Energy Ordering of Molecular Orbitals.

P Puschnig,A D Boese,G Koller,E M Reinisch,F S Tautz,M G Ramsey,M Willenbockel,M Meyer,T Ules,D Lüftner,S Soubatch

doi:10.1021/acs.jpclett.6b02517

Abstract

Orbitals are invaluable in providing a model of bonding in molecules or between molecules and surfaces. Most present-day methods in computational chemistry begin by calculating the molecular orbitals of the system. To what extent have these mathematical objects analogues in the real world? To shed light on this intriguing question, we employ a photoemission tomography study on monolayers of 3,4,9,10-perylene-tetracarboxylic acid dianhydride (PTCDA) grown on three Ag surfaces. The characteristic photoelectron angular distribution enables us to assign individual molecular orbitals to the emission features. When comparing the resulting energy positions to density functional calculations, we observe deviations in the energy ordering. By performing complete active space calculations (CASSCF), we can explain the experimentally observed orbital ordering, suggesting the importance of static electron correlation beyond a (semi)local approximation. On the other hand, our results also show reality and robustness of the orbital concept, thereby making molecular orbitals accessible to experimental observations.

Highlights

Despite the fact that orbitals are not, strictly speaking, quantum mechanical observables,[1] a number of experimental techniques have evolved that enable orbital imaging.[2−7] While both the amplitude and the phase of the highest occupied molecular orbital (HOMO) of N2 could be recovered in threedimensional space by high harmonics generated from intense femtosecond laser pulses, this tomographic reconstruction method seems to be applicable only for very simple molecules in the gas phase and only to the frontier occupied orbital.[3]
The frontier orbitals, i.e., the LUMO (A) and HOMO (B), as well the four lower lying π-orbitals (C−F) are depicted in Figure 1, where the alphabetical labeling refers to the energetic order as obtained from density functional (DFT) when employing a generalized gradient approximation (GGA)[24] for exchange-correlation effects
We have demonstrated that photoemission tomography is able to provide an orbital-by-orbital characterization of organic molecules, thereby creating a compelling benchmark for ab initio electronic structure theory

Summary

■ INTRODUCTION

Despite the fact that orbitals are not, strictly speaking, quantum mechanical observables,[1] a number of experimental techniques have evolved that enable orbital imaging.[2−7] While both the amplitude and the phase of the highest occupied molecular orbital (HOMO) of N2 could be recovered in threedimensional space by high harmonics generated from intense femtosecond laser pulses, this tomographic reconstruction method seems to be applicable only for very simple molecules in the gas phase and only to the frontier occupied orbital.[3] On the other hand, scanning probe techniques applied to larger molecules adsorbed on surfaces have led to fascinating real space images of more complicated orbital structures with submolecular resolution.[4,8−12] only frontier orbitals are accessible, and experiments require inserting an insulating decoupling layer between the metal substrate and the molecule and/or the use of functionalized tips It has been known for a long time that the angular dependence of the photoelectron emission from valence bands of molecular films contains rich information on the orbital structure of molecules which can be revealed by the angular resolved photoelectron spectroscopy (ARPES).[13,14] While standard angle-integrating photoemission experiments only reveal energy level positions of orbitals, the photoelectron angular distribution (PAD) is a fingerprint of the orbital structure, a momentum space image of the orbitals. This approach, termed photoemission tomography, has enabled the real-space reconstruction of molecular orbitals from ARPES data.[5−7,17] It provides an orbital-by-orbital characterization of experimental spectra, not restricted to only the HOMO and LUMO.[15,18−20] Thereby, it yields detailed information on the energetic order and spatial structure of orbitals, which can be used as a most stringent test for ab initio electronic structure theory including density functional (DFT) calculations[21] as well as wave function-based approaches

■ RESULTS

■ CONCLUSIONS

■ ACKNOWLEDGMENTS

■ REFERENCES