Reconstructing Chemistry from P₀ A Three-Dimensional Energy Continuum Framework

The first official version of the new chemistry; from now on, version numbers will follow the year-month-day format.

This paper develops the P0 energy-continuum framework for chemistry, derived from the compan
ion physics monograph [1], which establishes the continuum-mechanical foundations. The frame
work reconstructs chemical phenomena from one axiom (P0: total energy partitions into prop
agating and topologically locked components), two topological postulates (T1: electric charge
as vortex winding number; T2: electron geometry as horn-torus), and five empirical continuum
constants (ϵ0, µ0, c, ν, ℏ).
What the framework derives (Class A: structural derivations). The derivation chain
P0 → continuity → Euler → N-S → Madelung → NLSE → Schrödinger is algebraically exact
given the five empirical constants and two declared correspondences [DC1, DC8] whose precise
scope and dimensional status are documented in §1.14. From the resulting acoustic Schrödinger
equation, the framework derives the functional forms of the Nernst equation, Arrhenius equation,
Born–Landé lattice energy, Henderson–Hasselbalch equation, and Butler–Volmer kinetics without
additional postulates. All standard results of non-relativistic quantum chemistry that follow from
the linear Schrödinger equation are reproduced within this framework.
Non-trivial predictions (Class NT: zero-parameter results). Two results are derived
without fitting any parameter to the predicted quantity: (i) the tetrahedral bond angle (109.47)
as the global minimum of the four-body Thomson problem on S2—in exact agreement with the
methane geometry; (ii) the Hückel 4n+2 aromaticity rule from cyclic standing-wave boundary
conditions. These are the framework’s only predictions that are independent of empirical inputs
in the quantity being compared.
Consistency checks (Class B). All other numerical comparisons with experiment—including
the Daniell cell EMF (1.102 V), combustion enthalpies, ionic lattice energies, ionisation ener
gies, the Fe-catalysed Haber barrier (148 kJ mol−1, using the uncatalysed barrier as calibration
input), and quantum dot confinement energies (2–6% error using bulk effective masses)—are
computed by inserting NIST tabulated data into Class A equations. These results confirm inter
nal consistency with the NIST dataset; they are not independent predictions of the framework.
FP-New force field (Track 2). The proposed FP-New computational method pre-tabulates
acoustic stiffness constants fitted to quantum-chemical potential-energy surfaces and uses the
Fast Multipole Method (FMM; Greengard & Rokhlin 1987) to evaluate pair interactions in
O(N logN) operations. The O(N logN) scaling is a standard FMM result, not a novel P0
derivation. All force-field parameters (K, W, partial charges) are empirically fitted; FP-New is a
parameterised force field, not a parameter-free method. Its computational advantage over Kohn
Sham DFT [O(N3) SCF cycle] in scaling is established analytically; its quantitative accuracy
relative to DFT benchmarks has not yet been validated and remains an open experimental
question.
Acknowledged open gaps (OG-0 through OG-7). The framework contains eight docu
mented structural gaps: the Burgers-vortex stability threshold (OG-0); the two-phase viscosity
inconsistency between background (νbg ≈2×10−35 m2s−1) and vortex-core (νcore =ℏ/(2me)≈
5.79×10−5 m2s−1) regimes, which prevents a globally self-consistent single-phase N-S description
(OG-0b); the Gaussian-ansatz approximation for the NLSE quintic coefficient γ (OG-1); the un
computed particle mass ratio mp/me from the NLSE eigenvalue problem, the 6π5≈1836 value
having been retracted (OG-2); the planar approximation in the spin angular-momentum integral
(OG-3); the spin-statistics theorem, invoked from relativistic quantum field theory (OG-4); the
zero-temperature limit in the α(s) interpolation (OG-5); and the E2 anti-periplanar preference,
not derivable from acoustic phase-matching alone (OG-E2). All gaps are labelled [OPEN GAP]
or [LIMITATION] at their point of occurrence.
Relationship to standard quantum chemistry. The P0 framework is a reinterpretation, not
a replacement, of quantum chemistry: it demonstrates that the mathematical structure of the
Schrödinger equation and associated formalism can be obtained from classical viscous compress
ible fluid mechanics given the five empirical constants above. It does not reduce the number of
independent empirical inputs below five, does not derive the values of those constants, and for the
cases examined here does not provide predictive accuracy beyond standard quantum chemistry.
The open gaps define a concrete research agenda; the falsifiable experimental predictions listed
in the Epilogue provide the tests required to assess the framework’s validity beyond its Class NT
results.
Axiom P0 and primary consequences:
Etotal = Espace + Elocked
Axiom P0
∂ϵ
∂t +∇·(ϵv) = 0
Master conservation law (Gauss theorem applied to P0)
c = 1
√
µ0ϵ0
Transverse wave speed (identifies µ0,ϵ0 among the five constants