Free Energy Calculations

Compute ΔG of binding, solvation, or mutation via alchemical transformations — coupling/decoupling atoms along a λ pathway. Gold standard for lead optimization in drug discovery: accuracy ~1 kcal/mol for congeneric series.

When to Use This Skill

• Predict ΔΔG_bind between two ligands (RBFE / lead optimization)
• Compute absolute ΔG_bind of a ligand to a protein (ABFE)
• Calculate ΔG_solvation or ΔG_hydration for ADME
• Rank compounds from a small congeneric series (~5-50 molecules)
• Validate force field parameters against experimental affinities
• Analyze convergence of FEP simulations (MBAR, overlap matrix)

Key Methods

Method	Estimator	Windows	Notes
FEP (Zwanzig)	Exponential avg	Any	High variance; avoid for large ΔG
TI	Numerical integration of ⟨∂H/∂λ⟩	10-20	Requires smooth integrand
BAR	Bennett Acceptance Ratio	Adjacent pairs	Better than TI for same data
MBAR	Multistate BAR	All pairs	Best variance; recommended
RBFE	Relative: A→B via alchemical	12-24 λ	Lead optimization
ABFE	Absolute: ligand → unbound	~20 λ	More expensive, independent

Accuracy Expectations

System	Typical error	Sim. time per edge
Congeneric RBFE (neutral)	0.5-1.5 kcal/mol	5-10 ns/window
RBFE with charge change	1-3 kcal/mol	10-20 ns/window
ABFE	1-3 kcal/mol	20-50 ns/window
Solvation ΔG	0.3-1.0 kcal/mol	2-5 ns/window

Quick Start

# pymbar: MBAR from energy matrix (u_kln)
import numpy as np
from pymbar import MBAR

# u_kln[k, l, n] = u_l(x_n^k) / kBT
# k: state from which sample was drawn
# l: state at which energy is evaluated
# n: sample index

K = 12  # number of lambda windows
N_k = np.array([1000] * K)  # samples per window

# u_kln shape: (K, K, max(N_k))
mbar = MBAR(u_kln, N_k)
results = mbar.compute_free_energy_differences()

dG = results['Delta_f'][0, -1]           # ΔG (kBT units)
ddG = results['dDelta_f'][0, -1]         # uncertainty
kBT = 0.5961  # kcal/mol at 298 K

print(f"ΔG = {dG * kBT:.2f} ± {ddG * kBT:.2f} kcal/mol")

Router — What to Read

Task	Reference
FEP/TI/BAR/MBAR theory, thermodynamic cycles, alchemical path	references/fep-theory.md
OpenMMTools: AlchemicalFactory, ThermodynamicState, MCMC sampling	references/openmmtools-alchemical.md
RBFE protocol: edge network, protein-ligand, results	references/rbfe-protocol.md
ABFE: restraints, double-decoupling, standard state correction	references/abfe-protocol.md
pymbar, overlap matrix, convergence, uncertainty, phase space	references/pymbar-analysis.md

Software Stack

Package	Install	Role
pymbar	pip install pymbar	MBAR/BAR/FEP estimators
openmmtools	conda install -c conda-forge openmmtools	Alchemical factories, MCMC
perses	conda install -c conda-forge perses	RBFE pipeline (OpenMM-native)
openfe	pip install openfe	FE campaign management (Lomap + OpenMM)
alchemtest	pip install alchemtest	Test datasets for FE code
lomap2	pip install lomap2	Ligand network RBFE planning

Related Skills

• force-fields — system parameterization; OpenFF Sage for ligands
• docking — starting poses for ABFE; initial ranking before FEP
• mdanalysis — trajectory analysis from FEP runs
• scientific-skills:rowan — cloud FEP without local HPC