University of Illinois at Urbana-Champaign Spectroscopic Studies of the H3+ + H2 Reaction at Astrophysically Relevant Temperatures Brian A. Tom, Brett A. McGuire, Lauren E. Moore, Thomas J. Wood, Benjamin J. McCall June 24, 2009 University of Illinois at Urbana-Champaign

Astrophysical Motivation H3+ + H2 → H2 + H3+ most common bimolecular reaction in the universe H2 and H3+ used as probes of ISM ortho-H3+ para-H3+ Indriolo et al., ApJ., 671, 1736, (2007) June 24, 2009 University of Illinois at Urbana-Champaign

University of Illinois at Urbana-Champaign H3+ + H2 → H2 + H3+ Is this really a reaction? YES! 86.96 cm-1 64.121 cm-1 ½ + ½ + ½ = 3/2 ortho-H3+ ½ + ½ - ½ = 1/2 para-H3+ ½ + ½ = 1 ortho-H2 ½ - ½ = 0 para-H2 R(1,0) (ortho) 2725.898 cm-1 R(1,1)u (para) 2726.219 cm-1 Is this really a reaction? Yes! Both H2 and H3+ exist in different nuclear spin states designated “ortho” and “para.” In H3+, the ortho state has all three spins aligned, for a total nuclear spin of 3/2, while the para state is anti-aligned for a total spin of ½. Similarly the ortho state of H2 is aligned while the para state is anti-aligned. These states are fundamentally different species: they have different heat capacities, different ground state energies, and different spectra. The only way to readily interconvert between these species is through chemical reactions such as between H3+ and H2. So how can we monitor what is going on in this reaction? The R(1,0) ortho and R(1,1) para H3+ rovibrational transitions are accessible in the mid-infrared and are separated by about 0.3 cm-1. This allows for observations of both the ortho and para H3+ lines at the same time or in quick succession. Difference of ~0.32 cm-1 June 24, 2009 University of Illinois at Urbana-Champaign

H5+ Reaction Dynamics H3+ + H2 → (H5+)* → H3+ + H2 1 H5+ “identity” 3 So what actually happens in this reaction? An H3+ and an H2 collide to form an H5+ intermediate. At some point the H5+ breaks apart and the protons separate into H3+ and H2 again. Given that there are five protons involved, there are 10 possible combinations of protons in the final products. The products can form in the same configuration as the reactants; we call this the “identity” and there is only one possible way for this to occur. One of the protons from the H3+ can appear to have jumped to the H2, forming a new H3+ molecule; we call this the “hop” and there are three ways for this to occur given the three protons on H3+. Or it could appear that the H3+ and H2 swapped a proton with each other, giving us the “exchange” pathway, for which there are 6 possibilities. It is important to stress that these labels do not represent what actually happened in the reaction – protons are indistinguishable. They are only labels used to group the possible outcomes by what appears to have happened. As we’ll see later, the “hop” and “exchange” pathways have very interesting effects on the dynamics of the reaction and so it is helpful to define a relationship between them that we will call “alpha”, that is the ratio of the rate coefficients of the hop to the exchange reaction. Note that if the reaction proceeded in a purely statistical fashion, then there are three ways for the hop to occur, six for the exchange, giving a value for alpha of 3 over 6 or 0.5. “hop” if purely statistical: α = khop/kexchange = 0.5 6 “exchange” June 24, 2009 University of Illinois at Urbana-Champaign

Nuclear Spin Considerations o-H3+ + p-H2 → p-H3+ + p-H2 3/2  ≠ 1/2  p2 p3 [para-H2] [para-H2] + [ortho-H2] So how do we understand the underlying dynamics of what is going on in this reaction? Conservation of nuclear spin can provide a great deal of information. Let’s take for an example case the reactants of ortho H3+ and para H2 and say we want information about the forming para H3+ and para H2 as products. As you’ll recall ortho H3+ has a total spin of 3/2, para H of 0, para H3+ of 1/2, and para H2 again of 0. Obviously there is no way that 3/2 + 0 could ever yield ½ + 0, which tells us that the formation of these products is forbidden by the conservation of nuclear spin! By doing these calculations for all of the possible combinations and permutations, we can begin to get a look at the big picture, but how do we observe what’s going on experimentally? Well, we can do that by looking at two quantities which we’ll call p2 and p3. p2 is the fraction of the H2 which is in the para state, while p3 is the fraction of the H3+ which is in the para state. [para-H3+] [para-H3+] + [ortho-H3+] June 24, 2009 University of Illinois at Urbana-Champaign

High Temperature Model Based on work by Cordonnier and Oka Assumes all reactions are possible High energy Assume steady state for p3 [H2] >> [H3+] p2 p3 ¼ ½ So we have two models for looking at the situation with the intention of calculating alpha, which again is the ratio of the rates of the hop and the exchange reaction. The first model, the high temperature model, is based on the conservation of nuclear spin and assumes all reactions that are allowed by that algebra are possible. The model also makes the assumption that at these high temperatures, there is enough energy to overcome any barrier to reaction. Finally, we assume a steady state for p3, our para H3+ fraction, because there is so much H2 relative to H3+ that collisions are occurring quite rapidly. Given these assumptions, we can manipulate the detailed rate equations for all of the possible reactions, combine these with the nuclear spin data, and simplify down to an expression containing p2, p3, and alpha, shown here. Note that the high temperature model predicts a linear relationship between p2 and p3, with the slope being directly related to alpha. Finally, this model converges to a value for alpha of 0.5 in the case of normal-H2. α+1+2α p2 3α+2 p3 ≡ [p-H3+]/[H3+] = M. Cordonnier et al., J. Chem. Phys. 113, 3181 (2000) June 24, 2009 University of Illinois at Urbana-Champaign

University of Illinois at Urbana-Champaign Low Temperature Model Based on work done by Park and Light of Chicago Accounts for the energetic considerations of the reactions Predicts a non-linear relationship between p2 and p3 Plug in α and T, model gives a curve which is compared to the data p2 p3 ¼ ½ The second model, the low temperature model, is based on work first done by Park and Light. This model takes into account considerations such as energetic barriers to some of the possible reaction pathways that the high temperature model assumes are easily overcome, but which sufficient energy may not be present at these lower temperatures. It also takes into account differences in the energies of ortho and para H2 and H3+. For example, if we look at the ground states of H2, the ortho and para states are separated by 118.5 cm-1 or about 170 K which is a big difference in energy when we’re talking temperature-scales in the ISM. The result of this model is a non-linear relationship between p2 and p3. Further, unlike the high temperature model where p2 and p3 were parameters and we solved for alpha, in this model alpha and temperature are the parameters and the model provides a fit which we can then compare to the data. K. Park and J. C. Light, J. Chem. Phys., 126, 044305 (2007) June 24, 2009 University of Illinois at Urbana-Champaign

How do we get para-H2 enrichment (p2)? Helium Cryostat Enrichment controlled by T or mixing Catalyst @ ~14 K > 99.9% p-H2 Purity monitored by NMR and thermal conductance So we have our observables for our experiment, p2 and p3. How do we observe them? We can arbitrarily choose the value of p2 by producing the H2 used in the experiment using a home-built para-hydrogen converter system. The system passes pure hydrogen through a ferric oxide catalyst housed in a helium cryostat. We can control the enrichment of para-H2 leaving the converter by either varying the temperature of the system (down to ~14 K for pure para-H2), by mixing the gas with other known purities after production, or a combination of the two. We can achieve purities greater than 99.9% and we monitor the enrichment by NMR and thermal conductance. Method: B. A. Tom, S. Bhasker, Y. Miyamoto, T. Momose, B. J. McCall, Rev. Sci. Instr. 80, 016108 (2009) June 24, 2009 University of Illinois at Urbana-Champaign

How do we measure the para-H3+ fraction (p3)? Takayoshi Amano ~310 K ~130 K ~180 K H2 We generate our plasma in a hollow cathode cell based largely on designs graciously provided by Takayoshi Amano. The 1.5” diameter copper cathode is ~1.4 m long and is housed in a glass shell which is evacuated to about 13 mTorr. The cathode is wrapped in ¼” copper tube through which we can flow a variety of cooling liquids and gasses. A constant flow of about 1.85 Torr of hydrogen from our converter fills the cell. During the experiment we strike a discharge every five seconds by sending a 200 microsecond, 1 kV pulse to the anode which drew about 1.25 amps of current. We then monitor the H3+ absorption using a mid-IR Difference frequency laser system and a DC Indium-Antimonide detector. We ran the experiment at a variety of temperatures. Using water as the cooling source we achieved temperatures of about 300 K. Using liquid nitrogen at two different flow rates, we got a very frosty cell and temperatures of about 130 and 180 K. Hollow cathode plasma cell pump June 24, 2009 University of Illinois at Urbana-Champaign

University of Illinois at Urbana-Champaign Data Analysis It Io = e -ανL ανL |μ2|  nL ανL Now we have our data, how do we get p3 from this? I show here the absorption of the R(1,1) para and the R(1,0) ortho transitions at a variety of para-H2 enrichments. To determine p3, we would ratio the baseline absorbance with the peak absorbance of the transition and calculate a factor alpha nu L, where alpha nu is an absorption coefficient not to be confused with the other alpha. By dividing this by the transition dipole moment, we can directly relate this quantity to the number density of H3+ in the plasma. We can then determine p3 by looking at the total number densities of para and ortho H3+ present. ανL p3 =  npara  npara +  northo June 24, 2009 University of Illinois at Urbana-Champaign

Results – High Temperature Model I’ve plotted here p3 versus p2 to help visualize the effectiveness of the models. As you can see, when we fit the water cooled, room temperature measurements, the high temperature model seems to fit quite nicely, predicting a value for alpha of 2.15. Attempts to fit the data at lower temperatures, however, do not correlate well at all. Of note, however, is the general trend of both the experimental data and the model for lower values of alpha at lower temperatures. Thus favoring the exchange reaction. There are so many points here, however, that some of the detail is lost, so lets take a look at some of the individual temperature sets on their own. June 24, 2009 University of Illinois at Urbana-Champaign

University of Illinois at Urbana-Champaign 310 K As you could see on the previous plot, the high temperature model does a very reasonable job of fitting the 310 K data. June 24, 2009 University of Illinois at Urbana-Champaign

University of Illinois at Urbana-Champaign 180 K The 180 K data, on the other hand, is not well represented by either model. While it is difficult to claim a good or a bad fit based solely off of three points, you can see that points at these lower temperatures may be beginning to show some of the “bowing” effects predicted by the low temperature model. June 24, 2009 University of Illinois at Urbana-Champaign

University of Illinois at Urbana-Champaign 130 K This becomes much more obvious in the 130 K data, but so do the flaws in the low temperature model. While it certainly seems to replicate the non-linear nature of the data to some degree, you’ll notice that in order to really fit the data in any reasonable fashion, the model has to have an input temperature of 160 K, a full 30 K above what our temperature measurements indicate for this plasma! This seems to indicate a flaw in the way the low temperature model predicts data at low temperatures – not the most ideal of situations. June 24, 2009 University of Illinois at Urbana-Champaign

Experimental Conclusions α is dependant on T khop and kexchange not constant Lower T → Lower α → exchange dominates Neither models work well High temperature Linear relationship Ignores energetics Low temperature Must use high temperatures to replicate data p3 does not converge to 0.5 So what can we take away from this data? Read slide. June 24, 2009 University of Illinois at Urbana-Champaign

Astronomical Observations So how does our data compare with astronomical observations? I’ve changed the graph around to plot an astronomically observable quantity, the ratio of the ground state populations of ortho and para H3+ with the ratio of the ground state populations of ortho and para H2. The pluses on this graph represent where these ratios should fall if H2 and H3+ were to exist in a thermal ratio. But as I said earlier, H2 and H3+ do not readily interconvert between states except through chemical reactions. Astronomical observations towards zeta and X per find values that fall within our data range and NOT on the thermally predicted curve. This seems to indicate that it is the H2 + H3+ reaction that is driving the ortho:para ratio in these environments and not thermalization! June 24, 2009 University of Illinois at Urbana-Champaign

University of Illinois at Urbana-Champaign Future Work More low temperature measurements Refine our models for α More astronomical observations Read slide June 24, 2009 University of Illinois at Urbana-Champaign

University of Illinois at Urbana-Champaign Acknowledgments McCall Group Brian Tom Lauren Moore Tom Wood Team Hydrogen June 24, 2009 University of Illinois at Urbana-Champaign

University of Illinois at Urbana-Champaign Acknowledgments McCall Group Brian Tom Lauren Moore Tom Wood Team Hydrogen June 24, 2009 University of Illinois at Urbana-Champaign

University of Illinois at Urbana-Champaign Temperature As you’ll recall we’re also interested in determining the role this reaction plays in the mystery of excitation temperature. We can calculate excitation temperature over the course of the pulse by using the number densities determined from the ortho and para transitions. I show here an example plot of temperature versus time for the lifetime of a single pulse showing the warming of the plasma as time passes. For calculations of alpha, we use data (and thus the temperatures) near the beginning of the pulse where p2 is best known. For comparison, we also performed several experiments where instead of sitting on the transition and monitoring the absorption, we scanned over the peak. We could then fit a gaussian to the peak and calculate the kinetic temperature of the plasma from the doppler broadening of the line. As expected, the kinetic temperature was significantly warmer than the excitation temperature. June 24, 2009 University of Illinois at Urbana-Champaign