Computational Chemist's Notebook
# work in progress, big project, I am excited, stay tuned ...
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Handwritten notes on the core ideas behind probability, fluctuations, free energy, many-body systems, collective variables, free-energy methods, biasing, rare events, and machine-learning approaches
Microstates, Macrostates, Phase Space and Ergodicity - [PDF]
Probability Distribution and Expectation Values - [PDF]
Entropy (Gibbs. vs. Boltzmann vs. Shannon) - [PDF]
Partition Function - [PDF]
Free Energy: Helmholtz and Gibbs - [PDF]
The Ensembles (NVT, NPT, μVT) - [PDF]
Thermodynamic Potentials and Legendre Transformation - [PDF]
Chemical Potential - [PDF]
Boltzmann Distribution - [PDF]
Fluctuations and Thermodynamics Observables - [PDF]
Time Correlation Function - [PDF]
The Fluctuation-Dissipation Theorem - [PDF]
Central Limit Theorem and Error Estimation - [PDF]
Linear Response Theory (Kubo Formalism) - [PDF]
Detailed Balance - [PDF]
Radial Distribution Function - [PDF]
Structure Factor - [PDF]
Potential of Mean Force and Free Energy Landscape - [PDF]
Ornstein-Zernlike Equation - [PDF]
Polymer Scaling Theory (Random Walks) - [PDF]
Order Parameters - [PDF]
Landau Free Energy - [PDF]
The Ising Model - [PDF]
Mean Field Theory - [PDF]
The re-normalization Group - [PDF]
Brownian Motion and Langevin Equation - [PDF]
Fokker Plank Equation / Smoluchowski Equation - [PDF]
The Master Equation - [PDF]
Transition State Theory and Kramer's Rate Theory - [PDF]
Generalized Langevin Equation - [PDF]
Metropolis-Hasting Algorithm - [PDF]
Free-Energy Perturbation (Zwanzig Equation) - [PDF]
Thermodynamics Integration - [PDF]
Jarzynski Equality - [PDF]
Coarse-Graining Strategies - [PDF]
Overlap Problem and Rare Event Sampling - [PDF]
Markov Process and Transition Matrices - [PDF]
Diffusion, Einstein Relation, and Green Kubo Relations - [PDF]
Finite Size Effects - [PDF]
Monte Carlo Simulation - [PDF]
Molecular Dynamics Simulation - [PDF]
Coarse Grain Simulation - [PDF]
Long Range Forces - [PDF]
Periodic Box, Periodic Boundary Condition, and Minimum Image Convention - [PDF]
Non Bonded Interactions - [PDF]
Analysis of Simulation Trajectories - [PDF]
Speed up Molecular Dynamics Code - [PDF]
Verlet/ Neighbor List - [PDF]
Link-Cell - [PDF]
Constrained Dynamics - [PDF]
Reaction Coordinates
Committor Probability
Metastability
Timescale Seperation
Autocorrelation Function
Covariance Matrix
Eigenvalues and Eigenvectors
Principal Component Analysis (PCA)
Time Independent Component Analysis (TICA)
Linear Discriminant Analysis (LDA) / Fisher Discriminant
Deep-LDA / Deep-TDA
Deep-TICA / VAMP
Descriptors / molecular representations
Bias potential
Importance Sampling
Reweighting
Effective Sample Size (ESS)
Distribution Overlap
Metadynamics
Well-tempered Metadynamics
On-the-fly Probability Enhanced Sampling (OPES)
Kernel Density Estimation (KDE)
Umbrella Sampling
Weighted Histogram Analysis Method (WHAM)
Multistate Bennett Acceptance Ratio
Surrogate Models + Uncertainity Quantification
Active Learning
Variational Enhanced Sampling
Transition Path Sampling
Markov State Model
Autoencoders for CV
State Predictive Information Bottleneck
Gaussian Process Regression
Minimum Energy Path
Normalizing Flows
Boltzmann Generators
Diffusion Models for Sampling
Generative CVs (RAVE)
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