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

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 <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mi>π</a:mi></a:math> and 23 <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mi>σ</b:mi></b:math> orbitals from the experimental data of the prototypical organic molecule bisanthene (<c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mrow><c:msub><c:mi mathvariant="normal">C</c:mi><c:mn>28</c:mn></c:msub><c:msub><c:mi mathvariant="normal">H</c:mi><c:mn>14</c:mn></c:msub></c:mrow></c:math>) 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.