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Foundations of Chemistry

Why molecular structure cannot be strictly reduced to quantum mechanics

Juan Camilo Martínez González, Sebastián Fortín, Olímpia Lombardi

Published Mar 7, 2018• 45 citations
Publisher
DOI
10.1007/s10698-018-9310-2

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We present a rigorous reformulation of molecular quantum mechanics and electronic structure theory under the Three-Dimensional Complex Necessity (3DCN) framework. Standardquantum chemistry algorithms, such as Hartree-Fock and Density Functional Theory (DFT),rely axiomatically on complex Hilbert spaces, introducing exponential computational bottlenecks when modeling multi-electron molecular systems on classical architectures. By replacingthe imaginary unit i with the dynamically locked universal complex structure operator JU(J2U = −I), we reconstruct the multi-electron Schrodinger equation as a strictly real, antisymmetric matrix system. We mathematically prove that the geometric interaction lockingmechanism forces a systematic compression of the active electronic phase space via first-classDirac constraints. This realification eliminates unphysical complex phase degrees of freedom,reducing the computational scaling of non-local electron correlations and providing a purely realgeometric mechanism for molecular orbital hybridization and covalent bonding.
With local realism quantum mechanics established, we can simply describe an extranuclear electron as a large-scale elastic ring with an elastic phase trajectory. Several small molecules can thus be strictly calculated through the logical method of establishing an accurate mechanical equilibrium equation describing the molecular structure, then solving the strict solutions of this mechanical equation and the corresponding wave equation. The results (bond length and dissociation energy) are in good agreement with observed results—i.e. if it is only coincidence, there should not be such a high probability of agreement between calculated and observed results. The method of local realism quantum mechanics is no longer the semi-empirical method. The method to calculate the electron pairing energy uses a linear regression of the ionization energy obtained through experiment. Nonetheless, it is exciting that there are diatomic molecules such as Na2, K2 and asymmetric HF molecules that possess a non-zero non-bonding electron number in the calculation examples. Moreover, the molecular structures are very intuitive, and the calculation method is much simpler than existing methods.