Vibrational fingerprint of localized excitons in a two-dimensional metal-organic crystal

Long-lived excitons formed upon visible light absorption play an essential role in photovoltaics, photocatalysis, and even in high-density information storage. Here, we describe a self-assembled two-dimensional metal-organic crystal, composed of graphene-supported macrocycles, each hosting a single FeN4 center, where a single carbon monoxide molecule can adsorb. In this heme-like biomimetic model system, excitons are generated by visible laser light upon a spin transition associated with the layer 2D crystallinity, and are simultaneously detected via the carbon monoxide ligand stretching mode at room temperature and near-ambient pressure. The proposed mechanism is supported by the results of infrared and time-resolved pump-probe spectroscopies, and by ab initio theoretical methods, opening a path towards the handling of exciton dynamics on 2D biomimetic crystals.

where G is the Gibbs free energy of the adsorbed system, and FePc and CO are the chemical potentials of the FePc and CO molecules, respectively. The DFT total energies are evaluated within a given volume V of the unit cell and therefore the Gibbs free energy can be expressed in terms of the Helmholtz free energy plus the volume contributions, i.e.: ( , ) = ( , ) + The term pV can be neglected since p is of the order of 10 mbar in the present case, and V is smaller than 10 4 Å 3 , yielding pV  6 10 -5 eV, much lower than the energy differences characterizing nonequivalent configurations (0.1 eV). The Helmholtz free energy can be further detailed as: with ( , ) = ( , ) − • ( , ) that includes energy and entropy contributions from the vibrational modes of the system. However, since vibrational energies Fvibr are generally small with respect to adsorption energies, they can be neglected as a first approximation. Using all the assumptions above we obtain that * ( , ) ≅ − − ( , ) The chemical potential for CO can be adequately parametrized with the expression valid for ideal gases where From thermochemical tables CO(300 K, patm) = -0.53 eV. Collecting all the terms and setting the zero of the free energy scale for the clean FePc molecule (no CO adsorbed), the free energy difference that contributes in the CO adsorption process is In the isothermal-isobaric ensemble, the probability of CO adsorption on a FePc molecule is with  = 1/(kBT). Consequently, the coverage of CO at the Fe sites of the FePc monolayer is where r(T,p) is the ratio between the number of available molecules in the gas phase Ngas(p) and the number of available adsorption sites Nsites: In our setup the volume of the high pressure cell is Vchamber ~ 10 -3 m 3 , the surface area of the unit cell of the FePc monolayer is Aunit cell ~ 200 Å 2 and the sample surface is Asample ~ 50 mm 2 . The full ab initio thermodynamic expression for the surface coverage is finally which is formally equivalent to the well-known Langmuir formula for isothermal adsorption. The curve plotted in Fig. 3 together with the experimental data points is directly obtained from this ab initio model, with no fitted parameters. This plot shows that the experimental data are well reproduced by the adsorption of only one CO molecule per iron phthalocyanine. Multiple carbonylation of FePc remains thermodynamically unfavorable, even when taking into account the effect of temperature and pressure. Further calculations of the adsorption energy as a function of the distance of the carbon atom of CO from the equilibrium adsorption length show no barrier for the single adsorption process, which is therefore not activated. The conclusions again confirm the exclusion of the cooperative adsorption hypothesis.
The dipole-dipole interaction hypothesis. We have shown that the relative intensities of the multiple peaks observed in the SFG spectra depend on the degree of order of the FePc monolayer (see main text). Therefore, interaction between neighboring phthalocyanines plays a role. The dipole-dipole interaction hypothesis is based on a direct interaction of the dipoles of CO molecules adsorbed at adjacent phthalocyanines. We considered the potential energy for this interaction: U(r) = p 2 CO/(4πε0r 3 ). Setting r = 13.6 Å and pCO = 0.112 D, 4 we obtain U = 3 × 10 -6 eV, three orders of magnitude smaller than the peak spacing in the SFG spectra. Thus, the dipole-dipole interaction hypothesis had to be discarded.
The harmonic coupling hypothesis. Another possible hypothesis about the nature of the interaction between the (CO)FePc molecules consists in assuming that the CO-CO interaction is indirectly mediated by the vibrations of the FePc 2D molecular lattice. We have calculated the frequency of the C-O stretching mode for this system by using density functional perturbation theory (DFPT). A finite dispersion of phonon modes in the first Brillouin zone would have demonstrated that intermolecular coupling is responsible for the appearance of several peaks in the SFG spectra. Instead, at different k-points the modes differ at most by 3 cm -1 , i.e. no direct effect on the vibrational modes could be observed, leading to the rejection of the harmonic coupling hypothesis, consistently with the PM-IRAS measurements.
The excitonic hypothesis. After discarding the harmonic coupling hypothesis, where the interaction is of pure phononic nature, we analyze the influence of electronic effects. The excitonic hypothesis assumes that, upon illumination with visible light in a SFG experiment, a fraction of the molecules turns in an electronically excited state. Provided the lifetime of the latter is long enough, the SFG process occurs on the set of populated states. The multiplet of peaks would then originate from the non-equivalent vibrational modes of both the electronically excited and ground states. To prove the excitonic hypothesis, the vibrational modes of an excited state have been investigated. Since the ground state is a singlet, a virtually excited state was obtained by imposing a total magnetization of the system equal to 2.00 μB in the calculations. The vibrational frequencies were calculated both with DFT and with DFT+U. DFT yields frequencies of 1994, and 1996 cm -1 for the singlet and the lowest-lying triplet states, respectively. The obtained triplet state is associated with the HOMO to LUMO transition. DFT+U yields values of 2016 and 2049 cm -1 , respectively, and 2055 cm -1 for another excited configuration. As shown in Supplementary Figure  2, imposing a total magnetization of 2.00 μB in the calculation forces one electron originally occupying a HOMO-1 state to be lifted into a LUMO+1 state. The other excited state was instead obtained by imposing a fixed occupation on the orbitals, forcing the second highest minority spin state below the Fermi energy to be empty and the second lowest majority-spin state above the Fermi energy to be occupied. The vibrational energy differences are compatible with the experimentally observed values, thus lending support for the excitonic hypothesis.
Dependence of the IR-Vis SFG spectra on temperature and laser parameters. In Supplementary Figure 3 we plot the IR-Vis SFG spectra collected in situ in the C-O stretching region on the FePc monlayer on graphene in 6 (left) and 12 (right) mbar CO for increasing surface temperature, starting from 300 K (top). The relative amplitude of the features is plotted in Supplementary Figure 4 (left axis) together with the inhomogeneity gaussian broadening (right axis). As a rule of thumb, the lowest energy features gain relative intensity with annealing temperature at the expense of the peak at 2011 cm -1 . This is accompained with a progressive broadening of the resonances due to an increased gaussian width, starting from 320 K. By plotting the same quantities measured at room temperature but on samples obtained with a different 2D crystal growth temperature (Supplementary Figure 5), a similar trend can be observed. In the latter case the features at 1986 and 1992 cm -1 increase their relative amplitude at the expense of the higher energy features for increasing FePc deposition temperature. Also the gaussian broadening increases (right axis). All these trends can be interpreted as due to a different degree of order of the molecular crystal (Fig. 1C), reflecting in different relative amplitudes of the observed split components and in an inhomogeneous gaussian braodening of the spectral lineshapes. Changes in the IR intensity or a non-perfect temporal overlap of the IR and visible beams translate in a relative modulation of the resonant and non-resonant amplitudes (Supplementary Figure 6 and Supplementary Table 2).
Time-resolved spectroscopy of the electronic excited states. Supplementary Figure 7a shows a pseudo-color (intensity) representation of TR-2PPE as a function of the pump-probe delay. The spectra at each delay were normalized by subtracting the signal obtained at negative delay times, which is the background produced by the sum of 2PPE signals from both the pump and the probe taken separately. Such procedure isolates the pump-induced signal. We observed delay-dependent intensities in two kinetic energy regions of the plot, corresponding to short-lived (SL) and longlived (LL) excited states. In order to improve the signal to noise ratio in our data we identify region SL, obtained by integrating the photoemission signal in a 0.3 eV wide kinetic energy region centered at 1.3 eV, and region LL, obtained in a 0.3 eV wide kinetic energy region centered at 0.6 eV. Supplementary Figure 7b shows the intensity profiles of SL and LL as a function of the pumpprobe delay. Due to the fact that the full delay scan lasted for about 12 hours, a further normalization had to be performed for the longer delay part of the plot (t > 1 ps) in Supplementary  Figure 7b, in order to remove intensity fluctuations due to the detection apparatus. This was achieved by dividing the intensity profile of LL by SL, since after the decay of the short-lived state there is no other time-dependent feature in that energy region. The short-lived state (SL) is fitted by a Gaussian curve yielding a full-width at half-maximum of 570 ± 100 fs, close to the crosscorrelation of our pump-probe laser pulses. Therefore, we can conclude that the lifetime of the SL state is τSL < 570 fs. The low energy long-lived state (LL) displays an exponential decay of the intensity, with the best fit yielding a time constant of τLL = 28 ± 8 ps.  (111). The color scale represents the normalized photoemission intensity. The spectra were recorded with hν1 = 2.4 eV (pump) and hν2 = 4.8 eV (probe). The integrated intensities for the two regions delimited by the blue (SL) and red (LL) contours are displayed in (b). SL (blue markers) has been fitted with a Gaussian peak (blue, dashed line), while for LL (red markers) an exponential decay (red, solid line) has been adopted.