“design” in chemical synthesis—an illusion?

Design in ChemistryDOI: 10.1002/anie.200504510

“Design” in Chemical Synthesis—An Illusion?**Martin Jansen* and J. Christian Sch�n

Keywords:chemical synthesis · configuration space · solid-statechemistry · supramolecular chemistry ·theory of science

1. Introduction

The development of scientific under-standing in the natural sciences pro-ceeds in a stepwise, even hierarchicalfashion. At the beginning, a phenomen-on is observed and measured, and theresults are integrated into the everincreasing foundation of factual knowl-edge. In the next steps, these individualobservations are systematized, and pat-terns and relations are revealed whichare formalized in the language of math-ematics. Finally, at the highest level,universally valid laws are derived, al-lowing us to recognize cause-and-effectrelationships. In this sense, the maturityof a scientific field can be related to thedegree to which novel experiments canbe performed in a controlled and pur-poseful fashion, or, to say it more

generally, to what extent and with whatprecision events and phenomena in ourenvironment can be correctly predicted.This is the stage where theory begins tochallenge the experiment; hypothesesare presented that are to be verifiedexperimentally, and the inductive pro-cedure described above begins to trans-form into a deductive one.

In chemistry, the inductive approachhas proven to be especially successful. Ifone reduces this field to one of its maingoals, that is, the synthesis of newcompounds, and tries to evaluate thefield!s current state, one reaches theconclusion that over the past two cen-turies great achievements have beenmade. This progress has predominantlytaken place along experimental lines: Inimportant subfields of synthetic chemis-try one is able with impressive reliabilityto both devise still unknown compoundsas synthetic targets and plan feasiblesynthetic routes for their realization.The countless well-documented exam-ples of the nearly complete control ofsyntheses have led chemists to conjureup appealing terms such as “tailoring”or “synthesis strategy”. In recent timesthe term “design” has also enjoyed greatpopularity in this context. Here, thisterm is employed not only in the senseof the “design” of the composition orstructure of a new compound but alsowith respect to the set (or some) of itsproperties. A small selection of titles ofrecent publications may serve as evi-dence: “Turning Down the Heat: De-sign and Mechanism in Solid-State Syn-thesis”,[6] “Design of Solids from Mo-lecular Building Blocks: Golden Oppor-tunities for Solid-State Chemistry”,[7]

“Reticular synthesis and the design ofnew materials”,[8] “Looking for design inmaterials design”.[9]

These and many more examples notmentioned here may illustrate howcommon the use of this term, whichimmediately commands attention andrecognition, has become today. Howev-er, speaking of “design” in reference tothe synthesis of chemical compoundsand, even more, to certain properties ofa compound, is the first step towardmisleading implications of the ability ofchemists to shape a material to theirwill. Furthermore, the incorrect choiceof words is often accompanied by aninaccurate understanding of the basicconcepts involved.

According to the generally accepteddefinition, the process of “design” in-corporates the creation of a topology/shape/form, which fulfills a given func-tion as well as possible, and is alsoconsidered aesthetically pleasing. Anadditional fundamental aspect of “de-sign” is that in general it is imbued withan artistic component and thus is asso-ciated with the self-expression of thedesigner. On this basis, classical schoolsof design, such as the Bauhaus, havedeveloped their specific styles (see Fig-ure 1). Besides this main meaning of“design”, which is the same in alllanguages and cultures, a number ofmore restrictive definitions exist. Inmost instances, these deal with thecompetition, proper weighting, or mu-tual dependence of functionality andaesthetics. The most restrictive defini-tion of the term acknowledges “design”as a purely technical process of theproduction of an object according to asketch, without any valuation of itsfunction or beauty. However, everyone of these definitions presupposesthe existence of creative freedom, andthe mere selection from among givenand unchangeable topologies is never

[*] Prof. Dr. M. Jansen,Priv.-Doz. Dr. J. C. Sch+nMax-Planck-Institut f.r Festk+rperfor-schungHeisenbergstrasse 1, 70569 Stuttgart(Germany)Fax: (+49)711-689-1502E-mail: [email protected]

[**] The authors do not claim to have fullycovered the barely surveyable literaturethat pertains directly or indirectly to thetopics discussed in this essay. Instead,representative examples are cited. Theessay is based on presentations by M.J.(e.g. M. Jansen, 405th Meeting of theNorthrhine-Westphalian Academy of Scien-ces, 1994 ;[1] M. Jansen, Egon Wiberg Lec-ture, LMU M.nchen, 2004 ; M. Jansen,Plenary Lecture, 7th International MaterialsChemistry Conference, Edinburgh, 2005 ; M.Jansen, 55th Meeting of the Math.-Nat. Sci.Session of the Berlin-Brandenburg Academyof Sciences, 2005 ; M. Jansen, Berlin LocalMeeting of the German Chemical Society,2005); excerpts are published in Refs. [1–5].

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associated in any language with the term“design”. In the following, we willendeavor to show that this type offreedom in shaping a species does notexist in the context of the synthesis ofnew chemical compounds.

2. The Concept of the EnergyLandscape of Chemical Systems

As a basis for a general discussion(valid for all classes of chemical sys-tems) of the possibility of creative free-dom in the sense of “design” available toa synthetic chemist, we refer to ourconcept of synthesis planning in solid-state chemistry.[1–5] For in contrast to thechemistry of molecules, in particularcarbon-based compounds, which com-mands a great repertoire of efficientmethods for the detailed planning ofsyntheses, one is usually not able toreliably plan the preparation of newsolids and thus must still rely on anexplorative approach. We have longbeen occupied with the search for waysand means to improve this unsatisfac-tory situation, and for the past 14 yearswe have been following a specific con-ception. The foundation of our approach

is the projection, onto an energy land-scape, of the whole world of knowncompounds as well as those that havenot yet been synthesized but are capableof existence.[1–5] In a simplified way, ourconcept can be elucidated with the helpof the configuration space that is definedin the Appendix together with and inrelation to several other relevant spaces.As explained there, a point in configu-ration space corresponds to a configu-ration of atoms, and the union of allatom configurations that together forma locally ergodic region on the time scaleof observation represents a (meta)stablechemical compound capable of exis-tence on this time scale. In particularat low temperatures, the region aroundeach individual local minimum of thepotential energy represents a compoundthat is at least kinetically stable.[1–5] Tosimplify the nomenclature in the follow-ing discussion, we will always refer tominima instead of the more generallocally ergodic regions, even thoughthe locally ergodic regions may be largeand encompass many local minima.

Such a description of the world ofchemical compounds in terms of theconfiguration space and the energylandscape associated with it leads to

immediately accessible fundamental in-sights.

1) In a unique relation, each localminimum of the energy landscape cor-responds to a compound capable ofexistence, and conversely every synthe-sized or realizable chemical compoundis associated with such a minimum. As aresult of this correspondence, this rep-resentation of the chemical world is all-encompassing and contains all kineti-cally and thermodynamically stablecompounds, independent of the state ofaggregation, the existence or lack ofcrystalline order, or the particle size(nano-, meso-, or macroscopic). As awelcome side effect, construed contrastsand essentially artificial opposites suchas between natural and synthetic com-pounds,[10] living and nonliving matter,or between solid-state and molecularchemistry, are obviated and vanish orare at least relativized.

2) The question of whether a hypo-thetical compound is “thermodynami-cally stable” was often asked reflexively,without much thought, in the past andstill today. This question is shown to beinappropriate as far as the compound!srealizability is concerned. The onlynecessary condition for the compoundbeing accessible synthetically is that it isassociated with a local minimum, that is,it must be kinetically stable.

3) The structure of the energy land-scape associated with the space of allpossible configurations of atoms is de-termined by the laws of nature (bymeans of the sum of all atomic inter-actions, cf. Appendix). Thus, for givenboundary conditions, the global as wellas local minima, and therefore all stableand metastable compounds, are prede-termined.

4) The approach discussed here isdeductive and thus represents a changein paradigm from the inductive onepreviously preferred in chemistry.

According to our view, working inthe field of synthetic chemistry is equiv-alent to exploring the landscape of freeenthalpy. While in the past this explora-tion was mostly undertaken by thepreparative chemist by way of experi-ments, today this procedure is joinedincreasingly by the theoretical explora-tion, which, understandably, has beendeveloped the furthest for small mole-cules. These two approaches are not in

Figure 1. Teapot designs by Walter Gropius for Aluminium Ltd., London, 1935 (background)and the only type of teapot made based on these designs. Bauhaus-Archiv Berlin.

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opposition; indeed, they complementeach other. In the long run, computa-tional chemistry will be cheaper andfaster, and it will be called on to supportthe preparative-explorative approachon a broad front. Classical preparativechemistry remains indispensable, how-ever, since practical applications of amaterial can be tested only if it isavailable in reality. The demands onthe synthetic skills of the chemist willmost likely increase, for modeling cal-culations result in truly surprising evenexotic structure proposals, and theirrealization sets tremendous challengesfor even the most modern synthesismethods. Furthermore, as a matter ofprinciple, experimental verification re-mains the final authority for the evalua-tion of the correctness of a prediction.

The quintessence of these consider-ations with respect to the topic of thisessay is clear: Owing to the equivalencementioned above of compounds capableof existence with well-defined, predeter-mined, locally ergodic regions on theenergy landscape of chemical systems,there is no room for either the free or thearbitrary shaping of compositions and/ortopologies of chemical systems by humanefforts. Thus, “design” is not possible,and “humans are the explorers, and notthe creators of chemical worlds”.[2] It isparticularly misleading to try to “de-sign” a new material starting with thedesired material property,[9, 11] since aphysical property by itself cannot be acriterion of whether a compound mightexist. First of all, one must show that thecompound is capable of existence, andthereafter one might derive the set ofproperties based on its composition andstructure.

3. Why Is the Belief in the Possi-bility of “Designing” ChemicalCompounds So Widespread?

In light of these easily understoodconsiderations it is amazing how widelyspread and tenaciously the belief per-sists in the possibility of freedom inshaping a compound, in the sense of“design”, by the scientist in chemicalsynthesis. This view can be understoodfrom a psychologically standpoint per-haps if one considers the truly remark-able degree of control and predictability

of syntheses attained in some areas ofchemistry. Together with the unimagin-able plethora of possible chemical com-pounds (“combinatorial explosion!”),[4]

this can easily convey the impressionthat one can create ensembles of atomswith a definite structure or even prop-erty in a creative act, in analogy to apiece of art. But the landscape of com-pounds remains discrete even in regionsof closely neighboring minima, and theequilibrium topologies are unchangea-ble, of course. In reality a successfulsynthetic plan always corresponds to theanticipation (based on a prediction,identification, or intuitive hunch) of astill unknown compound, that is, of apredetermined local minimum on theenergy hypersurface. The correspondingstructures, including possible isomersand polymorphic modifications, equilib-rium distances, and material propertiessuch as, for example, melting points ordensities, are inherent to the chemicalsystem and are not accessible to “de-sign”.

The differences in sophistication ofthe tools available for planning a syn-thesis in the different classes of chemicalsystems are quite striking. Without anydoubt the synthesis of organic com-pounds is most advanced in this respect.Here one can, with seemingly playfuleffortlessness, construct the structures ofeven quite complex molecular com-pounds capable of existence, withoutthe assistance of complex tools.[12] Thereasons for this are manifold. Clearly,the most of the resources available tochemistry over the past two centurieshave been devoted to the chemistry ofcarbon. The resulting rich treasure troveof experience, together with a certainuniformity in the bonding behavior ofcarbon (e.g. its tendency to form C�Clinkages), allow particularly effectiveextrapolations and thus the predictionof not-yet-synthesized molecular com-pounds. The physical reason behind thissystem of practically universally com-binable structure increments is that thestereochemistry of carbon and of manyother nonmetals is mostly determinedby local covalent bonding interactions;long-range forces can be neglected or atleast are not dominant in structureformation. For the realization of theparticular synthesis goals an effective setof synthesis tools and methods is avail-

able.[12–14] The decisive feature is theselectivity through kinetic control,whereby using functional groups, pro-tective groups or auxiliaries the specificdesired chemo-, regio-, or stereoselec-tivity or positional selectivity is ach-ieved. Some subfields of inorganic mo-lecular chemistry can come quite closeto this state of the art in those cases inwhich a particular target configurationcan be realized by specific reactionroutes based on well-understood proce-dures, for example, employing electron-ic or steric effects and the use of reactionsteps with high directionality such as salteliminations.[15]

Currently, the field of “coordinationpolymers”[16,17] (a term coined already in1964[18]) is burgeoning worldwide[8, 19,20]

and boasts truly spectacular results[21,22]

(e.g. Figure 1 in Ref. [21]). A particularfocus is on open-pored, three-dimen-sional framework structures, since theyare thought to have high potential forimportant applications such as gas stor-age and heterogeneous catalysis. For thisclass of compounds, a nearly inflationaryuse of the term “design” has developed.As in organic chemistry, one employs asystem of independent structure incre-ments that are connected by means ofpolycondensation or donor–acceptor in-teractions. The required building unitsmust be stable under the reaction con-ditions and on the time scale of thereaction, and they must exhibit thenecessary correctly matching sites forthe interconnection. With a cleverchoice of increments, a very reliableprediction of the structures is possible,even without a large computationaleffort. However, since the desired com-pounds are collective solids, the tradi-tional concepts of molecular chemistryfor directing the synthesis process do notapply. Steering the reaction towards thetarget compound must, in contrast, becontrolled by means of the solubilityproduct, and nucleation and growthprocesses.[4] In this regard, the gapbetween the control that is claimed andthat actually achieved is disturbinglylarge. Also, one should critically notethat typically in those cases in which asynthesis is claimed to have been suc-cessfully designed, the design and theactual synthesis are published in thesame paper. This does not strike us asvery convincing.

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In solid-state chemistry, predictionsusing classical approaches are possibleonly in a very restricted fashion. Theyusually refer to extra- or interpolationsof structure families such as perovskites,spinels, or rock-salt variants.[23,24] Forparticular classes of materials, for exam-ple, the oxosilicates, systematizationsand predictions have been performedsuccessfully on the basis of the tetrahe-dral building unit SiO4.

[25] Most difficultby far is the prediction of possiblecompositions and structures of interme-tallic phases.[26,27]

All classes of materials for which“designed” synthesis routes and targetshave been claimed have in common thatthese compounds can be visualized asbeing divisible into structure incre-ments, from which they can be readilyconstructed. Such planning and system-atizing of chemical compounds in termsof adjoining monomeric and oligomericbuilding units has a long tradition inchemistry. We mention as examples thehydrocarbons and their isomers, thechemistry of silicates,[25,28] and the de-scription of zeolites by means of secon-dary building units,[29] where mathemat-ical tools such as graph theory have alsobeen called upon.[30, 31] As we have dis-cussed above, this restriction to certainclasses of compounds is surmountable,of course, if one proceeds towards theglobal exploration of the energy land-scape of chemical systems.[1–5] While thisprocedure requires considerably moreeffort, it is more correct and moreinclusive insofar as no building unitsare fixed a priori and subsequentlyassumed to be unchangeable duringthe synthesis process. Strictly speaking,all species in homogeneous systems(such as solutions) participate in systemsof interdependent chemical equilibria.Even benzene exchanges hydrogenagainst deuterium under surprisinglymild conditions, and complex oxometa-lates can be crystallized in a single phasefrom mother liquors that contain anplethora of oligomers coupled by dy-namic equilibria.[32]

Yet regardless of the degree ofperfection of synthesis planning in thedifferent fields of chemistry, it is gen-erally not correct and thus inappropriateto employ the term “design” to describethe process of chemical synthesis. Onecould argue that the issue of whether

words are used according to their cor-rect meaning should be of secondaryrelevance for our field of science, andshould be relegated to the field oflinguistics under the heading “seman-tics”. We have only limited sympathy forsuch an opinion and point out thedangers of incorrect word use. As thewell-established Sapir–Whorf hypothe-sis implies,[33–35] the terminology andassociated meaning both reflect andcircumscribe our imagination, and thusan incorrect development of terminol-ogy can lead to grave misconceptions. Inour field of science, too, we can only besuccessful in the long run, if images andconcepts are as “correct” as possible,that is, correspond as closely as possibleto reality. And an incorrect linguisticdescription of scientific concepts provesto be particularly perilous when onedeals with nonexperts and, in particular,students and pupils, who might be led toa wrong understanding of the topic athand.

In fact, one sometimes encountersexamples even in the specialist chemicalliterature, where incorrect terminologyappears to go hand in hand with a wrongconceptual understanding. For instance,it has been suggested that one can take adesired physical property as a startingpoint in order to design a compoundthat exhibits exactly this property.[9] Butthis is not possible, in principle, for atleast two reasons. Firstly, there is noone-to-one correspondence between aproperty and compound (a given prop-erty can be related to several differentcompounds). Secondly, a property cannever serve as a criterion for the stabilityof a compound.[11] Similarly, with respectto the synthesis route, formulations arefrequently chosen (see e.g. Ref. [36])that evoke the impression of a goal-oriented operation and complete con-trol, although the desired control of thereaction to give the crystalline productinvolving nucleation, selection, andgrowth, is not even remotely achieved.The very commendable elegance of theprocedure chosen[36] is actually found inthe adroit restriction of the space ofchemical configurations. Here oneshould not forget that besides the “de-signed” and published topology manyothers might be accessible by employingall species present in the system and byincluding additional building principles

(e.g. interpenetration of nets) togetherwith modifications of the selection ofnuclei for growth (by variation of con-centration, solvent, pressure, tempera-ture, etc.).

We consider it particularly risky tocompare synthesis planning on theatomic level with planning and realiza-tions in the macroscopic world, thoughthese are sometimes employed to visual-ize or even justify the use of the term“design” in chemistry. Buildings con-structed using bricks that are used asmodels for three-dimensional solidsbuilt from structure increments (e.g.Figure 1 in Ref. [37]) evoke wrong asso-ciations in at least two regards. Bricksare continuously adjustable in theirdimensions on the length scales envi-sioned for their function, but chemicalstructure increments do not possess thisproperty. They are variable, but thisvariability cannot be influenced by thechemist. Similarly, on a macroscopicscale, there is a wide latitude in thecontinuously adjustable combination ofmacroscopic building blocks. In con-trast, chemical structure incrementscan be combined only in particularcompositions and for each such combi-nation only in well-defined ways, theparticulars of which are beyond humancontrol.

We are sure that essentially allauthors (only a few examples are men-tioned) who have employed the term“design” in a misleading or even incor-rect fashion in the context of theirsynthesis planning are fully aware ofthe physico-chemical foundations oftheir experiments. But quite independ-ently of this, we express with a certainurgency the view that in the interest ofprogress, one should use as few aspossible, but at the same time as “cor-rect” as possible, model pictures anddescriptions, and that the limitations ofeach model should always be clear inone!s mind.

4. Where Does Design Begin?

The highest control currently possi-ble with regard to the realization ofstructures on the microscopic levelmight be found in the manipulationand localization of single atoms andmolecules on surfaces[38] or in the con-

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struction of heterogeneous semiconduc-tor structures in monoatomic layers[39]

by molecular-beam epitaxy. Confrontedwith such purposeful manipulations onemight again give in to temptation andassume we are dealing with “design”.But here, too, the atoms always occupydiscrete equilibrium positions, beyondhuman influence. Thus the actions ofscientists again consist in the selection ofone particular equilibrium configurationfrom among the multitude of possibleones.

Whether one is justified to speak of“design”, that is, the presence of latitudefor shaping and formation on the part ofhumans, depends on the length scale ofthe system. The possibility for “design”is available only if the desired functioncan be realized by a structure withessentially macroscopic dimensions. Ob-viously, when macroscopic objects areplanned and realized, the materialsemployed also must be (kinetically)stable in a chemical sense, that is,correspond to minima of the energylandscape of the chemical system, andshould at most degrade over long timescales, for example, by corrosion orupon being exposed to high temper-atures. Furthermore, these objectsshould be stable with respect to theirshape on the level of continuum me-chanics, both with or without appliedstrains. Yet even with these restrictionsthe latitude necessary for “free” plan-ning exists, and one can generate arbi-trary topologies (see Figure 1) withcontinually tunable dimensions downto sizes on the order of a few atomicdiameters. In our opinion, a suitablecriterion for deciding whether a situa-tion permits “design” might be whetherstructure formation takes place bymeans of atomic (chemical) or mechan-ical processes. This drawing of a boun-dary would, for example, correspond tothe distinction between nano- and mes-ostructures generated in bottom-up vs.top-down processes.

5. On the Role of HumanCreativity and the Origin ofChemical Structure Information

Those readers who have been willingto follow our considerations might befeeling disillusioned or even frustrated

on hearing that their field of study isrestricted to “merely” discovering pre-determined worlds without the truefreedom of shaping new compounds.Yet though this limitation prevails on afundamental level, dealing with theunfathomable multitude of possiblecompositions and structures of chemicalcompounds[4] sets demands of a type andextent that reach or often far exceed thelimits of human intellectual potential.Thus, we do not share the opinion ofsome philosophers such as GeorgeSteiner, who denies the natural sciencesall creativity.[40] In their daily encounterschemists must call upon all of theirknowledge, imagination, and intuition inorder to anticipate and finally synthesize(new) compounds that fulfill their con-ceptual expectations. More often thannot, during these efforts bitter setbacksmust be overcome.

If one transfers these considerationsto the macroscopic world and reviewsthe role of creativity in the visual arts,for a designer of everyday objects or anarchitect conceiving of a building, onequickly notes here the actual possibilityfor self-expression because within wideboundaries the topologies of the objectscan be varied continuously. It is precise-ly from this that the freedom of forma-tion indispensable for design is derived.Now one can without any contradictiontake the attitude that the creative act of,for example, a sculptor, consists in“selecting” exactly one from amongthe essentially infinite number of sculp-tures that can be produced from a givenblock of granite. This view would allowus to relate the activities of syntheticchemists and of artists, as has beenproposed, for example, by Roald Hoff-mann,[41] however, on a completely dif-ferent level of reference where onesupposes that in both regimes one“only” selects from among a fixed setof possibilities. Yet through this parallelthe fundamental difference noted abovebetween the microscopic (atomic)length scale and the macroscopic worldis by no means removed.

In the context of the central subjectof this essay—the multitude of atomicstructures and their variability—thequestion is often posed, whether struc-ture information is encoded somewherein the material world,[42] for example,like the genetic building plans contained

within the DNA. Often it is suggestedthat analogous building plans for thestructure of matter should have beengenerated and stored in the moment ofthe big bang or shortly thereafter. HansJonas gives an immediately convincinganswer to this problem: “Informationrequires for itself already, as its physicalsubstrate, a differentiated and stablesystem … Information is thus not onlythe cause but is itself already the result oforganization, embodiment, and expres-sion of previous achievements, which arethus perpetuated but not elevated.”[*][43]

With this, one can surely agree, and inour view the structures of chemicalcompounds follow immediately fromthe nature of matter and its differentinteractions. Understanding the originsof these interactions is, however, beyondthe authors and probably most of thereaders.[44]

Appendix: Energy-LandscapePicture of Chemical Systems

Every chemical system is describedon the quantum mechanical level by atime-dependent wave function, whichdepends on the coordinates of theelectrons (r1…rn) and nuclei (R1…RN).In the Born–Oppenheimer approxima-tion (separation of electronic and nu-clear degrees of freedom), the contribu-tion of the electronic degrees of freedomto the total energy is given by the energyof the electronic ground state Eel(R) fora given spatial arrangement of theatomic nuclei R= (R1…RN), called anatomic configuration. If one adds to thisthe electrostatic interaction of the nucleiEKK(R) and the operator of the kineticenergy of the nuclei, one obtains the,still quantum mechanical, energy oper-ator (Hamiltonian) of the atoms.

If tunnel effects, zero-point vibra-tions, and other typical quantum me-chanical effects are neglected, one canperform the transition to the classicalenergy landscape: Rather than by a

[*] “Information braucht f&r sich selbst schon, alsihr physisches Substrat, ein differenziertes undstabiles System… . Information ist also nichtnur Ursache, sondern selber schon Ergebnisvon Organisation, Niederschlag und Ausdruckdes vorher Erreichten, das dadurch perpetuiert,aber nicht erh-ht wird.

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wave function, the chemical system isnow described by the position vectorsR= (R1…RN) and the momentum vec-tors P= (P1…PN) of the N atoms of thesystem, and the classical energy functionis the sum of the kinetic energy of theatoms Ekin =SiP

2i /2 mi and the potential

energy Epot =Eel(R) + EKK(R). Onedenotes the 3N-dimensional space of thevectors R as the configuration space,and the 6N-dimensional space of thevectors (R,P) as the phase space of thesystem of N atoms, respectively. Thehypersurface of the function Epot(R):R3N!R defines the landscape of thepotential energy, often simply called theenergy landscape.

The time evolution of the system isrepresented by the trajectory R(t) on theenergy landscape, which results from thesolution of the classical Newtonianequations: Fi =mid

2Ri/dt2, where mi isthe mass of atom i, and the force onatom i is given by the gradient of thepotential energy with respect to Ri, Fi =

�gradi Epot(R). A physical measurementprocess is given by the time average hOit

of an observable O along the trajectoryover the measurement interval tobs,

hOit = (1/tobs)Rtobs

0

O(R(t))dt. If this trajec-

tory explores a region R of the energylandscape on the time scale teq sodensely that the ensemble average ofthe observable O, for example, accord-ing to the Boltzmann distribution of theconfigurations k in the region R : pB(k)=exp(�Ek/T)/Sl2R exp(�El/T)= exp-(�Ek/T)/Z(R), over this region R,hOiens =Sk2R pB(k)O(k), equals the timeaverage of O, hOiens = hOit, then onedenotes the region R as locally ergodic,and the system as locally equilibrated ontime scales tobs > teq(T). In general, thetrajectory leaves the region R on acharacteristic time scale tesc(T), the so-called escape time. For time scales tobs,for which tesc @ tobs @ teq holds, the sys-tem can be considered as being meta-stable, and one can compute a local freeenergy F(R)=�T lnZ(R).[3,5]

A decisive point is that each of theselocally ergodic regions corresponds to achemical compound that is kineticallystable on the time scale tobs at a temper-ature T. At T¼6 0, a multitude of config-urations contribute to the compound—the “structure” of the compound is theappropriate average over these config-

urations. In particular, at low enoughtemperatures the basins around localminima of the potential energy consti-tute locally ergodic regions. Since bothtesc and teq are temperature dependent,the resulting landscape of the freeenergy also depends on temperature.

If one introduces the pressure p asan external thermodynamic variable,one has to replace the landscape of thepotential energy by the landscape of theenthalpy H=Epot + pV. On this one,too, one can determine locally ergodicregions, for which on the time scale tobs

the free enthalpies G(R) can be com-puted and the landscape of the freeenthalpy can be constructed.[3–5] Onenow calls the region with the lowest freeenergy the thermodynamically stablemodification of the chemical compoundon the time scale tobs, and the remainingregions the metastable ones. In thethermodynamic space, which is de-scribed by the variables p,T, etc., thereexists therefore for each point (p,T) aplethora of discrete modifications thatare kinetically stable on the time scaletobs. Usually, one includes only the ther-modynamically stable phase in a phasediagram since one implicitly assumes anessentially infinite observation timetobs!1, for which the system with high-est probability is found in the regionwith the lowest free energy: pB(R)=�k2R pB(k)/�l pB(l)= exp(�(F(R)�Fglobal))/T takes on its maximum for theregion R whose local free energy F(R) isminimal.

This approach to the understandingof chemical systems by the analysis oftheir energy landscape is valid for mol-ecules as well as for crystalline andamorphous phases of the system. Thedifference between a crystalline low-temperature phase, which correspondsto the basin around one local minimum,a partially disordered high-temperaturephase, where the locally ergodic regionencompasses a multitude of structurallyrelated minima, and an amorphousphase, where tesc and teq are of similarsize and thus aging phenomena and ratedependence of physical properties arepresent, is only one of complexity andnot of principle.

[1] M. Jansen, Wege zu Festk�rpern jenseitsder thermodynamischen Stabilit6t,

Vol. N420, Proceedings of the North-rhine-Westphalia Academy of Scienes,Wissenschaftsverlag, Opladen, 1996.

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[3] J. C. SchLn, M. Jansen, Z. Kristallogr.2001, 216, 307 – 325; J. C. SchLn, M.Jansen, Z. Kristallogr. 2001, 216, 361 –383.

[4] M. Jansen, Angew. Chem. 2002, 114,3896 – 3917; Angew. Chem. Int. Ed. 2002,41, 3746 – 3766.

[5] J. C. SchLn, M. Jansen in Solid StateChemistry of Inorganic Materials V(Eds.: J. Li, N. E. Brese, M. G. Kanatzi-dis, M. Jansen), Materials ResearchSociety, Warrendale, 2005, pp. 333 – 344.

[6] A. Stein, S. W. Keller, T. E. Mallouk,Science 1993, 259, 1558 – 1564.

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“design” in chemical synthesis—an illusion?

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