Probing the resonance potential in the F atomreaction with hydrogen deuteride withspectroscopic accuracyZefeng Ren*, Li Che*, Minghui Qiu†, Xingan Wang*, Wenrui Dong*, Dongxu Dai*, Xiuyan Wang*, Xueming Yang*‡,Zhigang Sun*§, Bina Fu*, Soo-Y. Lee§, Xin Xu¶, and Dong H. Zhang*‡

*State Key Laboratory of Molecular Reaction Dynamics, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian 116023, Liaoning, China;†Department of Physics, Dalian Jiaotong University, Dalian 116028, Liaoning, China; §School of Physical and Mathematical Sciences, Nanyang TechnologicalUniversity, Republic of Singapore 637616; and ¶Department of Chemistry, Xiamen University, Xiamen 361005, Fujian, China

Edited by F. Fleming Crim, University of Wisconsin, Madison, WI, and approved January 3, 2008 (received for review October 19, 2007)

Reaction resonances are transiently trapped quantum states alongthe reaction coordinate in the transition state region of a chemicalreaction that could have profound effects on the dynamics ofthe reaction. Obtaining an accurate reaction potential that holdsthese reaction resonance states and eventually modeling quanti-tatively the reaction resonance dynamics is still a great challenge.Up to now, the only viable way to obtain a resonance potential isthrough high-level ab initio calculations. Through highly accuratecrossed-beam reactive scattering studies on isotope-substitutedreactions, the accuracy of the resonance potential could be rigor-ously tested. Here we report a combined experimental and theo-retical study on the resonance-mediated F � HD3 HF � D reactionat the full quantum state resolved level, to probe the resonancepotential in this benchmark system. The experimental result showsthat isotope substitution has a dramatic effect on the resonancepicture of this important system. Theoretical analyses suggest thatthe full-dimensional FH2 ground potential surface, which wasbelieved to be accurate in describing the resonance picture of theF � H2 reaction, is found to be insufficiently accurate in predictingquantitatively the resonance picture for the F � HD 3 HF � Dreaction. We constructed a global potential energy surface byusing the CCSD(T) method that could predict the correct resonancepeak positions as well as the dynamics for both F � H2 3 HF � Hand F � HD 3 HF � D, providing an accurate resonance potentialfor this benchmark system with spectroscopic accuracy.

crossed molecular beams scattering � potential energy surfaces �reaction dynamics � reaction resonances

Reaction resonance has been a central topic in reactiondynamics research for the last few decades (1–3). The F �

H2 3 HF � H system has played a key role in the study ofreaction resonances (4, 5). Theoretical predictions of reactionresonances in the F � H2 reaction were made in the 1970s (6–9)based on a collinear potential. In a crossed-beams study on theF � H2 reaction by Lee and coworkers (10) in 1984, a forwardscattering peak was observed for the HF(v� � 3) product, whichwas attributed to a reaction resonance. However, theoreticalstudies (11, 12) based on the Stark–Werner potential energysurface (SW-PES), in which the spin–orbit effect was notincorporated, did not concur with this conjecture. On the otherhand, results of full quantum mechanical (QM) calculationsbased on the SW-PES were found to be in good agreement withthe negative-ion photodetachment spectra of FH2

� by Neumarkand coworkers (13). More recently, the F � H2(j � 0) reactionwas investigated in a high-resolution crossed-beams reactivescattering study (14, 15). A pronounced forward scattering peakat the collision energy of 0.52 kcal/mol for HF(v� � 2) wasobserved and attributed to the constructive interference of twoFeshbach resonance states, the ground and the first excitedFeshbach resonance states, in this system based on a recentlycalculated, full-dimensional FH2 ground potential energy sur-

face (XXZ-PES) (16), which has included the spin–orbit effect.In addition, experimental evidence of dynamical resonances inthe F � H2(j � 1) reaction has also been found (17).

For the F � HD 3 HF � D reaction, a detailed crossedmolecular beam study was also carried out recently (18). In thisstudy, a step in the total excitation function at �0.5 kcal/mol wasobserved clearly. This step was attributed to a single reactionresonance state based on the theoretical analysis using theSW-PES. Differential cross-sections have also been measuredfrom 0.4 to 1.18 kcal/mol (19) and from 1.3 to 4.53 kcal/mol (20).However, the resonance step in the total excitation functionpredicted theoretically by using the SW-PES is to appear at 0.7kcal/mol, which is �0.2 kcal/mol higher than is observed exper-imentally. Furthermore, when the spin–orbit effect was includedin the SW-PES, the predicted step in the excitation functiondiffered even more markedly from experiment. A modifiedpotential based on the SW-PES has also been constructed (21),but this modified PES has an energetic problem similar to theSW-PES. In addition, the first excited resonance state in F � H2disappears on this modified PES. This result is not consistentwith the result of the recent high-resolution crossed-beamexperiment on F � H2 (14).

The XXZ-PES appeared to be quite accurate in predicting thecollision energy-dependent forward scattering peak as well asthe differential cross-sections for the F � H2 reaction (14). Thepredicted resonance step in the F � HD 3 HF � D reactioncalculated by using the XXZ-PES is, however, still considerablyhigher in energy than the previous crossed-beams result (18)(supporting information (SI) Fig. 7). This finding suggests thatthe XXZ-PES in the resonance region is not sufficiently accurateand thus predicts an incorrect isotope shift of the resonance statein F � HD 3 HF � D. Therefore, no PES currently availablefor this benchmark system can predict quantitatively the correctresonance picture for both F � H2 and F � HD reactionssimultaneously, suggesting that the essential part of the PES, theresonance potential well, is still not accurate at the level of thepresent state-of-the-art molecular beam scattering experiment.

Recently, we have carried out a full quantum state resolvedreactive scattering study on the isotope-substituted F(2P3/2) �HD(j � 0) 3 HF � D reaction, in an effort to probe the

Author contributions: Z.R. and L.C. contributed equally to this work; X.Y. and D.H.Z.designed research; Z.R., L.C., M.Q., Xingan Wang, W.D., D.D., Xiuyan Wang, X.Y., Z.S., B.F.,S.-Y.L., and D.H.Z. performed research; X.X. contributed new reagents/analytic tools; Z.R.and L.C. analyzed data; and X.Y. and D.H.Z. wrote the paper.

The authors declare no conflict of interest.

This article is a PNAS Direct Submission.

‡To whom correspondence may be addressed. E-mail: xmyang@dicp.ac.cn or zhangdh@dicp.ac.cn.

This article contains supporting information online at www.pnas.org/cgi/content/full/0709974105/DC1.

© 2008 by The National Academy of Sciences of the USA

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resonance potential experimentally, using the high-resolutionand highly sensitive H-atom Rydberg tagging method (22).State-to-state scattering studies have recently provided greatinsights into the dynamics of elementary chemical reactions(23–26). The experimental method used in this work is similar tothat used in refs. 14 and 15. A detailed description of theexperimental method used here can also be found in refs. 27 and28. Theoretically, we have used a new efficient approach inconstructing a highly accurate PES by using the CCSD(T)method, paying special attention to the resonance part of thepotential. To compare with the experimental results, quantumscattering calculations have been performed on this PES toexplore the effect of isotope substitution on the resonancepicture for this system.

Time-of-f light (TOF) spectra of the D atom products from theF � HD reaction were measured at many laboratory angles at�10o intervals, with the collision energy changing from 0.3 to 1.2kcal/mol. Fig. 1 shows three typical TOF spectra for the F � HD3 HF � D reaction at the collision energy of 0.48 kcal/mol.More TOF spectra at other collision energies can be found in SIFigs. 8–10. The pronounced sharp features in these TOF spectracan be assigned to the HF(v � 2) product rotational–vibrational(ro-vibrational) states from the ground state F(2P3/2) reactionwith HD. Clearly, the D-atom TOF spectra are almost allro-vibrational state resolved for the HF product. These spectrawere then converted to the center-of-mass frame by using astandard Jacobian transformation to obtain the product kinetic

energy distributions. The kinetic energy distributions obtainedexperimentally in the laboratory frame were then fitted by simplyadjusting the relative populations of the ro-vibrational states ofthe HF product. From these fittings, relative population distri-butions of the HF product at each ro-vibrational state weredetermined at different scattering angles and different collisionenergies. Quantum-state distributions of the HF product in thecenter-of-mass frame (�cm � 0o to 180o) were then determinedby a polynomial fit to the above results, and from these distri-butions, full ro-vibrational state-resolved differential cross-section (DCS) values were determined. Fig. 2 shows four exper-imental 3D DCS contour plots for the F � HD reaction at fourcollision energies: 0.43, 0.48, 0.52, and 0.71 kcal/mol.

The most intriguing observation in the experimental DCS isthe dramatic change of the 3D DCS, �0.5 kcal/mol. Within thecollision energy range of 0.28 kcal/mol, or 98 cm�1, the DCS goesthrough a series of remarkable changes. A step in the collisionenergy from 0.48 to 0.52 kcal/mol (only 0.04 kcal/mol or 14 cm�1)caused a considerable change in the DCS.

To further investigate the resonance phenomenon, we havealso measured the scattering signal at the exact backwardscattering direction for HF(v� � 2) product in low rotationalstates (j� � 0–3) in the collision energy range between 0.2 and1.2 kcal/mol. Fig. 3 shows the summed signal of HF(v� � 2, j� �0–3) as a function of collision energy. The experimental resultsshow a clear peak �0.39 kcal/mol for the backward scatteredHF(v� � 2, j� � 0–3) product. The peak in the collisionenergy-dependent backward-scattered HF(v� � 2) product isobviously related to the resonance phenomenon in the reaction.

From the present experiment, we have found that the rota-tional distribution of the HF(v � 2) product from the F � HDreaction is also very intriguing. At the lowest collision energiesstudied from 0.31 to 0.64 kcal/mol, the distribution appearstrimodal with two clear peaks at j� � 2 and 9, with another smallbump around j� � 6 (see Fig. 4). At higher collision energies, thesmall middle bump becomes less obvious while the two mainpeaks persist. The distribution observed in this work is quanti-tatively different from the previous experimental result (19) atsimilar collision energies for the same system. Clearly, therotational distribution observed in F � HD is considerablydifferent from that of the F � H2 reaction. The dynamical originof this trimodal distribution is not immediately clear at thismoment, and certainly deserves more detailed investigations.

There are obvious differences between the results of thecurrent experiment and those of ref. 19. First, substantial

Fig. 1. TOF spectra of the D atom product from the F(2P3/2) � HD(j � 0)reaction at the collision energy of 0.48 kcal/mol. TOF spectra at three labora-tory angles shown at �L � �45°, 35°, and 115° correspond roughly to theforward, sideways, and backward scattering directions (with respect to the Fatom beam) for the HF(v� � 2, j � 0) product in the center-of-mass frame,respectively.

Fig. 2. The experimental 3D contour plots for the product translationalenergy and angular distributions for the F(2P3/2) � HD(j � 0) reaction at variouscollision energies: 0.43 kcal/mol (a); 0.48 kcal/mol (b); 0.52 kcal/mol (c); and0.71 kcal/mol (d).

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differences are seen in the 3D DCS between this work and ref.19 at the collision energy �0.5 kcal/mol. In addition, there arenoticeable differences between the HF rotational state distri-butions in the two experiments in which we have observed atrimodal distribution whereas ref. 19 shows a slightly bimodaldistribution. These differences between the two studies couldbe attributed to the considerably different experimental con-ditions used. In this work, the experimental conditions werecontrolled very precisely. The collision energy resolution ofthis experiment at 0.5 kcal/mol is �0.06 kcal/mol (FWHM).This remarkable energy resolution is due mainly to the use ofthe cold HD beam expansion at the liquid nitrogen temper-ature and partly to a better controlled discharged F atombeam. Collision energy resolution in a crossed-beam experi-ment is normally limited by the speed ratios of the two crossingbeams. Because the HD beam used in ref. 19 is obtained in aroom temperature expansion, the collision energy resolution islikely 3–4 times larger than in our experiment. This differencewould certainly result in a considerably larger averaging effectin both the DCS and the HF product rotation state distribu-tion. Furthermore, the HD molecules in the current experi-ment are nearly all in the j � 0 level because of the cold

expansion, whereas the HD beam in ref. 19 is obtained in aroom temperature expansion and has an 18% j � 1 contribu-tion (19). Because of these large differences between theconditions of the two experiments and the extremely sensitivenature of the resonance, the substantial differences betweenthe results of the two experiments in both the DCS and HFrotational state distribution are not too surprising.

To understand these intriguing experimental observations, wehave carried out full quantum dynamical calculations using theABC code (29) based on the XXZ-PES for a comparison withthe above experimental results. A full comparison with thecurrent experimental results suggests that the XXZ-PES couldnot model the DCSs quantitatively for the F � HD3 HF � Dreaction. Furthermore, Fig. 3 shows that the predicted peak forthe backward scattered HF(v � 2, j � 0–3) product falls at awrong collision energy, suggesting that the resonance state onthe XXZ-PES is likely too high for the F � HD reaction. Becausethe resonance state in the F � HD reaction predicted by theXXZ-PES lies at a higher energy than its real position, thedynamical picture for the DCS at different collision energies istherefore distorted. This is the reason that the calculated DCSon the XXZ-PES is in strong disagreement with the presentexperimental result.

With the hope to obtain a more accurate PES for thisbenchmark reaction, we have constructed a PES based on thespin-unrestricted, coupled cluster method, including single anddouble excitations with perturbative accounts of triple excita-tions, using an augmented, correlation consistent, polarizedvalence quintuple zeta quality basis set [UCCSD(T)/aug-cc-pV5Z] (30). The correlation energies for all of the ab initio datapoints were scaled by a factor of 1.01 to get the exact reactionexothermicity with the spin–orbit interaction energy considered.A global PES was then obtained by employing the 3D cubic-spline method. Finally, the spin–orbit interaction energy func-tion used in XXZ-PES was added to the new PES to include thespin–orbit interaction. The key parameters of this newCCSD(T)-PES for the F atom reaction with H2 are listed inTable 1.

Full quantum scattering calculations have been also carriedout on the new PES by using the ABC program (29) to obtainfully converged DCS for both the F � H2 and F � HDreactions. It turns out that for the F � H2 reaction the overallagreement between experiment and theory on the new PES isas good as, or even better than, on the XXZ-PES. The collisionenergy dependence for the forward-scattering HF(v� � 2)

Fig. 3. Collision energy-dependent DCS for the backward scattering HF(v� �2) products summed over j� � 0 to 3. A resonance-like peak is clearly presentat the collision energy of �0.39 kcal/mol. The filled circles are the experimentaldata, and the solid lines are the calculated theoretical results based on the XXZsurface and the CCSD(T)-PES.

Fig. 4. The HF(v � 2) product rotational state distribution at the collisionenergy of 0.48 kcal/mol. Experimental data (red) are from this work, theoret-ical results are from the full quantum dynamical calculations based on theCCSD(T)-PES in this work.

Table 1. Key parameters of the CCSD(T)-PES for the F � H2

(HD) reaction

Parameter Value

Static barrierHeight, kcal/mol 1.77Geometry

HH distance, bohr 1.46HF distance, bohr 2.90HHF angle, ° 115

�H for F � HD(v � 0, j � 0)3 HF(v�, j� � 0) � D, kcal/molv� � 0 31.19v� � 1 19.85v� � 2 8.91v� � 3 �1.34

�H for F � H2(v � 0, j � 0)3 HF(v�, j� � 0) � H, kcal/molv� � 0 32.01v� � 1 20.68v� � 2 9.84v� � 3 �0.515

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product obtained on the new PES agrees with the experimentalresults very well, with a clear narrow peak predicted at 0.52kcal/mol (see SI Fig. 11). In contrast, for the F � HD reactionthe collision energy dependence for the backward-scatteringHF(v� � 2, j� � 0–3) product calculated on the new PES isshifted down to lower energy by �0.16 kcal/mol compared withthat on the XXZ-PES, giving rise to a nearly perfect agreementwith the experimental result as shown Fig. 3. The degree of theagreement on the DCSs between experiment and theory is alsoremarkable. As pointed out above, the experimental DCSvaries dramatically in a very small collision energy range from0.43 to 0.48, 0.52, and to 0.71 kcal/mol, as shown in Fig. 2.Remarkably, the theoretical results obtained on the new PEScan reproduce closely this dramatic variation in DCS as shownin Fig. 5. Furthermore, the theory on the new PES is able toreproduce almost all of the finest structures in the DCSsobserved experimentally, in particular the intriguing trimodalstructures in the HF(v� � 2, j�) rotational distribution at thelow collision energies (see Fig. 4).

Further analysis reveals that all these fascinating phenom-ena observed at low collision energy for the F � HD reactionare directly related to the ground resonance state trapped inthe peculiar HF(v� � 3)-D adiabatic well, denoted as (003)state, as shown in Fig. 6B in one dimension along the reactioncoordinate. Interestingly, for the total angular momentum J �0, the energy for that resonance state, 0.40 kcal/mol, is ratherclose to the peak position (�0.39 kcal/mol) of the backward-scattering HF(v� � 2, j � 0–3) signal, because the backward-scattering product is mainly produced by the low total angularmomentum partial waves. As shown in Fig. 6B, the HF(v� �3)–D adiabatic potential on the new PES is almost identical tothat on the XXZ-PES when the distance between HF and Dis larger than 5.5 bohr. However, for smaller values of thedistance, the adiabatic potential on the new PES is consider-ably different from that on the XXZ-PES. The well of the newPES is deeper than that on the XXZ-PES by �0.3 kcal/mol.And the small bump between the inner well and the van derWaals (vdW) well at the distance of 4.5 bohr on the XXZ-PESvanishes on the new PES. However, a shoulder in the vdWinteraction region is present on the new potential, suggestingthat the vdW interaction is still important in this system.Consequently, the energy of the ground resonance state on thenew PES shifts down by 0.16 kcal/mol, resulting in the shift of

the backward-scattering peak of the HF(v� � 2, j� � 0–2)product as shown in Fig. 3.

The implication of the new PES on the resonance states forF � H2 reaction is shown in Fig. 6A. The energy shift for theground resonance state (003) of 0.12 kcal/mol is quite sub-stantial. However, because the energy of the (103) state ismainly determined by the potential at large distance, this stateshifts down by merely 0.01 kcal/mol. The phenomenon ofpredominantly forward-scattering HF(v� � 2) product at thecollision energy of 0.52 kcal/mol is a result of the interferencebetween the (003) and (103) states, and it is largely determinedby the (103) state. Because both the new PES and theXXZ-PES are at the same level of accuracy in describing the(103) state, both of them give the correct forward-scatteringHF(v� � 2) product signal.

In conclusion, through extensive experimental and theoreticalstudies on the F � HD 3 HF � D reaction, an adiabaticresonance potential obtained by using the CCSD(T) method forthis important system has been strictly tested by high-resolution

Fig. 5. The theoretical 3D contour plots for the product translational energyand angular distributions for the F(2P3/2) � HD(j � 0) reaction made by usingthe full quantum dynamical calculations on the CCSD(T)-PES at various colli-sion energies: 0.43 kcal/mol (a); 0.48 kcal/mol (b); 0.52 kcal/mol (c); and 0.71kcal/mol (d).

Fig. 6. The one-dimensional adiabatic resonance potentials and the reactionresonance states or the F � HH and F � HD reactions for the XXZ-PES and thenew PES. (A) The 1D adiabatic resonance potentials of HF(v � 3)–H for the F �H2 reaction traced out from the XXZ-PES and the new PES. The groundresonance state was shifted considerably to lower energy on the new PES fromthe XXZ-PES surface, whereas the excited resonance here was shifted negli-gibly. (B) The 1D adiabatic resonance potentials of HF(v � 3)–D for the F � HDreaction traced out from the XXZ-PES and the new PES. The ground resonancestate was shifted considerably to lower energy on the new PES from theXXZ-PES, similarly to the F � H2 reaction.

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reactive scattering experiments and is found to be at nearlyspectroscopic accuracy. Through detailed study of this isotope-substituted reaction, we have provided an extremely powerfuland sensitive probe to the reaction resonance potential in thisbenchmark system. Such an accurate resonance potential is thekey to obtain a quantitative physical picture of the reactionresonance in this benchmark system, and it is important in

developing possible schemes of controlling resonance-mediatedreactions.

ACKNOWLEDGMENTS. X.Y. and D.H.Z. are grateful to Rex T. Skodje and KopinLiu for insightful discussions. This work was supported by the Chinese Acad-emy of Sciences, the Ministry of Science and Technology, and the NationalNatural Science Foundation of China.

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