Global ab initio potential energy surfaces for the ClH2 reactive systemWensheng Bian and Hans-Joachim Werner Citation: J. Chem. Phys. 112, 220 (2000); doi: 10.1063/1.480574 View online: http://dx.doi.org/10.1063/1.480574 View Table of Contents: http://jcp.aip.org/resource/1/JCPSA6/v112/i1 Published by the American Institute of Physics. Additional information on J. Chem. Phys.Journal Homepage: http://jcp.aip.org/ Journal Information: http://jcp.aip.org/about/about_the_journal Top downloads: http://jcp.aip.org/features/most_downloaded Information for Authors: http://jcp.aip.org/authors

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JOURNAL OF CHEMICAL PHYSICS VOLUME 112, NUMBER 1 1 JANUARY 2000

Global ab initio potential energy surfaces for the ClH 2 reactive systemWensheng Biana) and Hans-Joachim Wernerb)

Institut fur Theoretische Chemie, Universita¨t Stuttgart, Pfaffenwaldring 55, D-70569 Stuttgart, Germany

~Received 16 August 1999; accepted 4 October 1999!

Two new globalab initio potential energy surfaces~called BW1 and BW2! for the ClH2 reactivesystem are presented. These are based on internally contracted multireference configurationinteraction calculations using a very large basis set, performed at 1200 geometries. Accurateanalytical fits have been generated using the functional form proposed by Aguado and Paniagua.The BW1 surface is based on the originalab initio points. This surface slightly underestimates thedissociation energies of the diatomic fragments and overestimates the barrier height. Therefore, asecond surface~BW2! has been computed by scaling the correlation energies at all geometries witha constant factor, which was chosen such that the dissociation energies of HCl and H2 arereproduced more accurately. The barrier heights for the collinear transition state of the Cl1H2

→HCl1H reaction are computed to be 8.14 kcal/mol and 7.61 kcal/mol for the BW1 and BW2surfaces, respectively. To these values the spin–orbit correction of 0.84 kcal/mol has to be added,yielding a best estimate for the true barrier height of 8.45 kcal/mol. In the entrance channel of theCl1H2→HCl1H reaction a T-shaped van der Waals well with a depth of 0.51 kcal/mol is found,while in the exit channel a van der Waals well with a collinear geometry and a depth of 0.45kcal/mol is predicted. For the H1ClH exchange reaction, which also has a collinear transition state,the barrier heights are computed to be 18.5 kcal/mol and 17.9 kcal/mol for BW1 and BW2,respectively. It is shown that the topology of the new surfaces differs qualitatively from previoussemiempirical surfaces, and the implications on the dynamics of the H21Cl reaction are discussed.© 2000 American Institute of Physics.@S0021-9606~00!30201-X#

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I. INTRODUCTION

The dynamics of the ClH2 reactive system has been thsubject of many theoretical and experimental studies1–10~andreferences therein!. Recently, new crossed-molecular beaexperiments have provided detailed information aboutmicroscopic dynamics of the Cl1H2→HCl1H ~Refs. 8, 9!and Cl1HD→HCl1D/DCl1H reactions.11,12Particularly in-teresting is the finding that the spin–orbit excited2P1/2 stateof chlorine has a surprisingly strong reactivity.11 On the the-oretical side, several potential energy surfaces~PESs! for theClH2 system have been constructed5,10 ~and referencetherein! and many dynamical calculations on these surfahave been performed. However, there are still discrepanamong various theoretical and experimental results.5,10,13

Most notably, recent molecular beam experiments12 forCl1HD at low collision energies gave HCl1D/DCl1Hbranching ratios in strong disagreement with quantcalculations12 on the semiempirical G3 potential energy suface developed by Truhlar and co-workers,10 which has beenconsidered to be the best surface for the ClH2 system to-date.

So far, most of the proposed PESs for the ClH2 systemare of empirical or semiempirical nature. The first PESthis system was suggested by Eyring and co-workers1936.14 This LEP-type surface was modified into a LEPtype surface by Sato15 in 1955, and was applied extensive

a!Present address: Institute of Theoretical Chemistry, Shandong UniveJinan, 250100, People’s Republic of China.

b!Author to whom correspondence should be addressed.

2200021-9606/2000/112(1)/220/10/$17.00

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later. Several extended and generalized LEPS-type16–18 andDIM-type19 surfaces were also proposed. In 1985 Truhlagroup4 compared 11 semiempirical surfaces for the ClH2 sys-tem in rate-constant calculations using variational-transitistate-theory~VTST! with semiclassical-tunneling correctionand found that the GSW surface, a generalized-LEPS-tPES produced in 1973 by Stern, Persky, and Klein17 gavemost accurate results. However, they also pointed outthe GSW surface was not satisfactory for the exchange rtion. Various dynamics calculations on the above-mentionsemiempirical surfaces have been performed, and gagreement with experimental rate constants for the absttion reaction was achieved, but the agreement with expmental data for the exchange reaction was not satisfacto5

In 1989, two new surfaces, which were based onabove-mentioned GSW surface and some newab initio data,were developed by Schwenkeet al.5 The second of these twosurfaces, which is believed to be more accurate, is denGQQ. The newab initio data were obtained by multireference configuration interaction calculations with a relativesmall basis set. Basis set deficiencies were accounted foscaled external correlation~SEC! corrections.5,20 The calcu-lations were performed at 13 H–Cl–H geometries and 5 CH–H geometries in the vicinity of the saddle points for texchange and abstraction reactions. GQQ is better than Gin particular in the saddle point region of the exchange retion. Some VTST studies5 as well as exact three-dimensionquantum scattering calculations21,22 were performed on thissurface.

In 1996, an improved PES called G3 was presented

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© 2000 American Institute of Physics

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221J. Chem. Phys., Vol. 112, No. 1, 1 January 2000 ClH2 potential energy surface

Allison et al.10 G3 was developed by modifying the GQbending potential in the Cl–H–H saddle point region. Theimprovements were based on additionalab initio data, ob-tained by fourth-order MÖller–Plesset perturbation theor~MP4! with scaling corrections~SAC, scaled all-electron correlation! at 63 Cl–H–Hgeometries near the saddle poinVarious dynamics calculations, including quantum mechacal ~QM! reactive scattering,13 VTST,10 and QCT~Ref. 9!~quasiclassical trajectory! calculations, were performed othe G3 surface, and good agreement with experimentalconstants was obtained for Cl1H2 and Cl1D2 over a widerange of temperatures. Furthermore, detailed QCT and qtum mechanical reactive scattering calculations on thepotential energy surface have been found to be in exceagreement with the HCl(v850) product angular distributions measured in molecular beam experiments.9

This success of the G3 surface is quite remarkable csidering the fact that it has been developed from thesemiempirical GSW surface withab initio calculations atonly 84 geometries, all of which are near the saddle po~except 3 geometries for the atomic and diatomic limit!.However, as already mentioned above, recent molecbeam experiments of Lai and Liu12 for Cl1HD at low colli-sion energies gave HCl1D/DCl1H branching ratios instrong disagreement with exact quantum calculationsformed by Skouteris and Manolopoulos12 on the G3 potentialenergy surface. While the QM Cl1HD(v50,j 50,1) reac-tive scattering calculations on the G3 surface predictedHCl and DCl products to be produced almost equally,crossed molecular beam experiments on the reactionvealed a dramatic preference for producing DCl.

In the present work we present two new global thredimensional PES for Cl1H2 which have been computed uing the most accurate electronic structure methods and bsets presently available. These surfaces have alreadyemployed in QM rate constant calculations, and the prefeone ~BW2! gave even better agreement with experimendata than the G3 surface.23,24 Moreover, in sharp contrast tthe G3 surface, the exact QM reactive scattering calculatfor Cl1HD on the BW2 surface predicted the large DCl/Hbranching ratios at low collision energies correctly andexcellent agreement with the recent crossed molecular bexperiments. The difference of the dynamics on the G3BW2 surfaces originates mainly from the different topoloof these surfaces in the entrance channel.12

Due to the tremendous improvement of both the coputer hardware and the electronic structure methods duthe last decade,ab initio calculations of three-dimensionapotential energy surfaces are now quite routinely possiHowever, as has been demonstrated in most detail forF1H2→HF1H reaction and its isotopic variants,25 the shapeof the PES is very sensitive to electron correlation effecand shortcomings in the electron correlation treatmenthave large effects on the dynamics. The reason for this plem is the fact that usually the electron correlation energmaximal in the barrier region, where all electrons are clostogether. This means that inclusion of electron correlatoften strongly lowers the barrier height, and this effectvery slowly convergent with the size of the basis set. F

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thermore, in order to describe bond breaking and formatcorrectly, a multireference correlation treatment is necessThus, reliable potential energy surfaces require calculatiof the highest possible complexity and quality.

The feasibility of such accurate calculations has recenbeen demonstrated for the F1H2 reaction. Stark andWerner25 have computed a global PES~called SW! using theinternally contracted multireference configuration interact~MRCI! method26,27 with complete active space selconsistent field~CASSCF! reference functions28,29and a verylarge basis set. Using this surface exact quantum scattecalculations30–34 as well as quasiclassical trajectocalculations35–38 have yielded much better agreement wexperimental data than any previous surface. The quanscattering and quasiclassical trajectory calculations onSW surface have successfully reproduced vibrational andtational product distributions, differential cross sections, athe photodetachment spectrum of FH2

2 .30,32 Recently, thesecalculations have been extended to include the spin–ocoupling in the entrance channel,34 and first QM dynamicscalculations on three coupled potential energy surfaces hbeen reported.39

The BW1 surface presented in the present paper is cputed using similar techniques as the SW surface forvalence-isoelectronic F1H2 system. However, since the corelation energy contribution in Cl1H2 converges even moreslowly than for F1H2, it was not possible to approach thbasis set limit closely enough, even though a very large bwas used. We therefore produced a second surface, denBW2, by scaling the correlation energy with a constant fator, which was chosen to reproduce the dissociation enerof HCl and H2 as accurately as possible.Ab initio calcula-tions were performed at about 1200 geometries, and thesulting energies were fitted to the analytical functional foproposed by Aguado and Paniagua40 with high precision.

The organization of the present article is as follows: SII describes theab initio electronic structure calculationsThe fit of theab initio energy points is presented in Sec. IThe fitted surfaces are discussed and evaluated in SecFinally, a summary is presented in Sec. V.

II. Ab Initio ELECTRONIC STRUCTURECALCULATIONS

All calculations reported in the present work were caried out using theMOLPRO suite ofab initio programs.41 Thepotential energy surface was computed using internally ctracted multireference configuration interaction~MRCI!wave functions26,27 with complete active space selconsistent field~CASSCF! reference wave functions.28,29TheDavidson correction42 (1Q) was applied to the final energies in order to account approximately for unlinked cluseffects of higher excitations. It has been demonstratedF1H2 that the CASSCF/MRCI1Q method gives closeagreement of the barrier height and exothermicity with fconfiguration interaction~FCI! results for a triple-zeta pluspolarization basis set.43 A full valence active space was usein the CASSCF reference wave functions. At the Cl1H2 as-ymptote, this active orbital set corresponds to the chlor3s,3p and the hydrogen 1sg , 1su orbitals, and therefore

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222 J. Chem. Phys., Vol. 112, No. 1, 1 January 2000 W. Bian and H.-J. Werner

allows for proper dissociation and bond formation. In oearlier calculations for the F1H2 system,25 an additionalp-shell was included in the active space, but test calculation the Cl1H2 system showed that this does not lead to snificant variations of the barrier height or the diatomic dsociation energies. We therefore decided to use the smactive space, but to compromise as little as possible inone-electron basis set, which turned out to be much mdifficult to saturate.

In order to avoid artifacts in the long range region duemixing of the chlorine 2p and 3p orbitals, it was necessarto determine the inner shell orbitals in a preceding staaveraged CASSCF calculation, in which the average eneof the 1A8,2A8,1A9 states, which asymptotically correlawith the three degenerate chlorine2P states, was minimizedIn a subsequent CASSCF calculation, in which only the 1A8state was optimized, the 1s, 2s, and 2p orbitals were takenfrom the state-averaged CASSCF and kept frozen. Thesner shell orbitals were not correlated in the final MRcalculation.

The atomic orbital~AO! basis set for chlorine was derived from the augmented correlation consistent quintuzeta basis set (aug-cc-pV5Z,@8s7p5d4 f 3g#) of Kendall,Dunning, and Harrison44 by omitting theh-functions; for hy-drogen, the aug-cc-pVQZ@5s4p3d2 f # was used. In total,this basis set contains 289 primitive AOs, contracted to 2functions. It is expected that this large and diffuse basiscovers a large fraction of the correlation energy and aaccounts well for the long-range dispersion energy.

Extensive test calculations revealed, however, that ewith this large basis set neither the barrier height nordissociation energy of HCl was converged. As mentionedthe Introduction, electron correlation lowers the barrheight, and even small errors of the correlation treatmenthave a significant effect on the barrier height. In ordercompensate for such errors, we scaled the correlation enwith a constant factor, similar to what was done in Truhlascaled external correlation~SEC! correction,5,20

EScaled5F•~EMRCI1Q2ECASSCF!1ECASSCF. ~1!

This scaling amplifies the differential correlation effects, atherefore increases the dissociation energies of the diatoand reduces the barrier height. The scaling factorF can bedetermined such that the dissociation energies of theatomic molecules are reproduced correctly, i.e.,

F5De~exp!2De~CASSCF!

De~MRCI1Q!2De~CASSCF!, ~2!

where De are the calculated and experimental dissociatenergies of HCl or H2. The experimental dissociation energof HCl has been corrected for the spin–orbit effect, i.e.,spin–orbit free value was used, since we plan to accounspin–orbit effects explicitly at a later stage. It turned out ththe values ofF calculated from HCl and H2 are slightlydifferent, and we therefore decided to use the average vof 1.05485~we did not attempt to modify the basis set so ththe scaling factors for both diatomics become the samedone in the SEC method20!. This value indicates that oucalculations account for about 95% of the differential cor

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lation energy explicitly. Nevertheless, the remaining 5%fect the barrier height by 0.53 kcal/mol, which is not neggible. In fact, recent quantum mechanical rate constcalculations on the scaled and unscaled surfaces showedexcellent agreement with experimental data is obtained wthe scaled surface.24 Adjusting the scaling factor by minimizing the error between computed and experimental rate cstants would give virtually the same scaling factor as uabove.

In order to cover the global potential energy surfacethe ClH2 system,ab initio calculations were performed aabout 1200 symmetry unique geometries. These were chcarefully to represent the dynamically important regiomost accurately, in particular the saddle point and vanWaals areas. In these important regions points were cputed with small increments of 0.05–0.1 bohr for bond dtances and 10° for bond angles. In other regions coarser gof 0.2–1.0 bohr and 30° were used. Geometries with engies higher than 110 kcal/mol above the Cl1H2 asymptotewere neglected. The 84 geometries for which explicitab ini-tio calculations were performed for the G3 and GQQ sfaces form a subset of our geometry set.

III. FIT OF THE POTENTIAL ENERGY SURFACES

Two analytical fits were generated from the computenergies at 1200 geometries; the first one, denoted BW1based on the original MRCI1Q energies without scaling; thesecond one, denoted BW2, was generated from the scenergies. For the analytical representation of the potenwe chose the functional form proposed by Aguado aPaniagua,40 which uses a many body expansion,

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Vn(2) (n5AB,BC,AC) are the diatomic potentials of HC

and H2, and VABC(3) is a three-body potential, which shoul

become zero at all dissociation and united atom limits. Infollowing we assume that the indexA refers to the Cl-atom,andB,C to the hydrogen atoms. The diatomic potentials aexpressed as

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Since the MRCI1Q energies are not exactly size consistethe diatomic potentials were obtained by setting one bolength in the triatomic system to a very large value. For eadiatom, about 15 points were used to determine the pareters in Eq.~4!. The rms deviations of the HCl fits wer0.008 and 0.006 kcal/mol for the BW1 and BW2 surfacrespectively. The corresponding deviations for the H2 poten-tial were 0.0017 and 0.0019 kcal/mol. In order to demostrate the quality of these potentials we present a compar

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223J. Chem. Phys., Vol. 112, No. 1, 1 January 2000 ClH2 potential energy surface

of some computed and experimental spectroscopic consin Table I. For the unscaled BW1 surface, the dissociatenergies of HCl and H2 are too small by about 1.0 and 0kcal/mol, respectively. These errors are reduced by the sing procedure to20.2 kcal/mol for HCl and10.2 kcal/molfor H2. Unfortunately, the scaling does not much improthe endothermicity of the reaction,DE5De~H2)2De~HCl!, which is 2.64 kcal/mol for BW1 and 2.58 kcamol for BW2 ~exp. 2.17 kcal/mol!. All these values, includ-ing the experimental one, are without spin–orbit couplin@The spin–orbit coupling lowers the HCl dissociation enerby about 0.84 kcal/mol for the Cl(2P3/2) asymptotic state.#The equilibrium distances and harmonic and anharmonicbrational constants are in excellent agreement with theperimental values; it appears that the scaling slightlyproves the accuracy, in particular for HCl.

The three-body termVABC(3) in Eq. ~3! was expressed as

polynomial of orderM,

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with the constraintsi 1 j 1k<M and i 1 j 1kÞ iÞ j Þk. Forthe sake of symmetry, we havedi jk5dk ji , bAB5bAC . Thethree-body parameters were determined by fitting the difence of theab initio energies of the ClH2 system and the sumof the one-and two-body energies at the correspondingometries.

The Levenberg–Marquardt technique was used fornonlinear optimization. We found that forM>10 there arenumerical problems due to near linear dependence ofparameters, and thus quadruple precision arithmeticneeded to obtain convergence. To improve the fit, enepoints below 25 kcal/mol relative to the Cl1H2 asymptotewere given a weight of 10 and those close to the minimenergy path~particularly in the vicinity of the saddle points!were weighted by a factor of 100. Many test calculatiowere performed with different polynomial ordersM, and thebest final results were obtained withM513. Despite thishigh value, which corresponds to 283 independent pareters for the fit of about 1200 energies, we found the fitpotentials to be smooth and without artificial oscillations.

The fit for the BW1 has a rms error of 0.326 kcal/moand a maximum error of 3.43 kcal/mol. Below 25 kcal/m

TABLE I. Comparison of computed and experimental spectroscoconstantsa for the diatomic molecules.

r e /bohr Deb ve vexe Be ae

HClBW1 2.411 106.29 2984.38 52.61 10.57 0.30BW2 2.410 107.09 2988.53 52.48 10.58 0.30Exptc 2.409 107.30 2989.20 52.82 10.59 0.30

H2

BW1 1.402 108.93 4400 121.75 60.77 3.03BW2 1.401 109.67 4409 121.60 60.88 3.02Exptc 1.401 109.47 4403 121.33 60.85 3.06

ar e in bohr,De in kcal/mol. other values in cm21.bWithout spin–orbit coupling, see text.cReference 46.

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relative to the Cl1H2 asymptote, the rms error is 0.053kcal/mol and the maximum error is 0.419 kcal/mol. Belo10 kcal/mol, the rms and maximum errors are 0.0362 kcmol. and 0.234 kcal/mol, respectively. The fit for the BWhas an even somewhat smaller rms error of 0.272 kcal/mand a maximum error of 3.08 kcal/mol. Below 25~10! kcal/mol, the rms and maximum errors are 0.0568~0.0398! kcal/mol and 0.484~0.295! kcal/mol, respectively.

Fortran programs which can be used to computeabove mentioned potentials for arbitrary geometries candownloaded from the web.45

IV. DISCUSSION OF THE FITTED SURFACES

A. The abstraction reaction

1. The entrance valley

The BW1 and BW2 surfaces are qualitatively very simlar, and we will therefore discuss only the latter one, whwe believe is more accurate. The BW2 and G3 potentialsthe entrance channel of the H21Cl reaction are compared inFig. 1. In this region it is most appropriate to describe tpotentials in Jacobi coordinatesR, r, anda, whereR is thedistance of the chlorine atom to the center of mass ofhydrogen molecule,r is the H2 bond distance, anda is theangle between vectorsR and r . In the contour plots the potentials are shown as function ofR anda, and ther coordi-nate is optimized for each pair ofR anda. The BW2 poten-tial has a well at a T-shaped geometry (a590°); theminimum occurs atR55.78 bohr, r 51.403 bohr, and thewell depth amounts to 0.51 kcal/mol. At collinear geometrthe potential is also attractive, but the linearly constrainminimum has a depth of only 0.3 kcal/mol. The strongattraction at the T-shaped structure is due to the quadrupquadrupole interaction of the fragments. At shorterR thepotential rises towards the barrier. Even though the barriecollinear, Fig. 1 shows that in the long-range region thepulsion is strongest for collinear geometries and smallesta590°. The above features of the BW2 surface are in shcontrast to those of the G3~Ref. 10! surface. As seen in thelower panel of Fig. 1, this potential has no minimum, andmost repulsive fora590°, even though the anisotropyquite small. It has been demonstrated in Ref. 12 that thdifferences lead to a completely different dynamical behior at low collision energies~cf. Sec. V!. Clearly, the G3potential is qualitatively wrong in this region.

Aquilanti et al.47 determined the long-range potential fothe Cl1H2 reaction from experimental scattering data.their work, the H2 molecule was treated as a spherical spcies, and therefore the anisotropy of the potential wasaccounted for. In this approximation, the well depth of tpotential for theS state was determined to be about 0.kcal/mol atR56.18 bohr. These findings are in reasonaagreement with our results for the BW2 surface.

A similar T-shaped van der Waals minimum was fouon the SW potential25 for the F1H2 reaction. Comparison othe F1H2 and Cl1H2 surfaces shows that the well of thCl1H2 potential is 0.14 kcal/mol deeper and the minimuoccurs at anR value that is 0.9 bohr longer than for F1H2.

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224 J. Chem. Phys., Vol. 112, No. 1, 1 January 2000 W. Bian and H.-J. Werner

These differences are to be expected from the larger vanWaals radius and the larger polarizability of the Cl atom.

2. The barrier region

In contrast to the F1H2 reaction, which has a nonlineatransition state in the entrance channel, the barrier ofH21Cl reaction is collinear and more central. Figure 2 shothe collinear potential near the barrier as function of the bodistancesRCIH andRHH . It can be seen from this figure thathese two coordinates are strongly coupled. Figure 3 shthe saddle point regions as function ofRCIH andQCIHH ; inthis case theRHH distance is optimized for each pair ofRCIH

andQCIHH .The geometries, vibrational frequencies, and bar

heights of the optimized transition states for the BW1, BWG3, and GQQ surfaces are summarized in Table II. Itfound that the barrier properties of the BW2 and G3 surfaare quite similar. The saddle points of the BW1 and BW

FIG. 1. Contour plots of the BW2~upper panel! and G3 ~lower panel!surfaces in the entrance valley of the abstraction reaction as function oJacobi coordinatesR ~in bohr! anda, whereR is the distance of the Cl atomto the center of mass of H2 anda is the angle betweenR and the H2 bond.The H2 distancer is optimized for each pair ofR and a. The values indi-cated on the contour lines are in kcal/mol relative to the Cl1H2 asymptote.

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surfaces are located a little earlier in the entrance chanthan those of the G3 and GQQ surfaces, i.e., the optimiRCIH distance for the BW2~BW1! surface is slightly longerand RHH is somewhat shorter than that for G3~GQQ!. Thebarrier height of the BW2 PES is quite close to that of thesurface, but it should be noted that the BW2 surface doesinclude the spin–orbit effect, which is implicitely accountefor in G3. Thus, a correction of10.84 kcal/mol@1/3 of theasymptotic splitting of the Cl(2P1/2) and Cl(2P3/2) states#should be added to the BW2 barrier height, and we estimthat the true barrier height is about 8.45 kcal/mol relativethe Cl(2P3/2)1H2 asymptote. This is supported by the fining that QM calculations of rate constants on the BWsurface24 yield excellent agreement with experimental dafor a wide range of temperatures. These rate constant calations account for the asymptotic spin–orbit effect. On tother hand, the calculations in Ref. 24 showed that theconstants obtained with BW1 are too small, while thosetained with G3 are too large. From these results we estimthat the true barrier height is 8.4560.2 kcal/mol.

heFIG. 2. Contour plots of the BW2~upper panel! and G3 ~lower panel!surfaces in the collinear saddle point region of the Cl1H2 abstraction reac-tion as a function ofRClH and RHH . The values indicated on the contoulines are in kcal/mol relative to the Cl1H2 asymptote.

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225J. Chem. Phys., Vol. 112, No. 1, 1 January 2000 ClH2 potential energy surface

Table II also shows that the symmetric stretching fquencies of all surfaces are in excellent agreement; alsobending frequencies of BW2 and G3 are in good agreemHowever, the BW2 imaginary frequency correspondingthe asymmetric stretch is substantially smaller than the

FIG. 3. Contour plots of the BW2~upper panel! and G3 ~lower panel!surfaces in the saddle point region of the Cl1H2 abstraction reaction as afunction of RClH andQClHH . The H2 distance is optimized for each pair oRClH andQClHH . The values indicated on the contour lines are in kcal/mrelative to the Cl1H2 asymptote.

TABLE II. Comparison of barrier properties for the Cl1H2 abstractionreaction.

Surface RClHa RHH

a Qb Ec v id vb

e vsf

BW1 2.710 1.850 180 8.14 1333i 543 1356BW2 2.704 1.854 180 7.61 1294i 540 1360G3g 2.648 1.870 180 7.88 1520i 581 1358GQQh 2.64 1.88 180 7.70 1497i 712 1362

aBond distance in bohr.bBond angle in deg.cBarrier height in kcal/mol.dImaginary frequency in cm21.eBending vibration frequency in cm21.fSymmetric stretching vibration frequency in cm21.gReference 10.hReference 5.

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value, indicating that the G3 barrier is somewhat thinnleading to more tunneling. In fact, it was already pointed oin Ref. 10 that the barrier of G3 is too thin, and this iscommon shortcoming of generalized LEPS-type surfaces

Figure 4 shows contour plots of the collinear BW2 anG3 surfaces. Both surfaces look qualitatively similar, evthough the differences of the positions and widths of tbarriers can be recognized on closer inspection. Furthermthe van der Waals minima in the entrance and exit channare absent on the G3 surface. Apparently, the most signcant differences of the two surfaces occur at nonlinear geoetries, as discussed above and seen in Fig. 1.

3. The exit valley

The topologies of the exit valleys of the BW2 and Gsurfaces are displayed in Fig. 5 as function ofRHH andQClHH . RClH is optimized for each pair ofRHH andQClHH .For both surfaces the minimum energy path proceeds alcollinear geometries. However, as in the entrance chan

l FIG. 4. Contour plots of the BW2~upper panel! and G3 ~lower panel!surfaces for the Cl1H2 collinear abstraction reaction as function ofRClH andRHH . The contour line values are in kcal/mol relative to the Cl1H2 asymp-tote.

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226 J. Chem. Phys., Vol. 112, No. 1, 1 January 2000 W. Bian and H.-J. Werner

the anisotropy of the two surfaces differs strongly. The BWsurface has a well in the exit channel; the minimum is clinear and lies atRHCl52.411 bohr andRHH54.77 bohr. Thewell depth is 0.45 kcal/mol, and as in the entrance chanthis well is substantially deeper than for the F1H2 reaction~0.25 kcal/mol!. The G3 surface does not have such mimum, and is much less anisotropic in the exit channel. Thdifferences could lead to strong differences in the rotatioproduct distributions.

B. The exchange reaction

The fitted surfaces are also suitable for the study ofH81ClH→H8Cl1H exchange reaction. As for the earlier Gand GQQ surfaces, the barrier is found to be collinear. Fig6 shows contour plots of the collinear BW2 and G3 potetials for the exchange reaction. Both potentials look vesimilar, but the BW2 surface has wells in the entrance aexit channels, which are absent on the LEPS surfaces.well is displayed on a larger scale in Fig. 7, which shows

FIG. 5. Contour plots of the BW2~upper panel! and G3 surfaces~lowerpanel! in the exit valley of the abstraction reaction as function ofRHH andQClHH . RClH is optimized for each pair ofRHH andQClHH . The contour linevalues are in kcal/mol relative to the HCl1H asymptote.

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long range parts of the potentials as function ofQHClH8 andRHCl . RClH8 is optimized for each pair ofRHCl andQHClH8 .The well depth is 0.306 kcal/mol, and the well is locatedRHCl56.16 bohr, RClH852.408 bohr. The barrier region othe exchange reaction is displayed in Fig. 8, and the barproperties are summarized in Table III.

The barrier height and geometry of the BW2 and Gsurfaces are in close agreement. Our barrier height of 1kcal/mol is in excellent agreement with recent large scbenchmark calculations of Peterson and Dunning,48 who ob-tained a best estimate of 18.0 kcal/mol for the classical brier height. The computed harmonic vibrational frequencfor the BW2 and G3 surfaces differ quite significantly,particular for the bending and asymmetric~imaginary!stretching modes. The BW2 surface has a much flatter being potential, while the stretching frequencies are largThese differences cancel approximately when considethe zero-point corrections at the barrier, which are 10cm21 and 1155 cm21 for BW2 and G3, respectively. Sinc

FIG. 6. Contour plots of the BW2~upper panel! and G3 ~lower panel!surfaces for the H81ClH collinear exchange reaction as function ofRClH

andRClH8 . The contour line values are in kcal/mol relative to the HCl1Hasymptote.

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227J. Chem. Phys., Vol. 112, No. 1, 1 January 2000 ClH2 potential energy surface

the G3 surface is based on only relatively fewab initio data,in particular in the region of the barrier for the exchanreaction, and furthermore the currentab initio calculationsare of much higher quality, it is likely that our new surfacemore accurate.

V. SUMMARY

State-of-the-artab initio calculations have been peformed at about 1200 geometries covering all importantgions of the potential energy surface of the ClH2 reactivesystem. A very large basis set has been used, and aboutof the electron correlation energy has been accountedexplicitely. In order to correct for the remaining error, thcorrelation energies have been scaled by a constant fact1.054 85. The resulting energies have been fitted accuraby analytical functions of the form proposed by Aguado aPaniagua. Two such fits have been produced: the firstdenoted BW1, is based on the originalab initio data, while

FIG. 7. Contour plots of the BW2~upper panel! and G3 ~lower panel!surfaces in the entrance valley of the exchange reaction as function ofRHCl

and QHClH8 . RClH8 is optimized for each pair ofRHCl and QHClH8 . Thecontour line values are in kcal/mol relative to the HCl1H asymptote.

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for the second one, denoted BW2, the scaled energies wused. The latter surface is believed to be more accurate

The new surfaces have been compared in detail withprevious semiempirical G3 and GQQ surfaces. Whilebarrier properties of the Cl1H2→HCl1H abstraction reac-tion of the BW2 and G3 are relatively similar, the potentiadiffer qualitatively in the entrance and exit channels. T

FIG. 8. Contour plots of the BW2~upper panel! and G3 ~lower panel!surfaces in the saddle point region of the exchange reaction as functioRHCl andQHClH8 . RClH8 is optimized for each pair ofRHCl andQHClH8 . Thecontour line values are in kcal/mol relative to the HCl1H asymptote.

TABLE III. Comparison of barrier properties for the H1ClH exchangereaction.

Surface RHCla RClH

a Qb Ec v id vb

e vsf

BW1 2.800 2.800 180 18.46 1468i 256 1859BW2 2.796 2.796 180 17.89 1441i 242 1867G3g 2.794 2.794 180 18.1 1251i 583 1727

aBond distance in bohr.bBond angle in deg.cBarrier height in kcal/mol.dImaginary frequency in cm21.eBending vibration frequency in cm21.fSymmetric stretching vibration frequency in cm21.gReference 10.

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228 J. Chem. Phys., Vol. 112, No. 1, 1 January 2000 W. Bian and H.-J. Werner

BW1/2 surfaces have long-range van der Waals minimwhich are entirely absent in the earlier LEPS-type surfacMoreover, the anisotropy of the potentials between thwells and the barrier is stronger and different on our nsurfaces. In particular, in the entrance channel our potenis least repulsive for perpendicular~T-shaped! approach ofCl and H2, while the G3 surface is most repulsive foT-shaped structures. Recent exact quantum scattering clations for Cl1HD performed by Skouteris anManolopoulos12 have shown that this leads to a dramadifference of the dynamics and DCl/HCl product branchiratio at low collision energies. On the G3 surface there itorque acting towards collinear alignment of the reactaand this leads to about equal production of DCl and HCl.the other hand, the torque is opposite on the BW2 surfasince T-shaped structures are preferred at long range. Trtories which are deflected away before the collinear tration state is reached are reflected and do not react. This eis more pronounced if HD attacks the chlorine with theside, since the center of mass is closer to D, which makesH atom experience the torque at a larger Cl to HD separatand therefore the production of DCl is much preferred. Tcomputed DCl/HCl branching rations at low temperaturesthe BW2 surface are in excellent agreement with reccrossed molecular beam experiments of Lai and Liu.12

Our new potentials also describe the HCl1H8→ClH81H exchange reaction. In this case the geometry of the tsition state and the barrier height are in close agreementthe G3 surface, but the vibrational frequencies at the tration state differ quite substantially. In particular, our BWpotential has a flatter bending potential than the G3 surfaSimilar to the Cl1H2 abstraction reaction, our potentiahave van der Waals wells in the entrance and exit channwhich are absent on the G3 surface. This also leadsstronger anisotropy of our potential in the long range regi

Quantum mechanical rate constant calculations forCl1H2→HCl1H reaction have recently been performedManthe on the BW1, BW2, and G3 surfaces.24 Best agree-ment with experimental results was obtained for the BWsurface, indicating that our predicted barrier height of 860.2 kcal/mol is accurate. This value includes tasymptotic spin–orbit correction of 0.84 kcal/mol; the raconstant calculations account for this correction underassumption that the barrier region is simply shifted up0.84 kcal/mol relative to the asymptote, without changingform of the potential in the dynamically relevant region. This a very good approximation, since in the barrier regionexcited states which couple to the ground state via spin-ocoupling are very high in energy.

On the other hand, the spin–orbit coupling, which hnot yet been included in the present work, will affect tshape of the potentials in the long range region. As has bshown for F1H2,

25 in the absence of spin–orbit couplingthe asymptotically degenerate2S1(1 2A8) and 2Px(2

2A8)states strongly mix in the entrance channel; the diabatictential correlating with the latter state has a van der Waminimum at collinear geometries, while the2S state has aminimum at a T-shaped geometry. This leads to nonadiabcoupling along the bending coordinate and a conical in

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section at the point where the collinear2S1 and 2P poten-tials cross. This situation is strongly changed by the SO cpling, which lifts the asymptotic degeneracy of the statand therefore reduces the nonadiabatic mixing. Howespin–orbit coupling leads to another nonadiabatic effect;asymptotic Cl(2P1/2) and Cl(2P3/2) states are mixtures of th2S1 and2P states. In the region where the2P state rises inenergy~it correlates with an excited3P state of HCl! strongrecoupling occurs, leading to a sudden change of the abatic wave functions along the reaction coordinate. Possithis nonadiabatic effect is responsible for the unexpectestrong reactivity of the excited Cl(2P1/2) state, which hasrecently been reported.11 In order to study these effects imore detail, we are presently in the process of producfurther coupled potential energy surfaces for the H2Cl sys-tem, which fully include the spin–orbit coupling in the entrance channel. A final judgment about the quality of onew surfaces will only be possible once detailed dynamcalculations on these spin–orbit corrected surfaces haveperformed.

ACKNOWLEDGMENT

W. Bian acknowledges the Alexander von HumboldStiftung for a research fellowship.

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