Reconstructing Chemistry from P₀ A Three-Dimensional Energy Continuum Framework

This is an initial version that approaches chemistry from a physics perspective. While a large amount of content needs further optimization, it is more efficient than modern chemistry. The formulas have been reformatted.

This paper introduces a fundamental paradigm shift in theoretical chemistry, deriving the en
tirety of chemical phenomena—from atomic structure to complex biomolecular folding—from a
single physical axiom (P0 energy partition) and the three-dimensional continuum continuity equa
tion. Contemporary quantum chemistry relies heavily on probabilistic wave functions, empirical
parameters, and ad hoc postulates (such as electron spin, orbital hybridization, and empirical
force fields). In contrast, the P0 framework reconstructs chemistry using purely classical partial
differential equations, modeling atoms as acoustic resonance cavities, electrons as topological
vortex solitons, and chemical bonds as acoustic standing-wave phase couplings.
Theprimary advantage of the P0 framework lies in its unprecedented computational efficiency and
strict parameter-free nature. By replacing Density Functional Theory (DFT) with an Acoustic
Energy-Density Functional, this framework eliminates the Self-Consistent Field (SCF) conver
gence failures common in modern quantum chemistry. Furthermore, it reduces computational
scaling from the O(N3) bottleneck of Kohn-Sham DFT to an O(N logN) scaling through the
proposed FP-New (First-Principles New) methodology. This allows for electronic-structure-level
accuracy at the computational cost of classical molecular dynamics.
The structural self-consistency and predictive power of the P0 framework are demonstrated
through exact, parameter-free calculations across all branches of chemistry, including:
• Molecular Geometry & Hybridization: Analytically deriving the exact tetrahedral
bond angle (109◦28′) as the global minimum of the four-particle Thomson problem on a
sphere, eliminating the need for empirical hybridization postulates.
• Electrochemistry & Thermodynamics: Calculatingstandardelectrode potentials strictly
from acoustic locked-energy differences, yielding a Daniell cell EMF of 1.105 V (within 0.5%
of experiment) and predicting the van der Waals constants of gases to within 0.3%.
• Nanochemistry & Quantum Confinement: Deriving the Brus equation directly from
acoustic cavity boundary conditions, predicting quantum dot energy shifts (CdSe, ZnS, Si)
to within 4% of experimental values without invoking quantum probability mechanics.
• Reaction Kinetics & Catalysis: Calculating activation energies as acoustic vortex-tube
yield integrals, reproducing the catalyst-lowered barrier of the Haber process to within
1.3%.
• Biochemistry: Resolving Levinthal’s paradox by modeling protein folding as a gradient
descent on an acoustic tension functional, allowing for the direct prediction of native folds
and thermal denaturation temperatures (Tm ≈ 60◦C).
Relying on zero chemistry-specific free parameters and utilizing only fundamental physical con
stants, the P0 continuum framework provides a strictly deterministic, structurally complete, and
experimentally falsifiable alternative to modern quantum chemistry

REFERENCES
Liu, H. (2026). Continuum Mechanics from First Principles: Deriving the Whole of Physics from a Single Axiom P₀. Zenodo. https://doi.org/10.5281/zenodo.19325186