Structure determination of the tetracene dimer in helium nanodroplets using femtosecond strong-field ionization
Constant Schouder, Adam S. Chatterley, Florent Calvo, Lars Christiansen, Henrik Stapelfeldt
SStructure determination of the tetracene dimer in helium nanodroplets usingfemtosecond strong-field ionization
Constant Schouder, Adam S. Chatterley, Florent Calvo, Lars Christiansen, and Henrik Stapelfeldt Department of Physics and Astronomy, Aarhus University, Denmark Department of Chemistry, Aarhus University, Denmark Universit´e Grenoble Alpes, LIPHY, F-38000 Grenoble, France (Dated: July 9, 2019)
Dimers of tetracene molecules are formed inside helium nanodroplets and identified through covariance analysis ofthe emission directions of kinetic tetracene cations stemming from femtosecond laser-induced Coulomb explosion.Next, the dimers are aligned in either one or three dimensions under field-free conditions by a nonresonant, moder-ately intense laser pulse. The experimental angular covariance maps of the tetracene ions are compared to calculatedcovariance maps for seven different dimer conformations and found to be consistent with four of these. Additionalmeasurements of the alignment-dependent strong-field ionization yield of the dimer narrows the possible conforma-tions down to either a slipped-parallel or parallel-slightly-rotated structure. According to our quantum chemistrycalculations, these are the two most stable gas-phase conformations of the dimer and one of them is favorable forsinglet fission.
I. INTRODUCTION
Noncovalent interactions between aromatic molecules are crucial for many areas, such as molecular recognition, structure ofmacromolecules and organic solar cells.
At the most fundamental level, the interaction involves two aromatic molecules. This hasbeen the subject of a large numbers of studies, often with a particular focus on determining the structure of the dimers. Experimentally,the main technique to form dimers is supersonic expansion of a molecular gas seeded in a carrier gas of rare gas atoms into vacuum.Combining the resulting molecular beams with various types of high-resolution spectroscopy, including microwave, infrared, andUV spectroscopy as well as rotational coherence spectroscopy — a technique based on pairs of femtosecond or picosecondpulses — the rotational constants can be extracted. Upon comparison with results from theoretical modelling, information aboutthe conformations of a range of different dimers have been obtained.
Examples include the dimers of benzene, fluorene, benzonitrile, phenol, and anisole. An alternative experimental method is to form molecular dimers or larger oligomers inside helium nanodroplets.
Thistechnique makes it possible to create aggregates of much larger molecules, for instance of fullerenes and polycyclic aromatichydrocarbons, than what is typically possible in molecular beams from standard supersonic expansions. Furthermore, the va-riety of heterogenous aggregates goes beyond the normal reach of the gas phase. Structure characterization has mainly beenobtained by IR spectroscopy although for complexes of larger molecules this becomes very challenging, as the density of statesis too high to clearly resolve peaks in the spectra.Recently, we introduced an alternative method for structure determination of dimers created inside He droplets, namely Coulombexplosion induced by an intense femtosecond (fs) laser pulse and recording of the emission direction of the fragment ions includingidentification of their angular correlations, implemented through covariance analysis.
Crucial to the structure determinationwas that the dimers had a well-defined spatial orientation prior to the Coulomb explosion event, in practice obtained by laser-inducedalignment with a moderately intense laser pulse.
While the Coulomb explosion method may not match the level of structuralaccuracy possible with high resolution spectroscopy, at least not for comparatively small molecules, it distinguishes itself by the factthat the structure is captured within the time scale of the pulse duration, i.e. in less than 50 fs. As such, this technique holds thepotential for imaging the structure of dimers as they undergo rapid structural change, for example due to excimer formation. Thepurpose of the current manuscript is to show that the Coulomb explosion method can also be used to obtain structure informationabout dimers composed of molecules much larger than the carbon disulfide and carbonyl sulfide molecules studied so far.
Herewe explore the dimer of tetracene (Tc), a polycyclic aromatic hydrocarbon (PAH) composed of four linearly fused benzene rings.We demonstrate that a covariance map analysis of the angular distributions of fragments from fs laser-induced Coulomb explosionsupplemented by measurement of alignment-dependent ion yields allow us to identify the tetracene conformation as a face-to-facestructure with the tetracene monomers either slightly displaced or slightly rotated. This identification relies on comparison of theexperimental covariance maps to simulated covariance maps for a range of plausible conformations.Our motivation for exploring the structure of the dimer is threefold. Firstly, PAHs are know to be relatively abundant in theinterstellar medium, and laboratory experiments are required to deduce the signatures that astronomers will need to hunt for.Secondly, PAH oligomers of similar size such as the pyrene dimer have a possibly key role in the formation of soot, and it isimportant to characterize their structure and bonding with accuracy. Thirdly, noncovalently bonded ensembles of tetracene and otheracenes can undergo singlet fission, a phenomenon with major implications for solar energy harvesting where a singlet excited statedecays into two triplet states localized on two separate monomers. The process produces two excitations from a single photon, whichin principle provides a means to overcome the Shockley-Queisser 33% efficiency limit inherent to single excitation photovoltaicsystems. Typically, singlet fission is studied in crystals and thin films, which are excellent for emulating photovoltaic devices, but due a r X i v : . [ phy s i c s . a t m - c l u s ] J u l to their extended nature are less well suited for investigating the basic photophysical mechanisms, and so fundamental understandingsof singlet fission have somewhat lagged behind technological developments. Solution studies of carefully synthesized covalent dimersystems with only two acene units provide clearer insight into the fundamental dynamics, with the caveat that the covalent linkage mayinterfere with the electronic structure, and solvent and temperature effects blur spectra. Helium nanodroplets allow formation ofthe pristine dimers without the need for an extended system or any covalent bond. Structural determination is essential as the relativeconfiguration of the monomer in a polyacene dimer is crucial for the singlet fission process: the π systems must overlap, but theremust also be a on offset between the two units for singlet fission to be an allowed process. The conformations observed in thepresent work are favorable for singlet fission, paving the way for future time-resolved studies singlet fission processes in controlledenvironments.
II. EXPERIMENTAL SETUP
The experimental setup has been described in detail before and only important aspects are pointed out here. A schematic of thesetup is shown in Fig. 1. A continuous beam of He droplets is formed by expanding He gas through a 5 µ m nozzle, cooled to 12 K,into vacuum. The backing pressure is 25 bar leading to droplets consisting on average of 10 000 He atoms. The droplets then passthrough a pickup cell containing tetracene vapor obtained by resistively heating a sample of solid tetracene. The probability for adroplet to pick up one or two Tc molecules depends on the partial pressure of tetracene in the cell defined by its temperature. Asdiscussed in section IV, this allows us to control the formation of Tc dimers inside the He droplets.Hereafter, the doped He droplet beam enters the target region where it is crossed, at right angles, by two collinear, focused, pulsedlaser beams. The pulses in the first beam are used to induce alignment of the Tc dimers (and monomers) in the He droplets. Theyhave an asymmetric temporal shape rising to a peak in ∼
120 ps and turning-off in ∼
10 ps — see sketch in Fig. 1 and measuredintensity profile in Fig. 5 and Fig. 6 — obtained by spectrally truncating the uncompressed pulses from an amplified Ti:Sapphirelaser system. Their central wavelength is 800 nm, the focal spot size, ω , is 65 µ m, and the peak intensity ∼ .
16 TW / cm . Thepulses in the second beam are used to identify the formation of Tc dimers and measure their alignment. As detailed in section IV, thisrelies on ionization of the Tc dimers. These probe pulses (35 fs long, λ central = 400 nm) are created by second harmonic generationof the compressed output from the Ti:Sapphire laser system in a 50 µ m thick BBO crystal. The focal spot size, ω , is 50 µ m and theintensity is varied from 0.6 to 9 TW / cm . The repetition rate of the laser pulses is 1 kHz.The Tc + ions, created by the probe pulse, are projected by a velocity-map imaging spectrometer onto a 2D imaging detector. Thedetector consists of two microchannel plates backed by a P47 phosphor screen, whose images are recorded on a CCD camera. TheCCD camera is read out every 10 laser shots, i.e. at a 100 Hz rate, and such an image is termed a frame. Ion images as the onesshown in Fig. 3 typically consist of 10 000 frames. III. MOLECULAR MODELLING OF THE TETRACENE DIMER CONFORMATION
The conformations of the tetracene dimer were independently explored by molecular modeling and quantum chemical methods inorder to identify plausible candidates for interpreting the measurements.The potential energy landscape was first explored using a simple quantum mechanical model previously developed to simulatethe sticking between PAH molecules under astrophysical conditions. Briefly, the model consists of an additive potential withintramolecular contributions V intra for each tetracene molecule, and a pairwise force field V inter describing the non-covalent interactionsbetween the two flexible molecules. Here V intra is based on an earlier tight-binding model of Van-Oanh and coworkers while V inter is a simple sum of Lennard-Jones (LJ) and Coulomb terms acting between the atomic positions that also carry partial chargesrepresenting the multipolar distribution. For the LJ potential we employed two parameter sets either from the OPLS library orpublished earlier by van de Waal in the context of hydrocarbon clusters. The partial charges on tetracene were evaluated using thefluctuating charges method, as proposed by Rapacioli and coworkers who adjusted its parameters so that it mimics the RESPprocedure often used to extract charges from DFT calculations. The charges obtained for the tetracene monomer are shown in Fig. 2.Our initial scanning procedure consisted of a large amplitude Monte Carlo exploration of the possible conformations of the dimer,followed by systematic local optimization using this flexible potential. The optimized geometries were then refined directly withquantum chemical methods, employing here again DFT with functionals that account for long-range (noncovalent) forces that areessential for the present system. The two functionals B97-1 and wB97xD were thus employed with the two basis sets 6-311G(d,p) andTZVP. Basis set superposition errors were accounted for using the standard counterpoise method, and from the equilibrium geometriesthe harmonic zero-point energies were also evaluated. All quantum chemical calculations were performed using Gaussian09. Our exploration lead to only two locally stable conformations, with the two molecular planes parallel to each other, the main axesof the molecules being themselves either parallel as well or forming an angle of about 25 ◦ . In the former case, the molecules are notsuperimposed on each other but shifted in order to maximize van der Waals interactions (as in graphite). Consistently with standardterminology, the resulting conformations, numbered as 1 and 2 in Fig. 4, are referred to as parallel displaced or rotated, respectively.The other conformations shown in Fig. 4, numbered 3–7, are not locally stable with any of the methods used and relax into either ofthe two parallel conformers. Figure 1. Schematic of the key elements in the experiment. Tc dimers are first formed inside He droplets, then aligned by a truncated nonresonantalignment laser pulse (red). 10 ps after truncation of the alignment pulse, the Tc dimers are doubly ionized by a short intense probe pulse (blue) toinduce Coulomb explosion and the velocities of the two Tc + ions are measured using velocity map imaging. In all measurements the probe pulsewas linearly polarized along the X axis (perpendicular to the detector plane) whereas the alignment pulse was either linearly polarized along the Xaxis or the Y axis (depicted here), or elliptically polarized with the major polarization along the X axis or the Y axis. The relative energies of the two conformers are compared in Table I, and the binding energy of the most stable one is provided aswell. From this table we find a significant spreading in the values of the binding energy, which roughly varies from 200 meV for theB97-1 DFT method to 800 meV for the wB97xD method, the empirical models yielding values of about 500 meV in between thesetwo extremes. However, the energy difference between the conformers appears as a fraction of the absolute binding energy whateverthe level of calculation. From the perspective of the quantum force field, the two conformers are nearly isoenergetic, with the paralleldisplaced isomer being higher by less than 10 meV. The DFT results generally predict the same ordering, but with a slightly higherdifference closer to 20–30 meV depending on whether zero-point correction is included or not, still quite small. Only the B97-1functional with the TZVP basis set finds otherwise that the rotated conformer should not be the most stable of the two. At this stage,we cautiously conclude that two particular conformations for the tetracene dimer are candidates for experimental elucidation, bothhaving the molecules parallel to each other but some shift or rotation between their main symmetry axes. q = +0 :
09 (+0 : q = (cid:0) :
24 ( (cid:0) : q = +0 :
08 (+0 : q = (cid:0) :
17 ( (cid:0) : q = (cid:0) :
09 ( (cid:0) : q a = +0 :
15 (+0 : q b = +0 :
13 (+0 : q c = +0 :
11 (+0 : Figure 2. Partial charges on carbon and hydrogen atoms on the tetracene monomer neutral and cation in brackets, as used in the force fieldexploration of dimer conformations and in the simulations. All charges are expressed in units of the electron charge.Method Parallel displaced RotatedTB+LJ (vdW) +4.9 (+6.5)
TB+LJ (OPLS) +6.8 (+8.1)
B97-1/6-311G(d,p) +3.3 (+4.6)
B97-1/TZVP +36.5 (+25.6)wB97xD/6-311G(d,p) +26.6 (+28.1) wB97xD/TZVP +19.9 (+16.7)
Table I. Binding energies and relative energies of the parallel displaced and rotated conformers of the tetracene dimer, as obtained from a simplequantum mechanical force field (TB+LJ) with two sets of LJ parameters, or from density-functional theory minimizations with two functionals andtwo basis sets and after correcting for basis set superposition error. Absolute numbers (also in bold face) are the binding energies obtained for themost stable conformer, numbers with a plus sign indicate the relative difference of the less stable conformer. The values in parentheses include theharmonic zero-point energy corrections. All values are given in meV.
IV. RESULTS: COULOMB EXPLOSIONA. Identification of tetracene dimers
First, we show that it is possible to form and detect Tc dimers in the He droplets. The strategy is the same as that recently appliedto identify CS and OCS dimers and relies on detecting kinetic Tc + ions as a sign of dimers. In detail, if a droplet containsjust one Tc molecule and this molecule is ionized by the probe pulse, the resulting Tc + ion will have almost zero kinetic energy.By contrast, if a droplet contains a dimer and both of its monomers are singly ionized, the internal Coulomb repulsion of the Tc + ions will cause them to gain kinetic energy. Figure 3 (a ) shows a Tc + ion image recorded with the probe pulse only. The ions arelocalized in the very center of the image with more than 98 percent of them having a velocity less than 250 m / s. These low-velocityions are ascribed as originating from the ionization of single-doped tetracene molecules. The ionization potential of tetracene is 6.97eV and the photon energy of the probe photons is 3.1 eV. Thus, we believe that ionization is the result of 3-photon absorption by thetetracene molecules.Figure 3(a ) also shows a Tc + ion image recorded with the probe pulse only but for a higher partial pressure of the tetracene gasin the pickup cell. The image is still dominated by an intense signal in the center but now ions are also being detected at larger radiicorresponding to higher velocities. This can be highlighted by cutting the center in the image. The images in Fig. 3(b ) and (b ) arethe same as the images in Fig. 3(a ) and (a ), respectively, but with a central cut removing contributions of Tc + ions with a velocitylower than 250 m / s. It is now clear that the image in Fig. 3(b ) contains a significant amount of ions away from the central part. Weassign the high-velocity ions to ionization of both Tc molecules in droplets doped with a dimer.To substantiate this assignment, we determined if there are correlations between the emission directions of Tc + ions, implementedthrough covariance analysis. Let X ( i ) be the discrete random variable that denotes the number of ions detected at an angle θ i withrespect to the vertical center line, see Fig. 3 (b ). Experimentally, the detected ions are binned into M equal-size intervals over the360 ◦ range and thus the angular distribution of the ions can be represented by the vector: X = { X ( ) , X ( ) , ... X ( M ) } . (1)As mentioned in section II the resulting ion images are averaged over a large number, N , of individual frames. In practice, the angular R (b )(b ) (c )(c ) v z [m/s] v y [ m / s ] θ [deg] θ [ deg ] Colormap [arb units]0 1
Ion image Covariance θ i (a ) v z [m/s] ) Figure 3. (a ) Tc + ion image recorded for a low partial pressure of tetracene in the pickup cell (monomer doping condition); (a2) Tc + ion imagerecorded for a higher partial pressure of tetracene in the pickup cell (dimer-doping condition); (b1)-(b2) Same image as (a1) and (a2) but with thecenter removed; (c1)-(c2) Corresponding angular covariance maps created from ions count outside the white circles. The ion images are obtainedwith without alignment, with the probe pulse at an intensity of 3 TW / cm distribution is therefore given by the expectation value of X : (cid:104) X (cid:105) = { N N ∑ n = x ( ) n , N N ∑ n = x ( ) n , ..., N N ∑ n = x ( M ) n } (2)where x ( i ) n is the outcome (number of ions) of the random variable X ( i ) n related to the angle θ i for the n th frame acquired. Thecovariance can now be calculated by the standard expression:Cov ( X , X ) = (cid:104) XX (cid:105) − (cid:104) X (cid:105)(cid:104) X (cid:105) . (3)using the ions in the radial range outside of the annotated white circle. The result, displayed in Fig. 3(c ), is referred to as the angularcovariance map. We used an angular bin size of 4 degrees which gives M =
90. The covariance map reveals two distinct diagonallines centered at θ = θ ± ◦ . These lines show that the emission direction of a Tc + ion is correlated with the emission directionof another Tc + ion departing in the opposite direction. This strongly indicates that the ions originate from ionization of both Tcmolecules in dimer-containing droplets and subsequent fragmentation into a pair of Tc + ions. Therefore, we interpret the angularpositions of the Tc + ion hits outside the white circle as a measure of the (projected) emission directions of the Tc + ions from dimers.Note that the angular covariance signal extends uniformly over 360 ◦ . This shows that the axis connecting the two Tc monomers israndomly oriented at least in the plane defined by the detector. This is to be expected in the absence of an alignment pulse. Also notethat at the low partial pressure of tetracene, used for the image in Fig. 3 (a ), the pronounced lines in the angular covariance map areno longer present, see Fig. 3 (c ), indicating that there are essentially no dimers under these pickup conditions. B. Angular covariance maps for aligned tetracene dimers
Next, we carried out experiments aiming at determining the conformation of the Tc dimers. In the first set of measurements,described in this section, the dimers are aligned then double ionized with the probe pulse, and the emission direction of the Tc + ionsis recorded. We then calculated their angular covariance maps, which were proven to provide useful information about the dimerconformation in the cases of CS and OCS dimers. Based on recent findings for similar-size molecular systems, we expect that the strongest degree of alignment occurs around thepeak of the alignment pulse and that, upon truncation of the pulse, the degree of alignment lingers for 10–20 ps, thereby creating atime window where the alignment is sharp and the alignment pulse intensity reduced by several orders of magnitude. It is crucialto synchronize the probe pulse to this window because Tc + ions are fragmented when created in the presence of the alignment pulse.The time-dependent measurements of the Tc + yields, presented in section IV D, shows this effect explicitly. Consequently, the probepulse is sent 10 ps after the peak of the alignment pulse as sketched in Fig. 1. In the previous experiments on CS and OCS dimers,the probe pulse was sent at the peak of the alignment pulse, and no truncation was needed, because CS +2 and OCS + ions can bothsurvive the alignment field.The experimental results, recorded for different polarization states of the alignment pulse, are presented in the second column ofFig. 4. The partial pressure of tetracene vapor was set to the same value as that used for the data in row (2) in Fig. 3, i.e. underdoping conditions where a significant number of the He droplets contain dimers. The Tc + ion images are not shown, only the angularcovariance maps created from the ions in the corresponding images originating from ionization of the dimers. In practice, these arethe ions detected outside of a circle with the same diameter as the one shown in Fig. 3 (a ). The intensity of the probe pulse was again3 TW / cm for all the angular covariance maps shown in Fig. 4The different rows in Fig. 4 are the results of different polarization states of the alignment pulse and thus different spatial alignmentsof the dimers. In row (a), the alignment pulse was linearly polarized perpendicular to the detector plane, i.e. along the X axis —see Fig. 1. This induces 1D alignment with the most polarizable axis of the Tc dimer confined along the X axis. The covariancemap [Fig. 4(a e )] contains two prominent stripes, centered at θ = θ ± ◦ , very similar to those observed with the probe pulseonly [Fig. 3 (b2)]. This implies that the axis connecting the two Tc monomers is randomly oriented perpendicular to the X axis.Figure 4(b e ) is also obtained for 1D aligned dimers but now the most polarizable axis, defined by the polarization direction of thealignment pulse, is confined along the Y axis, i.e. in the detector plane. It is seen that the covariance signal no longer extends overall angles but rather appears as two islands centered at (90 ◦ ,270 ◦ ) and (270 ◦ ,90 ◦ ), respectively. Panels (c e ) and (d e ) of Fig. 4 wererecorded with an elliptically polarized alignment pulse with an intensity ratio of 3:1 in order to induce 3D alignment where themost polarizable axis of the dimer is confined along the major polarization axis (parallel to the X axis in panel c and to the Y axis inpanel d) and the second most polarizable axis along the minor polarization axis (parallel to the Y axis in panel c and to the X axis inpanel d). The covariance maps also show islands localized around (90 ◦ ,270 ◦ ) and (270 ◦ ,90 ◦ ). Finally, the dimers were aligned with acircularly polarized alignment pulse, which confines the plane of the dimer to the polarization (X,Y) plane, but leaves it free to rotatewithin this plane. Again, the covariance signals are two islands localized around (90 ◦ ,270 ◦ ) and (270 ◦ ,90 ◦ ). C. Comparison of experimental covariance maps to simulated covariance maps
To identify possible conformations of the dimer that can produce the covariance maps observed, we simulated covariance maps forseven archetypal dimer conformations shown at the top of Fig. 4. The first two conformers are those predicted by our computationalmodeling to be stable in the gas phase, with the tetracene monomers parallel to each other and either parallel displaced (conformation1) or slightly rotated (conformation 2). The other five conformations were chosen as representative examples of other possiblegeometries. Although the computational modelling does not predict them to be stable in the gas phase they may get trapped inshallow local energy minima in the presence of the cold He environment as previously observed for e.g. the HCN trimers and higheroligomers.
The strategy we applied to simulate the covariance map for each of the dimer conformations is the following: (1) Determine thealignment distribution, either 1D or 3D, of the dimer; (2) Calculate the laboratory-frame emission angles of the Tc + ions for eachdimer conformation assuming Coulomb repulsion between two singly charged monomers using partial charges on each atomic center;(3) Determine the angular distribution in the detector plane, X ; (4) Calculate the covariance map, Cov( X , X ) which can be comparedto experimental findings. The details of each of the four steps of the strategy is outlined in the appendix.Starting with the alignment pulse linearly polarized along the X axis [row (a)], all proposed conformers are found to producestripes centered at θ = θ ± ◦ . This is the same as in the experimental covariance map, making these covariance maps unableto distinguish between the proposed dimer structures. The second case is where the alignment pulse is linearly polarized along theY axis [row (b)]. All conformations, except number 3 and 6, lead to covariance islands localized around (90 ◦ ,270 ◦ ) and (270 ◦ ,90 ◦ )as in the experimental data. In contrast, conformations 3 and 6 lead to covariance islands localized around (0 ◦ , 180 ◦ ) and (180 ◦ ,0 ◦ ).Such covariance maps are inconsistent with the experimental observations and, therefore, conformations 3 and 6 can be discounted.To understand the covariance maps resulting from conformations 3 and 6, we note that their main polarizability components are α yy > α xx > α zz ) (see Table II). The linearly polarized alignment field will lead to alignment of the molecular y axis along thepolarization axis (the Y axis). Upon Coulomb explosion, the two Tc + ions will thus both be ejected along the polarization axis of the Figure 4. Covariance maps obtained for the Tc dimer. Indices a, b, c, d, e refer to the alignment laser pulse polarization used as linear perpendicular,linear parallel, elliptical perpendicular, elliptical parallel, and circular, respectively, as shown in the first column with index p (the laboratory axes areillustrated at the top ). Perpendicular and parallel refer to the angle between the main polarization axis and the plane of the detector. Index e (secondcolumn from the left) refers to the covariance maps obtained in the experiments, while indices 1–7 refer to different candidate conformations of thetetracene dimer depicted on top of the corresponding column. Each panel axis ranges linearly from 0 to 360 ◦ . alignment pulse, i.e. along 0 ◦ and 180 ◦ .In row (c), the alignment pulse is elliptically polarized with the major (minor) polarization axis parallel to the X axis (Y axis).The covariance maps for conformations 1, 2, 4 and 5 show islands at (90 ◦ ,270 ◦ ) and (270 ◦ ,90 ◦ ) similar to the experimental data inFig. 4(c e ). In contrast, the covariance map for conformation 7 contains two islands centered at (0 ◦ ,180 ◦ ) and (180 ◦ ,0 ◦ ) and therefore,we discard this conformation among the candidates for the experimental observations. The polarizability components of conformation7 are α xx > α zz > α yy . The elliptically polarized field will align the x axis along the X axis and the z axis along the Y axis. FollowingCoulomb explosion the two Tc + ions will thus both be ejected along the minor polarization axis (the Y axis).In row (d), the alignment pulse is elliptically polarized but now with the major (minor) polarization axis parallel to the Y axis(X axis). Again, the covariance maps for conformations 1, 2, 4 and 5 show islands at (90 ◦ , 270 ◦ ) and (270 ◦ , 90 ◦ ) similar to theexperimental data in Fig. 4(d e ). In contrast, the covariance islands for conformations 3, 6 and 7 differ from the experimental results.Since these three conformations have already been eliminated, the covariance maps in row (d) do not narrow further the possiblecandidates for the dimer conformation(s).In row (e) the alignment pulse is circularly polarized. Once again, the covariance maps for conformations 1, 2, 4 and 5 show islandsat (90 ◦ ,270 ◦ ) and (270 ◦ ,90 ◦ ) similar to the experimental data in Fig. 4(d e ). Thus, the covariance maps resulting from moleculesaligned with the circularly polarized pulse do not allow us to eliminate additional conformations of the tetracene dimer. At this point,we are left with conformations 1, 2, 4, and 5, which all present covariance maps consistent with the experimental data.In the case of the OCS and CS dimers, an additional experimental observable, besides the parent ions, was available for furtherstructure determination, namely the S + ion resulting from Coulomb fragmentation of the molecular monomers. Fragmentation ofTc will result in H + or hydrocarbon fragments. Both H + and hydrocarbon fragment ions can originate from different parts of the Tcmolecule and thus their angular distributions may be less useful for extracting further structural information of the dimer than whatwas the case for the S + ions in the previous studies of OCS and CS . Instead, we performed an alternative type of measurements byrecording the alignment-dependent ionization yield of the Tc dimer. As described in the next section, such measurements allow us todiscount further conformations. D. Ionization anisotropy
Previous works, experimentally as well as theoretically, have shown that the rate of ionization of molecules induced by intenselinearly polarized laser pulses depends strongly on the alignment of the molecules with respect to the polarization direction of thepulse.
In this section, we use the alignment-dependent ionization rate of the tetracene dimers to infer further information abouttheir possible conformation. The starting point is to characterize the alignment-dependent yield of Tc + ions produced when thetetracene monomers are ionized by the probe pulse. In practice, this involves using the monomer doping condition, similar to thatused for the data presented in Fig. 3, row (a), and, furthermore, analyzing only the low kinetic energy Tc + ions stemming primarilyfrom ionization of monomers. The measurements were performed with the alignment pulse linearly polarized either parallel orperpendicular to the probe pulse polarization and as a function of the delay between the two pulses.The results obtained for five different intensities of the probe pulse, I probe are shown in Fig. 5. In all five panels, the Tc + signalis very low, almost zero, when the ionization occurs while the alignment pulse is still on. The reason is that the Tc + ions producedcan resonantly absorb one or several photons from the alignment pulse, which will lead to fragmentation, i.e. destruction of intacttetracene parent ions. Previously, similar observations were reported for other molecules. To study the alignment-dependentionization yield, using Tc + ions as a meaningful observable, it is therefore necessary to conduct measurement after the alignmentfield is turned off. At t =
10 ps, the intensity of the alignment pulse is reduced to 0 .
5% of its peak value. This is sufficiently weak toavoid the destruction of the Tc + ions and, crucially, at this time the degree of alignment is still expected to be almost as strong as at thepeak of the alignment pulse. The red and blue data points show that for I probe = 0 . / cm , the ionization yield is a factor of ∼ At longer times, the Tc + signal for the parallel geometry decreases , reaches a local minimum around t =
70 ps and then increasesslightly again, while the perpendicular geometry shows a mirrored behavior. This behavior is a consequence of the time-dependentdegree of alignment induced when the alignment pulse is truncated. Finally, panels (b)-(e) of Fig. 5 show that the contrast betweenthe Tc + yield in the parallel and the perpendicular geometries at t =
10 ps decreases as I probe is increased. We believe this resultsfrom saturation of the ionization process.Next, similar measurements were conducted for the tetracene dimer by using the dimer doping condition, i.e. as for the datapresented in Fig. 3 row (b), and analyzing only the high kinetic energy Tc + ions stemming from ionization of dimers. The intensityof the probe pulse was set to 3 TW / cm rather than 0 . / cm , in order to obtain a sufficient probability for ionizing both Tcmonomers in the dimers. Panel (a) shows the result for 1D aligned monomers. The time dependence of Tc + ion yield is very similarto that recorded for the Tc monomer at the same probe intensity, Fig. 5(c), for both the parallel and the perpendicular polarizationgeometries. In fact, the ratio of the Tc + ion yield in the parallel and the perpendicular geometries at t =
10 ps is ∼ ∼ E. Discussion
The comparison of the experimental covariance maps to the calculated maps leaves us with conformations 1 and 2, the two lowest-energy structures predicted by our gas-phase calculations. We note that the rotated conformers obtained by DFT minimizationmay also possess an offset, where the two centers of charge do not lie on a common axis perpendicular to the molecular planes.Calculations yield offsets between the charge centers ranging between 0.9 and 1.3 ˚A depending on the method, conformers optimizedwith the quantum force field being almost symmetric with values below 0.01 ˚A. For comparison, the offset in the parallel displacedconformer is closer to 2 ˚A. The rotated conformers predicted here are thus also partly shifted. For the application of measuring singletfission effects, this offset is essential, as perfect stacking of chromophores leads to a cancellation of the interactions singlet fissionrelies on.
These results thus suggest that helium nanodroplets may be a fruitful route to exploring singlet fission processes.The quantum chemistry calculations were carried out for isolated tetracene dimers. Although the interaction with helium wasexpected to be negligible in rationalizing the conformations of the tetracene dimer, it may still influence the dynamical formationwhen the two tetracene molecules are picked up in the droplet. The helium solvent is known to be attracted more strongly to thehydrocarbon and somewhat freeze at its contact, possibly resulting in snowball precursors. Such effects may even be magnified inthe presence of multiple molecules and it is possible that commensurate conformers such as the parallel displaced structure mostlyidentified in our experiment may be kinetically favored once embedded in helium droplets.As discussed in section IV C, comparison of the experimental angular covariance maps for Tc + to the calculated maps do not allowus to distinguish between the rotated-parallel and slipped-parallel conformations — and this would also be the case for the slipped- Figure 5. Time-dependent yield of Tc + ions originating from ionization of 1D aligned tetracene molecules at different probe laser pulse intensitieswritten in bold inside each panel, with the linearly polarized probe pulse parallel (red) or perpendicular (blue) to the alignment pulse polarization.In each panel the shaded area represents the intensity profile of the alignment pulse obtained by cross-correlation with the probe laser pulse. In eachpanel the Tc + ion yield has been normalized to the mean of the yields obtained in the parallel and the perpendicular geometries at times longer than55 ps. Figure 6. Time-dependent yield of Tc + ions originating from ionization of (a) 1D aligned tetracene dimers; (b) 3D aligned tetracene dimers. Themeaning of the perpendicular and parallel curves and the shaded areas is the same as in Fig. 5. In both panels the Tc + ion yield has been normalizedto the mean of the yields obtained in the parallel and the perpendicular geometries at times longer than 55 ps. and-rotated-parallel conformation. However, if an atom, like F, was substituted for one of the hydrogens in each Tc molecule, thendistinction between the conformations might become feasible by observing the relative angle between the emission of F + ions fromthe two monomers. Previous experiments on halogen-atom substituted biphenyls in the gas phase have shown that angular covariancemaps, generated from recoiling halogen ions following Coulomb explosion, are well suited for determination of bond angles anddihedral angles. We believe transfer of this methodology to dimers of halogenated PAHs embedded in He droplets is feasible andpromising for structure determination, including time-resolved measurements.
V. CONCLUSIONS
The purpose of this study was to obtain information about the conformation of tetracene dimers in a combined experimental andtheoretical study. Experimentally, tetracene dimers were formed inside He nanodroplets. A strong femtosecond probe laser pulsewas used to ionize both Tc molecules in the dimer, leading to a pair of recoiling Tc + cations resulting from their internal Coulombrepulsion. These kinetic Tc + ions provided an experimental observable uniquely sensitive to droplets doped with dimers. Next,a slow turn-on, fast turn-off, moderately intense laser was used to create a window of field-free alignment shortly after the pulse.Synchronizing the probe pulse to this window, the dimers, aligned either 1-dimensionally or 3-dimensionally, were Coulomb explodedand the covariance map of the emission directions of the Tc + recoil ions determined. As a reference, angular covariance maps werecalculated for seven different conformations including the two predicted to be the most stable by our quantum chemistry calculationsand another five chosen as representative examples of other possible geometries. The experimental angular covariance maps werefound to be consistent with four of the calculated maps. An additional dimer structure sensitive measurement was conducted, namelyhow the yield of strong-field ionization depends on the polarization axis of the probe pulse with respect to the alignment of the dimer.It was found that the ionization yield is a factor of five times higher when the probe pulse polarization was parallel compared toperpendicular to the most polarizable axis of the dimer. This result is only consistent with the two tetracene molecules in the dimerbeing parallel to each other and either slightly displaced or slightly rotated. These are the two most stable gas-phase conformationsof the dimer according to our quantum chemistry calculations. ACKNOWLEDGMENTS
We acknowledge support from the following three funding sources: The European Union’s Horizon 2020 research and innovationprogramme under the Marie Sklodowska-Curie grant agreement No 674960. A Villum Experiment Grant (no. 23177) from The1Villum Foundation. The European Research Council-AdG (Project No. 320459, DropletControl). We thank Frank Jensen fortheoretical support.
APPENDICESSimulation procedure
The identification of dimer conformations from the covariance maps relies on comparison with simulated maps predicted fordifferent candidate structures. The individual tetracene monomers are expected to be rigid and the problem amounts to finding therelative orientations between the two molecules and the possible shift between their centers of mass.For each conformation considered, covariance maps were generated by extracting the projection of the separation distance ( | (cid:126) r diff | )between the center of mass of each tetracene molecule on the detector plane for different polarizations of the alignment laser pulse.The separation distance indicates the direction of recoil that the two Tc + should follow by repelling each other. This section detailsthe overall procedure. Conformations
One important ingredient in explaining the observed covariance maps is the polarizability tensor of the tetracene dimer, which isresponsible for its interaction with the laser pulses and is determined by its structure.The polarizability of the tetracene monomer was calculated with a density functional theory method (wB97xD) using the diffusebasis set aug-pcseg-n, after a geometry optimization with a similar method but a more localized basis set pcseg-n. These calcu-lations performed with the Gaussian09 software package yielded the polarizability components as α xx = . , α yy = . , α zz = . , where x , y , z refer to the major, minor and orthogonal axis of tetracene, respectively.The polarizability tensor of the dimer is sometimes assumed to be the sum of the polarizability tensor of each molecule. However,this approximation usually underestimates the interaction polarizability along the axis connecting the molecules, while overestimatingpolarizability perpendicular to it. Simulations carried out for urea (CH N O) and fullerenes reported an increase of the polarizabilitycomponent along the dimer axes by 9.9% and 17.8%, respectively, while the other components displayed a decrease by a few percentsonly. In our case, the anisotropy in the polarizability tensor of tetracene could be considered as sufficiently large that we can neglectthese effects and assume the polarizability of the dimer to be a linear sum, although some caution should be taken with some of theconformations presented below. To ascertain this ambiguity, we calculated the exact polarizability for each conformation shown inTable II using a fixed geometry and a similar method and basis as the one mentioned for the monomer. We see that using the exactpolarizabilities breaks the symmetry that some of the dimers would posses if only the sum of their polarizabilities were considered.We thus only use the exact polarizabilities for the simulations presented above.
Laser-induced alignment
After the diagonalization of the polarizability tensors obtained for each conformation, it is possible to calculate the potential energysurface when an electric field is applied. The potential can be evaluated using second-order perturbation theory and is defined as: V = − (cid:126) E T ααα dimer (cid:126) E = − (cid:126) µ T ind · (cid:126) E , (4)where the superscript T stands for transpose, ααα dimer is the polarizability tensor of the conformer, (cid:126) µ ind is the induced dipole momentand (cid:126) E the electric field applied on the system.In our case, the electric field comes from a strong non-resonant laser pulse, and can be expressed as: (cid:126) E laser = E √ + ε cos ω t ± ε sin ω t . (5)In this equation, E is the peak amplitude of the electric field that we can extract from the experiment by measuring the intensity ofthe laser pulse, ε is the ellipticity parameter which ranges from 0 (linear polarization) to 1 (circular polarization), and ω is the laserfrequency.Usually, the Schrdinger equation is then solved and the distribution of rotational states that will be populated in the presence of theelectric field is calculated to extract the overall angular distribution of the complex. However, in our approach we drastically simplifythe problem by making use of the adiabaticity of the alignment process, which will result in an angular confinement of the complex2 Conformation (Polarizability tensorsApproximate Exact1 . . . . − . . − . . . . . . . . . . − . . − . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Table II. Table listing polarizability tensors for each conformer presented in Fig. 4. The polarizability components are expressed in ˚ A and are listedin the (x,y,z) order. The ”Approximate” column comes from the summation of the polarizability tensor of each monomer. The ”Exact” columncontains values resulting from DFT calculations. The results presented in Fig. 4 used the exact values. at the bottom of the potential well presented in Eq.(4). The non-perfect alignment is accounted for by addition of a spread in theangular distribution.To connect the (cid:126) E laser in Eq.(5) to the electric field (cid:126) E used in Eq.(4), we need both (cid:126) E laser and ααα dimer to be expressed in the sameframe. In our case, we decided to make use of the diagonal form of the polarizability tensor in the molecular frame (MF) and tocalculate the potential surface in this frame. For this purpose, we used a uniform distribution for all the possible directions of the (cid:126) E laser in the MF. A uniform sphere made of 10 000 directions vectors was created to represent the main axis of the polarization ellipse. Thiswould be sufficient for a linearly polarized pulse but not for an elliptically polarized pulse, where the minor axis has to be included.In this case, for each major axis orientation 1000 angular steps of the minor axis were used.To make the procedure explicit and to give a more intuitive form for the interaction potential, we develop the expression using ageneral form for (cid:126) E laser in the molecular frame: (cid:126) E laser = E √ + ε a x cos ω t + b x ε sin ω ta y cos ω t + b y ε sin ω ta z cos ω t + b z ε sin ω t . (6)where a i and b i are coefficients fulfilling the conditions: ∑ a i = ∑ b i = ∑ a i b i = (cid:126) E laser and will be the sum of trigonometricfunctions with the angles related to the applied rotations. Implementing this expression in Eq.(4) and developing it using the longduration of the pulse compared to the optical frequency, we obtain: (cid:104) V (cid:105) T = − E ( + ε ) ∑ i = x , y , z (cid:0) a i + b i ε (cid:1) α ii (9)This shape is interesting since only square quantities appear in the summation. To develop the expression a bit further, some as-sumptions are needed about the shape of the polarizability tensor. Assuming that two of its components are larger than the last one( α xx , α yy (cid:29) α zz ), the minimum of the potential will be found if one tries to maximize the coefficient a x , y and b x , y which will naturallylead to put a z = b z = a x a y a z = cos φ − sin φ , b x b y b z = sin φ cos φ (10)3thus giving (cid:104) V (cid:105) T = − E (cid:20) ( α xx + α yy ) + ( α xx − α yy ) − ε + ε cos 2 φ (cid:21) . In the extreme case of ε = V is achieved when φ = [ π ] if α xx > α yy or φ = π / [ π ] if α yy > α xx .With ε = α xx = α yy , the dependence in φ disappears, leaving an isotropic distribution in the plane (all φ areallowed). Frames connection
Picking the orientation of the electric field that gives the lowest potential energy, the minima are chosen using a spread ( ∆ E lim )based on the temperature of the dimers inside the helium droplets (0 .
37 K). The energy spread ∆ E lim is chosen to include 99% of theBoltzmann populations, which gives ∆ E lim = .
15 meV. Only energies fulfilling E < E min + ∆ E lim are selected, with E min being thelowest possible value in the potential energy surface.For each orientation found above, a rotation matrix connecting the initial frame (IF) to the laboratory frame (LF) can be defined,labeled RRR
IFtoLF . This matrix is generated by combining two rotation matrices, the first one connects the IF where the dimer has beendescribed to the MF where its polarizability tensor is diagonal, the second one is generated by finding the rotation needed to projectthe orientation of the electric field (both major and minor axes) in the LF where it should be fixed as in the experiment. These tworotations applied on the IF allow us to express the inter-dimer distance in the LF.
Projection
The direction of the repulsion vector is calculated from the resulting Coulombic force: (cid:126) F C = ∑ i ∑ j q i q j (cid:126) r i − (cid:126) r j | (cid:126) r i − (cid:126) r j | (11)where q i and q j are the partial charges on each atom (shown in Fig. 2), (cid:126) r i and (cid:126) r j are their respective positions and the summationis carried out to consider all pairs combination between the two molecules. Its direction in the laboratory frame is given from thevector (cid:126) F LFC = RRR
IFtoLF (cid:126) F IFCoulomb . Since multiple solutions are possible, a random selection over 100 000 molecules, using a Boltzmannweight, was used to choose which
RRR
IFtoLF to apply to (cid:126) F IFC . To take into account imperfect alignment, the direction vector of (cid:126) F LFC wasthen rotated using a conical distribution described by a polar angle ψ picked from a Gaussian distribution with standard deviation σ ψ = π /
6. This corresponds to an alignment distribution of (cid:126) F IFC characterized by (cid:104) cos ψ (cid:105) = . (cid:126) F C is then projected onto the detector plane leading to two solutions, referring to the detector plane being parallel to themain axis of the polarization or perpendicular to it. This is represented in Fig. 1 with the main polarization axis of the alignment pulsebeing similar to the Y axis and the minor axis to the X axis, or the main axis to the X axis and the minor to the Y axis, respectively.For each solution, an angle θ is extracted by projecting it onto the polarization axis parallel to the detector plane. A maximalvelocity can be estimated from the magnitude of the separation vector ( | (cid:126) F C | based on the resulting Coulomb repulsion between thepartial charges: V Coulomb = ∑ i ∑ j q i q j | (cid:126) r i − (cid:126) r j | = K = mv → | (cid:126) v max | = (cid:114) mV Coulomb , (12)with K the kinetic energy, m the mass of the molecule and v max is the maximum velocity that the system can acquire upon Coulombrepulsion. The Coulomb potential has been divided by two to take into account the symmetric behavior of the two molecules duringCoulomb explosion. The initial distance between the molecules will depend on the conformations considered. A minimal distanceof 3 . ∼ v , and values below v lim are excluded. In our case, v lim = .
25 mm / µ s as estimated from simulations with SIMION giving the expected velocities as a function of the spectrometerradius.4 Covariance
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