# What Are the Electrons Really Doing in Molecules? A Space-Time Picture

### Abstract

This is fundamental and pedagogical work in quantum physics/chemistry, where we try to illustrate the Mulliken question, “what are the electrons really doing in molecules?”; and we briefly review the development of the most popular numerical approaches in computational chemistry. We examine in a novel approach, how we can overall describe the electronic interactions in atomic systems with the conceptual help of a space-time picture of quantum mechanics. This is not a research article initially looking for new numerical results, but for the imperative fundamental reinterpretation of the (non-classical and stabilizing) electronic exchange and correlation energies, from the point of view of space-time scattering events between electrons. Consistently, we introduce Feynman type diagrams as pictorial representation of the (abstract) enthalpic integrals, scattering mechanisms, in quantum chemistry. In atomic structures, it is almost impossible to fully understand, covalent bonding, electronic enthalpies, surface science, orbital magnetism, catalysis… without computational chemistry. How well do we know the physical meaning of the quantum mechanisms behind the numerical approaches? We give an educational hit to this question, following the philosophy of R.P. Feynman, “just recognizing old things from a new point of view”. The possibility of interpreting Coulomb and Fermi holes with space-time of diagrams goes deep into the quantum behaviour of electrons, because the Coulomb forces in atomic systems create interreference patterns and then electrons cannot fill the electrostatic potentials everywhere as in classical mechanics. Quantum mechanics allows electrons in atoms to collide in scatting events, introducing space-time mechanisms that reduce the repulsion energy; and actual successful computational chemistry methods include an average approximation to these stabilization mechanisms.### References

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Přecechtělová, J., Bahmann, H., Kaupp, M., and Ernzerhof, M. (2014). Communication: A non-empirical correlation factor model for the exchange-correlation energy J. Chem. Phys. 141 111102.

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Schrödinger, E. (1926). Quantisierung als Eigenwertproblem Ann. Phys. 385 437–90 Schrödinger, E. (1926). An Undulatory Theory of the Mechanics of Atoms and Molecules Phys. Rev. 28 1049–70.

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Yirmiyahu, Y., Niv, A., Biener, G., Kleiner, V., and Hasman, E. (2007). Excitation of a single hollow waveguide mode using inhomogeneous anisotropic subwavelength structures Opt. Express 15 13404.

Bracken, P. (2013). The Schwinger Action Principle and Its Applications to Quantum Mechanics Advances in Quantum Mechanics (InTech).

Dirac, P. A. M. (1926). On the Theory of Quantum Mechanics Proc. R. Soc. A Math. Phys. Eng. Sci. 112 661–77.

Dirac, P. A. M. (1933). The Lagrangian in quantum mechanics Phys. Zeits. Sowjetunion 3 64–72.

Feynman, R. P. (1948). Space-Time Approach to Non-Relativistic Quantum Mechanics Rev. Mod. Phys. 20 367–87.

Goldstone, J. (1957). Derivation of the Brueckner many-body theory Proc. R. Soc. London. Ser. A. Math. Phys. Sci. 239 267–79.

Hartree, D. R. (1928). The Wave Mechanics of an Atom with a Non-Coulomb Central Field. Part I. Theory and Methods of Math. Proc. Cambridge Philos. Soc. 24 89.

Heisenberg, W. (1926). Mehrkorperproblem und Resonanz in der Quantenmechanik Zeitschrift Phys. 38 411–26.

Kelly, H. P. (1963). Correlation Effects in Atoms ed R LeFebvre and C Moser Phys. Rev. 131 684–99.

Kohn, W., and Sham, L. J. (1965). Self-Consistent Equations Including Exchange and Correlation Effects Phys. Rev. 140 A1133–8.

Magnasco, V. (2006). Post-Hartree-Fock Methods Methods of Molecular Quantum Mechanics (Chichester, UK: John Wiley & Sons, Ltd) pp 133–9.

Mattuck, R. D. (2012). A Guide to Feynman Diagrams in the Many-Body Problem: Second Edition (Dover Publications).

Møller, C., and Plesset, M. S. (1934). Note on an Approximation Treatment for Many- Electron Systems Phys. Rev. 46 618–22.

Pan, X. Y., and Sahni, V. (2012). Hohenberg-Kohn theorem including electron spin Phys. Rev. A 86 042502.

Přecechtělová, J., Bahmann, H., Kaupp, M., and Ernzerhof, M. (2014). Communication: A non-empirical correlation factor model for the exchange-correlation energy J. Chem. Phys. 141 111102.

Paldus, J., and Čížek, J. (1975). Time-Independent Diagrammatic Approach to Perturbation Theory of Fermion Systems Advances in Quantum Chemistry vol 9 pp 105–97.

Phillips, F. R. (2011). Richard Feynman — The Strange Theory of Light and Matter The Quantum Adventure (IMPERIAL COLLEGE PRESS) pp 191–211.

Ramirez, S. A. (1991). Diagrammatic second order Moller-Plesset multi-reference perturbation theory Rev. Mex. Fis. 38 179–204.

Ruggenthaler, M., Tancogne-Dejean, N., Flick, J., Appel, H., and Rubio, A. (2018). From a quantum-electrodynamical light-matter description to novel spectroscopies Nat. Rev. Chem. 2 0118.

Schrödinger, E. (1926). Quantisierung als Eigenwertproblem Ann. Phys. 385 437–90 Schrödinger, E. (1926). An Undulatory Theory of the Mechanics of Atoms and Molecules Phys. Rev. 28 1049–70.

Slater, J. C. (1929). The Theory of Complex Spectra Phys. Rev. 34 1293–322.

Szabo, A., and Ostlund, N. (2018). Modern quantum chemistry : introduction to advanced electronic structure theory / Attila Szabo, Neil S. Ostlund.

Weinberg, S. (1995). The Quantum Theory of Fields vol 9 (Cambridge: Cambridge University Press).

Yirmiyahu, Y., Niv, A., Biener, G., Kleiner, V., and Hasman, E. (2007). Excitation of a single hollow waveguide mode using inhomogeneous anisotropic subwavelength structures Opt. Express 15 13404.

Published

2020-01-08

How to Cite

GRACIA, Jose.
What Are the Electrons Really Doing in Molecules? A Space-Time Picture.

**European Journal of Physics Education**, [S.l.], v. 11, n. 1, p. 1-19, jan. 2020. ISSN 1309-7202. Available at: <http://eu-journal.org/index.php/EJPE/article/view/252>. Date accessed: 16 feb. 2020.
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Classroom Physics

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