molecular geometry: geometry vs. measured vs. QM
A head-to-head docket. Does BSM-SG output a bond angle from prism structure — no fitted constants — and does it match the diffractometer as well as DFT does?
Scaffold — to be filled from BSM-SG (main book) chapter by chapter.
The claim under test: molecular geometry follows from the geometry and packing of proton substructures — you can see the next atom’s shape in your head, no orbital cartoons. The honest test is symmetric: a geometric picture that postdicts a known shape (“roughly tetrahedral because the prisms pack that way”) is doing exactly what hybridization does with lobes — the thing BSM-SG rightly calls retrofit. To beat QM, geometry has to output the number from structure, with no fitted constant, and match the diffractometer.
So: three columns. BSM-SG derivation (empty until derived), the measured value (X-ray / neutron / microwave — the referee), and what QM/DFT computes (the incumbent’s public record). A row is won only when column 1 is filled from first principles and lands on column 2 without peeking at it.
| Molecule | Quantity | BSM-SG (derive) | Measured | QM/DFT |
|---|---|---|---|---|
| Water (H₂O) | H–O–H angle | — | 104.5° | 104.5° (CCSD(T), sub-degree) |
| Methane (CH₄) | H–C–H | — | 109.47° | 109.47° |
| Ammonia (NH₃) | H–N–H | — | 106.8° | ~107° |
| Phosphine (PH₃) | H–P–H | — | 93.5° | ~93° (minimal hybridization — the “near-90°” case) |
| Phosphate (PO₄³⁻) | O–P–O | — | ~109.5° (tetrahedral) | 109–110° |
| DNA phosphodiester | P–O(ester) length | — | ~1.60 Å | matched |
| DNA phosphodiester | P=O length | — | ~1.48 Å | matched |
Calibration note: the DNA-backbone phosphorus is tetrahedral (~109.5°), not 90°. The ~90° figure belongs to PH₃/H₂S (minimal hybridization), not to phosphate. This row exists to keep the geometric intuition honest against the measured angle.
mechanism to cash out (BSM-SG side)
Claims to be turned into the numbers above:
- Valence protons couple to the proton core differently than core protons — this sets their angular flexibility. Quantify the coupling → predict the angle spread.
- Surrounding deuterons (proton/neutron pairs) perturb via supergravity (Casimir-type) and their electron orbits → predict the distortion from ideal tetrahedral in real phosphate vs. free PO₄³⁻.
- The prism packing of P’s substructure → the base tetrahedral angle, before perturbation.
the incumbent’s record (for the bar)
DFT/coupled-cluster predict bond angles to <1° and lengths to ~0.01 Å for arbitrary molecules, including ones never synthesized — the basis of in-silico drug and materials design (Nobel Chemistry 1998 Kohn/Pople; 2013 multiscale models). That is the number to beat. Not “understandable in a primate’s head” — matched to the diffractometer, predicted before measurement, bet on with industry budgets.
why this page is the fair fight
Small enough to actually run. Sharp enough to actually decide. If BSM-SG fills column 1 from prism geometry and hits column 2, it is the first head-to-head win over QM on QM’s home turf, and it goes on the front of the physics page. If column 1 only ever says “roughly tetrahedral,” that is a postdiction of a known shape — and the standard was symmetric from the start.