Poster abstracts
Poster number 37 submitted by Narayanan Puthillathu
Benzene Dimer XSAPT Mixture-of-Experts: Statistical Mechanics and Information-Theoretic Diagnostics
Narayanan Puthillathu (Biophysics Interdisciplinary graduate program), John Herbert (Chemistry and Biochemistry )
Abstract:
We evaluate two-expert MoE surrogates trained separately for XSAPT electrostatics, exchange, induction, exchange-induction, and dispersion over 765 benzene-dimer geometries. Exchange, i.e. short-range Pauli repulsion, is predicted accurately (MAE 0.63 kcal mol^-1, R^2 0.997), whereas electrostatics, induction, and dispersion remain much less accurate (MAEs 16.5-23.7 kcal mol^-1). Errors rise at shorter center-of-mass separation, with Spearman rho(|error|, d_com) = -0.83 to -0.89 for the long-range terms versus -0.66 for exchange, indicating failure near the repulsive wall where overlap and charge penetration matter. Although total interaction energies show strong Pearson correlation (r = 0.954), the weak rank correlation (rho = 0.516) reveals poor ordering of benzene-dimer stabilities.
To interpret these failures, we apply statistical-mechanics and information-theoretic diagnostics to routing and error ensembles over configurational space, not to bulk thermodynamic phases of benzene. A routing scan identifies a crossover near 3.49 Angstrom with susceptibility peak 4.12, separating long-range van der Waals behavior from the short-range overlap regime. The gate shows replica-symmetry breaking (mean overlap 0.692) and a frozen fraction of 0.616. Exchange has the smallest fluctuation-dissipation-style ratio (nu = 5.01), whereas the other components are more volatile (36.6-50.4); dispersion has the shallowest surrogate free-energy landscape (flatness 1.71). Center-of-mass distance is the dominant geometric coordinate (mutual information 0.899 nats), and transfer entropy peaks for dispersion -> exchange (0.189 nats) when intermolecular approach is treated as pseudo-time, suggesting that errors in long-range correlation propagate into the short-range repulsive regime. These diagnostics connect ML failure modes directly to pi-stacking physic
Keywords: machine learning, Energy decomposition analysis, computational quantum chemistry