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In an atom, the negatively charged electrons are attracted to the positively charged nucleus. In a multielectron atom, electron-electron repulsions are also observed. The attractive and repulsive forces are dependent on the distance between the particles, as well as the sign and magnitude of the charges on the individual particles. When the charges on the particles are opposite, they attract each other. If both particles have the same charge, they repel each other.
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Orbitals are the areas outside of the atomic nucleus where electrons are most likely to reside. They are characterized by different energy levels, shapes, and three-dimensional orientations. The location of electrons is described most generally by a shell or principal energy level, then by a subshell within each shell, and finally, by individual orbitals found within the subshells.
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Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra.
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Nuclear-electronic orbital Ehrenfest dynamics.

Luning Zhao1, Andrew Wildman1, Zhen Tao2

  • 1Department of Chemistry, University of Washington, Seattle, Washington 98195, USA.

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|December 15, 2020
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The new NEO-Ehrenfest method accurately models coupled nuclear-electronic dynamics by combining quantum protons and electrons with classical nuclei, enabling detailed study of molecular vibrations and spectroscopy.

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Area of Science:

  • Quantum chemistry
  • Theoretical chemistry
  • Chemical dynamics

Background:

  • The real-time nuclear-electronic orbital (RT-NEO) method treats electrons and protons quantum mechanically.
  • RT-NEO neglects the motion of other nuclei, limiting its scope in coupled nuclear-electronic dynamics.

Purpose of the Study:

  • To develop a method that incorporates the dynamics of all nuclei in quantum-mechanical simulations.
  • To enable a complete description of coupled nuclear-electronic dynamics and spectroscopy.

Main Methods:

  • Introduced the NEO-Ehrenfest approach, combining RT-NEO with mixed quantum-classical Ehrenfest dynamics.
  • Propagated electrons and quantum protons via RT-NEO within a time-dependent variational framework.
  • Treated remaining nuclei classically, moving on an average electron-proton vibronic surface.

Main Results:

  • Successfully incorporated non-Born-Oppenheimer effects for both electron-proton and classical nuclei-electron-proton subsystems.
  • Resolved spectral features for vibrational modes involving both quantum and classical nuclei.
  • Demonstrated the method's capability to study complex dynamical processes.

Conclusions:

  • The NEO-Ehrenfest method is a powerful computational tool for simulating systems with coupled electronic and nuclear degrees of freedom.
  • This approach provides a more complete description of nuclear-electronic dynamics and spectroscopy than previous methods.