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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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The vacuum level denotes the energy threshold required for an electron to escape from a material surface. It is usually positioned above the conduction band of a semiconductor and acts as a benchmark for comparing electron energies within various materials.
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Orbital-Based Correlated Electron-Nuclear Dynamics for Extended Systems with Exact Factorization.

Daeho Han1,2, Jae Hyeok Lee1, Seung Kyu Min1,2,3

  • 1Department of Chemistry, School of Natural Science, Ulsan National Institute of Science and Technology (UNIST), 50 UNIST-gil, Ulju-gun, Ulsan 44919, Republic of Korea.

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|November 16, 2025
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Summary
This summary is machine-generated.

We developed an efficient computational framework for simulating electron-nuclear dynamics in large systems using the exact factorization method. This approach accurately models quantum effects, leading to physically realistic simulations of material properties.

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Area of Science:

  • Quantum Chemistry
  • Computational Materials Science
  • Condensed Matter Physics

Background:

  • Simulating electron-nuclear dynamics is crucial for understanding chemical reactions and material properties.
  • Existing methods often struggle with large, extended systems due to computational complexity.
  • The exact factorization (XF) formalism offers a rigorous way to separate electronic and nuclear motion.

Purpose of the Study:

  • To introduce a practical orbital-based framework for simulating correlated electron-nuclear dynamics in extended systems.
  • To merge real-time time-dependent density functional theory (TD-DFT) with the XF formalism.
  • To develop an efficient algorithm for nonadiabatic processes in systems with thousands of atoms.

Main Methods:

  • Implementation of the exact factorization (XF) formalism.
  • Application of the classical path approximation.
  • Incorporation of pairwise XF-derived decoherence corrections in the Kohn-Sham basis.
  • Development of time-dependent Kohn-Sham (TDKS) equations merging TD-DFT and XF.

Main Results:

  • An efficient algorithm for simulating nonadiabatic processes in extended systems was developed.
  • The first application of XF-based methods to extended systems was demonstrated on spiro-type hole-transport materials.
  • Inclusion of XF-derived decoherence corrected unphysical persistent coherences, yielding physically consistent relaxation.

Conclusions:

  • The developed framework provides a practical and efficient approach for simulating complex electron-nuclear dynamics in extended systems.
  • XF-derived decoherence is essential for obtaining physically accurate results in nonadiabatic dynamics.
  • This work paves the way for accurate simulations of quantum dynamics in large-scale materials.