Computational Chemistry

What a computed number means, and when to disbelieve it

About this course

Computing chemistry on the potential energy surface — geometry optimisation, force fields and molecular dynamics, free energy, Hartree-Fock, correlated methods and DFT, solvation, docking and machine-learned potentials, judged against benchmarks.

What you will be able to do

  • Locate minima and transition states on a potential energy surface and verify them
  • Explain why only energy differences are meaningful, and use error cancellation deliberately
  • Run and interpret force-field molecular dynamics and free-energy calculations
  • Choose a wavefunction method, basis set and functional, and state the errors each introduces
  • Assess solvation models, docking scores and machine-learned potentials against benchmarks

What this course covers

  • The central thesis: model's question vs. yours
  • The potential energy surface as a construct
  • The Born-Oppenheimer bargain and its expiry
  • The dimensionality problem: surfaces that cannot be mapped
  • Why the field is tractable: soft coordinates and error cancellation
  • Precision vs. accuracy in computed numbers; method spread is not an error bar
  • Restraints as part of the surface, not a view of it
  • Practical checklist for evaluating a computed number
  • Force field parameter space and the rules-vs-data reality
  • Force field functional form and its deliberate absences
  • Coverage signalling: MMFF refusal vs UFF generation
  • The silent MMFF-to-UFF fallback and its logging fix
  • Conformer disagreement and hydrogen-bonding molecules
  • Fitted methods have no self-uncertainty term — the central result
  • The continuum solvation trade-off
  • Born's formula and the continuum model structure
  • Dielectric saturation of the continuum model
  • Cavity radius sensitivity and the 13-to-1 ratio
  • Circularity of fitting radii to hydration energies
  • Hydrogen bonds and the cost of isotropy
  • Applying continuum solvation critically: worked case and checklist
  • Exponential scaling of the exact wave function
  • Hartree-Fock approximation and the self-consistent field
  • Correlation energy as the name of Hartree-Fock's error
  • Bond dissociation failure of restricted Hartree-Fock
  • Unrestricted Hartree-Fock and spin contamination
  • Error cancellation and the limits of agreement with experiment
  • The Hohenberg-Kohn Theorem and the DFT Prize
  • The Unknown Exact Functional and What Must Hide Inside It
  • Thomas-Fermi Kinetic Energy Failure and the Kohn-Sham Fix
  • Self-Interaction Error in Approximate Exchange Functionals
  • Error Cancellation and the Absence of a Variational Bound
  • Practical Use of DFT Without a Bound: Diagnosis and External Validation
  • Local optimization and the stationary-point problem
  • Conformational census: minima count and global-minimum probability
  • Restart arithmetic and its circular requirement
  • Two-stage conformational search and its hidden ordering assumption
  • Hessian eigenvalues and stationary-point classification
  • Finite-difference Hessian bug and external validation
  • The timescale gap in molecular dynamics
  • Velocity Verlet and the shadow Hamiltonian
  • Stability edge and thermostat masking
  • Exponential barrier crossing and sampling collapse
  • Confident numbers from unsampled trajectories
  • Practical diagnostics for sampling adequacy
  • Ranking vs. accuracy as independent axes
  • Error-to-spread ratio governs ranking power
  • AUC interpretation and base-rate dependence
  • Decoy set composition controls the metric
  • What docking is and why it remains useful
  • Recurring structure: fitted metrics certify themselves
  • Basis set incompleteness error and its scale
  • Why Gaussian basis functions are used
  • Basis set convergence and the angular-momentum wall
  • Basis set superposition error (BSSE) and counterpoise correction
  • Better basis sets have larger superposition error
  • Two independent axes of error and the rule against single-axis improvement
  • Critical appraisal checklist for reported binding energies
  • Jacob's Ladder hierarchy: structure and claim
  • Code validation via the uniform-gas limit
  • The first rung is real: gradient corrections vs. local density
  • Ordering inside a rung inverts with system
  • Absence of a variational guarantee on the DFT ladder
  • Benchmark errors scale with system, not just functional
  • Cancellation as a sharp, structural effect
  • Absolute computed energies and moving zeros
  • The isodesmic criterion and why it fails
  • The homodesmotic criterion: counting environments
  • Mechanism of cancellation: local error terms
  • Consistency vs accuracy: limits of benchmarking
  • Reference-scheme strategy for unbalanced reactions
  • Semi-local functional structure and its two blindnesses
  • Debugging by checking explanations against data
  • Dispersion as an exact zero, not a small number
  • Decay-ratio test distinguishing overlap from power-law
  • Self-interaction as delocalization error (directional bias)
  • Why the self-interaction correction is rarely used
  • Two failures as one: non-locality as the common cause
  • Dispersion correction as a force field bolted on
  • Practical checklist and 'first principles' reassessment
  • The Zwanzig Relation and Exponential Averaging
  • Insertion–Deletion Asymmetry in Sampling Direction
  • Staging and the Overlap as the Sizing Quantity
  • Umbrella Sampling, WHAM Reconstruction, and Window Overlap
  • Orthogonal Slow Coordinates and Conditional Free Energies
  • Practical Validation Checklist for Free Energy Calculations
  • The correlation ladder and its computational costs
  • Local correlation and density-fitting approximations
  • What a systematic hierarchy actually buys
  • Performance of the ladder on a known exact system
  • Size consistency and why CISD was abandoned
  • Single-reference breakdown and the reference-weight diagnostic
  • Practical reading of correlated calculations: a capstone checklist
  • The repulsive wall failure case
  • Interior accuracy and the learning curve
  • Label quality ceiling: random vs. systematic error
  • Extrapolation failure: silent settling outside training data
  • The novelty warning term and its practical use
  • Speed crossover and when to build a machine-learned potential
  • Four diagnostic questions for evaluating ML potential results
  • The scale problem: why cancellation is compulsory
  • Error cancellation: mechanism and magnitude
  • Partial cancellation and derivable error sign
  • Complete cancellation failure at bond dissociation
  • Checks that cannot fail and method disagreement as diagnostic
  • The four-question procedure for evaluating a computed number

Syllabus

  1. The Surface and Its Energies

    1. L1 · What a Computed Number Is: the Surface and the Bargain
    2. L2 · Geometry Optimisation: Minima, Saddles, and the Ones You Did Not Find
    3. L3 · Energies Are Differences: Cancellation and Reference States

  2. Force Fields and Sampling

    1. L4 · Force Fields: Fitting a Function to Chemistry
    2. L5 · Molecular Dynamics: Sampling and the Timescale You Cannot Reach
    3. L6 · Free Energy: You Only Get Back What You Pushed Along

  3. Wavefunction Methods

    1. L7 · Hartree-Fock: the Approximation That Defines the Error
    2. L8 · Basis Sets: the Other Error, and an Attraction That Is Not Chemistry
    3. L9 · The Correlation Hierarchy, and the Wall at the Fifth Power

  4. Density Functional Theory

    1. L10 · DFT: an Exact Theory with an Unknown Ingredient
    2. L11 · Choosing a Functional: the Ladder That Is Not a Ladder
    3. L12 · Dispersion and Self-Interaction: Failures to Know By Name

  5. Environments, Scale and Trust

    1. L13 · Solvation: Replacing an Ocean with a Constant
    2. L14 · Docking and Scoring: Ranking Without Computing
    3. L15 · Machine-Learned Potentials: Interpolation at Scale
    4. L16 · Benchmarks, Error Cancellation, and When to Disbelieve a Number