H 3 + versus H 2 O Competition for trapping noble gases

H3+ versus H2O

Competition for trapping noble gases

Implications for the outer solar system composition

F. Pauzat & Y. Ellinger Laboratoire de Chimie Théorique

UPMC

O. Mousis & D. Cordier Observatoire de Besançon

UTINAM

Observations:Deficiency of Titan’s atmosphere

in primordial noble gases

Surprising since Titan was expected to be made from the same building blocks as those accreted by Saturn and to share a composition similar to that of the noble gases-rich planetesimals that took part in the formation of Jupiter …if the gas-phase conditions were homogeneous in the solar nebula

No noble gases other than argon detected by the Gas Chromatograph Mass Spectrometer aboard the Huygens probe

(January 2005)

The only detected argon is primordial 36Ar (the main isotope) and the radiogenic isotope 40Ar, a decay product of 40K. 36Ar/14N is about 6 orders of magnitude lower than the solar value, indicating that the amount of trapped 36Ar is poor for Titan (Niemann et al. 2005).

The other primordial noble gases 38Ar, Kr, and Xe were not detected.

Astrophysics

H3+ abundance profile

in the solar nebula(Mousis et al 2006)

H3+ is ubiquitous in space.

The calculated abundance profile of H3+ shows

an important increase

in the outer solar nebula

ChemistryWhat kind of association between noble gases and H3

+ ?

These complexes are thermodynamically stable

Complexes between noble gases and H3+ do exist

Mass spectrometry experiments by Hiraoka and Mori (1989) Argon multiple trapping

Experiments on Argon by Bogey et al (1988)

microwave spectrum

Chemists + Astrophysicists’ view

Observed deficit in some bodies could be due to the sequestration of the noble gases by H3

+ during the early stages of the solar nebula

Correlation between noble gases abundancies and H3+ ?

H3+ as a trap for noble gases: 1- The case of Argon

Pauzat, F., & Ellinger, Y. 2005 Planet. Space Sci. 53, 1389

Sequestration of noble gases by H3+ in the outer solar nebula- Implications for the formation of comets

Pauzat F., Ellinger Y., Mousis O. 2006, LPS C 37, 1331

H3+ as a trap for noble gases: 2- Structure and energetics of XH3

+ complexes from X=Neon to Xenon

Pauzat, F., & Ellinger, Y. 2007 J. Chem. Phys.127, 14308

Sequestration of noble gases by H3+ in protoplanetary disks and outer solar system

composition Mousis O., Pauzat F., Ellinger Y., Ceccarelli C. 2008 , ApJ 673, 637

H3+ as a trap for noble gases:3- Multiple trapping of Neon, Argon, and Krypton in XnH3

+

Pauzat, F., Ellinger, Y., Pilmé, J. & Mousis, O. 2009 J. Chem. Phys.130, 174313

Determination of the Minimum Masses of Heavy Elements in the Envelopes of Jupiter and Saturn

Mousis, O., Marboeuf, U., Lunine, J. , Alibert, Y., Fletcher, L. N., Orton, G. S., Pauzat, F. & Ellinger, Y. 2009., ApJ. 696, 1348

Clathration of Volatiles in the Solar Nebula and Implications for the Origin of Titan's Atmosphere

Mousis, O., and 10 colleagues 2009, ApJ. 691, 1780

Interdisciplinary collaboration

XH3+

Stable structure Transition states

Energetics of complexes

Reaction Ar Kr Xe

XH3+ X + H3

+ 7.22 12.71 21.98

XH3+ XH+ + H2 17.04 9.53 3.52

Reaction Ar

XH3+ X + H3

+ 7.22

X2H3+ X + XH3

+ 4.15

X3H3+ X + X2H3

+ 3.93

Binding energies

expressed in kcal/mole

Examples (1,2) by MP2/ccpVQZ

(3) by CCSD(T)/Aug-cc-pVQZ

all with ZPE and BSSE included

Multiple trapping(2)

Stabilitiy of the complex versus two dissociatve ways

(1)

X+ + H + H2

X + H+ + H2

XH+ + H2

X + H3 +

XH3+

(3)

(1.1) (7.3) (8.5) (2.8)

A tricky artifact: the Basis Set Superposition Error

Ne Ar Kr Xe

deq(X-Hx) Ǻ 1.794 1.831 1.724 1.645

without correction 1.764 1.797 1.716 1.653

A GHz 1353.9 1463.0 1585.1 1744.9


B GHz 35.147 30.607 29.502 22.997


C GHz 34.258 29.979 28.963 22.697


∆Edissoc Kcal/mol 1.10 7.35 13.5 23.6


Whatever the observable corrections are mandatory

Distances

RotationalConstants

EnergyDifferences

CCSD(T)//Aug-cc-pVQZ

Modeling of the noble gases - H3+ interaction

with ab initio chemical calculations

Ne H3+ Ar H3

+ Kr H3+ XeH3

+

Isosurfaces of the basins of the Electron Localisation Function (ELF code)

Electronic structures are different

Difficult to define the interacting fragments

in particular when dealing with the XnH3+

HH

H

Ia Ib

X HH

HX

X = Ne, Ar X = Kr, Xe

Topological analysis of the noble gases - H3+

interactionfrom ab initio calculations

More questions chemistry relevant I

Calculations of the zero point vibrational energies of H2D+ and XH2D+ show that:

the variation of the stability of the deuterated complexes

with respect to the hydrogenated parents

is too small to alter the trapping mechanism

(a few tenths of kcal/mole)

Due to H/D fractionation, one may ask the question :

Could H2D+, also abundant in the gas phase, modify the complexation energetics?

II

Helium gives much weaker complexes

that cannot interfere with the trapping processes considered.

The HeH3+ binding energy (~ 0.1 kcal/mole)

is about two orders of magnitude below that of the XH3+ (X=Ar, Kr, Xe).

What about the first of the noble gas series i.e. helium

the most abundant element after hydrogen ?

IIITaking into account the large quantity of H2 available,

could it happen that H2 saturates large amounts of H3+, which

then will no longer be free for X trapping?

Reaction Ar Kr XeX + H3

+ XH3+ 7.22 12.71 21.98

X + H5+ XH3

+ + H2 1.78 7.27 16.54

The exothermicities (kcal/mole) of the last reaction

show that in fact H5+ cannot play such role in the process.

IVIs trapping of the noble gas by H2O present in the gas phase

to be considered?

Reaction Ar Kr XeXH3

+ X + H3+ 7.22 12.71 21.98

XH3+ XH+ + H2 17.04 9.53 3.52

XH2O X + H2O 0.37 0.29 0.55

The XH2O binding energies (kcal/mole) are more than one order of magnitude smaller than those of XH3

+. Together with the much larger distance between X and the molecular fragment

(A) it is the illustration of van der Waals versus ion molecule interactions.

This result rules out any possibility of direct trapping by water in the gas phase.

Ar 1.82 2.87Kr 1.76 2.96 Xe 1.66 3.13

X

V

Case of crystalline ice, currently under investigation

Preliminary studies of Ar in crystalline ice

(solid-state aspect studied using a periodic description of crystalline ice with plane wave basis functions (VASP code))

Show that

the noble gas cannot be significantly trapped at the surface,

neither inside the ice bulk.

Clathrate trapping being considered in models,

is it worth to consider trapping by crystalline ice?

Competition H3+ versus H2O

gas phase

The high proton affinity of H2O compared to H2

(~170 compared to ~101 kcal/mole)

suggests that H3+ and H2O may not coexist in the gas phase.

H3+ + H2O H3O+ + H2

highly exothermic reaction (64.40 kcal/mole).

First Principles dynamics calculations performed (PINY code):

starting with zero kinetic energy of the fragments,we found 100% efficiency for the reaction in less than one picosecond (ps).

Quantum Dynamics procedure

0.0

-72.0

-66.4+ H2O

0.76

H3O+ + H2

H H

1.53

H

H

O+

H

1

2

3

+HH

H

Initial geometries drawn at random.Calculations at DFT level.Energies (~ 0) within +/- one degree of vibration

Trajectory analysis as a function of d(OH) distances

Direct Rotation of H2 Vibration of OH + Rotation of H2

Release of H2

Competition H3+ versus H2O

solid phase

In presence of solid amorphous ice (here modelled by small clusters)

the same quantum dynamics shows three possible exit channels,

all with proton transfer, all releasing H2:

H3+ + (H2O)n [(H2O)n]H+ + H2 ice protonation (major)

[(H2O)n-1]H+ + H2O + H2 ice protonation + destruction

[(H2O)n-1] + H3O+ + H2 ice destruction

The branching ratios are currently being refined using longer simulation times (several ps) (Zicler et al. in progress).

Ice destruction: Analysis of destructive trajectories

5 (out of 20) destructive events :

– 2 obvious total destructions

– 3 destructions not complete

ex:

(to be checked by increasing simulation time)

H2 + H2O + [H2O…H3O]+

partial destruction with H2 et H2O released;

the ice cluster itself might not be destroyed

even if energy is sufficient

25% collisions efficient

for destruction of ice

Simulation at E = -5,6 kJ.mol-1

0.0

-111,0

H2 + [H3O+ - - - (H2O)2]

-86,7

-112,2

(H2O)3 + H3+

[H2...H7O3]+

H5O2+ + H2O + H2

H3O+ + (H2O)2 + H2

-49,5

-55,1 2 H2O + H3O+ + H2

Example of analysis by O-O distances : case of the trimer

Unexpected outcome : H3O+, as formed in the reaction, may be also a

noble gas trapping agent

with the noble gas linked to a hydrogen atom

and binding energies ranging from 4 to 9 kcal/mole

Reaction Ar Kr Xe

XH3O+ X + H3O+ 4.35 5.99 8.15

XH3O+ XH+ + H2O 78.58 67.24 54.09

Ar 1.82 2.87 2.06 1.28

Kr 1.76 2.96 2.17 1.41

Xe 1.66 3.13 2.32 1.60

X

dXH(Ang)

XH3+ versus H2O

What about the stability of the XH3+ complex itself

in presence of H2O?

Energetics of the two destruction reactions:

XH3+ + H2O XH3O+ + H2

XH3+ + H2O X + H3O+ + H2

show that the XH3+ complexes should be destroyed

with H2 released in the gas phase.

The large exothermicity of the reaction could lead to the release of X, allowing its recycling in the gas phase

Reaction Ar Kr Xe

XH3O+ X + H3O+ -4.35 -5.99 -8.15

XH3+ + H2O XH3O+ + H2 61.53 57.71 50.57

XH3+ + H2O X + H3O+ + H2 57.18 51.72 42.42

(Exothermicities in kcal/mole)

Computational Chemistry contribution • Complexes of XH3

+ generic formula (X=Ar, Kr, Xe) could lead to an efficient trapping of rare gases by H3

+

• H2O in presence of H3+ gives H3O+ that is eligible for noble gases sequestration.

• In the gas phase, XH3+ complexes could be destroyed by H2O, if available , with

H2 and X released in the gas phase , X being available for recycling.

• In addition, it is demonstrated that :

He, irrespective of its abundance, has no impact on the sequestration of the noble gases.

Deuteration plays no role in the process in the sense that there is no energetic difference between complexation by H3

+ or by H2D+.

Sequestration of noble gases by H2O in the gas-phase, giving very weak complexes, should be inefficient.

• Preliminary simulations show no accretion on crystalline ice but this has to be confirmed. The last plausible mechanism worth to be studied remains trapping in clathrate cages.

The H3+ abundance in the inner 30 AU of the solar nebula

H3+ is formed by the ionization of H2 from energetic particles, such as those in

the cosmic rays or those emitted by the young Sun, at a rate ep, and destroyed by the reactions with the most abundant molecules, namely H2O, CO and N2, at rates kdH2O, kdCO and kdN2, respectively.

At steady state, the formation and destruction rates balance, and this provides the following relation:

This equation shows that the H3+ abundance is inversely proportional to the

H2 density and linearly depends on the ionization rate ep.

€

€

xH3

+ =ζ ep

nH2KdH2O xH2O +KdCO xCO +KdN2

xN2( )

The H3+ abundance in the inner 30 AU of the solar nebula

H3+ abundance in the disk’s midplane as a function

of the distance from the center in the case of a cosmic-ray ionization rates of 1 and 1,000 times the standard value(Mousis et al. 2008).

ep is estimated to range between 10-17 s-1

(Webber 1998) and 10-15 s-1 (Payne et al. 1984).

Here we adopt the higher value to consider the most optimistic case of H3

+ abundance.

Additional sources of energetic particles might have existed in the early solar system:

- Inner source: irradiation of energetic particles from the young Sun (Gounelle et al. 2001, 2006)

- External source: presence of a nearby supernova during solar system formation (Busso et al. 2003; Tachibana & Huss 2003)

Considering these possible enhancements, we made the assumption that at least Kr and Xe could be efficiently trapped by H3

+ in the primordial nebula.

Two different reservoirs of ices in the nebula

• Ices located at distances higher than 30 AU remained pristine (amorphous ices)

• Ices transported at distances lower than 30 AU vaporized and condensed again in crystalline form (Chick & Cassen 1997)

CO:CO2:CH3OH:CH4 = 70:10:2:1 and N2:NH3 = 1:1 in the gas phase

Formation of clathrates and pure condensates in the outer solar nebula

grainsgrains

planetesimalsplanetesimals

condensation/trapping

condensation/trapping

accretionaccretion

diskdisk

Formation of icy planetesimals in protoplanetary disks assuming a solar abundance for all elements

Ices are stable in domains located below their stability curves

Structure of clathrates

Water molecules (hosts) form cagesstabilized by the inclusion of volatile molecules (guests)

Three different structures according to the size of the included guest molecule

Structure I: 2 small cages, 6 large cages X-5.75H2O

Structure II: 16 small cages, 8 large cages

X-5.66H2O

Structure H

In situ measurements by the Galileo probe of the volatile enrichments in Jupiter

Owen et al. (1999)

Matching the volatile enrichments in Jupiter from different gas phase compositions of the disk

Red bars correspond to observations. Green and blue bars correspond to calculations based on the assumption that C/O = 0.5 (solar case) and C/O = 1 (C-rich case) in the disk.

Conclusion: Jupiter could be carbon rich!!!! Testing this hypothesis requires the measurement of O in Jupiter by Juno

Mousis, Madhusudhan, Lunine & Johnson (2012)

Formation of XH3+ complexes: implications for

Jupiter’s noble gas content

If the H3+ abundance were comparable to those of Kr and Xe in

Jupiter’s feeding zone (H3+/H2 ≈ 10-9–10-10), then the resulting

enrichments of these two nobles gases in the Jovian envelope should be lower than the calculated values and would match the observed values.

For example, if H3+/H2 ≈ 5 x 10−10 in the feeding zone of Jupiter and if

similar amounts of Kr and Xe have been trapped by H3+, their

corresponding enrichments are now 2.4 and 1.9 times solar and match the observed values.

Characteristics of Titan

Atmosphere dominated by N2 and CH4

CO/CH4 << 1 --> What happened to CO?

N2 would result from the NH3 photolysis or shock chemistry (Atreya et al. 1978; McKay et al. 1988). So, N2 is probably not primordial!!

High CH3D/CH4 ratio (Orton 1992; Bézard et al. 2007): atmospheric methane probably formed in the solar nebula and NOT via hydrothermal reactions in the interior of Titan (Mousis et al. 2009a) or via gas phase chemistry in Saturn’s subnebula (Mousis et al. 2002)

D/H ratio found to be cometary in Enceladus: the building blocks of Titan and Enceladus were formed in the nebula (Waite et al. 2009).

Deficiency of Titan’s atmosphere in primordial noble gases. Only low amounts of 36Ar have been detected (Niemann et al. 2005)

Formation sequence of ices in Saturn’s feeding zone and the origin of Titan

Mousis et al. (2009a)

A formation of Titan in the 25-50 K temperature range is required to explain at least partly its atmospheric composition.

In these conditions, building blocks of Titan are Ar- and CO-poor

However, major issue: Kr and Xe are trapped in the building blocks of Titan!!

Formation of Titan’s building blocks in presence of H3+

in the gas phase

Mousis, Pauzat, Ellinger & Ceccarelli (2008) ApJ 673, 637-646

Species X (X/H2)

Ar 8.43 x 10-6

Kr 4.54 x 10-9

Xe 4.44 x 10-10

Protosolar abundances of noble gases (Lodders 2003)

;

H3+ abundance in the disk midplane as a function

of the distance from the center in the case of a cosmic-ray ionization rate of 1 time the standard value and in the case of an enhancement of 1000.

Formation of XH3+ complexes in the gas phase of the nebula (with X = Kr and

Xe) that impede the formation of X-nH2O clathrates or pure condensates X

Implications for Saturn’s noble gas content

Saturn and Titan formed from building blocks formed at the same formation locations.

Kr and Xe should be in solar abundances in Saturn’s atmosphere.

The H3+ abundance profile: a probe to investigate the formation location of

comets in the nebula?

The D/H enrichment observed in H2O in

Saturn’s satellite Enceladus is remarkably similar to the values observed in Oort Cloud comets (OCCs) (Waite et al. 2009). Given the predicted strong variation of

D/H with heliocentric distance in the solar nebula, this observation links theprimordial source region of the these comets with the formation location of Enceladus.

Because both Enceladus and Titan are expected to have formed from planetesimals sharing similar compositions (Mousis et al. 2009b), one can predict that OCCs also present important impoverishments in Kr and Xe.

Deuterium enrichment profile in solar nebula ices (Kavelaars et al. 2011)

Predictions for the Rosetta target

Short Period Comets, such as the Rosetta target Comet 67P/Churyumov-Gerasimenko, are expected to have formed at different locations.

Dynamical and chemical models of the nebula predict the formation locations of these comets

at higher heliocentric distances than OCCs (Kavelaars et al. 2011).

Recent measurement of the D/H ratio in H2O in the Jupiter Family Comet 103P/Hartley 2, which has been found to be equal to the SMOW value,(Hartogh et al. 2011), suggests that this family of comets may have formed at lower heliocentric distances.

The strong variation of H3+ abundance with

heliocentric distance in the solar nebula could help to disentangle the different formation locations of these populations of comets.

Comets formed closer to the Sun than OCCs should present higher Kr and Xe abundances. Comets formed at higher distances than OCCs should present at least similar Kr and Xe impoverishments.

H 3 + versus H 2 O Competition for trapping noble gases

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