Low temperature quantum rate coefficient of the H þ CH1

reaction

T. Stoecklin and Ph. Halvick

Laboratoire de Physico-Chimie Moleculaire, UMR5803-CNRS, Universite Bordeaux I,351 cours de la Liberation, 33405 Talence Cedex, France

Received 14th March 2005, Accepted 4th May 2005First published as an Advance Article on the web 24th May 2005

In this paper we report the first theoretical study of the title reaction. A global, single-valued model of theground-state potential energy surface has been obtained by fitting to an extensive set of high-level ab initiocalculations. The surface is found to be attractive apart from linear geometries where energy barriers appear dueto conical intersections. This model was then used to calculate the reactive reactant state selected cross sectionsfor collision energies ranging from threshold up to 4000 cm�1. These calculations were performed using ourversion of the Baer’s approach of the RIOSA-NIP method which is based on the use of a negative imaginarypotential. We find that the reaction probability is extremely oscillatory as a function of kinetic energy as it is acase for insertion reactions with a low exoergicity. The resulting reaction rate coefficient is found to first increaseslowly as a function of temperature up to a broad maximum around 20 K and then to decrease slowly whentemperature keeps increasing.

1. Introduction

The methylidyne cation CH1 is a key species of carbonchemistry in diffuse interstellar molecular clouds. It was iden-tified in 19411 and since then, it has been a problem to explainthe observed overabundance of CH1. Indeed, the primaryprocesses able to produce this ion are the collisions of C1 withatomic and molecular hydrogen.

C1 þ H - CH1 þ hn (1)

C1 þ H2 - CH1 þ H (2)

However, the observed abundance could not be accountedby these reactions because reaction (1) is very slow (k ¼ 10�17

cm3 molecule�1 s�1) and reaction (2) is endothermic by 0.4 eV.The difficulty to explain the CH1 abundance was recognized in19512 and it was the origin of many works focusing on theconditions that could favour reaction (2) in the interstellarmedium. It was proposed that the reaction occurs in high-temperature shocked gas,3–6 as a consequence of the shockwaves travelling through interstellar clouds. However, furtherworks have shown that the shock hypothesis is not fullyconclusive when compared to observations.7,8 The shock mod-els have difficulties in reproducing altogether the observationalconstraints.

The title reaction is the reverse reaction to 2, and account forthe loss of CH1. In any case, this reaction must be included inany attempt to model CH1 concentrations in diffuse interstel-lar clouds. The inelastic process is also of interest, as it willaffect the rotational temperature of CH1.9

Experimental data about the H þ CH1 reaction are hardlyavailable. Only one measurement of the rate coefficient hasbeen published.10 The value reported is large (k300 K ¼ 7.5 �10�10 cm3 molecule�1 s�1) and decreases as the mean averagekinetic energy increases, which suggests a reaction with nobarrier or a very small one. We may also mention a separateevaluation11 of this rate coefficient based solely on data of theC1 þ H2 reaction.

No theoretical work has been published specifically on thetitle reaction, but the inverse reaction has been the subject of

many calculations of potential energy surfaces (PES). Theseworks12–16 were mainly devoted to the search of the lowestenergy path toward the products CH1 þ H. The essentialresult is that no barrier in excess of the endothermicity wasfound.Finally, let us mention some recent spectroscopic works on

the methylene cation CH21. Experimental data on the struc-

ture17 and vibrational frequencies18,19 have been reported forthe ground state X 2A1.In the first part of this work, we constructed an accurate 3-D

single-valued potential energy surface. A large grid of ab initiopoints was computed, using an extensive multiconfigurationalwavefunction and the augmented correlation consistent (aug-cc-pVQZ) basis set of Dunning. The potential energy surfacewas then fitted to a global analytical form including long-rangeinteraction and ad-hoc terms for conical intersections. In thesecond part of this work we performed time independentdynamics calculations using negative imaginary potential with-in infinite order approximation, as proposed by Baer and thenused by different groups. The reactant state selected crosssections were computed for a large grid of collision energyranging from 10�5 up to 4000 cm�1 and then used to obtain therate coefficient as a function of temperature.The paper is organised as follows. In Section 2 we outline a

description of the ab initio calculations and detail the potentialenergy surface functional form, along with the method for thequantum dynamics. In Section 3, the potential energy surface isdiscussed, and then the parameters used to make the dynamicscalculations are briefly detailed and the resulting reactive crosssection and rate coefficients are presented.

2. Method

2.1. Ab initio calculations

The ground state of the diatomic molecule CH1 is X 1S1 andthe first excited state is a 3P. The collision with H(2S) yields the2P and 2S1 states of linear CH2

1, which become two 2A0 andone 2A00 states for bent CH2

1. Because CH1(X 1S1) has noelectron available for bonding, the approach of a hydrogenatom yield a repulsive potential energy for CH2

1(2S1), as long

R E S E A R C H P A P E R

PC

CP

ww

w.rsc.o

rg/p

ccp

DO

I:1

0.1

03

9/b

50

37

14

j

2446 P h y s . C h e m . C h e m . P h y s . , 2 0 0 5 , 7 , 2 4 4 6 – 2 4 5 2 T h i s j o u r n a l i s & T h e O w n e r S o c i e t i e s 2 0 0 5

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as the three atoms are in a line. However, the first excited statea 3P of CH1 has the configuration 1s22s23s11p1. Thus, anelectron is available for linear bonding, leading to the forma-tion of a strong bond. As a result, there is a crossing betweenthe 2P and 2S1 states of linear CH2

1. Of course, this crossingbecomes an avoided crossing between the two 2A0 states whenCH2

1 is bent. This is the well known case of a conical intersec-tion. Note that both the H–C–H and H–H–C linear config-urations display a conical intersection. Therefore, in order toget a realistic model of the ground state PES of CH2

1, it isnecessary to use a method that accounts for the importantelectronic rearrangements produced by the conical intersec-tions and by bond breaking. We have chosen the completeactive space self consistent field (CASSCF) method along withthe contracted multireference configuration interaction(CMRCI) method,20 and with the basis set aug-cc-pVQZ.21

The complete active space (CAS) wavefunction was developedover 6 orbitals (five a0 orbitals and one a00 orbital) containingfive electrons, while the two electrons belonging to the 1sorbital of the carbon atom were not correlated. This definesthe molecular orbitals set computed with the CASSCF method.Then, with the CMRCI method, all electrons were correlatedby all single and double excitations from the CAS wavefunc-tion. The Davidson correction was also included. The MOL-PRO package22 has been used to perform these calculations.

2.2. Functional form of the potential energy surface

The potential energy function is written as a sum of two-bodyV(2) and three-body V(3) terms

V(R1, R2, R3) ¼ V(2)HH(R1) þ V(2)

CH(R2) þ V(2)CH(R3)

þ V(3)(R1, R2, R3) (3)

where R1, R2 and R3 are, respectively, the internuclear dis-tances of the diatomic fragments H–H, C–H, and C–H (Fig. 1).

The two-body potentials have been built within the frame-work of the reproducing kernel Hilbert spaces (RKHS) meth-od.23,24 In the case of 1-D semi-infinite interval [0,N], thereciprocal power reproducing kernel qn,m is of particular inter-est because it can be adjusted to the correct long-rangebehaviour. With N data points xj, the interpolated energycurve for any diatomic molecule can be written

Vð2ÞðRiÞ ¼XNj¼1

cjq2;mðRi; xjÞ ð4Þ

For n ¼ 2, the kernel qn,m is given by

q2;mðx; x0Þ ¼ 4x�m�14

ðmþ 1Þðmþ 2Þ 1� ðmþ 1Þxoðmþ 3Þx4

� �

x4 ¼maxðx; x0Þ

xo ¼minðx; x0Þ

ð5Þ

It is easy to see that for Ri 4 max(xj), j A [1,N], the energycurve V(2) becomes a sum of two terms

V ð2ÞðRiÞ ¼Am

Rmþ1i

þ Bm

Rmþ2i

ð6Þ

with

Am ¼4

ðmþ 1Þðmþ 2ÞXNj¼1

cj

Bm ¼�4

ðmþ 2Þðmþ 3ÞXNj¼1

cjxj

ð7Þ

Therefore, by simply selecting the suitable value for m, thelong-range behaviour of the interpolated energy curve can betailored to reproduce correctly the long-range interactions.25

The values m ¼ 3 and m ¼ 5 were used, respectively, for CH1

(charge – induced dipole) and H2 (dispersion).The three-body potential is the sum of two terms VSR and

VLR that represent, respectively, the short-range part and thelong-range part of the potential energy.

V(3) (R1, R2, R3) ¼ VSR (R1, R2, R3) þ VLR (R1, R2, R3) (8)

VSR is defined as a product of a 3-D polynomial and adamping function26,27 plus the ad-hoc local term Vc necessaryto represent the small potential peak due to the conicalintersection induced by the crossing of the 2P and 2S1 statesof CH2

1.

VSRðR1;R2;R3Þ ¼ PðQ1;Q2;Q3ÞY3i¼1½1� tanhðgiðRi � R0

i Þ=2Þ�

þ VcðR1;R2;R3Þð9Þ

where P is the sixth-order polynomial

P(Q1,Q2,Q3) ¼ c0 þ c1Q1 þ c2Q3 þ c3Q12 þ c4S2a

2

þ c5Q1Q3 þ c6S2b2 þ c7Q1

3 þ c8Q1S2a2

þ c9S33 þ c10Q1

2Q3 þ c11Q1S2b2 þ c12Q3S2a

2

þ c13Q14 þ c14Q1

2S2a2 þ c15S2a

4 þ c16Q1S33

þ c17Q13Q3 þ c18Q1

2S2b2 þ c19Q1Q3S2a

2

þ c20Q3S33 þ c21S2a

2 S2b2 þ c22Q1

5

þ c23Q13S2a

2 þ c24Q1S2a4 þ c25Q1

2S33

þ c26S2a2 S3

3 þ c27Q14Q3 þ c28Q1

3S2b2

þ c29Q12Q3S2a

2 þ c30Q1Q3S33

þ c31Q1S2a2 S2b

2 þ c32Q3S2a4 þ c33S2b

2 S33

þ c34Q16 þ c35Q1

4S2a2 þ c36Q1

2S2a4

þ c37Q13S3

3 þ c38Q1S2a2 S3

3 þ c39S2a6

þ c40S36 þ c41Q1

5Q3 þ c42Q14S2b

2

þ c43Q13Q3S2a

2 þ c44Q12Q3S3

3

þ c45Q12S2a

2 S2b2 þ c46Q1Q3S2a

4

þ c47Q1S2b2 S3

3 þ c48Q3S2a2 S3

3

þ c49S2a4 S2b

2 (10)

S2a2 ¼ Q2

2 þ Q32 (11a)

S2b2 ¼ Q2

2 � Q32 (11b)

S33 ¼ Q3

3 � 3Q22Q3 (11c)

and Qi (i ¼ 1,2,3) are the D3h symmetry coordinates defined by

Q1

Q2

Q3

24

35 ¼ 1=

ffiffiffi3p

1=ffiffiffi3p

1=ffiffiffi3p

0 1=ffiffiffi2p

�1=ffiffiffi2p

2=ffiffiffi6p

�1=ffiffiffi6p

�1=ffiffiffi6p

24

35 R1 � 1

R2 � 1R3 � 1

24

35 ð12Þ

These coordinates can be used for an AB2-type molecule,as long as R2 and R3 are chosen to label the two AB bondlengths.As a consequence of the conical intersection, a small poten-

tial energy barrier is observed for linear configuration of CH21.

This barrier disappears progressively when CH21 is bending.

Then, depending on the angle between the CH1 internuclearaxe and the axe going from the approaching H atom to theCH1 center of mass, the PES of the ground state 2A0 will beFig. 1 Definition of the coordinates systems.

P h y s . C h e m . C h e m . P h y s . , 2 0 0 5 , 7 , 2 4 4 6 – 2 4 5 2 2447T h i s j o u r n a l i s & T h e O w n e r S o c i e t i e s 2 0 0 5

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repulsive (angle near 0 or 1801) or attractive. In order toreproduce this behaviour, the Vc term has been added to theshort-range potential. Keeping in mind that the potential mustbe symmetric with respect to the permutation of hydrogenatoms and that the conical intersection appears for H–C–Hand H–H–C linear configurations, we write

Vc(R1,R2,R3) ¼ F1(R2,R3,y1) þ F1(R3,R2,y1)þ F2(R1,R3,y2) þ F2(R1,R2,y3) (13)

FnðRi;Rj ; ykÞ ¼ e�atðp�ykÞe�arðRj�Rð0ÞÞ2GnðRi; ykÞ ð14aÞ

GnðRi; ykÞ ¼ gn1ðRiÞ þ gn2ðRiÞ

�ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðgn1ðRiÞ � gn2ðRiÞÞ2 þ ð2v sin ykÞ2

qð14bÞ

where the functions gn1 and gn2 are 1-D local approximationsof the energy along the reaction coordinate of the linear 2P and2S1 states just around the crossing point

gnkðRiÞ ¼ anke�bnkRi ð15Þ

Note that Vc is only an ad-hoc corrective term for the PES ofthe ground state. Therefore, this PES can be used only fordynamics at collision energy lower than the lowest point of thecrossing seam, and by assuming that the rate of electronictransition is negligible in that case, which is quite realistic atvery low collision energy.

Let us now define the functional form for long-range poten-tial energy

VLRðR1;R2;R3Þ ¼X3i¼1

fiðR1;R2;R3ÞXnmaxi

n¼nmini

Uinðri;jiÞwinðriÞ

ð16Þ

where the sum on i runs over the three dissociation channelsH0 þ CH, H þ CH0 and C þ H2. The sum on n runs overthe various contributions to the long-range interactionenergy which are defined below. For each channel, ridenote the distance between the atom and the center ofmass of the diatomic and ji the corresponding Jacobi angle(Fig. 1). The function fi is a switching function which selects thechannel i.

fiðR1;R2;R3Þ ¼1

2f1� tanh½gsi ð3di � dj � dkÞ�g ð17Þ

with di ¼ Ri � Rie, where Ri

e is the equilibrium distance of thediatomic molecule for the i-th channel. wi is a short-rangedamping function defined by

win ¼ [1 � exp(�a0n�a1 ri � b0 exp (�b1n)ri2)]n (18)

In the case of the H þ CH1 arrangement, we have a long-range interaction between an atom with a zero quadrupolemoment and a charged diatomic with a permanent dipolemoment. The interaction energy can be written25 as a sum ofthree contributions

X6n¼4

Uinðri;jiÞ ¼ �e2aH

2r4i ð4px0Þ2� 2eaHmCHþ cosðjiÞ

r5i ð4px0Þ2

�aHm2CHþ ½3 cos

2ðjiÞ þ 1�2r6i ð4px0Þ

2ð19Þ

With the second arrangement C1 þ H2 we have the long-range interaction between a charged atom and a diatomic withno permanent dipole moment. Then, the interaction energy issimply

Ui4ðri;jiÞ ¼ �e2aH2

2r4i ð4px0Þ2

ð20Þ

2.3. Dynamics

Since the first paper of Baer et al.28 introducing the use ofnegative imaginary potential within a time independent ap-proach, many different versions of his method29–31 have beenproposed. All of them combine inelastic scattering calculationsand the presence of a negative imaginary potential (NIP) whicheither absorbs the reactive flux in the product channel ordefines the initial conditions of the propagation as it is thecase in the recent version of the adiabatic capture methodproposed byManolopoulos (see ref. 36). Here, we use one of itssimpler version which is based on the reactive infinite ordersudden approximation and will be denoted RIOSA-NIP inorder to distinguish it from the traditional RIOSA method. Wewill only remind of the main steps of a RIOSA-NIP calculationand mention the specificities of our version of the method sinceit is very close to the one presented in great details by Huarte-Larranaga et al.31 For the sake of simplicity, we will in whatfollows use the common notations (R,r,g) for the Jacobicoordinates associated with the H þ CH1 channel. We thenhave to solve for each value of the total angular momentum, J,and for each value of the Jacobi angle, g, the RIOSA Schro-dinger equation for reactive collision in the reactant H þ CH1

Jacobi coordinates:

� �h2

2m@2

@R2þ @2

@r2

� �þ �h2

2mJ J þ 1ð Þ

R2þ Vmod R; r; gð Þ � E

� �

CJ R; r; gð Þ ¼ 0

ð21Þ

The only element which distinguishes this equation from itsnon-reactive32 counterpart lies in the potential which is heremade of the summation of the potential energy surface of thereaction and of an optical potential which absorbs the reactiveflux and is located in the product channel after the transitionstate.

Vmod (R,r,g) ¼ V(R,r,g) þ VNIP (R,r,g) (22)

This negative imaginary potential was taken to be a linearramp

VNIPðR; r; gÞ ¼ �iu0ðgÞr� rmin

r� rmaxfor rmin � r � rmax ð23Þ

where the range of R is unlimited and the two parameters Dr ¼rmax � rmin and u0(g) are chosen according to the conditionsobtained by Baer in order to minimise total reflection:

1

Dr

ffiffiffiffiffiffiE

8m

soju0joDr

ffiffiffiffiffiffi8m

pE

32 ð24Þ

The range of propagation of the R coordinates is dividedinto N sectors. In each sector, the function CJ(R,r,g) isexpanded in a local adiabatic basis set. In the i-th intervalcentered around R ¼ Ri one writes:

CJ R; r; gð Þ ¼Xn

fJn;iðRi; r; gÞwJn;iðRÞ ð25Þ

The local basis set is obtained by solving the reducedSchrodinger equation

� �h2

2m@2

@r2

� �þ �h2

2mJðJ þ 1Þ

R2i

þ VðRi; r; gÞ � en;i

� �wJn;iðr; gÞ ¼ 0 ð26Þ

The resulting close-coupling equations are propagated for agiven total energy E from the origin outwards to the asympto-tic region where the asymptotic boundary conditions for aninelastic problem are imposed. The resulting vibrationallyinelastic SJ(E,g,ni,nf) matrix is non-unitary and its default tounitarity is precisely the reactive probability to obtain any stateof the products for a value of J, a given Jacobi angle, g, and a

2448 P h y s . C h e m . C h e m . P h y s . , 2 0 0 5 , 7 , 2 4 4 6 – 2 4 5 2 T h i s j o u r n a l i s & T h e O w n e r S o c i e t i e s 2 0 0 5

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given ni vibrational state of the reactant

PJreactionðE; g; viÞ ¼ 1�

Xnf

SJðE; g; ni; nf Þ�� ��2 ð27Þ

The usual RIOSA integration over the g Jacobi angle andsummation over J gives then the reactive cross section for atotal energy E and a given ni vibrational state of the reactant.

sreactionðE; viÞ ¼p

2kvi

Zp0

dg sin g

�XJ

1�Xnf

jSJðE; g; ni; nf Þj224

35

8<:

9=;ð28Þ

The rate coefficient for reaction is then obtained by Boltz-man averaging over both the vibration and the collisionenergy.

3. Results and discussion

3.1. Potential energy surface

A set of 3291 ab initio points was used to compute theparameters of the short-range three-body potential VSR [eqn.(9)]. The determination of the polynomial’s parameters [eqn.(10)] was performed with a try and error process. First, guessvalues were given to the parameters gi and R0

i of the dampingfunction [eqn. (9)] and then the parameters ci were computedwith the linear least-squares method. Then, this step wasrepeated several times with different values for the parametersof the damping function until the root-mean-squares (RMS)deviation reached a minimum of 0.0594 eV. Separate sets ofab initio points were used for computing the parameters of two-body potentials. The numerical values of all coefficients andparameters are available on request.

Fig. 2 shows a comparison between ab initio data and thefitted PES for linear configurations. An overall good agree-ment is observed. The effect of the corrective term for theconical intersection [eqns. (13)–(15)] is also shown.

The two-body potential for CH1 has a dissociation energyDe ¼ 4.270 eV and an equilibrium distance re ¼ 2.130 a0, which

compares well with the experimental value 4.255 eV and 2.137a0. For H2, the same quantities are, respectively, 4.737 eV and1.402 a0, with the experimental values 4.751 eV and 1.401 a0.This yields an exoergicity of 0.467 eV, while the experimentalvalue is 0.496 eV.The minimum energy of the fitted PES is found at R2 ¼ R3 ¼

2.075 a0 and y1 ¼ 137.31. The corresponding experimentalvalues17 are 2.088 a0 and 139.81. The H þ CH1 dissociationenergy is 4.861 eV. This is close to the previous theoreticalvalue (4.794 eV) proposed by Jaquet et al.16

The barrier to linearity is 0.189 eV. The top of this barriercorresponds to a DNh saddle point with the structure R2 ¼R3 ¼ 2.075 a0 for the ground state X 2A1 PES. It correspondsalso to a minimum on the first excited state A 2B1, because thetwo electronic states are degenerate (2P) at linear configuration.Figs. 3 and 4 display equipotential energy contours for linear

configurations of the processes

H þ CH1 2 HCH1 2 HC1 þ H (29)

Fig. 2 Comparison between the ab initio energies (þ) and the fittedpotential energy with (solid line) or without (dashed line) the correctiveterm for the conical intersection. The geometry of CH2

1 is linear withy1 ¼ 1801 and R3 ¼ 2.14 a0.

Fig. 3 Contour plot of the PES for linear configuration H–C–H. Inthis figure and the following ones, the contour lines are equally spacedby 0.5 eV and the highest contour is �2 eV.

Fig. 4 Contour plot of the PES for linear configuration C–H–H.

P h y s . C h e m . C h e m . P h y s . , 2 0 0 5 , 7 , 2 4 4 6 – 2 4 5 2 2449T h i s j o u r n a l i s & T h e O w n e r S o c i e t i e s 2 0 0 5

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CH1 þ H 2 CHH1 2 C1 þ H2 (30)

In Fig. 3 (process 29), the potential energy is perfectlysymmetric with respect to the exchange of hydrogen atoms asexpected. The minimum of the potential well correspond to theDNh saddle point. The crossing seams can be observed in bothdissociation channels. In Fig. 4 (process 30), the crossing seamis also shown for the CH1 þ H channel. However, there is nodeep potential well, because the linear C–H–H structure is notvery stable. Fig. 5 displays potential energy for process 29 innon-linear configuration, with the equilibrium value of thebending angle (y1 ¼ 137.31). Then, the bottom of the deeppotential well corresponds to the equilibrium geometry ofCH2

1(X 2A1). Of course, the dissociation channels exhibitsmooth potential energy surface because all effects of theconical intersection have disappeared at such bending angle.Again, the hydrogen atoms exchange symmetry is observed.

Fig. 6 shows potential energy contours for the approach of C1

toward a perpendicular H2 (j1 ¼ 901). The CH21(X 2A1)

potential well is shown at small values of r1, and the top ofthe barrier to linearity is located at r1 ¼ 0 and R1 ¼ 4.15 a0. Asecondary potential minimum can be observed around r1 ¼2.8 a0. A calculation of the Hessian matrix at this point showsthat it is a saddle point because one of its eigenvalues isnegative. This means that the potential energy is lowered whenthe angle j1 is displaced from 901.

3.2. Dynamics

We wrote a computer code which follows the steps of thecalculation described in section 2.3. This code was checked byreproducing, on the one hand, the inelastic and reactiveprobabilities obtained by Neuhauser et al.33 in a paper dedi-cated to a systematic examination of the NIP parametersoptimisation in the case of the H þ H2 collinear reaction,and on the other hand the variation as a function of totalenergy of the state-to-all collinear reaction probability for theCl þ HCl symmetric exchange reaction as calculated byHuarte-Larranaga et al.34 The main differences with the ver-sion of Huarte-Larranaga et al.31 is that we use a Chebychevpolynomials quadrature grid for the discrete variable repre-sentation (DVR) of the vibration coordinate and that we useinstead of the standard R matrix propagator, the Magnuspropagator as introduced by Light and coworkers.35 Becauseof the presence of the long range charge induced dipolepotential we have to propagate far away in the asymptoticregion. Also, instead of using a constant width step for thepropagation coordinate we use outside of the region of strongvariation of the potential a logarithmic progression of the stepsize. The maximum propagation distance was 50 a0 and con-vergence was checked as a function of the propagator step size.We used a Legendre polynomial quadrature grid of 30 RIOSAangles ranging in the [0,p] interval and 100 points ranging from0.2 a0 to 10 a0 for the vibrational Chebychev DVR. Thenumber of vibrational states propagated was varied and con-vergence was reached for a basis set of 22 adiabatic states. Thecollision energy relative to the fundamental vibrational staten ¼ 0 was ranging from 10�5 to 4000 cm�1 in order to obtain agood estimate of the rate coefficient up to 500 K. The opticalpotential parameters were optimized in order to minimizereflection. This yielded a ramp height of 3.5 eV and a rampwidth of 1.5 A starting at r ¼ 3.5 A. We performed thecalculations using this unique set of parameters for the wholeset of collision energies. It was necessary to include the value ofJ up to 50 in order to obtain convergence for the highestenergies.

Fig. 5 Contour plot of the PES for non-linear configuration H–C–H(y1 ¼ 137.31).

Fig. 6 Contour plot of the PES for C2v triangular configuration(j1 ¼ 901).

Fig. 7 RIOSA-NIP reaction probability for J ¼ 0 as a function oftotal energy for the n ¼ 0 and n ¼ 1 vibrational state of CH1 incollision with H.

2450 P h y s . C h e m . C h e m . P h y s . , 2 0 0 5 , 7 , 2 4 4 6 – 2 4 5 2 T h i s j o u r n a l i s & T h e O w n e r S o c i e t i e s 2 0 0 5

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Fig. 7 shows the J ¼ 0 reaction probability as a function oftotal energy for the two lowest vibrational levels of CH1. Thestrong oscillation patterns are typical of insertion reactions likeC(1D) þ H2 or S(1D) þ H2

36 with a deep complex and a lowexoergicity. We can also see in this figure that the reactionprobability is larger for the first excited vibrational level ofCH1.

Fig. 8 shows the integral reactive cross section for thefundamental vibrational state of the CH1 diatom as a functionof kinetic energy. As can be seen in this figure the reaction crosssection associated with the fundamental vibrational level ofCH1 decreases almost monotonously and its averaged slope issimilar to the one of the Langevin cross section associated withthe long range charge induced dipole potential also reported inthe same figure. This is, however, only in the Wigner regimewhich extends up to 10�4 cm�1, that the two curves are strictlyparallel as it is expected. Furthermore, the Langevin crosssection which is two orders of magnitude larger than theRIOSA-NIP values at very low kinetic energy is only oneorder of magnitude larger than the RIOSA-NIP values athigher energy showing the decreasing effect of the potentialenergy barriers for both linear approaches. We used theRIOSA-NIP cross section to obtain the rate coefficient shownin Fig. 9. This figure displays the rate coefficient from theWigner regime—where the rate coefficient is constant as afunction of temperature—up to 500 K. The rate coefficientincreases when temperature is increased up to a temperature of

approximately 20 K where it reaches a maximum and thenstarts to decrease. The only experimental data available for thisreaction10 is the value of the rate coefficient at 300 K: 7.5 �10�10 cm3 molecule�1 s�1. This value is bigger than theRIOSA-NIP value which we found to be 1.0 � 10�10 cm3

molecule�1 s�1. However, it is known from a previous calcula-tion dedicated to the study of the Ne þ H2

1 reaction37 that theRIOSA method underestimates reactivity by a factor of thesame order for that system. This is supposed to be the result ofneglecting the reorientation during the approach of the attack-ing atom towards the diatomic molecule. As stated in the samepaper the qualitative law of variation of the cross sectionshould nevertheless be correct and the presence of a maximumof the calculated rate coefficient is an interesting feature whichwe hope to be confirmed at a higher level of calculation and ina new experiment38 which is underway.

4. Conclusion

We performed the first theoretical study of the H þ CH1

reaction. We produced an analytical model of the globalpotential energy surface of the reaction which was obtainedby fitting to a large grid of accurate ab initio points. Twoenergy barriers were found in linear configurations as a resultof the crossing between the 2P and 2S1 states of both linear H–C–H and H–H–C configurations of CH2

1. We then used theRIOSA-NIP method of Neuhauser and Baer to calculate thereactant vibrationally state selected, reaction cross section andrate coefficient. This is, to our knowledge, the first time thatthis method is used to calculate the rate coefficient of achemical reaction as a function of temperature. Our resultsshow, in agreement with experiment, that the Langevin modelstrongly overestimates the value of the reaction cross section asa result of the presence of the energy barriers in collinearapproaches. Our calculated value of the reaction rate coeffi-cient is below its available experimental counterpart at 300 K.The RIOSA-NIP method is known to underestimate reactivity,but the relative variation of the reaction rate coefficient as afunction of temperature should be realistic. It is in the tem-perature range going from 2 K up to 300 K that the ratecoefficient is the largest, above 10�10 cm3 molecule�1 s�1.Because dense and diffuse interstellar clouds fall in this tem-perature range, the title reaction has to be considered as animportant channel for the loss of CH1 species.

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