arXiv subjects

Kyunghoon Han

Publications and source records attributed to Kyunghoon Han.

5 recordsLinked to original sources

arXiv2026

Category Theoretic Framework for Chemistry I: a Tower of Chemistry

Many laws of chemistry are exact within a limited scope and acquire a separate caveat outside it, and the caveats are usually treated as unrelated. This work argues that they share one cause. Each caveat marks a point where a question is asked of a description too coarse to answer it: the question belongs to a richer level of structure than the description carries. To make these levels explicit, the paper builds a tower of categories over the free symmetric monoidal category of a Petri net, the simplest categorical presentation of a reaction network. The levels, from the bottom up, are stoichiometry, thermochemistry, equilibrium, reaction kinetics, reaction mechanism, molecular geometry, and electronic structure. Each adds one kind of chemical content over the level below, and a forgetful functor runs back down. One question runs through the tower: what can a level express that the level below cannot? Answering it places each measurable quantity at the level where it lives, and identifies the content the levels below could record but not account for. The method is then turned on with two pieces of known chemistry. It recasts a classical criterion for when a reaction network has a unique stable equilibrium, the deficiency-zero theorem, as the rigidity of a single forgetful fibre. It also follows one familiar reaction up the tower: the ring opening that the Woodward-Hoffmann rules govern. At each level, from stoichiometry to electronic structure, the reaction becomes a distinct categorical object.

physics.chem-ph↗

arXiv2026

Symplectic and Thermodynamically Consistent Molecular Dynamics in the Frequency Domain

We introduce Fourier integrator molecular dynamics (FIMD), a method for propagating selected vibrational motion of Hamiltonian systems stably and reversibly in time while analyzing and controlling dynamics in the frequency domain. This makes band selection and vibrational analysis features of the integrator rather than post-processing steps. We demonstrate the method with classical force fields, a machine-learned force field trained on quantum data, and semi-empirical quantum chemistry for CO$_2$ and the capped Ace--Phe--Tyr--NMe peptide. The method reproduces spectra within the chosen band, suppresses out-of-band response, reveals mode coupling, and demonstrates force-field dependence of spectral features, especially for the thermodynamically important low frequencies. FIMD offers an efficient and transparent way to probe the vibrational physics underlying spectroscopic and calorimetric observables.

physics.chem-ph↗

arXiv2026

Categorification of Chemical Reactions: a bottom-up tower from stoichiometry to quantum structure

Chemistry's rules carry exceptions: the octet rule, Hess's Law, detailed balance, orbital symmetry selection rules, all with disclaimers memorised separately. Their cause: a question from a richer structural level posed in the vocabulary of a simpler one, i.e. level incompleteness. This monograph makes the levels explicit, constructing a canonical tower of nine categorical levels from stoichiometry through thermochemistry, equilibrium, kinetics, electron-pushing mechanisms, stereochemistry, potential energy surfaces, and electronic structure to all-particle quantum mechanics. Each level emerges from pairs of reactions distinct yet indistinguishable at the previous level; the minimal extension resolving each ambiguity is provably unique, certified by a non-trivial cokernel in an automorphism exact sequence, and recovers Feinberg's deficiency theorems as homological corollaries. A perpendicular dimension: every ML model for chemistry (yield predictors, neural kinetic networks, equivariant force fields, learned wavefunctions) is a morphism in the Para-enrichment of one tower level, with equivariance and thermodynamic consistency as universal properties. Three incompleteness results (Eyring, Wegscheider, topological output gaps) apply to the current literature. The framework descends to code: an operational functor from a Para-enriched product of the first four levels into the Kleisli category of the probabilistic sub-monad of Haskell IO, instantiated as a simulator of the Briggs-Rauscher oscillating reaction: the first Kleisli semantics of Gillespie's next-reaction method and first Para application outside ML. The passage to all-particle quantum mechanics, Born-Oppenheimer as the classical limit of a continuous field of C*-algebras, remains the deepest open construction; four candidate conjectures including Woolley-Primas have obstructions the framework makes specific.

physics.chem-ph↗

arXiv2026

Partial Information Decomposition of Electronic Observables Along a Reaction Coordinate

A reaction-coordinate--resolved information-theoretic analysis of chemical reactivity is developed using mutual information and partial information decomposition (PID). Along an intrinsic reaction coordinate (IRC), a local empirical distribution is constructed at each position $s$ that couples a coarse-grained geometric progress variable (target) to two electronic readouts (sources), and the joint mutual information $I(T;X,Y)$ is decomposed into redundant, unique, and synergistic contributions using the Williams--Beer PID formalism. In the numerical demonstrations, the target is a binned bond-asymmetry coordinate $\xi=d_{\mathrm{C}\!-\!\mathrm{nuc}}-d_{\mathrm{C}\!-\!\mathrm{LG}}$, while the sources are DDEC6 net atomic charges on the nucleophile and leaving-group centres. Application to three prototypical S$_\mathrm{N}$2 reactions (identity exchange $\mathrm{F^-+CH_3F}$, halide substitution $\mathrm{F^-+CH_3Br}$, and hydroxide substitution $\mathrm{OH^-+CH_3CH_2Br}$) yields compact, symmetry-sensitive signatures of bonding evolution: the identity reaction exhibits mirror-related information profiles with exchange of unique-information contributions between equivalent centres, whereas asymmetric reactions show shifted, centre-specific redistribution among redundancy and synergy as C--X cleavage couples to C--Nu formation. This Supplementary Information provides the formal construction, chemically motivated limiting toy models, a solvable analytic symmetric-transfer model, and the computational protocol used to obtain IRC-resolved PID curves.

physics.chem-ph↗

arXiv2026

Quantum-Accurate Conformational Stabilities and Vibrational Dynamics in Molecules and Proteins with Machine-Learned Force Fields

Biomolecular thermodynamics and spectroscopy depend on relative conformer energies, local curvatures, and collective dipole fluctuations on the potential-energy surface. Conventional molecular mechanics force fields enable large-scale simulations, but their fixed functional forms can misrepresent infrared intensities, mode character, and environment-dependent vibrational response. Here we assess general-purpose machine-learned force fields across small molecules, finite-temperature infrared spectra, gas-phase peptides, and monomeric, oligomeric, and solvated protein assemblies. To enable this analysis, we introduce QVib, a dataset of 293 molecules and 1365 conformers, together with peptide amide-band benchmarks and p53 oligomerization-domain models, to evaluate vibrational transferability from DFT references to experimental spectra. Across these systems, machine-learned force fields substantially improve over molecular mechanics in reproducing DFT-level forces, vibrational frequencies, densities of states, mode eigenvectors, conformational energetics, and experimental infrared spectra. Among models with explicit long-range electrostatics, SO3LR provides the most favourable accuracy-cost balance for the biomolecular systems considered. These results show that machine-learned force-field dynamics can recover collective, environment-dependent vibrational landscapes at near-DFT fidelity, enabling spectroscopically validated biomolecular simulations at force-field-like cost.

physics.chem-ph↗