Matrix Isolation Spectroscopy and Nuclear Spin Conversion of NH3

Article pubs.acs.org/JPCA

Matrix Isolation Spectroscopy and Nuclear Spin Conversion of NH3 and ND3 in Solid Parahydrogen Mahmut Ruzi and David T. Anderson* Department of Chemistry, University of Wyoming, Laramie, Wyoming 82071, United States S Supporting Information *

ABSTRACT: We present matrix isolation infrared absorption spectra of NH3 and ND3 trapped in solid parahydrogen (pH2) at temperatures around 1.8 K. We used the relatively slow nuclear spin conversion (NSC) of NH3 and ND3 in freshly deposited pH2 samples as a tool to assign the sparse vibration− inversion−rotation (VIR) spectra of NH3 in the regions of the ν2, ν4, 2ν4, ν1, and ν3 bands and ND3 in the regions of the ν2, ν4, ν1, and ν3 fundamentals. Partial assignments are also presented for various combination bands of NH3. Detailed analysis of the ν2 bands of NH3 and ND3 indicates that both isotopomers are nearly free rotors; that the vibrational energy is blue-shifted by 1−2%; and that the rotational constants and inversion tunneling splitting are 91−94% and 67−75%, respectively, of the gas-phase values. The line shapes of the VIR absorptions are narrow (0.2−0.4 cm−1) for upper states that cannot rotationally relax and broad (>1 cm−1) for upper states that can rotationally relax. We report and assign a number of NH3-induced infrared absorption features of the pH2 host near 4150 cm−1, along with a cooperative transition that involves simultaneous vibrational excitation of a pH2 molecule and rotation− inversion excitation of NH3. The NSCs of NH3 and ND3 were found to follow first-order kinetics with rate constants at 1.8 K of k = 1.88(16) × 10−3 s−1 and k = 1.08(8) × 10−3 s−1, respectively. These measured rate constants are compared to previous measurements for NH3 in an Ar matrix and with the rate constants measured for other dopant molecules isolated in solid pH2.

1. INTRODUCTION Beginning in the early 1990s, the unique properties of highly enriched parahydrogen (pH2) quantum solids were investigated1−7 for potential use as “an excellent matrix [host] for impurity spectroscopy”.8 The specific properties that make solid pH2 advantageous for matrix isolation spectroscopy have been articulated in numerous review articles.9−13 The optimum matrix host minimally perturbs the high-resolution gas-phase rovibrational spectrum of the dopant species while simultaneously isolating and localizing the species of interest to prevent cluster formation or chemical reaction at exceedingly low temperatures. A striking example of pH2 matrix isolation infrared (IR) spectroscopy is provided by the ν4 rovibrational spectrum of CH4.7,14−17 The IR spectrum of the lowestfrequency ν4 vibrational mode of CH4 suspended in solid pH2 displays a progression of crystal-field-split rovibrational transitions with exquisitely sharp (∼0.01 cm−1) homogeneous line widths. Detailed analysis of the CH4 rovibrational spectrum reveals a freely rotating (Bmatrix ″ > 90% Bgas ″ ) spherical-top molecule that fits well in the D3h single-substitution site of the hexagonal-close-packed pH2 crystal structure.8 One of the main reasons this spectrum is esthetically pleasing is that the simple rotational progression of the band is readily apparent even at temperatures below 5 K because of slow CH4 nuclear spin conversion (NSC), which permits transitions from the metastable |J,K⟩ = |1,1⟩ rotational state to be observed even hours after crystal growth. After this seminal work on the © 2013 American Chemical Society

rovibrational spectrum of a dopant molecule in a pH2 matrix, only a short list of dopants have been shown to rotate freely in solid pH2. In addition to CH4, the list includes HCl,18 CO,19 and H2O.20 One glaring omission is ammonia (NH3), which is well-known to rotate freely in rare-gas matrixes.21−23 We suspect that the reason for this lack is not that NH3 does not freely rotate in a pH2 matrix, but rather that a clear spectroscopic assignment has been lacking24,25 because of one of the peculiarities of matrix isolation spectroscopy in solid pH2. Specifically, even in highly enriched pH2 samples, there are always orthohydrogen (oH2) impurities present that can cluster to the dopant and cause additional peaks that complicate tentative assignments.26−29 In most cases, the rotational redundancies that can be exploited in gas-phase rovibrational assignments are absent in the low-temperature spectrum of a freely rotating molecule trapped in solid pH2. It is also a truism that molecules with large rotational constants (light rotors) typical show free rotation, but at the expense that only the ground rotational state has appreciable population at low temperature, making “one-peak” rovibrational assignments tricky. Rigorous assignment of the measured rovibrational Special Issue: Oka Festschrift: Celebrating 45 Years of Astrochemistry Received: December 15, 2012 Revised: March 22, 2013 Published: March 22, 2013 9712

dx.doi.org/10.1021/jp3123727 | J. Phys. Chem. A 2013, 117, 9712−9724

The Journal of Physical Chemistry A

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dipole selection rules for a polar molecule with an inversion tunneling motion that result in pure tunneling emissions in the wavelength range of λ = 1 cm.36 The nuclear spin restrictions placed on the total NH3 wave function are also significant in the astronomy of NH3.37,38 Neither nonreactive collisional nor radiative transitions change the spin orientations of the indistinguishable hydrogen nuclei in NH3, and therefore, there is no nonreactive mechanism by which ortho-NH3 and para-NH3 can interconvert.36 Although these selection rules can be relaxed partially by higher-order intramolecular interactions (spin−rotation, spin−spin),39 this nonconversion between the ortho and para nuclear spin manifolds provides the recipe for how, at very low temperatures, the higher-energy para-NH3 rotational states can become kinetically trapped. The energy gap between the lowest energy levels of ortho-NH3 and para-NH3 is ΔE/kB = 23.4 K, where kB is the Boltzmann constant, and therefore, the measured ortho-to-para abundance ratio provides an equilibration temperature (NH3 nuclear spin temperature, T spin) that sometimes is found to differ significantly from the Boltzmann temperature.40 However, to better interpret Tspin using NH3 as a probe molecule, detailed measurements of the NSC rate must be made under the conditions experienced by the NH3 molecules. One frequently used assumption is that NSC is rigorously forbidden, so that Tspin reflects the NH3 formation conditions.32,38,40,41 The degree to which the NSC rate is nonzero therefore provides the time frame over which information about the formation temperature is lost due to equilibration to the current conditions. As we show herein, the NSC rate of NH3 at temperatures below 2 K is high for NH3 molecules suspended in pH2 matrixes; however, the effective pressure experienced by an NH3 molecule under these conditions is many orders of magnitude greater than the ultrahigh-vacuum conditions of interstellar space. Nonetheless, these measurements at low temperature for pH2 matrixes provide important benchmarks for the development of the theoretical understanding of NSC in NH3 that ultimately should allow for better interpretation of NH3 astronomical observations.

spectrum, therefore, requires either comparison to sophisticated theoretical analysis or some other experimental handle that allows the monomer spectrum to be disentangled from all of the observed peaks. In some cases, the reversible temperature dependence of the rovibrational spectrum can be used to identify freely rotating monomer peaks.18 Alternatively, as in the case of CH4, slow NSC can be used, which allows the oneto-one relationship between nuclear spin symmetry and rotational symmetry to be exploited to unambiguously identify the different rotational states of the monomer. In the present work, we use the relatively slow NSC of NH3 trapped in solid pH2 as a tool to assign the sparse vibration− inversion−rotation (VIR) spectra and then to quantify the NSC rates for NH3 molecules trapped in solid pH2 at temperatures of around 2 K. Typically, rapid vapor deposition30,31 of a roomtemperature gas-phase dopant into a pH2 matrix results in rapid collisional cooling, and only transitions originating from the lowest rotational levels of the ground vibrational state can be detected using traditional FTIR spectroscopy. However, for molecules with identical nuclei such as NH3, this deposition process does not result in fast NSC, and thus, the populations of levels with different nuclear spin symmetries for the deposited molecule are roughly the same as the original room-temperature sample. For NH3, this implies that, immediately after deposition nearly 50% of the NH3 molecules reside in the |J,K⟩ = |1,1⟩ rotational level, which is the lowestenergy rotational state of para-NH3, and the remaining 50% populate the |J,K⟩ = |0,0⟩ level of ortho-NH3. Because NH3 freely rotates in solid pH2, one can easily resolve the different VIR transitions for these two nuclear spin isomers using highresolution FTIR spectroscopy (0.05 cm−1). Immediately after deposition, however, NSC begins to convert the para-NH3 molecules in the higher-energy rotational state to the ground rotational state of ortho-NH3. This means that the intensity of transitions from the |1,1⟩ level decreases with time after deposition and, conversely, the intensity of transitions from the |0,0⟩ level increases. By constructing IR difference spectra from spectra measured at short and long times after deposition, one can selectively identify only the peaks that are undergoing NSC and thereby disentangle the NH3 monomer spectrum from all of the observed absorption peaks. Further, the relative phase of the peak (negative versus positive) in the difference spectrum unambiguously identifies the ground-state rotational quantum numbers involved (|J,K⟩ = |1,1⟩ or |0,0⟩) for the different transitions, thus making the VIR assignments straightforward. This powerful experimental method combined with the short deposition times possible with the “rapid vapor deposition” method of Fajardo and Tam30,31 allows the transitions from the metastable |1,1⟩ rotational state to be identified easily, even though, as we will show, the intensity of these transitions decays with a single-exponential time constant of ∼500 s. We then used a similar experimental strategy to assign the rovibrational spectra of ND3. Another reason contributing to our decision to study the IR spectroscopy and NSC of NH3 trapped in solid pH2 is the important role that NH3 plays as a probe molecule in astrophysics.32 Indeed, NH3 was the first polyatomic molecule detected in the interstellar medium,33 which changed our picture of the universe from atomic to molecular, thereby launching astrochemistry as a new and exciting research area.34,35 The importance of NH3 in observational interstellar chemistry stems from (1) the high abundance of NH3 throughout the universe and (2) the pure rotational electric

2. EXPERIMENTAL METHODS Ammonia- (NH3- and ND3-) doped pH2 crystals were prepared using the rapid vapor deposition method developed by Fajardo and Tam.31,42 Here, we outline the general procedure and emphasize the specific details for these studies. The crystal was grown by codeposition of independent gas flows of ammonia and pH2 onto a precooled BaF2 optical substrate held at ∼2.5 K within a sample-in-vacuum liquid-He cryostat. The NH3 (Sigma-Aldrich, 99.9%) or ND3 (Sigma-Aldrich, 99% D) gas was introduced into the cryostat through a stainless steel tube equipped with a needle valve after repeated freeze−pump− thaw cycles. The NH3 (ND3) concentration in the pH2 samples was determined using the measured flow rates of dopant and pH2 gas. For these studies, the dopant concentration ranged from 10 to 100 ppm. The pH2 solids were prepared by enriching normal H2 gas to greater than 99.97% pH2 enriched levels using a variable-temperature ortho/para converter operated near 14.0 K. For the NSC studies reported here, the oH2 concentration in the sample can be checked using the integrated intensity of the oH2-induced Q1(0) feature31 and the measured crystal thickness.13 No attempt was made to study the oH2 concentration dependence on the NSC rate of NH3 or ND3; only highly enriched pH2 matrixes were investigated. 9713



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levels, and therefore, three distinct nuclear spin weights are possible, and the ortho−para labeling scheme is no longer appropriate.51 Accordingly, we use the ortho and para labels to discuss NH3, but the A and E symmetry labels to discuss ND3. 3.A. VIR Spectroscopy of NH3 in Solid pH2. As discussed in the Introduction, one of the main difficulties in making detailed rovibrational assignments of the IR spectrum of 14NH3 (hereafter NH3) trapped in solid pH2 is the presence of additional peaks in each spectral region that are likely due to NH3 clusters, such as NH3-(oH2)n, (NH3)2, or NH3−H2O. To better illustrate this problem, we show IR spectra in Figure 1 of

To create nonequilibrium concentrations of excited rotational states of NH3 and ND3 in the low-temperature-deposited pH2 sample, the deposition rate must be significantly greater than the NSC rate. Accordingly, in this work, we performed depositions at higher H2 flow rates (>500 mmol/h) than we typically use (250 mmol/h) in an effort to build up and detect VIR transitions from the metastable |1,1⟩ rotational state. Highresolution FTIR spectroscopy (0.05 cm−1) was performed on the sample using a normal-incidence transmission optical setup. Right after a deposition was stopped, repeated FTIR spectra were recorded in rapid-scan mode (e.g., acquisition times of 98 s for nine scans at 0.05 cm−1 resolution) using the minimum spectral resolution necessary to record the NH3 or ND3 rovibrational peaks in high fidelity. The FTIR spectrometer (Bruker IFS 120HR) used to record IR spectra was equipped with a glowbar source and a Ge-coated KBr beamsplitter. We used a liquid-nitrogen-cooled HgCdTe detector to record spectra from 700 to 3900 cm−1 at 0.05 cm−1 resolution and an InSb detector to record spectra from 1800 to 7000 cm−1 at 0.04 cm−1 resolution. The optical path outside the cryostat and spectrometer was purged with dry air to minimize atmospheric absorptions.

3. RESULTS AND DISCUSSION The VIR energy levels of ammonia have long fascinated and challenged spectroscopists.43−45 The barrier to inversion is approximately 1830 cm−1 and results in a ground-state tunneling splitting of 0.79 and 0.05 cm−1 for NH3 and ND3, respectively.46 In this work, we use a symmetric-top notation (ΔKΔJ(J″,K″) with tunneling labels s (symmetric) and a (antisymmetric) to specify the parity of the lower state with respect to inversion.47 Ammonia has six normal modes of vibration, two of which are of A symmetry (ν1 and ν2) and the other two of which are degenerate (ν3 and ν4) modes of E symmetry.48 The degenerate modes ν3 and ν4 therefore can have vibrational angular momentum as well, usually designated by the quantum number l. There are both parallel and perpendicular infrared bands for ammonia with the usual ΔK = 0, ΔJ = 0, ±1 and ΔK= ±1, ΔJ = 0, ±1 selection rules, but this also results in different s ↔ a and s ↔ s, a ↔ a tunneling selection rules.48 The various ammonia isotopomers have different possible nuclear spin wave functions to describe the indistinguishable H/D nuclei for the 3-fold rotational symmetry of the intramolecular potential. Each VIR level of ammonia therefore combines with just one nuclear spin wave function of a specific symmetry to satisfy the Pauli principle. For NH3 with three identical H nuclei (fermions), the nuclear wave functions for NH3 in levels with K = 0, 3, 6, ..., have A symmetry, and the levels with K = 1, 2, 4, 5, ..., have E symmetry.49 Traditionally, the nuclear spin wave functions with A symmetry are denoted as ortho levels, and the levels with E symmetry are denoted as para levels.50 This shorthand notation for labeling the nuclear spin symmetries of ortho-NH3 (A, I = 3/2, gI = 12) and paraNH3 (E, I = 1/2, gI = 6) is prevalent throughout the literature. One of the interesting outcomes of the NH3 nuclear spin statistics, and also the reason that the ortho and para labels are appropriate, is that all of the VIR states with A1′ and A1″ symmetries are missing or have zero nuclear spin weights; there is no nuclear spin wave function of the appropriate symmetry to be paired with these particular VIR levels to satisfy the Pauli principle.49 In contrast, for ND3, which involves three equivalent deuterons (bosons), there are no missing VIR

Figure 1. IR spectra of an NH3-doped pH2 sample {[NH3] = 31 ppm, [oH2] = 140 ppm, d = 0.23(1) cm] recorded at 1.8 K in the ν2 region (a) immediately after deposition was stopped and (b) 88 min later. Spectrum a is the average of 9 scans at 0.05 cm−1 resolution for a total acquisition time of 98.3 s, and spectrum b is an average of 64 scans with an acquisition time of 724.7 s. Note that the spectra are offset and the strong aR(0,0) peak in trace b is artificially cut off at 0.65 to prevent overlap.

NH3 trapped in solid pH2 in the region of the ν2 symmetric bend (the umbrella mode). Trace a of Figure 1 is the spectrum recorded at 1.8 K immediately after deposition is stopped, and trace b is the spectrum of the same sample recorded 88 min later. There are numerous peaks in this region. Assuming that only the |0,0⟩ a and |1,1⟩ s/a rotational states of ortho-NH3 and para-NH3, respectively, are populated right after deposition, we expect to observe the aR(0,0) transition for ortho-NH3 and the aQ(1,1), sQ(1,1), aR(1,1), and sR(1,1) VIR transitions of paraNH3.52 It is easy to tentatively assign the most intense peak in the spectrum to the aR(0,0) transition of ortho-NH3. This peak at 968.07 cm−1 is always the dominant peak in this region even for samples where the NH3 concentration is substantially reduced. The peak at 949.35 cm−1, which is observed only in trace a and not in trace b, is likely the aQ(1,1) peak of paraNH3. This peak is reasonably sharp and falls in a region where it decays to zero-baseline values as the |1,1⟩ rotational state of para-NH3 slowly converts to the lower-energy |0,0⟩ rotational state of ortho-NH3. Given this tentative assignment, we expect to observe approximately three additional VIR transitions from the |1,1⟩ rotational state of para-NH3. There are a number of unassigned peaks in this region, some even at approximately the right peak positions for the missing VIR transitions. However, by constructing difference spectra recorded at short and long time delays after deposition, we can selectively identify only the VIR transitions that are due to NH3 monomers. Some of the peaks in Figure 1 are therefore likely cluster peaks of NH3 with oH2; however, we will not assign these cluster peaks in this work and rather focus only on the freely rotating NH3 monomer transitions. 9714



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VIR transitions sQ(1,1), aR(1,1), and sR(1,1), which make detection of these peaks more difficult using high-resolution FTIR spectroscopy; in fact, these peaks were more easily detected in FTIR spectra for which we intentionally degraded the resolution. A similar behavior was observed in the IR depletion spectra of NH3 monomers trapped in He droplets.52 Both the relatively sharp aR(0,0) and aQ(1,1) VIR transitions terminate on upper levels where there is no possibility of rotational or tunneling relaxation. For example, the aR(0,0) transition terminates on the |1,0⟩ s level, which is the lowestenergy rotational level because the |0,0⟩ a VIR state is anomalously higher in energy because of the large tunneling splitting in the ν2 = 1 excited vibrational state. Similarly, the aQ(1,1) transition terminates on the |1,1⟩ s level, which is the lower tunneling component of the lowest rotational state in the para-NH3 upper vibrational state. Therefore, because these two excited VIR states can relax only through vibrational relaxation, the peaks are not significantly broadened by energy−time uncertainty due to the relatively long vibrational relaxation times of molecules embedded in solid pH2.9 In contrast, the sQ(1,1) transition accesses the upper tunneling component of the lowest rotational state and can relax to the lower tunneling component, approximately 35.58 cm−1 lower in energy in the gas phase.44 Similarly, both the sR(1,1) and aR(1,1) transitions access different tunneling components of the |2,1⟩ rotational state and, therefore, can relax by rotational and/or tunneling relaxation. Interestingly, the sR(1,1) transition is significantly broader than the aR(1,1) transition, which might imply that tunneling relaxation is faster than rotational relaxation. Using the same difference spectrum in Figure 2, we can now move to the region of the ν4 antisymmetric bend and make additional assignments. In this case, the tunneling splitting in the v4 = 1 excited state is comparable to that in the ground vibrational state,54 and the tunneling selection rules have changed to a ↔ a and s ↔ s; therefore, we do not expect to resolve separate peaks for the different tunneling components. Accordingly, we look for one positive peak for ortho-NH3 and three negative peaks for para-NH3. Shown in Figure 3 is the NH3 ν4 difference spectrum that has three negative peaks due to para-NH3 and one positive peak due to ortho-NH3. We assign the three negative peaks to the spP(1,1), spQ(1,1), and srR(1,1) transitions and assign the one positive peak to the arR(0,0) transition of ortho-NH3. In this case, ν4 is a perpendicular band, and therefore, we include the additional

We constructed difference spectra by subtracting the spectrum recorded at long times after deposition from that measured immediately after deposition; therefore, all of the negative peaks are due to para-NH3, and all of the positive peaks are due to ortho-NH3. The NH3 ν2 difference spectrum generated from the two spectra in Figure 1 (trace b − trace a) is shown in Figure 2 over the same spectral region. Now, four

Figure 2. IR difference spectrum in the NH3 ν2 region generated from the spectra in Figure 1 showing the four allowed para-NH3 peaks (negative) and the one allowed ortho-NH3 peak (positive). The assignments of the transitions are shown using the notation ΔK ΔJ(J″,K″) and the a and s inversion tunneling symmetry labels.

negative peaks and only one positive peak are evident. The one positive peak corresponds to the single expected aR(0,0) transition for ortho-NH3, as already tentatively assigned. There is only one peak for ortho-NH3 in this region because only one of the tunneling levels is allowed in the K = 0 manifold for each rotational state. Further, ν2 is a parallel band, and only the aR(0,0) transition is possible. Note that, in the gas phase,44 the first excited ortho-NH3 state |1,0⟩ s is 19.89 cm−1 higher in energy and, therefore, has negligible population at 1.8 K. Four negative peaks need to be assigned; the one near 949.35 cm−1 is assigned to the aQ(1,1) transition, and the three additional peaks are assigned to the sQ(1,1), aR(1,1), and sR(1,1) transitions of para-NH3. Some of the peaks assigned to paraNH3 have broad line widths, and all fall in regions where it is difficult to pick them out in the raw absorption spectra because of overlap with nonmonomer absorptions. The VIR assignment of the difference spectrum was accomplished by inspection under the assumption that the peaks are not too shifted from the gas-phase values.53 Note that the small positive and negative peaks in the difference spectrum in Figure 2 on the low-energy side of the main aR(0,0) absorption are not due to NH3 monomers. The added piece of information not contained in just a single difference spectrum is the time evolution in the intensity of these peaks; these small difference peaks have very different time dependence behaviors, which means that they can be ruled out as potential NH3 monomer peaks. Thus, by using the correlated decay and enhancement of the intensity of all of the para-NH3 and ortho-NH3 peak with time that accompany NSC, difference spectra can be used as an effective means to assign the NH3 monomer spectra. The five NH3 VIR peaks shown in the difference spectrum display a range of widths from 0.28 to ∼5 cm−1. Indeed, early in this investigation, we detected the sharp aQ(1,1) peak, but we were puzzled as to why we did not observe any other transitions from the |1,1⟩ rotational state of para-NH3. Part of the reason is the broad line widths associated with the three

Figure 3. IR difference spectrum in the NH3 ν4 region generated from the spectra in Figure 1 showing the three allowed para-NH3 peaks (negative) and the one allowed ortho-NH3 peak (positive). This is a perpendicular band and has different selection rules than the ν2 parallel band shown in Figure 2. 9715



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superscript to indicate the ΔK = ±1 selection rule. Note that, although the assignment of the spQ(1,1) peak seems tentative based on the one difference spectrum shown in Figure 3, examination of the full series of difference spectra allows even peaks with low signal-to-noise ratios such as spQ(1,1) to be definitively assigned based on groupings of the peaks with similar decay kinetics. To illustrate the power of this approach, we show in Figure S1 in the Supporting Information multiple difference spectra recorded right after deposition, which clearly indicate that the three peaks assigned to para-NH3 decay in similar fashions. As for the ν2 region, we can reject a number of the weaker peaks simply because they do not show the same decay behavior as the peaks assigned to the NH3 monomer. For example, the weak negative peaks on either side of the spQ(1,1) feature and the small and broad positive peak near 1625 cm−1 are all clearly not due to the NH3 monomer and are most likely due to NH3 clustered to oH2. Only one tunneling level is allowed for the lower |0,0⟩ a VIR state of ortho-NH3, and thus, we can assign a tunneling label to this peak. As we will show for the ν1 band, the population of the two tunneling levels of the |1,1⟩ rotational state of para-NH3 is strongly weighted toward the lower tunneling level by Boltzmann statistics at 1.8 K. Thus, although we did not spectroscopically resolve both tunneling components of the para-NH3 peaks in the ν4 band, we can assign the peaks to the greater-intensity transition from the lower tunneling level. However, expanded views of the sharpest spP(1,1) peak near 1608.3 cm−1 do show evidence of two closely overlapping peaks (see Figure S2 in the Supporting Information). The lowerenergy peak has a greater intensity than the higher-energy peak, consistent with the energetic ordering of the two tunneling components of the pP(1,1) transition in the gas phase54 and the greater thermal population of the lower (s) tunneling component in the lower |1,1⟩ rotational state. All of the peaks assigned to NH3 in the ν2 and ν4 regions are listed in Table 1. As in the ν2 region, the para-NH3 VIR peaks have varying line widths. The spP(1,1) peak accesses the |0,0⟩ s VIR state in the upper v4 = 1 vibrational state, which is the lowest rotational state, and thus, this is the sharpest para-NH3 peak (∼0.17 cm−1) in this region. Both the spQ(1,1) and srR(1,1) peaks are significantly broader. The srR(1,1) peak is the narrower [1.517(1) cm−1] of the two, likely because the upper state is the lowest J rotational state for the K = 2 manifold and thus can rotationally relax only through ΔK = −2 collisions with the matrix. In a separate experiment, a difference spectrum was generated from spectra recorded in the 3-μm region using the InSb detector. The NH3 concentration in this sample was slightly greater ([NH3] = 45 ppm), allowing us to measure the weaker VIR transitions associated with the 2ν4, ν1, and ν3 vibrations. Detailed assignments of these VIR bands are helpful because these same three bands were investigated52 in studies of NH3 embedded in He nanodroplets, permitting direct comparison between the two quantum matrixes. The difference spectrum in the 3-μm region is shown in Figure 4. In the case of the 2ν4 band, only the strong arR(0,0) peak of ortho-NH3 is observed, along with a weaker negative peak tentatively assigned to the srR(1,1) peak of para-NH3. In the region of the ν1 symmetric stretch, three negative peaks and one positive peak are detected. The ν1 band is a parallel band with the tunneling selection rules a ↔ s such that each rovibrational transition is split into two with the splitting equal to the sum of

Table 1. Peak Positions and Widths (fwhm) of NH3 Trapped in Solid pH2 at 1.8 K peak position (cm−1) band

transition

gasa

pH2

width

shift

ν2 ν2 ν2 ν2 ν2 ν4 ν4 ν4 ν4 ν4 ν4 2ν4 2ν4 ν1 ν1 ν1 ν1 ν3 ν3 ν3 ν3 ν1+ν2 ν2+ν3 ν1+ν4 ν3+ν4 ν3+ν4 ν3+ν4 ν1+ν3

aQ(1,1) aR(0,0) sQ(1,1) aR(1,1) sR(1,1) spP(1,1) apP(1,1) spQ(1,1) arR(0,0) arR(0,0) srR(1,1) arR(0,0) srR(1,1) aQ(1,1) sQ(1,1) aR(0,0) sR(1,1) spP(1,1) spQ(1,1) arR(0,0) srR(1,1) aR(0,0) arR(0,0) arR(0,0) spP(1,1) arR(0,0) srR(1,1) arR(0,0)

931.63 951.78 968.00 971.88 1007.54 1610.10 1610.41 1630.46 1646.49 1646.49 1661.12 3251.78 3258.18 3335.17 3336.95 3355.01 3376.32 3427.46 3446.99 3458.62 3470.75 4313.47 4450.00 4975.60

949.35 968.07 976.5 986.7 1012.0 1608.25 1608.38 1625.4 1641.60 1641.78 1655.67 3244.83 3251.3 3328.59 3329.62 3345.4 3366.2 3420.14 3436.6 3449.51 3460.87 4320.16 4448.33 4964.27 5026.31 5053.56 5062.43 6609.64

0.38 0.28 2.2 2.0 5.0 0.17 0.14 − 0.05 0.05 1.3 0.19 − 0.43 0.35 4.8 − 0.79 − 0.40 1.2 0.64 0.73 0.41 0.71 0.54

+17.72 +16.29 +8.5 +14.82 +4.46 −1.85 −2.03 −5.06 −4.89 −4.71 −5.45 −6.95 −6.88 −6.58 −7.33 −9.61 −10.12 −7.32 −10.39 −9.11 −9.95 +6.69 −1.67 −11.33

0.81

−14.84

5065.79 6624.48

−12.23

ν2 values from ref 53; ν4 values from ref 54; 2ν4, ν1, and ν3 values from ref 55; and combination bands from ref 56.

a

the tunneling splittings for the lower and upper vibrational states.55 However, in the case of the one positive peak, the lower |0,0⟩ s level is missing, and thus, the one positive peak is assigned to aR(0,0). Interestingly, the aR(0,0) peak in the ν1 region is considerably broader (1.8 cm−1) than the aR(0,0) peak in the ν2 region. Once again, this experimental observation can be explained by facile rotational relaxation of the excited state by collisions with the matrix. In the case of the ν2 band, the tunneling splitting is so large in the v2 = 1 excited state that the |1,0⟩ s state is lower in energy than the |0,0⟩ a state. In contrast, in the ν1 region, the tunneling splitting in the v1 = 1 excited state is much smaller,55 and the |1,0⟩ s state can relax to the lower-energy |0,0⟩ a state. The aR(0,0) peak in the ν1 region was similarly observed to be broad [1.25(5) cm−1] in the IR depletion measurements of NH3 in He nanodroplets.52 The two negative peaks near 3229 cm−1 in the ν1 region are sharp (0.59 and 0.34 cm−1) and can be assigned to the a/s tunneling components of the Q(1,1) peak. Again rotational relaxation is not feasible for these upper states, and the corresponding line shapes are narrow. Similarly, the same aQ(1,1) and sQ(1,1) peaks were determined to have 0.35(5) and 0.33(1) cm−1 widths, respectively, in the He droplet studies, which are comparable to the laser line width (0.3 cm−1).52 Indeed, the relative intensity of these two peaks can be analyzed to determine the relative populations in the lower and upper tunneling levels in the metastable para-NH3 |1,1⟩ VIR state, and the splitting between these two peaks can be used to 9716



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Figure 5. IR difference spectrum in the ND3 ν2 region generated from the spectra for a ND3-doped pH2 sample {[ND3] = 44 ppm, [oH2] = 70 ppm, d = 0.28(1) cm} recorded immediately after deposition (16 scans, 178 s) and 120 min after deposition (64 scans, 724.6 s). Transitions from the E nuclear spin state are negative, and transitions from the A nuclear spin state of ND3 are positive.

assigned to transitions from the |0,0⟩ rotational state of the A nuclear spin state. Based on these initial groupings, the specific VIR assignments were made using the well-known gas-phase transition frequencies.51,58 The two positive peaks measured in the ND3 ν2 difference spectrum can be assigned to the two tunneling components of this specific transition. These two peaks can be resolved in the ν2 band because the tunneling splitting increases significantly (e.g., from 0.05 to 3.55 cm−1) in the v2 = 1 excited state.58 Although the relative intensities of the two transitions cannot be measured quantitatively because the sR(0,0) transition is saturated in the IR absorption spectra used to generate the difference spectrum, the aR(0,0) transition is considerably weaker, consistent with the expected 10:1 nuclear spin weights for the lowest two inversion tunneling levels of the |0,0⟩ VIR state.51 Both tunneling components of the Q(1,1) transition are also resolved. In this case, the 8:8 nuclear spin weights for the two tunneling levels of the |1,1⟩ state are equal, and because the 0.04 cm−1 tunneling splitting is small compared to the 1.8 K temperature of the sample, the two tunneling states have approximately the same population.51 The assigned ND3 VIR transitions are listed in Table 2. In the ν4 region for ND3, as shown in the difference spectrum in Figure 6, there are three negative peaks and one positive peak that can be assigned to ND3 monomers. In this case, the small inversion splittings for ND3 in the v4 = 1 excited state combined with the inversion tunneling selection rules for the perpendicular ν4 vibrational mode result in no resolved tunneling components. However, we did detect three different VIR transitions for the E nuclear spin state of ND3 that we later used to determine the NSC rate constant. We resolved a splitting in the rR(0,0) transition, but the relative intensities of the two components did not match the expected 10:1 nuclear spin weights for the two tunneling components. Therefore, we believe that the measured splitting is due to a breaking of the MJ degeneracy of the upper |1,1⟩ VIR state and not a resolved tunneling splitting. A similar splitting in the same VIR transition for NH3 was also observed. Once again, the unassigned negative and positive peaks in the ν4 difference spectrum in Figure 6 are not due to ND3 monomers because they evolve in time with a different rate constant than the peaks assigned to ND3. In addition to the peaks observed for ν2 and ν4, peaks for the ν3 and ν4 vibrational modes were also detected and assigned. All of the peaks assigned to ND3 are presented in Table 2.

Figure 4. IR difference spectrum in the 3-μm region generated from the spectra for an NH3-doped pH2 sample {[NH3] = 45 ppm, [oH2] = 50 ppm, d = 0.24(1) cm} recorded at 1.8 K. The three spectra labeled a−c show the ν3, ν1, and 2ν4 regions, respectively, of the spectrum, along with detailed assignments for the ortho-NH3 (positive) and paraNH3 peaks (negative).

directly determine the sum of the inversion splitting in both the lower and upper vibrational states.52 A representative fit is shown in Figure S3 in the Supporting Information, and from the fitted peak areas measured at 1.8 K, the ground-state tunneling splitting is determined to be 0.81(2) cm−1. This value of the ground-state splitting is, within experimental error, equivalent to the gas-phase value55 of 0.79 cm−1. The relative intensities of the aQ(1,1) and sQ(1,1) peaks at 1.8 K also allow the single broad peak observed near 3366.2 cm−1 to be assigned to the sR(1,1) transition from the more populated |1,1⟩ s lower tunneling level. Finally, three negative peaks and just the one positive peak are observed in the region of the ν3 antisymmetric stretch. The ν3 band is a perpendicular band with the tunneling selection rules s ↔ s, a ↔ a.55 As for the ν4 perpendicular band, the one positive peak is assigned to the arR(0,0) transition of ortho-NH3, and the three negative peaks are assigned to transitions from the |1,1⟩ s lower tunneling level. In addition, we used this assignment strategy to assign the sharp lines for about five combination bands56 of NH3 up to around 7000 cm−1 and all assignments are presented in Table 1. 3.B. VIR Spectroscopy of ND3 in Solid pH2. We next employed this same methodology to assign the VIR spectra of ND3 trapped in solid pH2. The ND3 isotopomer is interesting because there are no missing VIR levels; the inversion tunneling splitting is greatly reduced (0.05 cm−1);57 and the rotational constants have decreased significantly such that, even at 1.8 K, there should be some equilibrium population of ND3 in excited rotational states of the E spin isomer. Further, to our knowledge there are no previous measurements on the NSC rate for this isotopomer. Shown in Figure 5 is the difference spectrum for ND3 in the ν2 region. In this case, we observe approximately three negative peaks and two positive peaks. Analogous to NH3, the negative peaks in the ND3 difference spectrum are assigned to transitions from the |1,1⟩ rotational state of the E nuclear spin state, and the positive peaks are 9717



Article g m Evib − Evib = aR(0, 0)m − aR(0, 0)g − 2(Bm − Bg ) 1 + (Δm − Δg ) 2

Table 2. Peak Positions and Widths (fwhm) of ND3 Trapped in Solid pH2 at 1.8 K peak position (cm−1)

a

band

transition

gasa

pH2

width

shift

ν2 ν2 ν2 ν2 ν2 ν2 ν4 ν4 ν4 ν4 ν4 ν1 ν1 ν3 ν3 ν3 ν3

aQ(1,1) sQ(1,1) aR(0,0) sR(0,0) aR(1,1) sR(1,1) p P(1,1) p Q(1,1) r R(0,0) r R(0,0) r R(1,1) Q(1,1) R(0,0) p P(1,1) p Q(1,1) r R(0,0) r R(1,1)

745.49 749.08 755.79 759.37 765.97 769.53 1182.23 1192.68 1200.96 1200.96 1209.14 2420.33 2430.63 2555.65 2565.80 2571.28 2576.62

754.99 757.43 764.71 767.05 774 777.3 1180.21 1190.16 1197.87 1198.19 1206.04 2415.5 2425.2 2549.6 2559.0 2564.41 2569.3

0.51 0.45 0.36 0.50 − − 0.54 0.5 0.3 0.3 − − 0.2 0.3 − 0.49 0.5

+9.50 +8.35 +8.92 +7.68 +8.03 +7.77 −2.02 −2.52 −3.09 −2.77 −3.10 −4.83 −5.43 −6.05 −6.80 −6.87 −7.32

(1)

where the superscripts m and g stand for the matrix and gasphase values, respectively. The calculated values along with values for the gas phase and other matrixes are listed in Table 3. Table 3. Physical Constants (cm−1) Derived from the ν2 Bands of NH3 and ND3 shifta

B

Δ

9.97 9.11 9.9 8.6 8.9

36.37 27.15 34.5 21.8 23.6

5.22 4.9 − − −

3.60 2.4 − 2.7 1.7

NH3 gasb pH2 Hec Ned Are

0 13.4 2.1 4.9 18.6

gasb pH2 Hec Ned Are

0 9.0 − − −

ND3

ν2 and ν4 values from ref 58; ν1 and ν3 values from ref 51.

Shift = aR(0,0)m − aR(0,0)g + 1/2(Δm − Δg) − 2(Bm − Bg), where m indicates matrix and g indicates gas. bNH3 from ref 53; ND3 from ref 58. cReference 52. dReference 23. eReferences 21 and 22. a

One can clearly see from Table 3 that the ν2 vibrational frequency is shifted to higher energies in all of the matrixes. The measured blue shift is anomalous and is a defining feature of VIR transitions that involve ν2 excitation. The known vibrational dependence59 for the NH3 dipole moment μ predicts, assuming that electrostatic induction is the dominant intermolecular interaction between NH3 and the matrix,27 a blue shift (i.e., a decreases in |μ|) upon ν2 excitation consistent with experiment. Indeed, this electrostatic-induction-caused matrix shift should scale with the polarizability of the matrix host. A plot of the measured vibrational shift versus the polarizability60 of the matrix host shows an interesting trend as displayed in Figure 7. The three rare-gas matrix values all fall on a straight line with a slope of 11.38(19) cm−1 per 10−24 cm3. This suggests that the matrix-induced shift for all three rare-gas matrixes is electrostatic induction and is not especially sensitive

Figure 6. IR difference spectrum in the ND3 ν4 region generated from the same spectra as used in Figure 5. There are three allowed transitions from the E nuclear spin state and one allowed transition from the A nuclear spin state of ND3. The unlabeled peaks are not due to ND3 monomers.

3.C. Matrix Shifts, Rotational Constants, and Inversion Tunneling Splittings. We wanted to quantify the changes in the vibrational, rotational, and inversion tunneling constants for both NH3 and ND3 for the molecules solvated in solid pH2. However, the net shift in the aR(0,0) VIR peak position upon solvation is due to a combination of changes to the upper-state B rotational constant, the lower- and upper-state tunneling splittings, and the matrix shift of the vibrational frequency. To decouple the three contributions, we established a protocol to evaluate the various quantities. For the analysis of the ν2 band, we calculated the upper-state rotational constant by taking the difference between the R(1,1) and Q(1,1) peak positions averaged over the two tunneling components [R(1,1)avg − Q(1,1)avg = 4B]. We determined the sum of the tunneling splittings in the lower and upper states by taking the difference in the tunneling components of the Q(1,1) transitions [δ0 + δ1 = Δ = sQ(1,1) − aQ(1,1)]. Once we had obtained the two quantities B and Δ, we determined the shift in the vibrational frequency using the formula

Figure 7. Plot of the determined ν2 vibrational shift as a function of the polarizability of the matrix host. The data points for the three raregas atom fall on a line (y=mx, where m = 11.38(19) cm−1 per 10−24 cm3), but the measured blue shift in the pH2 matrix is greater than the trend line. 9718



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predict that the tunneling splitting measured in Ne should be greater than that in either pH2 or Ar. However, once again, this analysis does not take into account the size of the solvation site, such that, if the NH3 molecules can occupy a larger solvation site, the tunneling splitting is greater. Rotational isomerization studies of a dopant trapped in a series of low-temperature matrixes has shown that the tunneling rate from a high-energy isomer to a lower-energy isomer scales with the polarizability of the matrix for formic acid, but not acetic acid.65 As pointed out in that case, tunneling in polyatomic molecules is inherently multidimensional, and thus, simple trends can be deceptive. These two cases of tunneling are not exactly equivalent: isomerization tunneling is between two conformations that differ significantly in energy, whereas the NH3 inversion tunneling motion is an example of resonance tunneling between two nearly degenerate energy levels. Nonetheless, understanding how the solvent perturbs the tunneling rates is an important area of research. Especially considering that advances in calculating tunneling splittings using molecular dynamics might soon make it possible to study these same benchmark systems from first principles.66 3.D. NH3-Induced IR Activity and Cooperative Transition. Dopant-induced IR activity and dopant−host cooperative absorptions in solid pH2 have been reported previously.18,26,27,30,67−69 Figure 8 shows the dependence of the

to the superfluid nature of the liquid helium droplets. However, the vibrational shift measured for solid pH2 does not follow this simple empirical correlation and, instead, has a larger blue shift than predicted given the polarizability of pH2. This suggests that, although electrostatic induction is causing the majority of the blue shift, there is another contribution to the blue shift in solid pH2 that is not present in the rare-gas matrixes. Note also that the determined blue shift for NH3 is roughly 1.5 times greater than that for ND3. There are likely two contributions to this difference: First, the magnitude of the shift usually scales with vibrational frequency,61 resulting in a factor of 1.27 greater shift in ν2 for NH3 compared to ND3. Second, the anomalous change in dipole moment associated with ν2 excitation leads to a further reduction in the shift for ND3. The change in dipole moment in the ground and excited ν2 vibrational states is strongly correlated to the magnitude of the inversion splitting.62 Therefore, because the inversion splitting in ND3 is much smaller than that in NH3, the change in dipole moment with ν2 vibrational excitation is about a factor of 2 smaller for ND3 (Δμ = −0.14 D) compared to NH3 (Δμ = −0.23 D), resulting in a smaller blue shift for ND3. Next, one can see from Table 3 that the matrix-induced perturbations to the rotational and inversion tunneling motions of NH3 are smallest for the two quantum matrixes. The rotational B values determined for NH3 solvated in liquid He and solid pH2 are 99.3% and 91.4%, respectively. For liquid He droplets, the combination of superfluidity and extremely weak intermolecular forces is responsible for the barely perturbed rotational motion of the dopant.63 The nearly free rotation in solid pH2 is likely due to inflation of the single-substitution solvation site by the extensive zero-point motion of solid pH2 even at 1.8 K and the angularly flat potential energy surface for a single substitution site.9−13 For Ne and Ar matrixes, the B rotational constant is 86% and 89%, respectively, of the gasphase value.21−23 The NH3 molecule still freely rotates, and in this case, it is likely the size of the single-substitution site that results in the slightly greater B value for NH3 in Ar compared to Ne. This finding for NH3 underscores an important point that sometimes is missed, namely that free rotation of dopants in solid pH2 is nearly equivalent to rare-gas matrix results. Molecules that do not freely rotate in rare-gas matrixes are also unlikely to rotate in solid pH2 matrixes, and vice versa. The last figure of merit is how the different matrixes perturb the inversion tunneling motion in NH3. Note once again that the inversion tunneling splittings for NH3 solvated in the two quantum matrixes He and pH2 are 94.9% and 74.6%, respectively, of the gas-phase values, whereas the corresponding values in Ne and Ar are 60.0% and 64.9%. Once again in terms of matrix isolation spectroscopy, the liquid-helium droplets are superior, but the difference between solid pH2 and the other solid matrixes is greater for the inversion tunneling motion compared to rotation. Comparison of the Ne and Ar tunneling splittings suggests that the greater size of the solvation site, not the strength of the intermolecular interactions, has the greater influence on preserving the inversion tunneling motion. The magnitude of the sum of inversion splittings offers a unique test of the matrix properties. One interpretation would be that the effective barrier to inversion is likely increased for NH3 solvated in a particular matrix, specifically, the pyramidal geometries (up or down) with sizable permanent electric dipole moments64 are solvated to a greater extent than the planar transition state (μ = 0) structure, and consequently, the inversion barrier is increased and the tunneling splitting decreases. This would

Figure 8. IR and difference spectra for the sample depicted in Figure 4 in the region from 4130 to 4180 cm−1. The NH3-induced Q1(0) and Q1(1) transitions are labeled along with the Q1(0) pH2 + aR(0,0) ortho-NH3 cooperative transition. The negative and positive peaks in the difference spectra are induced by para-NH3 and ortho-NH3, respectively.

NH3-induced IR absorptions with NSC of the NH3 dopant. The sharp peaks centered around 4149 cm−1 correspond to the ortho-NH3- and para-NH3-induced Q1(0) peaks of the pH2 host. These sharp peaks (∼0.04 cm−1) are likely instrumentlimited and correspond to the Q1(0)-induced IR transition (v,J = 1,0 ← 0,0) of pH2 molecules that are nearest neighbors of the NH3 dopant. Intermolecular interactions between the NH3− pH2 pair induce a transition dipole moment very similar to that of collision-induced absorption in the gas phase. The Q1(0) transition is absent in pure pH2 solids but acquires oscillator strength in pH2 solids doped with NH3, and thus the intensity of this feature directly reflects the NH3 concentration.18 The NH3−pH2 intermolecular interaction also shifts the vibrational 9719



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increased separation between these features implies that the ortho-NH3 interaction with oH2 is significantly greater than that with pH2. This also means that the greater oH2−ortho-NH3 attractive intermolecular interaction leads to preferential formation of these clusters at low temperature. To our knowledge, no high-resolution gas-phase studies of H2−NH3 clusters have been reported in the literature; however, the dimer was studied in a Ne matrix.71 That matrix isolation study reported that oH2−NH3 complexes readily form where it is believed the H2 coordinates with the lone-pair electrons on the NH3 molecule to form a complex in which the H2 bond axis is aligned along the 3-fold symmetry axis of the NH3.71 Further, the oH2 molecule in this complex “exhibits a relatively prominent infrared absorption”.71 Therefore, we ascribe the anomalously large splitting between the ortho-NH3-induced Q1(0) and Q1(1) features and the prominent ortho-NH3induced Q1(1) features to a strong intermolecular interaction between oH2 and ortho-NH3. The more interesting peak in terms of the present study is the broad cooperative peak centered at 4165.52 cm−1. This cooperative peak corresponds to the Q1(0) pH2 + aR(0,0) NH3 double transition in which the dopant undergoes a rotational transition simultaneously as a pH2 molecule is vibrationally excited. Similar cooperative transitions have been observed for other small molecules that freely rotate in solid pH2.18,27,67 Thus, this cooperative transition provides information on the pure rotational transition of the ortho-NH3 dopant, but is upshifted by the vibrational frequency of the pH2 molecule from the far-IR to the near-IR region. Rigorously, this is the pure rotational transition for an ortho-NH3 molecule next to a vibrational excited pH2 molecule. For our purposes, however, it will serve as a spectroscopic model of the aR(0,0) pure rotation−inversion transition of ortho-NH3 embedded in solid pH2. We can estimate the approximate rotation−inversion transition frequency from the difference between the peak position of the cooperative transition and the ortho-NH3induced Q1(0) transition to be 16.79 cm−1. This value compares favorably with the 19.89 cm−1 gas-phase value,44 and the measured transition energy reflects changes in both the ground vibrational state tunneling splitting and the rotational constant for NH3 isolated in pH2. However, one of the striking features of the cooperative transition is the line shape and breadth (2.96 cm−1) of the peak. The line shape of the cooperative transition is reminiscent of some of the VIR transitions of NH3 where facile rotational relaxation is possible. That is, there is likely an energy−time homogeneous contribution to the observed width, but additionally, there is a clear asymmetry to the line shape that shows a low-energy shoulder and a high-energy tail. This asymmetry signals inhomogeneous contribution as well. Regardless of the details, the peak identified with the pure rotation−inversion transition to the |1,0⟩ s state of the ortho-NH3 monomer (positive peak in the difference spectrum) displays a very broad asymmetric line shape. This indicates that, although the ortho-NH3 molecule can still freely rotate in solid pH2, the |1,0⟩ s excited rotational state is significantly broadened and perturbed by interactions of the NH3 with the solid pH2 matrix. In other words, the rotating ortho-NH3 molecule is not in a well-defined eigenstate but rather a superposition state in which the mixing coefficients are constantly modulated by intermolecular interactions of the NH3 and pH2 quantum solid. 3.E. Nuclear Spin Conversion. Now, we can quantify the rates of NSC for both NH3 and ND3 using the repeated FTIR

frequency of the neighboring pH2 molecules to lower energies such that the vibration gets shifted to below the Q1(0) vibron band of solid pH2.18,27 This shift in the excited-state vibrational energy therefore breaks the coupling to the vibron band, and the absorption is localized on pH2 molecules next to the NH3 dopant.70 This also has the effect of making the NH3-induced Q1(0) line extremely sharp. By using the difference spectrum generated in the same way as the difference spectra used to assign the VIR transitions of NH3, we can assign which NH3 nuclear spin isomer is inducing the Q1(0) feature. For example, two peaks in the region of the Q1(0) features are negative peaks in the difference spectrum, whereas only one is positive, as shown in Figure 8. The positive peak in this region must therefore be induced by the ortho-NH3 spin isomer because the concentration of ortho-NH3 is increasing with time after deposition. This allows the peak at 4148.73 cm−1 to be assigned to the ortho-NH3-induced Q1(0) peak. The two negative peaks in the difference spectrum identify the para-NH3-induced Q1(0) features at 4147.47 and 4147.89 cm−1. These para-NH3-induced Q1(0) peaks are also noticeably broader (0.26 and 0.23 cm−1) than the ortho-NH3induced Q1(0) features, and in expanded views, they appear as doublets with the higher-energy component greater in intensity (see Figure S4 in the Supporting Information for an expanded view). The measured widths of the NH3-induced Q1(0) peaks are also consistent with the assignment; the ortho-NH3 molecule in a |0,0⟩ a rotational state has no electrostatic moments that survive rotational averaging, and thus, the sharp Q1(0) feature is characteristic of short-range induction (overlap-induced).27 In contrast, the para-NH3 molecules in a |1,1⟩ rotational state have electrostatic moments that survive rotational averaging over the angularly anisotropic rotational wave function such that longer-range electrostatic induction is operative. Typically, electrostatic induction by a nonspherical perturber results in greater widths of the induced Q1(0) features; very similar results were measured for the ortho-H2Oand para-H2O-induced Q1(0) features.27 Note also that the peaks in this region whose intensities remain constant (not observed in the difference spectrum) are most likely induced by NH3 clusters. An electrostatic induction mechanism relies on the magnitude of the electrostatic moments of the dopant, which, if enhanced in a cluster species [i.e., (NH3)2], can lead to observable cluster-induced Q1(0) features even though the cluster concentration is much less than the monomer concentration. The peaks centered around 4135 cm−1 are the NH3-induced Q1(1) transitions of oH2 impurities clustered to NH3. The intramolecular vibration−rotation interaction in H2 shifts the J = 1 excited-state vibrational energy to lower energy, and thus dopant-induced Q1(1) transitions are usually around 7−10 cm−1 lower in energy than the dopant-induced Q1(0) features.18,69 In this case, no negative peaks corresponding to oH2−para-NH3 are observed in the Q1(1) region, likely because of signal-to-noise limitations. However, there are two closely spaced ortho-NH3-induced Q1(1) peaks assigned at 4134.96 and 4135.18 cm−1 and shown in an expanded view in Figure S4 (Supporting Information). The small splitting in the ortho-NH3-induced Q1(1) features likely arises from lifting of the H2 MJ degeneracy in the cluster. That these dopant-induced Q1(1) peaks are observable means that oH2−ortho-NH3 clusters are present even in these as-deposited highly enriched pH2 solids. The 13.77 cm−1 shift between the ortho-NH3induced Q1(0) and Q1(1) peaks is anomalously large. The 9720



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scans after deposition. Plots of the integrated intensity of various peaks of NH3 and ND3 for transitions from the |1,1⟩ rotational state are shown in Figure 9. For NH3, the integrated

Table 4. Nuclear Spin Conversion Rate Constants for Various Species species

T (K)

k (s−1)

matrix

ref

NH3 ND3 H2O D2 O CH4 CD4 CH3OH NH3

1.8 1.8 2.4 2.4 2.50 1.80 3.5 5

1.88(16) × 10−3 1.08(8) × 10−3 5.3(3) × 10−4 1.16(6) × 10−3 3.82(5) × 10−5 1.2(3)x210−4 5.3(6) × 10−6 ≤2 × 10−5

pH2 pH2 pH2 pH2 pH2 pH2 pH2 Ar

this work this work 27. 27. 17. 17. 72. 76.

this work for NH3 and ND3 are two of the largest rate constants measured, and all of the values together span nearly 3 orders of magnitude. One of the possible reasons that NSC is the fastest for NH3 is that the |1,1⟩ a state of para-NH3 is only 2.93 cm−1 lower in energy (in the gas phase) than the |1,0⟩ s level of orthoNH3. As first described by Curl et al.73 and later developed by others39,74,75 and termed the quantum relaxation model, conversion is thought to consist of two steps. First, a paraNH3 molecule in the |1,1⟩ a state “collides” with the matrix, which perturbs the energy of the state such that the VIR wave function becomes a superposition of the two close-lying |1,0⟩ s and |1,1⟩ a eigenfunctions. Second, a subsequent “collision” collapses the superposition wave function back into one of the ortho or para eigenfunctions, creating a finite probability for NSC. The superposition state is generated by the accidental near resonance between the two VIR states and the mixing induced by the NH3 intramolecular nuclear spin-rotation or spin−spin interactions.39 It turns out that the |1,0⟩ s and |1,1⟩ a pair, which includes the upper tunneling component of the lowest rotational state into which all of the para-NH3 molecules quickly collapse during deposition, is coupled by spin-spin and spin-rotation intramolecular interactions. In a previous theoretical study,39 this particular pair of states was identified as one of the main contributing pairs involved in the NSC of NH3 in the gas phase at 296 K. Indeed, the accidental degeneracy between this pair of nuclear hyperfine coupled states and the fact that all of the para-NH3 molecules get kinetically trapped in the |1,1⟩ state during deposition is the likely explanation for the large NSC rate constant. The rate of NSC depends therefore on the energy difference and coupling strength between the |1,0⟩ s and |1,1⟩ a pair. For a given molecule, the coupling strength is relatively constant because it depends on the intramolecular magnetic properties of the dopant. The energy difference between the two states, however, is likely different from the gas-phase value and also is expected to be matrix-host-dependent. Another important quantity is not just the average energy difference, but the width or breadth of the energy levels as well; a greater width increases the probability that the two energy levels are nearly degenerate and, therefore, creates a greater coupling. In the case of NH3, both states in the pair are associated with rotationally excited states, and therefore, the width should reflect both homogeneous and inhomogeneous contributions. The |1,1⟩ a state can relax only to the |1,1⟩ s state, and it is unclear whether this tunneling state relaxation creates extensive lifetime broadening. In contrast, the |1,0⟩ s can relax to the |0,0⟩ a state and thus is expected to be extensively homogeneous broadened. To gauge the extent of the broadening we can use the breadth of the Q1(0) pH2 + aR(0,0) ortho-NH3 cooperative peak. This peak is approximately 3.0 cm−1 broad with an

Figure 9. Plots of the NSC kinetics for (a) NH3 and (b) ND3 embedded in solid pH2 at 1.8 K. The circles are the integrated intensities determined from each repeated scan, and the lines are leastsquares fits of the data to single-exponential functions. The average measured rate constant with standard deviation in parentheses is indicated for each plot. In panel a, the color coding is blue, ν2 aQ(1,1); green, ν4 rR(1,1); and red, ν4 pP(1,1). In panel b, the color coding is blue, ν2 aQ(1,1); green, ν4 rR(1,1); red, ν4 pP(1,1); and black, ν4 p Q(1,1).

intensity decays to zero with time as the lowest |1,1⟩ rotational state of para-NH3 relaxes to the |0,0⟩ state of ortho-NH3. Because the two tunneling levels of the |1,1⟩ rotational state of para-NH3 are at considerably higher energy (i.e., 16.17 and 16.96 cm−1 in the gas phase)44 than the |0,0⟩ a rotational state of ortho-NH3, at 1.8 K, the equilibrium concentration of paraNH3 is exceedingly small. Numerical calculation of the NH3 rotational partition function shows that, at 1.8 K, the para-toortho ratio is 1.05 × 10−5. In contrast, because of the smaller rotational constant and tunneling splitting for ND3, even at 1.8 K, we estimate that the E/A ratio should be 5.1 × 10−3, and thus the |1,1⟩ state population should decay to a finite value. Indeed, examination of the ND3 data shows that all of the peaks with a |1,1⟩ ground rotational state decay to values greater than zero. This is especially apparent for the plot of the aQ(1,1) ND3 integrated intensity versus time (see Figure 9b). At 1.8 K, the para-NH3 population decays with a single-exponential rate constant of k = 1.88(16) × 10−3 s−1. The reported rate constant represents the average, and the error represents the standard deviation from a total of seven independent least-squares fits: five measurements for the sample shown in Figure 8 and two measurements using a different sample. For ND3, five measurements on a single sample give k = 1.08(8) × 10−3 s−1. We did not investigate the effect of temperature, oH2 concentration, or IR radiation from the FTIR spectrometer on the measured NSC rates. The NSC rates for NH3, H2O,27 CH4,16,17 and CH3OH72 have now all been measured for the dopant molecule trapped in solid pH2. All of the fitted NSC rate constants are presented in Table 4 for comparison. The NSC rate constants measured in 9721



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The other major component of this work is that it allows the NSC rate constants to be quantified for both NH3 and ND3 in solid pH2. The NSC rate constant is k = 1.88(16) × 10−3 s−1 for NH3 and 1.08(8) × 10−3 s−1 for ND3 at 1.8 K. Comparison of the measured NSC rate constants for other molecules isolated in solid pH2 shows that the NH3 rate constant is the largest measured to date. This is likely one reason that the spectral assignment of the NH3 ν2 spectrum has not been reported previously; if special care is not taken, NSC is nearly complete as soon as the first IR spectrum is recorded. The reason the NSC rate is relatively large for NH3 is likely related to the nearly degenerate pair of |1,0⟩ s and |1,1⟩ a rotational states for the two spin isomers of NH3. This pair of states provides a doorway by which the |1,1⟩ a state of para-NH3 can decay by intramolecular magnetic interactions that weakly couple the two states. The measured NSC rate depends on the coupling strength of just this pair, but we speculate also on the details of the true nature of the |1,0⟩ s excited rotational state of NH3 in solid pH2. As discussed previously by Momose and coworkers,17 the IR spectroscopy of molecules trapped in solid pH2 provides a simple and effective way to experimentally measure NSC in molecules that can be used to test our theoretical understanding of the chemistry of nuclear spin conversion.

asymmetric line shape that tails to the blue. We therefore speculate that the width of the |1,0⟩ s state plays a key role in determining the NSC rate constant. For comparison, in an Ar matrix76 at 5 K, the NSC rate constant was determined to be k ≤ 2 × 10−5 s−1, which is significantly lower than the rate constant measured here for pH2. We would expect the shifts in the energy levels for Ar and pH2 matrixes to be somewhat comparable, but the details of how the quantum pH2 matrix perturbs the rotational motion of the NH3 are responsible for the approximately 100-fold increase in the NSC rate constant. In the gas phase, the analogous levels for ND3 are separated57 by approximately 1.73 cm−1, and thus, to a first approximation, we would expect the ND3 NSC rate to be comparable to the NH3 rate, if not a slighty higher. However, this assumes that the intramolecular magnetic interactions are similar in ND3 and NH3, but they are not because of the differences between deuterons (I = 1) and hydrogen atoms (I = 1/2). Indeed, the theoretical treatment of the NSC of NH3 in the gas phase examined only the 14NH3 and 15NH3 isotopomers and not the deuterated species;39 we hope this work will stimulate theoretical work on NSC for ND3. Another contributing factor is the spread in the energy levels, and we suspect that, for ND3 the widths are smaller. Unfortunately, the spectra used in this work for the induced region of ND3-doped pH2 solids are complicated by overlapping lines due to ND2H and NH2D present as impurities in the pH2 solid. However, we can tentatively assign a peak to the analogous Q1(0) pH2 + aR(0,0) ND3 cooperative peak, which is only 0.25 cm−1 broad. The smaller width would be consistent with the slower NSC for ND3, but more work is required to clean up the ND3-doped pH2 sample for a more definitive assignment.

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ASSOCIATED CONTENT

S Supporting Information *

Series of IR difference spectra in the ν2 region for an NH3doped pH2 sample showing the time dependence, expanded views of the select para-NH3 transitions in the ν4 region, a twostate Boltzmann analysis of the ground-state tunneling splitting of para-NH3 using a least-squares fit to the a/sQ(1,1) VIR transitions of the ν1 mode, and expanded views of the NH3 induced Q1(0) and Q1(1) transitions of solid pH2. This material is available free of charge via the Internet at http:// pubs.acs.org.

4. CONCLUSIONS In this work, we studied the IR spectra of NH3 and ND3 isolated in solid pH2 and present full VIR assignments for all the fundamentals bands along with limited assignments for some NH3 combination bands. To assign the VIR spectra we take advantage of the relatively slow NH3 and ND3 NSC rates to kinetically trap populations in excited rotational states that are metastable on the time scale of rapid scan FTIR. Repeated FTIR spectra recorded immediately after deposition display IR absorptions that decrease and increase in intensity with time as the system slowly equilibrates to the low 1.8 K temperature of the pH2 solid. The one-to-one relationship between the nuclear spin and VIR wave functions means that all transitions originating from the excited |1,1⟩ rotational state decrease in intensity while transitions from the ground |0,0⟩ VIR state increase; this permits us to unambiguously assign the lower state quantum numbers for each transition and then use comparisons with gas-phase measurements to make complete assignments. With the new spectroscopic assignments, we then can determine how the vibrational, rotational, and inversion tunneling motions are perturbed when the NH3 molecule is trapped in solid pH2. The NH3 molecule is truly a spectacular spectroscopic probe of the properties of solid pH2 as a matrix host. We show that the NH3 and ND3 molecules continue to freely rotate in solid pH2 and that the inversion tunneling motion is approximately 67−74% of the gas-phase value. The resolved VIR absorption peaks display a range of spectral widths that we interpret as evidence for facile rotational relaxation, but slow vibrational relaxation. We also compare the IR measurements for NH3 and ND3 in solid pH2 to analogous studies in other matrix hosts.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank the National Science Foundation for its generous support through Grant CHE 08-48330. We benefitted from conversations of one of us (M.R.) with Patrice Cacciani on the details of the quantum relaxation model. We thank Dr. Mario E. Fajardo for developing the rapid vapor deposition technique and sparking our interest in NH3 so many years ago.

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REFERENCES

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