Momentum-selective orbital hybridisation

Abstract

When a molecule interacts chemically with a metal surface, the orbitals of the molecule hybridise with metal states to form the new eigenstates of the coupled system. Spatial overlap and energy matching are determining parameters of the hybridisation. However, since every molecular orbital does not only have a characteristic spatial shape, but also a specific momentum distribution, one may additionally expect a momentum matching condition; after all, each hybridising wave function of the metal has a defined wave vector, too. Here, we report photoemission orbital tomography measurements of hybrid orbitals that emerge from molecular orbitals at a molecule-on-metal interface. We find that in the hybrid orbitals only those partial waves of the original orbital survive which match the metal band structure. Moreover, we find that the conversion of the metal’s surface state into a hybrid interface state is also governed by momentum matching constraints. Our experiments demonstrate the possibility to measure hybridisation momentum-selectively, thereby enabling deep insights into the complicated interplay of bulk states, surface states, and molecular orbitals in the formation of the electronic interface structure at molecule-on-metal hybrid interfaces.

A minimalist approach to 3D photoemission orbital tomography: algorithms and data requirements

“…Such 3D-POT is highly promising, as the combination with time-resolved photoemission orbital tomography [21][22][23][24] will access spatio-temporal properties of the dynamic electronic wavefunction that are so far inaccessible by experimental means. Additionally, 3D-POT promises a crucial insight at hybrid interfaces, where strong modifications of the electronic structure are known to occur [25,26].…”

Ab Initio Modeling of Mixed-Dimensional Heterostructures: A Path Forward

“…However, it has been shown that it is not necessary to simulate the entire interface explicitly to predict the occurrence of orbital hybridization, which is predicated on just a few properties of the subsystem wave functions. 24,96 To exemplify, we put the |c k | 2 for H 2 Pc in relation to the band structure of MoS 2 [Figure 3a]. Most of the occupied π orbitals are found to be represented by Bloch states close to K and M; the spectral weight of the HOMO of H 2 Pc is mainly concentrated at the K point and negligibly small at the zone center.…”

“…Plotting | c k | 2 for all energies along a high-symmetry path in the BZ of MoS 2 , we obtain the equivalent of an unfolded band structure, which, if computed for atomistically modeled interfaces, contains rich information about intersubsystem orbital hybridization. However, it has been shown that it is not necessary to simulate the entire interface explicitly to predict the occurrence of orbital hybridization, which is predicated on just a few properties of the subsystem wave functions. , …”

“…However, it has been shown that it is not necessary to simulate the entire interface explicitly to predict the occurrence of orbital hybridization, which is predicated on just a few properties of the subsystem wave functions. 24 , 96 …”