Atomic-scale Stark-shift spectroscopy and microscopy of organic molecules

Abstract

In conventional optical Stark-shift spectroscopy, molecules are exposed to spatially homogeneous static electric fields that shift the energies of their spectral lines. These shifts are attributed to the molecular electronic properties, such as variation of dipolar moment and polarizability of the molecule associated with photo(de)excitation. In realistic environments containing structural defects and nanoscale heterogeneities, however, molecules experience internal electric fields that vary strongly on the molecular scale, rendering the standard Stark selection rules inapplicable. Here we develop an extended theory of atomic-scale Stark shift, addressing such scenarios. Specifically, we present a detailed theoretical analysis of an experimentally relevant configuration where the atomically sharp tip of a light-assisted scanning tunneling microscope is used to controllably apply inhomogeneous electrostatic fields to representative molecular dyes spanning several molecular families. We decompose the total Stark shift into linear and quadratic contributions and show that they contain different information about the molecular properties. Concretely, spatial variations of the linear Stark shift as the tip scans across the molecule enable subnanometric mapping of the charge redistribution between ground and excited electronic states, with high sensitivity to molecular composition and chemical functionalization. The quadratic Stark contribution, in contrast, reflects changes in the conventional dipolar polarizability upon excitation. Together, these results establish nanoscale Stark-shift spectroscopy as a powerful tool for resolving excited-state charge dynamics in single molecules under realistic, strongly inhomogeneous electric fields.

Figures (7)

• Figure 1: Illustration of Stark shifts in homogeneous and inhomogeneous fields. (a) Schematic of the standard Stark effect under a homogeneous electric field. (b) Stark shift of a molecular emission line induced by an external electric field. For centrosymmetric molecules, only quadratic Stark shift is expected under a uniform electric field $\mathbf{F}$. The application of a general inhomogeneously distributed potential $\phi_{\rm ext}$ allows even centrosymmetric molecules to exhibit both linear and quadratic Stark shifts. See the text for details. (c) Schematic of the STM setup, which produces an inhomogeneous electric field in the gap by applying a potential difference between the tip and substrate. (d) Simplified model of the STM configuration, represented by two point charges (the tip charge $-Q$ and its image $Q$) that mimic the strong field localization. The point charges are positioned at a distance from the molecule $z_1=1.3\;\mathrm{nm}$ and $z_2=1.9\;\mathrm{nm}$, and an applied $V=$1V corresponds to a charge magnitude of $Q$ = 0.425e, where e is the elementary charge.
• Figure 2: Chemical structure of the molecules analyzed in the work. (a) Free-base phthalocyanine (H$_2$Pc), free-base porphyrine (H$_2$P), free-base naphtalocyanine (H$_2$Nc) and Zn phthalocyanine with an asymmetric extension of the aromatic core (ZnPc+2/D$_{2\mathrm{h}}$) (b) Pentacene (PE) and quinacridone (QA). (c) Perylene and perylene-, naphthalene-, terrylene- tetracarboxylic dianhydride (PTCDA, NTCDA, and TTCDA respectively). Atom color code: H (white), C (black), N (blue), O (red), and Zn (grey). The molecules marked with (SI) are shown grayed out and are explicitly analyzed in section S3 of the supporting information.
• Figure 3: Electronic structure and spatially resolved Stark-shift maps for the H$_2$Pc molecule. (a) Isosurface plots of frontier molecular orbitals ($\psi$). (b) Schematic depiction of electronic configurations of states S$_0$, S$_1$, and S$_2$ of the molecule, highlighting the dominant single-electron excitation contributing to the S$_0$ to S$_1$ and S$_0$ to S$_2$ optical transitions. (c) Charge-density difference $\Delta\rho_{01}$ of H$_2$Pc, obtained from the calculation of the isolated molecule (without the STM tip), plotted as an isosurface with a value of $5\times10^{-4}e/a_0^3$, $a_0$ being the Bohr radius. (d) Difference in the field-induced charge density, $\Delta\delta\rho_{01}$, plotted as an isosurface with a value of $5\times10^{-6}e/a_0^3$, calculated by positioning the external charges where the quadratic Stark shift (shown in panel g) is maximal. In (c) and (d) red and blue lobes represent regions of positive and negative density, respectively. (e) Total Stark shift map, (f) linear Stark shift map, and (g) quadratic Stark shift map as a function of the lateral position of the tip for S$_0$ to S$_1$ excitation of the H$_2$Pc molecule.
• Figure 4: Electronic structure and spatially resolved Stark-shift maps for the H$_2$P molecule. (a) Isosurface plots of frontier molecular orbitals ($\psi$). (b) Schematic depiction of electronic configurations of states S$_0$ and S$_1$. The S$_0$ to S$_1$ optical transition is expressed as a linear combination of the HOMO-1 to LUMO and the HOMO to LUMO+1 single-electron excitations, with the corresponding weighting coefficients $\alpha=0.75$ and $\beta = 0.64$ calculated from TDDFT. (c) Charge density difference plotted as an isosurface with a value of $5\times10^{-4}e/a_0^3$. (d) Total Stark-shift map as a function of the lateral position of the tip for S$_0$ to S$_1$ excitation. (e) Charge-density differences associated with the HOMO-1 to LUMO transition, $\Delta\rho_{0\mathrm{A}}$, and with the HOMO to LUMO+1 transition, $\Delta\rho_{0\mathrm{B}}$. (f) Linear Stark-shift maps corresponding to the charge-density differences from panel e: $\Delta E_{0\mathrm{A}}^{(1)}$ for the HOMO-1 to LUMO transition and $\Delta E_{0\mathrm{B}}^{(1)}$ for the HOMO to LUMO+1 transition calculated from Eq. \ref{['eq:linear_shift']}.
• Figure 5: Electronic structure and spatially resolved Stark-shift maps for PE and QA molecules. (a) Isosurface plots of frontier molecular orbitals for PE (top) and QA (bottom). (b) Schematic depiction of electronic states S$_0$ and S$_1$ for both QA and PE, highlighting that the S$_0$ to S$_1$ optical transition for both molecules is dominated by the HOMO to LUMO single-electron excitation. The corresponding isosurface plots of $\Delta\rho_{01}$ (PE top, QA bottom) are also shown at a value of $5\times10^{-4}e/a_0^3$. (c) Total Stark shift, (d) linear Stark shift, and (e) quadratic Stark shift maps as a function of the lateral position of the tip for PE. (f) Total Stark shift, (g) linear Stark shift, and (h) quadratic Stark shift maps as a function of the lateral position of the tip for QA.