Lorenz
Kranabetter
^{a},
Nina K.
Bersenkowitsch
^{a},
Paul
Martini
^{a},
Michael
Gatchell
^{ab},
Martin
Kuhn
^{a},
Felix
Laimer
^{a},
Arne
Schiller
^{a},
Martin K.
Beyer
^{a},
Milan
Ončák
*^{a} and
Paul
Scheier
*^{a}
^{a}Institut für Ionenphysik und Angewandte Physik, Universität Innsbruck, Technikerstr. 25, A-6020 Innsbruck, Austria. E-mail: Milan.Oncak@uibk.ac.at; Paul.Scheier@uibk.ac.at
^{b}Department of Physics, Stockholm University, 106 91 Stockholm, Sweden
First published on 8th November 2019
We investigate the photodissociation of helium-solvated cesium dimer cations using action spectroscopy and quantum chemical calculations. The spectrum of Cs_{2}He^{+} shows three distinct absorption bands into both bound and dissociative states. Upon solvation with further helium atoms, considerable shifts of the absorption bands are observed, exceeding 0.1 eV (850 cm^{−1}) already for Cs_{2}He_{10}^{+}, along with significant broadening. The shifts are highly sensitive to the character of the excited state. Our calculations show that helium atoms adsorb on the ends of Cs_{2}^{+}. The shifts are particularly pronounced if the excited state orbitals extend to the area occupied by the helium atoms. In this case, Pauli repulsion leads to a deformation of the excited state orbitals, resulting in the observed blue shift of the transition. Since the position of the weakly bound helium atoms is ill defined, Pauli repulsion also explains the broadening.
Whereas only very few He atoms can be attached to singly-charged ions in cold traps, ions can be solvated with almost any number of He atoms when formed in doped helium nanodroplets. In the case of C_{60}^{+}, a remarkable linear red-shift of the absorption lines for the first 32 He atoms attached could be used to extrapolate to the absorption line of the bare ion.^{31–33} In combination with theory, the experimental results of the matrix shift as well as the width of the absorption lines provide unprecedented insight into the details of the solvation of ions with helium, including phase transitions and isomeric effects.
Alkali metal atoms reside on dimples at the surface of helium droplets, as shown in numerous experimental^{21,34–40} and theoretical studies.^{41–46} Alkali metal clusters, however, are submerged into the cluster above a critical cluster size.^{46–48} The groups of Ernst and Stienkemeier investigated photoionization of Cs atoms and the submersion of Cs^{+} into He droplets.^{34,39} Chen et al. managed to solvate Cs^{+} ions with several million helium atoms via pickup of Cs^{+} formed upon thermionic emission into large He droplets.^{49} Dopant ions ejected from charged helium droplets are sometimes complexed with a few helium atoms when recorded via mass spectrometry. The first solvation layer is particularly strongly bound, and its closure is typically reflected as a clear intensity drop of the ion series MHe^{+}_{n} (with M^{+} the alkali metal ion) in mass spectra.^{48,50–52} Path integral or basin-hopping methods reproduce the experiments very well.^{44,45} It was also shown previously that helium adsorption might lead to appreciable spectral shifts.^{53}
Spectroscopic properties of the Cs_{2}^{+} ion were investigated previously in experimental^{54,55} and theoretical studies^{56–58} within the series of alkali metal dimers, assigning the lowest electronically excited states. In the present study, we explore photodissociation of Cs_{2}He^{+}_{n}via action spectroscopy to assess helium solvation effects in a seemingly simple diatomic system. Single-reference and multi-reference ab initio calculations including spin–orbit coupling reproduce the experimental results and provide an assignment of the electronic transitions. A pronounced blue-shift of more than 0.1 eV (850 cm^{−1}) for absorption into the 1^{2}Σ^{+}_{u} state for Cs_{2}He^{+}_{n} with n = 10 provides clear evidence that the He atoms preferentially occupy positions along the axis of the cesium dimer cation.
To obtain a quantum chemical description of the optical spectra, ground state structures of Cs_{2}He^{+}_{n} ions were first modelled at the coupled cluster singles doubles (CCSD) level with the def2QZVP basis set on Cs and def2TZVP on He. The position of the weakly bound He atoms, residing in shallow potential wells, is very sensitive to the quality of the basis set used on Cs. With the triple-zeta quality basis set def2TZVP used on Cs, a bent structure is predicted for Cs_{2}He^{+}; a linear Cs_{2}He^{+} structure is obtained with the def2QZVP basis set on Cs and def2TZVP on He, and this does not change when the def2QZVPPD basis set is used on both Cs and He. To validate the theory as much as possible, excited states were modelled on various theory levels: time-dependent density functional theory (TDDFT) with the CAM-B3LYP functional; equation of motion – CCSD (EOM-CCSD); multi-reference configuration interaction (MRCI) with an active space of one electron in 5 or 17 orbitals, MRCI(1,5) and MRCI(1,17), respectively; def2QZVPPD basis set was used on all atoms for excited state calculations. Spin–orbit coupling was calculated using the state-interacting method as implemented in the Molpro program^{63,64} along with the ECP46MDF basis set.^{65} The D_{2h} symmetry group was used for calculations; irreducible representations (IRs) in the D_{∞h} symmetry group were reconstructed from the respective IRs in D_{2h}D_{2h}. “Very Tight” optimization criteria were used for optimization; for optimization in the floppy excited state in Cs_{2}He^{+}, even stricter criteria for solving the EOM-CCSD equations were used, with convergence criteria of 10^{−9}, 10^{−11} and 10^{−10} for energy, wavefunction and CCSD and ground-state Z-vector iterations, respectively. In all calculations, only 17 electrons in Cs_{2}^{+} were treated explicitly, with the rest described within an effective core pseudopotential (ECP).
Purely dissociative as well as bound excited states are encountered in Cs_{2}^{+}. The absorption spectra of the dissociative states were modeled using the linear reflection principle (LRP) within the harmonic approximation^{66–68} and by the standard reflection principle projecting the vibrational wavefunction (calculated for the Cs_{2}^{+} potential on a grid) onto the excited state potential energy surface. The spectra of the bound states were calculated using the Franck–Condon approximation within the harmonic regime as implemented in the Gaussian software^{69} or directly by calculating the overlap of the ground state vibrational wavefunction in the electronic ground state with both ground and excited vibrational wavefunctions in the electronically excited state.
Gaussian 16 was used for TDDFT and (EOM-)CCSD calculations, Molpro for MRCI and spin–orbit calculations.
Fig. 1 (a) Photodissociation spectra of Cs_{2}He^{+}_{n} ions, n = 1, 2, 3, 6, 8, 10, 12 obtained as a differential spectrum with and without laser irradiation of clusters and scaled with laser power (see ESI† for details). A fit of the peak at 2.8 eV by two Gaussian functions is shown for n = 1. Band centers for Cs_{2}He^{+} are marked by vertical lines to guide the eye. Electronic state assignment is based on calculations (Table 1). (b) Multiple Gaussian fit to the vibrational progression of the transition into the 1^{2}Π_{u} state in Cs_{2}He^{+} and determination of the vibrational spacing. |
For a more quantitative interpretation and reliable assignment of these features, we performed EOM-CCSD and MRCI calculations and analyzed the contribution of spin–orbit coupling effects. Fig. 2 shows the potential energy curves of Cs_{2}^{+}. The Cs_{2}^{+} ion has D_{∞h} symmetry and, when disregarding spin–orbit coupling, its ground electronic state is 1^{2}Σ^{+}_{g}. From this state, the only symmetry allowed transitions are perpendicular and parallel transitions into ^{2}Π_{u} and ^{2}Σ^{+}_{u} states, respectively. Within 3 eV, two ^{2}Σ^{+}_{u} and two ^{2}Π_{u} states can be found. Among these states, only the 1^{2}Π_{u} state is bound, the others are dissociative. When accounting for spin–orbit effects (see Table S3 in the ESI†), the Σ states are only slightly affected, with shifts of up to 5 meV. However, the doubly-degenerate Π states split into two states, separated by ∼10–35 meV (80–280 cm^{−1}).
Fig. 2 Potential energy curves in Cs_{2}^{+} calculated at the EOM-CCSD/def2QZVPPD level. Excited states to which electronic transitions are allowed from the ground state are shown with full lines, forbidden ones with dashed lines. In the inset, the vicinity of the 1^{2}Π_{u} minimum is shown, along with states including spin–orbit coupling (dotted lines, calculated at the MRCI(1,17)/ECP46MDF level of theory). Only selected states are shown. See the ESI† for excluded electronic states and method benchmarking. |
Comparison of the calculations with experiment, summarized in Table 1, allows us to assign the three main bands observed in the experiment as 1^{2}Σ^{+}_{u}, 1^{2}Π_{u}, and 2^{2}Π_{u}, reproducing the excitation energy to within 0.1 eV. The fourth allowed transition into 2^{2}Σ^{+}_{u} at ∼3.1 eV (see Table S2, ESI†) is not observed in the experiment due to insufficient laser power in this region. For the dissociative states 1^{2}Σ^{+}_{u} and 2^{2}Π_{u}, calculations within the reflection principle approximation also predict a realistic width of the observed bands, see Table 1.
State | 1^{2}Σ^{+}_{u} | 1^{2}Π_{u} | 2^{2}Π_{u} | |
---|---|---|---|---|
Experiment, Cs_{2}He^{+} | E | 1.41 | 1.55; 1.59 | 2.82; 2.86 |
w | 83 | — | 39; 30 | |
ΔE_{split} | — | 39 | 42 | |
Theory, Cs_{2}^{+} | E | 1.43 | 1.51 | 2.85 |
w | 64 | — | 26 | |
ΔE_{SO} | — | 28 | 13 | |
Theory, Cs_{2}He^{+} | E | 1.44 | 1.51 | 2.84 |
ΔE_{SO} | — | 28 | 14 |
As mentioned above, the 1^{2}Π_{u} state is bound and, therefore, the measured photodissociation spectrum reflects its vibrational structure. The 1^{2}Π_{u} state is calculated to have a very similar equilibrium distance as the 1^{2}Σ^{+}_{g} ground state (Fig. 2). The excited state potential well is less steep, reflected in the calculated harmonic vibrational frequencies of 30 and 20 cm^{−1} for the 1^{2}Σ^{+}_{g} and 1^{2}Π_{u} state, respectively, for Cs_{2}^{+} (at the (EOM-)CCSD/def2QZVPPD level). The respective values for Cs_{2}^{+}He are 31 and 19 cm^{−1}, with a stronger Cs_{2}^{+}–He interaction in the excited states, shortening the Cs–He distance from 4.4 Å in the 1^{2}Σ^{+}_{g} state to 4.0 Å in 1^{2}Π_{u}. The harmonic Cs_{2}^{+}⋯He vibration is located at 30 cm^{−1}. The calculated frequency in the 1^{2}Π_{u} state of 19 cm^{−1} fits well to the measured spacing of 22 cm^{−1}. Note that only the higher 3/2u(1^{2}Π_{u}) state shows clear vibrational resolution shown in Fig. 1b. The 1/2u(1^{2}Π_{u}) state interacts with the repulsive 1/2u(1^{2}Σ^{+}_{u}) state, and the potential energy surface will be deformed due to the avoided crossing of the states. From a computational perspective, the equilibrium distance in the 1^{2}Π_{u} state depends heavily on the choice of the basis set (Fig. S4, ESI†). As a direct consequence, our attempts to reproduce the experimental spectrum shown in Fig. 1b using Franck–Condon simulations failed to grasp correctly the relative intensity of the contributing peaks (see the ESI† for details).
Finally, the calculated weak spin–orbit splitting of the ^{2}Π_{u} states results into two states 1/2u and 3/2u with a different Ω value following Hund's rule 3. The splitting is well reproduced for 1^{2}Π_{u} (see also inset in Fig. 2). For 2^{2}Π_{u}, the calculated spin–orbit splitting is significantly smaller than the experimentally observed splitting. These observations can be rationalized if one takes into account the additional splitting induced by the asymmetric distribution of the He atom relative to the singly occupied molecular orbital (SOMO) in the excited state. Fig. 3 illustrates how the energy of the several electronic states in Cs_{2}He^{+} depends on the position of the He atom in Cs_{2}He^{+}. For this calculation, the Cs–Cs–He angle is fixed, and the Cs–Cs and Cs–He distances are optimized in the electronic ground state, 1^{2}Σ^{+}_{g}. From 180° to 150°, the ground state energy hardly changes, i.e. the He atom moves more or less freely in this range of Cs–Cs–He angles. The repulsive 1^{2}Σ^{+}_{u} state reacts more sensitively to the position of the He atom, and this effect contributes to the broadening of the absorption band, which is 19 meV larger than expected from the linear reflection principle approximation, Table 1. For the 1^{2}Π_{u} and 2^{2}Π_{u} states, the degeneracy of the two contributing π orbitals (see Fig. 4) is lifted by the presence of the He atom, which leads to an additional splitting. For 1^{2}Π_{u}, this effect is negligible down to 150° Cs–Cs–He angle, because the He atom does occupy the same space as the singly occupied π orbitals. In contrast, the SOMO of the 2^{2}Π_{u} state is much more diffuse, and in one of the two orientations exhibits significant overlap with the position of the He atom. The splitting of the two orientations of the SOMO in the 2^{2}Π_{u} state amounts to 31 meV at 150°, which constitutes the dominant contribution to the experimentally observed splitting. For larger clusters, the same effect is responsible for the significant broadening of the 2^{2}Π_{u} band.
Let us now concentrate on the shift of the spectra induced by solvation, i.e. the He matrix shift. As shown in Fig. 1a and Table 2, pronounced shifts to higher energies are recorded for the 1^{2}Σ^{+}_{u} and 2^{2}Π_{u} states, reaching values of more than 0.1 eV already for Cs_{2}He_{10}^{+}. Note also that the shift in the 1^{2}Σ^{+}_{u} state exceeds the He binding energy. In the n = 1–10 range, the energy of the 1^{2}Σ^{+}_{u} state shifts linearly with solvation by 12 meV (100 cm^{−1}) per helium atom. The 2^{2}Π_{u} band at ∼2.8 eV seems to shift slightly non-linearly, its structure is however not well resolved in the experiment for larger ions. The 1^{2}Π_{u} state at 1.6 eV, on the other hand, is shifted only by ∼20 meV (160 cm^{−1}) to lower energies within n = 1–12 (Table 2).
Experiment | Theory | |||
---|---|---|---|---|
n _{He} | 1^{2}Σ^{+}_{u} | 1^{2}Π_{u} | 1^{2}Σ^{+}_{u} | 1^{2}Π_{u} |
2 | 11 | −3.4; −3.7 | 6 | −0.8 |
3 | 23 | −6.1; −6.6 | 15 | −2.1 |
6 | 59 | −13.3; −15.2 | 41 | −6.1 |
10 | 98 | −9.2; −19.3 | 96 | −12.0 |
12 | 124 | −18.5; −41.0 | 109 | −14.2 |
The shifts can be directly connected to the interplay between the position of He atoms around the Cs_{2}^{+} ion and the character of the respective excited state. Our calculations show that Cs_{2}^{+} is preferentially solvated by He atoms on its ends, along the Cs–Cs axis for the smallest ions (see Fig. 4). For Cs_{2}He^{+} and Cs_{2}He_{2}^{+}, the most stable configuration is linear, but deformation from linearity down to a Cs–Cs–He angle of 150° requires very little energy, see Fig. 3; in Cs_{2}He_{12}^{+}, conformations with six and five/seven He atoms on each end are the most stable ones (Table S1, ESI†). As expected, the binding energy of helium atoms is low, within 2.4–3.1 meV He^{−1} for up to 12 helium atoms. In addition to the shifts, the presence of a large variety of almost isoenergetic isomers leads to significant broadening of the spectra upon solvation (see Fig. S1, ESI†).
Due to Pauli repulsion, the presence of He atoms deforms the orbitals of both ground and excited electronic states that extend along the Cs–Cs axis, shifting them to higher energy. This is the case for the HOMO orbital as well as the orbitals corresponding to excitations into the 1^{2}Σ^{+}_{u} and 2^{2}Π_{u} states (Fig. 4). The diffuse orbitals in the excited state are deformed more than the HOMO orbital, shifting the excitation energy considerably to higher values (Fig. 1a). The π orbital corresponding to the excitation into the 1^{2}Π_{u} state at 1.6 eV represents a different case. Here, the surrounding helium atoms do not approach the orbital and the shift to lower energies reflects the slight destabilization of the HOMO orbital. Our calculations can reproduce the shifts for excitations into 1^{2}Σ^{+}_{u} and underestimate those observed for 1^{2}Π_{u} (Table 2); for n = 12, the sudden increase observed in the 1^{2}Π_{u} experimental shift might be induced by the fitting procedure (see Fig. S12, ESI†) or appearance of new isomers. This is most likely caused by the neglect of He delocalization around the Cs_{2}^{+} core due to zero-point motion and the presence of multiple isomers.
Footnote |
† Electronic supplementary information (ESI) available: Relative stabilities of calculated isomers, method benchmarks, spin–orbit couplings, complete experimental spectra, Cartesian coordinates. See DOI: 10.1039/c9cp04790e |
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