THE JOURNAL OF CHEMICAL PHYSICS 135, 044319 (2011)

Structural dynamics and energy flow in Rydberg-excited clusters of N,N-dimethylisopropylamine Sanghamitra Deb, Michael P. Minitti,a) and Peter M. Weberb) Department of Chemistry, Brown University, Providence, Rhode Island 02912, USA (Received 14 April 2011; accepted 13 June 2011; published online 29 July 2011)

In molecular beams, the tertiary amine N,N-dimethylisopropyl amine can form molecular clusters that are evident in photoelectron and mass spectra obtained upon resonant multiphoton ionization via the 3p and 3s Rydberg states. By delaying the ionization pulse from the excitation pulse we follow, in time, the ultrafast energy relaxation dynamics of the 3p to 3s internal conversion and the ensuing cluster evaporation, proton transfer, and structural dynamics. While evaporation of the cluster occurs in the 3s Rydberg state, proton transfer dominates on the ion surface. The mass-spectrum shows protonated species that arise from a proton transfer from the alpha-carbon of the neutral parent molecule to the N-atom of its ionized partner in the dimer. DFT calculations support the proton transfer mechanism between tightly bonded cluster components. The photoelectron spectrum shows broad peaks, ascribed to molecular clusters, which have an instantaneous shift of about 0.5 eV toward lower binding energies. That shift is attributed to the charge redistribution associated with the induced dipoles in surrounding cluster molecules. A time-dependent shift that decreases the Rydberg electron binding energy by a further 0.4 eV arises from the structural reorganization of the cluster solvent molecules as they react to the sudden creation of a charge. © 2011 American Institute of Physics. [doi:10.1063/1.3609110]

I. INTRODUCTION the cluster dynamics of species excited to molecular valence states. Molecular clusters, loosely bound aggregates of In our recent work we have found that Rydberg levels molecules that are bound by van der Waals or electric are intriguingly capable reporters of the structure of isolated multipole interactions, are intriguing intermediates between molecules.18, 19 The Rydberg electron, orbiting a positively the isolated molecules of the gas phase and the densely charged ion core at a large distance, probes the molecular packed systems of condensed phases.1–4 Frequently observed structure because part of its wave function penetrates the ion in the cold environments of molecular beams,5, 6 the study core. This leads to structure-specific phase shifts in the wave of clusters sheds light on the molecular basis of essential function that are reflected in the Rydberg electron’s binding chemical phenomena such as solvation and intermolecular energy. The binding energy can be conveniently measured us- interactions that precede chemical reactions. ing photoelectron spectroscopy. Implemented with ultrashort While many clusters have been studied using a vari- laser pulses, the ionization from Rydberg states is a very ca- ety of spectroscopic techniques,2, 7–11 the dynamical, struc- pable tool for studying the structural dynamics of molecular tural motions of clusters and their molecular components systems. have remained difficult to unravel. Multiphoton ionization Because the potentials governing the vibrational motions coupled with mass spectrometry, which can be implemented of the ion core barely change when the Rydberg electron with ultrashort laser pulses to allow the observation of time- is ejected, the resulting spectra are free of vibrational pro- dependent phenomena, can be difficult to interpret because gression but show the structure-specific ionization transitions the clusters observed at the detector may not necessarily from the Rydberg states. For rigid molecules, the resulting be the ones of which the dynamics is followed during ion- spectra feature lines with spectral widths that are determined ization. In comparison, time-resolved photoelectron spec- only by the bandwidth of the ionizing pulsed laser or the pho- troscopy (TRPES) has the advantage that the electrons are toelectron spectrometer. For flexible molecules we have found ejected at the time of ionization, yielding a very direct signa- that different conformeric forms give rise to separate spectral ture of the time-dependent dynamical processes. During the peaks, and that the width of the lines reflect the structural dis- last decade, TRPES has also been applied to isolated clusters persion of the Rydberg excited molecules.20 This has enabled in gas phase.11–15 TRPES is also useful because it directly in- us to observe the structural dynamics of conformational trans- terrogates the evolving electronic structure along an excited- formations in molecular systems with internal rotations about state reaction coordinate.16, 17 Most of those studies explored single bonds.21, 22 Our goal in the present work is to extend the explo- a) Present address: LCLS Laser Department, SLAC National Accelerator ration of structural dynamics in floppy systems to molecular Laboratory, Menlo Park, California 94025, USA. b)Author to whom correspondence should be addressed. Electronic mail: clusters. Because the Rydberg electron wavefunction is large [email protected]. Fax: +1-401-863-2594. compared to typical molecular dimensions, even in clusters

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Author complimentary copy. Redistribution subject to AIP license or copyright, see http://jcp.aip.org/jcp/copyright.jsp 044319-2 Deb, Minitti, and Weber J. Chem. Phys. 135, 044319 (2011) of modest size, the Rydberg electron binding energy is sensi- tive to the global molecular structure. We therefore expect the cluster formation to have a profound impact on the Rydberg states. The structural sensitivity also offers the opportunity to observe, in real time, how the global structure of the cluster system evolves. For our studies we choose N,N-dimethylisopropylamine (DMIPA), a tertiary amine in which the nitrogen atom acts as an ionization chromophore and the aliphatic substituents provide for interesting structural and chemical dynamics. DMIPA is an attractive model system because the structural and electronic relaxation dynamics of the monomer are well understood.23 Excitation in the UV, at 209 nm, leads to exci- tation of the 3p Rydberg states, which rapidly decays to 3s. Because the ground state potential features a double well that is well known from ammonia,24 while in the Rydberg state the molecule is close to planar, excitation in the Franck-Condon region inserts a large amount of energy into vibrational co- ordinates. This energy, plus the energy that is converted in the electronic relaxation from 3p to 3s, is available to induce FIG. 1. The two-color ionization scheme to probe the dynamics of DMIPA fragmentation of the α carbon-carbon bond. However, studies in the Rydberg states. The molecules are excited to 3p by absorption of a have shown that, in the parent molecule, the lifetime of 3s is photon at 209 nm, and ionized by a time-delayed 418 nm photon. The kinetic energy spectrum of the ejected electrons is recorded as a function of time. As so short that any such fragmentation occurs in the ion state revealed by those spectra, the parent ion P+ generated by ionization out of 3p 23 25 instead. In the related work on ammonia clusters and on has insufficient energy to fragment, while the ion generated by ionization out mixed clusters with ammonia26 evidence for proton/hydrogen of 3s can do so. transfer has been observed. Being amongst the most impor- tant and ubiquitous phenomena, proton/hydrogen transfer re- actions have been widely studied in clusters.27–32 We have laser pulse overlap was determined by monitoring the cross- found that DMIPA easily forms molecular clusters when ex- correlation time between the fourth harmonic excitation and panded in argon as a carrier gas, permitting us to study their second harmonic ionization pulses using the molecular re- dynamics from a structural point of view. sponse function of 1,4-dimethylpiperazine, which has a very In our experiments, we excite the molecules and the clus- fast response time. ters from the ground state to the 3p Rydberg state using a The molecular beam is generated by expanding DMIPA single photon at 209 nm (Fig. 1) and ionize it using a time- vapor through a nozzle orifice and a skimmer with diameters delayed probe photon at 418 nm. The kinetic energy of the of 100 μm and 150 μm, respectively. To vary the admixture ejected photoelectron yields the electronic state at the time of of DMIPA in the carrier gas, we bubble the rare gas at 1.15 bar ionization, as well as the structure-specific electron binding through the reservoir of liquid sample at various temperatures. energy of the Rydberg orbital. The mass spectrum reveals the At reservoir temperatures of −30 ◦C and 0 ◦C, the vapor pres- cluster composition, although the flight time to the spectrom- sure of DMIPA is 5 Torr and 35 Torr, respectively.35 At either eter is so large that fragmentation during the flight can mask temperature, helium expansions result in beams consisting al- the true cluster composition at the time of ionization. most exclusively of parent molecules. For argon as a carrier gas we observe the formation of molecular clusters, with a II. EXPERIMENT mass distribution that depends on the reservoir temperature. The mass resolution of our instrument was m/m = 300. The photoelectron-mass spectroscopy apparatus and the Anhydrous DMIPA (99.8%) was purchased from Sigma- ultrafast laser system used to generate femtosecond laser Aldrich and used without further purification. Our mass spec- pulses have been described previously.20, 33, 34 For the present tra show no signs of impurities. time-resolved experiments the regenerative amplifier, operat- ing at 5 kHz repetition rate, produces pulses with ∼70 fs du- ration at 836 nm. The output of the amplifier is upconverted III. RESULTS AND DISCUSSION to the second and fourth harmonics using β-barium borate crystals, providing pulses at 418 and 209 nm that are used The ejection of a photoelectron is fast compared to the as the probe and pump pulses, respectively. The pulse ener- time scale of structural motions of a cluster or the time scale gies at the second and fourth harmonic wavelengths were 16 of its fragmentation. As a result, photoelectron spectra show μJ and 0.6 μJ, respectively. The beams were focused onto the molecular species at the time of ionization. However, since the molecular beam in the photoelectron spectrometer using a all clusters are ionized and give rise to photoelectron signal, 200 mm UV-grade fused silica lens. The resulting intensities and since the computational modeling of Rydberg electron at the focus are 3.1 × 1013 and 3.4 × 1011 W/cm2 for the sec- binding energies is not yet sufficiently advanced to assign an ond and fourth harmonics, respectively. The time zero of the observed photoelectron energy to a cluster and a structure, the

Author complimentary copy. Redistribution subject to AIP license or copyright, see http://jcp.aip.org/jcp/copyright.jsp 044319-3 Ultrafast dynamics of DMIPA clusters J. Chem. Phys. 135, 044319 (2011) photoelectron spectra alone do not suffice to understand the dynamics. Mass spectra are similarly difficult to interpret: while the mass spectrum does give an accurate molecular composition of the cluster, it measures the mass of the cluster as it trav- els toward the detector. Upon ionization in our instrument, it takes several hundred nanosecond to accelerate the clus- ter. If the newly generated cluster ion dissociates faster than that, the instrument records a fragment mass. Therefore, the mass spectrum is the result of a convolution of the mass of the cluster that is initially ionized, the amount of energy in- serted into vibrations during the ionization process, and the heights of the barriers to fragmentation. Especially in clusters that have sufficient internal energy to do interesting chemical and structural dynamics, this convolution makes an identifi- cation of specific clusters impossible with mass spectrometry. While photoelectron spectroscopy and mass spectrome- try alone are thus fraught with difficulty, their combination allows the elucidation of many – but not all – dynamical phenomena. To understand the processes in DMIPA and its molecular clusters we begin with the monomer.

A. Electronic and fragmentation dynamics in the monomer Expanding DMIPA with helium as a carrier gas, espe- cially when the sample is held at a low temperature, results in spectra that are almost exclusively due to monomers (Fig. 2). The photoelectron spectrum (panel (a)) shows a very fast tran- FIG. 2. Time-dependent photoelectron spectra (a) and mass spectra (b) of sient signal at 2.27 eV, which is assigned to the 3p states.23 DMIPA parent molecules, obtained by expanding DMIPA, held at a reservoir temperature of –30 ◦C, with helium. The 3p state gives rise to the short lived Our time-resolved experiment does not separate the close- transient with a binding energy of 2.27 eV (panel (a)), while the longer-lived lying magnetic quantum number states. The 3p signal decays 3s state is at 2.88 eV. The color represents the intensity on a logarithmic with a time constant of 700 fs, which is mirrored by a rise of scale; the color bar gives the natural logarithm of the intensity in arbitrary the 3s signal at 2.88 eV with the same time constant. The 3s units. The mass spectrum (panel (b)), which is integrated up to 10 ps with each time point equally weighted, is dominated by the parent at mass 87 and a signal itself decays much slower, with a 90 ps time constant. fragment at mass 72. Under these expansion conditions almost no clusters are The mass spectrum has only two dominant peaks: the observed. The parent decay and fragment rise time is 700 fs and the fragment mass 87 is the parent ion while mass 72 is a fragment that is decay time is 90 ps. formed by α C–C bond cleavage and loss of a methyl group. The time dependencies of the mass peaks mirror those of the fragmentation observed in the mass spectrometer arises from 3p and 3s peaks of the photoelectron spectrum. This close a bond cleavage in the molecular ion. correlation suggests that the parent ions are observed when ionization is out of 3p while the fragment ions are seen when ionization is out of 3s. B. Spectra of molecular clusters As pointed out by Gosselin et al.,23 the excitation to 3p and relaxation from 3p to 3s deposit a large amount Molecular clusters of modest size form easily when of energy into vibrational coordinates, sufficient to break DMIPA is expanded in argon. Figure 3 shows the mass the α C–C bond. Yet even so, any fragmentation on the 3s spectrum recorded in an argon expansion with a DMIPA Rydberg surface must compete with the decay of the 3s partial pressures of 4.0 × 10−2 (0 ◦C, 35 Torr). Comparison state itself. In DMIPA, the fragmentation is apparently so with Fig. 2 shows that the formation of molecular clusters slow, and the molecular decay so fast, that the fragmentation is favored by the argon expansion, where we readily observe essentially does not occur on the 3s surface.23, 36 However, cluster sizes up n = 10. Interestingly, we never observe any during the ionization out of 3s the molecule retains its signal from clusters that contain argon atoms. vibrational energy, so that the newly created ion is born It is striking that while for all expansion conditions with sufficient energy to fragment before it is accelerated to the monomer peak is always accompanied by the M/Z 72 the mass spectrometer detector. Ionization out of 3p leaves fragment peak as discussed above, none of the cluster peaks the molecular ion with too little energy to fragment, so that is associated with a corresponding fragment. One might argue only the parent masses are observed. Thus, while the time that the process of fragmentation could lead to the dissoci- dependence of the mass signal gives an illusion of dynamics ation of the cluster and that only the isolated fragment ions on the Rydberg surface, in reality the delay-time dependent survive, which are then observed together with those from

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FIG. 3. Mass spectra of molecular clusters of DMIPA, integrated up to delay times of 10 ps with each time point equally weighted. This spectrum was obtained by expanding DMIPA, held at a temperature of 0 ◦C with Ar. The parent (monomer) at mass 87 and the fragment at mass 72 are the most intense peaks. Peaks from molecular clusters are present up to n = 10. the dissociation of monomer ions. This seems not entirely plausible, though, because one would expect that at least some of the fragmented ions remain partially clustered. More likely is that in the cluster, the ions no longer have sufficient energy to fragment. We already observed an absence of fragmentation when the monomer is ionized out of 3p, which deposits 0.93 eV of energy into the molecular ion.36–38 Since fragments do form when ionized from 3s, the barrier to frag- mentation is bracketed between 0.93 and 1.54 eV.38 Because FIG. 4. Time-dependent photoelectron spectrums at two different expansion the energy levels shift in the formation of the clusters (see conditions (a) DMIPA at –30 ◦C, seeded with Ar and (b) at 0 ◦C, seeded discussion below), we do not know the exact energy content with Ar. Both spectra show the short-lived monomer 3p state at 2.27 eV for each of the clusters in its 3s state. We do know, however, and the long-lived monomer 3s state at 2.88 eV. The time-dependence of the that compared to the monomers, the clusters have many more monomer peaks is same as Fig. 2(a). The broad peaks between 1.8 eV and 2.7 eV are the cluster 3s peaks, whereas the cluster 3p peaks are very short degrees of freedom that act as a bath for the energy. It thus lived and are around 1.7 eV. The color represents the intensity on a logarith- seems most likely that the clusters distribute the energy that mic scale; the color bar gives the natural logarithm of the intensity in arbitrary is deposited in the molecule during the ionization between units. so many degrees of freedom that fragmentation is no longer possible on the time scale of the acceleration to the mass spec- trometer detector. Further, it is possible for clusters to cool 3p component is initially excited, while the 3s component is their internal energy content by evaporating molecules from populated by decay from 3p and decays more slowly. The the surface. Both processes imply that the rate of vibrational temporal decay characteristics therefore identify the cluster relaxation in the cluster is larger than the rate of molecular signals from the different electronic states. We conclude that fragmentation. Given that at least in the monomer, the latter the Rydberg electron binding energies of clusters are shifted is slow on a 90 ps time scale, this seems quite plausible. to lower values compared to their monomers: for the 3p sig- Figure 4 shows the time dependent photoelectron spec- nal, the shift is about 0.8 eV while for the 3s signal it is as tra taken with argon expansions at the two partial pressures, large as 1.0 eV. These shifts are large. The clustering has a 5.7 × 10−3 and 4.0 × 10−2, respectively. Both spectra show dramatic effect on the Rydberg electron binding energy! the intense, short-lived signal at 2.27 eV that stems from the For expansion conditions that lead to less clustering initially excited 3p level of the monomer molecule. They also (Fig. 4(a)), we see shifts that are smaller than for expansion show the long-lived signal at 2.88 eV that is due to the 3s Ry- conditions that favor larger clusters (Fig. 4(b)). The Rydberg dberg state of the monomer. Additional photoelectron signal, electron binding energy is therefore shown to shift to lower between 1.5 and 2.7 eV, is assigned to the molecular clusters values as the cluster size increases. The photoelectron signal that are observed in the corresponding mass spectra. from clusters is diffuse, showing no discernable features or Several observations are noteworthy about the cluster peaks in the intensity. Apparently, each cluster mass gives photoelectron signal. First, there is a very short-lived com- rise to a distribution of binding energies such that the spectral ponent, stretching from 1.5 to about 2.2 eV, and a longer- signatures of neighboring cluster masses overlap. This can lived component between 1.8 and 2.7 eV. As Fig. 4 shows, be understood to result from the structural dispersion that the decay characteristics of those signals show similar time is presumably present in the clusters subsequent to the dependent dynamics as the monomer 3p and 3s signals: the excitation, which deposits a large amount of energy in the

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FIG. 5. The time dependence of the DMIPA parent ions and the mass 88 ions in absence and presence of clusters. (a) Mass spectrum obtained with a He as a carrier gas and the sample at a reservoir temperature of −30 ◦C; (b) mass spectrum obtained with Ar as a carrier gas with the sample reservoir temperature at 0 ◦C. No clusters were present in case of panel (a), whereas in case of panel (b) clusters up to n = 10 were present. The color represents the intensity on a logarithmic scale; the color bar gives the natural logarithm of the intensities in arbitrary units.

FIG. 6. Structures of (a) the dimer in the ground state, (b) the dimer ion, and cluster.20 It is also likely that different molecular components (c) the proton transferred dimer ion. The red dotted lines show the interactions within a cluster have a unique spectral signature in the between different atoms in the cluster. In the ground state the dimer is weakly bound and the N ···H distance is 2.9 Å. Both the dimer ion and the proton Rydberg binding energy spectrum. Finally, we note that the transferred dimer ion have strong hydrogen bonding. In the case of the dimer entire broad cluster bands are shifting on a time scale of tens ion, the N ···H distance is 1.88 Å, whereas in case of the proton transferred of picoseconds, an observation that we will discuss below. dimer ion the C ···H distance is 1.96 Å.

C. Proton transfer (Fig. 6(a)) is a van der Waal’s cluster that is weakly bonded Close inspection of the mass spectra reveals that all of (25 meV) by interactions between the nitrogen atoms and the the mass peaks are associated with additional signal at one hydrogen atoms of the N-methyl group. Each nitrogen atom unit higher mass. While of course all molecules have heavy is bonded to the other molecule in that way, yielding a sym- isotopes at integer mass increments, as Fig. 5 shows on the metric structure with a cyclic bonding motif. example of the parent mass, the heavy mass signals have a Ionization switches the local charge of the nitrogen: the different time dependence and can therefore not be due to neutral atom with partially negative lone pair electrons turns the natural isotopic composition. Because there are no colli- into a positively charged ion core. This switch disables the sions in the molecular beam, the protonated parent molecule, bond between the nitrogen and its neighboring hydrogen at M/Z 88, must originate with a dimer or a higher cluster. atom. The positive charge on the nitrogen also withdraws Computational studies of clusters in their Rydberg states electron density from the hydrogen atom at the methyl group, are, to date, prohibitively difficult. However, calculations of so that the most stable ion state structure (Fig. 6(b)) features the ground state molecule and molecular ion are readily a strong hydrogen bond between the positively charged within reach of DFT calculations and can guide our thinking. molecule on the right and the neutral molecule on the left. Applying GAUSSIAN’03 (Ref. 39) at the B3LYP level with a The distance between the nitrogen and the hydrogen, calcu- 6-311++G(2df,2p) basis set we obtained the optimized struc- lated to be 1.88 Å, is typical for a hydrogen bond. Protonated tures shown in Fig. 6. The neutral dimer in the ground state species have been reported in mass spectra before.14, 25, 40–43

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For example, in ammonia clusters Farmanara et al.have observed a dominance of protonated species.40, 41 In almost all these cases the proton is bonded to an electronegative atom. In our case the proton is attached to the alpha-carbon, which is made acidic by the ionization of the nearby nitrogen atom. The hydrogen-bonded structure suggests that the pro- tonated species observed in the mass spectrum can be generated by proton transfer from a methyl group of the ion- ized molecule to the neutral molecule’s nitrogen atom. The proton-transferred dimer ion structure is shown in Fig. 6(c). The positive charge now resides on the left molecule. Disso- ciation of the intermolecular bond of this proton-transferred structure would give rise to the protonated species seen in the mass spectrum. In this model it is therefore the originally un-excited molecule of the cluster that ends up as the posi- tively charged protonated ion. The molecule that originally absorbs the UV radiation ends up as a hydrogen deficient molecule with mass 86, which we do not observe as it carries no charge. Panel (a) of Fig. 5 shows the time dependence of the mass 87 and 88 peaks obtained with a He expansion (–30 ◦C), and panel (b) shows the same signals with Ar as a carrier gas (0 ◦C). In case of He, the parent peak (M/Z 87) shows only the very fast decay that was discussed in the context of Fig. 2. A small amount of signal at M/Z 88 is due to isotopes. This FIG. 7. Time dependencies of (a) the parent ions and (b) the mass 88 ions fast-decaying signal is also present in the Ar-seeded spectrum. ◦ But in the Ar spectrum, there are two additional features: first, (Ar as carrier gas at reservoir temperature of 0 C). The solid dots are exper- imental data and the solid lines are fits using the kinetic scheme of Fig. 8. there is a slow rise of the M/Z 87 parent ions and second there Both traces have a fast transient (700 fs) at early times that results from the is a slowly decaying component of the protonated species at fast 3p to 3s decay of the monomer. For the parent ions (a), the slow rise of M/Z 88. Because both those signals are not present in the 24 ps represents the monomer formation on 3s state due to cluster evapora- tion. The inset of panel (a) shows the fitted parent rise separately. (b) The spectrum with the helium expansion, they must result from initial fast transient of monomeric decay is present due to the 6% natural clusters. abundance of higher isotope. Subtracting out this part gives the decay time Figure 7 plots the time traces of the different signals to- of the protonated species (21 ps), shown in the inset. The maximum of the gether with their fits. Panel (a) represents the M/Z 87 ions parent trace in panel (a) is arbitrarily set to 1000. This gives an initial parent ion (M/Z 87) intensity rise from I(t = 0) = 5 to the final intensity, I(t =∞) = while panel (b) shows the protonated species at M/Z 88. Both 102 (inset – panel (a)), whereas the protonated parent ion intensity goes from traces show the very fast transient at early times that results I(t = 0) = 56 to I(t =∞) = 0 (inset – panel (b)). from the fast 3p to 3s decay of the monomer. This signal is present in the M/Z 88 trace of panel (b) because of the 6% natural abundance of heavy isotopes. Subtracting out the could happen on the Rydberg surface on the time scale of the monomer signal from the two traces yields the plots of the in- pump-probe delay times, or on the ion surface on much dif- sets. The slow rise time of the M/Z 87 signal is 24 ps, while ferent time scales. The photoelectron spectrum shows no rise the decay time of the M/Z 88 signal is 21 ps. Setting the max- or fall of any particular peak, suggesting that a reaction on the imum of the trace of panel (a) arbitrarily to 1000, the slow ion surface is more likely. However, given the broad nature rise of M/Z 87 starts at 5 and ends, at infinite time, at 102, of the cluster signals, it is conceivable that photoelectron sig- while the M/Z 88 signal decays from 56 to 0. We have found nal from proton-transferred species hide underneath the broad that some of these time constants and relative amplitudes are band. slightly variable between different expansion conditions, with The energy difference between the dimer ion and the pro- time constants most of the times between 20 and 25 ps, but oc- ton transferred dimer ion is very small. With both structures casionally as high as 44 ps. This suggests that the parent ions relaxed, the DFT calculation shows the proton-transferred and protonated parent ions may be generated in multiple ways species to be stabilized by 60 meV at its equilibrium posi- by dissociation of different clusters. While all the higher order tion. The barrier to proton transfer is about 100 meV. Given protonated cluster ions have similar decay times (26 ps), the that the total vibrational energy content of the dimer after ion- formation kinetics of the product ions may depend on the ex- ization is 1.93 eV (see below), proton transfer may be easily act distribution of cluster sizes, which can depend sensitively possible in the ionic state. Since we cannot identify any photo- on the experimental conditions. electron signature of the proton transferred species we cannot On which surface the proton transfer takes place, and on calculate the energy differences between the dimer species in what time scales, are interesting questions to which our exper- the Rydberg state. The calculation therefore is silent about the iments can provide only partial answers. The proton transfer possibility of a proton transfer in 3s.

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time-dependent intensity profiles reveal how the ions are gen- erated. In particular, the initial and final concentrations reveal the balance of the equilibria in the Rydberg and the ion states. A complete and accurate determination of all the kinetic parameters is not possible with our experiment. Unknown are not only the equilibrium constants of the proton transfer reac- tions and the cluster dissociation reactions, but also the ion- ization cross sections and the lifetimes of the different species in their Rydberg states. Because of the unresolved nature of the photoelectron spectrum and the multiple ways to gener- ate ions of the same mass, there are too few observables to determine all parameters independently. Nevertheless, we can derive an approximate estimate of the placement of the pro- ton transfer equilibria by assuming that all the ionization cross sections are equal and that the dissociation of the clusters are on roughly equal time scales. With those assumptions, the analysis of the dimer along the line of Fig. 8 shows that P+ or (P+H)+ signal generated through the dissociation of the clus- ter (dimer or proton transferred dimer) on the Rydberg sur- face comes in the form of exponentially rising curves, with the equilibrium constant revealed by the ratio of intensities of + + FIG. 8. Kinetics scheme to analyze reactions of DMIPA dimers. The vertical P and (P+H) at infinite time. From the inset of Fig. 7(b) axis represents energy, the abscissa represents the proton transfer coordinate, we conclude that at infinite time, there is no (P+H)+ signal and the axis going out of the plane is the cluster evaporation coordinate. The Rydberg state species are color coded in blue while the ion state species are present, implying that any equilibrium is fully on the side of in black. The red arrows represent pathways that we observe as dominant, the D3s species. The dissociation of the cluster on the ion sur- whereas the black arrows represent possible pathways we find to be of minor face is associated with exponentially decaying time traces of importance. The schematic intensity vs. time plots shown as insets illustrate P+ or (P+H)+, with the same time constant as the rise, and the time dependence of ion signals generated from the respective pathways. The model includes proton transfer dynamics on the 3s Rydberg surface and with the equilibrium constant revealed by the ratio of intensi- on the ion surface as equilibria between the dimer and the proton-transferred ties at time zero. From the insets of Fig. 7 we see that those dimer. A quantitative analysis of Fig. 7, following the scheme of Figure 8, intensities are 5 and 56, respectively for the P+ and (P+H)+ shows that in the Rydberg state, the equilibrium is on the side of the dimer, ions. Thus, in the ion, the ratio of proton-transferred species whereas in the ion state it is toward the proton-transferred dimer ion. to dimer ions is about 11:1. We conclude that on the Rydberg state the equilibrium is fully on the side of the dimer, but that To interpret the time-dependent spectra we point to in the ion the equilibrium is strongly on the side of the proton Fig. 8. Excitation of the dimer, D, to 3p leads via rapid transferred species. internal conversion to 3s. We allow for the possibility of a The assumptions going into this analysis may seem ten- fast equilibrium between the dimer and its proton-transferred uous. Yet it is reasonable to assume that the ionization cross form, (P+H) ···(P−H), in 3s as well as on the ion surface. sections of closely related cluster structures are, in fact, not Because the energetics are different in the Rydberg state very different. One might argue that the assumption that the and the ion state, the equilibrium constants need not be the P+H molecule has a long lifetime in the 3s Rydberg state same. We postulate that in either the 3s Rydberg state or the might be invalid, and that a rapid decay of that species in fact ion state, the dimer dissociates to produce parent molecules, prevents us from seeing the corresponding reaction channel, + i.e., P3s or P , respectively. The proton transferred species thereby obscuring part of the equilibrium. This is, however can also dissociate and generates (P+H) in either 3s or the not likely, as the total signal from the un-dissociated species + ion state, i.e., (P+H)3s or (P+H) , respectively. Important (t = 0: 56 + 5 = 61) is in fact smaller than that from dissoci- for the interpretation of the data, the dissociation of the ated species (t =∞: 102). A loss of molecules through a hy- dimer must be leaving the parent with too little energy to pothetical rapid decay of (P+H)3s is therefore not consistent fragment. Further, the parent molecules generated on the with the data. It is, however, to be understood that the product 3s Rydberg state by cluster dissociation must have a much ions can also be created by reactions of higher clusters, so that longer lifetime than those generated in 3s after excitation of the quantitative aspects of this analysis are tentative. a monomer, presumably also because of their greatly reduced To summarize this section we repeat that proton trans- internal vibrational energy. Consequently, the parent ions are fer is evident in the mass spectra. Proton transfer may happen recovered from dimers (or clusters) that dissociate either on as a fast equilibrium between the different species. Both the the 3s surface or on the ion surface. detailed analysis of the kinetics of the different ions as well According to Fig. 8, the parent ions P+ and the proton- as the general appearance of the photoelectron spectrum sug- transferred species (P+H)+ can be generated either by a dis- gest that this proton transfer equilibrium is heavily on the side sociation reaction on the Rydberg surface or by a reaction of the proton transferred species in the ion, but almost exclu- on the ion surface. Because D3s decays whereas P3s (gen- sively on the side of the original species while in the Rydberg erated from cluster dissociation) does not, the shapes of the state.

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butions, are lower than those of smaller molecules with tighter charges.44 In the case of the clusters, the induced dipole mo- ments in the cluster ligands distribute the charge away from the charge center, and this more diffuse charge center leads to a lowering of the Rydberg electron binding energy. The im- mediate, substantial shift of the Rydberg electron binding en- ergy in the clusters is therefore a result of the induced dipole moments in the neighboring cluster molecules. The temporally resolved decline of the 3s electron bind- ing energy can now be readily understood. As shown ear- lier, the excitation of a nitrogen atom destroys one of the van der Waals bonds holding the cluster together. This process is expected to lead to a rearrangement of the cluster’s struc- FIG. 9. Time dependence of the photoelectron peaks of the cluster band. ture. Additionally, all molecules adjacent to the newly created The broad cluster peaks for the two different Ar expansion conditions in charge in the cluster have dipole moments that tend to respond Fig. 4 were fitted with a Gaussian distribution and the center positions plotted to the new charge distribution by reorienting themselves. All as a dot for each time point. The vertical axes represent the differences of the those structural reorganizations tend to further distribute the cluster peak centers with respect to the respective monomeric 3p or 3s peaks. Panels (a) and (b) are the 3p and 3s shifts for Ar –30 ◦C(Fig.4(a)), whereas charge away from the center, leading to a shallower Coulomb panels (c) and (d) represent the 3p and 3s peak shifts for Ar 0 ◦C(Fig.4(b)). potential at the core and thereby to smaller Rydberg electron The fits (solid lines) use exponential functions. In both cases, the 3s peaks binding energies. This dynamic effect is in addition to the shift with a time constant of 35 ps. In panel (b), the peak shifts from an initial value of –0.48 eV to a final value of –0.71 eV; in panel (d), the shift is from immediate polarization effect and thereby adds to the bind- –0.55 eV to –0.92 eV. ing energy shifts. The time constant at which the Rydberg electron binding energy adjusts to its new value is therefore the time scale of the structural reorganization of the solvent D. Energetics and structural dynamics of clusters molecules in the cluster. in 3s Clearly, for the structure reorganization process to occur With the kinetics of the proton transfer established, we in the Rydberg state, the cluster must go energetically down- are now in a position to discuss the energy levels and the time hill on the multidimensional potential energy surface of the dependent structural dynamics of the molecular clusters. As cluster structure, i.e., the energy of the cluster Rydberg state the photoelectron spectra (Fig. 4) show, the binding energies decreases. However, during this process, as the photoelectron of the Rydberg electrons of clusters are shifted toward lower spectra show (Fig. 4), the cluster 3s binding energy decreases values compared to the binding energy of the 3s Rydberg with time, i.e., the energy needed to ionize the Rydberg elec- electron of the monomer. Fitting the broad, featureless bands tron becomes smaller. It thus follows that during the structural with a Gaussian distribution one can, for each time point, de- rearrangement, the ionization energy of the cluster must de- termine a center position. These band centers are plotted in crease even more than the Rydberg electron binding energy. Fig. 9 for the two different argon expansion conditions. Upon The DFT calculation shows that while in the ground photoexcitation, the 3s and 3p Rydberg electron binding en- state the dimer has a weak van der Waal’s bond (25 meV) ergies are shifted with respect to the monomer molecule, by and therefore is weakly stabilized compared to the monomer, about 0.5 eV. Subsequently, with a time constant of 35 ps, the dimer ions are stabilized by 670 meV compared to the there is a further shift, making the total shift of the centers monomer. This implies that the adiabatic ionization potential as large as 0.9 eV. The immediate and the time-delayed shifts of the dimer is much lower than that of the monomer. can be explained as follows. Fig. 10 shows an approximate energy diagram for the dimer The excitation of an electron from the lone pair at the and compares it to the monomer. One of the main reasons for amine group to the Rydberg state leaves a positively charged the ion state stabilization is the strong H-bonding in the dimer ion core. The Rydberg electron orbits this charge at a distance ion. The Rydberg electron binding energies of the cluster are that is large compared to the size of the molecule, even in the lower than that of the monomer, by some 0.3 to 1 eV. This cluster. In the monomer, the positive charge is reasonably cen- reduction in the Rydberg electron binding energies partially tered at the nitrogen atom, defining the Coulomb potential of counters the reduction in the ionization energies, so that the the Rydberg electron. In the cluster, the photoexcitation cre- energy of the Rydberg levels above the ground state is only ates a charge at one of the cluster molecules, which induces slightly reduced. Thus, both the ion state and the Rydberg dipoles in the neighboring ground state molecules. These in- state of the dimer are lowered compared to the monomer, but duced dipole moments are aligned such that their negative the ion state is much more depressed than the Rydberg state. ends point toward the positive charge, while the positive sides The time scale of the structural reorganization (35 ps) is point away from the charge center. This alignment of the in- quite similar to that of the dissociation of the cluster described duced dipole moments tends to distribute the positive charge in the “Proton transfer” section. The two may well be re- away from the ion core, so that the Coulomb potential for the lated, but are not the same. The dissociation of the dimer, and Rydberg electron is more diffuse at the center. As a general for larger clusters the evaporation of constituent molecules, observation, the Rydberg electron binding energies of larger would always reduce the size of the cluster. We have al- molecules, presumably with more delocalized charge distri- ready concluded that larger clusters have larger changes in the

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conditions have uncovered new insights into the dynamics of this floppy system. Specifically, we found that the 3s Rydberg electron binding energies are reduced by large amounts, about 1/2 eV, immediately upon excitation to the Rydberg state. We attribute this large reduction to the immediate distribution of the charge in the ion core toward the outside of the cluster on account of the induced dipoles of the cluster molecules. Separately, on a time scale of about 35 ps, the static dipole moments of the cluster components respond to the newly created charge by aligning accordingly. This reorganization is accompanied by a further decrease in the Rydberg electron binding energy by 0.22 to 0.36 eV. Proton transfer in DMIPA appears to be facile and fast, but confined to the ion surface. The mass peaks of the pro- tonated species stand out prominently through their distinct time dependence. Interestingly, there is no indication for pro- ton transfer in the Rydberg states. This is a stunning result, because one typically thinks of Rydberg electrons as highly delocalized, non-bonding, and generally not affecting the ion core to any extent. But apparently, they do have a profound effect on the possibility of proton transfer in the cluster. One can surmise that this effect might be due to the cusp of the 3s wave function at the nitrogen charge center, which would therefore withdraw less electron density from the α hydrogen FIG. 10. Energy diagram for the dimer compared to the monomer. The adi- atom, which thereby would be less acidic than in the ion; or abatic IP’s of both the monomer and the dimer are calculated. The vertical IP one can speculate that the proton transferred structure has a for the dimer is calculated, while the vertical IP of the monomer is experimen- higher energy in the Rydberg state, so that the proton transfer tally obtained (Ref. 46). The placement of the Rydberg levels follows from these values, using approximate electron binding energies from the observed would be energetically unfavorable. Ultimately, our experi- spectra of 2.07 eV for the 3p state and 2.67 eV for the 3s state. ments cannot tell the origin for this interesting phenomenon, but they do suggest further computational studies. The dimer and the higher clusters dissociate in the 3s state by ejecting the monomer with about a 30 ps time con- electron binding energy compared to the monomer. A cluster stant. After this dissociation, the molecule no longer frag- evaporation would therefore tend to increase the 3s binding ments by splitting an α C–C bond as the monomer does. The energy – the opposite of what we observe. Therefore, the shift evaporation of the solvent molecule apparently removes suf- in the Rydberg electron binding energy of Fig. 9 cannot be due ficient energy for the molecule to become stable. We also ob- to the cluster evaporation, but must be due to the structural re- serve that after the dissociation, the lifetime of the 3s level is arrangements. It is possible, however, that cluster evaporation greatly increased. This is consistent with the general trends of does contribute an increase of the binding energy, and that the fluorescence lifetimes (higher vibrational energy states have reduction in the binding energy of a single cluster size is even shorter lifetimes), but could also be consistent with a cross- more dramatic than the observed overall shift. ing to a σ * surface similar to that observed recently in 2- We finally note that the dynamic change in the 3s binding phenylethyl-N,N-dimethylamine.45 energy could not be related to the proton transfer. The calcu- Looking forward, implementing the structurally sensitive lations show that in the dimer ion, the transfer of a proton is Rydberg ionization spectroscopy in a coincident photoelec- favored by 60 meV. During its decay on a 30 ps time scale, the tron – photoion scheme could be quite rewarding, as that cluster binding energy decreases by 0.22 eV for the expansion would enable the observation of time-dependent binding en- conditions of Fig. 9(b), and by 0.36 eV for the conditions of ergy spectra of specific clusters. Such experiments might lead Fig. 9(d). If these shifts in the binding energies were from the to a more detailed elucidation of the structural motions of in- proton transfer, the data would imply that in the Rydberg state dividual clusters. Additional progress could be made by fur- the proton transfer would be energetically uphill by 180 meV ther separating the different cluster signals spectroscopically and 300 meV for the two conditions, respectively. This is not through double resonance experiments. possible. Consistent with our earlier conclusion we therefore find that the change in the 3s binding energy is unrelated to the transfer of protons that is witnessed in the mass spectrum. ACKNOWLEDGMENTS This project is supported by the Division of Chemical IV. CONCLUSIONS Sciences, Geosciences, and Biosciences, the Office of Basic Our explorations of the time resolved Rydberg electron Energy Sciences, the U.S. Department of Energy by Grant binding energy spectra of DMIPA at different expansion No. DE-FG02-03ER15452.

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