Global 11A00 potential energy surface of CH2 and quantum

dynamics of a sideways insertion mechanism for the

C(1D) þ H2 - CH(2P) þ H reaction

Beatrice Bussery-Honvault,* Jerome Julien, Pascal Honvault and Jean–Michel Launay

PALMS, UMR 6627 du CNRS and Universite de Rennes 1, Campus de Beaulieu,35042 Rennes Cedex, France. E-mail: Beatrice.Honvault@univ-rennes1.fr

Received 20th December 2004, Accepted 16th February 2005First published as an Advance Article on the web 25th February 2005

A global adiabatic potential energy surface (PES) corresponding to the second singlet state 1 1A00 (1 1B1) of CH2

has been computed in a similar way as the first singlet state 1 1A0 in our previous work [B. Bussery-Honvaultet al., J. Chem. Phys., 2001, 115, 10 701]. This PES has a calculated well depth of 79.9 kcal mol�1 relative to theC(1D) þ H2 asymptote and correlates to CH(2P) þ H. It presents large barriers in the C(1D) þ H2 arrangementfor both collinear and perpendicular geometries but no barrier for geometries about 601 and leads to a sidewaysinsertion mechanism for the reaction C(1D) þ H2 - CH(2P) þ H. The ab initio calculations were carried out for4644 geometries and the resulting energies were fitted to a many-body expansion. Accurate three-dimensionalquantum mechanical scattering calculations have been performed for the C(1D) þ H2(v ¼ 0, j ¼ 0) reaction onthis ab initio 1 1A00 PES in the collision energy range [0–11.5 kcal mol�1]. The J ¼ 0 reaction probabilities showdense resonance structures as those obtained with the 1 1A0 PES. However some different dynamical features havebeen found.

I Introduction

In our previous study1 of the slightly exoergic reaction

C(1D) þ H2(X1S1

g) - CH(X 2P) þ H(2S);

DH00 ¼ �6.3 kcal mol�1 (R1)

we have been involved in a global determination of the firstsinglet state 1 1A0 of CH2 correlating to the above mentionedreactants and products. This ab initio potential energy surface(PES) has since been used in several dynamical studies of thisreaction.1–7 In our previous work we pointed out that this PESpresents no barrier for the perpendicular C2v approach while itpresents a large barrier (9.9 kcal mol�1) for the collinear CNv

geometry. This result is in good agreement with the previousdeterminations of Whitlock et al.8 based on the valence bonddiatomics-in-molecules (VB-DIM) method and those of Blintand Newton9 based on configuration interaction from onereference configuration.

From the experimental point of view, investigations concernthe kinetics10 and the product internal energy distributions11–15

of the title reaction and of its isotopic variants. Recent crossedmolecular beam studies of this reaction leading to productangular and TOF distributions16 have motivated the presenttheoretical work. Comparison between previous calculationsand these experimental results has shown a general goodagreement with small remaining discrepancies.17 Here, wecompute the second singlet surface of CH2 of 1

1A00 symmetryleading to the same reactants and products as the 1 1A0 singletsurface. We then perform a preliminary quantum dynamicalstudy (J ¼ 0 total angular momentum) to investigate itscontribution to the reaction (R1).

The lowest singlet states of CH2, 11A1, 1

1B1 and 2 1A1, havebeen widely studied because of their spectroscopic interest.18–21

Indeed, Bunker et al. proposed an assignment of the nearultraviolet band system of singlet methylene, taking intoaccount the Renner–Teller interaction between the 1 1A1 and1 1B1 states which are degenerate at linearity with a 1Dg

symmetry. The red absorption band of CH2 was previouslyassigned by Green et al.22 who generated the PESs of thesestates in the region of spectroscopic interest.We report in Section II the method and the theoretical

details for the determination of the electronic structure of thesecond singlet state 1 1A00 of CH2. We then outline the fittingprocedure and discuss the results. In Section III we describe thequantum dynamical calculations for total angular momentumJ ¼ 0 on the present PES. Concluding remarks are givenin Section IV.

II Potential energy surface calculations

The C(1D) þ H2 interaction leads to five molecular states (seeTable 1 and Fig. 1). Three singlet states, (1,2) 1A0 ((1,2) 1A1)and 1 1A00 (1 1B1) are bound relative to dissociation in C(1D) þH2 while the other two singlet states, 3 1A0 (1 1B2) and 2 1A00

(1 1A2) are above this dissociation. Only two molecular states(1 1A0 and 1 1A00) lead to the CH(X 2P) þ H products.

A: Ab initio method and potential energy surface

representation

The calculations are classified in terms of three possiblesymmetry groups for the CH2 system: the C2v symmetry isused for the perpendicular approach, the CNv symmetry forthe collinear approach and the Cs symmetry for generalapproaches. We have performed ab initio calculations of thesecond excited state 1 1A00 (1 1B1) state of CH2 with the samemethodology and basis set as previously used in the determina-tion of the first excited state 1 1A0 (1 1A1). A multireferencesingle and double configuration interaction (MR-SDCI) spacehas been built up from a complete active space involving sixelectrons and six active orbitals, CAS (6e,6o). The Davidsoncorrection (noted þ Q)23 has been added to correct for theerror of size-consistency of the SDCI method. The atomic basissets have been chosen as large atomic natural orbital (L-ANO)sets of Widmark et al.24 i.e. we have a (14s9p4d3f) -

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

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[5s4p3d2f] set for the carbon and a (8s4p3d)- [3s2p1d] set forthe hydrogen, both are taken from the MOLCAS code li-brary.25 All the calculations presented here have been per-formed with the MOLCAS code.

The total and relative energies of the products, reactants andintermediate complex of CH2 are evaluated without and withthe Davidson correction to compensate for the effect of higherorder excitations. From the electronic energy difference forreaction (R1) and the zero point energy difference between CHand H2, we obtained a value for DH0

0 of 6.1 kcal mol�1 for thetitle reaction which is in good agreement with the experimentalvalue of 6.3 kcal mol�1 found by Bergeat et al.16

A grid of 4644 (43 � 27 � 4) geometries has been used tocover all important regions of the potential energy surface ofCH2. It is built with 43 values of R ((0.0–4.0) with a step of 0.2,and (4.5–16.0) with a step of 0.5), 27 values of rHH ((0.9–3.5)with a step of 0.2, (5.1–10.1) with a step of 1.0, and (0.5, 1.4,3.9, 4.3, 5.5, 7.5, 9.5)), and 4 values of y (0, 30, 60, 90). R, rHH

and y are the Jacobi coordinates of the reactant arrangement asdescribed in Fig. 2. Distances are in bohr units and anglesin degree.

To represent the potential energy surface in all regions ofconfiguration space, we use a many-body expansion26 andcompute the three-body term of the interaction potential onthe above grid. Within the grid, this term is interpolated with amixed numerical and analytical method (2D-Spline representa-tion for the R, rHH dependence and expansion in Legendrepolynomials for the y dependence). Outside the grid, the three-body term is extrapolated using the Aguado–Paniagua analy-tical expansion.27 This procedure has been described in moredetails in ref. 1 and provides an accurate representation of allthe details of the potential energy surface such as barrierheights, cusps and potential wells.

In the following we will denote for brevity A0 the 1 1A0 stateand A00 the 1 1A00 state.

B: Results and discussion

Contour plots of the A00 potential energy surface of CH2 arepresented in Fig. 3 for y ¼ 01 (a), 301 (b), 601 (c) and 901 (d).The zero of energy is taken at the C(1D) þH2(X

1S1g) reactant

arrangement as noted in Table 2. At collinear geometries

(y ¼ 01) the A00 state is degenerate with the A0 state andpresents a high potential barrier (9.9 kcal mol�1) in thereactant arrangement. Thus the reaction is not possible atthermal collision energies in this configuration, i.e. via theabstraction mechanism. For y ¼ 301, there is a smaller poten-tial barrier of 4.8 kcal mol�1 in the reactant arrangement (seeFig. 3(b)) while this barrier vanishes completely at y ¼ 601.This configuration thus constitutes a pathway for a sidewaysinsertion mechanism at low temperatures or collision energies.This is to our knowledge a completely new feature, never seenbefore for a reactive collision. Furthermore, in contrast withthe O(1D) þ H2 reaction,

30 the two PES (A0 and A00) involvedin the title reaction do not present any potential barrier in theentrance arrangement and both are of insertion type. Thisshould lead to new effects in the dynamical treatment.For y ¼ 901 there is a global minimum of 79.9 kcal mol�1 on

the PES (see Fig. 3(d)) while a huge barrier of 83 kcal mol�1

arises in the reactant arrangement. We may explain this hugebarrier at y ¼ 901, not seen in the A0 PES, by a differentbonding mechanism leading to CH2. Indeed, an unfavorablebonding results from the overlap and the electronic exchangebetween the antibonding orbital of H2 (of b2 symmetry in theC2v group) and the 2py orbital of carbon lying parallel to H2

(also of b2 symmetry). Due to the antibonding character of theH2 orbital, the bonding leads at first to a repulsive potentialand to a potential barrier. With R decreasing and rHH increas-ing at y ¼ 901, the b2 orbital becomes more bound followingstronger overlap between H2 and C. It leads to an attractivepotential and then to a global minimum. At y ¼ 601, theoverlap between the 1s orbital of the closest H atom and thetwo 2p orbitals of C in the plane of CH2 leads to a favorablebonding, so that the electronic exchange gives an attractivepotential.In Table 3 we present the Jacobi coordinates of these

extrema and compare in Table 4 the geometric characteristicsof the global minimum of the potential with previous theore-tical and experimental determinations.19,28,31,32 Our values ofre and ae are in very good agreement with the experimentalwork of Herzberg et al.31 which asserts the quality of ourab initio calculations. The A00 state is less bound than the A0

state by 17.4 kcal mol�1, in good agreement with ref. 8(20 kcal mol�1) and with the work of Yamaguchi et al.28

(23 kcal mol�1) as shown in Table 2.In Fig. 4, we have plotted the contours of the PES at the

fixed bond angle aHCH ¼ 1411 which is the bond angle of theglobal minimum. In addition, we have plotted a contour at

Fig. 1 Correlation diagram for the dissociation of CH2 into CH þ Hor C þ H2. Full lines represent states dissociating into C(1D) þ H2.

Fig. 2 Coordinate systems for CH2: R ¼ RCM, r ¼ RHaHb¼ rHH, y is

the angle between the Jacobi vectors R and r, R1 ¼ RCHa, R2 ¼ RCHb

and R3 ¼ rHH.

Table 1 Correlation between states of different symmetries

Csa C2v

b CNv

C(3P) þ H2(X1Sg

1) 1 3A00 2 3A00 1 3A0 X3B1 13B2 1

3A23P 3S�

C(1D) þ H2(X1Sg

1) 1 1A0 2 1A0 3 1A0 1 1A00 2 1A00 1 1A1 21A1 1

1A2 11B1 1

1B21P 1D 1S1

C(1S) þ H2(X1Sg

1) 4 1A0 3 1A11S1

a The molecule is in the xy plane. b The molecule is in the yz-plane.

P h y s . C h e m . C h e m . P h y s . , 2 0 0 5 , 7 , 1 4 7 6 – 1 4 8 1 1477T 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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�3.0 kcal mol�1 in order to indicate a small potential barrier of0.8 kcal mol�1 above the product arrangement. Howeverthis barrier lies under the reactant arrangement and thuscannot hinder the reaction. For this configuration there is aminimum energy path at nearly constant RCH (B2.12 bohr)which is close to the equilibrium distance of CH(X 2P). Incontrast the H–CH linear configuration shows a barrier of4.4 kcal mol�1 relative to the reactant arrangement in theproduct arrangement (R ¼ 0.84 bohr and rHH ¼ 5.88 bohr,see Fig. 3(a)).

III Quantum dynamical calculations

We have performed quantum-mechanical scattering calcula-tions on the second singlet surface A00 of CH2 for the C(

1D) þH2(v ¼ 0, j ¼ 0) - CH þ H reaction for total angularmomentum J ¼ 0. We use a time-independent method basedon body-frame hyperspherical democratic coordinates. This ispresented in detail in ref. 33 and thus a brief summary willsuffice here. It has previously proved successful in describingthe quantum dynamics of atom–diatom insertion reactions

Fig. 3 Contour plots (in kcal mol�1) of the potential energy surface of the 1 1A00 state of CH2 as a function of R and rHH (in bohr units) at y ¼ 01(a), y ¼ 301 (b), y ¼ 601 (c) and y ¼ 901 (d). Contours are spaced by 10 kcal mol�1 with negative values labelled by dotted lines. On panel (b), the5.0 kcal mol�1 contour has been added.

Table 2 Total and relative energies of the reactants, products and intermediate complex of the reaction at the MRCI level with (þQ) or without the

Davidson correction. The origin in energy for Erel is at the C(1D) þ H2 asymptote

System MR-SDCI þ Q Others

CH2(11A1) Etot

a �39.070 922 �39.075 768

Erelb �98.9 �97.35 �89.5c

CH2(11B1) Etot

b �39.041 578 �39.047 995

Erelb �80.5 �79.9

E(1 1B1) � E(1 1A1)b 18.4 17.43 20c, 23d

C(3P) þ H2(X1Sg

1) Etota �38.961 226 74 �38.964 484 26

Erelb �30.1 �29.9 �29.15e

CH(X 2P) þ H(2S) Etota �38.919 065 93 �38.922 932 93

Erelb �3.67 �3.82 �3.8c

C(1D) þ H2(X1Sg

1) Etota �38.916 855 11 �38.920 623 76

Erelb 0.0 0.0

a In hartrees. b In kcal mol�1. c Ref. 8. d Refs. 19 and 28. e Ref. 29.

1478 P h y s . C h e m . C h e m . P h y s . , 2 0 0 5 , 7 , 1 4 7 6 – 1 4 8 1 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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such as N(2D) þ H2 - NH þ H,34 and O(1D) þ H2 - OH þH,35,36 and also ultracold alkali–dialkali collisions.37,38

At each hyperradius r, the scattering wave function isexpanded on a set of hyperspherical adiabatic states of areference Hamiltonian H0 ¼ T þ V which incorporates thekinetic energy T arising from deformation at fixed hyperradiusand the potential energy V. The expansion coefficients aresolution of a set of coupled second-order differential equationswhich are solved using the Johnson–Manolopoulos log–deri-vative propagator.39 The adiabatic states are obtained by avariational expansion on a basis of hyperspherical harmonics.At small hyperradius, they span a large fraction of configura-tion space and allow for atom exchange. At large hyperradius,the adiabatic states concentrate into the arrangement valleysand describe H2 and CH molecules. We include 285 adiabaticstates which correlate to rovibrational states of H2 with vibra-tional quantum numbers v ¼ 0, 1,. . ., 4 and even rotationalquantum numbers up to jmax ¼ 18, 16, 12, 10, 4 and rovibra-

tional states of CH with vibrational quantum number v ¼ 0,1,. . ., 8 and all rotational quantum numbers up to jmax ¼ 39,36, 34, 31, 28, 25, 21, 17, 10.Total and state-to-state J ¼ 0 reaction probabilities for the

reaction C(1D) þ H2(v ¼ 0, j ¼ 0) - CH(v0,j0) þ H with v0 ¼0,1,2 are shown as a function of collision energy in Figs. 5 and6. Calculations have been performed in the [0–11.5] kcal mol�1

collision energy range on a grid of 2000 equally spacedenergies.The total reaction probability PJ¼0 and the vibrationally

state-resolved reaction probability PJ¼0(v0 ¼ 0) show noenergy threshold as was also the case for the probabilitiesobtained on the first singlet surface A0 (See Fig. 6 of ref. 1). ForCH2 (A

00) this results from the absence of a barrier in the PESat y ¼ 601 as discussed in Section II and confirms that theC(1D) þ H2 reaction proceeds through this geometry.Fig. 5 also shows another important feature. In strong

contrast with the insertion O(1D) þ H2 and N(2D) þ H2

reactions these probabilities show many structures, especiallyat low energies (below 3 kcal mol�1) corresponding to quan-tum resonances. These resonances have been seen for the firsttime in a neutral atom þ H2 reaction in our group.1 They areassociated to a long-lived intermediate complex formed in thedeep well of the PES which supports many quasi-bound states.However such a deep well is also found in the H2O or NH2

PES. The very small exoergicity of the title reaction thus

Fig. 4 Contour plot (in kcal mol�1) of the potential energy surface ofthe 1 1A00 state of CH2 for aHCH ¼ 1411 as a function of RCHa

and RCHb

(in bohr units). Contours are spaced by 10 kcal mol�1 with negativevalues labelled by dotted lines. In addition, the �3.0 kcal mol�1 energycontour has been added.

Fig. 5 Panel a: J ¼ 0 total reaction probability for C(1D) þ H2

(v ¼ 0, j ¼ 0) - CH þ H as a function of collision energy. Panel b:J ¼ 0 vibrationally state-resolved probabilities for C(1D) þ H2(v ¼ 0,j¼ 0) - CH(v0) þ H as a function of collision energy.

Table 3 Properties of the global surface 1 1A00 evaluated in the present

study at theMR-SDCIþQ level. The origin in energy is at the C(1D)þH2 asymptote

Extrema E/kcal mol�1 y/1 R/bohr rHH/bohr

Barrier 9.9 0 3.4 1.9

Barrier 4.8 30 3.0 2.0

Barrier 83 90 2.6 1.9

Global minimum 79.9 90 0.6 3.9

Table 4 Equilibrium distance re (bohr) and bond angle ae (1) for the1 1B1 state of CH2

Ref. re ae

Present work 2.02 141

28 2.02 142.94

19 2.01 144

31 1.99 140

32 2.05 139.3

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appears as an essential feature to obtain narrow resonances.Less product channels are available for the decay of theseresonances which is therefore much slower than in the O(1D) þH2 and N(2D) þ H2 cases. Such structures have also beenfound in ionic reactions such as He þ H2

1,40 Ne þ H2141 and

N1 þ H242,43 or other neutral reactions, such as S(1D) þ H2

44

and Li þ HF.45 The amplitudes of the structures found in thepresent dynamical calculations on the A00 PES are smaller thanthose obtained on the A0 PES especially at energies larger than5.5 kcal mol�1.

The total reaction probability (Fig. 5(a)) is close to unityover all the energy range considered with an average prob-ability of 0.9 except from 0 to 2 kcal mol�1. This value is largerthan the average of 0.5 obtained with the A0 PES. Reactivescattering is thus more efficient on the A00 PES.

As in our previous study with the A0 PES we find (Fig. 5(b))that the average reaction probability for CH(v0 ¼ 0) decreaseswhen collision energy increases whereas it increases for v0 ¼ 1and v0 ¼ 2. However the difference in reactivity between thetwo PESs A0 and A00 comes from a higher PJ ¼ 0(v0 ¼ 1) on theA00 PES for collision energies above 4 kcal mol�1. Fig. 5(b)shows also that PJ¼0(v0 ¼ 0) and PJ¼0(v0 ¼ 1) have an oppositebehaviour: when the v0 ¼ 1 reaction probability presents amaximum, the v0 ¼ 1 reaction probability presents a minimum(for instance near 7.7 and 9.5 kcal mol�1). PJ¼0

(v0 ¼ 2) is zero or negligible in the considered energy range.Fig. 6 shows some rotationally state-resolved reaction prob-

abilities for CH(v0 ¼ 0) as a function of collision energy. Wefind again numerous resonances which are pronounced at lowenergy and broad at high energies. An interesting feature isthat the reactivity is highly specific. We find large reactionprobabilities for j0 ¼ 0, 1, 3, 4, 5, and very small for otherrotational states, such as j0 ¼ 2, 6, 7 (the label j0 refers to theCH rotational quantum number). For j0 ¼ 2, the reactionprobability is near zero for energies above 2 kcal mol�1.

IV Conclusion

Using the same methodology (MR-SDCI þ Q) and basis set asthe one used for the 1 1A0 PES of CH2, we have generated aglobal PES for the second singlet 1 1A00 state of CH2 whichcorrelates to the same reactant and product arrangements. ThePES has no barrier in the reactant arrangement for bent

geometries about 601 while a large barrier exists for linearand perpendicular approaches.The long range part of the potential is extrapolated from an

analytical fit based on the Aguado–Paniagua polynomial ex-pansion of the three-body term. At short distances the three-body term is interpolated with a mixed Legendre-spline pro-cedure. We have carried out J ¼ 0 quantum dynamicalcalculations of the C(1D) þ H2(v ¼ 0, j ¼ 0) - CH(v0, j0) þH reaction on the present 1 1A00 PES. The total reactionprobability has been calculated in the [0–11.5] kcal mol�1

collision energy range and is close to unity except at energiessmaller than 2 kcal mol�1 in contrast with the probabilityobtained on the 1 1A0 PES. Reaction probabilities for specificrovibrational states have also been computed and show differ-ences with the results obtained on the 1 1A0 PES. These newdynamical features seen for J ¼ 0 on the second excited 1 1A00

PES may help to resolve the remaining discrepancies withrecent crossed beam experiments.16,17

In the future, we plan to take into account J > 0 partialwaves in order to compute state-to-state differential crosssections and thus assess the role of excited 1 1A0 and 1 1A00

PESs together with the nonadiabatic effects for the C(1D) þH2

reaction.

Acknowledgements

We thank the ‘‘Pole de Calcul Intensif de l’Ouest’’ (PCIO,Universite de Rennes 1) and the ‘‘Institut du Developpementdes Ressources en Informatique Scientifique’’ (IDRIS, CNRS,Orsay) for providing us computer time.

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Fig. 6 J ¼ 0 rotationally state-resolved reaction probabilities for C(1D) þ H2(v ¼ 0, j ¼ 0) - CH(v0 ¼ 0, j0 ) þ H as a function of collision energy.

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