Tomographic identification of all molecular orbitals in a wide binding-energy range

Authors: A. Haags, D. Brandstetter, X. Yang, L. Egger, H. Kirschner, A. Gottwald, M. Richter, G. Koller, F. C. Bocquet, C. Wagner, M. G. Ramsey, S. Soubatch, P. Puschnig and F. S. Tautz

Phys. Rev. B 111, 165402 – Published 2. April 2025

Abstract: In the past decade, photoemission orbital tomography (POT) has evolved into a powerful tool to investigate the electronic structure of organic molecules adsorbed on surfaces. Here we show that POT allows for the comprehensive experimental identification of all molecular orbitals in a substantial binding energy range of more than 10 eV. Making use of the angular distribution of photoelectrons as a function of binding-energy, we exemplify this by extracting an orbital-resolved projected density of states for 15 𝜋 and 23 𝜎 orbitals from the experimental data of the prototypical organic molecule bisanthene (C₂₈⁢H₁₄) on a Cu(110) surface. These experimental results for an essentially complete set of orbitals within the given binding-energy range serve as stringent benchmarks for electronic structure methods, which we illustrate by performing density functional calculations employing four frequently used exchange-correlation functionals. By computing the respective molecular-orbital-projected densities of states, a one-to-one comparison with experimental data for an unprecedented number of 38 orbital energies became possible. The quantitative analysis of our data reveals that the range-separated hybrid functional HSE performs best for the investigated organic/metal interface. At a more fundamental level, the remarkable agreement between the experimental and the Kohn-Sham orbital energies over a binding-energy range larger than 10 eV suggests that—perhaps unexpectedly—Kohn-Sham orbitals approximate Dyson orbitals, which would rigorously account for the electron extraction process in photoemission spectroscopy but are notoriously difficult to compute, in a much better way than previously thought.

Tomographic identification of all molecular orbitals in a wide binding-energy range — Intramolecular σ-band dispersion of σ(n,7), σ(n,6), σ(7,m), and σ(3,m) bands, combining experiment and theory in a direct comparison. Orbital energies are extracted from momentum-resolved data (hν = 57 eV) using multiple fitting strategies—linear models, MLA pattern recognition, and Monte Carlo analysis—demonstrating consistent results across methods. These experimental values are benchmarked against DFT calculations (PBE0, B3LYP, HSE). Each data point is placed at the momentum of strongest emission, emphasizing how the bands disperse in k-space. The highlighted energy windows indicate the fitting range, while simulated graphene band maps provide visual guidance through cuts across the dominant orbital lobes.

Contact

Dr. Anja Meier

Scientific Coordinator at Peter Grünberg Institute (PGI-3)

Building 02.4w /
Room 326

+49 2461/61-85879

E-Mail

Last Modified: 13.02.2026