molecular spectra, reaction dynamics, symmetries and life

LAUREATES: AWARDS AND HONORS (SCS) 147CHIMIA 2003, 57, No. 4

Chimia 57 (2003) 147–160© Schweizerische Chemische Gesellschaft

ISSN 0009–4293

Molecular Spectra, Reaction Dynamics, Symmetries and Life#

Martin Quack*Paracelsus Prize Winner 2002

Dedicated to Jack D. Dunitz on the occasion of his 80th birthday

Abstract: We provide a short review of the work of the group for molecular kinetics and spectroscopy atthe Laboratory for Physical Chemistry of ETH Zürich contributing to our understanding of the fundamentalphysical-chemical primary processes in chemical reactions. After a brief historical introduction, we presenta selection of recent progress and thinking in three areas: 1. Experiments in high resolution molecular spectroscopy leading us from an elucidation and unraveling ofmolecular infrared spectra to the understanding of the molecular reaction dynamics and fast intramolecularprocesses from the nanosecond (1 ns = 10–9 s) to the femtosecond (1 fs = 10–15 s) and even sub-fs or at-tosecond (1 as = 10–18 s) domain. 2. Theory of fundamental symmetries of physics and their violations in molecular spectra and dynamics ofchiral molecules with a discussion of possible consequences for the role of chirality in the origin of life.3. Speculative considerations on the relationship of spectra and dynamics of chiral molecules with theCPT theorem of physics and with the origin of matter and chiral life, and on the relationship of time reversalsymmetry violation with the molecular origin of irreversibility and with the possible molecular origin of thought.

Keywords: Chirality · CPT theorem · Fundamental symmetries · High-resolution infrared spectroscopy ·Molecular reaction kinetics · Origin of life · Parity violation · Quantum dynamics

*Correspondence: Prof. M. QuackLaboratorium für Physikalische ChemieETH Zürich Hönggerberg HCICH–8093 ZürichTel.: +41 1 632 44 21Fax: +41 1 632 10 21E-Mail: [email protected]

#Summary of the Paracelsus lecture held on Thurs-day 17 October 2002 on the occasion of the fallmeeting of the Swiss Chemical Society during ther + d in life sciences fair, Basel

Martin Quack studied in Darmstadt, Grenobleand Göttingen, where he received his chemistrydiploma in 1971 working on his diploma thesison high-resolution fluorescence spectroscopywith Manfred Stockburger and Albert Wellerat the Max-Planck-Institutes for Spectroscopyand Biophysical Chemistry. He received hisdoctoral degree from the Ecole PolytechniqueFédérale de Lausanne in 1975 after work withJürgen Troe in reaction kinetics. As Max KadeFellow he stayed with William H. Miller at theUniversity of California Berkeley 1976/77 andhabilitated in Göttingen in 1978, where he wasPrivatdozent and later Professor (C2) until 1982.In this year he was appointed full professor atthe University of Bonn and in 1983 was electedProfessor Ordinarius for Physical Chemistry atETH Zürich, where he has been since then.Chemistry with its sometimes striking trans-formations through the processes of molecularkinetics, spectroscopy and fundamental sym-metries in nature leading to conservation lawsand their subtle violations have been his scien-tific hobbies ever since his school days. He hasbeen honored for his work in these areas for in-stance by the Nernst-Haber-Bodenstein Prize,the Otto Klung Prize and the Otto Bayer Prize.He has been Hinshelwood lecturer and Chris-tensen fellow (Oxford 1988), was elected fellowof the American Physical Society in 1990 andlater member of the Deutsche Akademie derNaturforscher Leopoldina (1998) and the BerlinBrandenburg (formerly Prussian) Academy ofSciences (1999). He is a member of the boardof the Swiss Chemical Society as well as amember of several further scientific societies.

Motto: That everything changes is an un-escapable fact which from time immemorialhas moved poets, exercised metaphysiciansand excited the curiosity of natural philoso-phers. Slow chemical transformations pur-suing their hidden ways are responsiblefor corrosion and decay, for development,growth, and life. And their inner mecha-nisms are mysteries into which it is fasci-nating to inquire. (C.N. Hinshelwood [1])

1. Introduction

The occasion on which the SwissChemical Society has asked me to presentthis lecture is connected with the name ofParacelsus – a scientist born in Einsiedelnin 1493 and educated here at the Universityof Basel after 1510, who may be justlycalled one of the founders of the scienceof chemistry in the transition period fromalchemy to chemistry, and a founder ofthe chemistry of life in the form of iatro-chemistry or pharmaceutical or medicinalchemistry – greatly honors the work ofmy research group. It provides deep satis-faction and encouragement to me to know


that I have scientific colleagues and friendsaround who share the ideals of our research,as it was also always the greatest pleasureto have young coworkers with me whoshared our scientific goals and efforts andwithout whom little of what I report belowwould exist as finished results.

Being selected to present this lecture isalso a challenge in view of the group of pre-vious Paracelsus lectures [2]. I shall resistthe temptation here to connect this with awell-known joke about series of predeces-sors, recently retold in print [3], as I alsoshall resist the temptation to say more aboutParacelsus (see [4], for instance), however,I shall mention some earlier Paracelsuslectures which have some scientific rela-tionship to the present report. Otto Hahn’slecture [4] dealt with a connection of thefundamental physics of the nucleus withchemistry, a connection which shall be ad-dressed from a current point of view in sec-tion 3. C.K. Ingold’s lecture [5] dealt withorganic reaction mechanisms and stereo-chemistry (see section 2 and 3), ManfredEigen’s lecture with his work on fast reac-tions [6][7] (see section 2), V. Prelog’s workwith organic stereochemistry [8], J.-M.Lehn’s work with the role of intermolecularinteractions in ‘supramolecular’ chemistry[9], (section 2), J.D. Dunitz’s work relatingcrystallography transition states and reac-tions [10] (section 2) and finally AlbertEschenmoser’s work with prebiotic chem-istry [11] to which we relate in sections 3and 4. It seems that the printed record ofthese lectures is not altogether complete.Given these historical connections to atleast those authors mentioned above, theoutline of the present lecture is briefly asfollows.

In a first part (section 2) we shall pro-vide some examples of our experimentalspectroscopic approaches to fast molecu-lar reaction dynamics and intramolecularprocesses (see also [12–21]). We shallbriefly discuss here some recent results ontunneling hydrogen bond rearrangementand predissociation dynamics [22–26], fastentropy production in the quantum dynam-ics of femtosecond intramolecular vibra-tional redistribution in certain functionalgroups such as the alkyl CH-chromophore[19–21], and the stereomutation dynamicsin ammonia isotopomers and other com-pounds in various limits of chiral symmetrybreaking [14][15].

This leads us to the second part (sec-tion 3) on the recent theory of fundamentalsymmetry violations in chiral moleculesand the new orders of magnitude discov-ered by us for parity violating energy dif-ferences between chiral molecules [27–33],which greatly change the outlook on the

tative chemical kinetics is clearly LudwigWilhelmy [41], who in the investigation onthe ‘inversion’ of sugar in 1850 introducedtime-dependent spectroscopic measurementby means of the study of the time-depend-ent optical activity of the solution contain-ing sugar and acid. Secondly he introducedthe quantitative time-dependent descriptionby means of a differential equation for a(pseudo) first order rate law for the conver-sion of sugar (Z in the original) and its inte-gration to exponential form with an effec-tive rate constant k (M · S in the original),and finally implicitly introduced catalysiswith the dependence of that rate constantupon the concentration of the acid (S in theoriginal). Reaction times then could be eas-ily measured by ordinary clocks. It tookabout half a century to clarify the role ofreaction mechanisms composed of elemen-tary reactions and properly define a com-posite reaction with its rate law followingfrom the elementary steps, including a care-ful introduction of catalysis by Ostwald. Inthe period after 1900 the analysis of fastchemical reactions in terms of such ele-mentary steps became a dominant theme ofexperimental research, with the need forever faster measurements in order to prop-erly isolate true elementary steps. As pio-neers of this era we might mention MaxBodenstein and Cyril Hinshelwood amongmany others, later also B. Chance. It be-came clear that mixing of reactants wouldbe a limiting step thus leading to theconcept of ‘immeasurably fast reactions’,which were faster than any conceivablemixing scheme. The history of this has beenlucidly told by Manfred Eigen [7], whointroduced after 1950 in response to thisdifficulty the experimental concepts of re-laxation techniques (such as T-jump tech-niques), where the mixing step is circum-vented by a fast physical perturbation ona system initially in equilibrium, whoserelaxation into the new equilibrium is thenanalyzed in terms of its reaction kinetics. Inparallel to these developments the flashphotolysis techniques, which used a photo-chemical perturbation, were introduced byNorrish and Porter (see [42]), including theidea of pump-probe experiments. Shockwave techniques were developed by a num-ber of authors (see [18][43][44] and refer-ences cited therein). In the same period wefind also developments which circumventtime-dependent measurements altogetherby reducing the measurement of rates of bi-molecular reactions to measuring cross sec-tions in molecular beams, and the names ofTaylor, Datz, Herschbach, Lee, Bernsteinand Toennies might be recalled here (see [45][46] and references cited therein). For con-densed phase reactions dynamic NMR spec-

importance of this still very small effectin chemistry compared to results of earliercalculations [34–36].

In the third and last part of the lecture(section 4) we will address possible con-nections between the spectra and dynamicsof chiral molecules with one of the mostfundamental symmetries of physics (CPT[37][38]), looking at our current findingof predominantly matter (as opposed toantimatter) in the universe, our finding ofpredominantly L-amino-acids and D-sugarsin the biopolymers of life on earth (as op-posed to D-amino-acids and L-sugars) andour observation of time running uniquelyin a forward direction in physical chemicalprocesses (never really perfectly in thereverse way ‘backwards’) as possible ‘fos-sils’ of the evolution of the universe oflife. Finally we shall conclude with a spec-ulation on the irreversibility of molecularprocesses as related to possible molecularorigins of thought [39].

In entering the details of our subjectmatter, we should perhaps provide somequalifications on the contents of the variousparts. Even though theoretical analysis is animportant part of our approach in section 2,the results on molecular processes pre-sented (and referred to) therein are solidlybased on spectroscopic experiment, a foun-dation which we consider to be among themost precise and reliable available in thephysical-chemical sciences.

The second part (section 3) of our lec-ture dealing mostly with molecular parityviolation is based on theory only. While weconsider the underlying theory [27–33]now as well founded and quantitativelyreliable, to the best of our knowledge, pastexperience teaches us that experimentalcheck remains desirable and necessary, andit should become possible in the near future[32][33][40].

The third and last part of our lecture islargely based on speculation. Experimentaland theoretical support or rejection maybecome available only in the more distantfuture, but it is possible, in principle, as weshall discuss.

2. From Molecular Spectra to Molecular Motion and Reaction Dynamics

2.1. Brief History of Fundamental Ideas for Experiments in Chemical Kinetics

Table 1 provides a greatly abbreviatedhistory of the development of experimentalideas in quantitative ‘fast’ reaction kinetics,where what is fast depends on the time inhistory considered. The pioneer of quanti-


where the {qk} represent the set of all spinand space coordinates of all particles inthe molecule, ϕn are the time-independentstates depending only on these coordinatesand not on time, with En the energy levels.The primary measurement concerns thusan energy measurement (strictly energy dif-ferences En – Em) from spectroscopic linepositions and when theoretical constraintson the molecular hamiltonian and line in-tensities are taken into account also ϕn. Thisis the bread and butter of all molecularspectroscopists. However, the same hamil-tonian ^H governs also molecular time evo-lution by means of the time-dependentSchrödinger equation [66]

with the formal solution

Ψ({qk},t)= Û(t,t0)Ψ({qk},t0) (3)

and which would be valid both for ^H and ^H′(including external interactions), with a

general time evolution operator ( Û and U′),which takes an especially simple form if weconsider only ^H for the isolated moleculereaction dynamics

Û(t,t0)= exp[–2πi ^H(t–t0)/h] (4)

and which allows us to derive the molecu-lar wavefunction Ψ({qk},t) given an initialstate Ψ({qk},t0) and the hamiltonian ^H fromspectroscopy.

An even simpler understanding can beachieved from the general form of the so-lution of the time-dependent Schrödingerequation in terms of the stationary states ϕnin the case of an isolated molecule

with complex, time independent coefficientscn determined by the initial state at t = 0.

While we have given here only the sim-plest presentation for the isolated moleculecase and pure quantum mechanical states,the treatment can be generalized to interac-

troscopy with analysis by reduced densitymatrix Liouville techniques was developedin about the same period (see [47–50] andreferences cited therein). While molecularbeam techniques [45][51–53] and other sin-gle collision experiments using quantumstate preparation and detection with lasers[54–58] have contributed enormously to ourunderstanding of bimolecular gas phase re-actions, perhaps the most dramatic develop-ments in terms of time scales in reaction ki-netics came from the development of shortpulse lasers and their use in pump-probe experiments [42][59–61], where the namesof Rentzepis, Eisenthal and Kaiser may benamed as representatives of the picosecondera following 1970 and Shank, Fleming,Hochstrasser, Zewail, Mathies, Laubereau,Zinth, Elsässer, and Keller for the femto-second era following 1980 (see Table 1).

While a certain final point was reachedwith the report of the ‘0 fs pulse’ [62], wemight mention here the most recent reportson time-resolved electronic processes inKr atoms with 8 fs lifetimes and a claimedtime resolution in the sub-fs (about 200 as)domain [63][64]. In mentioning here also a different type of ‘attosecond micro-scope’ developed for electronic processes inatoms, using relativistic heavy ions [65], weturn our attention now to a new experimentalconcept to derive molecular processesreaching the femtosecond, and if relevantthe attosecond time domain, followed anddeveloped systematically by our group in theyears after 1980 (Table 1, point 5) (see[12][15][17–21] for some more detailed re-views of this).

2.2. Quantum Chemical Kinetics in the Nanosecond to Attosecond Domain as Derivedfrom High-resolution MolecularSpectroscopy Without Time-resolved Measurement

The basic idea behind this experimentalapproach can be traced to the work ofSchrödinger in the early days of quantummechanics [66][67]: A careful analysis ofmolecular line spectra at high resolutionshould allow us to derive under certain con-straints the molecular hamiltonian ^H gov-erning the molecular dynamics under isola-tion, and if we include the analysis of lineintensities also the hamiltonian ^H′ includ-ing interaction with the radiation field[17][68]. Indeed, molecular spectra areusually analyzed in terms of time-inde-pendent stationary states, following thetime-independent molecular Schrödingerequation (Eqn. (1))

^Hϕn({qk})=Enϕn({qk}) (1)

Table 1. Brief history of fundamental ideas for experiments in chemicalkinetics.

(2)

(5)


tions with external fields and to a statisticalmechanical treatment of mixtures [17]. Thein principle infinite sum in Eqn. (5), whichis turned into an integral in the case of con-tinuous spectra, is in practice experimen-tally truncated by the energy range coveredby the spectra, which defines the effectivetime resolution ∆t of the experimental ap-proach by means of

∆t≥ 14π∆v

=1

4πcv~=

h4π∆E

(6)

Thus, if a rovibrational infrared spectrumhas been analyzed (and fully understood interms of ^H) over a wavenumber range of∆v~ = 15’000 cm–1, which is realistic forexperiments already carried out on somemolecules [19][69–71], the correspondingtime resolution would be somewhat betterthan about 200 as = 0.2 fs.

The above equations, which can befound even in initial textbook quantummechanics, might generate somewhat toosimple a picture of the process. Historical-ly, there were several stumbling blocks inthis development. The first was intellectual,as molecular spectroscopists over manydecades restricted attention to time-inde-pendent analyses (Eqn. (1)) considering thetime dependence either as absent or trivial(in the analyses of some ultrasimple process-es connected to Lorentzian line widths ortwo level energy splittings). Neither of theseintuitive assumptions is correct. Indeed, al-though time-dependent quantum mechan-ics in principle was largely understood fromthe work of Heisenberg and Schrödingerin 1925/26, in practice it remained a sleep-ing beauty in molecular reaction kineticswhose awakening may be related to thework on molecular electronic radiationlesstransitions by Jortner and his colleaguesand further, related work (see [72][73], forinstance). Another, highly nontrivial com-plication in the above analyses concernsusual spectroscopic analyses giving onlyimmediate access to molecular ‘spectro-scopic constants’ relating to effective hamil-tonians, which do not directly provide ac-cess to the real hamiltonian ^H for a poly-atomic molecule. The more recent historyof this development has been told else-where [19].

Finally, the spectroscopic analysis lead-ing to an adequate representation of the sumin Eqn. (5) needs the accumulation andanalysis of a huge amount of spectroscopicinformation, which provides further exper-imental and theoretical difficulty. Whilesome of this information is redundant whenmaking appropriate model assumptions, theexperimental requirements remain serious.

On the other hand, and on the positive sidefor this approach, the actually very largeamount of very precise experimental in-formation from high-resolution molecularspectra provides frequently much morestringent constraints on an analysis thanthe usually more limited data from time-resolved kinetics, which in many cases canprovide only very few significant parame-ters with rather limited numerical precision.

In addition to providing a new experi-mental approach, the spectroscopic quan-tum chemical kinetics also provides a freshlook at the theory of molecular reactiondynamics. In the past – and in today’s text-books – this is dominated by statistical me-chanical or ‘thermodynamical’ quasiequi-librium theories such as Henry Eyring’stransition state theory of thermal reactionsor quaisequilibrium theory of mass spectra,‘RRKM theory’ or the statistical adiabaticchannel model [13][18][74][75]. Theselead in their simpler forms to expressionsfor the quasiequilibrium rate constants interms of transition state quantities markedby the famous special cross ‡, say for a uni-molecular rate constant at temperature T

k(T)=γ kTh

Q‡

Qexp(–E0/kT ) (7a)

or a specific unimolecular rate constant atenergy E:

k(E)=⟨γ(E)⟩W‡(E–E0)hρ(E)

(8)

We shall not discuss these equations indetail here (see [74][75], but note that rateprocesses are described here by purelystatic, quantum statistical quantities W‡ andQ‡, in essence. Some students may havewondered why Eyring chose that specialcross. An answer is that under this crossat the saddle point or reaction barrier heburied all dynamics (Fig. 1). We shall dis-cuss below the revival of real-time-depend-ent quantum molecular dynamics for twotypes of processes, where the failure of qua-siequilibrium theories is most prominent (i) Molecular tunneling reaction dynamics

[15][24] and(ii) Processes limited by the rate of intramol-

cular vibrational redistribution [14][19][76][77].We shall turn now to a brief discussion

of current spectroscopic techniques in ourgroup and then give a few examples ofapplication. We might mention here alsosome pitfalls in the sometimes oversim-plified presentation of the route from ener-gy-resolved spectra to time-dependentdynamics: Neither the uncertainty relation∆E∆t ≥ h/4π nor the Fourier transform rela-tionship between energy and time represen-tation allows us to derive significant infor-mation on time-dependent molecular dy-namics, in general (see [20] for a discussionof this point, which is very frequently mis-represented in ‘elementary’ discussions).

2.3. Some Experimental Techniquesfor High-resolution Infrared Spectra

The infrared range of the spectrum ismost closely related to reaction dynamicsin electronic ground states under ordinaryconditions. There has been an enormousdevelopment of techniques in this rangepartly driven by the separate goal of im-

Fig. 1. Picture of Eyring’s cross (slightly modified) at a mountain pass taken by R. Quack at Seiser-alm in the fall of 2002. It is under this type of cross standing at a saddle point or mountain ‘bar-rier’ that Henry Eyring buried time-dependent molecular reaction dynamics.

(7b)k(T)


proved spectroscopic analysis of trace gas-es in the atmosphere [78], but for our ownwork mostly driven by the need for betteranalysis of quantum chemical kinetics.Table 2 summarizes some developments inour laboratory. This Table collects somecharacteristic quantities defining the ‘pow-er’ of a given spectroscopic tool. Besidesthe obvious quantities resolving power RPand effective instrumental bandwidth δνwe need to consider also the scanning range∆v~ indicating over which range the tech-niques allow a molecular spectrum to be‘scanned’ and the scanning power ∆ν/δν,which is a measure of the potential infor-mation content in a complete spectrum asscanned by this technique using its bestresolution. The analytical sensitivity is re-lated to the effective achievable absorptionlength L of direct absorption methods, orby other quantities, when indirect measuresof photon absorption (such as ion currentin resonantly enhanced multiphoton ion-ization REMPI) are important. The Tableshould help to free oneself from the notionthat only one quantity – such as δν or Rp –defines the ‘power’ of a technique. One re-ally needs to consider all those in Table 2and in addition also further technical capa-bilities such as combination with superson-ic jet techniques [19].

In considering Table 2 one clearly rec-ognizes the outstanding scanning ranges ofFTIR and ISOS/IRSIMS together with stillgood resolutions (the most recent Brukerprototype FTIR system built specially forthe Zürich group and still singular world-wide achieves δν ≅ 20 MHz at a specifiedresolving power of ≅ 2 × 106 [79]. The for-mer BOMEM prototype system at a some-what lower resolution has a long record ofdevelopment with supersonic jet techniquesat high resolution in our laboratory [19].ISOS/IRSIMS in addition to wide scanningrange achieves high sensitivity in superson-ic jets and in addition mass selection as aspecial feature [80][81]. Near infrared cw-diode laser cavity ring down supersonic jetspectroscopy, on the other hand, is a newdevelopment [82][83], which performs su-perbly by three of the four standards (ex-cept for ∆v~, where it is still quite good, andwhere we plan improvements in the future).It is not the place here to review these tech-niques in detail. But we note that it is thecombination of these developments in ourgroup which has allowed progress in thespectroscopic analysis of molecular kinet-ics. As noted in section 2.2. the achievabletime resolution is defined by the scanningrange ∆v~, but it is the resolution (δν) andeffective sensitivity (‘L’), which providesthe basis for the necessary analyses of thespectra.

Table 2. Spectroscopic tools developed and used in the Zürich molecularkinetics and spectroscopy group.

Fig. 2. FTIR Spectrum of fluorooxirane at room temperature (after ref. [84]). Because of the rigidstructure of this chiral molecule with only relatively light atoms the spectrum could be analyzedwithout supersonic jet data (see simulation in upper part of lower panel).


Fig. 3. IR-Diode laser spectrum of CFCl3 tak-en in a supersonic jet expansion (after [85])with an effective temperature T = 20 K. Theroom-temperature spectrum is too complexfor analysis without prior data from super-sonic jet spectroscopy.

We shall give here some examples ofcharacteristic spectroscopic results fromthese techniques. Fig. 2 [84] shows a surveyof one band and small section of this ina high-resolution FTIR spectrum of fluo-rooxirane, one of the very few examplesworldwide still today where a high-resolu-tion analysis of an infrared spectrum wasachieved for a chiral molecule (all these ex-amples were pioneered by the Zürich group)and which is relevant for our discussions insections 3 and 4.

Fig. 3 shows a small section of the diodelaser supersonic jet spectrum of CFCl3 inthe range of the ‘atmospheric window’,where we achieved an analysis after manyyears of effort by combining FTIR super-sonic jet and direct diode laser absorptionspectroscopy [85]. Here, the application ofthe spectra is in the field of atmosphericspectroscopy, and attempts of other labora-tories in this rather vast research field toachieve such an analysis had failed formany years.

As a last example we show a measure-ment of isolated lines in the near infraredspectrum of methane by pulsed supersonicjet cw-diode laser cavity ring down spec-troscopy in Fig. 4 [83]. Here the measure-ment of a single line P(1) at high precisiontogether with the precisely known rotation-al levels in the vibrational ground state pro-vides the term values for the rotationless(J = 0) vibrationally highly excited level(ν2 + 2ν3)0 = (7510.3378 ± 0.001) cm–1.This level F1

– has well-defined (negative)parity and combines with nuclear spin I = 1for the four protons and thus has a threefolddegeneracy (total angular momentum F = 1due to the spin [32]). In principle, therewould be a hyperfine structure (F = 0, 1, 2in the lower level with J = 1, I = 1). This ishowever not resolved for hydrogen, where-as with iodine substitution and for the io-dine atom we have resolved even this usingsuch techniques [86][87]. The Doppler lineshape can be fitted (Fig. 4) providing aneffective translational temperature of (53.7± 0.2) K in the jet. The effective resolutionis determined here by the precision of theline center measurement close to about 107,fixing the upper level in the near infraredto within 0.001 cm–1. The instrumental re-solving power in principle would allow for> 2 × 108 (see Table 2). After this precisesingle line center determination, which can

Fig. 4. Near infrared spectrum of methane measured by pulsed slit jetcw-near infrared laser cavity ring down spectroscopy. The upper panelshows the clearly resolved spectrum, including a Doppler shape analy-sis with Teff = 53.7 (2) K for P(1), whereas the lower panel shows the lev-el scheme for the P(1) transition including full symmetry assignments inthe MS*4 group [32].

a)

b)


be further related to vibrational dynamicsand IVR [83], we shall now turn to morecomplex spectra of tunneling problems.

2.4. Tunneling Reaction Dynamicsand Predissociation in HydrogenFluoride Clusters (HF)n

We have used the pulsed slit jet cw-NIR-laser cavity ring down spectroscopytechnique illustrated in Fig. 4 to study thenear infrared vibrational, tunneling rotationspectrum of (HF)2. A preliminary analysishad been achieved for this range by FTIRspectroscopy by us in 1989 [22], but onlythe recent experimental developments haveallowed us to completely analyze thesespectra. The long-term goal of the analysisof such spectra is a full quantum kineticunderstanding of hydrogen bonded systemsfrom the vapor to the condensed liquid andsolid phases [22–25]. We shall discuss herea small section of this larger project. TheScheme shows the hydrogen bond disso-ciation and rearrangement processes. Thistype of kinetic process is of fundamentalimportance for understanding many kindsof hydrogen bond kinetics in hydrogenbonded liquids and in biomolecules withhydrogen bonds (for instance hydrogenbond breaking in the DNA double helix).The processes considered are based on tun-neling dynamics and on–off resonant non-sequential or quasi-sequential intramolecu-lar vibrational redistribution [12][22–25],and are highly non-statistical and mode-selective in complete contrast to traditionaltransition state, RRKM and related quasi-equilibrium theories of reaction kinetics.

For more details and general reviewsof this important topic of hydrogen bonddynamics in (HF)n clusters we refer to[22–25][88]. We shall report here in somemore detail on very recent results on themode-selective hydrogen bond switchingand hydrogen bond dissociation dynamicsin the (HF)2 complex in the energy regionof the N = 2 polyad corresponding to exci-tation with two quanta of HF stretchingbetween 7500 and 8000 cm–1, exceedingmore than seven times the dissociationthreshold for breaking the hydrogen bond(1060 cm–1). Loosely the two quanta of(HF) stretching can be distributed in threeways: (a) two quanta in the hydrogen bond-ed (HF) stretching mode, (b) two quantain the ‘free’ non-hydrogen bonded (HF)stretching mode and (c) one quantum ineach of the two modes. It turns out thatthese three different types of excitation leadto very different hydrogen bond dissocia-tion and switching dynamics. While the de-tailed interpretation of these spectra and dy-namics has been a long-standing questionstarting with early work in our group [22],

Scheme. Predissociation and hydrogen bond switching rearrangement in (HF)2.

a satisfactory experimental and theoreticalsolution has come about only very recently[26][89]. Table 3 summarizes these results.

2.5. Tunneling and StereomutationDynamics in Various Limits of Symmetry Breaking

A second large class of tunneling reac-tions concerns stereomutation in ‘nonrigid’molecules [90–93]. The historical proto-type is inversion in ammonia [93]. Whilein ordinary ammonia, interconversion doesnot exchange chemically distinguishablestructures, it is nevertheless a particularlyinteresting system, which can be extendedby appropriate substitution to, in principle,chiral amines [81]. Work in our group hasaimed at systematically deriving the fullquantum dynamics in ammonia isotopomersfrom systematic investigations of spectraand potential hypersurfaces [90–93]. Asan example we mention stereomutationdynamics which was recently investigatedwith the aid of a full dimensional potentialhypersurface for ammonia and tunnelingquantum wavepacket calculations in a mostrelevant 4-dimensional subspace [91] of theNHD2 isotopomer. Coherent infrared mul-tiphoton excitation leads to energies sub-stantially exceeding the barrier for stereo-mutation by inversion. Nevertheless, theinversion process remains essentially dom-

Table 3. Mode-selective tunneling switching and predissociation dynamics in the N = 2 polyadof (HF)2. The first column gives the polyad level assignment (ordered by energy), the secondcolumn the approximate number of quanta in bonded (nb) and in free (nf) HF stretching modes,column three gives the band centers and the remaining columns the predissociation (PD) andswitching (sw) times (after [26][89]). Theoretical results [89] are based on SO-3 surface [25].

inated by tunneling. While this molecularexample has been under investigation formany decades, our quantum wavepacketdynamics provide completely new insights.

More generally, we consider tunnelingstereomutation in chiral molecules. Fig. 5represents schematically three different dy-namical limits. The first case (A) concernsstereomutation in molecules with achiralequilibrium geometries. By distortion awayfrom the equilibrium geometry one finds achiral structure. Wavepacket evolutionshows stereomutation between these achiralstructures and racemization due to in-tramolecular vibrational redistribution.These phenomena have been studied forCHDT2 and CHD2T by extensive quantumdynamical wavepackets in appropriate sub-spaces drawn from a full 9-dimensional po-tential hypersurface [14][94][95]. We maytalk here of dynamical chirality with ‘zero’barrier for stereomutation [32].

The second type of system (B) haschiral equilibrium geometries but low bar-riers for stereomutation with large tunnel-ing splittings. In these cases, enantiomerscannot be isolated as stable entities in ‘bot-tles’, but they can be generated for veryshort times and show stereomutation on thetime scale of femtoseconds to picoseconds.Hydrogen peroxide [15][96][97] and ani-line-NHD (C6H5NHD) are examples that


Fig. 5. Three dynamical limits of chiral symmetry breaking: A. concernsmolecules that are achiral in their equilibrium geometry and becomechiral by distortion, for instance due to coherent excitation [95]. B.concerns chiral molecules that have a chiral equilibrium geometry andfast stereomutation by tunneling [81][96–98]. C. concerns normal chiralmolecules, where in fact parity violation dominates over tunneling[69–71][106].

Fig. 6. Time-dependent micronanonical entropy production in a singleisolated molecule of CHFClBr that is initially excited with 6 quanta ofCH stretching (the results are from an analysis of high-resolution spec-troscopic experiments [69–71], see also [38]).

we have studied [81][98]. These reactionsystems have been analyzed with full di-mensional quantum dynamical treatmentseither exactly (6-d for H2O2) or approxi-mately (36-d for C6H5-NHD). We shall re-turn to stereomutation in the case of stablechiral molecules (case C in Fig. 5) in sec-tion 3.

2.6. Quantum Dynamics of Intramolecular Vibrational Redistribution (IVR) of FunctionalGroups in Organic Molecules

The general question to be addressedhere are the time-dependent primary kinet-ic processes of energy migration in poly-atomic molecules. We have derived ratesof such processes in extensive spectroscop-ic investigations over the last two decades.One finds very wide ranges of time scalesfrom 10–50 fs for the fastest redistributiontimes in the alkyl CH chromophore tonanoseconds in the acetylenic CH, the NH,the OH, and HF chromophores under cer-

tain conditions. As we have reviewed thisfield on several occasions [12][14][19][21][77][99], we shall not discuss these in detailhere but summarize only the outlook thatarises from our findings of very mode- andgroup-specific redistribution times. On theone hand, this will have consequences forour future understanding of unimolecularreactions. Quasiequilibrium theories willhave to be replaced by quantum kinetic the-ories taking the rates of energy redistribu-tion into account explicitly. We have made

a first step towards such theories already atthe start of our investigations [76]. Second-ly, our findings open many new possibili-ties to the so far elusive ‘mode-selectivelaser chemistry’ above and beyond isotope-and state-selective chemistry which all maywell become routine techniques in the fu-ture, making use of our understanding ofenergy redistribution in molecules [17][20][100–102].

It may be instructive here to consider atleast one of the more recent examples, in


a)

b)

Fig. 7. Calculated torsional potential (full line, right ordinate scale) and parity violating potential(left ordinate scale, lines with various symbols for various approximations) for Cl2S2, where theequilibrium structure and the definition of the torsional angle τ is shown in the upper part of thefigure.

which we choose entropy production afterexcitation with six quanta of CH stretchingin the N = 6 polyad of CHFClBr [71](Fig. 6). The initial time evolution shown inFig. 6 in terms of the molecular entropyevolution can be considered to be a relax-ation process with an entropy productiondS/dt ≅ 5 × 1014 JK–1mol–1, which can becompared with typical values of 107 to 1012

for fast reactions and 3 × 1013 JK–1mol–1 fortypical vibrational relaxation processes inliquids. This very large entropy productioncould be made the basis of molecular ma-chines, if coupled to appropriate processes.Independent of such speculative applica-tions, it is of fundamental interest. Besidesthis broad view of relaxation and entropyproduction in isolated, single molecules,we draw attention also to the fundamentaldiscovery of two types of intramolecularvibrational redistribution (IVR), the classi-cal IVR, which roughly follows our classi-cal picture of exchange of energy betweenotherwise separable oscillations in a chem-ical molecular structure, and quantum delo-calization IVR, with loss of localized mo-lecular structure during the IVR process[14][103][104].

We shall conclude here with a brief dis-cussion of the time scales that we were con-cerned with here, to provide a rough orderof magnitude overview [18]. Taking atypical age of a still young human being tobe about 30 years or 109 s (about one humangeneration), then there are about as manynanoseconds in one second, as there areseconds or heartbeats in the time span ofthis one person or human generation. Fur-thermore, given the age of the universearound 13 × 109 years, there are in a roughorder of magnitude somewhat fewer humangenerations in the whole lifetime of the uni-verse, as there are nanoseconds in a second.Furthermore, if we take the attosecondas our ultimate time limit for electronicmolecular and atomic processes then wefind again this time factor of 109 in goingfrom nanoseconds to attoseconds. High-resolution vacuum ultraviolet electronicspectroscopy is being developed and willopen this time window in the future [105].

3. From Fundamental Symmetriesof Physics to the Theory of Parity Violation in the Spectra and Dynamics of Chiral Moleculesand its Role in the Origin of Life

Whereas the fast processes discussed inthe previous chapter provide us with therich possibilities of change in molecularkinetics, the fundamental symmetries ofphysics are at the origin of conserved quan-

tities or constants of the motion, permanentand immutable for eternity [38]. However,small violations of these symmetries leadto slight disturbances in this static pictureand introduce some fundamentally newpossibilities for slow changes. We have re-cently reviewed several aspects of thesephenomena in molecules and concentratehere on the three discrete symmetries C, P,T and their violations [32][33][38].

In traditional quantum molecular andparticle physics it was assumed that thehamiltonian is invariant under the follow-ing operations1. Inversion of all particle coordinates in

the center of mass (‘Parity’ operation Por E*, which changes x → –x, y → –y, z→ –z)

2. Reversal of all momenta and spins ofall particles (‘time reversal’ or T opera-tion).

3. The exchange of all particles by theirantiparticles (or operation C for ‘chargeconjugation’).We know today that these three symme-

tries taken individually are all inexact or‘violated’ in elementary particle physics,while the combined (simultaneous) opera-tion CPT is still assumed to be an exactsymmetry in all of known physics [37].

Of these three, parity violation has im-mediate consequences in molecular physics[33], the most striking being a predictionof a slight ground state energy differenceof enantiomers corresponding to a nonzeroreaction enthalpy for the stereomutationreaction

(9)

Strictly speaking, this is true only in thedynamical limit (C) of Fig. 5, where tun-neling becomes negligible. As the energiesinvolved are exceedingly small, of the orderof 10–11 Jmol–1 in typical cases [33], theyhave so far not been measured althoughschemes for such experiment have beenproposed [32][33][40]. As we have dis-cussed [33], such experiments in combina-tion with accurate calculations could pro-vide an alternative route to certain funda-mental aspects of the ‘standard model’ ofparticle physics, complementary to the verycostly and demanding experiments in highenergy physics at CERN, Fermilab etc.

Until recently, there were actually alsono cases known quantitatively, for whichboth the stereomutation tunneling splittings∆E± and parity violation had been calculat-ed to demonstrate that Eqn. (9) would bevalid with ∆pvE >> ∆E±. Such a case hasbeen recently studied theoretically in ourgroup with the example dichlorodisulfaneCl2S2 [106]. Fig. 7 shows the equilibriumgeometry calculated for this molecule to-gether with the calculated torsional poten-tial V(τ) for stereomutation as well as theparity violating potential Epv. From this onesees two important facts. Firstly the tor-sional potential V(τ) is symmetrical withrespect to the inversion point, whereas theparity violating potential Epv is antisym-metrical. Secondly, the amplitudes of thetwo differ by about 15 orders of magnitude.We have calculated, that because of the highbarrier of stereomutation (> 5’000 cm–1)and the relatively heavy reduced mass forthis motion, the tunneling splittings in theground state for the hypothetical symmetri-cal potential would be about another 60 or-ders magnitude smaller. Thus it is theoreti-cally calculated that the stereomutation dy-namics of this molecule is in fact dominatedby parity violation and = NA∆pvEwould be about 1.4 × 10–11 Jmol–1 [106], inprinciple measurable by spectroscopic ex-periment on single, isolated molecules ina molecular beam, for example. Table 4summarizes a series of molecules for whichsuch calculations have been carried outwhich nicely show the transition betweenthe cases of large tunneling splittings


Table 4. Parity violating energy differences ∆Epv and times (∆tpv) for chiral molecules as well astunneling splittings ∆E± (and tunneling periods τ) for the symmetrical potentials (roughly round-ed results[89] only for survey).

∆E± >> ∆pvE, where is not observ-able, and the opposite case ∆pvE >> ∆E±,where becomes observable. Futureexperiments should provide such observa-tions [33].

In a meeting under the general theme r+din life sciences a few words should be saidabout the relevance of such calculations forour understanding of the origin of chiralselection of L-amino acids and D-sugars inthe origin of life. Fundamentally this boilsdown to the very old question of a selectionby chance (de facto) or by necessity (delege), due to parity violation [27][32][33][38]. In spite of many discussions and re-peated claims and proposals [109][110], wehave pointed out in recent work and re-views [33][38][111] that the answer to thisquestion is simply open today, and is likelyto remain open for some time, in spite of theprogress on parity violation reported above.

4. Speculations on CPT, the Originof Matter and of Chirality in Life, theMolecular Origin of Irreversibilityand of Thought

We live in a world of matter and notof antimatter, which occurs only in smallamounts as an exception such as withpositrons from β-decay. We find that thebiopolymers of life are made of L-aminoacids and D-sugars and not L-sugars and D-amino acids. Finally time seems to exclu-sively run forward, never exactly back-wards. We have discussed elsewhere [38]that this observed apparent asymmetry can

be related in a speculative way to CPT sym-metry and its potential violation de lege ata fundamental level. It turns out that chiralmolecules provide an ideal test of CPTsymmetry [112]. Past tests of CPT symme-try have been concerned with comparingthe mass of proton and antiproton, provingequivalence (and thus CPT symmetry) at alevel of precision measured by ∆m/m ≅ 10–9

[113]. It has been suggested to compare theoptical spectrum of neutral hydrogen andantihydrogen atoms, providing a relativeaccuracy in the test of about ∆m/m ≅ 10–18

[114], and recently larger amounts of neu-tral antihydrogen useful for spectroscopyhave been produced [115], although opticalspectra have not yet been measured. Ourproposal [112] suggests to compare thespectra of L(S) enantiomers of matter andD*(R*) enantiomers of antimatter as de-scribed in the scheme of Fig. 8. With CPTsymmetry the spectra would be identicaland because of the close degeneracy of L(S)and R(D) enantiomers the spectra could betested at an estimated accuracy of ∆m/m ≅10–30 using the special technique suggestedfor parity violation tests in [40]. This wouldbe by far the most sensitive test proposedfor CPT symmetry. At the time we first sug-gested this and still today the realizationof such an experiment might seem very re-mote, indeed. That would still seem so to-day, if we were proposing the synthesis of achiral antimatter molecule of fluorooxiraneor of CHFClBr. However, meanwhile, withlarge amounts of neutral antihydrogen be-ing available, possibilities have much im-proved. Indeed we suggest here to produce


potentially chiral clusters of the type (H2)nor protonated (Hm

+) (of the type [H3+(H2)n]

etc), perhaps also negative ion clusters.Spectroscopic experiments on such chiralclusters and their antimatter equivalentsfollowing the scheme of Fig. 8 [112] wouldprovide the type of information required.While this approach is still to be situatedsomewhat in the future, it is not as remoteas it may have appeared a decade ago [112].It may be noted that the structure of thelarger clusters (H2)n or (Hm

+) is not too wellknown, but it seems likely that some arechiral with a tunneling splitting satisfying∆E± << ∆pvE.

What would be the consequences if atiny difference between spectra of L andR* molecules or clusters were to be foundin such experiments? The first consequencewould be a complete revision or revolutionof the standard model and in fact even allalternative current fundamental theoriesof microscopic physics. A second conse-quence would be the fundamental joint ‘ob-servability’ of matter vs antimatter, left andright handedness of space and time direc-tions forward and backward, which wouldnot be granted with CPT symmetry beingvalid (see [38]), that is a very fundamentaladditional information about the structureof nature. It would also provide us with fur-ther insight in why it is that we observe thestructure of the world in the way describedat the beginning of this section. This can beillustrated by a game modestly called the‘world game’ [21] in Fig. 9 and inspired by[116].

The world game is directed fundamen-tally towards the question of whether the

Fig. 8. Scheme of enantiomers (L and R) madeof matter and antimatter (L* and R*, using aphysicist’s notation for enantiomers insteadof R/S or D/L). With CPT symmetry L and R*(and L* and R) have the same energy and thus|∆E*

pv|=|∆Epv|=|∆ELcv|=|∆ER

cv|. The experimentproposed in [112] would test for a deviationfrom these relations making use of the ex-perimental principle proposed in [40] and thustesting the validity of CPT symmetry at about10–30 relative precision.

Fig. 9. The world game. The different types of dice used in the game areshown schematically with their four tetrahedral faces and the de legebox (bottom left) and the de facto box (bottom right). In the middle weshow the single face allowed for observation, ‘L’ in the example.

current prevalence of matter over antimat-ter originating after the big bang and theprevalence of L-amino acids over D-aminoacids originating in the evolution of liferesults from a ‘chance’ (de facto) or ‘neces-sity’ (de lege) symmetry breaking [21][38][112][117].

Citing from [21] the world game illus-trated in Fig. 9 consists of a game leaderwho draws tetrahedral dice arbitrarily fromtwo boxes shown at the bottom of Fig. 9, (I)the de lege box with four different types ofdice each one having only one letter on allfour faces, say L, or else R, or L* or R*, (II)the de facto box, where each die has fourdifferent faces (L, R, L*, R*). The playersare allowed to make one throw with theselected die and observe the one face of thetetrahedron showing towards them. Thenthe players, who may be also called the ‘sci-entists’ must guess from which box the diehas been drawn, that is what are the ‘rules

of the game’ (de facto or de lege, there willbe a reward for the right guess of the rulesof the game as there would be in science bythe gain of insight). Now, if the de lege boxhas equal numbers of each die (L, R, L*, R*)and if the game leader is a statistically hon-est person, the statistics are fairly simpleand the player does not have much of awinning strategy against the other players.If one player knows, however, that the delege box contains a bias towards one type ofdie (say 40% L, and 20% of each of theothers as indicated in Fig. 9), then he willwin with the strategy of guessing ‘de lege’if he sees an L in a single throw, as shownat the bottom of Fig. 9 in the middle, and ‘defacto’ if he sees any of the other faces. In-deed, however small the known bias is, hewill always win in the long run over thosewho do not know the bias and that is why itis important to know the bias also in theanalogous physical situation. In our world


we observe living matter being made ofbiopolymers involving L-amino acids andof ordinary matter, for instance, and not ofantimatter. The actually observed symme-try breaking in these terms is essentially100%. However, this complete symmetrybreaking relates to a relatively small ther-modynamic bias, at room temperature per-haps with a ratio of the order of (1 ± 10–15

to 10–16), distinguishing L and D (R) aminoacids, and in cosmology one estimates fromthe ratio of cosmic background photon tobaryon numbers (109) a primordial bias ofmatter over antimatter with an initial ratioof (1 + 10–9) after the big bang. Thus in bothcases an almost complete selection resultswith a very small original underlying bias,leaving open here the detailed mechanismsof the selection. One obvious conclusionconcerning the physical situation in bio-chemical evolution can be drawn from thesingle observation of an ‘L-amino acidworld’: The bias cannot be 100% in favor ofany combination of L*, R, R*.

After having thus ventured in cosmolo-gy, which for many is at the borderline be-tween serious science, pure speculation,philosophy, or even worse, we shall crossthat borderline – with appropriate warning– in conclusion of this lecture by a few cur-sory remarks on the molecular origin ofthought and decision. One may wonder howa thought arises at the molecular kineticslevel in the brain – if that is how it arises.The clearest crystallization of a humanthought is a human decision, frequently as-sumed to be free, the famous ‘homo viatorin bivio’ or ‘alea iacta’ (see Fig. 9). Let usassume that an ‘elementary thought’ at theorigin of such a decision arises at the mo-lecular level through a kinetic process in asingle molecule, somewhat comparable tothe elementary light signal observed in hu-man vision arising through a photochemicalcis-trans isomerization of a retinal moleculeby absorption of a single photon and a longchain of subsequent events in the retinaand finally the brain. We might call this thefirst hypothesis of ‘molecular psychology’.Its understanding might be of importance inhuman life, although some might question,whether it can be made the subject of scien-tific, experimental and theoretical inquiry.We see no compelling reason why not.

Three related fundamental questionsarise in this context from molecular dy-namics . Firstly, is the ‘molecular decision’reversible (related to time reversal and ulti-mately CPT symmetry), secondly is it re-peatable and predictable, thirdly can it beinfluenced by an independent action of aseparate phenomenon that we might call‘free will’? The first is related to the possi-bility of generating a time-reversed state

and by two time reversals ‘repeat history’.This would question the uniqueness of ahistorical event and decision. It is obviousthat in ordinary mechanics such a unique-ness does not exist, but in real life it does.The symmetry breaking leading to thisuniqueness could be de lege or de facto; wedo not know the answer to this.

The question of predictability of the‘molecular decision’ is related to the quan-tum uncertainty of molecular motion. Wehave shown elsewhere [38][39] that molec-ular dynamics is at a borderline of ‘quasi-harmonic’classical, and quantum dynamicsand that depending on the type of moleculeboth practically predictable (in the deter-ministic quasiharmonic quasiclassical lim-it) and unpredictable dynamics (in the high-ly anharmonic quantum limit) can arise(closely related to CIVR and DIVR gov-erned essentially by the anharmonicity ofthe underlying dynamics). One might spec-ulate about nature’s choice of the moleculesof decision (if any) in evolution. Unpre-dictable dynamics based on quantum un-certainty can be made a physical basis forwhat we have called ‘objective freedom ofthought’ (or will) [39]. The experimentallyin principle testable existence of such aphenomenon would be consistent with ourcurrent understanding of quantum molecu-lar physics.

The question of an ‘extraphysical’ psy-chological influence on the ‘molecules ofdecision’, which we might call ‘subjectivefreedom of will or thought’ [39] does notseem to be consistent with what we know atpresent about the laws of molecular quan-tum kinetics, in fact of all of microscopicphysics. Nevertheless in our daily life mostof us assume intuitively – and act on the hy-pothesis – that it exists. This is no proof,though, that is does.

5. Conclusion

We have started from the foundations ofmolecular kinetics solidly based on spec-troscopic experiment , where some impor-tant questions have been answered duringthe last decades, but many exciting prob-lems still exist. One direction of researchhere led us to fundamental symmetries ofphysics to be studied by the theory of quan-tum molecular kinetics and in the future byspectroscopic experiment. Sooner or laterthis will be successful. On the other hand,the questions on evolution, cosmology and‘molecular psychology’ raised at the end ofour lecture are likely to remain open forsome time, although at least partially theymight be made a subject of serious experi-mental research in the more distant future.

AcknowledgementThe work summarized here briefly (and in-

completely) has resulted from the contributionof numerous coworkers over many years, grad-uate students: Georg Seyfang, Hans-RudolfDübal, Emile Sutcliffe, Hermann J. Thöne,Marius Lewerenz (Prof. Paris), Norbert Spirig,Katharina von Puttkamer-Al Shamery (Prof.Oldenburg), Roberto Marquardt (Prof. Paris),Roman Widmer, Peter Dietrich, Andreas Amrein(Prof. Winterthur), Martin Suhm (Prof. Göttin-gen), David Luckhaus, (vis. Prof. Göttingen),Jürgen Stohner, (Doz. ZHW), Heike Gross,Andreas Beil, Roland Ranz, Jörg Pochert, AlexSchmid, René Schwarz, Holger Müller, Ben-jamin Fehrensen, Ioannis Thanopulos, HeikoSchmid, Michael Gottselig, Achim Sieben,Manfred Caviezel, postdoctoral and senior re-search associates: Hans Hollenstein, Don Lupo,Uli Schmitt, Tucker Carrington (Prof. Mon-tréal), Lauri Halonen (Prof. Helsinki), AmandaRoss (Prof. Lyon), Marcel Snels (Doz. Rome),Erik Richard (Sen. Res. Boulder), Yabai He,Michael Hippler, Jürgen Paff, Ayaz Bakasov,Martin Willeke, Robert Berger, Greg Tschumper(Ass. Prof. USA), Vincent Boudon (Sen. Res.Dijon), Maud Rotger, Sieghard Albert, LarsOeltjen; undergraduate (diploma) students, visi-tors and external collaborators with whomwe have published on various subjects relatedto our research: B. Vogelsanger, P. Locher,Claudius Kormann, Renato Zenobi (Prof.ETHZ), Frédéric Merkt (Prof. ETHZ), JonGutow, Christian Ruede, Christian Jeitziner,Bernd Kuhn, Oliver Monti, Jochen Blumberger,Elizabeth Donley, E.U. Wallenborn, DavidRueda, Hans Bürger, T.K. Ha, Peter Hackett,Wim Klopper, Sigrid Peyerimhoff, Tom Rizzo,Paul Schleyer, Fritz Schaefer, Richard Zare.Thanks go to all of them as well as to our tech-nical and secretarial staff Edi Peyer, HansjürgSchmutz, Guido Grassi, Ruth Schüpbach. Ourwork has been financially supported by the ETHZürich (including C4, CSCS, and AGS) and theSwiss National Science Foundation.

Received: March 8, 2003

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molecular spectra, reaction dynamics, symmetries and life

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