Shared-Proton Mode Lights up the Infrared Spectrum of Fluxional

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Shared-Proton Mode Lights up the Infrared Spectrum of Fluxional Cations H5þ and D5þ Timothy C. Cheng,† Biswajit Bandyopadyay,† Yimin Wang,‡ Stuart Carter,‡,§ Bastiaan J. Braams,‡,# Joel M. Bowman,*,‡ and Michael A. Duncan*,† †

Department of Chemistry, University of Georgia, Athens, Georgia 30602, ‡Cherry L. Emerson Center for Scientific Computation and Department of Chemistry, Emory University, Atlanta, Georgia 30322, and §Department of Chemistry, University of Reading RG6 2AD, England

ABSTRACT We report experimental and calculated infrared spectra of the highly fluxional cations H5þ and D5þ. These cations have been postulated to exist in the interstellar medium and to play a central role in the deuterium fractionation. The experiments produce these ions in a pulsed discharge supersonic nozzle ion source and utilize mass-selected photodissociation spectroscopy in the 2000-4500 cm-1 region. Vibrational bands apparently broadened by rapid predissociation are detected throughout this region for both isotopologues. The calculated spectra make use of an ab initio potential energy surface and a new dipole moment surface and are based on results from fixed-node quantum diffusion Monte Carlo and variational vibrational calculations. The successful assignment of the experimental spectra requires a proper treatment of the delocalized anharmonic shared-proton mode and indicates a major breakdown of the harmonic approximation. Several calculated intense spectral features associated with this mode in the far-infrared region could guide future observational searches of these cations. SECTION Kinetics, Spectroscopy

ith the observation of H3þ in the interstellar medium (ISM),1,2 aided greatly by theory,3 the reactions of this cation and its deuterated isotopologues with molecular hydrogen and its deuterated isotopologues are believed to play central roles in the deuterium fractionation in the ISM.4-7 Since H5þ and its deuterated analogues are stable species, the spectroscopic detection of these cations in the ISM should be possible and would be of primary importance. This cannot be done in the absence of laboratory-based or predictive calculated spectra. A lowresolution action spectrum8 of H5þ published in 1988 reported three broad features at 3532, 3910, and 4230 cm-1. These features, especially the last one, were interpreted cautiously in view of the (correctly) suspected highly fluxional nature of the vibrations based on ab initio calculations of scaled harmonic frequencies and intensities.9 The highly fluxional nature of the ground vibrational state of H5þ and all of the deuterated isotopologues has been established from recent rigorous quantum diffusion Monte Carlo (DMC) calculations10,11 using a high-quality ab-initiobased potential energy surface (PES) that is invariant with respect to the 5! permutations of the H atoms.10 An approximate anharmonic treatment of the vibrational modes also emphasizes the highly anharmonic character of these vibrations.12 The combination of this highly anharmonic shared-proton mode plus the highly fluxional nature of the H5þ cation make exact quantum calculations of the IR spectrum unfeasible.

W

r 2010 American Chemical Society

Thus, our approach is to use state-of-the-art methods to obtain the infrared (IR) spectra of H5þ and D5þ reported here. These are compared with new and improved photodissociation spectra, which also report new bands for H5þ and the first spectra for D5þ. The calculations reported here make use of an ab initio PES10 and a new full-dimensional dipole moment surface (DMS) that is a fit to roughly 5000 dipole moment values obtained using density functional theory data with the B3LYP functional and the aug-cc-pvtz basis using the code MOLPRO.13 The representation of the DMS is invariant with respect to all permutations of the H atoms. It does not assume a linear form; however, it is limited to the bound and neardissociation regions of H5þ and thus does not describe the dipole of the infinitely separated fragments. The previous DMC calculations of the ground vibrational state showed a highly symmetric wave function,11 which has maximum amplitude at the saddle point configuration (of D2d symmetry) which is only 52 cm-1 above two equivalent minima (of C2v symmetry). This indicates both delocalization of the wave function and the singular importance of this saddle point instead of the global minimum as the configuration of most relevance. With that in mind, we show the

Received Date: January 14, 2010 Accepted Date: January 25, 2010 Published on Web Date: February 01, 2010

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DOI: 10.1021/jz100048v |J. Phys. Chem. Lett. 2010, 1, 758–762

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Figure 2. Diffusion Monte Carlo trajectories for the ground state and first excited shared-proton mode. The energies of these two states are given in Table 1.

complex. The shared-proton coordinate in such dimers provides direct access to the intermolecular potential corresponding to shared-proton reactions. Vibrational spectra of these dimers generally contain complex band patterns that cannot be reproduced by harmonic theory,14-19 but anharmonic treatments have been successful in some systems.18,19 Benchmark calculations for the ground vibrational state of H5þ are provided by DMC calculations, which are exact (within statistical uncertainties). In addition, fixed-node DMC calculations can give accurate energies of low-lying fundamental energies. In brief, these calculations use a random Gaussian process to solve the imaginary time Schr€ odinger equation in Cartesian coordinates to obtain the lowest vibrational energy, ER.20-22 Details of these calculations are given in the SI. To extend the DMC approach for excited states, we use a fixed-node approximation,21,22 which assumes the preknowledge of the nodal surfaces. On the basis of symmetry considerations, the nodal surface for the shared-proton excited-state wave function of H5þ can be easily constructed in Cartesian coordinates. The node is placed where the central proton is equidistant from the center-of-mass of the two surrounding H2 groups. In the excited-state DMC calculations, we also include the recrossing correction which accounts for the probability of recrossing in a finite (imaginary) time step.21 This nodal surface takes note of the fact that the barriers for H-atom exchange are more than 2000 cm-1, and therefore, unlike superfluxional CH5þ, exchange is not very significant. Nevertheless, we found it necessary to prevent this rare exchange from occurring, and this was done with an “exchange node”. Details of these calculations including this additional exchange node are also given in the SI. The imaginary time trajectory of the energy of this important excited state, denoted νHþ, along with the one for the ground vibrational state is given in Figure 2. From these, we determined the zero-point energy (ZPE) and the νHþ fundamental excitation energy to be 7210 and 334 cm-1, respectively. A second fixed-node calculation was carried out for the torsional mode, defined as the mutual planar rotation of the two H2 groups with the proton

Figure 1. Relaxed potential along the imaginary frequency mode of the D2d saddle point and corresponding ground-state vibrational density.

relaxed potential as a function of the imaginary frequency normal mode of this saddle point, which spans both minima, and the corresponding one-dimensional ground-state quantum density in Figure 1. As seen, the density maximum is at the saddle point configuration, in accord with the results of full-dimensional DMC calculations. Clearly, this wave function is determined by a highly nonharmonic double well of this potential. The energy of this approximate 1d ground vibrational state is also indicated in the figure, and as expected, it is well above the saddle point energy. On the basis of these results, a standard harmonic analysis done at the global minimum would obviously be unrealistic. The normal-mode eigenvectors and frequencies of this saddle point, the global minimum, and another second-order saddle point of D2h symmetry are given in the Supporting Information (SI). For computational convenience, the variational calculations, described briefly below and in detail in the SI, are referenced to the D2h saddle point, and thus, mode assignments made below are based on those saddle point modes. The components of the dipole moment along the five IR-active D2h saddle point normal modes are plotted in the SI. As seen there, the variation of the dipole moment along the imaginary frequency shared-proton normal mode is the largest one, indicating that transitions involving that mode should have large intensities. Mode 8, an HH stretch, shows the next largest variation in the dipole moment. On the basis of the above, it is clear that H5þ is another, and indeed the smallest, example of a proton-bridged dimer


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Table 1. Vibrational Energies (cm-1) of H5þ and D5þ Obtained Using Diffusion Monte Carlo (DMC), Reaction Path, and MULTIMODE (MM-RPH) H5þ

zero-point energy νHþ Δνtorsion

D5þ

DMC

MM-RPH

DMC

7210 334

7244 382

5152 222

66

32

80

MM-RPH 5174 257 28

2νHþ

1718

1241

3νHþ

2751

1821, 1834

equidistant between their centers of mass (depicted in detail in the SI) to obtain the tunneling splitting of that mode. Thus, the three DMC energies, that is, the ZPE, the νHþ fundamental, and the ground-state torsional splitting are taken as benchmark results. We did not attempt higher-energy, fixed-node DMC calculations due to very strong mixing that occurs for such states, which precludes making nodal assignments based on simple symmetry arguments. The code “MULTIMODE” (MM),23-25 “reaction path” version,17,26,27 denoted MM-RPH, was used to calculate the IR spectrum of H5þ and D5þ. The “reaction path” is the above torsional mode, shown in Figure S3 of the SI. Details of these calculations, which also ignore H-atom exchange, are given in the SI; however, we note that these are zero total angular momentum “vibrational-only” spectra. This type of spectrum is reasonable to compare to the experimental spectra, which are not rotationally resolved. These are the first fully coupled anharmonic spectra reported for these cations. Table 1 contains a summary of selected energies from the DMC and MM-RPH calculations. The MM-RPH energies are in good agreement with the benchmark DMC ones. Note especially the strong positive anharmonicity for the overtones of the “bright” shared-proton mode. The calculated IR spectra over a large spectral range, shown as sticks and also broadened with a 30 cm-1 Gaussian window function, are given in Figure 3. The very intense feature seen in both spectra corresponds to the shared-proton fundamental. From the fixed-node DMC calculations, this feature is predicted to occur at around 334 and 222 cm-1 for H5þ and D5þ, respectively. Features above 2000 cm-1 will be discussed in detail below in connection with the experiment. There are noteworthy additional features indicated in Figure 3 below 2000 cm-1. Also note that the energies given in this figure and Figure 4 are for the broadened peak positions and are close to but not the same as any molecular eigenvalue. Experimental infrared photodissociation spectra and calculated absorption spectra are shown in Figure 4 over the spectral region of the former. These cover the region of the IR spectrum where the photon energy exceeds the dissociation energy, D0. From DMC calculations,11 D0 is 6.37 and 6.87 kcal/ mol28 for H5þ and D5þ respectively, with uncertainties of roughly 0.01 kcal/mol. These energies correspond to threshold frequencies of 2227 and 2402 cm-1 for H5þ and D5þ, respectively. Note that the peak positions of these photodissociation spectra correspond to those of the IR absorption


Figure 3. Calculated spectra of H5þ and D5þ over a large spectral range.

spectra, but the intensities are not quantitatively comparable. With this in mind, consider the comparison between the experimental and calculated IR spectra. As seen, the experimental spectrum for H5þ contains four bands at 2603, 3520, 3904, and 4232 cm-1. The three higher-energy bands correspond well to the broader features reported previously with much lower signal levels.8 The spectrum for D5þ, which has not been studied previously, contains bands at 2546, 2815, and 3044 cm-1. The lower-energy bands therefore establish firm upper limits to the dissociation energies (D0) for each ion, which are consistent with, but higher than, the computed values. The widths and relative intensities of these features are invariant over a wide range of laser powers down to the limit of detection and are concluded to represent the intrinsic one-photon spectra of these features. The bandwidths (40-60 cm-1) are much greater than the 1 cm-1 laser line width, suggesting that these arise, at least in part, from predissociation. However, the bands are not symmetric, and therefore, some contribution is likely also present from the rotational contour. The calculated spectra, with assignments, are in good accord with experiment. Note that the peaks at 3950 (for H5þ) and 2874 cm-1 (for D5þ) have two assignments since the molecular eigenstate has almost equal contributions from both zero-order states. Also, the calculated peaks at 4268 (H5þ) and 3037 (D5þ) cm-1 have no assignments because these are many contributing zero-order states, including a number with excitation of the “bright” shared-proton mode, mode 1 (indicated in Figure 1). Also recall that mode 8 is an

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Figure 4. Calculated (with assignments) IR and experimental action spectra of H5þ and D5þ. Arrows indicate the theoretical threshold for dissociation.

IR-active HH stretch and mode 9 is a higher-energy HH stretch. Thus, from the calculations, most of the experimental spectral features involve combination bands or overtones of the shared-proton mode. The exceptions are the bands labeled ν8 for both H5þ and D5þ. Agreement between theory and experiment for this fundamental is quite good, 3560 and 3520 cm-1, respectively, for H5þ and 2572 and 2546 cm-1, respectively, for D5þ. For transitions involving the sharedproton stretching mode, theory is above experiment. This is consistent with the MM-RPH energies for this mode being higher than the DMC result and likely significantly higher for overtones of this mode. According to theory, the experimental peaks for the D5þ spectrum at 2546, 2815, and 3044 cm-1 correspond to, that is, have the same assignments as, the experimental H5þ peaks at 3520, 3904, and 4232 cm-1. That these D5þ peaks are red-shifted by factors very close to the 21/2, that is, 1.40, 1.42, and 1.39, respectively, provides additional assurance that the theoretically based correspondence is correct. As noted above, bands at nearly the same positions as the 3520, 3904, and 4232 cm-1 features, but with greater line widths, were reported previously8 and tentatively assigned based on ab initio harmonic frequencies at the global minimum. Specifically, the first band was assigned as an overtone of a fundamental at 1746 cm-1, the second was assigned to the H2 normal-mode stretch fundamental, and the third band was signed to a combination of the H2 fundamental with a low-frequency H3þ-H2 stretch mode. The present assignments, which are based on saddle point normal modes, are, not surprisingly, completely different from the previous tentative assignments. Finally, note some additional weaker features in the calculated spectrum for H5þ at roughly 2300 and 3200 cm-1, with


hints of these features in the experimental spectrum. These features are difficult to assign to a single state, and therefore, we have not done that. In summary, new experiments and calculations have revealed and assigned unusual features in the infrared spectra of the highly fluxional H5þ and D5þ cations. The delocalized and highly anharmonic shared-proton stretch mode was shown to carry very large oscillator strength, and excitation of this mode was found to play a major role in the assignment of experimental spectral features. In addition, several very intense features in the far-IR region have been predicted.

EXPERIMENTAL METHODS Hnþ and Dnþ cations are produced in a pulsed discharge cluster source29 using needle electrodes mounted in the throat of a pulsed supersonic expansion of pure hydrogen. Efficient cooling is obtained by pulsing the discharge for 5-10 μs at the temporal center of a 300 μs gas pulse. The ions produced are analyzed and mass-selected in a specially designed reflectron time-of-flight mass spectrometer.30 The density of these selected ions is too low for absorption spectroscopy, and therefore, we employ photodissociation measurements. To accomplish this, the ions are excited with the tunable output of an optical parametric oscillator/amplifier (OPO/OPA) laser system (Laser Vision), which tunes smoothly throughout the 2000-4500 cm-1 region. Upon resonant excitation, dissociation proceeds by the elimination of H2 (D2), and the spectrum is recorded in the resulting H3þ (D3þ) fragment ion channel.

SUPPORTING INFORMATION AVAILABLE Details of the diffusion Monte Carlo and MULTIMODE calculations, normalmode eigenvectors, and plots of the dipole moment and torsional

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potential. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION Corresponding Author:

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*To whom correspondence should be addressed. E-mail: joel. [email protected] (J.M.B.); [email protected] (M.A.D.).

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Present Addresses: #

International Atomic Energy Agency, Division of Physical and Chemical Sciences Vienna, Austria.

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ACKNOWLEDGMENT Y.W. and J.M.B. thank the National Science

Foundation (CHE-0848233) for financial support. M.A.D. also thanks the National Science Foundation (CHE-0551202) for support.

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Shared-Proton Mode Lights up the Infrared Spectrum of Fluxional

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