Absorption Spectroscopy, a Tool for Probing Local Structures and the

Article pubs.acs.org/JPCA

Absorption Spectroscopy, a Tool for Probing Local Structures and the Onset of Large-Amplitude Motions in Small KArn Clusters at Increasing Temperatures Published as part of The Journal of Physical Chemistry A virtual special issue “Spectroscopy and Dynamics of Medium-Sized Molecules and Clusters: Theory, Experiment, and Applications”. Slim Awali,†,‡,¶ Lionel Poisson,*,‡,† Mounir Ben El Hadj Rhouma,¶ and Jean-Michel Mestdagh‡,† †

Laboratoire Francis Perrin, URA 2453, CEA/IRAMIS/LIDyL, F-91191 Gif-sur-Yvette Cedex, France Laboratoire Francis Perrin, URA 2453, CNRS/IRAMIS/LIDyL, F-91191 Gif-sur-Yvette Cedex, France ¶ Laboratoire d’Etudes des Milieux Ionisés et Réactifs (EMIR), Institut Préparatoire aux Etudes d’Ingénieurs, Monastir, Tunisia ‡

ABSTRACT: Photoabsorption spectra of KArn (n = 1−10) are simulated at temperatures ranging between 5 and 25 K. The calculations associate a Monte Carlo (MC) method to sample cluster geometries at temperature T, with a oneelectron ab initio model to calculate the ground-state and excited-state energies of the cluster. The latter model replaces the K+ core electrons and all the electrons of the Ar atoms by appropriate pseudopotentials, complemented by core polarization potentials. It also provides the necessary oscillator strengths to simulate the spectra. Global optimization by basin-hopping is used in combination with MC simulation at low temperature (5 K) to identify the most stable isomer and remarkable isomers of ground-state KArn clusters, which are stable with respect to deformations of the order of those expected with Zero Point Energy motions. The absorption spectra calculated for each of these isomers at 5 K suggest that absorption spectroscopy can probe sensitively the local environment of K atom: surface location of K with respect to a close-packed Ar moiety, number of Ar atom in close vicinity, and local symmetry about K. Simulation at increasing temperatures, up to the evaporation limit of K out of the cluster, shows the onset of large amplitude motions above 20 K, when the K atom experiences a variety of local environments.

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INTRODUCTION The electronically excited states of a chromophore bonded to rare-gas atoms are very sensitive to the interaction between the chromophore and its environment. This has motivated numerous experimental and theoretical works for two reasons, essentially. One was to explore microsolvation by rare-gas atoms. For instance, the microsolvation of aromatic molecules was pioneered in the group of Leutwyler1 and further developed elsewhere.2−4 The second motivation appeared in theoretical works, where the chromophore spectroscopy is proposed as a sensitive probe of the structure and phase (liquid or solid) of the rare-gas moiety that interacts with the chromophore. This point of view appeared in a series of works where the chromophore is a single alkali,5−7 alkaline earth,8,9 or boron10 atom. The photoabsorption spectrum of Ca in CaArn cluster was also proposed as a way to prove the relaxation dynamics of these clusters when placed out of equilibrium.11 The issue of phase changes in small rare-gas clusters, which appeared a long time ago,12,13 has been recently revisited by path-integral Monte Carlo (MC) approaches in the smallest possible clusters, Ar2 and Ar3, as the onset of diffusive motions.14,15 Probing such movements directly in experiments © 2015 American Chemical Society

seems difficult, although the imaging of Ar2−4 by Coulomb explosion has been reported recently.16 The theoretical works mentioned above, for instance, those on CaArn clusters,8,9,11 suggest that the spectroscopy of a single chromophore attached to a small Ar cluster could be extremely sensitive to the onset of diffusive motions. The present work aims to address theoretically how photoabsorption spectroscopy reveals the onset of such motions in KArn clusters, which have deserved no such study yet. Predicting spectroscopic changes in the chromophore due to phase changes in the rare-gas cluster from ab initio calculations faces the difficulty of describing excited states of the chromophore interacting with the numerous electrons of the rare-gas atoms. Several methods are reviewed in ref 17. A way to address this difficulty is to use the diatomic-in-molecule model as exemplified for the Na(Arn)7 and Ca(Arn)8 systems. An alternative route was pioneered in refs 6 and 17−20 and further developed in ref 21. Accordingly, the active electrons are described ab initio, whereas the other electrons, including Received: July 24, 2015 Revised: August 21, 2015 Published: August 24, 2015 9729

DOI: 10.1021/acs.jpca.5b07192 J. Phys. Chem. A 2015, 119, 9729−9738

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The Journal of Physical Chemistry A all those of the rare-gas atoms, are replaced by appropriate pseudopotentials. The electron problem thus reduces in alkalirare clusters to that of a single electron (the valence electron of the alkali atom) and can be treated very simply at the Hartree− Fock level. This methodology, which we call the one-electron model, was recently applied to simulate the absorption spectrum of Li and Na in small argon clusters.22,23 The present work associates the one-electron model to an MC exploration of the ground-state phase space to simulate the absorption spectrum of a single potassium atom bound to a few argon atoms. These spectra, used as a tool to explore local structures about the K atom and the onset of large-amplitude motions in KArn (n = 1−10) clusters, are simulated at cluster temperatures between 2 and 25 K.

This methodology has been used quite recently to calculate ground and excited potential curves of the LiAr, NaAr, and KAr diatomics.33 All states, up to those dissociating as Li(4p), Na(5p), and K(5f), were considered. An excellent agreement was found with the available experimental data. This suggests that the one-electron description of these systems is reliable, as the parameters used to define the pseudopotentials, and the core−core interaction. Hence, the parameters used for the KAr diatomics in this work are adapted in the present work to treat of the KArn clusters. The same uncontracted 5s4p basis is used on argon. However, since low-energy excited states only are desired in the present work, a smaller basis set is used on the potassium atom: an uncontracted 7s6p7d basis (see parameters on Table 1). The K+−Ar potential was fitted on the

THEORETICAL The absorption spectra are simulated in three steps. First, an MC random walk is used to select a series of geometries that are representative of ground-state KArn clusters at temperature T. The random walk is initiated from the absolute minimum of the ground-state potential energy surface (the procedure used to find this geometry will be described in a later section). The global minimum of the KArn (n = 1−10) clusters as several remarkable isomers of higher energy are also presented in the present work. The cluster energies required by the MC algorithm are provided by the one-electron ab initio model. The same model is used in the second step to provide electronic energies and oscillator strengths for exciting the KArn clusters from the ground state. This calculation is performed for each cluster geometry selected in the first step. A histogram of the transition intensities (deduced from the oscillator strengths) is built in the third step as a function of the excitation energy. It simulates the absorption spectrum according to the vertical transition approximation. This approach is semiclassical since the transition energies and strengths are obtained quantum mechanically and the geometries, classically. The One-Electron ab Initio Model. The one-electron model is fully described in ref 22. Shortly, works in the late 1960s showed that the interaction in alkali−rare gas pairs is governed primarily by the unique valence electron of the alkali atom and can be described accurately using ultralarge core pseudopotentials complemented by core-polarization potentials, which substitute all the electrons of the rare-gas atom and all those of the alkali ion core.24−27 This approach was generalized in the 1990s and later to describe alkali atoms interacting with several (or many) rare-gas atoms.6,17−20,28−30 The pseudopotentials used here are of the l-dependent semilocal type, according to the expression of Barthelat and Durand31 and F. Spigelman.32 The single valence electron pseudopotential for the [K+] core has been widely used in accurate standard valence calculations.33 Argon was treated as a zero-electron atom with all its electrons in the core via an atomic [Ar] core pseudopotential determined by Duplaa and Spiegelman.32 The pseudopotentials also incorporate core polarization operators (so-called core-polarization potentials) using the l-dependent formulation of Foucrault and coworkers34 generalizing the initial formulation proposed by Muller and Meyer.35 This method solves the electronic problem, whereas the full Hamiltonian includes the core− core interactions as additive terms: ∑ A r V K + − A r + ∑Ar∑Ar′ Eki , i i

(

according to the exp −

E0k + 1 − E0k kBT

) probability. The number of

MC steps used for the calculations was limited to 50 000 by atoms of the clusters up to KAr7 and 20 000 above. This choice allows performing the calculation in a reasonable time (a few weeks for clusters larger than KAr7). 9730


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The Journal of Physical Chemistry A This methodology provides an MC trajectory within the configuration space of the KArn clusters. It corresponds to a series of cluster geometries, labeled ℜk , that are representative of those populated at temperature T. Determination of Structures. Structures are identified using the basin-hopping technique.42 Their stability with respect to Zero Point Energy (ZPE) motions was checked qualitatively by running an MC simulation at 5 K. The latter temperature was chosen to be close to the expected ZPE. Of course, since the atoms are considered classically in the present work, we do not claim ZPE motions are taken into account quantitatively. The objective here is to check that the structures that were identified are stable with respect to motions that are of the same order of magnitude as the expected ZPE. Furthermore, at this temperature it was demonstrated that the ZPE effect on the properties of the cluster was negligible.9 Arn clusters were also shortly investigated using the interaction potential previously presented. MC trajectory was calculated at T = 20 K, followed by a freezing at 1 K for identified structures. The optimal structures found fit perfectly the one of the Cambridge Cluster Database,43 using the same potential. The present calculation provides also isomers and the corresponding energies, which will be used in the following discussion. Simulation of the Absorption Spectrum. At each geometry ℜk , electronic energies Em(ℜg ) and transition dipole moments D0m(ℜk ) are calculated using the one-electron model. A histogram is built from integration of the transition energies ϵ0i(ℜk ) = Ei(ℜk ) − E0(ℜk ) and the transition intensities

Figure 1. Lowest-energy isomers of KArn (n = 1−10) clusters in the ground electronic state and remarkable isomers.

8π 2

(given by I(ϵ0i) = 3 ϵ0i|D0i|2 in atomic units.) along the MC trajectory. The horizontal scale of the histogram is the transition energies. Its full range is [12 000−15 000 cm−1], divided into intervals of 6 cm−1. The transition intensities are summed in the proper intervals of the histogram.

calculation. The Ar5 cluster has indeed a trigonal bipyramid structure where the five Ar atoms are nonequivalent whether they form the summits or belong to the base of the bipyramide. The two stable isomers of KAr4 appear as due to the substitution of either Ar atom. In the isomer of lowest energy, the K atom replaces a summit Ar atom (then, KAr4 has the C3v symmetry), whereas in the other isomer (49.7 cm−1 higher in energy) the K atom substitutes an Ar atom of the base (KAr4 of C2v symmetry). The average Ar−Ar distance in the KAr3 and KAr4 clusters reported in Figure 1 is 7.13a0, again, quite close to what was found experimentally in pure Ar3,4 clusters, where the edge length of the triangle is 7.18a0 for Ar3 and 7.27a0 for Ar4.16 We turn now to KArn clusters with n ≥ 5. For these clusters, Figure 1 indicates that the structure of their isomers may not be rationalized by the sole picture of substituted cluster. Actually, substituted structures compete with “face-deposited” ones where the K atom is deposited on a facet of the most stable isomer of Arn instead of substituting an Ar atom of Arn+1. Actually facedeposited structures may appear as a substituted one when considering high-energy isomers of Arn+1. We shall encounter such a situation below in KAr6. Depending on the K influence, the relative energy of the isomers can be switched when comparing structures of KArn and Arn+1. Face-deposited structure may also be lower in energy than substituted ones. In KAr5 the C4v substituted structure does not appear to be stable in the 5 K MC calculation. It switches to a more stable face-deposited structure where the K atom sticks to a facet of the trigonal bipyramidal Ar5 cluster. For KAr6 both the substituted and face-deposited structures coexist. The substituted one is the most stable. It has the K atom replacing one of the Ar atoms in the base of the bipyramid. Such a structure with seven atoms appears as the first building block of an icosahedron, when viewed from one of the C5 axis. Similar structures were

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RESULTS AND DISCUSSION Low-Energy Isomers of Ground-State KArn Clusters. The isomers of low energy that were found in the present work are shown in Figure 1. Their structure is similar to that reported for LiArn23 and NaArn22 clusters. Except for the lowest isomer of KAr10, K is indeed located at the surface of a close-pack Ar cluster. This observation is consistent with the deeper potential well and the shorter equilibrium distance in Ar−Ar than in K− Ar: De = 99.53 cm−1 and rm = 7.09a0 in Ar−Ar versus 41.7 cm−1 and 9.46a0 in K−Ar. The structure of the KArn reported in Figure 1 is compared below to that of the Arn clusters found or documented experimentally.16 We examine first the smaller KArn clusters (n = 2,3). In these clusters, the geometry of the argon moiety is very close to that of the corresponding pure argon clusters Ar2−3. The global minimum of KAr2 is found to be an isosceles triangle with RArAr′ = 7.09a0, close to the Ar−Ar equilibrium distance of the HFDC potential used in the present work (rm = 7.10a0). The latter compares well with the Ar−Ar distance found experimentally in Ar2 (7.18a0).16 The ground structure of KAr3 is found to have the C3v symmetry as a trigonal pyramid. We call such KArn structure “substituted” since the K atom appears as substituting an Ar atom in the Arn+1 structures reported by Wales and Doyes.42 This picture helps rationalizing the observed two isomers of KAr4 that are found for KAr4 at 5 K in the 2.5 × 105 steps MC 9731


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The Journal of Physical Chemistry A calculated in CaArn.9 The face-deposited structure of KAr6 lies 13 cm−1 higher in energy than the substituted one. This energy difference is smaller than the energy difference of 63 cm−1 found between the equivalent structures in Ar7. This is probably due to a destabilization of the most stable isomer. The facedeposited isomer is stable at 5 and 7 K for the 3.5 × 105 steps of the MC simulation, but unstable at 9 K. Note that the facedeposited structure, with its octahedral Ar8 substructure, is the first building block (unit cell) of the fcc-crystal of argon. For KAr7 and KAr8, the most stable isomers are the substituted structure. They are constructed on the same core as the KAr6 substituted structure. A remarkable face-deposited isomer of KAr7 was found (37 cm−1 higher in energy), based on the Ar7 core. This isomer can also be seen as the building block of the most stable structure of KAr8 since it shows the Ar7 block in its argon environment. This is not the case for the other isomers of KAr8 found, still based on the substituted structure (not presented here), but having the additional atoms located differently especially around the K atom: five (+56 cm−1) and six (+116 cm−1) argon atoms are in touch, respectively. The most stable KAr9 isomer is face-deposited upon an Ar9 cluster. Various isomers that are metastable at 5 K are found. Two of them deserve comments. One appears as a distorted fcc structure lying 118 cm−1 above the most stable structure. It shows typical two octahedral substructures, one being incomplete. In a sense, it appears as built from the facedeposited KAr6 isomer. Another remarkable structure lying 132 cm−1 above the most stable structure is a substituted structure of an Ar10 cluster, that is, half-icosahedron with a centered hexagonal face. There, the K atom substitutes a closed-shell argon atom of the first icosahedron shell, and shows also a C5 symmetry in its first solvation layer. The most stable isomer found for KAr10 is face-deposited with the K atom located on the main symmetry axis of the Ar10 cluster. Actually, this most stable structure is very floppy since the K atom travels almost freely at the cluster surface when sampled by the MC calculation at 5 K and even at 1 K. This suggests that if the ZPE were taken into account quantitatively, the K atom would be significantly delocalized. Another facedeposited isomer, 136 cm−1 higher in energy, was found. It appears as building block for a fcc-crystal of the argon moiety with two complete octahedral substructures. The energy difference of the corresponding Ar10 structure is calculated at 121 cm−1. The stabilization is due to the interaction between K and a larger number of atoms in the case of the ground isomer. Contour plots of the ground-state orbital of KArn are shown in Figure 2 for n = 3, 6, and 10. Fairly spherical orbitals are observed suggesting that they keep the 4s character of groundstate K. Hence, we found it convenient to label the electronic states that are vertically excited from ground-state KArn as a local excitation centered on the K atom. Accordingly,

K*(4p)Arn represents the three low-lying states of KArn. Very importantly, the ab initio calculation that provides these states does not follow this oversimplification since the presence of basis functions on each Ar atom allows delocalization of the valence electron of K on the entire cluster. Absorption Spectra. Probing the Local Environment. The purpose here is to illustrate the sensitivity of absorption spectra to the local environnement of the K. Hence, Figure 3 shows the absorption spectra of the stable and metastable isomers described earlier in the text. The simulations are performed at 5 K, a temperature that preserves the metastability of the isomers for clusters ranging from KAr1 to KAr10. An important result is that the 4s → 4p transition splits into two bands. For the larger clusters one band is strongly blue-shifted. The other band, sometimes resolved in two sub-bands, is only slightly displaced with respect to the atomic absorption (dashed line in the Figure 3). To facilitate the discussion of the spectra in Figure 3, Figure 4 displays contour plots of the three first excited states of the K*(4p)Ar2,4,6 clusters. This figure supports, at least qualitatively, that the excitation is local and that the three excited states of lowest energy correspond to the three possible alignments of the K(4p) orbital with respect to the cluster. This fits with the anticipation above that the excitation is localized on the K atom. When observing the alignment of the excited orbital in K*(4p)Ar6 a pseudo-diatomic picture of the K-cluster interaction can be drawn where the close packed argon cluster is replaced by its center of mass (CM). Accordingly, the two lowest states (the two left columns of Figure 4) correspond to a π-alignment of the 4p orbital with respect to the K-CM axis, whereas the third state corresponds to a σ alignment. For simplicity, we call Σ-state, the state where the excited orbital points toward the cluster and Σ-band, the band that is blueshifted in the absorption spectra and corresponds to excitation toward the Σ-state. Similarly, Π-state and Π-band refer to the two other states. Of course, when the local environment provided by the cluster about K does not have a cylindrical symmetry, the Π-band can split into two components. Σ-Band. Figure 5 shows how the blue shift of the Σ-band varies as a function of number of argon atoms present in a sphere of 7 Å radius about the K atom, shown by different colors. The 7 Å radius was chosen when considering the density function of Ar atom around the K atom (not reported here). It appears indeed that for all clusters KArn≤8, a second Ar layer, that is, a second solvation shell, starts growing beyond ca. 7 Å. Likely, the blue shift of the Σ-band is due to the proximity of argon atoms repelling the valence electron of K. This appears as reminiscent of the repulsive character of the B2Σ potential curve in the K−Ar diatomics where the K(4pz) orbital is pointing toward Ar (K−Ar potential curves can be found, for instance, in ref 33). In the cluster environment, the blue shift appears correlated with the number of argon atoms that are present in the first solvation shell. The larger this number, the larger the shift. Nevertheless a screening effect is present between the Ar atoms of this shell since the blue shift rises by step of 200 cm−1 from K to KAr3, by step of 100 cm−1 up to KAr5 then looks saturating. Π-Band. The main observation in Figure 3 is that the Πband splits into two sub-bands at specific cluster sizes or, at a given size, for a specific isomer. This effect is discussed below in terms of local environment of the K atom for increasing sizes of the KArn clusters.

Figure 2. Contour plots of the electronic ground-state orbital for the isomer of lowest energy of KArn clusters (n = 3, 6, and 10). 9732


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The Journal of Physical Chemistry A

Figure 3. Photoabsorption spectra for KArn clusters, n = 1−10 from the ground state to the 4p level. In green are presented the absorption spectra of the structure of lower energy; in blue and red the other remarkable structures are presented on Figure 1 and discussed in the text. The vertical reddashed line is the transition of the isolated K-atom, expected from the calculation (without spin−orbit coupling).

Figure 1 shows that K in the KAr3 complex is placed in an environment of C3v symmetry. According to the character table of this symmetry group, K(4s) is resolved into an A1 molecular state, whereas K(4p) leads to an A1 molecular state and an E doubly degenerate one. The former has the 4pz orbital pointing toward the CM of the three Ar atoms and is thus assigned to the Σ-state. The E molecular state is thus assigned to the Πstate, and because of the double degeneracy of the E state, the Π-band of KAr3 in Figure 3 appears with a single peak. We mentioned already that the KAr4 complex has two isomers belonging to two different symmetry groups. The most stable isomer belongs to the C3v point group and leads to a single peak in the Π-band, whereas the other isomer, which has a C2v symmetry, leads to a Π-band with two sub-bands. More generally, the local symmetry of the structure of the Πband informs on the close symmetry around the K atom, whether it is C2v (double band) or C3v (single peak). The observations in Figure 3 for KAr5−9 are easily rationalized on this basis. Finally, we saw in the previously section that the lowest isomer of KAr10 is extremely floppy. At 5 K the K atom explores the surface of the Ar cluster. As seen in Figure 3, this results in an averaging of splitted and not splitted bands, forming a very broad and almost structureless Π band compared to that of the other isomer.

We have seen, when discussing the structures, that the most stable isomer of KAr2 has the C2v symmetry. Accordingly, the ground-state K(4s)Ar2 leads to an A1 molecular state, whereas K(4p2P) splits into three components and forms the three lower-excited molecular states of the KAr2 cluster: A1 when the 4p orbital is parallel to the axis between K and the CM of the Ar2 moiety (4pz → A1); B1 and B2 when the 4p orbital is perpendicular to this axis, whether it is parallel (4py → B2) or perpendicular (4py → B1) to the Ar−Ar axis. Actually, 4p, A1 correspond to the Σ-state anticipated above, and 4p, B1,2 correspond to the Π-state. Hence the blue-shifted Σ-band is associated with the 4s A1 → 4p A1 transition, whereas the Πband corresponds to the 4s A1 → 4p B1,2 transition. Likely, the interaction between 4px,y and the argon environment is essentially attractive, except at short distances, as the A2Π potential curve in K−Ar. When looking at the 4px,y orbitals of KAr2 in Figure 4, it appears that the 4px and 4py orbitals are not equivalents. One has the two argon atoms located in its node plane, whereas the other one is certainly slightly destabilized by the argon atoms that are on both sides of this plane. These expectations fully account for the observed absorption spectrum in Figure 3 where the Π-band of KAr2 is split in two sub-bands. 9733


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ground-state complex at equilibrium geometry belongs to the C3v point group. As a result, the Π-band is not split into two sub-bands at low temperature but does so when, at increasing temperatures, the complex deviates from its equilibrium geometry. This is likely the origin of the asymmetrical tail of the Π-band at the larger temperatures. The broadening of the Σ-band is also very large, and at T = 21 and 25 K, the red tail of this band overlaps the Π-band. This suggests that at these temperatures, very deformed structures are experienced where the K atom moves quite far from the Ar atoms. The KAr6 cluster was studied for 3.6 × 105 MC steps. The corresponding spectrum is shown in Figure 8. We saw in the previous section that the two isomers of lowest energy do not belong to the same symmetry point group and therefore do not lead to the same shape of the Π-band. Two Π-sub-bands are observed with the isomer of lowest energy, whereas no substructure exists in the Π-band with the metastable isomer. The energy difference between both isomers is 13 cm−1 (19 K) only. Hence, increasing the cluster temperature populates the metastable isomer, up to 40% of the population at 21 K. This explains why the two Π-sub-bands, which are very distinct at 5 K, disappear at 21 K in favor of a single broad band. Not surprisingly, the latter looks very much like the superposition of the green and blue spectra shown at 5 K in Figure 8. It is interesting to bring together the present results on the KAr2−10 clusters and calculations of Calvo and co-workers where the absorption spectra of the CaAr6,10 clusters are simulated in the vicinity of the Ca(4s2 1S → 4s4p 1P) transition.8,9 The similarity of the present observations with those in Calvo’s work is striking. In the latter work indeed, three non-degenerate absorption lines were simulated at 0 K, corresponding to the Ca(4s2 1S → 4s4p 1P). These lines broaden and merge together as the cluster temperature is enhanced and above 20 K, the spectrum is dominated by a single band, which is close to the atomic transition of free Ca. This is attributed to the visit at these temperatures of a pentagonal bipyramidal isomer of CaAr6, which is 80 cm−1 higher in energy than the most stable isomer. The spectra that appear for CaAr6 in Figure 5 of ref 9 in Calvo’s work differ in their details from those of Figure 8 in the present work. However, the essential characteristics in these spectra is that their shape changes qualitatively when the cluster temperature reaches 20 K at the onset of large amplitude motions, which allows the cluster geometry to sample that of various isomers. In that sense, absorption spectroscopy appears as a sensitive probe of such motions. Comparison with Available Experimental Information. To our knowledge, no experimental information documents the absorption spectra of small size-selected KArn clusters as those simulated in the present work (n = 1−10). The only available information concerns much larger clusters, broadly distributed about the KArn≈800 average size44 (note that this work combines experimental information with numerical simulations, adapted to the large cluster environment). The cluster temperature was not measured in the latter experiment by Awali et al.44 where the K atom is deposited collisionally on the Ar clusters using the pick-up technique. Nevertheless, it can be estimated by comparison with the temperature of 30−34 K measured by Torchet and co-workers in the 1980s for pure Ar clusters of similar size.45,46 Since the K−Ar binding energy is approximately half that of Ar−Ar (41.7 vs 99.53 cm−1) only clusters of ≤30 K temperature can accommodate a K atom. Awali et al.44 have discussed that because of this effect, many pick-up events

Figure 4. Contour plots of the first excited-state orbital for the isomer of lowest energy of KArn clusters (n = 2, 4, and 6) ground-state geometry. (left to right) 4px, 4py (Π orbitals), and 4pz (Σ orbital).

Figure 5. Blue shift of the Σ-band as a function of the argon number at 5 K. The colors are correlated to the number of argon atoms within the first 7 Å around the K atom: magenta = 1, blue = 2, cyan = 3, green = 4, orange = 5, brown = 6.

Evolution as the Function of the Temperature for KAr2,4,6. Figure 6 shows the vertical K(4s → 4p)Ar2 transition spectra that were simulated at various temperatures by the MC calculation. Each spectrum is obtained for ∼7.5 × 104 MC steps. At T = 14 K, evaporation of K atom was observed. The two Π-sub-bands and the Σ-band, which are clearly identified in the spectrum at 2 K, are not affected in the same way when increasing the temperature. The Σ-band gets broader and moves toward the atomic transition, whereas the two Π-subbands merge together into a broad single band, peaking very close to the atomic transition. These observations are consistent with a picture where increasing temperatures break the C2v geometry of the complex by enabling the atoms to move far from their equilibrium position. Line-broadening is also due to the extension of geometry number explored by the system when raising the temperature. At 10 K and above, the shoulder in the red side of the Π-band thus appears reminiscent of the C2v symmetry in the KAr2 complex at equilibrium. The picture that can be drawn for KAr4 is actually quite similar to that just encountered with KAr2, except that now, the 9734


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Figure 6. Absorption spectrum of KAr2 for temperatures between 2 and 12 K (2 to 25 K were calculated by steps of 2 K, for 7.5 × 104 MC steps).


13 650 cm−1 in the large cluster experiment suggests that four Ar atoms forms the average neighborhood of the K atom. The large extension of this band, up to 14 500 cm−1, suggests that the K atom explores substitution sites at the surface of the cluster with six or more argon atoms as first solvation shell. The discussion above concerning the floppy character of the KAr10 clusters appears as the onset of such a surface exploration when the cluster size increases. Actually, such a surface motion in the large cluster experiment was successfully simulated in the theoretical part of the latter work for, for example, KAr560 clusters.44 The Π-band reported by Awali et al.44 in the large cluster experiment is quantitatively very close to that obtained here for

result into the late evaporation of the K atom. This result is consistent with the evaporation observed in the present calculations at temperatures above 25 K for the larger clusters. From this, we suggest that the temperature of the clusters that accommodate a K atom in the large cluster experiment of Awali et al. fall in the range of 20−25 K. The experimental absorption spectra in the large cluster experiment exhibits a Σ- and a Π-band implying that the K atom stays at the surface of such large clusters (this is actually confirmed by the simulations in the work of Awali et al.). The Σ-band is broad. It peaks at 13 650 cm−1 and extends to 14 500 cm−1. This observation is quantitatively consistent with the simulations shown in Figures 3 and 5. The Σ-band peaking at 9735


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the size of the cluster, K in KArn either substitutes an Ar atom in the Arn+1 or is face-deposited on a facet of the Arn cluster. The absorption spectra calculated for each of these isomers at 5 K suggests that absorption spectroscopy probes sensitively the local symmetry about the K atom. The surface location of K with respect to the cluster appears as a splitting of the 4s → 4p in two components called Σ and Π bands whether the excited orbital is pointing toward or perpendicular to the close-packed Ar atoms. The position and width of the Σ-band is quite sensitive to the number of Ar atoms in close vicinity with K, whereas the structure of the Π-band reveals the local symmetry about K. The C2v symmetry splits the Π-band in two sub-bands separated by ∼125 cm−1, whereas the C3v symmetry does not. Simulation at temperatures increasing to the evaporation limit of K out of the cluster shows the onset of large amplitude motions above 20 K, when the K atom experiences a variety of local environments. Note that the spin−orbit coupling is not included in the present calculation. Its effect would be also to split the Π-band into two components as the C2v environment. However, the spin−orbit constant of K is only 38.5 cm−1. Hence Π-band splitting due to the spin−orbit coupling is expected to be significantly weaker than that due to the local environment of the K atom: slightly broaden the single peaks and slightly increase the Π-splitting when it occurs. Nevertheless the spin− orbit coupling is expected to be of more dramatic influence when looking at the dynamics following the excitation.

KAr6 at 21 K. It features an asymmetric band peaking slightly on the red side of the atomic line, with a significant shoulder extending as a tail to the blue side of the same line. From the discussion above, this line shape was assigned as due to a large amplitude motion of the K atom with respect to the Ar atoms where K experiences environments of C2v and C3v local symmetry. This fits with the picture drawn above where K explores the surface of the large clusters, hence, experiencing sites of various symmetries. The simulation of the photoelecton spectra reported by Awali et al.44 requests the optimization of the excited states, which is under study and will be the object of a forthcoming paper.

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CONCLUSION The present paper has simulated the absorption spectrum of KArn clusters where a single K atoms is bound to a small number of Ar atoms (1 to 10). An MC method is used to sample a series of geometries that are representative of the ground-state KArn clusters at temperature T. Temperatures ranging between 5 and 25 K are explored. A one-electron ab initio model is used to calculate the ground-state energy and the energy of the first three excited states of the cluster. In the latter approach, the electron problem is reduced to the ab initio treatment of the sole valence electron of K, the core electrons of K, and all the electrons of the Ar atoms being replaced by appropriate pseudopotentials, complemented by core polarization potentials. The K + −Ar and Ar−Ar core−core interactions are described by available potentials of the literature. The technique of global optimization by basin-hopping of Wales and Doye42 is used to identify the most stable isomer and low-energy isomers of ground-state KArn clusters. MC simulation at low temperature (5 K) is used to check the stability or metastability of these isomers with respect to deformations of the order of those expected with ZPE motions. In the most stable isomers, the K atom is at the surface of a close-packed structure formed by the Ar atoms. Depending on

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS S.A. thanks EU-ITN Project ICONIC-238671 for funding. L.P. thanks the ANR for support through Contract No. ANR-09JCJC-0090-01 CHROMADYNE. We acknowledge the seventh 9736


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European Community Framework Program under COST ACTION CM1405 MOLIM. L.P. and S.A. thank Dr. B. Gervais and Pr. J. Douady for fruitful discussions.

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