Vibrational Excitation Mechanism in Tunneling Spectroscopy beyond the Franck-Condon Model

Abstract

Vibronic spectra of molecules are typically described within the Franck-Condon model. Here, we show that highly resolved vibronic spectra of large organic molecules on a single layer of MoS2 on Au(111) show spatial variations in their intensities, which cannot be captured within this picture. We explain that vibrationally mediated perturbations of the molecular wave functions need to be included into the Franck-Condon model. Our simple model calculations reproduce the experimental spectra at arbitrary position of the STM tip over the molecule in great detail.Vibronic excitations are resonant transitions from a molecular ground state to an electronically and vibrationally excited state. These excitations are typically described by the Franck-Condon model. The essence of it are fast electronic transitions treated in Born-Oppenheimer approximation, such that the excitations occur without changes in the nuclear coordinates or momentum. Vibronic excitations in single molecules on surfaces can be detected as resonant sidebands of positive or negative ion resonances in tunneling spectroscopy [1][2][3][4][5][6][7] with apparent submolecular variations due to distinct close-lying orbitals [8][9][10]. In contrast to these resonant excitations, inelastic vibrational excitations far below resonance [6,12,13] are described by a change in the nuclear coordinates, which leads to a modified tunneling matrix element and to the opening of a new tunneling path [7,15,16]. Hence, off-resonant inelastic tunneling and resonant vibronic transitions are treated in distinct and complementary models [17]. The combination of both models would be akin to phonon-mediated electronic transitions in crystal structures [18,19], where the activation of a phonon mode enables otherwise forbidden electronic transitions, as the initial and final state have different parallel momentum in the electronic band structure [20][21][22][23]. Signatures of such combined excitations in single molecules have not been reported to date.Recent tunneling experiments have revealed some limitations of the Franck-Condon model. In cases, where the electronic energy level spacing was similar to vibrational energies, it was found that avoided level crossings determine the resonant sidebands [24,25]. In other cases, intensity variations of the resonant sidebands along an organic molecule were interpreted in terms of coherent vibrational modes with different symmetries [8] or with vibration-assisted coupling of wave functions of different symmetry in molecule and tip [26]. Selection rules could not be derived, because the vibrational modes and associated nuclear displacements of the molecule could not be identified owing to an insufficient experimental energy resolution probably limited by non-adiabatic relaxation effects.Here, we show that vibration-assisted tunneling and Franck-Condon excitations are crucial for a complete vibronic model. To benchmark our model we use vibronic spectra of large organic molecules on a single layer of MoS 2 on Au(111). The van-der-Waals lay...

Extended iron phthalocyanine islands self-assembled on a Ge(001):H surface

“…Different insulating films have already been applied, ranging from ionic salts such as NaCl [8,9], KCl [10,11], or KBr [12], through oxide [13] or nitride [14] layers to molecular wetting layers [15] and two-dimensional materials, such as graphene [16,17], hBN [11,18], or even organic layers [19]. Recently, it has been proposed that a monolayer of transition metal dichalcogenides, for example, MoS 2 , may play a similar role [4,20,21].…”

Monolayers of MoS2 on Ag(111) as decoupling layers for organic molecules: resolution of electronic and vibronic states of TCNQ

“…The narrow width thus reflects that MoS 2 acts as a decoupling layer from the metal substrate. However, this resonance width is broader than what has been observed for the HOMO resonance of other organic molecules on MoS 2 on Au(111) [26,52,56]. In contrast to those cases, where the HOMO lay well inside the electronic gap of MoS 2 , the LUMO of TCNQ is located right at the onset of the conduction band.…”

“…6 fs of the excited state. This is almost one order of magnitude longer than on the bare metal surface, where the hot electron vanishes into the bulk on ultrafast timescales, but an order of magnitude shorter than for molecular resonances well separated from the band onsets [26,52,56]. Yet, the increase in the lifetime of the excited state allowed us to resolve vibronic states of the transiently negatively charged TCNQ molecule albeit only up to approx.…”

“…This value was chosen because it represents reasonable tunneling conditions in experiments. However, variation of the tip height by (±2 Å) does not have any influence on the observation of the main features within the map (i.e., nodal planes, or intensity maxima) [52].…”

“…We further note that the experimental spectrum was taken on a cyano group, where no nodal planes exist in the LUMO, as their presence may lead to vibration-assisted tunneling in addition to the bare Franck-Condon excitation [52].…”