Imaging the wave functions of adsorbed molecules

Abstract

The basis for a quantum-mechanical description of matter is electron wave functions. For atoms and molecules, their spatial distributions and phases are known as orbitals. Although orbitals are very powerful concepts, experimentally only the electron densities and -energy levels are directly observable. Regardless whether orbitals are observed in real space with scanning probe experiments, or in reciprocal space by photoemission, the phase information of the orbital is lost. Here, we show that the experimental momentum maps of angle-resolved photoemission from molecular orbitals can be transformed to realspace orbitals via an iterative procedure which also retrieves the lost phase information. This is demonstrated with images obtained of a number of orbitals of the molecules pentacene (C 22 H 14 ) and perylene-3,4,9,10-tetracarboxylic dianhydride (C 24 H 8 O 6 ), adsorbed on silver, which are in excellent agreement with ab initio calculations. The procedure requires no a priori knowledge of the orbitals and is shown to be simple and robust.photoemission spectroscopy | surface science | organic molecules | density functional theory A s the electronic, optical, and chemical properties of nanostructures are defined by their electronic orbitals, in the last decades experimentalists have striven to image them. This is despite the fact that orbitals are not, strictly speaking, quantummechanical observables. Molecules are arguably the best-defined nanostructures, and for simple diatomic molecules, such as N 2 , both the amplitude and the phase of the highest occupied molecular orbital (HOMO) in three-dimensional space have been recovered (1). This tomographic reconstruction requires higher harmonics generated from intense femtosecond laser pulses, focused on a series of molecular alignments, together with theoretical modeling (1). Although offering the exciting prospect of imaging orbitals on the time scale of chemical reactions, being both complex and only appropriate for simple molecules and orbitals, the technique is not generally applicable for the task of orbital reconstruction. Alternatively, scanning probe techniques offer real-space imaging of large molecules with submolecular resolution on surfaces. Although great advances have been made with understanding and controlling scanning probe tips, so-called "tip functionalization" (2), tips are still a factor of uncertainty. With an appropriate tip, the correct nodal structure of orbitals can be directly observed. Moreover, with tip molecules of p-wave structure the relative phase of the sample wave function may be inferred (3). Unfortunately, as the wave functions of the substrate generally spill out beyond the adsorbed molecules, decoupling layers such as NaCl are necessary to avoid direct tunneling into the substrate.The full angle dependence of valence band UV photoelectron spectroscopy from molecular films has been shown to contain rich information on the orbital structure (4, 5). In the past few years a number of studies on molecular films have demonstrated a...

Improved ground-state electronic structure and optical dielectric constants with a semilocal exchange functional

“…On the other hand, when the Slater determinant comprised of KS orbitals captures the physics of the true many-body wave function in a qualitatively correct way, then reliable understanding and insight can already be gained from the KS states. This has been demonstrated impressively, e.g., by photoemission experiments [20][21][22]. We have shown here that the AK13 functional can remedy some of the worst qualitative failures of typical (semi)local functionals.…”

“…1 By now it has been firmly established that relative energies of occupied KS eigenstates can accurately approximate ionization potentials I [19], and, e.g., photoemission experiments have even confirmed the physical interpretability of orbitals themselves [20][21][22].…”

Complete determination of molecular orbitals by measurement of phase symmetry and electron density

“…On the example of the model system PTCDA/Ag(110), we have shown how the phase symmetry can be revealed by group theory with the only presumption being the knowledge of the molecular symmetry, which is well known from both experiments and theory. This constitutes a substantial advance compared with recently published approaches 11 , since the CDAD of photoelectrons is an additional and independent experimental information that can be utilized for the phase reconstruction. In particular, this can provide a route to overcome the primary limitation of the so-called oversampling method applied, for example, in ref.…”

“…Recovering the phase however is if at all only possible by numerical routines 10 , which all require additional assumptions, for example, on the spatial extent of the wave function 11 , and thus intrinsically restrict the significance of the resulting information.…”

Anchoring and Bending of Pentacene on Aluminum (001)

“…19 The filling of the LUMO may even show a dependence on coverage as for pentacene/Ag(111), 4 a phenomenon that is in common with other adsorbed molecules. [20][21][22] 3 Aluminum is also a metal of potential interest for Si-free electronic devices. Pentacene coupled to aluminum could be used to fabricate devices like Schottky diodes and organic thin film transistors (OTFTs) due to the formation of Schottky barriers at their interface.…”