Panel Discussion: On “The Status ofthe Theory of Chemical Reactions,”Third CISTCP, Mexico City,November 8–13, 1999

MIGUEL CASTRODirector of the Third Congress of ISTCP

I n the evening of the first conference day, devotedto theoretical problems of chemical reaction ki-

netics, a panel discussion was organized to gatheropinions and experiences in this field in order togive a picture of the present status and its probabledevelopment. The panel members were Janos Ladik(Erlangen-Nürnberg), William H. Miller (Berkeley),Masataka Nagaoka (Nagoya), Peter Saalfrank (Lon-don), Dennis Salahub (Ottawa), Antonio Varandas(Coimbra), and Lutz Zülicke (Potsdam) as chair-man. In the following, some of the statements aresummarized.

Lutz Zülicke

OPENING REMARKS

Retrospectives, status analyses, and forecasts arefashionable at the present time since we are ap-proaching the end of a century and even of a mil-lennium. So let us start with a view backwards. Thetheory of chemical reactions is certainly an issue ofthe twentieth century, although the cornerstone ofthe building has been laid already in the late 80sof the nineteenth century, mainly by van’t Hoff andArrhenius. This work together with that of Boden-stein in Berlin, Semenov and Kondrat’ev in Moscow,and many others provided the basis of the phenom-enological theory of chemical reactions. Quantumtheory and the quickly developing molecular struc-ture research made it possible to elucidate more and

more the elementary molecular reaction events asstudied nowadays by advanced experimental meth-ods making use of molecular beams and laser tech-niques. The most recent highlights of this progressover several decades are the Nobel prizes in chem-istry awarded to Herschbach, Lee, and Polanyi in1986, to Marcus in 1992, and to Zewail in 1999.

Although most of the steps forward could beachieved, until now, in the field of gas-phase reac-tions of simple molecules, much effort has also beenspent on the extension of reseach to larger systems,solid surfaces, and condensed matter.

At this time a couple of questions are timely:

1. Do we already basically understand chemicalreactions (or, more general, the behavior ofchemically reactive systems) or are there stillopen fundamental problems concerning

a. small molecular systems,b. large molecular systems (clusters, bio-

molecules, organic and inorganic poly-mers, etc.),

c. interfaces (gas/solid, liquid/solid as be-ing important in heterogeneous catalysis,electrochemistry, corrosion, etc.),

d. solutions (in which most of practically im-portant chemistry takes place), and

e. solids (like building materials, etc.)?

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Which is the present status of understand-ing chemistry under extreme, nonequilibriumconditions?

2. In which fields we can already make reli-able predictions in order to help the practicalchemist?

3. In which directions we will probably see thestrongest activites in the first decade of thecoming century? Which are the most urgentproblems to be solved (phenomena and themethods to attack them)?

Let me conclude the opening with just a fewstatements reflecting my personal view on thesequestions:

1. There are certainly some problems of funda-mental nature that cannot be considered assatisfactorily elucidated. To mention some ex-amples: processes in molecular systems suchas nonlinear phenomena (relationships gov-erning the transition from regular to irreg-ular nuclear motion, the question of “quan-tum chaos” in molecular systems) and thedetailed behavior of complex molecular sys-tems under nonequilibrium conditions are stillinsufficiently understood, and likewise are theinteractions of molecular systems with strongelectromagnetic radiation fields.

2. Except for some simple prototype systems,theoretical predictions are at present prevail-ingly of qualitative, rarely of quantitative, na-ture and they concern mainly the gas phase.However, this range of practical applicabilityis going to be quickly extended, for example,to reactions at surfaces.

3. Other fields of rapid development are evi-dently the extension of semiclassical dynam-ics (in various versions) to larger systemsand to the condensed phase. Furthermore,the revival of time-dependent methods ap-pears very promising for studying the fastelementary steps in reaction dynamics includ-ing those that involve electronically excitedmolecular states.

Thus the theory will, in my opinion, soon con-tribute significantly to practical chemistry and, inparticular, to those branches that apply nononven-tional technologies like high-temperature chemistry,plasma chemistry, laser photochemistry, and others.

William H. Miller

Theoretical reaction dynamics seeks to describemolecular phenomena on a wide range of scales:for example, chemical reactions of small molecu-lar systems, involving only three or four atoms,and also reactions in complex environments, thatis, on surfaces, or in solution, clusters, proteins, ormembranes. Great progress has been made over thelast decade in developing rigorous quantum meth-ods for treating small molecular systems, but ina sense one has only scratched the surface: Onlytwo or so four-atom systems have been treated bythese rigorous quantum approaches, and only a fewthree-atom systems have been treated that involvenonadiabatic transition between different potentialenergy surfaces (PESs).

In parallel to further effort in rigorous ap-proaches for small systems, however, theoreticalmethods for treating complex systems are also pro-ceeding, perhaps even more enthusiastically. This isdriven, of course, by practical considerations: Thereis enormous interest in being able to treat biolog-ical and nanoscale molecular systems. Interest indynamical treatment has also been enhanced be-cause density functional theory has made it possibleto have PESs of useful accuracy. Classical mole-cular dynamics (CMD) is the most widely usedapproach for simulating the dynamics of these com-plex systems, even though its limitations are wellrecognized. Much current and future effort will bedevoted to trying to correct the defects of CMD, andthis in the context of my own reactivated interest insemiclassical theory.

Peter Saalfrank

GENERAL COMMENT

Concerning the issue of classical molecular dy-namics (MD) “on the fly” versus quantum dynamicson precomputed potential energy surfaces, I shouldlike to say that apart from the lack of quantumeffects in the MD calculations, the effort in theclassical treatment is not always so much loweras perhaps expected. This is due to the fact thatin classical dynamics one has to average possiblymany trajectories over initial conditions, whereas asingle quantum mechanical wave packet, say, is suf-ficient. Thus, if “good statistics” is an issue, manytrajectories may visit the same regions of the po-tential function several times thus making the effort

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comparable or larger than for a full quantum sim-ulation. For example, Gross and Scheffler neededup to 20,000 trajectories to model the dissociation ofH2 molecules on a Pd(100) surface, and the MD cal-culation became more time consuming than a full,six-dimensional quantum calculation [1].

It may further be noted that most quantum dy-namical calculations carried out for simple gas-phase reactions, for example, are basically “exact,”corresponding to “full-CI” in the language of elec-tronic structure theory. Approximate methods, suchas mean-field approaches, perturbation theory, ortruncated CI have not yet been fully exploited fornuclear dynamics. These approximate methods maywell be not as successful as in electronic structuretheory, but it is also clear that a full and accuratestate-to-state description is often not even necessaryfor complicated systems such as large molecules ormolecules in solution or at surfaces. Hence, I thinkthat (approximate) quantum dynamics has still notbeen pushed to its limits.

IN RESPONSE TO PROFESSOR ZÜLICKE, WHOASKED WHAT THE STATUS OF REACTIONTHEORY AT SURFACES IS

For reactions at surfaces, more approximationshave to be made than for gas-phase reactions (ofsmall molecules). For example, the motion of thesubstrate atoms (phonons) and, in the case of metalsurface, the creation of electron–hole pairs duringa gas-surface encounter are often neglected, thoughpotentially important. The best-studied “reaction”quantum mechanically is the dissociative adsorp-tion of H2 and D2 molecules at a rigid surface. Thisreaction seems quite simple, but the dissociativeadsorption is an often rate-limiting step in hetero-geneous catalysis and hence of practical importance,and, furthermore, even when treated as an adiabaticreaction at a rigid surface the underlying problemis six-dimensional (three degrees of freedom permoving atom). Thus, this problem is comparable incomplexity to a four-atom reaction in the gas phasesuch as H2 +OH, which is also six-dimensional. Thefirst six-dimensional quantum calculation was forH2/Pd(100) and was time-independent [2]; shortlyafterwards, the first time-dependent wave packetcalculations emerged—even for systems with a bar-rier to dissociation, such as H2/Cu(110) [3].

The agreement between theory and experimentin these high-dimensional applications of quantumtheory is generally good, but not as excellent as forgas-phase reactions. This is due to the rigid-surface

and adiabaticity approximations, and more impor-tantly so due to the limited accuracy of the electronicstructure calculations for the potential energy sur-faces of these systems. In both works [2] and [3], thepotential energy surfaces were precomputed withgradient-corrected periodic DFT calculations usinga “slab model,” and fitted afterwards to an analyticform. It is generally assumed that with this ap-proach the accuracy of the potential energy surfaceis perhaps 0.1–0.2 eV [3], thus not yet of “chemi-cal accuracy.” Again, the dynamics methods usedin [2] and [3] are basically “exact”; one is begin-ning now to extend the theory to more complexsystems, such as NH3 or CH4 molecules at sur-faces. For these calculations approximate quantummechanical methods will be useful, such as (mul-ticonfigurational) self-consistent field approaches.Also, (quantum mechanical) rate theory has beenapplied to include the surface motion duringa thermal many-dimensional dissociative stickingprocess [4]. For other complex processes at surfacesfor which thermal equilibrium is not maintained,such as molecular-beam experiments or surfacephotochemistry at “nonrigid” substrates, “system-bath” concepts such as open-system density matrixtheory are being more and more applied [5]. Also,Car–Parrinello type of MD is now often used forsurface problems that are complex and at the sametime sufficiently classical in behavior. Once more Ibelieve that approximate schemes are still not fullyexploited, and that their limited accuracy will besufficient for a wide range of phenomena in whichthe surface science community is interested.

References

1. Gross, A.; Scheffler, M. Phys Rev B 1998, 57, 2493–2506.2. Gross, A.; Wilke, S.; Scheffler, M. Phys Rev Lett 1995, 75, 2718–

2721.3. Kroes, G. J.; Baerends, E. J.; Mowrey, R. C. Phys Rev Lett 1997,

78, 3583–3586.4. Mills, G.; Jonsson, H.; Schenter, G. K. Surf Sci 1995, 324, 305–

337.5. Guo, H.; Saalfrank, P.; Seideman, T. Prog Surf Sci 1999, 62,

239–303, and references therein.

Janos Ladik

WHY NOT TRY SOMETHING ELSE?AN OUTSIDER VIEW ON THE THEORY OFCHEMICAL REACTIONS

The so-called absolute reaction rate (transitionstate) theory was proposed by Eyring almost 70

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years ago. In the meantime people have tried to im-prove it by taking into account correlation effectsand entropy contributions at least at most importantparts of the potential energy hypersurface. In a fewcases a few tunneling degrees of freedom were alsoconsidered.

In this way moderate insight was achieved forreactions between small and medium size mole-cules.

On the other hand using potential energy hyper-surfaces constructed partially theoretically, partiallywith the help of crossed molecular beam experi-ments, other scientists (e.g., Miller, Truhlar) haveused scattering theory, for very simple reactions, toobtain the reaction cross section. These sort of calcu-lations did not get further than reactions like HF +Cl→ HCl + F.

Most recently the scattering-theory people trieda middle way by still using potential hypersur-face and classical trajectory calculations, taking intoaccount a smaller number of quantum mechani-cal degrees of freedom. This compromise seems towork tolerably well if there is a single trajectorybut becomes very tedious if several trajectories crosseach other (in the case of potential surface cross-ings).

The Born–Oppenheimer (BO) approximation isa natural way to treat single molecules in theirdifferent stationary states. The overwhelming num-ber of quantum mechanical calculations is basedon this approximation. On the other hand, in myopinion, the BO approximation is rather artificialin the case of chemical reactions, when besides themotion of the electrons also the motion of the nu-clei of the reacting molecules plays a fundamentalrole. Therefore one feels one should not use thisapproximation for chemical reactions. Of course, anew time-dependent theory has to be worked out,using among other possibilities the ideas of the Car–Parrinello method.

Certainly the new theory at the beginning willbe still more difficult than the scattering theoreticalapproach. Therefore at first only extremely simplereactions like H2 + D → HD + H should be con-sidered. Afterwards this type of theory probablywill proceed to treat more complicated problems.One hopes, however, that with time the theory willbe developed further and experiences will be gath-ered that may possibly progress better than theapproaches used until now.

Lutz Zülicke

One important step in elaborating a theory is todevelop an appropriate model of the system to bestudied, and this will usually depend on the ques-tion asked and the phenomenon considered. Thustheories will persist on different levels of sophistica-tion: as simple as possible, as detailed as necessary.If Professor Ladik is looking for a basically newtheory, then this is certainly desirable, but mostprobably, the existing concepts will not become ob-solete. Maybe that reaction rate theory will appearalso in the future as a “patchwork theory,” in thissense.

Peter Saalfrank

It is true that most applications of chemi-cal (photo-) reactions start from the Born–Oppen-heimer approximation, and subsequently, if neces-sary, nonadiabatic corrections are included. For verysimple systems and reactions, however, electronsand nuclei can be treated on the same footing. Anexample is the photo-dissociation of H+2 in intenselaser fields, which has been studied as a three-bodyCoulombic system by Chelkowski et al. [1].

Reference

1. Chelkowski, S.; Foisy, C.; Bandrauk, A. D. Int J QuantumChem 1997, 65, 503–512.

Masataka Nagaoka

In relation to my recent research, I think now isthe time when chemical reactions can be studiedmuch more dynamically than before by virtue ofthe great development of computational chemistry.The first question in the opening—Do we alreadyknow all the basic theories to understand the chem-ical reaction?—reminds me of the famous statementby Paul Dirac when he insisted the basic laws forchemistry had already been known by the find-ing of quantum mechanics in the first quarter ofthe twentieth century. However, after more than 70years, even now, we have still been studying a sortof “chemistry.” As for the methodologies for sta-tic properties of chemical species, for example, theelectronic structure theory, they have accomplished

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a great advancement in this century. This is actu-ally proved by the historical event when John Popleand Walter Kohn got the Nobel prize in chemistrylast year. This fact is really epoch-making. Recently,I was interested in how nonequilibrium statisticalmechanics (NESM) can be translated microscopi-cally in perspective of energy transfer during chem-ical reactions. As you know, NESM is itself physics,but I feel the theories established already look veryaxiomatic and too theoretical. On the other hand, al-though the equilibrium SM (ESM) we use very oftenis based on the ergodic hypothesis, the origin of whyESM seems to work so well is still a big and openproblem. This is closely related to the fundamentalproblems in chaos theory. In my opinion, in the com-ing century, with the help of computer science andtechnology, such a method of research about chem-ical reaction will propose a good and meaningfulfunction to reconsider NESM much more micro-scopically and will play a role in answering thequestion of why ESM looks so correct. If we would

obtain any important information from such effort,it would mean that we might obtain, for the firsttime, a new and chemistry-originated fundamentallaw.

Lutz Zülicke

CONCLUDING REMARK

As every discussion, also the present one hasto be terminated at a certain point, determined bythe limitation of time given by the organizers. Ofcourse, we could not find completely new answersto the questions formulated at the beginning but,hopefully, some more general opinions and out-looks have been presented going beyond the sub-jects of the talks given today. In this way at least auseful exchange of ideas and of more or less per-sonal points of view has taken place that may behelpful in defining our position and research stra-tegy.

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