Improved low-temperature rate constants for rotational excitation of CO by H_2

0.14 MB·English

by  M. Wernli

Astronomy&Astrophysicsmanuscriptno.corr˙proof˙2 February5,2008
(DOI:willbeinsertedbyhandlater)
Improved low-temperature rate constants for rotational excitation
of CO by H
2
6
0 M.Wernli1,P.Valiron1,A.Faure1,L.Wiesenfeld1,P.Jankowski2,andK.Szalewicz3
0
2
1 Laboratoire d’Astrophysique de Grenoble, UMR 5571 CNRS-UJF, OSUG, Universite´ Joseph Fourier, BP 53, F-38041
n
a GrenobleCedex9,France
J 2 DepartmentofQuantumChemistry,InstituteofChemistry,NicholausCopernicusUniversity,Gagarina7,PL-87-100Torun´,

8 Poland
1 3 DepartmentofPhysicsandAstronomy,UniversityofDelaware,Newark,DE19716,USA

1 Received26July2005/Accepted12September2005
v
4
Abstract.Crosssectionsfortherotational(de)excitationofCObygroundstatepara-andortho-H areobtainedusingquantum
8 2
scatteringcalculationsforcollisionenergiesbetween1and520cm−1.AnewCO−H potentialenergysurfaceisemployedand
3 2
itsqualityisassessedbycomparisonwithexplicitlycorrelatedCCSD(T)-R12calculations.Rateconstantsforrotationallevels
1
0 ofCOupto5andtemperaturesintherange5−70Karededuced.Thenewpotentialisfoundtohaveastronginfluenceonthe
6 resonancestructureofthecrosssectionsatverylowcollisionenergies.Asaresult,thepresentratesat10Kdifferbyupto50%
0 withthoseobtainedbyFlower(2001)onaprevious,lessaccurate,potentialenergysurface.
/
h
Keywords.moleculardata−molecularprocesses−ISM:molecules
p
-
o
r
t 1. Introduction for para-H2. This result reflects the crucial importance of the
s
PES, whose inaccuracies are one of the main sources of er-
a
Sinceitsdiscoveryininterstellarspacemorethan30yearsago
: ror in collisional rate calculations, especially at low tempera-
v (Wilsonetal. 1970), carbon monoxide (CO) has been exten-
tures (see, e.g., Balakrishnanetal. (2002)). The JS98 surface
i
X sively observed both in our own and in other galaxies. CO has been checked against experiment by a couple of authors.
is indeed the second most abundantmolecule in the Universe
r Gottfried&McBane (2001), in particular, computed second
a after H and, thanks to its dipole moment, it is the principal
2 virial coefficientsbelow 300 K and showed thatthe attractive
moleculeusedtomapthemoleculargasingalacticandextra-
well of the PES was slightly too deep. A modification which
galacticsources.COisalsocurrentlytheonlymoleculetohave
consistsofmultiplyingthePESbyafactorof0.93wasthere-
been observed at redshifts as high as z = 6.42 (Walteretal.
foresuggestedbytheseauthors.Thismodificationwasapplied
2003).CollisionalexcitationofrotationallevelsofCO occurs
byMengeletal.(2001)anditwasindeedfoundtoproducebet-
inagreatvarietyofphysicalconditionsandemissionfromlev-
teragreementwithmeasurementsofpressurebroadeningcross
elswithrotationalquantumnumbersJupto39havebeeniden-
sections.Ontheotherhand,theoriginalPESwasfoundtogive
tifiedincircumstellarenvironments(Cernicharoetal.1996).
a very good agreement with experimental state-to-state rota-
Hydrogenmoleculesare generallythe mostabundantcol- tionalcrosssectionsmeasurednear1000cm−1(Antonovaetal.
liding partners in the interstellar medium, although collisions
2000).Attheseenergies,however,onlytheshort-rangerepul-
withH,Heandelectronscanalsoplayimportantroles,forex-
siveregionofthePESisprobed.Finally,Flower(2001)showed
ampleindiffuseinterstellarclouds.Ratecoefficientsforcolli-
that the scaling of 0.93 has only minor influence on the rota-
sions with H based on the potential energy surface (PES) of
2 tionalratesandheemployedtheoriginalPES.
Jankowski& Szalewicz(1998,hereafterJS98)havebeencal-
Very recently, a new PES has been computed by
culatedrecently(Mengeletal.2001;Flower2001).Theserates
Jankowski&Szalewicz(2005)(hereafterJS05).Incontrastto
were found to be in reasonable agreement(typically within a
the JS98 surface, which was calculated within the symmetry-
factorof2at10K)withthosecomputedonolderandlessac-
adaptedperturbationtheory(SAPT),theJS05surfacehasbeen
curatePES(e.g.Schinkeetal.(1985)).However,incontrastto
obtainedusingthesupermolecularapproximationbasedonthe
previousworks,Mengeletal.(2001)andFlower(2001)found
the inelastic rateswith ∆J = 1 largerthanthosewith ∆J = 2 CCSD(T)methodusingcorrelation-consistentbasissetscom-
plementedbybondingfunctionsandbasissetextrapolation.It
Send offprint requests to: M. Wernli e-mail: turnedthatthemajorinaccuracyofJS98wasduetotheuseof
[email protected] a correction for the effects of the third and higher orders ex-
2 M.Wernlietal.:improvedlow-temperatureCO−H rotationalrateconstants
2
tracted in an approximateway from supermolecularSCF cal-
culations. It recently became clear that this correction should 100 θθ21 == 9900oo θθ12 == 00oo θθ21 == 108o0o JJSS9085
notbeusedfornonpolarornearlynonpolarmonomers.Ifthis CCSD(T)-R12
term is removed from JS98, the agreement of the resulting -1m) 50
surfacewithJS05isexcellent.Jankowski&Szalewicz(2005) c
haveemployedtheirnewPEStocalculaterovibrationalenergy gy (
levels of the para-H2−CO complex and they obtained a very ener 0
goodagreement(betterthan0.1cm−1 comparedto1cm−1 for on
theJS98surface)withthemeasurementsbyMcKellar(1998). acti
Thecomputedvaluesofthesecondvirialcoefficientsalsoagree nter -50
I
verywellwiththeexperimentalones.Fulldetailscanbefound
in Jankowski&Szalewicz (2005). In the present paper, we
-100
present new rate constants for the rotationalexcitation of CO
by H based on the JS05 surface.Our results are restricted to 5 6 7 8 9
2
R (bohrs)
lowtemperatures(T<70K)becausethenewPEScalculations
arefoundtoaffecttherotationalcrosssectionsonlyatlowcol- Fig.1. H −CO interactionenergyas a functionof R for three
2
lision energy (E < 60 cm−1). As shown below, differences coplanar configurations:(θ ,θ )= (90o, 90o), (0o, 0o) and (0o,
coll 1 2
with theresultsofFlower(2001) rangefroma few percentto 180o). The dashed and solid lines denote the JS98 and JS05
50 %. Such effects, if not dramatic, are significant in view of calculations, respectively. The filled circles correspond to in-
the special importanceof the CO−H system in astrophysics. dependentCCSD(T)-R12calculations(seetext).
2
Furthermore, the present results are of particular interest for
comparisonswith futuremeasurementsplannedin Rennes by
bitalswerefrozen2intheCCSD(T)-R12calculations.Weem-
Simsandcollaborators(Sims2005).
ployedR12-suitedbasissetsincludinguptogfunctionsforC
andO,anddfunctionsforH(asdevelopedinNoga&Valiron
(2003); Kedzˇuchetal. (2005)). The R12 results are assumed
2. Method toapproachthebasissetlimitwithin1−2cm−1.Inparticular
theinclusionofalargesetofbondingfunctions(corresponding
2.1.PotentialEnergySurface to the R12-suitedH set) affects the interactionby ≈ 0.5cm−1
Following the conventions of JS98, the CO−H “rigid-body” onlyat 7 bohrsseparation,while the counterpoisecorrections
2 remainverysmall,generallybelow1cm−1.
PES is described by the following four Jacobi coordinates:
Here, we can observe that the JS05 surface agree very
threeanglesθ ,θ andφandthedistanceRdenotingtheinter-
1 2
well with the CCSD(T)-R12 results while the JS98 surface
molecularcentreofmassseparation.Theanglesθ andθ are
1 2
overestimates the depth of the CO−H potential well by
the tilt angles of H and CO with respect to the intermolecu- 2
2 about10−20%,asanticipatedbyGottfried&McBane(2001).
laraxis,andφisthedihedralangle.Inthelineargeometry,the
However, the JS05 surface lies slightly below the CCSD(T)-
oxygen atom points toward H when θ =0. The JS05 surface
2 2
R12 one. This agrees with the observation in JS05, based on
hasbeenobtainedbyaveragingovertheintramolecularground
extrapolationsinvolvingbasesuptoquintuplezetaquality,that
statevibrationofH ,whileCOwastreatedasrigidatitsvibra-
2 the potential is about 1-2 cm−1 too deep in the region of the
tional ground-state averaged geometry. The JS05 surface has
a global depth of -93.049 cm−1 for the linear geometry with global minimum. On the other hand, the comparison of the
theCatompointingtowardtheH molecule(θ =0,θ =180o, virialcoefficientsfromJS05withexperimentsuggeststhatthe
2 1 2
exact potential is still deeper, probably due to the effects re-
φ = 0) and for a centre of mass separationR =7.92bohrs.
min
sultingfromtheorylevelsbeyondCCSD(T).Wealsochecked
The(unscaled)JS98andJS05surfacesarepresentedinFig.1
thattheR12valuesarerecoveredwithin1cm−1 byabasisset
and compared to independent CCSD(T)-R12 calculations us-
extrapolation involving larger (triple and quadruple zeta) sets
ingground-stateaveragedgeometriesforCOandH .
2
andthepopularbondingfunctionsproposedbyWilliamsetal.
Thelattercalculationscanbeconsideredashighaccuracy
(1995). These comparisons provides a further check of the
state-of-the-art ab initio calculations. Indeed the CCSD(T)-
qualityofthenewCO−H PESandalsoconfirmthesuspected
R12approach1 hasbeenshowntoproduceintermolecularen- 2
inaccuraciesoftheJS98surface.
ergies with near spectroscopic accuracy without recourse to
In order to interface the JS98 and JS05 surfaces
extrapolation(Halkieretal. 1999; Mu¨ller&Kutzelnigg2000;
with the scattering code, the  routines of
Faureetal.2005).Inordertosavesomecomputingtimeandto
Jankowski&Szalewicz (1998); Jankowski&Szalewicz
improvethenumericalstabilityoftheR12operator,thecoreor-
(2005)wereemployedtogenerateagridof57,000geometries.
These grid points were distributed in 19 fixed intermolecular
1 TheR12coupledclustertheorywithsingles,doublesandpertur- distances R (in the range 4−15 bohrs) via random sampling
bativetriplesproperlydescribestheelectron-electroncuspbyinclud-
ing explicitly the inter-electronic coordinates into the wavefunction 2 Thisapproximationisoflittleconsequenceascorecorrelationef-
(Noga&Kutzelnigg(1994),seealsoNoga&Valiron(2002)forare- fectsareminorfortheCO-H interaction(about0.3cm−1 at7bohrs
2
view.) separation).
M.Wernlietal.:improvedlow-temperatureCO−H rotationalrateconstants 3
2
for the angular coordinates. At each intermolecular distance, 100
the interaction potential V was least-squares fitted over the JS05
followingangularexpansion: 1-0 JS98
V(R,θ1,θ2,φ)=Xl1l2lvl1l2l(R)sl1l2l(θ1,θ2,φ), (1) 2on (A ) 3-1
cti
mwhoenriecsthaendbaasreisefxupnlcictiiotendsisnl1El2lq.ar(eA9p)roodfuGctrseeonf (s1p9h7e5ri)c.aTlhheasre- oss se 10
functionsformanorthonormalbasisset,andtheexpansionco- Cr
efficientsv canthusbewrittenas3
l1l2l
v (R)= V(R,θ ,θ ,φ)s⋆ (θ ,θ ,φ)sinθ dθ sinθ dθ dφ(2)
l1l2l Zθ1Zθ2Zφ 1 2 l1l2l 1 2 1 1 2 2 10 100
E (K)
The latter expression remains valid for any truncated expan-
sion. Fig.2.InelasticdeexcitationcrosssectionsforCOincollisions
We selected an initial angular expansion including all withpara-H2 asafunctionoftotalenergy.Bothcurvesarethe
anisotropiesup to l =10 for CO and l =6 for H , resulting in resultsofourcalculationswiththeunscaledJS98PES(dashed
1 2 2
142s functions.Theaccuracyoftheangularexpansionwas curves),andtheJS05PES(solidcurves).
l1l2l
monitoredusingaself-consistentMonteCarloerrorestimator
(Ristetal.2005),whichalsopermittedtoselectthemostperti- andwasthusemployed.Theenergystepwas20cm−1between
nentangularterms.Theresultingsetwascomposedof60basis 160and340cm−1,and30cm−1 athigherenergies.Forortho-
functionsinvolvinganisotropiesuptol1 = 7andl2 = 4.Acu- H2, the same collision energy grid was used, resulting in to-
bicsplineinterpolationwasfinallyemployedoverthewholein- tal energiesin the range 126−642cm−1. The propagatorused
termoleculardistancerangeandwassmoothlyconnectedwith wasthelog-derivativepropagator(Alexander&Manolopoulos
standardextrapolationstoprovidecontinuousexpansioncoef- 1987).Parametersoftheintegratorweretestedandadjustedto
ficientssuitableforscatteringcalculations.Thefinalaccuracy ensure a typical precision of 1-2 %. All the calculations with
of this 60term expansionwas foundto be better than 1 cm−1 para-H useda j =0,2basis,whiletheortho-H calculations
2 2 2
in the global minimum region of the PES while the individ- used onlya j = 1basis. Tests ofthis basisweremadeatthe
2
ualexpansioncoefficientswereconvergedwithin0.01cm−1.It highestenergy,whereinclusionofthe j =3(closed)statewas
2
shouldbenotedthattheexpansiondoesnotreproduceexactly foundtoaffectcrosssectionsbylessthanonepercent.Atleast
the values of the potential energy at the grid points4, in con- threeclosedchannelswereincludedateachenergyfortheCO
trasttotheapproachfollowedbyFlower(2001)whousedthe rotationalbasis. Atthe highestenergy,we hadthusa j ≤ 18
1
same number (25) of angular geometriesand basis functions. basis.Transitionsamongalllevelsupto j =5werecomputed.
1
The main advantage of our approach is to guarantee the con- Finally,rateconstantswerecalculatedfortemperaturesranging
vergenceoftheindividualexpansioncoefficients,inparticular from5to70Kbyintegratingthecrosssectionsoveressentially
inthehighlyanisotropicshort-rangepart(R < 6bohrs)ofthe thewholecollisionenergyrangespannedbythecorresponding
interaction. Maxwell-Boltzmann distributions. The energy grid was cho-
sensothatthehighestcollisionforalltransitionsbeaboutten
2.2.Scatteringcalculations timeslargerthanthehighesttemperature.Theaccuracyofthe
presentratesisexpectedtoliebetween5and10%at70K,and
The  code (Hutson&Green 1994) was employed to probablybetteratlowertemperatures.
performtherigid-rotorscatteringcalculationsreportedbelow.
Allcalculationsweremadeusingtherigidrotorapproximation,
3. Collisionalcrosssectionsandrates
withrotationalconstantsB =1.9225cm−1andB =60.853
CO H2
cm−1. For para-H2 (j2 = 0), calculations were carried out at Figure 2 clearly illustrates the fact thatthe resonance pattern,
total energies (collision plus CO rotation) ranging from 4 to which is here of ’shape’ rather than ’Feshbach’ type as dis-
520cm−1.Fullclose-couplingcalculationswereperformedbe- cussed by Flower (2001), strongly dependson the interaction
tween4and160cm−1,withstepsof0.2cm−1intheresonance potential.Wealsonotethattheveryfinegridusedatthelowest
range4−120cm−1,andamuchcoarserstepof5cm−1between energies was necessary for a proper description of the reso-
120 and 160 cm−1. Between 160 and 520 cm−1, the coupled- nances. It can be observedthat the cross sections convergeat
stateapproximation(McGuire&Kouri1974)wasshowntore- higherenergies(abovetheresonanceregime),asthe collision
produce full close-coupling calculations within a few percent energy becomes large compared to the potential energy well
depth.As a result,rateconstantsare expectedtodiffersignif-
3 ⋆ denotes the complex conjugate. Note that the angular con-
icantly from those of Flower (2001) at very low temperatures
ventions of Green (1975) are slightly different from those of
Jankowski&Szalewicz(1998). only.
4 The residual differences indicate the cumulative effects of the We present in Tables 1 and 2 our rate constants at 10, 30
higherexpansionterms. and70K,andthoseofFlower(2001)forcomparison.Wenote
4 M.Wernlietal.:improvedlow-temperatureCO−H rotationalrateconstants
2
thatespeciallyat10K,ratescanvaryupto50%.Thesediffer- (2002).Itisgenerallyassumedthatrateswithpara-H (j =0)
2 2
encesreflecttheinfluenceofthreeindependentparameters:(i) shouldbeabout50%largerthanHeratesowingtothesmaller
thehighaccuracyofthenewabinitiopotentialenergycalcula- collisional reduced mass and the larger size of H . We have
2
tions,(ii)theuseofawellconvergedexpansionofthePESover checked that the present H (j = 0) rates are in fact within
2 2
the angularbasis functionsand (iii) the carefuldescription of a factor of 1−3 of the He rates. Thus, as already shown by
resonances.Itishowevernotclearhowtodiscriminateamong Phillipsetal.(1996)inthecaseofH O,ratesforexcitationby
2
the threeeffects. At70K(andbeyond),ourratesandthose of H arenotadequatelyrepresentedbyscaledratesforexcitation
2
Flower(2001)agreewithintypically10−20%, asanticipated byHe.
fromtheconvergenceofthecrosssectionsathighenergy.We Finally,foruseinastrophysicalmodelling,thetemperature
thereforeconcludethatthedifferencesbetweenourresultsand dependenceoftheabovetransitionratesk(T)havebeenfitted
thoseofFlower(2001)areastrophysicallyrelevantfortemper- bytheanalyticformusedbyBalakrishnanetal.(1999):
atures below 70 K. Above this value, the inaccuracies of the
4
JS98 PES have only a minor influence on the rotational rates
log k(T)= a xn, (3)
and the results of Flower (2001) and Mengeletal. (2001) are 10 X n
n=0
reliable.
The para-H rates presented in the 30 K panel in Table 1 wherethe xfactorwaschangedfromT−1/3toT−1/6toachieve
2
illustrate the respective contribution of the surface and of the abetterfittingprecision.Thequadraticerroronthisfitislower
subsequent angular expansion and collisional treatment. Data than0.1%foralltransitions.Thecoefficientsofthisfitarepro-
in columns 1 and 2 are based upon the same JS98 surface vided as online material. For those who plan to use them, we
and the differences are ascribable to the better convergence emphasizethatthesefitsareonlyvalidinthetemperaturerange
of the angular expansion and to the finer description of the 5≤T ≤70K.Finally,excitationratesarenotgiveninthispa-
resonances. Conversely, data in columns 2 and 3 are based per,butcanbeobtainedbyapplicationofthedetailedbalance.
upon the same angular expansion and collisional treatment,
andthedifferencesonlyreflecttheimprovementinthesurface.
4. Conclusion
Dependingoninitialandfinalrotationstates,varioussituations
mayoccur.Insomecasesthereisacompensationoferrorsfor Crosssectionsfortherotational(de)excitationofCObyground
thesurface(asfor2-1,3-0,3-2),orfortheexpansionandcol- state para- and ortho-H have been computed using quan-
2
lisional treatment (as for 5-0). Collisional and surface errors tum scattering calculations for collision energies in the range
mayalsopartiallycancelout,asforthe1-0rate,oraddupas 1−520 cm−1. A new, highly accurate, CO−H potential en-
2
for the 2-0 rate. While the detailed behaviourseems complex ergy surface has been employed and it has been shown to
andirregular,inaveragetheerrorsintroducedbytheolderJS98 stronglyinfluencetheresonancestructureofthecrosssections
surfaceareofthesameorderofmagnitudeastheerrorsintro- in the very low collision energy regime (E . 60 cm−1).
coll
ducedbythelimitedangularexpansionandenergymeshinthe Conversely, at higher energies, the effect of the new poten-
olderworkbyFlower(2001). tial was found to be only minor. As a result, the present rate
Itisinterestingtonotethatforcollisionswithpara-H ,in- constantsarefoundtodiffersignificantlyfromthoseofFlower
2
elastic rates with ∆j = 1 are larger than those with ∆j = 2 (2001),obtainedonapreviousandlessaccuratepotential,only
1 1
while the reverse applies for ortho-H . The propensity to fa- fortemperatureslowerthan70K.Transitionsamongalllevels
2
voreven∆j overodd∆j hasbeenexplainedsemiclassically upto j =5onlywerecomputedashigherstatesaregenerally
1 1 1
byMcCurdy&Miller(1977)intermsofaninterferenceeffect notpopulatedatthelowtemperaturesinvestigatedhere.
relatedtotheevenanisotropyofthePES.Thereversepropen- Thisworkillustratestherelationshipbetweentheaccuracy
sity can also occur if the odd anisotropy is sufficiently large, of the potentialenergy surface and the accuracy of the corre-
asobservedexperimentallyin the case ofCO-He (Cartyetal. spondinginelasticcrosssectionsforasimplesystemofastro-
2004). Here, the propensity depends on the quantum state of physical relevance. Even at low temperatures, moderate inac-
the projectile because in the para case (j = 0), some terms curacies in the surface (in the 10-20% range) result in semi-
2
ofthePESexpansion(thoseassociatedwiththequadrupoleof quantitative inelastic rates with typical errors in the 20-50%
H ) vanish identically. Therefore, the even anisotropy of the range with no dramatic amplification of errors. However,this
2
PESislargerwithortho-H thanwithpara-H and∆j =2are optimisticconclusionpresentsalsoahardercounterpart,aswe
2 2 1
favored.Note,however,thatthesepropensityrulesdependon showthatinordertoobtainaccurateinelasticratesonehasto
j , ∆j and the temperature. Another interesting point is that satisfyallthreeconditions,i.e.,useanaccuratesurface,aprop-
1 1
thedifferenceswiththeresultsofFlower(2001)aregenerally erlyconvergedangularexpansion,andadetaileddescriptionof
smaller with ortho-H than with para-H . This again reflects the cross-section resonances. Consequently, the improvement
2 2
thedifferentanisotropiesofthePESforparaandortho-H :in oftheaccuracyofinelasticrates,especiallyathighertempera-
2
the ortho case, cross sections are larger and scattering calcu- tureswhenthenumberofchannelsislarge,representsaconsid-
lationsare less sensitive to small changesin the PES. Similar erablecomputationaleffort.Inthisrespect,theworkbyFlower
effectshavealsobeenobservedrecentlyinthecaseofH O-H (2001)representedanexcellentcompromisetoachieveatypi-
2 2
(Dubernet&etal.2005). cal20%accuracybelow100K.
It is also of some interest to compare the present re- Thiswork extendsthe initialobjectivesof the “Molecular
sultswiththeCO-HeratesobtainedbyCecchi-Pestellinietal. Universe”EuropeanFP6network(2005-2008)andparticipates
M.Wernlietal.:improvedlow-temperatureCO−H rotationalrateconstants 5
2
tothecurrentinternationaleffortstoimprovethedescriptionof Phillips, T. R., Maluendes, S., & Green, S. 1996, ApJS, 107,
theunderlyingmicroscopicprocessesinpreparationofthenext 467
generationofmolecularobservatories. Rist,C.,Faure,A.,&Valiron,P.2005,inpreparation
Schinke, R., Engel, V., Buck, U., Meyer, H., & Diercksen,
Acknowledgements. CCSD(T)-R12 calculations were performed on G.H.F.1985,ApJ,299,939
the IDRIS and CINES French national computing centers (projects
Sims,I.R.2005,privatecomunication
no.051141andx20050420820).MOLSCATcalculationswereper-
Walter,F.,Bertoldi,F.,Carilli,C.,etal.2003,Nature,424,406
formed on an experimental cluster using a subset of the computer
Williams, H. L., Mas, E. M., Szalewicz, K., & Jeziorski, B.
gridtools(underprojectCigriofthe“ActionIncitativeGRID”)with
1995,J.Chem.Phys.,103,7374
the valuable help from F. Roch and N. Capit. This research was
Wilson,R.W.,Jefferts,K.B.,&Penzias,A.A.1970,ApJ,161,
supported by the CNRS national program “Physique et Chimie du
Milieu Interstellaire” and the “Centre National d’Etudes Spatiales”. L43+
MWwassupportedbytheMiniste`redel’EnseignementSupe´rieuret
delaRecherche.KSacknowledgestheNSFCHE-0239611grant.
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6 M.Wernlietal.:improvedlow-temperatureCO−H rotationalrateconstants
2
Table 1. Rotationaldeexcitationratesof CO in collision with Table 2. Rotationaldeexcitationratesof CO in collisionwith
para-H (j = 0)atthreetemparatures.IandFaretheCOini- ortho-H (j =1).Theconventionsarethesameasforthepara
2 2 2 2
tialandfinalrotationstates,respectively.Allratesaregivenin case.
unitsof10−10 cm3/s.ThirdcolumnrecallstheratesofFlower
(2001), obtained with the unscaled JS98 surface. Fourth col- I F Flower Thiswork
umn presents our rates obtainedwith the JS05 surface. In the Temp.:10K
1 0 0.388 0.379
30Kpanel,theratesobtainedwithourexpansionoftheJS98
2 0 0.596 0.559
surfacearealsopresented.
3 0 0.105 0.071
4 0 0.083 0.061
I F Flower Thiswork
5 0 0.015 0.016
Temp.:10K
2 1 0.730 0.712
1 0 0.281 0.332
3 1 0.842 0.831
2 0 0.229 0.305
4 1 0.159 0.124
3 0 0.064 0.052
5 1 0.124 0.105
4 0 0.020 0.031
3 2 0.801 0.748
5 0 0.007 0.010
4 2 0.862 0.894
2 1 0.697 0.722
5 2 0.188 0.150
3 1 0.412 0.502
4 3 0.827 0.786
4 1 0.114 0.096
5 3 0.896 0.972
5 1 0.042 0.062
5 4 0.871 0.695
3 2 0.816 0.794
I F Flower Thiswork
4 2 0.526 0.620
5 2 0.153 0.125 Temp.:70K
4 3 0.888 0.822 1 0 0.402 0.350
5 3 0.656 0.759 2 0 0.629 0.468
5 4 0.925 0.662 3 0 0.114 0.090
4 0 0.079 0.063
I F Flower Thiswork
5 0 0.027 0.028
Temp.:70K
2 1 0.684 0.620
1 0 0.336 0.344
3 1 0.858 0.728
2 0 0.300 0.320
4 1 0.199 0.174
3 0 0.098 0.083
5 1 0.124 0.111
4 0 0.035 0.044
3 2 0.732 0.686
5 0 0.020 0.024
4 2 0.871 0.808
2 1 0.636 0.602
5 2 0.236 0.216
3 1 0.486 0.509
4 3 0.757 0.711
4 1 0.177 0.161
5 3 0.880 0.844
5 1 0.061 0.080
5 4 0.779 0.719
3 2 0.681 0.659
4 2 0.567 0.591
5 2 0.221 0.205
4 3 0.678 0.689
5 3 0.631 0.654
5 4 0.748 0.705
I F Flower ThisworkJS98 ThisworkJS05
Temp.:30K
1 0 0.300 0.288 0.327
2 0 0.269 0.297 0.315
2 1 0.661 0.613 0.612
3 0 0.072 0.059 0.060
3 1 0.456 0.492 0.509
3 2 0.695 0.677 0.670
4 0 0.026 0.029 0.037
4 1 0.130 0.110 0.118
4 2 0.555 0.604 0.612
4 3 0.747 0.716 0.712
5 0 0.010 0.010 0.014
5 1 0.047 0.054 0.068
5 2 0.175 0.149 0.160
5 3 0.648 0.712 0.705
5 4 0.816 0.740 0.713
M.Wernlietal.:improvedlow-temperatureCO−H rotationalrateconstants,OnlineMaterialp1
2
Online Material
M.Wernlietal.:improvedlow-temperatureCO−H rotationalrateconstants,OnlineMaterialp2
2
I F a a a a a
0 1 2 3 4
1 0 -10.413 4.162 -20.599 32.563 -16.889
2 0 -9.202 -7.997 18.452 -18.717 6.910
2 1 -0.379 -59.429 131.662 -127.161 45.605
3 0 -3.319 -35.329 53.745 -29.641 2.471
3 1 -7.042 -20.755 48.788 -49.875 18.607
3 2 -1.976 -48.986 107.139 -102.134 36.288
4 0 -8.004 -16.164 28.359 -21.986 6.026
4 1 1.979 -69.801 140.821 -125.047 40.556
4 2 -5.102 -34.014 82.717 -87.211 33.665
4 3 -1.891 -49.861 109.419 -103.434 35.726
5 0 7.564 -106.151 220.187 -205.770 72.462
5 1 -5.209 -32.541 67.718 -63.996 23.105
5 2 4.736 -91.653 203.779 -201.295 73.681
5 3 -5.607 -31.380 78.077 -83.702 32.930
5 4 -0.510 -60.401 137.793 -134.344 46.449
Table .1. Fitting coefficients of CO-para-H rates, following
2
formula 3. I and F are the initial and final rotation states, re-
spectively.Theratesthusobtainedareincm3/s.
I F a a a a a
0 1 2 3 4
1 0 -7.351 -11.062 5.033 16.394 -14.176
2 0 0.331 -68.556 162.123 -167.243 63.863
2 1 4.370 -90.464 207.213 -207.995 77.557
3 0 4.128 -88.472 191.123 -181.945 64.170
3 1 -1.466 -57.252 138.316 -144.752 55.539
3 2 -0.194 -61.716 141.443 -142.699 53.788
4 0 -6.118 -31.232 70.967 -70.685 25.956
4 1 5.330 -96.359 215.047 -212.299 77.662
4 2 -2.940 -49.481 124.615 -135.311 53.609
4 3 -1.454 -53.713 122.102 -121.151 44.472
5 0 5.241 -96.162 206.655 -199.255 72.234
5 1 -6.365 -27.561 61.697 -61.299 22.802
5 2 6.689 -107.753 249.875 -256.409 97.478
5 3 -3.812 -45.669 119.845 -134.502 54.860
5 4 1.082 -71.954 169.486 -173.174 64.402
Table .2. Fitting coefficients of CO-ortho-H rates, following
2
formula 3. I and F are the initial and final rotation states, re-
spectively.Theratesthusobtainedareincm3/s.