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The combination of scanning-probe microscopy with an increasing number of spectroscopic techniques provides insight into the properties of individual molecules at their intrinsic atomic scale. Examples of such single-molecule studies with atomic-scale local information encompass structure determination1, orbital density imaging2 and electron-spin resonance3,4. In particular, the integration of optical spectroscopy into local-probe microscopy such as Raman5 and luminescence6 has recently provided atomic-scale insights into light–matter interaction: theoretical concepts can now be tested and visualized directly in space providing an understanding of the fundamental processes in light emission from organic materials7.

Despite its very direct access to well-defined single-molecule model systems, the unambiguous assignment of observations to specific electronic quantum transitions is not always straightforward. For example, the assignment of a scanning tunnelling microscopy (STM) luminescence signal as phosphorescence or trion-related fluorescence is contradictory in recent literature8,9. Similarly, in scanning tunnelling spectroscopy (STS), the discrimination of energetically higher-lying excited states from multiple charging effects is usually difficult10,11. One issue is that in STS the molecule typically reverts to its ground state, since a tip-to-molecule tunnelling event is followed by a quick molecule-to-substrate tunnelling event, and the two events are not detected separately. As the charge exchange with the surface is elusive in most STM experiments, it is in some cases very challenging to discern the different processes. For example, in STS, a feature at a higher bias voltage than required for tunnelling into the lowest unoccupied molecular orbital (LUMO) might be associated to either electron tunnelling into the LUMO+1 or to tunnelling of a second electron into the LUMO starting from a transient charge state. Even upon combining techniques such as luminescence with tunnelling spectroscopy, studying the individual electronic transitions separately remains out of reach, since several electronic transitions lead to one spectral feature.

The use of insulating films, thick enough to prevent tunnelling of charges to and from the underlying support, allows separating the individual electronic transitions by controlling and measuring the tunnelling of single electrons between a conductive tip of an atomic force microscope and a single molecule4,12,13,14,15,16. At the same time, several of the molecule’s charge states become accessible17. While select transitions between electronic states were measured18, mapping out the excitation spectrum of an individual adsorbed molecule remained out of reach.

In this Article, building on these developments, we propose a single-molecule spectroscopy method that allows probing many quantum transitions of different types individually, including radiative, non-radiative and redox transitions, in which the charge state changes. By controlled charge exchange between the conductive tip of an atomic force microscope and the molecule, we bring the latter into different electronic configurations, including those with different net charges. The detection proceeds via the force acting on the probe tip13,14. Guided by the different characteristic lifetimes of the states, we can thereby energetically map out the low-energy electronic states of individual molecules. We demonstrate the power of this spectroscopy by applying it to pentacene and perylenetetracarboxylic dianhydride (PTCDA), thereby shedding light on the interpretation of the recent prominent STM-induced luminescence experiments on PTCDA8,9.

Excitation and read-out scheme

A schematic of the experimental set-up is shown in Fig. 1a. Pentacene and PTCDA molecules were deposited on a thick NaCl film (>20 monolayers (ML)) on Ag(111), where the NaCl electrically isolates the molecules from the underlying metal17. Voltage pulses were applied as a gate voltage to the Ag(111) substrate. The gate voltage VG controls the alignment of the molecular electronic states with respect to the Fermi level of the tip, and steers single-electron tunnelling between the tip and the molecule, used for mapping out the electronic transitions.

Fig. 1: Experimental set-up, energy-level diagrams and gating.
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a, Sketch of the experimental set-up. Molecules (pentacene and PTCDA) were deposited on a >20 ML thick NaCl film that prevents tunnelling to the underlying Ag(111) substrate. A pump–probe voltage pulse sequence was applied to steer single-electron tunnelling between the tip and the molecule. b, Many-body energy diagram of the electronic states of a typical molecule with a closed-shell ground state. S, D and T refer to singlet, doublet and triplet states, respectively. The small diagrams depict the electronic configuration, that is, the occupation of the HOMO (bottom) and LUMO (top). The relative energetic alignment of the states depends on the specific molecule, work function of the surface and the applied gate voltage VG. c, Schematic of the double-barrier tunnelling junction. VG shifts the molecular levels with respect to the Fermi level EF of tip and Ag substrate. A part of VG, that is, (1 – α)VG, drops in the NaCl film, and the remainder, that is, αVG, drops in the vacuum between the tip and the molecule. In the situation shown, the applied voltage enables tunnelling of an electron from the tip to the LUMO. To simplify the illustration, it implies that at VG = 0, there is no electric field in the junction—without loss of generality for other situations. d, Many-body energy diagram showing the same gating and tunnelling processes as in c: tunnelling an electron into the LUMO of the ground-state molecule brings the molecule from the S0 to the D0− state. The shifts of the energy levels owing to VG with respect to EF of the tip are indicated in orange. In the many-body diagram on thick films, tip–sample tunnelling events correspond to transitions that go downward in the many-body diagram (blue arrow; the corresponding tunnelling event is also indicated in c).

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To guide the understanding and the interpretation of the results, we use a many-body description of the states. First, we consider a generic system of a molecule with a closed-shell ground state, without degeneracies of the frontier orbitals. Figure 1b shows the corresponding low-lying electronic states. Such molecules have the singlet state S0 as the ground state, in which all electrons are paired up, filling the orbitals up to the highest occupied molecular orbital (HOMO). Typically, the lowest-lying excited states are formed by exciting one of the electrons from the HOMO to the LUMO. Thereby, either the first excited triplet state T1 or the first excited singlet state S1 is formed, which are separated by the exchange interaction of the two unpaired electrons. For some molecules, a second excited triplet state T2 (not shown here) may be located energetically between T1 and S1. Upon removing or adding one electron, the doublet ground states D0+ and D0− of the charged molecule are formed, respectively. The corresponding lowest-lying excited states are D1+ and D1−, depicted here with one electron being excited from the HOMO to the LUMO. Throughout the paper, we refer to the orbital electronic levels according to the neutral molecule’s states. Depending on the molecule under study, D1+ and D1− may instead involve an excitation from the HOMO-1 to HOMO or from LUMO to LUMO+1, respectively. In any case, D1+ and D1− are characterized by an exciton in the molecule that carries a net charge, also called trion. Note that many of the states are expected to have a multi-reference character. For instance, we find by modelling that the S0 state described above has a non-zero contribution of a configuration with two electrons in the LUMO and none in the HOMO (Supplementary Section 12).

When comparing energies of states with different net charges in the many-body description on thick insulating films, one has to consider at which energy the molecule can exchange electrons with the tip. An applied VG shifts the molecule’s single-particle levels with respect to the Fermi level of the tip (Fig. 1c). This changes the energy of the many-body states with different net charges with respect to each other while leaving the energy differences within one charge state unaltered. Specifically, VG will shift the states by qαVG, with q being the net charge of the molecule and α the lever arm19,20,21, thus shifting the positive (+) and negative (–) charge states in opposite directions (Fig. 1d). α is a constant scaling factor between VG and the energy scale, because some part of the gate voltage VG drops across the NaCl film located between the molecule and the supporting gate (Fig. 1c).

To acquire a spectrum, we repeatedly apply a pulse sequence to the gate voltage, controlling cycles of driven tunnelling events and charge-state detection. In each sequence, we first bring the molecule with a set pulse to a defined state, for example, the D0+ state (Fig. 2a). Subsequently, a sweep pulse with a voltage Vsweep is applied, bringing the molecule via one or more tunnelling events to a variety of possible states. Finally, a read-out voltage is applied that corresponds to the charge-degeneracy point17 between S0 and one of the singly charged ground states, that is, D0+ or D0− (refs. 4,16) (Fig. 2a). At this voltage, the resulting charge state is read out by means of the electrostatic force acting on the tip14, as shown in Fig. 2c. Interconversion between the two degenerate charge states by single-electron tunnelling to/from the tip is prevented by the vanishing Franck–Condon overlap22 between their vibrational ground states owing to the large electron–phonon coupling. The Franck–Condon factors become large for much higher-lying vibrational states. Considering a phonon bath, this results in a Gaussian-shaped transition probability23 (Fig. 2b). These Gaussian-shaped transition probabilities being offset with respect to the vibrational ground states by the relaxation energies are schematically depicted in the many-body diagrams by rotated Gaussians (Fig. 2a).

Fig. 2: Pulse sequence, transition probabilities and read-out signal.
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a, Typical pump–probe voltage pulse sequence with the many-body energy diagrams (cf. Fig. 1b,d) showing possible transitions for the different phases of the sequence (only three states are shown for simplicity). Thicker arrows indicate dominating transitions (Supplementary Section 2). The molecule is initialized in a specific state (here D0+) by the set pulse with voltage Vset, followed by a sweep pulse with variable time tsweep and voltage Vsweep. The states are subsequently mapped onto two different charge states using a read-out voltage Vread-out, which is adjusted such that two different charge states are degenerate. The different charge states can be discriminated by AFM. b, Franck–Condon picture of the strong coupling between net charges in the adsorbed molecule and phonons in the ionic film23, depicted exemplarily for D0+ and S0. Because of the strong coupling, the two states have their energy minimum at significantly shifted nuclear coordinates. Therefore, there is a vanishing overlap of their vibrational ground states (red and yellow Gaussians) such that zero-phonon transitions are blocked (crossed-out arrow). Consequently, for a gate voltage, for which the states are (close to) degenerate, the molecule becomes charge bistable. The Franck–Condon factors (horizontal grey bars) become large for high-lying vibrational states (the wavefunction, for which the overlap with the ground-state wavefunction is largest, is shown exemplarily). Considering a phonon bath, this results in a nearly Gaussian-shaped transition probability23 (grey distribution), the maximum of which is offset to the ground state by the relaxation energy22,23. This Gaussian-shaped transition probability is indicated in the many-body diagrams (a), where transitions occur dissipatively from a vibrational ground state (black lines) to an excited vibrational state. c, Raw data trace measured for a pentacene molecule using the pump–probe voltage pulse sequence shown in a. The frequency shifts of the D0+ and S0 states are indicated by the red and yellow lines, respectively. The dotted lines indicate the start of every pump–probe voltage pulse cycle. The duration of the set and sweep pulses is negligible against the duration of the read-out interval (125 ms).

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This read-out scheme also allows differentiating certain electronic states that correspond to the same charge state. For example, S0 and T1 can be distinguished by projecting them onto different charge states4,16, such as S0 and D0+, respectively. At the read-out voltage corresponding to the S0–D0+ degeneracy point, the molecule will stay in S0 if it was in S0 at the end of the sweep pulse, while it will transit into D0+ if it was in T1. In general, all the resulting states after each sweep pulse are mapped onto the two different charge states being degenerate at the read-out voltage. Upon repeating this voltage pulse sequence 8 times per second, typically for 80 s for a given Vsweep, the population in the two resulting charge states was determined as a function of Vsweep (Fig. 2c shows part of a measured atomic force microscopy (AFM) data trace for one Vsweep). The further Vsweep differs from Vset, the more transitions become possible, allowing us to infer the transitions during the sweep pulse and in turn the energetic alignment of the low-lying electronic states, as follows.

Excited-state spectroscopy on pentacene

Figure 3a shows the results of such an experiment for a single pentacene molecule, with read-out at the S0–D0+ degeneracy. Here the set pulse prepares the molecule in D0+ (Fig. 3b). For Vsweep voltages close to Vread-out, the molecule remains in D0+ owing to the Franck–Condon blockade22,23 (Fig. 2b); hence at the end of each cycle, the state is read-out as D0+. Upon increasing Vsweep and thereby passing certain threshold voltages, labelled as (1, 2, …), various transitions open or close. To facilitate the understanding, schematic diagrams in Fig. 3g show the possible transitions when passing the corresponding Vsweep threshold voltages. Upon Vsweep passing (1), a first tunnelling channel opens and an electron can tunnel from the tip into the HOMO resulting in S0 (Fig. 3g). At (2) the electron can tunnel into the LUMO forming T1. Importantly, this T1 state has a lifetime of tens of microseconds16 and is mapped onto D0+ during the read-out interval, while the population in S0 remains in S0 (ref. 16) (Fig. 3c).

Fig. 3: Excited-state spectroscopy of pentacene, initialized in the cationic charge state.
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a,d, Plot of the read-out fraction (normalized population during the read-out phase) in the D0+ (a) and D0− (d) states, respectively, as a function of Vsweep. The voltage pulse sequence was similar to Fig. 2a (Vset = −3.795 V), using Vread-out at the S0–D0+ (Vread-out = −2.795 V) and S0–D0− (Vread-out = 1.416 V) degeneracies for a and d, respectively. Four different tsweep were used, as indicated. Each data point corresponds to the normalized discrete counts of 640 pump–probe cycles and the error bars are ± s.d. of the binominal distribution (Methods). Solid lines represent fits to the data (Supplementary Sections 7 and 8). Vertical dotted lines are guides to the eye; for fitted threshold voltages, see Supplementary Table 1. AC-STM images15 (insets) are measured for the same individual pentacene molecule (oscillation amplitude A = 1 Å): S0 → D0+ (HOMO), Δz = −2.6 Å, VG = −2.9 V, Va.c. = 1.2 V peak-to-peak (Vpp); S0 → D0− (LUMO), Δz = −2.0 Å, VG = 1.43 V, Va.c. = 1.2 Vpp. The tip-height offset Δz is relative to the set point Δf = −1.443 Hz at V = 0 V, A = 3 Å. Red dots indicate the positions at which the spectra were measured. b,c,e,f, Many-body energy diagrams (cf. Fig. 1b,d) of the transitions taking place during the set pulse (b,e) and at the beginning of the read-out phase (c,f) for the spectra shown in a and d, respectively. The initialization state is indicated by a blue dot. g, Many-body energy diagrams at the sweep voltages indicated by the dotted lines. The process(es) that cause the change in the spectra around the indicated voltage are represented by red arrows (opening of transitions) and crosses (closing of transitions). At (3) two new transitions open, indicated with A and B, and referred to as (3A) and (3B). The opening of a certain transition (horizontal red arrows) may also enable a cascade of further transitions (downward red arrows in (3) and (6)). The relative thicknesses of the different arrows connecting two charge states roughly indicate the ratio of the rates governed by their tunnelling barriers (Supplementary Section 2).

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In general, the assignment of features in the read-out signal to certain molecular transitions can be achieved by analysing the temporal evolution of the many-body state populations as follows. The transition rates associated to the tunnelling of electrons between tip and molecule can be controlled by the tip–sample distance and are chosen to be in the range of a fraction of a microsecond to a few microseconds (Methods). By contrast, the triplet-to-singlet transition occurs on a considerably longer timescale of tens of microseconds16, whereas optically allowed transitions are typically much faster than the chosen charge-transition rates24. By varying the duration of the sweep pulse, the temporal evolution of the populations can be extracted, providing insight into the transition rates.

The assignment of other features in the spectra at increased sweep voltages follows the procedure as outlined above, namely by considering which transitions sequentially open and which time dependence is associated to it. If several transition pathways are available, their competition must be considered. The interpretation of the features was further guided by repeating the experiments with a different read-out voltage, mapping the states onto D0− and S0 instead of D0+ and S0 (Fig. 3d). The assignment of the features in Fig. 3a,d is visualized in Fig. 3g and discussed in detail in Supplementary Sections 1, 3 and 6.

Importantly, next to the sequential opening of transitions starting at D0+, we can also detect transitions from the neutral state to the negatively charged state. For instance, we assign that at (3B) the T1 → D0− pathway opens. From an additional experiment, we can discriminate transitions starting at D0+ from those starting at the neutral molecule. To this end, we initialized the molecule in the neutral state, approximately equally populating S0 and T1 (Methods). The results are shown in Fig. 4 and discussed in detail in Supplementary Sections 1, 4 and 6, while Extended Data Figs. 1 and 2 summarize all spectra and many-body diagrams for pentacene, respectively.

Fig. 4: Excited-state spectroscopy of pentacene, initialized in the neutral charge state.
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a,d, Plot of the measured read-out fraction in the D0+ (a) and D0− (d) states, respectively, as a function of Vsweep. Measurements were performed with a voltage pulse sequence similar to Fig. 2a. A set pulse was used to initialize the molecule in S0 or T1, with approximately equal population (Methods). The read-out was at the S0–D0+ (Vread-out = −2.795 V) or S0–D0− (Vread-out = 1.416 V) degeneracies for a and d, respectively. Four different tsweep were used, as indicated. Each data point corresponds to the normalized discrete counts of 640 pump–probe cycles and the error bars are ± s.d. (Methods). Solid lines represent fits to the data (Supplementary Sections 7 and 8). b,c,e,f, Many-body energy diagrams of the transitions taking place during the set pulse (b,e) and at the beginning of the read-out phase (c,f) for the spectra shown in a and d, respectively. g, Many-body energy diagrams of the assigned transitions happening around the sweep voltages indicated by the dotted lines. The transitions that correspond to those present in Fig. 3 are indicated with the same number. The arrows, crosses and dots are analogous to Fig. 3g. Note that if the sweep voltage is close to the set voltage (between (8) and (3B)), the population remains in the T1 and S0 states (see diagram at Vsweep = Vset). Only upon reducing or increasing Vsweep outside this range different transition channels open and/or close as indicated.

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Many-body energies of pentacene

The relative energies of the electronic states can be derived by fitting the four sets of data shown in Figs. 3 and 4. To this end, we formulated a set of differential rate equations (Supplementary Section 7) based on the possible electronic transitions. On the basis of these rate equations, we fitted the four sets of data, including different tsweep, simultaneously, obtaining one common set of fitting parameters for all data. The resulting fits are indicated by the solid lines in the plots of Figs. 3 and 4, resembling the data very well and thereby supporting our interpretation of the processes mentioned above. For details of the fitting procedure, see Supplementary Sections 7 and 8.

From these fits, a many-body energy diagram can be derived. To this end, the determined voltages have to be rescaled to energies taking into account the partial voltage drop across NaCl, that is, the lever arm19,20,21 α. To derive α, we calibrated our energies using the S0–S1 energy difference determined as 2.26 eV by STM-induced luminescence for pentacene on NaCl(4 ML)/Ag(100)25 (Supplementary Section 9). This calibration implies a voltage drop of 30 ± 2% across NaCl in our experiments, corresponding to a lever arm α = 0.70 ± 0.02. To account for potential influences of the environment (for example, presence of nearby step edges), as well as the possible influence of the metallic tip and its work function, the measurements were repeated for four different pentacene molecules, using four different metallic tip apexes. The many-body spectrum was derived from the averaged energies found for the four experiments (Supplementary Section 10 and Supplementary Table 2). To derive energy differences, we take the difference between two processes starting at the same state and ending in the two states of interest (for example, D0+ → S0 and D0+ → T1 for the S0–T1 energy difference). We find a S0–T1 energy difference of (0.90 ± 0.06) eV and a D0−–D1− energy difference of (0.99 ± 0.04) eV (Supplementary Section 10). The obtained S0–T1 energy difference of pentacene matches within uncertainty margins the value determined for pentacene in a tetracene crystal (0.86 ± 0.03) eV (ref. 26), despite the difference of environments.

Deriving energy differences as described above is subject to the implicit assumption that the relaxation energies21 of the two involved transitions are similar. Because these transitions occur between the same charge states (for example, from positive to neutral), this assumption seems reasonable. Moreover, the validity of this assumption can be scrutinized experimentally by extracting the reorganization energies (sum of the relaxation energies) and the line widths from our spectroscopic data. To extract the reorganization energies, we consider pairs of transitions in opposing directions. For three of such pairs (D0+ ↔ S0, D0+ ↔ T1 and S0 ↔ D0−), we find reorganization energies of roughly 0.9 eV, differing only slightly (see Supplementary Section 10 for details). The similar line widths of the many different charge transitions observed in our data suggest that also the corresponding relaxation energies are similar23.

Excited-state spectroscopy on PTCDA

To demonstrate the wider applicability of this spectroscopic technique, we chose a system that is controversial in the literature. Specifically, the same STM-induced luminescence signal measured for PTCDA on thin NaCl films has been interpreted differently, on the one side, as phosphorescence of the neutral molecule8 and, on the other side, as fluorescence of the anion9, corresponding to either the T1 → S0 (ref. 8) or the D1− → D0− (ref. 9) transition, respectively. Figure 5 shows the resulting spectra for PTCDA for read-out of the signal at the D0+–S0 degeneracy. The analysis of the data was performed analogous to the one for pentacene, and the differences are discussed in Supplementary Section 5.

Fig. 5: Excited-state spectroscopy of PTCDA.
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a,d, Plot of the measured read-out fraction in the D0+ state as a function of Vsweep. Measurements were performed with a voltage pulse sequence similar to Fig. 2a. A set pulse was used to initialize the molecule in the cationic state D0+ (Vset = −5.30 V) (a) and in the neutral charge state with 20% in S0 and 80% in T1 (d) (Methods). The read-out was at the S0–D0+ degeneracy (Vread-out = −4.30 V). Five different tsweep were used, as indicated. Each data point corresponds to the normalized discrete counts of 640 pump–probe cycles and the error bars are ± s.d. (Methods). Solid lines represent fits to the data (Supplementary Sections 7 and 8). The transition voltages are indicated by dotted lines with numbers indicating the assigned level alignment (see Figs. 2 and 3 and Supplementary Fig. 4 for the many-body energy diagrams). The insets show AC-STM images15 measured for the same PTCDA molecule (oscillation amplitude A = 1 Å): S0 → D0+ (HOMO), Δz = −2.3 Å, VG = −4.55 V, Va.c. = 1.2 Vpp; S0 → D0− (LUMO), Δz = −1.5 Å, VG = 0.11 V, Va.c. = 1.2 Vpp. Δz is relative to the set point Δf = −1.75 Hz at V = 0 V, A = 3 Å. The red dots indicate the position at which the spectra shown in Fig. 5 and Supplementary Fig. 10 were measured. Note that these images were taken at a tip–sample distance being 2.3 Å and 1.5 Å smaller than used for the excited-state spectroscopy, respectively. b,c,e,f, Many-body energy diagrams of the transitions taking place during the set pulse (b,e) and at the beginning of the read-out phase (c,f) for the spectra shown in a and d, respectively. These diagrams are not quantitative and for illustration purposes only.

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Fitting the data results in the curves shown in Fig. 5a,d. The calibration of the lever arm was done at the S0–S1 transition of a pentacene molecule that was co-adsorbed on the same NaCl terrace as the PTCDA molecule under study (Extended Data Fig. 3). From the fits, the energies of the S0–S1, S0–T1 and D0−–D1− differences were determined as (2.39 ± 0.11) eV, (1.28 ± 0.07) eV and (1.34 ± 0.08) eV, respectively.

These values match closely those reported in the STM-induced luminescence experiments8,9 for PTCDA. The S1–S0 luminescence signal was reported to have an energy of 2.45 eV, while a second signal at 1.33 eV was controversially assigned either as T1–S0 or D1−–D0− (refs. 8,9). Our results indicate that both processes match in terms of energy the observed luminescence signal at 1.33 eV. The previous assignment of the luminescence signal as phosphorescence and, hence, to the T1–S0 transition was mainly based on comparing the photon energy with calculated energy differences of the two possible transitions8. Our data suggest that these two energies—extracted here experimentally—are too close to allow for an assignment of the transitions based on their energies.

Figure 6b shows the energy-level alignment that we determined for PTCDA on thick NaCl films (>20 ML). The alignment for ultrathin NaCl films (for example, 3 ML) can be extrapolated to comprehend how the molecule may cycle through different states during STM-luminescence experiments for a given bias voltage. For this extrapolation, one needs to consider increased screening2,27,28,29, the possibility of a change in the work function28,30, the different lever arm and tunnelling to the substrate. Guided by the energies that are available from the experiments on ultrathin films, the many-body diagram on ultrathin (3 ML) NaCl films can be derived (see Supplementary Section 11 for details).

Fig. 6: Many-body energy diagrams.
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a,b, Many-body energy diagrams of the electronic states of pentacene (a) and PTCDA (b) in the absence of gating, derived from fitting of excited-state spectroscopy measurements for four individual pentacene molecules and one PTCDA molecule, respectively. As in Fig. 2a, the rotated Gaussians (grey) indicate the broadening of the transitions owing to electron–phonon coupling, although they are not a property of the state, but of the transition being made. Here all relaxation energies and widths are set to their averaged values derived from fitting the experimental data. The relaxation energies are set to half of the reorganization energies. The excited triplet state T2 of PTCDA is assumed to have one electron in the HOMO and the other in a state higher in energy than the LUMO, that is, a higher-lying unoccupied orbital (T2 may also entail further contributions of other configurations). c, Many-body energy diagram of PTCDA extrapolated to ultrathin films (see Supplementary Section 11 for details) showing two possible pathways (orange and red) that could lead to the STM-induced luminescence signal with 1.33 eV photon energy for PTCDA8,9 (both starting with the transition from the ground state D0− to T1, blue arrow). This many-body energy diagram is drawn with respect to the chemical potential of the substrate and a bias voltage VB of −2.5 V applied. That way, tunnelling events to or from the substrate result in transitions that lower the energy. By tip-molecule tunnelling charge transitions that increase the energy by maximally eVB become possible, such as the D0− → T1 transition (involving molecule-tip tunnelling, blue arrow) shown here (note that at this voltage also the D0− → S0 transition is possible (not shown)). On ultrathin films the molecule will revert back to its ground state (here D0−) by molecule-substrate tunnelling. Next to the direct transition from T1 to D0− (not shown), pathways via S0 (orange) and D1− (red) are possible. Here the bias voltage also shifts (gates) the charged states with -q(1-α)VB, as explained in Supplementary Section 11, which is taken into consideration in the level alignment shown.

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In case of PTCDA on 3 ML NaCl films on Ag(111), the negative charge state is the ground state8,31. LUMO imaging at a threshold voltage of −0.55 V (ref. 8) suggests that at this voltage an electron tunnels out of the LUMO resulting in the S0 state. From our results, we can infer that T1 is 1.28 ± 0.07 eV higher in energy than S0, which matches with the reported observation of a second peak in STS at a voltage of −2.05 V (ref. 8), if a lever arm α of 0.89 is taken into account (Supplementary Section 11). The threshold voltage of this D0− → T1 process corresponds to the threshold voltage for observing the luminescence signal with a photon energy of 1.33 eV (ref. 8). This implies that the population of T1 is important for the cycle leading to the luminescence signal. One interpretation of the observed luminescence is that it is due to phosphorescence from T1 to S0 (orange, Fig. 6c). However, T1 being part of the luminescence cycle does not necessarily imply that the observed luminescence occurs from this state. Alternatively, T1 can decay to D1− by an electron tunnelling from the substrate into the LUMO, opening the D1− → D0− luminescence transition (red, Fig. 6c). Note that both pathways become accessible at the voltage where T1 can be formed. Which pathway is dominating is given by the rates of the involved processes: phosphorescence from T1 to S0 versus tunnelling from T1 to D1−. Recently, the lifetimes of out-of-equilibrium charge states on 3 ML of NaCl were found to be on the timescale of 100 ps (ref. 11). By contrast, we find a T1 state lifetime of approximately 300 µs on >20 ML NaCl (Extended Data Fig. 4) pointing towards a faster rate of T1 decaying into D1− than into S0. Note, however, that luminescence lifetimes can be strongly reduced on a few ML of NaCl. On the basis of our results, we can therefore not rule out the phosphorescence pathway. Note further that in case of a quinacridone molecule also both pathways were accessible, but in this case, luminescence mapping allows to disentangle the two pathways and assign the signal to luminescence of the charged exciton instead of phosphorescence10.

Conclusion

The method that we introduce provides insights into individual electronic transitions of single molecules. It allows extracting the energy levels of ground and excited states for different charges, as well as the reorganization energies of redox transitions. In addition, relative rates of competing transitions can be accessed. We expect that the method can be applied to a wide range of molecules and even to multiple-charged ionic states, with the requirement of the presence of a long-lived state. Previous knowledge of some of the electronic properties is helpful but not necessary. Thereby, our method can be used for the quantification of excitation energies that are difficult to access otherwise, for example, those of triplet excitations32. Similarly, it can guide the understanding of STM-induced luminescence experiments on ultrathin insulating films, for which sequential and competing transitions are extremely challenging to characterize individually. Further, we anticipate that the spatial dependence of this spectroscopic method could be exploited for a spatial mapping of excited states. Furthermore, our pump–probe pulse scheme allows preparation of a molecule in a specific excited state and control of subsequent transitions. This level of control represents a toolset to guide, understand and engineer tip-induced chemical reactions as well as phosphorescence and fluorescence of individual molecules.

Methods

Set-up and sample preparation

Experiments were carried out with a home-built atomic force microscope equipped with a qPlus sensor33 (resonance frequency, f0 = 30.0 kHz; spring constant, k ≈ 1.8 kNm−1; quality factor, Q ≈ 1.9 × 104) and a conductive Pt-Ir tip. The microscope was operated under ultrahigh vacuum (base pressure, P < 10−10 mbar) at T ≈ 8 K in frequency-modulation mode, in which the frequency shift \(\Delta f\) of the cantilever resonance is measured. The cantilever amplitude was 1 Å (2 Å peak-to-peak). AC-STM images10 were taken in constant-height mode, at a reduced tip height as indicated by the negative Δz values (tip-height change with respect to the set point).

As a sample substrate, an Ag(111) single crystal was used that was prepared by sputtering and annealing cycles (annealing temperature, T ≈ 600 °C). A thick NaCl film (>20 ML) was grown on half of the sample at a sample temperature of approximately 80 °C. In addition, a sub-ML coverage of NaCl was deposited on the entire surface at a sample temperature of approximately 35 °C. The tip was prepared by indentation into the remaining bare Ag(111) surface, presumably covering the tip apex with Ag. The measured molecules (pentacene and PTCDA) were deposited in situ onto the sample inside the scan head at a temperature of approximately 8 K.

The a.c. voltage pulses were generated by an arbitrary waveform generator (Pulse Streamer 8/2, Swabian Instruments), combined with the d.c. voltage, fed to the microscope head by a semi-rigid coaxial high-frequency cable (Coax Japan) and applied to the metal substrate as a gate voltage \({V}_{{\rm{G}}}\). The high-frequency components of the pulses of \({V}_{{\rm{G}}}\) lead to spikes in the AFM signal because of the capacitive coupling between the sample and the sensor electrodes. To compensate these spikes, we applied the same pulses with opposite polarity and adjustable magnitude to an electrode that also capacitively couples to the sensor electrodes. Reflections and resonances in the gate-voltage circuitry were avoided by impedance matching, absorptive cabling and limiting the bandwidth of the external circuit to approximately 50 MHz. Experimental tests showed no indication of severe waveform distortions.

Spectroscopy pulse sequence and data acquisition

The spectra shown in Figs. 2–4 and Supplementary Figs. 2–4 and 7–10 were measured using a voltage pulse sequence similar to the one shown in Fig. 2a, as detailed in the captions of the figures.

To initialize in the D0+ state, the set-pulse voltage and duration were chosen such that it reliably brings the molecule in this state. We chose, therefore, a set pulse with a voltage that exceeds the relaxation energy for the S0 → D0+ transition having a duration that is much longer than the decay constant of this transition. Specifically, a set-pulse voltage was chosen that is 1 V lower than the D0+–S0 degeneracy point, having a duration of 33.4 µs (one cantilever period). To initialize in the S0 and T1 states (for example, in Fig. 4), the set-pulse sequence consists of two parts: a pulse to bring the molecule to D0+ (the same parameters are used as for the pulse used to initialize in D0+) and another pulse to subsequently bring the molecule in the T1 state. The second pulse is at −0.3 V (Fig. 4a,d, pentacene) (in general, it was set to Vread-out + 2.5 V for pentacene) or −1.8 V (Fig. 5d, PTCDA), respectively. Note that this pulse sequence has the same effect as the set and sweep pulse for the data at −0.3 V in Fig. 3a or −1.8 V in Fig. 5a, respectively. The duration of the second pulse determines the ratio of population of the T1 and S0 states, since the T1 state will decay during this pulse to the S0 state according to its molecule-specific lifetime. At the end of a 33.4 µs long second pulse of the set-pulse sequence with Vset = −0.3 V, the T1 and S0 population is 0.51 ± 0.01 and 0.49 ± 0.01, respectively, in case of pentacene in Fig. 4. By contrast, the same set-pulse length with Vset = −1.8 V gives a T1 and S0 population of 0.79 ± 0.01 and 0.21 ± 0.01, respectively, for PTCDA in Fig. 5d. Supplementary Fig. 3 shows data for pentacene with different initial populations of the T1 and S0 states. To this end, pulse durations of 33.4 µs and 100.1 µs were chosen.

A cantilever oscillation amplitude of 1 Å (2 Å peak-to-peak) was chosen to optimize the signal-to-noise ratio for charge-state detection34. The oscillation amplitude modulates the tip height and thereby induces variations in the tunnelling rate and slight variations in the lever arm of the gate voltage. To minimize these effects, the voltage pulses were synchronized with the cantilever oscillation period, such that they started 2 µs before the turn-around point at minimal tip–sample distance. Furthermore, the sweep pulses were chosen to be short, such that the entire sweep pulse occurs around the point of minimal tip–sample distance. If this was not possible, full cantilever-period pulses were chosen. The resulting minor influence of the cantilever’s oscillation amplitude on the excited-state spectroscopy data was neglected in the modelling and, hence, in the fitting. For example, neglecting the cantilever’s oscillation likely causes the deviation between the fit and the data shown in Fig. 5a between voltages (1) and (2) for tsweep = 3.3 µs (yellow curve).

The tip height was chosen by setting the decay of D0+ into S0 at a voltage of 1 V above the voltage corresponding to the degeneracy of the D0+ and S0 states to around 1.5 µs. This tip height is sufficiently large to minimize tunnelling events between the two bistable states during the read-out phase of the pulse sequence, which gives a lower limit to the tip–sample height. The upper limit of the tip–sample height is given by the requirement that the tunnelling rates should be much faster than the slowest triplet decay rate. Typically, these two requirements restrict the possible tip–sample heights to a small range (less than 2 Å) around the relatively large tip–sample height used (estimated to be 9 Å; Supplementary Section 7).

The shortest sweep pulse duration was then chosen such that at the largest Vsweep used, the read-out fraction in the D0+ state was around 0.10. This allowed the observation of transitions at positive voltages, such as (6) in Fig. 3a. By contrast, a longer sweep pulse duration is crucial for the observation of transitions (7), (1) and (8). The longest pulse duration was, therefore, typically set such that the fraction in the D0+ state was close to zero at a voltage of 1 V above the voltage corresponding to the degeneracy of the D0+ and S0 states. Two or three additional sweep pulse durations were chosen in between the determined shortest and longest pulse duration to improve the reliability of the fitting.

To determine the population in the two charge states during the read-out, the voltage pulse sequences were typically repeated 8 times per second for 80 s for every sweep voltage. The error bars were derived as the s.d. of the binominal distribution (see below). The measurements were performed in constant-height mode. To correct for vertical drift, for example, owing to piezo creep, the tip–sample distance was typically reset every 15 min by shortly turning on the Δf-feedback. Lateral drift was corrected every hour by taking an AC-STM image (similarly as described in ref. 15) and cross-correlating it with an AC-STM image taken at the beginning of the measurement.

Data analysis

For data analysis, trigger pulses synchronized with the pump–probe voltage pulses were used to identify the start of every read-out interval (dotted lines in Fig. 2c). The remaining effect of the capacitive coupling described above as well as a possible excitation of the cantilever owing to the few µs sweep voltage pulses can cause spikes at the beginning of every read-out period (not present for the data in Fig. 2c), which were removed from the data trace. Subsequently, every read-out interval was low-passed and it was determined if the averaged frequency shift during this interval was above or below the value centred between the frequency shifts of the two charge states. Counting the number of read-out intervals for which the frequency shift was above this value and dividing it by the total number of intervals gives the read-out fraction in the charge state. For the metal tips that we have used, the D0+ and D0− states always had a less negative frequency shift compared with S0 (at the respective read-out voltage).

Error bars

The uncertainty on the determined read-out fraction in the charge state is dominated by the statistical uncertainty. Because of the two possible outcomes (charged or neutral), the statistics of a binomial distribution apply (ref. 16). The s.d. on the counts in a charged state Nc is, therefore, given by

$${\sigma }_{N{\rm{c}}}=\sqrt{\frac{{N}_{0}{N}_{{\rm{c}}}}{{N}_{{\rm{c}}}+{N}_{0}}},$$

with N0 being the counts in the neutral state. The error bars on the measured fractions in the charged state are then given by

$${\Delta }_{{\rm{c}}}=\frac{{\sigma }_{N{\rm{c}}}\,+\,1}{{N}_{{\rm{c}}}\,+\,{N}_{0}},$$

where the second term in the numerator accounts for the discrete nature of Nc.