Exciplexes with Ionic Dopants: Stability, Structure, and Experimental

May 30, 2014 - M+(2P)4Hen species, possibly involved in the post 2P ← 2S excitation dynamics of Sr+ and Ba+ in cold 4He gas or droplets, are studied...
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Exciplexes with Ionic Dopants: Stability, Structure, and Experimental Relevance of M+(2P)4Hen (M = Sr, Ba) Massimo Mella*,†,‡ and Fausto Cargnoni*,†,§ ‡

Dipartimento di Scienza ed Alta Tecnologia, Università dell’Insubria, via Valleggio 11, 22100 Como, Italy Istituto di Scienze e Tecnologie Molecolari (ISTM), Consiglio Nazionale delle Ricerche (CNR), via Golgi 19, 20133 Milano, Italy

§

S Supporting Information *

ABSTRACT: M+(2P)4Hen species, possibly involved in the post 2P ← 2S excitation dynamics of Sr+ and Ba+ in cold 4He gas or droplets, are studied employing both high level ab initio calculations to determine the potential energy curves (PEC) and diffusion Monte Carlo (DMC) to obtain information on their ground state structure and energetics. PEC for the excited M+(2P)He dimers were obtained using MRCI calculations with extended basis sets. Potential energy surfaces (PES) for M+(2P)Hen were built with the DIM model including spin−orbit coupling via a perturbative procedure. DMC simulations indicated several exciplexes (n > 2) to be stable against He dissociation whatever the ion state, a finding that is at variance with what was previously suggested for Ba+(2P1/2) due to the repulsive nature of the interaction potential obtained in [Phys. Rev. A 2004, 69, 042505]. Our results, instead, support the suggestion made in [J. Chem. Phys. 2012, 137, 051102] for the existence of Ba+(2P1/2)Hen exciplexes emitted following the excitation of the barium cation solvated into He droplets. In the 2P1/2 state, the Ba ion also shows a peculiar behavior as a function of n with respect to the location and binding strength of the attached He atoms compared to Sr+. Although the latter forms the usual equatorial He ring, Ba+ deviates from this geometry for 1 ≤ n ≤ 4, with the radial distribution functions strongly depending on the number of solvent atoms. Finally, a putative species is proposed to explain the emission band at 523 nm that follows D1 or D2 excitation of Ba+ in superfluid bulk helium.

1. INTRODUCTION

formation of bound species with the expulsion of the cation from the droplet. The observation made in ref 5 appears even more interesting if one also considers that previous spectroscopic experiments6 have left important details of the post−excitation dynamics of Ba+(2P) in liquid helium unclear. In particular, we refer to the simultaneous presence of free−atom like 2S1/2 ← 2P1/2 and 2 D3/2 ← 2P1/2 emission lines and of a third band at 523 nm with an unclear origin. The latter may be due to bound species formed during the post−excitation dynamics into the condensed He environment. Apart from the spectroscopic experiments in bulk helium and He droplets, the formation (and decomposition) of exciplexes was observed following the excitation of the D2 line of Ba+ in cold (3−20 K) He gas,7,8 perhaps as a byproduct of an investigation on fine-structure changing collisional processes involving alkali-earth-metal cations and He atoms.9 As a net result of these experiments, it emerged that Ba+(2P3/2) is capable of binding a single He atom, the possibility of binding more being hampered by the low He density employed during the experiments. Indeed, two He atoms would be expected to bind strongly to the cation due to the anisotropic density as

The usage of cold (0.37 K) and superfluid He droplets as nanocryostats for spectroscopically studying interesting species in isolation and quenching their internal degrees of freedoms continues to surprise in terms of unexpected observations, especially when cations are involved. In these cases, the charge−induced dipole interaction between the ion and the solvent He atoms should, in principle, ensure cation solvation whatever the vibrational or electronic state of the latter. Recent experiments, however, contradicted such common lore, suggesting that both vibrational (for molecular species1−4) and electronic (for simpler monatomic ions5) excitation may lead to ion expulsion from the droplet. Given the fact that ions seem to be expelled via a nonthermal mechanism, the process ought to hinge on the possibility that an excited species finds itself in a less attractive environment than the ground state one, or on its capability of “dumping” the excess energy into a relative translational mode with respect to the droplet center of mass. In this respect, the recent experiments on the postphotoionization dynamics of barium attached to He droplets and on the photoexcitation of the resulting Ba+, once solvated by the latter,5 attract interest due to the extreme simplicity of the dopant. Peculiarly, the analysis of the ejected species clearly indicated the presence of Ba+Hen clusters, which could be exciplexes according to Zhang and Drabbels’ analysis. If this were the case, there would be the need to reconcile the © 2014 American Chemical Society

Special Issue: Franco Gianturco Festschrift Received: March 19, 2014 Revised: May 30, 2014 Published: May 30, 2014 6473

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Figure 1. Interaction potentials between excited Sr+ or Ba+ and a single He atom. All the asymptotes have been set to zero for convenience. Distances in Å, energies in cm−1.

suggested by Dupont−Roc;10 additional atoms would bind only via weak dispersion forces. The presence of Sr+He excimer was also hinted at in ref 7 recording the fluorescence emission after D2 line excitation in similar conditions. The formation of He exciplexes with Ba+(2P1/2) was instead deemed to be impossible on the basis of the repulsive nature of the 2Π1/2 potential energy curve (PEC) for excimer; however, no methodological details were given about the PEC calculation. At the moment, the idea that Ba+(2P1/2) cannot form exciplexes with He atoms appears inconsistent with the mass spectrometry analysis of the Ba+ ejected from the droplets following both 2P1/2 ← 2S1/2 and 2P3/2 ← 2S1/2 excitations, an analysis that clearly indicates the presence of Ba+Hen. As the results of experiments in bulk He suggest a rapid fine-structure change,6 the mass spectrometry data may be interpreted as an indication of the formation of only Ba+(2P1/2)Hen exciplexes. These, however, may represent a secondary product obtained after the initial formation of Ba+(2P3/2)Hen species upon excitation of the D2 line. Such a process seems somewhat more likely for n = 1 and 2, as the 2P3/2 state of metal atoms are known to strongly bind no more than two He atoms. In the context just described, we deemed it interesting to investigate the stability and structural details of M+(2P)Hen species with M = Sr or Ba. The main goal would be to describe the effects related to the anisotropic interaction between He atoms and P-state like charged atomic species, with a particular aim toward interpreting the experimental results discussed in this section. To do so, we need accurate PESs describing the interaction between the ion and the surrounding He atoms, which we build starting from ab initio calculations on the

relevant dimers and employing the diatomics-in-molecules11 approach to generate many-body surfaces. Diffusion Monte Carlo simulations are subsequently employed to sample the ground state wave function Ψ0 of the title systems, and thus computing their lowest vibrational eigenvalue E0. With this data, we also discuss similarities and differences between the two metals and, when useful, compare with previously studied neutral exciplexes. In particular, we highlight a compelling behavior shown by Ba+ hinging on the relative strength of the interaction PECs and of the spin−orbit coupling constant. Finally, we pay some effort toward providing an unified picture of all the experiments discussed in the literature involving Ba+ interacting with He atoms.

2. POTENTIAL ENERGY CURVES AND AB INITIO METHODS In this study, we determined the potential energy curves (PEC) of M+−He dimers (M = Sr, Ba) which asymptotically correlate with the lowest lying 2P and 2D states of the metal. To obtain these potentials, we first performed Configurations Interaction (CI) computations on the isolated cations, including excited configurations up to triples. The excited 2P and 2D states are entirely described by single excitations of the outermost electron (5s in the case of Sr+, 6s in the case of Ba+) to the empty p and d shells. Accordingly, the interaction potentials with helium have been determined at the MRCI level of theory. The reference wave function consists of the ROHF term plus the single excitations of the outermost electron of the metal into the lowest lying empty p and d shells. Electron correlation is accounted for by including CI terms up to double excitations 6474

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well with recent literature data for this same system18 (see the discussion and Figure SI1 in the Supporting Information); instead, there are no available potentials for excited Sr+−He levels and for Ba+−He states correlating with Ba+(2D), at least to the best of our knowledge.

spanning the entire virtual space, which should be able to describe properly dispersion effects as well as intramonomer correlation on both the metal and the He atoms. As for the basis set, the core electrons of the metal atoms have been described with the Def2 pseudopotentials,12 and the outermost 9 electrons are assigned the QZVP gaussians basis sets.13 Helium is described with the aug-cc-pVTZ basis,14 and a 3s3p2d set of bond functions15 is located midway between the two nuclei. All the interaction energy data have been processed using the standard counterpoise technique proposed by Boys and Bernardi. Spin−orbit coupling is not described at this stage and is added a posteriori according to the scheme described in ref 16. Test computations at the CI singles and doubles level of theory proved that improving the quality of the basis set on He (up to the aug-cc-pV5Z set) has a very limited effect on the properties of the excited states PEC. As an example, the well depth of the highly attractive 2Π states asymptotically correlating with Ba+(2P) increases by roughly 3% as we increase the basis set quality from aug-cc-pVTZ to the aug-ccpV5Z, while the equilibrium internuclear distance decreases by about 0.1 Å. The interaction potentials have been computed at 30 internuclear separations, sampling more finely the regions where the PEC undergoes sudden changes. All computations have been carried out with the GAMESS-US17 code. The analytical expressions for the PEC have been determined fitting the ab initio energies with Morse-like model functions modified by using polynomials of exponential functions of the nuclear distance r, and including a short-range damped Cn/rn term to fit the PEC long-range regions. The main features of the interaction potentials are reported in Figure 1, and relevant data are collected in Table 1. As

3. DIFFUSION MONTE CARLO AND DIATOMICS-IN-MOLECULES POTENTIALS As deeply fluxional in nature, M+(2P)Hen species require the use of specialized methods not relying on geometrical reference points such as minimum energy structures employed during the harmonic analysis of vibrational modes. Also, the small size of our systems makes semi-phenomenological methods such as density functional theory19 less useful, as they tend to rely on a liquid-like description of the He part. Thus, we opted for employing DMC,20 which efficiently gives energies and ground state Ψ0 distributions for highly quantum systems. The interested reader would find methodological information in the extensive literature on the approach (e.g., see ref 21), thus we avoid lengthy discussions and provide only a few details on the particular choices made in this work. First, the deep well present in the M+*−He interaction potentials other than in the 2 + Σ states allows us to avoid guiding the DMC sampling by means of a trial wave function ΨT. Second, we employed the third-order “on the fly” algorithm developed in ref 22 that uses an intermediate half-step potential evaluation to extrapolate the branching weights to third order. A time step δt = 100 hartree−1 was found sufficiently small to guarantee a small systematic bias for all clusters simulated when used in conjunction with a total population weight around 2000 and uniformly distributed over the walkers. Third, we collected geometrical parameters while sampling Ψ0 to obtain structural information; this approach is used despite methods giving Ψ02 sampling are available23,24 as the latter are more expensive or complicate to implement. Besides, the simple approach taken in this work to extract structural details has already been shown to provide good quality information for reasonably bound species.25,26 As done previously by several research groups,16,26−33 we employed the DIM approach11 to build the many-body PES for M+(2P)Hen. This allows one to introduce completely the twobody terms and a part of the three-body contributions to the complete description,34 the latter components being mainly related to orbital rotation. Specifically, we used the same approach detailed in ref 26, including a treatment of the spin− orbit coupling based on distance-independent couplings assumed proportional to the atomic splitting values (Δ = 801.46 cm−1 for Sr+ and Δ = 1690.84 cm−1 for Ba+). Albeit more accurate approaches based on the diabatization of the diatomic PEC are available35 to generate a many-body PES, the DIM approach has been shown to provide a sufficiently high level of accuracy for the purpose of quantitatively extracting and comparing energy trends and structural features26,28,33 between the family of species. Besides, applying the diabatization approach proposed in ref 35 is made quite complicated by the CI wave function model used to compute the PEC, which include millions of configurations.

Table 1. Relevant Properties of the M+−He Interaction Potentials (M = Sr, Ba)a state

Rminb

Eminc

σd

Σ [Sr ( P)−He] Π [Sr+(2P)−He] 2 Σ [Sr+(2D)−He] 2 Π [Sr+(2D)−He] 2 Δ [Sr+(2D)−He] 2 Σ [Ba+(2P)−He] 2 Π [Ba+(2P)−He] 2 Σ [Ba+(2D)−He] 2 Π [Ba+(2D)−He] 2 Δ [Ba+(2D)−He]

6.84 2.60 6.12 2.54 2.79 7.50 2.90 5.74 2.86 3.09

−4.7 −682.9 −6.2 −602.8 −287.1 −3.5 −486.6 −9.3 −388.9 −211.9

5.99 2.23 5.13 2.20 2.41 6.54 2.51 4.97 2.49 2.70

2 2

+ 2

a

The asymptotes have been set to zero for convenience. bInternuclear distance at the minimum interaction energy, Å. cMinimum interaction energy, cm−1. dInternuclear distance where the interaction potential becomes repulsive, Å.

expected, 2Σ states are almost entirely repulsive due to the fact that the metal atom accumulates its valence electron density along the M+−He internuclear axis. Conversely, the helium atom can interact with the positive core of the metal when the valence electron of the latter is accommodated into a p orbital pointing away from the M+−He axis, and a quite deep well arises. The interaction potentials for Ba+−He are shifted at larger distances as compared to the corresponding states of Sr+−He, which is clearly an effect of the larger size of the barium cation compared to the strontium one. The excited Ba+−He PES asymptotically correlating with Ba+(2P) compare

4. RESULTS In the following sections, we describe the structural details and energetics of the stable exciplexes formed between He atoms and M+ in the 2P1/2 or 2P3/2 states. Initially, we would discuss the behavior of the spin−orbit coupled PEC for the M+He 6475

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spin−orbit splitting, and of the spin-averaged interaction curves. In particular, one notices the near-disappearance of the internal potential well in the 2Π1/2 state of Ba+(2P1/2)He, whose depth decreases to 35 cm−1 from the original 487 cm−1 in the 2 Π states. Notice, also, that the well of the 2Π3/2 for Ba+(2P3/2) He remains substantially unmodified compared to the ab initio results. A similar situation is found for Sr+, albeit the lower Δ value reduces the PEC couplings, so that the 2Π1/2 state of Sr+(2P1/2)He maintains a deep well and shows a low entrance barrier. In this respect, the spin−orbit coupled Sr+(2P) curves are akin to the one shown before for heavy alkali metals such as Rb30,31 and for the coinage metal Cu.26 Thus, one is tempted to predict the possible formation of stable exciplexes containing several He atoms when Sr+ is in the 2P1/2 state. Conversely, the narrow and shallow well in the Ba+(2P1/2)He PEC suggests as unlikely the existence of bound species. A similar situation is found when the previously published PEC18 is used (Figure SI2 in the Supporting Information). This conclusion, however, must be carefully checked as there is a second attractive well in the 5 Å ≤ R ≤ 12 Å range (De ∼ 6 cm−1). Turning to the higher states, one would expect to find, at least, M+(2P3/2)He2 species to be stable for both ions10 (the attractive wells are quite deep) and no stable species when the electronic state correlates with the 2Σ1/2 one despite the presence of a very shallow well (De ∼ 6 cm−1 in both cases) at large distances. According to the latter conclusion, we avoid to study aggregates with the cations in their highest excited state. 4.2. Exciplexes Formed with Metal Ions in the Spin− Orbit Coupled 2P1/2 State. Figure 4 shows the evaporation

dimers; this is done to allow one to form an educated guess on the chemical physics of larger systems. Successively, we provide the results of the DMC simulations for M+Hen clusters, basing our discussion on a chosen asymptotic electronic state of the metal ions rather than grouping the results by dopants. This approach has the advantage of stressing similarities and deviations in behavior that depends on differences in the electronic structure due to the atomic number. For convenience, however, any relevance of our findings to available experimental studies will be discussed in the conclusions. Notice, also, that we would focus on studying only cluster sizes that may be of some help in interpreting dynamical or spectroscopic experiments. In other words, we would mainly refer to small systems for which no more than a few He atoms are added to the ones forming the first solvation shell of M+. 4.1. Spin−Orbit Coupled 2P States. Figures 2 and 3 show the behavior of the M+(2P)He PEC after the introduction of

Figure 2. Spin−orbit coupled PEC for the Sr+(2P)He (distances in Å, energies in cm−1). The zero of the energy scale is chosen as the spin− orbit averaged energy of the ion plus the He atom. Dissociation energies De are computed with respect to the asymptotic threshold of each PEC.

Figure 4. He atom evaporation energy for M+(2P1/2)Hen (in cm−1).

energy for a single He atom from already formed M+(2P1/2)Hen; the zero of the energy is defined as the free metal ion in the appropriate spin−orbit coupled state plus the free He atoms resting at infinite distance. Although previous experience by us26 and others28−32 would suggest as likely the formation of exciplexes with a ring-like He distribution around Sr+, any prediction for Ba+ is far from being straightforward due to the coupling between the 2Π and 2Σ states induced by the large spin−orbit splitting. A similar effect has already been highlighted for Ag, whose 2P1/2 state is not able to bind any He atom due to a shallow and narrow interaction well. Albeit a substantial depth reduction and width narrowing of the well

Figure 3. Spin−orbit coupled PEC for the Ba+(2P)He (distances in Å, energies in cm−1). The zero of the energy scale is chosen as the spin− orbit averaged energy of the ion plus the He atom. Dissociation energies De are computed with respect to the asymptotic threshold of each PEC.

the spin−orbit coupling between P states. As one can notice, the shape and quantitative features strongly depends on the cation, and in particularly on the relative magnitude of Δ, the 6476

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appears also for Ba+ upon introducing the spin−orbit coupling, the dimer PEC still presents a well that is more than three times deeper than the Ag case and a non-negligible external well (see Figure 3 and the discussion in section 4.1). 4.2.1. Sr+(2P1/2)Hen. The data in Figure 4 confirm our expectation (vide supra section 4.2), suggesting that Sr+(2P1/2)Hen clusters have all the He atoms interacting in a very similar way with the metal ion. The fluctuations in the evaporation energy, not particularly wide given the energy scale imposed by the well depth in the 2Π1/2 dimer state, seem to follow an “odd−even” alternation, with the odd n clusters presenting a lower evaporation energy. This rule is violated by the n = 6 species; in this case, however, the sixth atom is the last one accepted into the inner shell, and one would thus expect energetic effects due to the compression of the already bound He atoms. We tested this conclusion adding a seventh and eighth atoms, which were found bound by only a few cm−1. To corroborate our analysis based on the energetic data, Figure 5 shows configurations randomly extracted during the

To better appreciate the peculiarities of the Sr+(2P1/2)Hen clusters, we stress that isotropic M−He potentials would be expected to produce either a uniform (apart from the atomic excluded volume) or slightly peaked He−Sr−He angular distribution; given the equilibrium Sr−He distance the peak should be located around a cosine value of 0.38 due to the He− He interaction. Hence, the strong preference shown by Sr+(2P1/2)He2 and Sr+(2P1/2)He3 in locating two He atoms opposite to each other seems to indicate that electronic effects are playing a key role, the details of which are better discussed considering Ba+(2P1/2)He2 (vide inf ra section 4.2.2). 4.2.2. Ba+(2P1/2)Hen. Turning to the clusters formed by Ba+, we begin by noticing that the evaporation energy does not behave smoothly and presents two downward “kinks” at n = 1 and 3. These are in stark contrast with the common expectation of a reasonably smooth change in total energy even during shell closure or opening upon adding He atoms. The results shown for n > 3, instead, are in line with what is discussed above for the strontium cation in the 2P1/2 state, the main difference being the fact that the filling of the first shell seems to happen at n = 7. This is indicated by the sudden drop by 150 cm−1 in evaporation energy. Retrospectively, the sudden drop in evaporation energy seen for Ba+(2P1/2)He3 may recall what already shown for Rb in the 2 P3/2 spin−orbit state;31 in this case, the third and all subsequent He atoms are more weakly bound than the first and the second, and this effect is due to the limited volume available around the diametrically opposite regions where the deep Rb−He interaction wells are present. The remaining He atoms are thus effectively screened by the tightly bound He atoms and allowed to interact only weakly with the metal.26,31 The situation just described is, however, not compatible either with the very low binding energy for Ba+(2P1/2)He shown in Figure 4, which should have an evaporation energy similar to the one of the second He atom,31 or with the fact that the evaporation energy of the second He atom is much larger than the depth of the inner well in Figure 3. The analysis of the distance distribution for Ba+(2P1/2)He and Ba+(2P1/2)He2 also highlights an interesting correlation between the evaporation energy and the Ba−He distance distribution for the two systems. Indeed, Ba+(2P1/2)He shows a very diffuse distribution concentrated in the region of the external well (R = 7 Å, Figure 3), whereas Ba+He2 has both He atoms distributed closer to the cation and inside the inner well (see Figure 6). Turning back to the energetics of Ba+(2P1/2)Hen, one notices that a substantial change in the electronic structure of Ba+ ought to take place upon adding the second He atom for the energy of the trimer to decrease to the level indicated by the data; we attribute such a change to the fact that contributions to the DIM matrix elements involving the 2Π states may be sufficiently negative to reduce the mixing of the states due to the spin−orbit coupling. Supporting this point of view, there is also the nearly linear geometry (with Ba between the two He atoms) found visualizing configurations sampled during DMC simulations (Figure 7) or their He−Ba−He angular distributions. The latter gives a clear indication for a strong preference of the He atoms to sit opposite each other while “sandwiching” the Ba cation. Again, this is at variance with common expectation for a more triangle-like geometry when isotropic potentials are involved, suggesting that the many-body PES presents angular terms connected to the forceful mixing of electronic states due to the spin−orbit coupling.

Figure 5. Sampled configurations during DMC simulations of Sr+(2P1/2)Hen. The number of He atoms is indicated as an inset close to the Sr cation.

DMC simulations for each Sr+(2P1/2)Hen (n = 1−6); from these, it becomes evident the nearly planar disposition of the He atoms around the cation. Also evident, there is the diametrically opposite location of the two He atoms in Sr+(2P1/2)He2 with respect to the cationic center, and that the Sr+(2P1/2)He3 cluster has a T-like shape with neighbor He atoms forming a right He−Sr−He angle. These structures differ from the ones of larger clusters, which show a relative He−He distribution that is compatible with the idea that the He atoms occupy the volume of a torus around the cation and the presence of a weakly attractive He−He interaction. Indeed, the distribution of the cosine for the He−Sr−He angle has a very strong maximum at −1 for both n = 2 and 3, and a secondary shallow peak around 0 for n = 3 (not shown). 6477

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while maintaining the second constrained at a chosen bond length (R1 = 3, 4, 5, 7 Å). Linear He−Ba−He and right angle (with Ba at the center) geometries have been explored, and the results are shown in Figure 8. The results shown indicate that, depending on the geometry and R1, the He atom may experience a potential that is quite close to the dimer one (both geometries when R1 = 7 Å), a substantially repulsive interaction (bent geometry with R1 < 5 Å), or a potential becoming increasingly more attractive and lowering its barrier as R1 (