Exploring three-dimensional orbital imaging with energy-dependent photoemission tomography

Abstract

Recently, it has been shown that experimental data from angle-resolved photoemission spectroscopy on oriented molecular films can be utilized to retrieve real-space images of molecular orbitals in two dimensions. Here, we extend this orbital tomography technique by performing photoemission initial state scans as a function of photon energy on the example of the brickwall monolayer of 3,4,9,10-perylene tetracarboxylic dianhydride (PTCDA) on Ag(110). The overall dependence of the photocurrent on the photon energy can be well accounted for by assuming a plane wave for the final state. However, the experimental data, both for the highest occupied and the lowest unoccupied molecular orbital of PTCDA, exhibits an additional modulation attributed to final state scattering effects. Nevertheless, as these effects beyond a plane wave final state are comparably small, we are able, with extrapolations beyond the attainable photon energy range, to reconstruct three-dimensional images for both orbitals in agreement with calculations for the adsorbed molecule.

Energy Ordering of Molecular Orbitals

“…1 This approach, termed photoemission tomography, has enabled the real-space reconstruction of molecular orbitals from ARPES data. 5−7,16 It also provides an orbital-by-orbital characterization of experimental spectra, not restricted to only the HOMO and LUMO. 14,17−19 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 20 as well as wave function-based approaches.…”

Can photoemission tomography be useful for small, strongly-interacting adsorbate systems?

“…Although the agreement between the simulated (figure 3(c)) and measured ( figure 3(d)) momentum maps may be not as convincing as in previous photoemission tomography studies for larger molecules with more repeat units, see e.g. [3][4][5][6]8], the assignment of orbitals of a molecule as small as benzene is still possible. This allows a number of conclusions to be drawn.…”

“…As a combined experimental/theoretical approach, PT uses angle-resolved ultraviolet photoemission spectroscopy (ARUPS) over a wide angular range and seeks an interpretation of the photoelectron angular distribution, so-called momentum maps, in terms of the molecular orbital structure of the initial state. PT has found many interesting applications including the assignment of molecular orbital densities in momentum and real space [3][4][5][6][7][8], the deconvolution of spectra into individual orbital contributions beyond the limits of energy resolution [9][10][11][12], or the extraction of detailed geometric information [13][14][15][16][17][18]. These successes have been on relatively large molecules adsorbed on noble metal surfaces and the usefulness of PT to smaller molecules and particularly on more reactive surfaces has not been investigated.…”

Ultrafast molecular orbital tomography of a pentacene thin film using time-resolved momentum microscopy at a free-electron laser

“…Angle-resolved photoelectron spectroscopy (ARPES) is a well-known and powerful method to investigate the electronic structure of molecules. In the last decade, orbital tomography has emerged as an exciting extension of the photoemission technique for imaging localized electronic wave functions in thin film molecules [5][6][7][8][9] . In this framework, the photoemission process can be described either in a one-step model where the final state is represented by a plane wave or using more sophisticated final state approximations [10][11][12][13] .…”