Jonathan Tennyson, Steven Miller and Hans Schild- First-principles Calculations on the Astrochemistry and Spectroscopy of H3^+

8/3/2019 Jonathan Tennyson, Steven Miller and Hans Schild- First-principles Calculations on the Astrochemistry and Spectroscopy of H3^+

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J. CHEM. SOC. FARADAY TRANS., 1993,89(13), 2155-2159 2155First-principles Calculations on the Astrochemistry and Spectros-copyof HCJonathan Tennyson, Steven Miller and Hans SchildDepartment of Physics and Astronom y, University College Lo ndon, London, UK W C I E 6BT

The H i molecular ion features prominently i n interstellar medium ( ISM) reaction s che me s. It is t h e main proto-nating agent and provides a major channel for deuterium fractionation. Yet all attempts to detect H3f in the IS Mby using infrared absorption techniques have so far failed.W e have performed a series of ro-vibrational calcu lation s of sp ectros cop ic accuracy using a high-qualitypotential-energy surface d u e t o Meyer , Botschwina and Burton. With the se we h a v e built up an extens ive da tas e t of ro-vibrational en ergy levels and transition intensities. From th e ene rgy lev els w e have generated parti-tion functions and hence temperature-dependent equilibr ium constants for the fractionation reactions

H i + D -+H,D+ + H and H i + HD + H,D+ + H , , as well as the H i orming reaction H + H .+H i + H. At thelow tem per atu res typical of the ISM, t h e fraction of H,D+ rises rapidly an d o u r theoretical estimates are at theirmost reliable .Emission sp ect ra of H i from both the v 2 and 2v , bands have been observed by several gr oups in the polarregio ns of Jupiter. Th es e are now being used to both monitor and map the complicated auroral activity ofJupi te r. Recently , we have a lso ass ign ed v 2 emiss ions in the spectrum of su perno va SN1987a and observedthe se e m is s ions in Uranus . These successes suggest tha t sea rching for H i in emission may well provide abetter ob serva tiona l handle on this chemically active and important sp ecie s. The role of proton in hopping in t h ethermalisation of the H3+ortholpara ratio will be discussed.

The fundamental molecular ion H3f is thought to play apivotal role in interstellar chemistry.' It is rapidly formedfrom ionised molecular hydrogen by the strongly exothermicreaction :H, + H; + H i + H ; AH = - 6300 K (1)

In models of the interstellar medium (ISM), H3f is responsiblefor starting the chain of ion-molecule reactions by proto-nation :

where X = CO, N,, O, , 0, , N, HCN etc. H3f is alsothought to be the main progenitor in deuterium fraction vi athe exothermic reactionsH i + HD+H2Df + H2; AH = -232 K (3)

H i + D = H , D + + H ; AH = -509 K (4)Despite its perceived importance, H: has yet to be observedin the ISM. A number of attempts have been made t o observeH3+ rom absorption features in the infrared continuum ofsuitable stars. These are difficult observations to make andthus far have led only to upper limits on the abundance ofH3f in a number of cold cloud^.^-^ These studies have alsocast dou bt4 on the tentative assignment of H 2 D + transitionin NGC2264.5Infrared spectra of H3f have been observed in emissionfrom Jup iter6 and recently U ranu s7 (see below). Emission fea-tures have also been assigned to H3f in the spectrum of super-nova SN1987a.* The lowest value of the H3f rotationaltemperature derived from these observations is 650 K.' Theseobservations suggest an alternative approach to searching forH; in the ISM via emissions in hot, possibly shocked,regions of the ISM.Besides our involvement in the above astrophysical detec-tions, we have for a number of years performed first-principles calculations of the ro-vibrational spectrum of H iand its isotoporners."-' These calculations have not onlybeen instrumental in assigning much of the laboratory

spectra of the ion,13 they also provide the oscillator strengthsneeded to t urn detections (non-detections) of H i into columndensities (upper limits).In this paper, we summarise the results of recent calcu-lations which are now yielding data suitable for modelling,address the problem of ortho/para ratios in H3+ and the roleof proton hopping in thermalising this ratio, finally we endwith a report o n recent attempts to observe H; .Ro-vibrational Calculations

The variational techniques used to calculate the ro-vibrational spectra of H3f and other triatomic systems haverecently been reviewed by Tennyson et The reader isreferred to this and the original for further infor-mation on these nuclear motion calculations. The electronicsimplicity of the H3+molecule has meant that highly accurateab initio electronic potential-energy surfaces are available forthese system^.'^,'^ With these we have been able to predictH3f transition frequencies with an accuracy of one part inloo00 in the best case.17

In the course of our calculation on H i we have built uplarge data sets of both energy levels, and transition fre-quencies and intensities. Some of the transition data havebeen publ ished18 and a new v e r ~ i o n '~s currently in prep-aration using our latest results12 and the m ost recent lab or-atory data. 'From such data com pilations one can generate parameterswhich form the input for astrophysical models. Fig. 1 andTables 1 and 2 show examples of the data these calculationscan yield as inp ut t o models.The deuterium fractionation reactions (3) and (4) are highlytemperatu re dependent in the tem perature range of the ISM .I t is possible to compute equilibrium constants, as a functionof temperature, using know n energy differences an d th e parti-tion functions obtained by explicitly summing over the ro-vibrational energy levels of H3f nd H 2 D + . This has beendon e by Sidhu et al." for these reactions and the H i forma-tion reaction (1).


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10h

ul- 5

0'0 500 1000 1500TIK

Fig. 1 Calculated equilibrium constants, K, as a function oftemperature" for reactions H + D --.) H,D+ + H (solid curve) andH + HD + H,D+ + H, (dashed curve)

Table 1 Calculated band origins (in cm-') and Einstein A coefi-cients (in s-') for the low-lying bands of H: from Dinelli et al . wherestates up to (0,44)at 9650 cm-' are considered"

A ' E A, A,symmetry (vl, v;) band origin (O,Oo) (0,l') (l,Oo) (0,2O)E (0,l') 2521.28b 128.8A, (1,OO) 3178.35' 0 0.846A , (0,2O) 4777.02 0 139.2 0E (0,2') 4997.42 144.6 256.0 0.211 0.024

" A , for E -+ A,/A, transitions in Dinelli et al. should be divided by2. Observed 2521.31.39'Observed 3178.3.40

/

0 . o f . U ' . . . ' . . . I - . . . ' . * A.'0 50 100 150 200 250TIK

Fig. 2 Equilibrium fractional abundances of ortho- and para-H,and resulting ortho and para fractions of Hi. ee text for details

For modelling, rate constants are generally used ratherthan equilibrium constants. However, as the forward deute-rium fractionation reactions are generally assumed toproceed at the Langevin rate, the equilibrium constants canbe used to determine the much more temperature-sensitivereverse rate constants.Full astrophysical information can be extracted only fromthe observed spectra via detailed models which consider therates for the processes determining not only creation anddestruction of the molecular species in question, but also theoccupancy of the various levels in the system. Such modellinghas recently been performed by Kim et aL21 for the auroralregions of Jupiter. However, these workers lacked detailedinformation on H: radiative rates. These have since been cal-culated by Dinelli et 0 1 . ' ~ using a new method proposed byLe Sueur et aL2, The results for states up to 2v,, the highestso far detected astrophysically, are given in Table 1.The corresponding results for H,D+ are given in Table 2.We note that the lower symmetry of H2 D + means that manymore transitions have to be considered. This is because of thesplitting of the degenerate v2 mod e and the loss of vibrationalselection rules which means that all transitions are symmetryallowed.Dinelli et al. treated all the vibrational states of H3f up to4v,. This is the highest vibrational sta te below the barrier tolinear H i . However, sufficient energy is generated in the for-mation of H3f by reaction (1) for states above linearity to bepopulated. Le Sueur et are presently extending the treat-ment of radiative rates to all the bound vibrational states ofH3f using wavefunctions obtained using a discrete variablerepresentation (DVR).24

Thermalisation of H:Observations of several H3f transitions can provide param-eters relating to the environmen t of the m olecule. Besides thecolumn density, n, information on the temperature of theemitting levels and fraction of ortholpara H3f can also beobtained. A typical emission spectrum in either the K or Lwindow yields a rotation temperature, T,,, . Comparisonsbetween the two windows can yield a vibrational tem-perature, T i b e For Jupiter, observation^^^ have found thatTo, i b suggesting that the emissions are thermal in origin.Mo re detailed modelling has suggested that this distributio nis only quasithermal because of the cooling effects on thevibrationally excited states of the infrared emissiom2' Theortho/para ratio can be determined from the H3f emissionspectrum althoug h experience has show n26 that highresolution is required for a useful determination as otherwiseortho and para lines tend t o blend,

Th e ro-vibrational state s of H3f can be classified using theS, permu tation grou p as having either A,, A, or E symmetry.Consideration of the nuclear spin couplings for H3f show that

Table 2 Calculated band origins (in cm-') and,Einstein,A, coeficients (in s-l) for the low-lying bands of H , D +'if

~~ ~

( 0 7 170) 2206.24" 20.0(0,0,1) 2334.99b 179.2 0.001

(0,191) 4460.84 104.7 152.3 16.6 0.01 8 0.012(0,072) 4602.15 52.9 15.6 287.3 0.601 0.007 0.002

(1,090) 2992.94' 53.2 0.144 0.449(0,270) 4287.50 19.2 25.4 20.3 0.103~~~~~" Observed 2205.87.41 Observed 2334.45.41 'Observed 2992.49.42


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I 1 1 I 1 L I 1 I3.526 3.528 3.530 3.532 3.534 3.536 3.538 3.540 3.542 3.544

wavelength/pmFig. 3 Detection of an H: emission line in L1457? The starred feature can be attributed to a slightly redshifted H: v 2 +0 R(3) transition at1, = 3.534pm. he vertical line shows a typical error bar

these states have nuclear spin degeneracies of 0, 4 and 2,respectively. In the absence of states of A, symmetry, theremaining levels can be classified as ortho (A,) or para (E). Athigh temperatures, there are twice as many occupied para Estates as A,, but because the E states have only half the spinweighting of the A, states, high-temperature equilibrium HZcontains equal amounts of the ortho and para forms. At lowtemperatures, however, the situation changes. Since A, statesare not allowed, the lowest available state is the para J = 1,K = 1 level. This is ca. 33 K lower in energy than the orthoJ = 1 , K = 0 level.In Fig. 2 the inverted triangles show the mixture ofortho/para-H; to be expected in a self-thermalised gas as afunction of temperature. At temperatures a little over 50 K,the ortho-H; fraction is ca. 0.5. (In fact, between 60 and 160K there is a slight favouring of the ortho form.) However,searches for H3+ in the interstellar medium which use thisself-thermalised curve to estimate relative abundances mayseriously overestimate the relative abundance of the orthoform, for the following reasons: When H; is formed in reac-tion (l), the ortholpara ratio depends critically on the ortho/para ratio of the neutral H, from which it forms;4 rulesgoverning such a process have been given by Q ~ a c k . ~ ~ ? ~ Stated briefly, they mean that para-H, can give rise only top a r a - H i and that ortho-H, produces 2/3 ortho-Hi and 1/3para-H,f . At room temperature, the equilibrium ortho frac-tion of H, is 0.75, but at lower temperatures, once more it isthe para form that predominates; the lowest available level ofpara-Hi, is ca . 170 K below that of ortho-H,. The full curvesin Fig. 2 show the fractional abundance of thermalised ortho-and para-H, and the circles that of ortho- and para-Hi pro-duced from such thermalised H , .In the interstellar medium, H3+ concentrations are typicallyof the order of to lo- of that of molecular hydrogen. Ithas been widely assumed that the H i ortholpara ratio willthermalise via proton h~p p i ng :~ -~ *~

H ,+H ,+eH 3+ +H ,As in the case of H i formation, [reaction (l)], it is theweaker ionic bond that breaks and a proton is transferredbetween hydrogen molecules.The assumption that H Z will thermalise seems to be basedon laboratory measurements, almost certainly made above150 K. At such temperatures, typical of most spectral mea-surements, it is clear from Fig. 2 the ortho-Hl fraction is

close to 0.5, with or without thermalisation. For temperaturesup to ca. 150K, however, there are marked differences in theortho/para-H,f ratios of the self-thermalised gas and thatformed from thermalised H,. At the temperature of a warm,70 K, molecular cloud, such as are found in the Orion Molec-ular Cloud, self-thermalised gas would produce more than50% ortho-H,f ; H i freshly produced from H, thermalised atthis temperature would have less than 30% of the ortho form.At lower tempertures, typical of cold clouds such as theTaurus molecular cloud, TMC-1, and NGC2264, the effect iseven more dramatic. At 20 K the self-thermalised H; has30% of the ortho form, the gas produced from H, has vir-tually none. Nor will the process of thermalisation uiaproton hopping change this situation. Unless two bonds arebroken during proton hopping, an extremely unlikely processeven at room temperature, let alone at temperatures of 70 Kor below, collisions between HZ and para-H, involving theexchange of a proton can result only in p a r a - H l ; these colli-sions cannot make up the deficit of ortho-Hi noted above tobring the ortho/para ratio closer to the self-thermalised value,and collisions between ortho-Hz and H i will once moreresult in the fraction of orth0-H: being equal to two-thirdsthat of ortho-H,. A relative overabundance of ortho-H;might thus be brought down to a level reflecting the ortho/para ratio of H,, but the fraction of ortho-Hi cannot beincreased. This argument leads to the conclusion that theortho/para ratio of H i in the interstellar medium ought tofollow the circles in Fig. 2 rather than the triangles.

This does not necessarily mean that ortho/para ratio of H idirectly reflects the temperature of the ambient molecularhydrogen. Even in cold regions of the ISM, H , is thought tobe formed on grains in its high-temperature form with anortho fraction of 0.75, thermalising slowly thereafter. Equili-bration times are typically of the order of lo6 years, andFlower et al. have suggested that using ammonia maser activ-ity to probe the ortho/para ratio of H, might be a useful wayof determining the age of molecular Analogously,one might argue that measurements of the ortholpara ratio ofH3+ would also be useful for dating molecular clouds, giventhat it is possible to detect H; at all in the ISM.

Recent ObservationsAlthough previous searches for H i in the ISM have concen-trated on looking for absorption lines against an infrared


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wavelength/pmFig. 4 Spectrum of Uranus between 3.89 and 4.09 pm by Trafton etal.' (filled circles) compared to a fit using calculated H 3 parameters(full line). The sticks give the position and relative intensity of the H:transitions included in the fit, T = 740 K;o = 0.51; = 6.5 x 10"

s ~ u r c e , ~ - ~he first detections of this ion outside of the labor-atory involved emission features. It is therefore plausible thatregions of the ISM which have conditions favourable for H3femission may be the best targets for future searches. We haverecently been involved in two separate sets of observationsusing the United Kingdom Infrared Telescope (UKIRT) forstudying H; emissions. The first run on February 2-4 1992(UT) which was awarded time specifically for the search forH; emission in shock and X-ray-excited molecular gas, wasadversely affected by bad weather. The second run (April 1-3,1992) was awarded time for continuing work mapping andmonitoring H l emissions from Jupiter (results of which willbe presented el~ewhere~~),ut, because Jupiter is not visibleall night, allowed some time for observing other objects.The detection of H; beyond the solar system (with theexception of SN1987a) has continued to prove more difficultthan expected. We concentrated our efforts to observe emis-sions in the Q and R branches of H; in the K and L bands.Astrophysical sites most likely to emit this radiation areshock-excited molecular clouds, where the local temperaturecan reach several thousand degrees, or X-ray-excited molecu-lar gas, where as model calculations have shown H; concen-trations may be very high.33 Shocks in the interstellarmedium are very common and are usually produced bystellar ejecta impinging on a molecular cloud or by collisionsbetween different molecular clouds, i.e. in merging galaxies.Stellar ejecta can be due to stellar winds from young stellarobjects (Herbig Haro objects), winds from OB stars (star-forming regions like Orion, starburst galaxies) or supernovaejecta.During our observations in February 1992 we seached fivestarburst or merging galaxies for H; emission with a nega-tive result. Galactic targets included the proto-planetarynebula CRL 618, parts of the supernova remnant IC443, andthe dark cloud L1457. The best candidate for a possible H;detection among these was L1457. Fig. 3 shows the result of a23 min observation of this object. It shows an emissionfeature (starred) at the 2a level which can be attributed to aslightly redshifted H3f v 2 -+ 0 R(3) transition at A, = 3.534pm. Unfortunately, poor weather prevented us from confirm-ing this tentative detection.

Dark clouds consist of molecules and dust. The latterabsorbs visible light but is transparent to infrared light.L1457 is, however, a special object in two respects with bothfactors facilitating the possibility of a H; detection. First,L1457 is the nearest object of this type at a distance of only65 pc from the Sun34and secondly it seems to contain a hardX-ray source35. The exact nature of this X-ray source is

unclear but the most likely candidate would be a luminous TTauri star.Even more recently, H; has been detected in the atmo-

spheres of Uranus7 and Saturn.36 Fig. 4 shows an emissionspectrum of Uranus taken on the 1st April 19927 using 1 hintegration on CGS4 with a 150 lines mm- ' grating and 150mm focal length camera which gives a resolving power ofR = 1150 (or a resolution of ca. 0.0035 pm). The spectrumwas fitted to calculated line frequencies and intensities'* withno background. This gives a temperature of 740 f 0 K forthe rotational levels of the emitting v2 level of H; .The sticksin Fig. 4 represent the positions and, on an arbitrary scale,intensities of the individual lines used in fitting the spectrum.These demonstrate that at this resolution many of the fea-tures actually comprise blends of H i transitions.

ConclusionsSince the first spectra of H3f in 1980,37*38irst-principles cal-culations have played an important role in the search for anassignment of laboratory spectra. With the observation of anH; emission spectrum in Jupiter,6 this role has now extendedto astrophysics. Furthermore, these calculations are nowbeing used to generate chemical reaction2' and radiativeI2data useful for modelling.

Despite the success of observing6y7 and assigning* H;emission spectra, H3f has yet to be observed in cool inter-stellar clouds. Attempts to observe cold H3+ in absorptionhave used transitions of both ortho and para-Hl , the lowerlevels of which have been assumed to be in thermal equi-librium. We suggest that the proposed thermalisation mecha-nism, proton-hopping, may not actually function inenvironments where para-H, is the dominant species. Underthese circumstances there may be an overabundance ofpara-H; relative to ortho-H; .We thank Dr. T. R. Geballe for help with our observations.S.M. thanks Dr. D. R. Flower for helpful discussions. Thiswork has been supported by a number of SERC grants and aNATO grant with Chicago.

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Paper 2/04483H; Received 19th August, 19 92

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Jonathan Tennyson, Steven Miller and Hans Schild- First-principles Calculations on the Astrochemistry and Spectroscopy of H3^+