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<p>Under nuclear motion, canonical molecular (or Kohn–Sham) orbitals often discontinuously change their characters due to the change in ordering of orbital energy eigenvalues, making it difficult to track a specific orbital along the nuclear trajectory. As one of the potential ways to avoid this problem, the present article examines the numerical properties of the time-dependent Kohn–Sham orbitals (TDKSOs), which are obtained by solving the electronic time-dependent Kohn–Sham equations tracing the classical nuclear trajectory. The numerical characteristics of TDKSOs were investigated for thymine, thymine dication, fullerene <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\hbox {C}_{60}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mtext>C</mtext> <mn>60</mn> </msub> </math></EquationSource> </InlineEquation>, and the conrotatory electrocyclization process of 1,3-butadiene, suggesting that the TDKSOs are continuous in their orbital characters, as expected by the fact that the time-dependent Kohn–Sham equations are differential equations with respect to time. In general, the many-electron states described by TDKSOs and canonical orbitals are not physically equivalent, but the present article discusses the degree of their similarity by quantitatively comparing the occupied (or virtual) Hilbert spaces spanned by these two set of orbitals.</p>

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Numerical assessment of time-dependent Kohn–Sham orbitals’ behavior under classical nuclear motion

  • 期刊论文

  • 发表日期：

    2026年3月9日

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  • Hiroki Uratani,
  • Hirofumi Sato

摘要

Under nuclear motion, canonical molecular (or Kohn–Sham) orbitals often discontinuously change their characters due to the change in ordering of orbital energy eigenvalues, making it difficult to track a specific orbital along the nuclear trajectory. As one of the potential ways to avoid this problem, the present article examines the numerical properties of the time-dependent Kohn–Sham orbitals (TDKSOs), which are obtained by solving the electronic time-dependent Kohn–Sham equations tracing the classical nuclear trajectory. The numerical characteristics of TDKSOs were investigated for thymine, thymine dication, fullerene \(\hbox {C}_{60}\) C 60 , and the conrotatory electrocyclization process of 1,3-butadiene, suggesting that the TDKSOs are continuous in their orbital characters, as expected by the fact that the time-dependent Kohn–Sham equations are differential equations with respect to time. In general, the many-electron states described by TDKSOs and canonical orbitals are not physically equivalent, but the present article discusses the degree of their similarity by quantitatively comparing the occupied (or virtual) Hilbert spaces spanned by these two set of orbitals.