SAMTI: Sampling Adaptive Thermodynamic Integration for Alchemical Free Energy Calculations.

Accurate and efficient calculation of alchemical free energies is a critical challenge in computational chemistry, frequently hindered by the inherent limitations of conventional thermodynamic integration (TI) methods. These limitations include poor phase-space overlap between discrete alchemical states, inefficient allocation of computational resources, and a fundamental time scale separation between alchemical transformations and molecular conformational sampling, which collectively lead to slow convergence and high statistical uncertainty. This work presents sampling adaptive thermodynamic integration (SAMTI), a unified computational framework designed to systematically overcome these challenges. SAMTI synergistically integrates four components: (1) serial tempering (ST) with a fine-grained alchemical grid to ensure phase-space continuity; (2) variance adaptive resampling (VAR) to dynamically allocate computational effort to high-uncertainty regions; (3) replica exchange (RE) to enhance conformational sampling; and (4) alchemical enhanced sampling (ACES) to resolve kinetic bottlenecks by selectively scaling torsional energy barriers. We evaluated SAMTI's performance against conventional TI across a benchmark suite of eight molecular systems of increasing complexity, including ion solvation, small molecule annihilation, and challenging protein-ligand transformations. The results demonstrate that SAMTI variants reduce statistical error by 40-75% and, for the most complex systems, the complete ST+VAR+RE (mACES) configuration consistently achieves chemical accuracy (σ