond Order

Longest path: 164 steps · 972 total prerequisite topics

Prerequisites (4)

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