Elementary Excitations of Superfluid Helium Droplets Probed by Ion

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Elementary Excitations of Superfluid Helium Droplets Probed by Ion Spectroscopy Xiaohang Zhang and Marcel Drabbels* Laboratoire de Chimie Physique Moléculaire, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland S Supporting Information *

ABSTRACT: Electronic spectra of molecules in helium droplets reveal spectral features that are related to the elementary excitations of the superfluid helium environment. In order to determine to what extent the interaction strength of the molecule with the helium affects these excitations, the spectrum corresponding to the B̃ 2A″ ← X̃ 2A″ transition of 2,5-difluorophenol cations in helium droplets has been recorded. The vibronic resonances reveal a sharp zerophonon line whose width is largely determined by the rotational band contour, followed by a broad structureless phonon wing at higher frequencies. The splitting between the zero-phonon line and phonon wing is approximately half of that found for neutral 2,5-difluorophenol. This difference is attributed to the increased helium density around the ion due to its strong interaction with the helium.

SECTION: Spectroscopy, Photochemistry, and Excited States splitting and/or fine structure is still highly debated, and several explanations have been proposed. The ZPL splitting was originally attributed to the existence of different binding configurations of localized helium atoms to the molecule, while the PW structure was ascribed to a nonsuperfluid helium solvation layer surrounding the dopant.15−19 Recently, other explanations for the observed fine structures have been offered, ranging from a quantum coherent set of helium atoms adsorbed on a quasi-planar molecular surface23 to the trapping of molecules on quantum vortices in the large He droplets.24 To date, no conclusive explanation has been offered that is able to account for all observations. Recently, first electronic spectra of ions in helium droplets have been reported.25,26 The large line width of the observed resonances has been tentatively attributed to intrinsically fast intramolecular relaxation processes in these ions. As a result, the influence of the helium environment on the spectra of these ions could not be determined. Because the interaction of an ion with helium is much stronger than that for a neutral molecule, it is not obvious whether the spectra of molecular ions will show the same characteristic ZPL and PW structure as neutral species or if the lines will be significantly broadened. In order to address this issue, we have recorded electronic spectra of 2,5difluorophenol (2,5-DFP) cations in helium droplets. The choice of 2,5-DFP+ is motivated by the absence of fast intramolecular relaxation pathways in the free ion when excited to the B̃ 2A″ state.27,28 One therefore expects that the line width

H

elium nanodroplets are unique quantum systems with extraordinary properties.1,2 Many of these properties can be traced back to the superfluid phase of helium. The superfluid character of helium droplets has been revealed in various experiments. For example, electron microscope images of deposited Ag clusters formed in helium droplets hinted to the presence of quantized vortices in droplets.3 Recent experiments on the ejection of electronically excited impurities from helium droplets revealed the existence of a critical Landau velocity in these finite-size systems.4 The superfluid character of the helium droplets can also be observed in the spectra of molecules. The best know example is undoubtedly the IR spectrum of OCS. It reveals a clearly resolved rotational structure that has been attributed to the free rotation of the molecules in a superfluid.5 However, the first evidence of superfluidity was provided by the electronic spectrum of glyoxal embedded in helium droplets.6 The individual rovibronic transitions were found to consist of an intense and sharp zero-phonon line (ZPL), corresponding to the excitation of the molecule, followed by a weak and broad phonon wing (PW) on the high-frequency side, corresponding to the simultaneous excitation of the molecule and the surrounding helium. The characteristic structure of the ZPL and accompanying PW could be simulated based on the dispersion curve of He II, thereby providing first evidence for superfluidity of helium droplets. Indeed, spectra of glyoxal recorded in 3He droplets do not reveal such a structure.7 The spectrum recorded for glyoxal turns out to be an exception because the electronic spectra of many other molecules reveal additional sharp transitions.8−22 Some of these have been attributed to a splitting of the ZPL, while others correspond to the structure of the PW. The origin of the © 2014 American Chemical Society

Received: July 21, 2014 Accepted: August 26, 2014 Published: August 26, 2014 3100

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sharp resonances followed by a relatively broad asymmetric tail on the blue side. The vibronic structure resembles strongly the spectrum recorded for gas-phase ions, except that most of the resonances in the present study are narrower due to the lower temperature of the ions. This largely accounts for the difference in peak intensities observed between the gas-phase and helium droplet spectra. The overall spectrum is shifted by 85 cm−1 toward lower frequencies. A shift of this magnitude is typical for electronic spectra of molecules in helium droplets. It is the net result of a red shift arising from the increased polarization of the helium induced by the excited ion and a blue shift due to the expansion of the solvation shell upon excitation.8 In contrast to the electronic energy, the excited-state vibrational frequencies are not affected by the helium, in line with vibrational spectra recorded for molecular ions in helium droplets, which reveal matrix shifts on the order of 1−2 cm−1.31,32 Although the gas-phase spectrum of 2,5-DFP+ has been recorded in the past, it has not been assigned.27 The fact that only the cis isomer of the neutral 2,5-DFP molecule is present in the helium droplets suggests that the spectrum of the ion corresponds to this specific isomer. This is supported by realizing that the internal energy of the created ions is considerably below the calculated isomerization barrier. We therefore assign the individual resonances based on the groundstate vibrational frequencies of the cis conformer that have been calculated at the B3LYP\6-311++G(df,pd) level of theory; see the Supporting Information. It is readily noticed in the lower panel of Figure 1 that the ZPL of the band origin at 23699 cm−1 is followed by two intense broad spectral features at 23753 and 23800 cm−1. The spectrum recorded at a reduced laser fluence (see the inset in Figure 1) reveals that the saturation behavior of these transitions differs from that of the spectral features of the band origin, which we take as evidence that these transitions correspond to vibronic transitions of the molecule and not to elementary excitations of the helium environment. The Lorentzian line widths of these two transitions determined at reduced laser intensities amount to 13 and 12 cm−1, respectively. The similarity of the widths and the vibrational frequencies of 54 and 101 cm−1 strongly suggest that these bands correspond to the fundamental and overtone transitions of a low-frequency vibration. This low-frequency vibration is tentatively assigned to the out-of-plane vibration of the C−F bonds, corresponding to the 17a vibration in benzene.33 Such a butterfly vibration is expected to be quickly damped by the helium environment,18,34 in agreement with the large line width of the corresponding transitions. The progression of the 17a vibration is also observed for other vibronic transitions, as indicated in Figure 1. Closer inspection of the electronic spectra reveals fine structure in the band origins of both neutral and ionic 2,5-DFP. To determine to what extent the different interaction strengths with the helium influence the fine structure, the band origins have been recorded as a function of laser intensity and droplet size. Figure 2 displays the band origin of neutral 2,5-DFP recorded at two different laser intensities. It is characterized by two sharp resonances labeled α and β that are separated by 1.7 cm−1 and have a width of 0.7 cm−1. These characteristics are found to be independent of laser intensity and droplet size. The PW is observed at higher frequencies; its maximum is located 5 cm−1 to the blue of the resonance labeled α. The spectra presented in Figure 2 have been normalized with respect to the intensity of the α resonance. The relative intensity of resonance

of spectral features recorded in helium droplets is limited either by the rotational band contour or by the interaction with the helium environment. The effect of the charge on the fine structure can be obtained by comparing the spectra of 2,5DFP+ cations to that of neutral 2,5-DFP. The excitation spectrum corresponding to the à 1A′ ← X̃ 1A′ transition of neutral 2,5-DFP in helium droplets is reported in the upper panel of Figure 1. The individual vibronic transitions

Figure 1. Electronic excitation spectrum corresponding to the à 1A′ → X̃ 1A′ transition of neutral 2,5-DFP in helium droplets containing an average of 2750 helium atoms (upper panel). The B̃ 2A″ → X̃ 2A″ excitation spectrum of 2,5-DFP cations in similar size helium droplets recorded at a pulse energy of 4 mJ (lower panel). The inset shows the band origin region recorded at a reduced pulse energy of 0.5 mJ.

are characterized by sharp resonances followed by a PW on the blue side, vide infra. As the spectrum has been recorded using relatively high laser intensities, it is dominated by the PWs.6 In this context, it should be noted that the broad structure observed in the 36000−36500 cm−1 energy range does not correspond to a PW but rather to the spectrum of 2,5-DFP dimers in the helium droplets. Because, to our knowledge, no gas-phase spectrum of 2,5-DFP has been reported, we base our assignment on a comparison with the spectrum of ofluorophenol, which has a very similar structure.29 Most importantly, a C−F bond is directly adjacent to the −OH functional group in both molecules, resulting in a strong intramolecular hydrogen bond that defines the skeletal structures. On the basis of these considerations and aided by DFT calculations at the B3LYP\6-311++G(df,pd) level of theory performed using the Gaussian 09 program suite,30 the observed resonances are assigned to vibronic transitions of the 2,5-DFP cis conformer; see the Supporting Information. The excitation spectrum of 2,5-DFP+ cations in helium nanodroplets corresponding to the B̃ 2A″ ← X̃ 2A″ transition is shown in the lower panel of Figure 1. Analogous to the spectrum of neutral 2,5-DFP, the spectrum is characterized by 3101

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therefore conclude that the observed PW fine structure is largely determined by the aromatic ring and that the functional groups have only a minor effect. The B̃ 2A″ ← X̃ 2A″ band origin of the 2,5-DFP+ cation recorded for different helium droplet sizes and laser intensities is shown in Figure 4. The spectrum consists of a sharp ZPL

Figure 2. Band origin of the à 1A′ → X̃ 1A′ transition of neutral 2,5DFP embedded in helium droplets consisting of 2750 He atoms recorded at two different laser pulse energies. The inset shows the spectrum recorded for helium droplets containing, on average, 8100 He atoms using a pulse energy of 0.1 mJ. Figure 4. Band origin of the B̃ 2A″ → X̃ 2A″ transition of 2,5-DFP cations in helium droplets containing 2750 He atoms, recorded at two different laser pulse energies. The inset shows the spectrum recorded in droplets containing 8100 He atoms using a pulse energy of 0.05 mJ.

having a width of 0.8 cm−1 and a broad PW shifted by 2.8 cm−1 to the blue of the ZPL. The ZPL and PW have a clearly different saturation behavior, that is, the relative intensity of the PW increases with increasing laser intensity. The spectral features as well as the saturation behavior are found to be independent of droplet size. On the basis of these observations, we conclude that the strong interaction of an ion with the helium does not lead to substantial line broadening and that the broad resonances previously observed for other ionic systems are indeed related to fast nonradiative processes in these molecules.25,26 The line width of the ZPL is very similar to that of neutral 2,5-DFP and appears to be largely determined by the rotational band contour. A simulation of the ZPL band contour using the rotational constants provided by the DFT calculation and scaled by a factor of 3 to take into account the helium environment2 yields a line width of 0.6 cm−1, compatible with the experimentally observed line width of 0.8 cm−1. We thus conclude that although the interaction of an ion is much stronger than that for a neutral molecule, the electronic excitation spectrum still reveals the characteristics that can be attributed to the elementary excitations of superfluid helium. In this respect, electronic spectroscopy of ions does not differ from that of neutrals. Combined with the fact that helium droplets can be doped with a wide variety of ions,39 this opens up new possibilities for the spectroscopic investigation of ionic systems. In contrast to neutral 2,5-DFP, the excitation spectrum of the 2,5-DFP+ cation reveals no additional sharp resonances. In this respect, it is one of the few systems whose spectral characteristics resemble that of glyoxal, that is, it only exhibits a sharp ZPL that is well separated from a broad, nearly structureless PW.6 The PW structure of glyoxal has been successfully reproduced by the Huang−Rhys model, which relates the PW intensity to the density of accessible phonon states.6 Using the density of states calculated from the dispersion curve of superfluid bulk helium, it was found that the gap between the ZPL and the PW is directly related to the roton energy of superfluid helium. The analysis of the band

Figure 3. Intensity ratio of the α/β resonances (upper panel) and the ratio of the β resonance to the integrated PW intensity as a function of the laser pulse energy.

β with respect to α clearly increases with increasing laser intensity; see the upper panel of Figure 3 for a quantitative analysis. The graph reveals a clear difference in saturation behavior for the two transitions. This is often taken as evidence that the two resonances do not correspond to a splitting of the ZPL but rather to fine structure in the PW.9,10 Indeed, the highfrequency resonance β shows the same laser power dependence as the PW; see the lower panel of Figure 3, which shows the ratio of the β resonance intensity to the integrated PW intensity as a function of laser power. We take this as evidence that the β transition corresponds to fine structure of the PW. The observation of a single ZPL agrees with the results of spectroscopic studies on benzene.35,36 The presence of only a single ZPL in these systems reinforces the idea that the splitting of ZPLs is related to different binding configurations of localized helium atoms to the molecule. Much less detailed information is available on the PW fine structure in these types of molecules. In the case of benzene, the PW is too weak to be observed.35,36 In contrast, the electronic spectrum of aniline is fully dominated by the PW and reveals some fine structure.37 A similar fine structure has been found in the spectra of phenol and toluene in helium droplets.38 The structure observed for 2,5-DFP in the present study fits well to these observations. We 3102

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origin of the 2,5-DFP+ cation reveals a gap of only 2.8 cm−1, which is approximately half of that of neutral 2,5-DFP or glyoxal.6 This suggests that the roton energy of the helium in the proximity of the ion is strongly reduced. As the roton energy of helium has been shown to decrease linearly with increasing helium density,40 it is tempting to use the ZPL−PW gap to provide information on the helium density surrounding an impurity. However, it should be realized that several approximations are made to calculate the ZPL−PW gap.6 Most importantly, the molecule is assumed to reside in a spherical cavity, which is clearly not compatible with the structure of the 2,5-DFP+ cation. Nonetheless, we here directly relate the ZPL− PW gap to the roton energy. From its density dependence,40 we calculate a helium number density of 0.0241 Å−3 for neutral 2,5-DFP and of 0.0352 Å−3 for the 2,5-DFP+ cation. As expected, the helium density is largest for the ion. However, the absolute values are only slightly higher than the helium number density of pure helium droplets, 0.0218 Å−3,41 and much smaller than calculated helium densities in the first solvation layer surrounding impurities. For neutral systems like OCS and SF6, these have been calculated to be 0.056 and 0.07 Å−3, respectively,42,43 while for ions, even higher densities have been found, 0.11 Å−3 for LiH+44 and 0.25 Å−3 for alkali ions.45 Clearly, within the current approximations, the ZPL−PW gap does not reflect the density of the helium in the first solvation shell surrounding an impurity. At best, it is related to some averaged density of the surrounding helium. Even so, we find that the calculated helium density for the 2,5-DFP+ cation corresponds to that of solid helium. This suggests that the ion is surrounded by a solid-like helium density, possibly forming a so-called snowball structure as suggested by calculations.45−47 The position of the PW maximum for the 2,5-DFP+ cation is very similar to the position of the fine structure observed in PWs of large planar aromatic molecules.10 This fine structure has been attributed to the presence of localized helium atoms within the first solvation shell that are strongly bound to the molecule. As the interaction of the ion with the helium is much stronger than that for a neutral, one expects this particular feature to become more prominent in the spectra of ions. The fact that the PW for 2,5-DFP+ has its maximum at a similar position as the fine structure seems to corroborate this assumption. Path integral Monte Carlo calculations indicate that the strongly bound helium atoms do not contribute to the superfluid fraction.48 As a result, the superfluid fraction in the first solvation shell for neutral SF6 is reduced by almost a factor of 2,48 while it is completely suppressed for the Na+ cation.46 This will certainly affect the dispersion curve and consequently the ZPL−PW gap. In this context, it is worth noting that recent neutron scattering experiments have revealed the existence of a localized superfluid component within solid helium in aerogel.49 This component is characterized by a roton dispersion curve having an energy minimum of approximately 3 cm−1 that has been attributed to the presence of superfluid double layers. As calculations indicate that the density of the second solvation layer surrounding an ion is also solid-like,46 the 2.8 cm−1 ZPL−PW gap observed for the 2,5-DFP+ cation is possibly related to a superfluid fraction analogous to that observed in solid helium. High-level theoretical calculations will be required to verify this hypothesis and to relate the ZPL−PW gap to the solvation structure of an ion. Concluding, the individual vibronic resonances corresponding to the B̃ 2A″ ← X̃ 2A″ transition in 2,5-DFP+ cations embedded in helium droplets reveal the same characteristic

spectral features related to the superfluid phase of helium as those observed for neutral molecules. The vibronic transitions consist of a narrow ZPL followed by a broad PW at higher frequencies. Like for neutrals, the line width of the ZPL is largely determined by the rotational band contour, thereby making high-resolution spectroscopy of molecular ions possible. The splitting between the ZPL and the maximum of the PW is found to be approximately half of that of neutral 2,5DFP. This reduction of the splitting is attributed to the increased helium density around the ion due to its strong interaction with the helium.

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EXPERIMENTAL METHOD

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ASSOCIATED CONTENT

The experimental setup has been described in detail before.50,51 Helium droplets are formed by expanding helium gas at 30 bar into vacuum through a cryogenically cooled 5 μm diameter orifice. The helium droplets pick up, on average, one single 2,5DFP molecule as they pass through a vacuum chamber that is filled with 10−6 mbar of 2,5-DFP. Electronic spectra of neutral 2,5-DFP are recorded using evaporation spectroscopy, which relies on the complete desolvation of the neutral chromophore upon excitation.36 At the center of a velocity map imaging spectrometer, the solvated neutral molecules are first excited by the weakly focused frequency-doubled output (265−280 nm) of a Nd:YAG pumped dye laser, having a pulse energy of 0.1− 0.5 mJ. After a time delay of 200 ns, the desolvated 2,5-DFP molecules are nonresonantly ionized by the 1 mJ output of an amplified Ti:sapphire femtosecond laser system tightly focused onto the molecular beam. Electronic spectra are recorded by monitoring the 2,5-DFP+ ion yield as a function of dye laser frequency. To record spectra of 2,5-DFP+ cations in helium droplets, the ions are produced in situ by ionizing the solvated 2,5-DFP molecules by the 266 nm output of a Nd:YAG laser, having a pulse energy of 5 mJ. Typically 100 ns after their creation, the solvated ions are excited by the unfocused output of a dye laser operating in the 430−500 nm wavelength range. Because the excitation of ions leads to their desolvation,26,32 spectra of the 2,5-DFP+ cations are recorded by simply monitoring the number of 2,5-DFP+ ion impacts on the detector as a function of dye laser frequency.

S Supporting Information *

Assignment of the spectra corresponding to the à 1A′ ← X̃ 1A′ transition of 2,5-DFP and the B̃ 2A″ ← X̃ 2A″ transition of 2,5DFP+ cations in helium droplets. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: Marcel.Drabbels@epfl.ch. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We gratefully acknowledge the financial support provided by the Swiss National Science Foundation through Grants 200020_140396 and 200021_146598. 3103

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dx.doi.org/10.1021/jz501530e | J. Phys. Chem. Lett. 2014, 5, 3100−3105