Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Experiment Videos

Koopmans' theorem for large molecular systems within density functional theory.

Ji Luo1, Zeng Quan Xue, Wei Min Liu

  • 1Surface Physics Laboratory, Department of Physics, Fudan University, Shanghai 200433, China. jluo@fudan.edu.cn

The Journal of Physical Chemistry. A
|October 27, 2006
PubMed
Summary
This summary is machine-generated.

Related Concept Videos

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

miR-4485-5p regulates the progression of periodontitis by targeting CDK9.

Odontology·2026
Same author

A Hybrid Experimental and in silico Platform for ITPK1 Chemical Probe Discovery.

SLAS discovery : advancing life sciences R & D·2026
Same author

The mechanism of action and therapeutic potential of macrophages in osteoporosis: from polarization balance to targeted regulation.

Frontiers in immunology·2026
Same author

Investigating the effects and underlying mechanisms of glycosylation sites on the immunogenicity of COVID-19 vaccines.

Signal transduction and targeted therapy·2026
Same author

Reengineering Aligned D-Orbital Energy Levels in FeMn Dual-Atom Nanozyme Inhibits Pyroptosis for Effective Alleviation of Inflammatory Diseases.

Advanced materials (Deerfield Beach, Fla.)·2026
Same author

Association between remnant cholesterol and stroke among patients with atrial fibrillation: A population-based cohort study.

Journal of clinical lipidology·2026

Density functional theory (DFT) Koopmans' theorem relates ionization energy to molecular orbital energies. This study generalizes the theorem and confirms its approximate validity for large systems like nanotubes.

Area of Science:

  • Quantum Chemistry
  • Computational Materials Science

Background:

  • Koopmans' theorem traditionally links ionization potential to the negative of the highest occupied molecular orbital (HOMO) energy in Hartree-Fock theory.
  • Extending Koopmans' theorem to density functional theory (DFT) for large molecular systems requires careful consideration of electron correlation and relaxation effects.

Purpose of the Study:

  • To formulate and validate a version of Koopmans' theorem within the framework of density functional theory (DFT) applicable to large molecular systems.
  • To investigate the relationship between ionization energy, highest occupied molecular orbital (HOMO) energy, and lowest unoccupied molecular orbital (LUMO) energy in DFT.

Main Methods:

  • Theoretical formulation of Koopmans' theorem in DFT, considering Coulombic interactions during electron removal.

Related Experiment Videos

  • Generalization and simplification of existing DFT Koopmans' theorem formulations.
  • Application of the derived theorem to computational modeling of a fullerene molecule, a single-walled carbon nanotube, and a boron nitride nanotube using DFT.

    • Main Results:

    • A novel statement of Koopmans' theorem for DFT is presented: Ionization energy equals -HOMO energy plus electron removal Coulomb energy, or the average of the N-electron HOMO and (N-1)-electron LUMO energies.
    • The generalized DFT Koopmans' theorem was found to hold approximately for the studied fullerene and nanotube systems.
    • The theorem's approximate validity persists even when accounting for orbital relaxation effects.

    Conclusions:

    • The developed DFT Koopmans' theorem provides a valuable theoretical tool for understanding ionization energies in large molecular systems.
    • The study confirms the applicability and approximate accuracy of the generalized theorem for complex nanostructures.
    • This work contributes to the refinement of theoretical methods for predicting electronic properties in materials science.