Tuesday, August 13, 2019
Quantum mechanics, Hund's paradox, empirical failure
Quantum mechanics can fail at will (the how-to)
Chain three published experiments, observe one carefully wicked molecule. Obtain a Hund’s paradox 10^(-36,900)/sec racemization rate constant. Observe quantum mechanics’ (QM) unremarkable failure.
“Like every particle in any matter-wave interferometer, each molecule only interferes with itself[1].” There is no wavefunction dissipation or decoherence within the grating's near field.
Particles traversing a grating diffract and interfere[2], QM’s beating heart, including 10,123 amu molecules[3]. Matter interference of chiral molecules passing through a grating is summed state chiralities, non-superposable reverse spatial coordinates, antipodes, that yield achiral output, Hund’s paradox[4]. Passing 100% right shoes or 100% left shoes (a resolved chiral molecular beam) through a grating must create a pattern whose content is 50% of each (racemic) when you look downstream of the grating, at the interference pattern..
Absent racemization, there is no wavefunction multi-slit interference and no pattern. Are classical energy barriers irrelevant in QM? Observe a high barrier, 2-trifluoromethyl-D_3-trishomocubane.
Racemization of this molecule requires simultaneous four carbon-carbon bond cleavages, simultaneous eight chiral center inversions, and simultaneous four carbon-carbon bond reformations.
Ignore hydrogens’ tunneling. The 2-CF_3 group confers a dipole moment for downstream enantiomer ratio detection. It must pass through the molecule as its 2-carbon attachment inverts and the CF_3 group passes through that 2-carbon, and itself inverts. Impossible? Ignore it. The apical 2- and 9-positions possess no local S_n symmetries (R reflects or inverts as S). They are CIP-unnamable chiral centers[5]
Pentacyclo[6.3.0.0^(2.6).0^(3,10).0^(5,9)]undecane core inversion requires all at once breaking at least four C-C bonds (ignore everything else). (CH_3)_2HC—CH(CH_3)_2 bond dissociation energy is 353.5 kJ/mol, re H_3C—CH_3 377.4 kJ/mol[6]. 2,3-Dimethyl butane’s two conformers weighted average 1.5488 Å center bond. This somewhat long, low energy C-C bond arises from steric hindrance then bond stretching. The cage hydrocarbon has six such apical plus three equatorial bonds, weighted average 1.5488 Å. Three pairs equatorial H_2C<CC bonds average 1.5283 Å. Shorter bonds are stronger. Ignore it.
Further down the bond energy table, H_3C—CF_3 dissociation energy is 429.3 kJ/mol. Ignore it. Award QM every possible advantage by considering only one aspect of the inversion.
Total bond dissociation energy cannot be less than (4)(353.5 kJ/mole) or 1414.0 kJ/mol, 1.4140×10^6 J/mol. If the supersonic expansion beam translates a paltry 100 m/s (300+ m/s typical) and the grating near field is a fat micron thick, interaction time is 10 nanoseconds. The kinetic barrier to racemization inversion is the Arrhenius equation, k = Ae^(-E_a/RT)[7]. Thermodynamics proposes, kinetics imposes.
k = rate constant, conversions/second.
A = frequency factor (success rate), /sec-mol. Unimolecular inversion here, first order reaction[8].
A = 10^12/sec-mol is an approximate empirical maximum value. Outcome is inert to 10^100/sec-mol.
E_a = activation energy, here 1.4140 ×10^6 J/mol. A mole here is C_12H_13F_3, 214.227 grams.
R = the gas constant, 8.31446 J/mol-K
T = temperature, here 2 kelvin rotational temperature after vacuum supersonic expansion
log10(x) = ln(x)/ln(10)
k = (10^12/sec-mol)e^[(-1.4140×10^6 J/mole)/((8.31446 J/mol-K)(2 K))]
k = (10^12)e^(-85,032.6)/sec = (10^12)10^(-36,929.2)/sec
k = 10^(-36,900)/sec at most
π-Bonds, cyclopropane rings, electron lone pairs, charges, unpaired spins allow anomalously low activation energies for rearrangement[9]. 2-Trifluoromethyl-D_3-trishomocubane has no footnotes.
Fewer than 10^5 diffracted C_60 molecules/s passed through Arndt's grating. The observable universe - quarks, electrons, neutrinos, photons - is estimated 10^97 particles. If Hund’s paradox fails, QM requires redefinition. 100 years of QM versus an interference pattern plus an enantiomer ratio...and a 10^(-36,900)/sec rate constant.
1) Synthesize and resolve 2-trifluoromethyl-D_3-trishomocubane[10]. One immediately obtains a 3:1 right:left ratio, then (chiral) HPLC of the product menthyl ester. Remove the two superfluous carbonyls (Wolff–Kishner reduction, modified), saponify to the free carboxylic acid, then R-COOH + SF_4 → R-CF_3 (HF catalysis) for each optical isomer. Microwave signal intensity varies as the square of the dipole moment. Bulky nitriles, ball-2-CN, are observed “sticky” and have N-14 nuclear quadrupole moment coupling, distributing signal intensity. into side bands[11].
Sodium metalization of 1,4-dimethoxybenzene. then menthyl chlorocarbonate from menthol into phosgene plus pyridine in ether. Order of addition matters.
Derivatized Cookson's diketone is best [2π + 2π] obtained by continuous flow thin film 365 nm LED photolysis, 2+ kg/day,
Balance of synthesis is re Sharapa, Scheme 2, DOI:10.1002/ejoc.201001731, updated.
3) Matter diffraction gratin [13] or photon diffraction grating, plus enantiomer ID[14].
4) The effluent from passing through (or around) the grating flows downstream into a cryogenic collector or directly into the microwave spectrometer for optical isomer ratio[15].
5a) No pattern emerges despite de Broglie matter waves. Quantum mechanics is falsified.
5b) The pattern emerges. The beam remains homochiral. Quantum mechanics is falsified.
5c) The pattern emerges. 100% left or right shoes enter. A racemic mixture must exit. Half the molecules must be inverted. Inverting the pentacyclo[6.3.0.0^(2.6).0^(3,10).0^(5,9)]undecane core requires simultaneously breaking at least four C-C bonds and rebonding correctly, plus other classical barriers. Bond breaking alone costs 1414 kJ/mol at 2 kelvin (0.016628 kJ/mol). 100 m/s beam plus a micron-thick grating obtains 10 nanoseconds interaction time. A 10^(-36,900)/s kinetic barrier is impassable. Thermodynamics is falsified.
Something that cannot be broken will break. Look. If it happens in practice, it does not matter if it does not happen in principle. Fantastical or not, observation defines theory.
[1] https://www.quantumnano.at/research/matter-wave-technologies/far-field-diffraction/the-origin-c60-diffraction/
[2] DOI:10.1002/prop.201600025; DOI:10.1038/nnano.2015.179, arXiv:1602.07578
[3] DOI:10.1039/c3cp51500a, arXiv:1703.02129;
[4] DOI:10.1103/PhysRevLett.103.023202, arXiv:0811.2140; DOI:10.1088/1361-6455/aa5115, arXiv:1701.00535; DOI:10.1039/C2CP40920H, arXiv:1202.0201
[5] https://en.wikipedia.org/wiki/Cahn%E2%80%93Ingold%E2%80%93Prelog_priority_rules
[6] http://staff.ustc.edu.cn/~luo971/2010-91-CRC-BDEs-Tables.pdf, re DOI:10.1021/ar020230d
[7] www.khanacademy.org/science/chemistry/chem-kinetics/arrhenius-equation/v/arrhenius-equation
[8] https://en.wikipedia.org/wiki/Collision_theory
[9] DOI:10.1021/ja00816a037
[10] DOI:10.2174/138527212804004508, DOI:10.1016/S0040-4020(98)00211-7
[11] DOI:10.1515/zna-1986-1107
[12] DOI:10.1002/anie.201704221
[13] J. Phys.: Conf. Ser. 1144 012053 (2018), and DOI:10.1126/sciadv.1500901
[14] arXiv:1906.10818
[15] DOI:10.1021/acs.jpclett.5b02443; DOI:10.1016/j.jms.2019.01.002
http://brightspec.com/wp-content/uploads/2015/06/ProductFlier-Chirality-Nov2014-Press.pdf
https://cefrc.princeton.edu/sites/cefrc/files/Files/2013%20Lecture%20Notes/Hanson/pLecture4.pdf
Second, test molecule chirality and rotational data,
Third, symmetric top rotor microwave rotational spectra. Organikers thank all the clever folk who ride hardware and interpret its outputs,
Validate our choice of a prolate top,
Take three published experiments and one carefully wicked molecule. Take down quantum mechanics for hugely not predicting an easily obtainable result. Were I physics fundamentally falsified by organic chemistry, I'd be embarrassed. I would NEVER look - nor allow anybody else to look.
Quantum mechanics can fail at will
Quantum mechanics can fail at will (Summary)
Observe matter [diffraction × inteference], re Arndt and C_60, falsify Hund's paradox. Quantum mechanics macroscopically fails given optically resolved 2-trifluoromethyl-D_3-trishomocubane as a 2 kelvin vacuum supersonic-expanded molecular beam.
The Arrhenius equation-calculated Hund's paradox racemization constant is 10^(-36,900)/sec at most. The observable universe - quarks, electrons, neutrinos, photons - is estimated 10^97 particles. Quantum mechanics fails to predict the observed outcome - no racemization.
“Like every particle in any matter-wave interferometer, each molecule only interferes with itself.” There is no wavefunction dissipation or decoherence within the grating's near field. If it happens in practice, that it is impossible in principle is irrelevant.
https://www.quantumnano.at/research/matter-wave-technologies/far-field-diffraction/the-origin-c60-diffraction/
Sodium metalization of 1,4-dimethoxybenzene. then menthyl chlorocarbonate from menthol into phosgene plus pyridine in ether. Order of addition matters.
Derivatized Cookson's diketone is best [2π + 2π] obtained by continuous flow thin film 365 nm LED photolysis, 2+ kg/day,
Balance of synthesis is re Sharapa, Scheme 2, DOI:10.1002/ejoc.201001731, updated.
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