Computational Chemistry

60 lessons, pages 4101–4160.

Computational Chemistry: Questions and Scales — Choosing electronic-structure, statistical-mechanical or dynamical models for a chemical question
From the Molecular Hamiltonian to Predictions — Kinetic and potential-energy terms in the nonrelativistic molecular Schrödinger equation
The Born–Oppenheimer Approximation — Separating nuclear and electronic motion and recognizing breakdowns of that separation
Wavefunctions, Observables and Variational Bounds — Expectation values, normalization and why variational energies lie above the exact ground state
Antisymmetry and Slater Determinants — Pauli exclusion, spin orbitals and exchange in many-electron wavefunctions
Hartree–Fock Self-Consistent Fields — Mean-field orbitals, Fock operators and iterative convergence
What Hartree–Fock Misses — Electron correlation energy and the distinction between exchange and dynamical correlation
Atomic Orbital Basis Functions — Slater-type and Gaussian-type functions as approximations to molecular orbitals
Basis-Set Size and Systematic Improvement — Minimal, split-valence and correlation-consistent basis families
Polarization Functions — Higher-angular-momentum flexibility for bonds, lone pairs and molecular response
Diffuse Functions — Representing spatially extended density in anions, weak complexes and excited states
Basis-Set Superposition Error — Artificial stabilization of complexes and the counterpoise diagnostic
Basis-Set Convergence and Extrapolation — Separating basis incompleteness from method error in a computed energy
Post-Hartree–Fock Correlation Methods — Configuration interaction, perturbation and coupled-cluster ideas at a conceptual level
Møller–Plesset Perturbation Theory — MP2 correlation corrections, useful cases and failure modes
Coupled-Cluster Theory — The exponential cluster ansatz and why CCSD(T) is a benchmark for suitable single-reference systems
Multireference Electronic Structure — Near-degenerate configurations, bond breaking and active-space reasoning
Density-Functional Theory Foundations — Electron density as the basic variable and the Kohn–Sham construction
Exchange–Correlation Functionals — Local, gradient-corrected, meta-GGA and hybrid approximations
Exact Exchange and Hybrid DFT — Mixing Hartree–Fock exchange with density-functional terms and its consequences
Dispersion Corrections in DFT — Long-range London forces, empirical corrections and nonlocal functionals
Self-Interaction and Delocalization Errors — Spurious fractional-charge behavior and its effect on barriers and charge transfer
Choosing an Electronic-Structure Method — Balancing system size, electronic character, accuracy targets and computational cost
Geometry Optimization — Energy gradients, convergence thresholds and local minima
Conformational Searching — Finding chemically relevant minima before comparing computed properties
Hessian Matrices and Vibrational Frequencies — Second derivatives, normal modes and the signature of a stationary point
Zero-Point Energy and Thermal Corrections — Converting electronic energies into enthalpies and free energies under stated approximations
Frequency Scaling and Anharmonicity — Why harmonic predictions differ from measured vibrational spectra
Computing Reaction Energies — Balanced stoichiometry, consistent methods and cancellation of electronic-energy errors
Computing Barrier Heights — Transition-state energies, thermal corrections and sensitivity to electronic structure
Implicit Solvent Models — Continuum dielectric treatments and the limits of cavity-based solvation
Explicit Solvent and Hydrogen-Bond Networks — Microscopic solvent configurations, sampling and local chemical effects
Solvation Free Energies and Thermodynamic Cycles — Connecting gas-phase calculations to solution reactions with consistent standard states
Computing pKa Values — Acid–base free-energy cycles, proton conventions and uncertainty
Noncovalent Interaction Energies — Hydrogen bonding, dispersion and electrostatics without basis-set artifacts
Population Analysis and Partial Charges — Why atomic charges are model-dependent descriptors rather than direct observables
Molecular Orbitals and Density of States — Interpreting computed orbital energies and avoiding overinterpretation
Computed IR and Raman Spectra — Normal-mode assignments, intensities and comparison with experiment
Computing NMR Shielding and Shifts — Magnetic response, reference compounds and solvent or conformer effects
Excited States with TDDFT — Vertical excitations, oscillator strengths and common failure modes
Wavefunction-Based Excited-State Methods — Configuration interaction and equation-of-motion concepts for electronic spectra
Spin States and Open-Shell Systems — Spin multiplicity, broken-symmetry solutions and spin contamination
Relativistic Effects in Heavy-Element Chemistry — Scalar-relativistic and spin–orbit effects on structure and spectra
Periodic Electronic-Structure Calculations — Unit cells, reciprocal space, k-point sampling and plane-wave basis sets
Pseudopotentials and Core Approximations — Replacing core electrons while retaining valence chemistry and assessing transferability
Surface Slabs and Adsorption Energies — Periodic surface models, vacuum spacing and consistent adsorption-energy definitions
Classical Molecular Mechanics — Force-field terms for bonds, angles, torsions and nonbonded interactions
Parameterizing and Validating Force Fields — Training data, transferability and tests against independent observables
Molecular Dynamics: Equations of Motion — Newtonian trajectories, finite time steps and numerical integration
Temperature and Pressure Control in MD — Thermostats, barostats and the statistical ensembles they approximate
Periodic Boundaries and Long-Range Forces — Minimum-image conventions, cutoffs and electrostatic summation
Sampling, Equilibration and Autocorrelation — Why trajectory length does not equal independent-sample count
Free-Energy Sampling — Umbrella sampling, thermodynamic integration and potential of mean force
QM/MM Multiscale Modeling — Combining quantum reactive regions with a classical environment
Machine-Learned Interatomic Potentials — Training on electronic-structure data, domain of validity and uncertainty
Uncertainty and Error Budgets in Computation — Method, basis, sampling and experimental-comparison uncertainty
Benchmarking Against Experiment — Comparable observables, standard states and independent validation sets
Reproducible Computational Workflows — Recording structures, charge, spin, software settings and convergence evidence
Responsible Interpretation of Computed Results — Distinguishing model predictions from measurements and reporting limitations
Computational Chemistry: Unit Review — Selecting and evaluating electronic-structure and simulation methods for chemical questions