A multiscale Hamiltonian framework for chemical interfaces: coupling quantum states, surface curvature, intermolecular interactions, and interfacial thermodynamics

Chemical interfaces involve a hierarchy of coupled phenomena spanning quantum confinement, interfacial geometry, electrostatic fields, molecular interactions, statistical mechanics, and macroscopic thermodynamics. Establishing a consistent connection among these levels remains a fundamental challenge in theoretical interface science. This work develops a multiscale Hamiltonian framework in which the quantum state of an interfacial system is formulated on a curved geometry and coupled to electrostatic, intermolecular, and thermodynamic degrees of freedom. Surface geometry enters the quantum description through the Laplace–Beltrami operator and the curvature-induced geometrical potential, while electrostatic interactions are described through a self-consistent Schrödinger–Poisson formulation extended to electrolyte-containing interfaces. London dispersion, specific Lewis acid–base interactions, residual polarization, exchange repulsion, and lateral interactions are incorporated as physically differentiated contributions, with an explicit reference-plus-residual construction introduced to prevent double counting between continuum electrostatics and additional interaction terms. A central distinction is established between fundamental quantum operators and experimentally parameterized coarse-grained interactions. In particular, Gutmann donor and acceptor descriptors retain their thermodynamic status, while the generalized five-parameter Lewis acid–base model provides an experimentally constrained effective contribution rather than a newly postulated microscopic quantum observable. Statistical mechanics subsequently connects the resulting interfacial energetics to finite-temperature ensemble properties and thermodynamic observables. The coupled equations are formulated within an explicit self-consistent computational architecture linking the quantum state, charge density, electrostatic potential, ionic distributions, geometry, and thermodynamic variables. Quantitative curvature analysis identifies the regimes in which geometrical quantum effects and electrostatic curvature become significant through their characteristic dependence on interfacial radius, particle mass, thermal energy, and Debye screening length. Computational tractability is further demonstrated through a self-consistent cylindrical Schrödinger–Poisson benchmark, for which electrostatic feedback produces a 9.58 meV shift in the lowest quantum level , compared with a −1.27 meV curvature-induced geometrical contribution for the representative nanoscale system considered. The framework recovers established planar, weak-coupling, and classical limits where the corresponding contributions become negligible. Experimental results from inverse gas chromatography, surface energetics, adsorption thermodynamics, and electrokinetic measurements provide independent constraints on the physical interaction sectors represented in the formulation. The resulting framework does not replace the established theories governing these individual regimes; rather, it provides a common multiscale architecture for connecting interfacial geometry, quantum states, physicochemical interactions, self-consistent electrostatics, and finite-temperature thermodynamics within explicitly stated assumptions and levels of description.