Model Dependence and Cancellation in a Fixed-Geometry Lactone Energy Cycle

A small signed energy response can conceal larger individual changes and may not transfer between computational models. We compare fixed lactone and methanolysis-product conformers through a balanced eight-state protonation-response cycle. Existing density-functional calculations give gas and implicit-methanol cycles of +18.327235 and +4.381410 kJ/mol. Matched 0.020 Å H-only displacements lower every cation energy but change the solvent cycle by −0.072625 kJ/mol. The four-arm first-order force-work prediction is −0.237920 kJ/mol, with a signed finite-step remainder of +0.165294 kJ/mol. A prospectively frozen challenge of 184 single-point calculations preserves qualitative medium attenuation in both tested approximate Hamiltonians but fails the complete predefined local-response rule: their solvent cycle changes become +0.047132 and +0.127370 kJ/mol. This distinguishes medium-response agreement from local-response transferability without establishing optimized structures or experimental accuracy. Original ωB97X with separately specified D3 dispersion and Becke–Johnson damping, def2-TZVP/def2-universal-jkfit density fitting and the solvation model based on density were used in PySCF 2.14.0. Stored gradients and accepted endpoints define the force-work analysis. GFN1-xTB and GFN2-xTB in xTB 6.7.1 evaluate gas and analytical linearized Poisson–Boltzmann methanol models across nine signed displacements, with 974/2030-point endpoint surface-grid controls. An independent raw-output reader and actual moved-package reproductions check the deterministic analysis; no fitting, optimization or uncertainty calibration is performed.