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Computational Chemistry

Explore molecular questions through code. The Python pathway builds from chemical calculations towards molecular dynamics; MATLAB focuses on molecular structure, evidence, and modelling workflows.

What helps

Chemistry, algebra, and units provide useful context. Depending on the pathway, later work draws on thermodynamics, matrices, quantum ideas, and numerical modelling.

Python pathway

Programming Foundations / Practice rooms / Track curriculum and enrollment

  1. Atoms, Units & Stoichiometry

    Use mole counts, supplied atomic-mass tables and balanced equations to calculate product masses, limiting reactants, yields and concentrations. The formula dictionary must use the table's supported elements.

    • The Mole: 5 lessons
    • Molar Mass of Compounds: 5 lessons
    • Stoichiometry: 5 lessons
    • Solutions & Concentration: 5 lessons
    • Capstone: Stoichiometry Toolkit: 5 lessons

  2. The Periodic Table & Atomic Structure

    Count subatomic particles and isotope averages, distinguish shell capacity from subshell filling order, and connect hydrogen energy levels to light. The Element class implements explicitly restricted classification and occupancy models.

    • Subatomic Particles & Isotopes: 5 lessons
    • Electron Configuration: 5 lessons
    • Periodic Trends: 5 lessons
    • Light & Energy Levels: 5 lessons
    • Capstone: The Element Class: 5 lessons

  3. Bonding & Molecular Geometry

    Represent atomic coordinates with NumPy, measure distances and angles, and apply selected VSEPR lookups. The Molecule report composes the two specified bond measurements around a chosen center; it does not infer connectivity for arbitrary molecules.

    • Counting Electrons: 5 lessons
    • Atoms in 3D Space: 5 lessons
    • Bond Angles: 5 lessons
    • VSEPR Geometry: 5 lessons
    • Capstone: Geometry Analyzer: 5 lessons

  4. Thermodynamics

    Calculate heat, coefficient-weighted enthalpy and entropy changes, and Gibbs driving force at a stated temperature. Track J versus kJ and distinguish thermodynamic favorability from reaction speed.

    • Heat & Enthalpy: 5 lessons
    • Entropy: 5 lessons
    • Gibbs Free Energy: 5 lessons
    • Calorimetry: 5 lessons
    • Capstone: Thermo Calculator: 5 lessons

  5. Chemical Equilibrium

    Reactions do not always run to completion; they settle at equilibrium. Write the equilibrium constant, compare it to the reaction quotient to predict direction, set up ICE tables, and solve the resulting equations with a bisection root-finder you build from scratch. Le Chatelier predicts how the balance shifts under stress.

    • The Equilibrium Constant: 5 lessons
    • ICE Tables: 5 lessons
    • Root-Finding from Scratch: 5 lessons
    • Le Chatelier's Principle: 5 lessons
    • Capstone: Equilibrium Solver: 5 lessons

  6. Acids, Bases & pH

    Use dilute aqueous approximations to calculate strong-acid pH, weak-acid dissociation and buffer ratios. The titration chapter covers specified pre-equivalence points; the report dispatches among these finite models.

    • The pH Scale: 5 lessons
    • Weak Acids: 5 lessons
    • Buffers: 5 lessons
    • Titration: 5 lessons
    • Capstone: pH Calculator: 5 lessons

  7. Reaction Kinetics

    How fast does a reaction go? Kinetics measures and predicts rates. Write rate laws, apply the integrated forms for first, second, and zero order, capture temperature dependence with the Arrhenius equation, and integrate the rate equation numerically with Euler and Runge-Kutta methods you build yourself. The capstone is a decay simulator.

    • Rate Laws: 5 lessons
    • Integrated Rate Laws: 5 lessons
    • The Arrhenius Equation: 5 lessons
    • Numerical Integration: 5 lessons
    • Capstone: Decay Simulator: 5 lessons

  8. Quantum Chemistry & Spectroscopy

    Atoms and molecules absorb and emit light at sharp, quantized energies. Compute the energy levels of a particle in a box and of hydrogen, connect them to the light absorbed or emitted, and quantify absorption with the Beer-Lambert law. The finite-difference chapter solves the Schrodinger equation numerically with a matrix you build and diagonalize.

    • Quantization: 5 lessons
    • The Hydrogen Atom: 5 lessons
    • Beer-Lambert Absorption: 5 lessons
    • Solving Schrodinger Numerically: 5 lessons
    • Capstone: Spectroscopy Toolkit: 5 lessons

  9. Molecular Dynamics & Monte Carlo

    Simulate matter atom by atom. Model interactions with the Lennard-Jones potential, sum forces and energies across a system with numpy, advance time with the velocity-Verlet integrator, and sample configurations with the Metropolis Monte Carlo method. These are the two engines that power computational chemistry.

    • The Lennard-Jones Potential: 5 lessons
    • Energy of a System: 5 lessons
    • Velocity-Verlet Integration: 5 lessons
    • Monte Carlo Sampling: 5 lessons
    • Capstone: Monte Carlo Simulator: 5 lessons

  10. Capstone: A Molecular Dynamics Engine

    Assemble a small reduced-unit, nonperiodic Lennard-Jones simulation class. Compute forces, advance state with velocity Verlet, and record kinetic, potential and total energy. Validate energy error and time-step dependence instead of assuming exact conservation.

    • Representing the System: 5 lessons
    • Computing Forces: 5 lessons
    • The Velocity-Verlet Stepper: 5 lessons
    • Observables: 5 lessons
    • The Engine: 5 lessons

MATLAB pathway

Programming Foundations / Practice rooms / Track curriculum and enrollment

  1. Are These Really the Same Conformer?

    Build an identity-safe conformer comparison from local internal coordinates through proper rigid alignment, labelled distance audits, inertia evidence, and tolerance sensitivity. The final dossier distinguishes row permutation and rigid placement from genuine internal deformation.

    • Identity Before Geometry: 5 lessons
    • Internal Shape Evidence: 5 lessons
    • Remove Rigid Motion: 5 lessons
    • Challenge the Comparison: 5 lessons
    • Publish the Verdict: 5 lessons

  2. Where Does the Molecule Prefer to Sit?

    Build and compare potential-energy models, verify analytic derivatives independently, search with complete trajectory evidence, classify stationary-point curvature, expose initial-condition and step sensitivity, and publish a bounded potential-surface dossier.

    • Build the Energy Landscape: 5 lessons
    • Do Not Trust One Derivative: 5 lessons
    • Search with a Ledger: 5 lessons
    • A Stop Is Not a Minimum: 5 lessons
    • Map Before You Claim: 5 lessons

  3. Which Reaction Mechanism Fits the Evidence?

    Build mass-action mechanisms, integrate them with solver evidence, fit kinetic and Arrhenius parameters, compare competing integrated laws, expose stiffness and identifiability, and publish a bounded mechanism dossier.

    • Write the Mechanism Before Solving It: 5 lessons
    • Integrate with Evidence: 5 lessons
    • Fit Without Hiding Residuals: 5 lessons
    • Make Mechanisms Compete: 5 lessons
    • Publish Mechanism Evidence: 5 lessons

  4. Why Are Molecular Energies Quantized?

    Discretize one-dimensional quantum operators, solve and audit eigenstates, measure observable evidence, challenge grid and domain convergence, and construct a bounded Hückel molecular-orbital dossier.

    • Discretize the Quantum Operator: 5 lessons
    • Solve and Normalize the States: 5 lessons
    • Measure Quantum Evidence: 5 lessons
    • Challenge the Numerical Quantum Claim: 5 lessons
    • Build a Hückel Molecular-Orbital Model: 5 lessons

  5. What Is Hiding in the Spectrum?

    Build mass-weighted normal modes, turn sampled motion into a traceable FFT spectrum, resolve candidate bands, fit overlapping signals and mixtures, and publish uncertainty-aware vibrational assignments.

    • Build the Vibrational Model: 5 lessons
    • Turn Motion into a Spectrum: 5 lessons
    • Resolve the Bands: 5 lessons
    • Fit Overlapping Signals: 5 lessons
    • Assign the Spectrum Without Overclaiming: 5 lessons

  6. Will This Molecular Simulation Behave?

    Build periodic systems and Lennard-Jones forces, integrate velocity-Verlet trajectories, challenge energy and ensemble evidence, measure radial structure, and publish a finite-size-aware simulation dossier.

    • Build the Periodic System: 5 lessons
    • Compute Pair Forces: 5 lessons
    • Integrate the Motion: 5 lessons
    • Audit the Ensemble: 5 lessons
    • Measure Liquid Structure: 5 lessons

  7. Can a Molecule Solve Its Own Electrons?

    Validate supplied electronic integrals, solve generalized orbitals, construct density and Fock matrices, retain a complete damped SCF history, challenge guess and basis sensitivity, and publish a bounded RHF dossier.

    • Gate the Electronic Model: 5 lessons
    • Solve the Generalized Orbitals: 5 lessons
    • Build Density and Fock: 5 lessons
    • Make SCF Convergence Earn Its Name: 5 lessons
    • Challenge the Electronic Conclusion: 5 lessons

  8. Can a Molecular Ensemble Support Its Free Energy?

    Build a statistical-thermodynamics investigation from energy levels and Boltzmann populations through thermal observables, Metropolis sampling, autocorrelation and effective sample size, potentials of mean force, and a bounded free-energy dossier.

    • Build the Thermal Ensemble: 5 lessons
    • Read Thermal Observables: 5 lessons
    • Sample the Distribution: 5 lessons
    • Challenge the Chain: 5 lessons
    • Publish Free-Energy Evidence: 5 lessons

  9. What Does the Solvent Change?

    Build and challenge a solvation calculation from continuum electrostatics and nonpolar terms through thermodynamic integration, exponential reweighting, uncertainty, thermodynamic-cycle closure, model sensitivity, and a complete solvation dossier.

    • Build the Electrostatic Solvation Model: 5 lessons
    • Model Nonpolar Solvation: 5 lessons
    • Integrate Along a Coupling Path: 5 lessons
    • Challenge Exponential Reweighting: 5 lessons
    • Publish the Solvation Dossier: 5 lessons

  10. Which Molecules Should We Test Next?

    Build a molecular-design workflow from candidate and descriptor contracts through transparent surrogate validation, Pareto tradeoffs, predictive uncertainty, applicability domains, diverse batch selection, and a decision dossier that proposes experiments without giving away a winning design.

    • Build the Molecular Design Space: 5 lessons
    • Fit and Challenge the Surrogate: 5 lessons
    • Map the Pareto Front: 5 lessons
    • Design Under Uncertainty: 5 lessons
    • Publish the Design Dossier: 5 lessons