Kinetic and dynamic studies of the Cl(2 P u) + H2O( X 1 A 1) HCl( X 1+) + OH( X 2)reaction on an ab initio based full-dimensional global potential energy surface of theground electronic state of ClH2OJun Li, Richard Dawes, and Hua Guo

Citation: The Journal of Chemical Physics 139, 074302 (2013); doi: 10.1063/1.4817967 View online: http://dx.doi.org/10.1063/1.4817967 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/139/7?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Jahn-Teller effect in CH2DO/CHD2O( X 2 E ): Vibronic coupling of all vibrational modes J. Chem. Phys. 138, 244309 (2013); 10.1063/1.4811517 Exact quantum scattering calculations of transport properties: CH2( X 3 B 1, a 1 A 1)–helium J. Chem. Phys. 138, 164305 (2013); 10.1063/1.4801789 Vibrations of the low energy states of toluene ( X 1 A 1 and A 1 B 2) and the toluene cation ( X 2 B 1) J. Chem. Phys. 138, 134303 (2013); 10.1063/1.4796204 The 2 bending vibrational structure of the X 2+ state of MgNC J. Chem. Phys. 135, 124311 (2011); 10.1063/1.3640024 Communication: State-to-state differential cross sections for H2O( B ) photodissociation J. Chem. Phys. 134, 231103 (2011); 10.1063/1.3604567

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THE JOURNAL OF CHEMICAL PHYSICS 139, 074302 (2013)

Kinetic and dynamic studies of the Cl(2Pu) + H2O(X̃ 1A1) → HCl(X̃ 1�+)+ OH(X̃ 2�) reaction on an ab initio based full-dimensional globalpotential energy surface of the ground electronic state of ClH2O

Jun Li,1 Richard Dawes,2,a) and Hua Guo1,a)

1Department of Chemistry and Chemical Biology, University of New Mexico, Albuquerque,New Mexico 87131, USA2Department of Chemistry, Missouri University of Science and Technology, Rolla, Missouri 65409, USA

(Received 13 June 2013; accepted 26 July 2013; published online 16 August 2013)

Extensive high-level ab initio calculations were performed on the ground electronic state of ClH2O.The barrier region for the title reaction was found to have significant multi-reference character, thusfavoring the multi-reference configuration interaction (MRCI) method over single-reference methodssuch as coupled-cluster. A full-dimensional global potential energy surface was developed by fittingabout 25 000 MRCI points using the permutation invariant polynomial method. The reaction pathfeatures a “late” barrier flanked by deep pre- and post-barrier wells. Calculated rate constants forthe forward reaction are in reasonable agreement with experiment, suggesting a good representationof the forward barrier. The dynamics of the forward reaction was also investigated using a quasi-classical trajectory method at energies just above the barrier. While the OH bond is found to bea spectator, the HCl product has significant rotational excitation. The reaction proceeds via bothdirect rebound and stripping mechanisms, leading to backward and sideways scattering. © 2013 AIPPublishing LLC. [http://dx.doi.org/10.1063/1.4817967]

I. INTRODUCTION

The hydroxyl radical (OH) is an important reactivespecies in combustion1 and atmospheric processes.2 Thefacile reactions between OH and hydrogen halides producehalogen atoms in their atomic form. In Earth’s atmosphere, inparticular, the primary source of chlorine, which is a causativeagent for stratosphere ozone depletion,3 is hydrogen abstrac-tion from HCl by OH by the reverse of the following reaction:

Cl(2Pu) + H2O(X̃1A1) → HCl(X̃1�+) + OH(X̃2�),(R1)

�H 0 = 15.36 kcal/mol.

Because of its importance in atmospheric chemistry, thekinetics for the reverse direction of (R1) has been exten-sively measured. For example, Smith and Zellner4 measuredthe rate constants over the temperature range 220–480 K,and Ravishankara and co-workers5 fitted their data in therange of 240–1055 K to a modified Arrhenius expression, k−1

= 5.44 × 10−13(T/298)1.65exp(112/T) cm3 molecule−1 s−1.Later, Sharkey and Smith6 reported the rate constants overthe low temperature range 138–298 K, and found that theirrate constants deviate significantly from the recommendedvalues by Ravishankara et al.5 and by Atkinson et al.7 Morerecently, Battin-Leclerc et al.8 reinvestigated the kinetics andrelevant kinetic isotope effects in the range from 200 to400 K. Bryukov et al.9 also reported the rate constantsas k−1 = 3.20 × 10−15T0.99exp(−62/T) cm3 molecule−1 s−1

a)Authors to whom correspondence should be addressed. Electronicaddresses: dawesr@mst.edu and hguo@unm.edu

over the temperature range 298–1015 K and pressure range5.33–26.48 kPa. There has been no kinetic data reported forthe forward direction of (R1), but the rate constants (k1) havebeen estimated based on k−1 and the equilibrium constant (K)(see http://kinetics.nist.gov/).9, 10

The dynamics of the forward reaction has been studiedexperimentally in the context of mode and bond selectivities.To this end, Sinha et al.11, 12 investigated the influence of thereagent vibrations on the endothermic Cl + HOD reactionand found that vibrational excitation in the OH excitation pro-duces at least an eightfold excess of OD over OH. On the otherhand, Thoemke et al.13 reported that the energy is largely dis-posed into the HCl internal excitation, suggesting OH as aspectator during the reaction. On the other hand, Smith andWilliams14 studied mode selectivity in the exothermic OD+ HCl reaction and Butkovskaya and Setser15 measured vi-brational excitation in the water product formed by the re-actions between OH/OD and HCl/DCl. In addition, Cireasaet al.16 explored stereodynamics in the inelastic collisions be-tween OH and HCl.

These interesting experiments have stimulated much the-oretical work. The bond selectivity in (R1) was first studied byKudla and Schatz17 using the quasi-classical trajectory (QCT)method on a model potential energy surface (PES). An ad hocfull-dimensional PES for (R1) was devised by Nyman andClary (NC)18 with the only parameter fit to available ab initiodata. These authors also performed three-dimensional quan-tum scattering calculations with the rotating bond approxima-tion (RBA) and found that the HOD stretching excitation en-hances reactivity more than bend excitation and translationalenergy enhances the reaction more than stretch excitation atlow total energies, but not generally at higher total energies.

0021-9606/2013/139(7)/074302/11/$30.00 © 2013 AIP Publishing LLC139, 074302-1

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074302-2 Li, Dawes, and Guo J. Chem. Phys. 139, 074302 (2013)

A three-dimensional wave packet study of intramolecularenergy flow in this reaction was later reported by Fair et al.19

and a four-dimensional quantum scattering calculation wasreported in 2007.20

A similar ad hoc PES was developed by Clary, Nyman,and Hernandez (CNH)21 for the reverse OH + HCl reac-tion. The mode selectivity was studied quantum mechanically,again with the RBA model, by the same authors.21 In 2003,Huarte-Larranaga and Manthe22 reported a full-dimensionalquantum mechanical calculation of the thermal rate constantsfor this reaction on the CNH PES and revealed significantdeficiencies of the PES by comparing with kinetic data. Inaddition, Yu and Nyman23 reinvestigated the quantum dy-namics of this reaction on an ab initio interpolated PES andfound the rate constants in good agreement with experiment.In 2002, another ab initio PES was reported for this reac-tion using the Largest Angle Generalization of the RotatingBond Order (LAGROBO) formulation, and QCT calculationson this PES yielded rate constants in good agreement withexperiment.24 In addition, the OH + HCl reaction was inves-tigated via ab initio direct dynamics.25 These authors also em-ployed variational transition-state (TS) theory with tunnelingcorrections to calculate the rate constants based on ab initiotransition state information and found good agreement withexperiment over the temperature range 138–1055 K.25 Thesestudies suggested that the original NC and CNH PESs areinaccurate.

It is clear that the existing PESs are insufficiently accu-rate for quantitative understanding of the title reaction. A full-dimensional global PES based on high-level ab initio calcu-lations is desired. Much recent effort has already been madetowards this goal. For example, Wormer et al.26 have devel-oped two four-dimensional diabatic PESs for the OH–HClvan der Waals complex based on ∼20 000 points calculated atthe coupled-cluster and multi-reference configuration interac-tion (MRCI) methods and bound states have been computedby Groenenboom et al.27 This van der Waals complex playsan important role in both inelastic and reactive scattering be-tween OH and HCl molecules.16 However, such semi-globalPESs are not suitable for studying the reaction dynamics. Inthis work, we report extensive ab initio calculations and thedevelopment of a full-dimensional global PES for the groundelectronic state of ClH2O, using the same strategy in our re-cent work on the X + H2O (X = F, O(3P)) PESs.28–30 Thenew PES is analyzed and tested with both kinetic and dynam-ical calculations. This work is organized as follows: Sec. IIpresents details of the ab initio calculations, the constructionof the PES, and the kinetic and dynamic calculations. ThePES is analyzed from stationary properties, kinetic and dy-namic studies in Sec. III along with relevant discussion. Fi-nally, concluding remarks are given in Sec. IV.

II. THEORY

A. Ab initio calculations

Similar to the F + H2O → HF + OH reaction,28, 29, 31, 32

(R1) involves at least the three lowest-lying doublet electronicstates, resulting from the threefold degeneracy in the reactant

asymptote and the twofold degeneracy in the product asymp-tote, and the lowest A′ and A′′ states correlate adiabaticallyto both the reactants and products of the title reaction. In thiswork, we focus on the lowest 2A′ state, and ignore all non-adiabatic couplings with other states. The spin-orbit (SO) cor-rections are also ignored because they are small compared tothe barrier height and reaction endothermicity.

As shown below, a multi-reference method is preferredto accurately map out the global PES of the title reaction.Following our recent work,28, 29 we employed the dynam-ically weighted state-averaged complete active space self-consistent field (DW-SA-CASSCF) method,31, 33 followed byMRCI calculations. It was found that the inclusion of thelowest five states in the DW-SA-CASSCF cycles was suffi-cient (the two highest states received negligible weights inmost regions). The augmented correlation-consistent polar-ized valence triple-zeta (aug-cc-pVTZ or AVTZ) basis set34

as implemented in MOLPRO,35 was used. Larger basis setsor complete basis set (CBS) extrapolation were not employedbecause the barrier height was found to exhibit only a smalldependence on basis set (see below), and the neglect of deriva-tive and spin-orbit couplings represent larger sources of error.

The electronic energy at a particular geometry was cal-culated as follows. Following an initial Hartree-Fock calcula-tion, a five-state DW-SA-CASSCF calculation was performedusing the full-valence active space (15e,10o) with the 1s,2s, 2p orbitals of the chlorine atom and 1s orbitals of theoxygen atom closed. Maximum weight was placed on theground electronic state, and weights for excited states wereassigned self-consistently according to their energy differ-ences from the ground state. In particular, we used the fol-lowing energy dependent weight: sech2(�) = [2/(exp(−β�)+ exp(β�))]2 with � being the energy difference from theground state, and β−1 = 3.0 eV. A series of iterations werethen performed until the energy of the ground electronic statewas converged to 10−6 a.u., which resulted in convergenceof the subsequent MRCI energy to ∼10−7 a.u.36 Internallycontracted MRCI calculations37, 38 were then carried out us-ing the DW-SA-CASSCF reference. The Davidson correction(Q) was included to promote size extensivity and thus approx-imate contributions from higher-order correlation.39 Specifi-cally, we used the rotated reference Davidson correction (Qrot)as implemented in MOLPRO, which has been found to givebetter results for multistate calculations, especially in the re-gion of avoided crossings.40 A multi-state MRCI scheme wasused because of the near degeneracy in certain regions ofthe configuration space. In addition to the standard MRCI+ Q calculations, we have also performed some stationarypoint benchmarks using explicitly correlated MRCI-F12 aswell as the F12 version of the coupled-cluster singles doublesand perturbative triples (UCCSD(T)-F12)41, 42 and MPW1K43

methods.

B. Construction of PES

As was done originally for the F + H2O system,28 thePES for the title reaction was constructed by connecting twoparts. The first describes the reactant asymptote and the strong

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074302-3 Li, Dawes, and Guo J. Chem. Phys. 139, 074302 (2013)

interaction region. The second characterizes the long-rangeinteraction between the two products HCl and OH, which isdominated by dipole-dipole interaction.

The first part of the PES, denoted as Vfit, was fit toab initio points using the permutation invariant polynomialmethod of Bowman and co-workers.44 The following expan-sion of symmetrized polynomials was used:

Vfit(y1 . . . y6) =M∑

n1...n6

cn1...n6yn11 y

n66

× [y

n22 y

n33 y

n44 y

n55 +y

n42 y

n53 y

n24 y

n35

](M ≤ 7),

(1)

where yi = e−ri / α , i = 1, 2,. . . , 6, and ri is the internucleardistance between two atoms and α = 1.8 bohrs. The distancesare defined as follows: r1 = rHH′ , r2 = rHCl, r3 = rHO, r4

= rH′Cl, r5 = rH′O, and r6 = rClO. The fitted PES is invari-ant by construction with respect to the permutation of thetwo identical hydrogen atoms. The total order of polynomialsM = n1 + n2 + n3 + n4 + n5 + n6 does not exceed seven(a total of 918 terms). The expansion coefficients were deter-mined by a weighted least squares method, for which a con-figuration at energy E (in a.u.) relative to the global minimumhas the weight 0.1/(0.1 + E).

In order to provide a globally accurate PES with reason-able computational costs, it is vital to choose the distributionof the ab initio points prudently. Our strategy for the construc-tion of Vfit is similar to that in our previous work.28–30, 45 Sincethe PES is designed for the title reaction, high energy chan-nels, such as HOCl + H (�E = 67.0 kcal/mol, electronic en-ergy calculated by us at the CCSD(T)-F12b/AVTZ level rel-ative to Cl + H2O reactant asymptote) and ClO + H2 (�E= 59.1 kcal/mol), were excluded.

The second part of the PES, denoted as Vdip, describesthe long-range interaction between the two products, HCl andOH. This term was introduced to achieve two goals. First, itrepresents a significant saving as the costs of ab initio calcu-lations in the product channel are substantial due to the long-range nature of the interaction potential. Second, it providesa better description of the asymptotic PES because the an-alytic form avoids fitting errors. The long-range potential isexpressed as follows:28

Vdip = VHCl,HO + Vdip,corr. (2)

Here, VHCl,HO represents the HCl and OH diatomic po-tentials, which were spline-interpolated from ab initio datapoints with a HCl–OH separation of 50.0 Å, and Vdip,corr isthe asymptotic dipole-dipole interaction

Vdip,corr = |�μA| | �μB || �RAB |3 (cos θAB − 3 cos θA cos θB) , (3)

where �μ denotes a dipole moment vector, with its magnitude| �μ| spline-interpolated from the ab initio points. The coordi-nates used in Eq. (3) were depicted in Fig. 2 in Ref. 28.

A switching function, defined using the centers-of-massdistance between OH and HCl (in Å),

S = 1 − tanh [0.8 (RCOM − 10.0)]

2, (4)

was used to smoothly switch the PES between the polynomialfitted PES in Eq. (1) and the dipole-dipole PES in Eq. (2)

V = SVfit + (1 − S)Vdip. (5)

C. Reaction path analysis and transition-state theory

The reaction path Hamiltonian46 for (R1) was determinedon the fitted PES using POLYRATE 9.7,47 starting from thesaddle point geometry and going downhill to both the reac-tant and product sides in mass-weighted Cartesian coordi-nates using Page and McIver’s method48 with a step size of0.00094 amu1/2 bohr. Along the minimum energy path (MEP),the reaction coordinate (s) is defined as the signed distancefrom the saddle point (s = 0), with s > 0 referring to theproduct side and s < 0 to the reactant side. The reaction pathwas followed between s = −2.83 and s = 4.72 amu1/2 bohrand the Hessian matrix was calculated every 10 points. Theseparameters have been tested for convergence. All calculationswere carried out in mass-scaled coordinates with a reducedmass equal to 1 amu. Along the MEP, a generalized normal-mode analysis was performed using a redundant curvilinearprojection formalism by projecting these modes along the re-action path as well as overall rotations and translations. Withsuch information, the vibrationally adiabatic potentials weredetermined

Va(n, s) = VMEP(s) + εint(n, s), (6)

where VMEP(s) is the potential energy along the MEP with itszero at the reactants, and εint(n, s) is the vibrational energyat s from the generalized normal-mode vibrations orthogonalto the reaction coordinate. Va(n = 0, s) corresponds to theground vibrational state adiabatic potential, V G

a (s).The rate constants were estimated by using the canon-

ical variational transition state theory (CVTST, or CVT).49

Quantum effects for motions transverse to the reaction pathwere included by using quantum mechanical vibrational parti-tion function under the harmonic approximation, while quan-tum effects in the reaction coordinate were included by usingthe micro-canonical optimized multidimensional tunneling(μOMT) approach,49 in which, at each total energy, the largerof the small-curvature (SCT) and large-curvature (LCT) tun-neling probabilities was taken as the best estimate. The rota-tional partition functions were calculated classically. The re-action symmetry factor is 4 for the title reaction in the forwarddirection because both H atoms are capable of reaction andR-vdW is of Cs symmetry and the electronic partition func-tion (Qe) is 2 / (4 + 2e−881 cm−1/kBT ), in which the Cl spin-orbit splitting of 881 cm−1 was used.

The barriers of the excited electronic states are higherthan that of the ground electronic state studied here. As a re-sult, contributions of the excited states are relatively small atthe temperatures studied here. In this work, hence, the rate

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074302-4 Li, Dawes, and Guo J. Chem. Phys. 139, 074302 (2013)

constants for the forward reaction are approximated by thosecalculated on the ground electronic state PES.

D. QCT calculations

Standard QCT calculations for (R1) were carried outbased on the fitted PES described above, using VENUS.50 Atotal of 5 × 106 trajectories were calculated at the collisionenergy Ec = 25.0 kcal/mol. The H2O reactant was initiated inits ro-vibrational ground state and sampled by a normal modemethod.51, 52 The maximal impact parameter (bmax) was de-termined using small batches of trajectories with trial values.The trajectories were initiated with a reactant separation of8.0 Å, and terminated when products reached a separation of15.0 Å, or when reactants were separated by 8.0 Å for non-reactive trajectories. During the propagation, the gradient ofthe PES was obtained numerically by a central-difference al-gorithm. The propagation time step was selected to be 0.10 fs,which conserves the energy to better than 0.04 kcal/mol formost trajectories. A few trajectories which failed to conserveenergy to 0.04 kcal/mol or were nonreactive after 10.0 ps werediscarded. The total integral cross section (ICS) was com-puted as follows:

σr (Ec) = πb2max(Ec)Pr (Ec) , (7)

where the reaction probability at the specified collision en-ergy Ec is given by the ratio between the number of reactivetrajectories (Nr) and total number of trajectories (Ntotal)

Pr (Ec) = Nr/Ntotal . (8)

The standard error is given by �

= √(Ntotal − Nr )/NtotalNr .

The reactive differential cross section (DCS) are thencomputed by

dσr

d�= σrPr (θ )

2π sin(θ ), (9)

where Pr(θ ) is the normalized probability for the scatteringproducts at the scattering angle θ . The scattering angle θ isgiven by

θ = cos−1

( �νi · �νf

|�νi ||�νf |)

. (10)

Here, �ν is the relative velocity vector, and the sub-scripts “i” and “ f ” denote “initial” and “final,” respectively,�νi = �νCl − �νH2O, �νf = �νHCl − �νOH. The signs of the relativevelocity vectors have been designed such that θ = 0◦ cor-responds to forward scattering and θ = 180◦ correspondsto backward scattering. To determine the final state distribu-tions of the products, generally, the Gaussian binning (GB)method,53 which enforces the vibrational quantization of theproducts, should provide a better description. Note that in theGB scheme, the Gaussian weights are applied to both prod-ucts. However, large numbers of trajectories are needed toachieve reasonable statistics. Due to the low reactivity in thissystem (only 1540 trajectories are reactive from ∼5 × 106 tra-jectories) and nearly all reactive trajectories violate zero pointenergy (ZPE) retention (1531/1540), the GB results have very

poor statistics. Consequently, we will only present results us-ing the traditional histogram binning (HB) method.

In addition to the micro-canonical calculations, we havealso computed the rate constants for (R1) at several temper-atures using QCT. In this case, the translational, vibrational,and rotational degrees of freedom of the reactants are sampledat the specified temperature under the Boltzmann distributionrules. Other conditions are same as above. The rate constantwas calculated as follows:

k1 = Qe

√8kBT

πμπb2

maxNr

Ntotal

, (11)

in which Nr and Ntotal are the numbers of reactive and totaltrajectories and μ is the reduced mass for the reactant channel.The electronic partition function (Qe) has been given above.

III. RESULTS AND DISCUSSIONS

A. Ab initio characterization

To choose an appropriate ab initio method for map-ping out the global PES in a large configuration space, wefirst determined the MEP at the MPW1K level of theory.Higher-level calculations were then performed at the MPW1KMEP geometries. In Fig. 1(a), T1 diagnostic54 values fromCCSD(T)-F12b calculations along the MEP are shown. Al-though the T1 values are small in both the reactant and productasymptotes, they are quite large (up to 0.15) near the transitionstructure (s = 0). We have also determined the saddle pointat the CCSD(T)-F12b level, which also has large T1 value(0.084). It was thus inferred that this reaction system has asignificant multi-reference character. This was confirmed bymultistate multi-reference calculations at the transition struc-ture, which yield a leading reference coefficient, χ1, of 0.82(see Table III), and locate the first excited electronic state,whose geometries are given in Table I, only about 9 kcal/molhigher in energy.

Our choice to fit the PES was thus the multi-referenceMRCI-Q method based on five-state DW-CASSCF. Similar to

FIG. 1. (a) The T1 diagnostics at the level of CCSD(T)-F12b/AVTZ alongthe DFT MEP. (b) Comparison of the MEP energies at various levels andbasis sets using DFT MEP geometries.

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074302-5 Li, Dawes, and Guo J. Chem. Phys. 139, 074302 (2013)

TABLE I. Optimized geometries in internal coordinates (distances in Å and angles in ◦) of the stationary points for the Cl + H2O → HCl + OH reaction onthe ground electronic state.

Species Method RHO ROH′ RH′Cl θHOH′ θOH′Cl φHOH′Cl

Cl + H2O PESa 0.9620 0.9620 104.36MRCIb 0.9663 0.9663 103.08F12bc 0.9586 0.9586 104.44

MPW1Kd 0.9508 0.9508 105.35CCSD(T)e 0.97 0.97 104.11

SACf 0.9573 0.9573 102.5Expt.g 0.958 0.958 104.48

R-vdW Cl· · ·H2O PESa 0.9657 0.9657 2.8602 105.12 67.36 93.83MRCIb 0.9639 0.9639 2.9447 104.62 63.72 99.58F12bc 0.9611 0.9611 2.8641 104.78 63.73 98.93

MPW1Kd 0.9532 0.9532 2.7583 105.74 65.81 95.33TS PESa 0.9761 1.3398 1.3889 101.98 142.00 56.28

MRCIb 0.9751 1.3297 1.3927 101.69 143.85 59.96F12bc 0.9718 1.3285 1.3910 102.50 143.97 56.45

MPW1Kd 0.9633 1.3044 1.3931 104.03 145.99 58.66CCSD(T)e 0.98 1.31 1.40 103.77 143.42 58.77

SACf 0.9682 1.2583 1.4050 103.9 142.0 52.0TS-2h MRCI 0.9768 1.2115 1.4997 103.72 179.18 59.60P-vdW ClH· · ·OH PESa 0.9735 2.1557 1.2845 123.19 173.61 180.0

MRCIb 0.9747 2.0673 1.2862 112.80 174.44 0.0F12bc 0.9716 2.0461 1.2848 113.10 174.41 0.0

MPW1Kd 0.9644 1.9951 1.2850 111.95 174.51 0.0SACf 0.9682 2.0029 1.2850 112.8 173.5 0.0

TZVPi 0.9755 2.1280 1.2855 122.97 175.74 − 0.01HO + HCl PESa 0.9737 1.2774

MRCIb 0.9713 1.2741F12bc 0.9703 1.2768

MPW1Kd 0.9631 1.2732CCSD(T)e 0.98 1.28

SACf 0.9660 1.2747Expt.j 0.970 1.275

P′-vdW HCl· · ·HO PESa 0.9799 3.6620 1.2772 27.76 73.53 0.0MRCIb 0.9747 3.6608 1.2799 30.42 72.49 0.0F12bc 0.9720 3.5641 1.2784 33.99 75.58 0.0

MPW1Kd 0.9653 3.8403 1.2744 26.33 66.53 0.0

aFitted PES, this work.b2-state-MRCI + Qrot-DW-CASSCF(15e,10o)/AVTZ, this work.cCCSD(T)-F12b/AVTZ, this work.dMPW1K/AVTZ, this work.eCCSD(T)/PVQZ//CCSD(T)/TZVP.25

fSAC, scaling all correlation.23

gExpt., see Ref. 61 and references cited herein.hTS-2 denotes the transition state on the first electronic excited state, which was calculated with a similar MRCI + Q scheme except the reference state was set as the second state inthe DW-CAS cycles.iCCSD(T)/TZVP.9jReference 62.

the F + H2O system, it was found that including five lowestelectronic states was sufficient in all regions.28, 31 In Fig. 1(b),the basis set effect is investigated at the MRCI level with theenergy zero set at the first point along the MPW1K MEP. Sin-gle state MRCI + Q calculations produce barriers of 24.35,23.85, and 23.97 kcal/mol with the AVnZ (n = D, T, Q) basissets, respectively. Using a multistate description, lower bar-riers in the range of 20-21 kcal/mol are obtained (Tables IIand III). The corresponding computational costs for a single-point calculation are 15, 50, and 400 min, respectively. Ad-ditional benchmarks up to quintuple zeta (Table III) confirma weak dependence on basis set size beyond double zeta. In

Fig. 2(a), the external correlation energies, defined as the dif-ference between the MRCI + Q and the DW-CASSCF ener-gies, Ecorr = EMRCI + Q − EDW-CASSCF, are plotted as a func-tion of the reaction coordinate along the MEP for the threebasis sets. The effect of increasing the basis size for captur-ing the external correlation energy is significant from AVDZto AVTZ, but diminishes from AVTZ to AVQZ. The normal-ized weights of the lowest five states in DW-CASSCF/AVTZare shown in Fig. 2(b), and they are insensitive to the basisset. The triple degeneracy in the reactant asymptote and thedouble degeneracy in the product asymptote are apparent inthe figure. State 3 switches smoothly from the reactant side to

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074302-6 Li, Dawes, and Guo J. Chem. Phys. 139, 074302 (2013)

TABLE II. Energies (kcal/mol) and frequencies (cm−1) of the stationary points for the Cl + H2O → HCl + OH reaction.

Harmonic Frequencies

Species Method E 1 2 3 4 5 6

Cl + H2O PESa 0 1622.11 3725.22 3870.20MRCIb 0 1669.23 3835.59 3938.25F12bc 0 1648.20 3834.14 3943.83

MPW1Kd 0 1665.4 3965.7 4071.6CCSD(T)e 0 1623 3786 3906

SACf 0 1636 3906 4020Expt.g 0 1648.5 3832.2 3942.5

R-vdW Cl· · ·H2O PESa − 3.92 135.72 226.03 302.43 1716.14 3960.06 3965.55MRCIb − 4.09 − 26.68 181.99 379.47 1653.66 3776.63 3890.06F12bc − 3.60 142.83 281.31 293.12 1637.94 3801.56 3913.50

MPW1Kd − 3.76 178.10 337.17 353.35 1653.87 3933.99 4041.71TS PESa 20.53 − 1266.33 240.95 502.50 918.26 1420.38 3706.86

MRCIb 20.03 − 1324.72 314.83 519.38 878.04 1355.64 3699.04F12bc 20.60 − 1322.99 270.36 487.71 859.61 1389.56 3732.84

MPW1Kd 17.69 − 1155.18 354.57 555.04 883.73 1397.52 3867.93CCSD(T)e 20.80 − 1413 395 511 858 1388 3695

SACf 22.32 − 2023 344 566 931 1400 3846P-vdW ClH· · ·OH PESa 14.13 98.45 133.10 239.73 335.89 3156. 54 3536.78

MRCIb 14.07 111.48 178.71 265.47 385.32 2885.39 3701.97F12bc 14.80 123.46 172.25 284.88 419.28 2892.73 3730.02

MPW1Kd 12.44 121.38 199.44 297.72 464.16 2887.76 3855.40SACf 14.80 130 135 331 450 2898 3838

TZVPh 111 160 254 375 2950 3720HO + HCl PESa 17.44 3015.90 3663.64

MRCIb 17.17 2981.64 3722.02F12bc 18.37 2994.38 3741.76

MPW1Kd 15.68 3058.84 3868.34CCSD(T)e 18.37 3009 3683

SACf 20.26 3043 3859Expt.i 18.57j 2991 3738

P´-vdW HCl· · ·HO PESa 15.34 86.84 151.75 220.69 427.68 3002.13 3948.17MRCIb 15.26 105.64 124.84 230.35 387.63 2999.13 3690.64F12bc 16.24 65.24 107.73 196.80 359.72 2980.87 3714.45

MPW1Kd 14.27 78.74 118.45 266.78 301.95 3047.53 3821.62

aFitted PES, this work.b2-state-MRCI + Qrot-DW-CASSCF(15e,10o)/AVTZ, this work.cCCSD(T)-F12b/AVTZ, this work.dMPW1K/AVTZ, this work.eCCSD(T)/PVQZ//CCSD(T)/TZVP.25

fSAC, scaling all correlation.23

gExpt., see Ref. 61 and references cited herein.hCCSD(T)/TZVP.9iReference 62.jDerived from experimental �H(0 K) = 15.36 kcal/mol, ZPEs and SO corrections.

the product side. The fourth state only makes significant con-tribution near the transition state, while the fifth state has arelatively small contribution throughout. Based on these char-acteristics, the MRCI + Q/AVTZ level of theory with 5-stateDW-CASSCF was chosen for the PES construction withoutbasis set extrapolation, as a compromise between cost and ac-curacy.

Figure 3 presents the schematic reaction pathway for thetitle reaction. The geometries of the stationary points in inter-nal coordinates with the H atom attacked by Cl being denotedas H′ are given in Table I, and the frequencies and energiesare listed in Table II. The available literature values are alsopresented for comparison. Generally, our results at the density

functional theory (DFT), MRCI, and CCSD(T) levels are con-sistent with each other and with the literature values. In par-ticular, the forward reaction is endothermic with a barrier of∼20 kcal/mol at both the MRCI and UCCSD(T) levels,in good agreement with previous ab initio studies.23, 25

The reaction endothermicity at the MRCI level is 17.17kcal/mol, about 1.2 kcal/mol smaller than that obtained atthe UCCSD(T) level (18.37 kcal/mol) and experiment (18.57cal/mol) derived from experimental enthalpy with ZPE andSO corrections for reactants and products. This difference hasa small effect on the forward direction of the title reaction, butmight be significant for the reverse direction especially at lowenergies or low temperatures.

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074302-7 Li, Dawes, and Guo J. Chem. Phys. 139, 074302 (2013)

TABLE III. Comparison of the classical barriers in kcal/mol of the title reaction between various methods.

Levels HF UCCSD UCCSD(T)

Basis sets Barriers T1 Barriers T1 Barriers T1

AVTZ 27.32 23.30 0.078 21.04 0.078AVQZ 27.40 23.25 0.077 20.93 0.077AV5Z 27.25 23.13 0.076 20.78 0.076apwCVTZ(AE) 23.14 0.057 20.71 0.057apwCVQZ(AE) 23.27 0.055 20.79 0.055apwCV5Z(AE) 23.36 0.055 20.84 0.055

Levels CASSCF MRCI MRCI + Q

Basis sets Barriers χ1 Barriers χ1 Barriers χ1

apwCVTZ 24.37 24.15 0.94 23.32 0.94apwCVQZ 24.63 23.97 0.94 22.97 0.94apwCV5Z 24.66 24.03 0.94 23.02 0.94apwCVTZ(AE) 24.97 0.94 24.07 0.94apwCVQZ(AE) 25.16 0.95 24.12 0.95apwCV5Z(AE) 25.27 0.95 24.22 0.95

Levels CASSCF MRCI-F12 MRCI + Q-F12

Basis sets Barriers χ1 Barriers χ1 Barriers χ1

VTZ-F12 24.64 24.09 0.94 23.08 0.94VQZ-F12 24.67 24.09 0.94 23.07 0.94CVTZ-F12(AE) 24.64 25.32 0.95 24.32 0.95CVQZ-F12(AE) 24.67 25.33 0.95 24.28 0.95

Levels DW-CASSCF DW-MRCI-F12 DW-MRCI + Qrel/rot-F12

Basis sets Barriers χ1 Barriers χ1 Barriers χ1

VTZ-F12 29.36 22.00 0.82 19.82/19.87 0.82/0.82VQZ-F12 29.45 22.02 0.82 19.82/19.87 0.82/0.82CVTZ-F12(AE) 23.07 0.84 20.92/21.02 0.84/0.82

Similar to F + H2O → HF + OH,28, 29 there is a potentialwell before and after the transition state. As discussed in ourrecent work,55 the pre-reaction complex is due to a weak two-center-three-electron hemi-bond, rather than van der Waals or

FIG. 2. (a) External correlation energy Ecorr (Ecorr = EMRCI + Q− EDW-CASSCF) for various basis sets at the MRCI + Q level. (b) TheDW-CASSCF weights as a function of reaction coordinate in 5-state-DW-CASSCF(15e,10o)/AVTZ.

electrostatic interaction. It features O and Cl atoms on theplane bisecting the two H atoms in Cs symmetry, due ap-parently to the O–Cl hemi-bond. For convenience, we willstill denote it R-vdW in the future discussion. At the MRCI+ Q-DW-CASSCF level (without spin-orbit), the depth ofthe well is 4.09 kcal/mol relative to the reactant asymptote,

FIG. 3. Schematic illustration of the reaction pathway for the Cl+ H2O → HCl + OH reaction on the ground electronic state PES. The MRCI+ Qrot/AVTZ energies are given above and the corresponding values of thefitted PES, which is in italic. The ZPE corrected values are given in wavylines. All energies are in kcal/mol and relative to the Cl + H2O asymptote.

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074302-8 Li, Dawes, and Guo J. Chem. Phys. 139, 074302 (2013)

slightly deeper than the UCCSD(T) value of 3.92 kcal/mol.The lowest frequency for R-vdW at the UCCSD(T)-F12blevel is 143 cm−1 compared with 136 cm−1 on the fitted PES.A numerical MRCI-based Hessian produced a small imagi-nary frequency (see Table II). On the other hand, there aretwo post-reaction complexes between the HCl and OH prod-ucts. One (P-vdW) corresponds to the ClH. . . OH hydrogenbonded complex, which is directly connected to the reactiontransition state and has been investigated by several authorspreviously.23, 26, 27 The other (P′-vdW) features the HCl. . . HOhydrogen bonded complex, which has not been reported. Theycan be interconverted by H atom rotation. At the MRCI level,the depths of the P-vdW and P′-vdW complexes are 14.07 and15.26 kcal/mol, compared with UCCSD(T) values of 14.80and 16.24 kcal/mol, respectively.

The transition state has a nonplanar geometry, similarto that of the FH2O system.28, 31, 32 As shown in Table I, theCl–H′–O is 144◦ at both UCCSD(T) and MRCI levels, whileCl–H′ and H′–O distances are 1.39 and 1.33 Å, respectively.The larger change in H′–O indicates that the transition stateis late, or product-like, consistent with the endothermicity ofthe reaction. The non-reactive HO bond and the H–O–H′ an-gle are near their equilibrium values, so that it is likely thatthe OH moiety will serve as a spectator during the reaction.

The barrier height is key to reactivity. Table III listsbenchmark calculations on the barrier height of the ti-tle reaction using the transition state geometry (shown inTable I) at the MRCI level described above. Due to the lack ofsize consistency in MRCI, reactants were treated as a widelyseparated supersystem in the MRCI based calculations. Thesingle-reference based methods, UCCSD or UCCSD(T), areconsidered less suitable for this system as the transition statehas a large T1 diagnostic value independent of the basis set.The effects of basis set completeness and core electron cor-relation are small at all single-reference levels. As mentionedabove, T1 values as large as 0.15 were noted in some regionsof the PES affirming the choice of a multi-reference methodto generate the global PES. At the MRCI transition structureitself, the value for T1 of 0.076 (AV5Z) with valence cor-relation reduces to 0.055 for the corresponding all-electroncalculation. Nevertheless, the UCCSD(T) barrier height fromthe largest basis set all-electron calculations are consistentwith the best multi-reference calculations and thus appearto be reliable. For quintuple zeta basis sets, the progressionwith correlation level is 27.25, 23.36, 20.84 kcal/mol for HF,UCCSD, UCCSD(T), respectively. As will be discussed ina future publication,56 this is quite different from the cor-responding results for F + H2O, for which the barrier pro-gresses as 43.12, 7.09, and 2.05 kcal/mol for HF, UCCSD, andUCCSD(T). In F + H2O, high-order correlation is much moreimportant, while multi-reference and multi-state effects areless important (the T1 value at the transition state in F + H2Ois only 0.022 and the lowest excited state is much higher in en-ergy). For Cl + H2O, the best estimate of the classical barrierwithout SO effects at the single reference UCCSD(T) levelis 20.9 kcal/mol with CBS extrapolation using UCCSD(T)-AE/aug-cc-pwCVnZ (n = 4, 5) (AE denotes all elec-tron, aug-cc-pwCVnZ was shortly as apwCVnZ hereafter)results.

For multi-reference methods, there are some interest-ing differences between FH2O28 and ClH2O. In CASSCFcalculations at the TS, the first excited state of F + H2Ois about 25 kcal/mol above the ground state. However,the corresponding gap is only 13 kcal/mol for Cl + H2O.For FH2O, the leading reference coefficient in a one-stateMRCI calculation at the transition state is about 0.91 and isunchanged in multistate MRCI calculations (no significantmixing is observed). In contrast, for Cl + H2O, significantmixing and a lower barrier are noted, as shown below. In one-state MRCI calculations, the leading reference coefficient atthe saddle point is 0.94, independent of basis set, or core elec-tron correlation. With such a large leading reference coeffi-cient (certainly in the absence of a low-lying excited state),one might expect a smaller T1 diagnostic. The standard one-state MRCI + Q converges to a barrier of ∼23 kcal/molor ∼24.3 kcal/mol with core-electron correlation, very sim-ilar to the UCCSD results. In this case, adding perturbativetriples (T) to the single reference UCCSD calculations hasa similar effect on the barrier to adding additional states tothe MRCI calculations. A dynamically weighted multi-stateMRCI calculation produces a leading coefficient of 0.82 forthe lowest MRCI state. There is significant mixing of con-figurations from the two lowest CASSCF states to form theground MRCI state. As seen in Table III, the barrier is de-creased significantly when two reference states are used forMRCI: the best estimate of the barrier is 19.9 kcal/mol withvalence correlation or 21.0 kcal/mol with all-electron corre-lation. The latter is very close to the best estimate based onsingle-reference calculations (20.9 kcal/mol) despite its sig-nificant T1 diagnostic value. Here, the basis set effect is alsofound to be small, the chosen method to fit the PES (2-state-MRCI + Qrot/AVTZ-DW-5-state-CASSCF exhibits a barrierof 20.0 kcal/mol), in close agreement with 19.9 kcal/mol thebest valence correlation estimate of the benchmark MRCIcalculations.

B. Properties of the PES

A total of 24 466 ab initio points at the level of 2-state-MRCI + Qrot/AVTZ-DW-5-state-CASSCF were calculated,and after discarding a few high energy data, 24 402 pointswith energies smaller than 300 kcal/mol relative to the globalminimum (R-vdW) were retained for constructing the PES.The majority of the sampled points (23 335) have energiesless than 100.0 kcal/mol, as shown in Fig. 4. The remainder(1067 points in the range 100.0-300.0 kcal/mol) are mostlyalong repulsive walls. The weighted least squares fit de-scribed above resulted in a total root mean square deviation(RMSD) from the data of 0.80 kcal/mol, while the RMSD forconfigurations with energies less than 50.0 kcal/mol is evensmaller (0.63 kcal/mol). The stationary properties such as ge-ometries, energies, and frequencies, are reproduced on thePES. As shown in Table I, the distances are typically within0.01 Å of directly optimized geometries, while angles arewithin 3◦. The geometries of the van der Waals wells are lesswell reproduced due to their floppy nature. Note that for P-vdW, the dihedral angle is 180◦, far different from the MRCI

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074302-9 Li, Dawes, and Guo J. Chem. Phys. 139, 074302 (2013)

FIG. 4. The distribution of ab initio data points as a function of the potentialenergy in kcal/mol relative to the reactant asymptote.

value of 0◦. However, the structures are almost identicalbecause the Cl–H′–O angle is essentially linear, which ren-ders the two dihedral angles equivalent.

As shown in Table II, the energies of the stationary pointson the PES are in good agreement with the MRCI + Qvalues, generally within 0.2 kcal/mol except the TS with alarger deviation of 0.5 kcal/mol. The barrier on the PES of20.53 kcal/mol is thus fortuitously even closer to the bestall-electron benchmark value of 21.02 (Table III). The MRCI+ Q frequencies are also reproduced well on the PES. At thesaddle point of the PES, the value for the imaginary frequencyof 1266i cm−1) is in reasonable agreement with the direct nu-merical MRCI + Q value (1324i cm−1), indicating a goodrepresentation of the potential along the reaction coordinate.

Figure 5 shows a contour plot of the PES representingthe two bond lengths involved in the reaction while all other

FIG. 5. Contour plot for the PES along the Cl–H and H–O distances withall other internal coordinates optimized. Energies are in kcal/mol relative tothe reactants. The contours are from −4 to 50 kcal/mol with an interval of3 kcal/mol. The inset, showing details around the transition state, is from −4to 40 kcal/mol with an interval of 2.5 kcal/mol.

FIG. 6. (a) Minimum energy path, VMEP, zero point energy, ZPE, and vi-brationally adiabatic ground state energy V G

a (all energies in kcal/mol) as afunction of the reaction coordinate s; (b) generalized normal mode vibrationalfrequencies (cm−1) as a function of s.

degrees of freedom are optimized. It is clear that the reactionhas a “late” transition state in the product channel.

C. Kinetic and dynamic studies

Figure 6 displays the classical MEP (VMEP), vibrationallyadiabatic ground state energy (Va

G), ZPE, and generalizednormal mode frequencies, as a function of the reaction co-ordinate s over the range from s = −2.83 (near R-vdW)to s = +4.72 (near the P-vdW well) amu1/2 bohr. The clas-sical barrier at the PES saddle point is 20.30 kcal/mol ats = 0.0 amu1/2 bohr, but the maximum of Va

G (30.28kcal/mol) is shifted to s = +0.17 amu1/2 bohr. This indicatesat least a slight variational effect. As shown in the figure,near R-vdW there are three H2O modes with the largest fre-quencies. In the vibrationally adiabatic picture, the symmetricstretching (labeled 2) and bending (labeled 3) modes gradu-ally soften as the two reactants approach each other, whilethe asymmetric stretching (labeled 1) mode maintains its fre-quency. Modes 1 and 2 eventually become the OH and HClstretching modes in the products, and the 3rd mode, alongwith the other two low-frequency (labeled 4 and 5) modes,transform into the rotational degrees of freedom in the prod-uct asymptote. The significant change in ZPE around the TSis responsible for the shifted maximum in Va

G along s. Thefrequencies along the MEP on our PES are similar to, butsmoother than results from Steckler et al.25 The qualitativebehaviors are also similar to that in the F + H2O57 and O(3P)+ H2O systems.30

To confirm the validity of the PES, the canonical rate con-stant for (R1) was calculated using QCT and CVT/μOMTmethods. In the QCT calculations, the translational and in-ternal degrees of freedom of H2O were thermally sampledat 1500, 2000, 2500, and 3000 K. 4 × 105, 2 × 105,1 × 105, and 1 × 105 trajectories were calculated at these tem-peratures and the statistical errors were 0.045, 0.036, 0.037,and 0.029, respectively. No QCT calculations were carriedout at lower temperatures because of the low reactivity. Thetransition-state theory calculations were performed over the

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074302-10 Li, Dawes, and Guo J. Chem. Phys. 139, 074302 (2013)

FIG. 7. Canonical rate constants calculated by CVT/μOMT and QCT for thetitle reaction with comparison to the available literature data.

temperature range 200–3000 K. As shown in Figure 7, athigh temperatures, the rate constants obtained from QCT andCVT/μOMT are consistent, both in reasonable agreementwith the recommended experimental rate constants for theforward direction,9, 10 and in the whole temperature range of200–3000 K, the experimental rate constants are also repro-duced by the CVT/μOMT calculations.

A total of 1540 trajectories were found reactive in a batchof 5 × 106, with the products HCl and OH mainly in their vi-brational ground states, independent of the binning methodused. The lack of vibrational excitation in the products arepresumably due to the energy constraint at Ec = 25 kcal/mol,which gives a total available energy of 11.74 kcal/mol. Hence,only the rotational distributions in the ground vibrationalstates of the products were analyzed and the results are dis-played in Fig. 8. Due to the poor statistics of the GB approach,we chose to only present the HB results. It can be seen thatthe OH product is essentially a spectator with moderate rota-tional excitation, while the HCl product is produced in rela-tively high rotational levels. This reflects the torque exertedon the HCl product near the transition state.

FIG. 8. Rotational state distributions of the HCl (a) and OH (b) products intheir vibrational ground states at Ec = 25.0 kcal/mol.

FIG. 9. (a) Product angular distributions (DCS, in 10−8 Å2/sr) for the titlereaction at Ec = 25.0 kcal/mol. (b) Opacity function p(b). (c) Correlationbetween the impact parameter and scattering angle.

Figure 9(a) presents the DCS for the title reaction. Thebackward bias is consistent with the direct rebound mech-anism of the reaction, but there is also significant sidewaysscattering. Figure 9(b) shows the opacity function, which hasa peak around b = 1.1 Å, indicating the large size of the Clatom. As shown in Figure 9(c), these sideways trajectories arecorrelated with large impact parameters, where the center ofmass velocity is reduced. Under such circumstances, the strip-ping mechanism dominates. The situation here is similar tothe H + CH4,58 Cl + CH3OH,59 and F− + CH3I reactions,60

where the direct rebound mechanism dominates at small im-pact parameters, while the stripping mechanism becomes im-portant for large impact parameters.

IV. CONCLUSIONS

In this work, we report a global full-dimensional PES forthe title reaction based on a large number of MRCI + Q calcu-lations. The region near the reaction saddle point is found tohave significant multi-reference and multi-state character, andconsequently single reference methods such as UCCSD(T)are less suitable. The barrier for the forward direction of thereaction is believed to be accurately determined, evidenced bythe good agreement with experimental rate constants. How-ever, the reaction energy is underestimated, with an error ofapproximately 1 kcal/mol for the reverse barrier. The dynam-ics of the forward reaction is investigated using a QCT methodon the new PES at 25 kcal/mol of collision energy. While OHis found to be largely a spectator, the HCl product is sig-nificantly excited in its rotational degree of freedom. Somecorrelation of the product rotational excitation exists. Thereaction proceeds via both the direct rebound and strippingmechanisms, leading to backward and sideways scattering.

Note added in proof: A recent publication also reportedthe stationary points along the reaction path,63 and the resultsare in good agreement with those reported here.

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074302-11 Li, Dawes, and Guo J. Chem. Phys. 139, 074302 (2013)

ACKNOWLEDGMENTS

This work was supported by (U.S.) Department of Energy(DOE) (DE-FG02-05ER15694 to H.G.) and National ScienceFoundation (NSF) (CHE-1300945 to R.D.). Parts of the cal-culations were carried out at NERSC.

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