modeling the adsorption of norbornadiene on the si(001) surface: the predominance of...

JOURNAL OF CHEMICAL PHYSICS VOLUME 119, NUMBER 2 8 JULY 2003

Modeling the adsorption of norbornadiene on the Si „001… surface:The predominance of non- †2¿2‡-cycloaddition products

Ante Bilic and Jeffrey R. ReimersSchool of Chemistry, The University of Sydney, NSW 2006, Australia

Noel S. HushSchool of Chemistry, The University of Sydney, NSW 2006, Australia and School of Molecularand Microbial Biosciences, The University of Sydney, NSW 2006, Australia

~Received 29 January 2003; accepted 3 April 2003!

Norbornadiene~NBE! chemisorbs to a Si~001! surface in a flagpolelike structure that has potentialas an anchor point for nanoscale molecular devices to the surface. Its bindings to the reconstructedSi~001!-~231! surface and a partially depassivated Si~001!-~231!-H surfaces are modeled byslab-based density functional theory using the PW91 density functional. This method is shown toquantitatively and qualitatively reproduce many known properties of bulk silicon, the silicon surfacereconstruction, and the gas-phase NBE molecule. Four strongly bound adsorbate configurations arefound, with the C–C bonds located either above a Si–Si dimer row or trough, oriented either parallelor perpendicular to each other. The calculated binding energies are 96, 85, 81, and 72 kcal mol21 forthe perpendicular row, perpendicular trough, parallel row, and parallel trough configurations,respectively, evaluated at quarter-monolayer coverage on the bare surface, with hydrogenpassivation of the surrounding sites having little influence. These results indicate that the observedstructural disorder for NBE adsorption on the bare surface at very high coverage results from kineticrather than thermodynamic control of the reaction products. Such kinetic control is shown to beassociated with large barriers in excess of 40 kcal mol21 for possible adsorbate annealing processes,with desorption into a~partially or fully! physisorbed precursor state being required. Enhanceddisorder is also predicted arising from the strong partial binding of NBE through one alkene linkageonly, with the analogous four structural motifs being calculated to be very similar in energy. Thelowest-energy single-alkene-bonded structure is predicted to be of the parallel–above-row type,consistent with the observed structures for most monoalkene adducts. Preference for the uncommonperpendicular binding of NBE is predicted to arise from unfavorable interactions within the siliconlattice when parallel binding occurs on adjacent rows, a binding motif that is observed for only thesimplest monoalkene, ethylene, and only at high coverage. The primary reaction products of NBEare not those predicted by a@212# cycloaddition reaction between CvC and SivSi double bonds,suggesting that, in general, this is not the mechanism for chemisorption of alkenes on Si~001!.Rather, the reaction products are those expected on the basis that the silicon dimer bond is biradicalin nature. Careful structural, polarization, and band-structure analyses of the reconstructed surfaceare also shown to provide no evidence for the existence for a doubly bonded silicon dimer. ©2003American Institute of Physics.@DOI: 10.1063/1.1577539#

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I. INTRODUCTION

Semiconductor surfaces continue to play a major rolethe development of new electronic devices, and in recyears an interest has arisen in the binding of unsaturorganic molecules to silicon surfaces and the subseqgrowth of thin organic films. This interest, which is duethe wide range of chemical properties that may be impaby molecular structures or films, offers many possibilitiesthe development of technological applications. Howevmost organic films on silicon grow in a disordered fashiowing to variability of the chemistry at the interface betwethe film and substrate, and as a result controlled combinaof organic molecules with the existing groundwork of silicotechnology is a considerable challenge. One type of appltion in which tight control of surface structure is requiredmolecular electronics, a promising technology that is a prospective successor to modern metal-oxide–semicondu

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based electronics. In particular, the design of moleculescan act as ‘‘glue,’’ attaching ‘‘molecular machines’’1–3 inspecific orientations to surfaces at specific locations, isprimary importance. Here, we investigate the design pciples of such a ‘‘glue molecule’’ for binding to the silicon~001! surface, later developing a specific technologicapplication for an appropriately functionalized molecule.4

So far, the majority of work in this area has concentraon the properties of thin films rather than on those of isolamolecules. A class of organic compounds that can formdered monolayer films on silicon~001! is the alkenes, withknown examples including ethylene,5–7 cyclopentene,8,9

cyclooctadiene,10 and cyclohexadiene.11 Silicon~001! is ahighly structured surface that is reconstructed12–17 from thestructure of bulk silicon to produce arrays of ‘‘silicodimers.’’ These dimers are usually8,9 considered as containing a silicon–silicon double bond, making the surface ato

© 2003 American Institute of Physics

P license or copyright, see http://ojps.aip.org/jcpo/jcpcr.jsp

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1116 J. Chem. Phys., Vol. 119, No. 2, 8 July 2003 Bilic, Reimers, and Hush

tetravalent, though early studies18 suggested an alternate bradical nature and modern summaries2 often depict mixedbiradial and double-bond character. The distinction is imptant, however, as the common features in the adsorptiounsaturated hydrocarbons on this surface originate fromreactive properties of carbon–carbon double bonds to thsilicon–dimer sites. Owing to the strongly oriented bonproduced, the interaction makes the dimerized surface aa template for propagating order throughout the thin filAnother significant factor contributing to this order is thpacking of the molecules in the film, and it is not guarantethat an isolated molecule on a surface has a well-defistructure even though a monolayer of that material maywell ordered. Surprisingly, few details are available conceing the energetics of the binding, with an important conbution the theoretical study just reported19 on the binding ofmaleic anhydride,

and the binding of the related molecule acetylene.20 Maleicanhydride is a particularly interesting adduct as it is conceable that its simple cyclic structure and synthetic accessity could prove the basis for its use as a glue for attachother materials to silicon. However, its binding19 is insuffi-ciently controlled for this purpose, with the main product narising from the naively expected@212# cycloadition reac-tion between CvC and SivSi double bonds.

An adduct that could have a desirable, well-definstructure for single-molecule binding to Si~001! is norborna-diene

[email protected]#hepta-2,5-diene!, and this has recently becomthe subject of extensive research.9,21–23 Norbornadiene~NBE! has two parallel carbon–carbon double bonds serated by 2.43 Å, a distance close enough to that betweenneighboring silicon dimers to suggest that it could retwice with the surface to bridge the adjacent Si dimers aloa dimer row. Such a binding should guarantee the azimuorientation of the apex atom of norbornadiene to the surfaand by appropriate control of the chemistry of this atonorbornadiene could be used as a glue that ensures thmolecule attached to it is oriented vertically from the sface. One of the initial studies of NBE adsorption oSi~001!,9 using scanning tunneling microscopy~STM! andFourier-transformed infrared spectroscopy~FTIR!, demon-strated that the expected azimuthal angle is obtained. Furrecent advances in nanotechnology have led to the excpossibility that isolated norbornadiene molecules canbound at individually chosen atomic sites on Si~001!.Norbornadiene is nonreactive to the Si~001!-~231!-Hmonohydride-passivated surface, and so by using scantunneling microscope lithography to selectively remove h


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drogen atoms from this surface, the formation of nanomescale regions of an NBE adlayer has been achieved.22 Sub-sequent work3,23,24 using feedback controlled lithograph~FCL! has enabled the formation of well-controlled arraysdepassivated sites on the surface, while making possibleisolation and imaging of individual NBE molecules. We evisage a future scenario in which FCL could be used tolectively remove four adjacent hydrogens from the surfaforming an individually chosen binding site for a single NBmolecule, a molecule that could be used to anchor larsystems to the surface in a controlled manner.

To date, the desired level of control of the bindingNBE to Si~001! has not yet been achieved. Some STstudies9 have found there to be little translational or rottional order in NBE monolayers, while others21,22find mono-layers with small regions of local order only. These studhave shown that the C–C double bonds can react withsurface in a number of ways and the binding is clearly mcomplex than was initially envisaged. Further, the local oris disturbed by the presence of isolated unreacted silidimers, and it is clear that the monolayers produced arein thermodynamic equilibrium. In principle, the designmodified norbornadienes that bind more specifically canenvisaged, but this requires very detailed knowledge of althe factors that cause the disorder. Further, it is possibleeven FCL techniques may require specially designed admolecules and operational procedures in order to achievedesired degree of order.

Typically, STM does not offer an unambiguous atomlevel picture of adsorbed molecules,25 especially for mono-layer adsorption, but basic descriptions of the bindingsome molecules such as maleic anhydride~Ref. 19! and NBE~Refs. 9, 21, and 22! are available. Here, we perform densitfunctional calculations for the binding of NBE to Si~001!.This study provides new insights into the nature of the boing, leading to a detailed understanding of the origin of tcounterintuitive structures found for maleic anhydride athe origin of the disorder found of NBE binding. Also, knetic barriers for thermal equilibration and translational mtions of NBE are considered. We describe in Sec. II the mels of the system and the computational methodology usTheir appropriateness for this problem is addressed in SIII in which calculations for the well-established key propeties of the bare and monohydride-passivated Si~001! surface,as well as the gas-phase properties of NBE, are presenteSec. IV, we consider the nature of the binding and meansits control. Fully optimized geometries for all structures agiven in the Supporting Information.

II. COMPUTATIONAL METHODOLOGY

The computations were performed using the Viennaabinitio simulation package~VASP!.26,27 VASP utilizes an itera-tive scheme to solve self-consistently the Kohn–Sham eqtions of density functional theory~DFT! using residuum-minimization techniques and an optimized charge-denmixing routine. A plane-wave basis set is employed to epand the electronic wave functions, which facilitates tevaluation of the Hellmann–Feynman forces acting onoms. Electron–ion interactions are accounted for through


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1117J. Chem. Phys., Vol. 119, No. 2, 8 July 2003 Adsorption of norbornadiene on Si(001)

use of ultrasoft pseudopotentials,28,29 which allow the use ofa low-energy cutoff for the plane-wave basis set. Felectron–electron exchange and correlation interactionsfunctional of Perdew and Wang~PW91!,30 a form of thegeneralized gradient approximation~GGA!, is used in thecurrent work. The relaxation of atom positions is performvia the action of a conjugate gradient optimization produre.

The lattice constant of Si was obtained from bulk coputations of total energy versus the size of the unit cell.energy cutoff of 150 eV was used for the plane-wave expsion. The Brillouin zone integration was performed onMonkhorst–Pack 43434 k-point mesh using a tetrahedromethod. The fit to an equation of state gives a lattice consof 5.455 Å, close to the experimental value of 5.43 Å.31 Thesilicon surface was modeled by supercells consisting of seral atomic layers and a vacuum layer; the applicationperiodic boundary conditions in all three Cartesian directioyields an infinite array of periodically repeated slabs serated by regions of vacuum into which adsorbed molecumay be added. Different unit cell sizes are used for differpurposes, however, as indicated in Fig. 1: structure~a! is asmall unit cell used for calculations at monolayer coveraon a clean surface, and~b! is an analogous cell used focalculations at quartermonolayer coverage, while~c! is afully hydrogen-passivated surface used also for calculatiat quartermonolayer coverage.

The unit cell used for the calculations at full coveracontains a silicon slab of 8 atomic-layer thickness andvacuum region of 14 atomic-layer equivalent thickness~19Å!, with a p(232) surface supercell containing 4 silicoatoms per layer, while the other unit cells are of justatomic-layer thickness with a vacuum region of justatomic-layer equivalent thickness, but the surface superis expanded top(434) and contains 16 silicon atoms player. The atoms on the surface layer of the full-coveraunit cell are numbered 1–4 in Fig. 1~a! while those in theadjacent layer are numbered 5–8. Experimental results aclose to monolayer coverage as is practically obtainabledicate either minimal short-range order9 or some propensityfor local order of varying symmetry. Indeed, at full monlayer coverage, two local-order symmetries are possible:p(232) symmetry adopted here, in which neighboring NBmolecules are located in parallel and perpendicular directto the silicon dimers, andc(234) symmetry, in which theneighbors are found diagonal to these directions. We chothe lesser importantp(232) symmetry as, for technical reasons, its resulting electronic structure is more readily inpreted in terms of chemical bonding motifs. Naively, onsmall energy differences are expected to be associatedvariations in the symmetry, and we repeat all important cculations at quarter-monolayer coverage for which the losymmetry is truly unimportant.

The bottom layers in Fig. 1 are terminated with twhydrogen atoms per silicon atom to simulate the tetrahecoordination of bulk silicon; only the top layer of atoms thcorresponds to ‘‘surface’’ atoms and only to these are Nmolecules possibly attached. In all computations the top flayers of silicon were allowed to relax, with other laye


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frozen so as to simulate a semi-infinite solid. The terminathydrogen atoms on the lower faces, once optimized to coplete a local tetrahedral environment of dangling bonds, wkept fixed at their deduced separation of 1.47 Å from theatoms.

The vertical component of the dipole moment arisifrom the asymmetric slab is offset via the introduction ofdipole sheet of the same strength and opposite direct

FIG. 1. ~a! The four-atom per layer supercell model of the clean Si~001!-~231! surface@reduced here top~232! symmetry# that is used also formonolayer coverage of norbornadiene; thex, y, z ~normal! directions areindicated, and the atoms in the top two surface layers are numbered.~b! The16-atom per layer supercell model of the clean Si~001!-~231! surface@re-duced here top(434! symmetry# that is used also for quarter-monolayecoverage of norbornadiene.~c! The 16-atom per layer supercell model of thmonohydride-passivated Si~001!-~231!-H surface@reduced here top(434!symmetry# that is used also after partial hydrogen removal for quartmonolayer coverage of norbornadiene.


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placed in the middle of the vacuum region.32 Brillouin-zoneintegrations have been calculated using a 23231 k-pointMonkhorst–Pack grid for the smaller and only theG pointfor the larger surface geometry, respectively, with a Gaussmearing of 0.2 eV. Calculations pertinent to free molecuemployed a cell of the same size as the (434) supercell andintegration using theG point. An energy of 287 eV, requireby the pseudopotential of carbon, has been used as the pwave basis-set cutoff in all computations involving surfacor molecules.

The energies of the transition states leading to thesorption of NBE from the surface and to the translationNBE along it have been evaluated using the nudged elaband ~NEB! method,33 a method of estimating transitiostates that is implemented inVASP. In this approach theminimum-energy path for a transition from the initial to finstate is found by representing the system by a series ofages that interpolate between these two states. The imare then connected by elastic springs, forming the elaband, the atomic coordinates of which need to be optimizThe concept of nudging is introduced by projecting out tagential forces that cause the collapse of images alongpath and normal forces that cause corner cutting. Notethe G point has also been used in all evaluations ofminimum-energy paths and transition states.

III. PROPERTIES OF THE ISOLATED SURFACESAND MOLECULE

It is essential that the computational methods useddict the known properties of the isolated silicon surfacesNBE molecule. In particular, the surface reconstructioncomplex, and the resulting geometrical structures formstarting point for discussions concerning the structurebinding of NBE. Fully optimized silicon lattice and gasphase NBE structures are provided in Supporting Informtion.

A. Reconstruction of the silicon surface

When the structure of bulk silicon is sectioned along~001! plane, a surface is exposed containing two nonbonsp3 hybrid orbitals per atom directed away from the surfaExamples of this topology remain apparent in the lowermatomic layers of the unit cells shown Fig. 1, but therecleaved orbitals are hydrogen terminated so that the bonof these layers continues to reflect that of bulk silicon. Oclean silicon surface, the exposed orbitals induce instabthat results in surface reconstruction. This process has bwell studied12–17 with the early literature summarized.34,35 Itcan be thought to occur in a number of steps, each of whis associated with changes to the surface structure and bing. The nature of the binding of NBE to silicon is madmanifest through the modifications that it introduces to thsurface reconstruction processes; hence, it is essentialour approach be demonstrated to reproduce the propertiethe clean surface.

The surface reconstruction can be considered to occu~at least17! four steps. First, neighboring surface atoms shlaterally towards each other, eliminating a dangling bondsilicon atom to form new Si–Si bonds aligned parallel to t


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surface, with the dimers forming ridges in parallel rowthese newly bonded atoms are known as symmetric sili‘‘dimers,’’ and the process is known as the Si~001!-(231)reconstruction. The hydride surface shown in Fig. 1~c! re-tains the top row of Si atoms in this reconstructed structuonly this reconstruction is prominent in STM and other lontime-scale measurements on surfaces at room temperaShallow channels, apparent in the figure, run betweendimer rows, with the Si–Si bond length being of order 2.Å while the distance across the channels is of order 5.36By constraining the geometry optimization to conform to thsymmetry, we deduce that the PW91 reorganization enefor this process is 1.39 eV~32 kcal mol21) per dimer. Thisvalue compares well to other modern [email protected]., 1.48 eVusing B3LYP Ref. 35!#, though a wide range of calculatevalues have been reported.35,36 Some key geometrical properties of this symmetrical dimer structure are given in TaI.

Second, a buckling is introduced into the surface ttilts the dimer rows in unison such that they no longer remparallel to the surface. This structure has been illustraelsewhere,17,20and key geometrical properties for it are givein Table I. In addition to those properties, the calculated vtical atomic separation between the dimer atoms is 0.75while the tilt angle is 18.5° in good agreement with pricalculations.13,15–17,36

PW91 predicts that this tilting relaxation further lowethe surface energy by 0.16 eV~3.7 kcal mol21) per dimer, avalue that is sufficiently small to be consistent with the aerage symmetric configuration observed at room temperain STM experiments.12 Early calculations of this energy werquantitatively restricted by computational limitations thprecluded optimization of the subsurface silicon layers,modern calculations predict buckling energies of this orde.g., 0.27 eV by B3LYP.35

Third, an alternating pattern in the dimer tilts alongrow occurs that contributes an extra gain of 0.12 eV~2.8

TABLE I. Bond lengths, given in Å, and angles, given in degrees, fromoptimized structures of the tilted and symmetric forms of the silicon dimon a clean Si~001! surface, as well as those for full-monolayer coveragenorbornadiene in structures1 and2 ~see Fig. 3!; the silicon atomic number-ing is indicated in Fig. 1~a!, and Si7,im stands for a periodic image of Si7 .

Tilted Symmetric 1 2

dimer bond 2.366 2.356 2.362 2.375dimer–dimer 3.857 3.857 3.585 3.390Si-C 1.953 1.966/ C-Si1–Si2 78.7 92.6/ C–Si1–Si5 114.5 102.0/ C–Si1–Si7,im 131.9 136.9/ Si2–Si1–Si5 117.7 107.2 107.1 106.4/ Si2–Si1–Si7,im 117.7 107.2 106.5 105.5/ Si5–Si1–Si7,im 120.5 111.5 109.2 109.3/ C–Si1–Si2 78.6 92.5/ C–Si1–Si5 129.5 136.6/ C–Si1–Si7,im 114.6 102.4/ Si2–Si1–Si5 90.6 107.2 106.5 105.7/ Si2–Si1–Si7,im 90.6 107.2 107.0 106.3/ Si5–Si1–Si7,im 98.4 111.5 111.3 109.2


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kcal mol21) per dimer to the total energy as calculatedPW91; the analogous value estimated using the~less reli-able! local-density approximation is 0.048 eV.36 This struc-ture hasp(232) symmetry and is shown in Fig. 1~a!; it isused for our adsorption studies at full monolayer coveragNBE. Rearranging the unit cell toc(432) symmetry allowsthe final structural reorganization to occur in which thedirections of dimers in adjacent rows also alternate~see,e.g., Ref. 17!. We also use a unit cell shown in Fig. 1~b! ofp(434) symmetry that embodies this reconstruction, butthe associated reorganization energy is known to be onlorder 0.002 eV~0.05 kcal mol21),36 its value is not deter-mined herein. This unit cell is used in the simulationsadsorbates at quarter-monolayer coverage. Other long-rrestructurings of the silicon surface have also besuggested17 but are not of concern herein.

Significantly, the surface reconstruction is associawith significant changes in the surface band structure, chdistribution, and hybridization of the surface atoms.17,34,36

Sectioned from the bulk, the~001! surface hassp3 hybrid-ization and the band structure~not shown! reveals the forma-tion of two surface states in the band gap—one doublycupied, comprising chiefly thes and pz components~lonepair orbital or the so-called dangling bond state!, and anotherunoccupied state, consisting mainly ofpx andpy orbitals~theso-called bridge state!. The states are well separated on tenergy scale, with the Fermi level lying in between, so tthe ideal Si~001! surface is semiconducting. Reconstructiof the surface to produce the symmetric dimers seesbridging state stabilized to form the new Si–Si bond whthe dangling bonds remain. These interact with each othea way reminiscent ofp bonding and the symmetric-dimestructure can naively be considered as containing a silicsilicon double bond. However, the evaluated band strucshows thep interaction to be very weak and thep andp*orbitals appear as two near-degenerate surface states sthe surface is actually metallic. The calculated bond angbetween the surface silicon atoms shown in Table I vbetween 107° and 112° and also indicate that the hybridtion remainssp3, while the calculated silicon-dimer bonlength of 2.356 Å is also very near the bulk value whichcalculated to be 2.362 Å@the observed bulk value is 2.35 Å~Ref. 31!#. Finally, the similarity of the symmetrically dimerized structure of the clean surface to that of the hydrogterminated surface also indicates that the hybridizationmainssp3.

Our calculations, like those before,20,35,36 thus providelittle evidence to support the existence of a silicon–silicdouble bond on the surface. Indeed, there has also bmuch interest in the possible existence of silicon–silicdouble bonds in molecular compounds, with only a few mecules known that display key double-bonding signatuIndeed, isolated molecules containing silicon–silicon doubonds are few in number~see, e.g., Refs. 37 and 38!, typi-cally showing low double-bond energies,39 unexpectedstructures,40 deviations from planarity,41 low rotationalbarriers,42,43 and poor Si–Si bond length contraction.41,43–45

Conversely, silicon is known to form a wide range of ochedrally coordinated compounds in which it mimi


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transition-metal chemistry, and its tendency to dehybridizewell understood.46,47

The buckled reconstruction provides further changesthe nature of the surface states. It leads to an increase inenergy splitting between the surface states, restoringobserved48 semiconducting nature of the surface. One psible explanation for this effect is that it arises from ancrease in the strength of thep bond as this would clearlyincrease the energy splitting between the surface statesdeed, the bond angles about the lowered atoms, those nbered 1 and 4 in Fig. 1~a!, lie between 118° and 121°~seeTable I!, indicating that the hybridization of these atoms hchanged tosp2. However, the bond angles about the raisatoms, atoms 2 and 3 from Fig. 1~a!, decrease to between 91and 98°, indicating that the hybridization of these atomsbeen eliminated.46,47Most importantly, buckling results in anincreaseof the silicon dimer bond length of 0.010 Å, clearindicating that buckling does not arise owing top-bond for-mation. Of the two midband states, the lower-energy ocpied one is predicted by PW91 to be localized more onupper atoms than the lower ones, imparting charge polartion within the dimer with the lower atoms expected toslightly positively charged while the upper atoms are slighnegatively charged, in agreement with experimenobservations.34 The buckling produced during the third stagof the surface reconstruction thus presumably occurs aresult of the need to optimize the electrostatic interactiobetween neighboring dimers.

Regarding the monohydride-passivated surfaceSi~001!, the present work predicts the retention of the symetric dimer structure shown in Fig. 1~c!, in agreement withprevious studies.49 The Si~001!-~231!-H phase has beenfound a promising candidate for the fabrication of atomwires.50 Using an STM modification method, it has beedemonstrated possible to remove a row of hydrogen atoleaving a line of Si dangling bonds that then form a ondimensional conductor.51,52 The removal of the other row ohydrogen atoms makes the surface semiconducting againevaluating the surface band structure we have reproduthese properties in agreement with previous calculations.51,52

B. Uncomplexed NBE

Observed53 and calculated~PW91 density functional using VASP! structural parameters of the isolated NBE moecule are given in Table II, and overall the agreementtained is very good. The calculated dipole moment is 0.07a rather small value that is in excellent agreement withexperimental value of 0.06 D.54 The Kohn–Sham eigenvalues provide estimates of the vertical ionization energiesthe molecule; these are provided in Table III along with mesured values from the observed photoelectron spectrum55 forthe lowest 12 valence ionizations. The correct orderingpredicted but the eigenvalues systematically underestimthe ionization energies by ca. 4 eV, an effect that arises frthe failure inherent in modern density functionals to repduce the correct asymptotic potential. The second and focolumns give the values relative to the highest occupied mlecular orbital~HOMO!, and these are in very good agrement with each other. As a result, PW91 is expected to p


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TABLE II. Bond lengths, given in Å, and angles, given in degrees, for the gas-phase observed~Ref. 53! andoptimized structure of norbornadiene, as well as those for monolayer coverage on the Si~001! surface inp(232) symmetry for structures1 and2 ~see Fig. 3!.

C–Hav C1–C2 C2–C3 C1–C7 /C1– C7–C4 u / H–CvC /H–C–H

Gas phase obs. 1.109 1.535 1.343 1.573 94.1 115.6 125.2 114Gas phase 1.091 1.539 1.335 1.559 92.1 114.9 128.2 111.1 1.100 1.560 1.594 1.552 94.7 123.4 110.0 109.52 1.100 1.559 1.601 1.537 94.1 113.6 108.4 109.0

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vide a reasonable description of the binding between Nand siliconprovidedthat a similar error is also predicted fothe Fermi energy. Unfortunately, the calculated Fermi enefor the silicon is not available; as a cautionary measure,note that, for metals at least, density functional schemesto predict quite accurately Fermi energies suggesting thmisalignment of the orbital energies of the molecule andsolid of a few eV can be anticipated.

IV. ADSORPTION OF NBE ON SILICON „001…

Optimized geometries obtained from a variety of reation scenarios of NBE on clean and partially depassivasilicon surfaces have been obtained at full- and/or quarmonolayer coverage. The results are provided as Cartescoordinate listings in Supporting Information; more sucinctly, the optimized structures at quarter-monolaycoverage are sketched in Fig. 2. This figure provides a sized plan view of the surface on which only the silicohydrogen, or carbon atoms involved in surface bindingsshown so that the key structural features are exposed. Tfeatures involve silicon-atom rearrangement, NBE transtion and rotation, and reaction of just one or both of tCvC double bonds with the surface. A total of 18 structuare presented and named1–18 in the figure; all odd-numbered structures have their reactive C–C bonds par

TABLE III. Comparison of experimental gas-phase valence ionizationtentials ~Ref. 55! Eion and VASP PW91 calculated molecular-orbital energieEB of norbornadiene. Energy differencesDEion andDEB are taken relativeto the HOMO energy; all energies are given in eV, while the symmelabels are taken from analogous calculations usingGAUSSIAN 98 ~Ref. 57!.

Orbital Eion DEion EB DEB

6b2 8.69 @0# 5.13 @0#10a1 9.55 0.86 5.92 0.793a2 11.26 2.57 7.67 2.546b1 11.7 3.01 7.85 2.725b2 12.51 3.82 8.12 2.999a1 12.75 4.06 8.62 3.495b1 13.3 4.61 8.63 3.508a1 13.5 4.81 9.18 4.054b2 14.24 5.55 9.80 4.673b2 15.66 6.97 11.47 6.344b1 16.52 7.83 11.96 6.837a1 17.16 8.47 12.59 7.462a2 13.38 8.256a1 13.52 8.395a1 16.75 11.623b1 17.17 12.042b2 18.14 13.014a1 21.83 16.70

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to the Si–Si dimers while all even-numbered structures hthem perpendicular. Calculated binding energies for estructure are indicated in the figure while the associated gmetrical properties for the indicative structures1 and 2 aregiven in Table I.

A. Reaction mechanisms and the natureof the products

Figure 3 shows three chemical mechanisms named~a!,~b!, and ~c! for the exocyclic reaction of as single carbocarbon double bond with silicon dimers. In~a!, additiontakes place across a silicon dimer bond, with the dimersumed to be double bonded. This is a forbidden@212# cy-cloaddition reaction. In~b!, the same type of addition takeplace, but now it is assumed that there is no Si–Si doubond and that the reactive electrons reside instead onbonding orbitals on each silicon atom. In~c! the two C atomsattach to Si atoms that are not bonded to each other; agais assumed that there is no double-bond character in thedividual Si–Si dimer bonds. Mechanisms~a! and~b! lead tothe same product in which the C–C bond is aligned vecally above a dimer row and parallel to the Si–Si dimbonds; examples of products of this type are structures1, 9,13, 15, and17. Mechanism~c! can occur in two ways, eithe~i! with the reacting silicon atoms located in the same dimrow so that the C–C bonds align perpendicular to the silicdimer bonds to produce all of the even-numbered product~ii ! with the reacting silicon atoms in different dimer rowforming products3, 5, 7, and11. If the dimers on the siliconsurface can truly be thought of as consisting of double bonthen mechanism~a! is favored and only products1, 9, 13, 15,and 17 are expected; this is the scenario historicaanticipated.22 However, as has been established by Liu aHoffmann20 and verified by our PW91 calculations describin the previous section, the silicon dimers should be thouof as being free radicals rather than as being doubly bondHence, only mechanisms~b! and~c! are expected to contribute, rendering all produces1–18 feasible. Further, as thechemical changes associated with these two mechanismanalogous, only more subtle effects such as the steric sof the silicon–carbon bonds and the silicon–lattice strainergy operate to control the relative stabilities of alternatreaction products. Quantitatively, these effects are mmanifest through the PW91-calculated binding energies,these are reported in Fig. 2.

Structures1–8 result from the complete reaction of botNBE C–C double bonds with a clean silicon surface whstructures9–12 result from reaction of just one of themStructures13–18 result from reactions on a partially depa

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FIG. 2. Optimized structures, withbinding energies in kcal mol21, forquarter-monolayer coverage and, in~!,full coverage, of norbornadienechemisorbed to clean or partially hydrogen passivated silicon~001! sur-faces: dots, exposed surface silicon aoms; single lines, bound C–C bonds tadsorbate; double lines, unbounCvC bonds of adsorbateH-terminating hydrogen atoms.

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sivated surface and are discussed in detail later. The prodformed by reaction with just one of the two alkene C–double bonds are analogous to those formed when simsystems such as maleic anhydride and acetylene bindsilicon, although the stereochemistry permits for two modof attachment: one in which the unreacted C–C double bis located nearly vertically above the reacted bond, andin which it is located nearly horizontally from it. In Fig. 2this stereochemistry is explicitly indicated.

Our PW91 calculations indicate that the above-rstructures are the most strongly bound; the binding energ1 is 77 or 81 kcal mol21 at full- or quarter-monolayer coverage, respectively, while those for2 are 92 or 96kcal mol21, respectively. This indicates that the reactionboth C–C double bonds of NBE via mechanism~c! is ener-getically more favorable than their reactions via eithmechanisms~a! or ~b!. Structures7 and8 are analogous to1and 2 except that NBE bonds over a trough rather thandimer row. At full-monolayer coverage, the distinctionlost, however, and identical energies are predicted, buquarter-monolayer coverage the above-trough structures9–11 kcal mol21 less stable than their counterparts. Theabove-trough structures involve significant~long-range! reor-ganization of the silicon surface, and intermediate lominima that have been identified are shown in structu3–6.

Experimentally, adsorption of NBE at low to intermedate coverage21–23 almost always produces adsorbates bouabove dimer rows as in structures1 and2; our calculations

FIG. 3. Three models for the exocyclic reaction of a carbon–carbon dobond with silicon dimers:~a! @212# cycloaddition of CvC oriented parallelto a silicon dimer, taken to be double-bonded SivSi; ~b! cycloaddition ofCvC oriented parallel to a silicon dimer, taken to be of free-radical natSi–Si; ~c! addition of CvC orientated perpendicular to the row of silicodimers, here reacting with free radicals S˙ i from different silicon dimers.


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indeed do predict above-row binding to be the most staHowever, the experimental studies cannot distinguishtween the two possible binding orientations, molecubound with their C–C bonds parallel and perpendicularthe Si–Si dimer bonds, respectively. Our PW91 calculatioclearly predict that the unusual perpendicular arrangemen2 is dominant. As the coverage increases, the experimestudies reveal that short-range order is either absent orrestricted, however, with the production of isolated unreacsilicon dimers that, without subsequent annealing of the sface, allow for reaction of at most one of the C–C doubbonds of NBE with the surface. Experimental studiesNBE on Si~001! at very high coverage9 result in a highlydisordered adsorbate layer. The observed infrared polartion appears randomly distributed,9 indicating that NBEbinding is commonly found in directions both parallel anperpendicular to the dimer rows. Also, under these circustances, a significant proportion of the molecules areserved to be bound by only one alkene linkage, and anificant proportion of molecules appear bound abovedimer troughs.9 It thus appears that annealing of the surfadoes not occur during adsorption, with the NBE molecusticking in their initial binding configurations. To understanthe binding of NBE molecules through just one C–C doubond, four structures numbers9–12 in Fig. 3 have been considered. For these, the above-row configuration producedmechanisms~a! or ~b! is the most stable, in agreement wiexperimental observations for ethylene binding.5 More sig-nificantly, the energy difference between the various bindconfigurations is reduced to just 3 kcal mol21 and hence amore random distribution of single-alkene linked NBE moecules is expected than is for the doubly linked ones tdominate the surface at lower coverage.

Quantitatively, the PW91-calculated energies for singalkene binding of up to 47 kcal mol21 are much larger thanthat evaluated using this method for ethylene binding,14 35kcal mol21 ~observed7 38 kcal mol21). This could arise fromthe alleviation of ring strain in the cyclic system owing to thchange in hybridization of the carbon atoms fromsp2 tosp3. Similar calculations for the binding of malei

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anhydride19 report binding energies of only 21–3kcal mol21, however. Our calculations for NBE revealed aternate local-minima structures for9–12 with binding ener-gies of this order, and it is possible that the results repofor maleic anhydride arise from poorly relaxed silicon sustructures. A ready explanation of the observed unexpetendency for maleic anhydride to bind above dimer trougcan be conjectured based on the 2 kcal mol21 energy differ-ence calculated for NBE binding above the dimer ro~structure9! and dimer troughs~structure10!.

It is noteworthy that while the reaction of two alkenlinks via mechanism~c! perpendicular to the dimer rows releases similar amounts of energy per alkene~consider 45kcal mol21 for 10 and 92 kcal mol21 for 2!, the second ad-dition parallel to the rows is far less exothermic~consider 47kcal mol21 for 9 and 77 kcal mol21 for 1!. Hence it is stericstrain within the silicon lattice that is responsible for tchange in preferred orientation for NBE binding comparedethylene and cyclopentene binding. The tendency forsorbed ethylene to avoid nearest-neighbor sites along ais well known,2,5 while larger molecules such acyclopentene8,9 and maleic anhydride19 are sterically hin-dered from binding in this fashion.

B. Nature of the binding and the origin of the stabilityof structure 2

Some of the key effects of the chemisorption are readmade manifest through changes in the valence bond lenand angles, values for which are shown in Table I. Thepact on the carbon–carbon double bond is evident asappropriate bond length changes quite dramatically fr1.34 Å in the gas phase to 1.60 Å in structure2. This productbond length is substantially longer than typical C–C sinbond lengths~1.50–1.55 Å! and is even longer than C–Cbond lengths for carbon atoms also attached to silico14

Such a large value could result from the considerable ststrain present in the bicyclo ring system as well as tpresent in the underlying silicon lattice. The most notachange concerning the silicon surface structure is themoval of the dimer tilt, with the dimer returning to its paralel structure found in the monohydrided surface. Onlysmall increase of 0.01 Å is predicted for the Si–Si bolength, again indicating that mechanism~a! is inappropriate.However, a significant reduction is predicted in the distanbetween the two silicon dimers whose atoms bind toNBE: this drops from 3.86 to 3.39 Å, introducing strawithin the silicon lattice that, like the stretching of the C–bonds, arises from the incommensurate nature of the Cbond length and the inter-silicon–dimer spacing.

Interestingly, for structure 1, the carbon–carbonsilicon–silicon ~dimer!, and silicon–carbon bonds are aslightly shorter than in2, implying stronger bonds, andmay be this effect that produces the typically observedhanced stability for binding parallel to the dimer rows thattypified for results for structures9 and 10. The enhancedstability of the doubly-alkene-bonded structure2 comparedto 1 appears to arise from the angle strain associated withC–Si1–Si2 bond angle. As shown in Table I, this angle


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uncomfortably small at 93° in2 but decreases even further79° in 1.

Further qualitative insights into the nature of chemisotion can be obtained from the differential charge density, ithe charge density of the whole system from which the dsities of the isolated adsorbate and lattice have beentracted. The latter are evaluated at the distorted atomicometries taken from the calculation of the adsorbatsubstrate complex, rather than at relaxed geometries.permits visualization of the charge flow arising from the asorption but not the charge flow associated with dimuntilting.34 Isosurfaces of the differential charge for structu2 are displayed in Fig. 4. The isosurfaces are drawn at ralarge values, especially for the electron surplus, indicatthat significant charge rearrangements do occur as a resuthe reaction. The greatest electron loss is found localichiefly along carbon–carbon double bonds, with some adtional loss also found at the silicon lone pairs. Clearly, treaction occurs between the C–C double bond and thecon lone pairs and does not involve silicon–silicon doubonding. The electron surplus is predicted to occur almentirely along the newly formed silicon–carbon bonds,one would expect due to the formation of C–Si bonds. Aflow of charge from the molecule double bonds toward sface dimer atoms is apparent, however, and this is manthrough a calculated increase of 1.63 D of the vertical coponent of dipole moment of adsorbate relative to the fmolecule and surface. Loosely, this change can be interpras arising from an electron transfer of 0.08e per carbonmoved through ca. 1 Å.

The differential charge analysis for1 ~not shown! differsnotably from that of2 only in one feature—a rather largloss of charge from the apical carbon atom. While this ismanifest in the total dipole change which is 1.67 D for~1!

FIG. 4. Isosurfaces of differential charge for norbornadiene chemisorto the Si~001!-~231! surface at full-monolayer coverage in structure2~see Fig. 3!, as seen from both front and side views. Upper panels: negavalue indicating electron loss upon chemisorption~isovalue 0.062e/Å3).Lower panels: positive value indicating electron gain upon chemisporp~isovalue 0.106e/Å3).


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compared to 1.53 D for~2!, it does suggest that nucleophilsubstitution of this site may preferentially stabilize1.

C. Process of chemisorption

We have also performed calculations for the scenariowhich a free NBE molecule is brought up to a clean scon~001! surface. Optimization of the coordinates usiPW91 then results in the production of a physisorbed swith a binding energy of 2–3 kcal mol21, essentially inde-pendent of the position of the NBE relative to the substraExperimentally, low concentrations of physisorbed mecules have in fact been detected on silicon~001! surfacesexposed to alkenes.9 In this physisorbed state, only minochanges to the surface and molecular structures occurachieve chemisorption, the carbon atoms at the base omolecule must get closer to the surface, a process intricaassociated with the change in the hybridization of the carform sp2 to sp3, and PW91 clearly predicts that an enerbarrier is associated with this process. Using the Nmethod33 with eight intermediate images, in addition to ainitial physisorbed state and final chemisorbed state~struc-ture 2!, the minimum-energy path has been evaluated.energy of the images are given in Fig. 5, along with the msignificant atomic structures. Along this path, the barrierchemisorption is evaluated to be only 2.3 kcal mol21. Theprediction of such a low value is in qualitative agreemewith the experimental observation that chemisorption taplace virtually uninhibited at room temperature, a procexpected20 to be quite general for the addition of unsaturatorganic molecules to Si~001!. The barrier is sufficient, however, to qualitatively explain the detection of some phisorbed molecules on the surface.9

D. Surface mobility

In the design of molecular circuits often a key requirment is a stable attachment of molecules to the substwhile a desired property for adsorbed monolayers is unimity in the adsorbate structure. At near-monolaycoverage,9 the adsorption of NBE on silicon~001! produces

FIG. 5. The linearly interpolated relative energies of images of norbodiene interacting with the Si~001!-~231! surface at full-monolayer coveragalong the minimum-energy path from a physisorbed structure to chesorbed structure as calculated by the nudged elastic band method.


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structures with no long-range order although some degreshort-range ordering can be obtained. The reasons fordiscussed earlier, include the availability of a variety of bining sites and the isolation of single unreacted silicon dimon the surface. Clearly, the observed structures are nothermal equilibrium or an annealing process would occureliminate unreacted or half-reacted silicon sites and placeNBE molecules in their optimal structures, implying that treaction products reflect kinetic rather than thermodynacontrol.

To understand the adsorption process more thorougknowledge is required of the processes that facilitate surfmigration and rearrangement. We evaluate translationalfusion barriers using the NEB method, considering just tindicative processes of the manifold of possible onesvolved in surface diffusion: one in which the NBE molecuin structure2 moves along the dimer row to the next equivlent position and one in which that molecule moves acr

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FIG. 6. The linearly interpolated relative energies of images of norbordiene interacting with the Si~001!-~231! surface at full-monolayer coveragalong the minimum-energy path for translation of the norbornadiene frstructure2 to an equivalent configuration along a dimer row.

FIG. 7. The linearly interpolated relative energies of images of norbordiene interacting with the Si~001!-~231! surface at full-monolayer coveragalong the minimum-energy path for translation of the norbornadiene frstructure2, above a dimer row, to structure8, above a dimer trough; thestarting and finishing structures are equivalent~at full-monolayer coverageonly!, while the high-energy local minimum near image No. 6 in fact cresponds to structure12.


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the row to sit above what once was a trough on the surfai.e., is converted to structure8. The calculations are performed at full-monolayer coverage for which structures2and8 are equivalent in energy but embody significant comensurate silicon–lattice rearrangements. Using the Nmethod, eight intermediate images have been optimizedboth translational processes and the results are showFigs. 6 and 7, respectively. The dashed lines in Figs. 6 anrepresent crude linear interpolations through the points;plateau at the top of the energy profile of Fig. 6 is realishowever, as it depicts the translation at nearly constantergy of the physisorbed NBE molecule apparent in imaNo. 4 to that in image No. 5. We see that no low-energy pat monolayer coverage is found for the translation of Nalong a dimer row, but rather that the molecule must fidesorbe before it can translate. The energy barrier for tralation is thus very large. For the hop across the dimer roFig. 7 shows a reaction coordinate with two transition staseparated by a high-energy local minimum on the potenenergy surface. The transition states correspond to the brage of two C–Si bonds, an event which interestingly occafter the other carbons have migrated from one silicon dimto the next, while the local minimum~not indicated explicitlyin the figure! is in fact the previously identified singlyalkene-bonded structure12.

Note that as both migration processes considered invtranslations between equivalent sites, the reaction coordiis naively expected to be symmetric in shape. Indeed,path for translation along a dimer row shown in Fig. 6symmetric~images No. 4 corresponds to Nos. 3–6, etc.! butthe path shown in Fig. 7 is not. The absence of symmetryacross-row translation arises as the reaction inherentlyvolves two different types of motion: translation of the NBand rearrangement of the silicon dimers. A symmetric pcan be found, but this traverses a high-energy saddle pointhe potential-energy surface; the NEB method finds a patmuch lower energy that, as a single path, does not fullyflect the symmetry of the potential-energy surface. In sumary, we see that both processes considered face barrieconsiderable heights that, for example, greatly surmothose for a Si adatom hop on Si~001!.15 As these calculationsare performed for monolayer coverage, they clearly showkinetic difficulty involved in obtaining thermodynamic equlibrium of large-scale samples. Similar calculations at locoverage are also likely to reveal large barriers.

E. Binding to an incompletely passivated surface

We placed NBE on a fully monohydride-passivated sface and found no binding, a result in accord with expemental observations.21,22 To understand this result, we havconsidered the energy change for a hypothetical proceswhich NBE approaches a fully passivated surface, displactwo gas-phase H2 molecules as it binds to the surface. PWpredicts that it costs 12 kcal mol21 to complete this substitution, indicating that the reaction is thermodynamically ufavored. As significant activation barriers would also bevolved, the calculations clearly support the experimenobservations.


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It is now possible3 using feedback-controlled lithographto selectively depassivate regions of this surface, andbinding of NBE in such pockets is particularly relevant fthe construction of molecular devices on silicon. To invesgate this, we take the passivated unit cell shown in Fig. 1~b!and depassivate four of the 16 hydrogen atoms, attachinNBE molecule to achieve quarter-monolayer coverage. Otwo binding geometries are possible for full reaction; theare shown as structures13 and14 in Fig. 3 and correspond to1 and2 on the unpassivated surface, respectively. The biing energies are found to be 81 and 95 kcal mol21, respec-tively, very close to those found on the clean surface witfull coverage. Passivation of the surrounding silicon dimbonds thus does not significantly effect the binding.

The possibility arises, however, that a NBE molecumay land on the depassivated region but bind with theverse orientation to that which is desired, resulting in strtures such as15–18. Indeed, kinetically such a single cycloaddition would be an intermediate step before theattachment of the molecule. Our result that the bindingquarter coverage to a surface region surrounded by pavated silicon atoms is similar to that for binding to a clesurface suggests that incorrectly oriented, single-alkebound NBE molecules are likely to be strongly held, anlike other analogously-bound molecules,9 are likely not toshow great propensity for annealing. This effect would limthe use of this technology for the construction of molecumachines on silicon~001!.

V. CONCLUSIONS

The binding of NBE to Si~001!-~231! and Si~001!-~231!-H has been modeled by slab-based DFT usingPW91 density functional. This method is shown to quantitively and qualitatively reproduce many known propertiesbulk silicon, the silicon surface reconstruction, and the gphase NBE molecule. Four strongly bound adsorbate cfigurations are found, with the C–C bonds located eithabove a Si–Si dimer row or trough, oriented either paralleperpendicular to the Si–Si bonds. The calculated bindingergies from Fig. 3 are 96, 85, 81, and 72 kcal mol21 for theperpendicular row and trough, and parallel row and trouconfigurations, respectively, evaluated at quarter-monolacoverage on the bare surface, with hydrogen passivatiothe surrounding sites having little influence. These resindicate that the observed9 structural disorder for NBE adsorption on the bare surface results from kinetic rather tthermodynamic control of the reaction products. Such kinecontrol is shown to be associated with large barriers incess of 40 kcal mol21 for annealing processes. The lowesenergy annealing process found required the breakage ofof the two alkene to silicon dimer links, while other processes required the breaking of both links, placing the Nin a physisorbed state whose energy is only 3 kcal mol21 lessthan that required for complete dissociation. At high covage, enhanced disorder is also predicted arising fromstrong partial binding of NBE through one alkene linkaonly, with the analogous four structural motifs being calclated to be very similar in energy to each other. The lowe


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energy single-alkene-bonded structure is predicted to hparallel C–C and Si–Si bonds located above the dimer roconsistent with the observed structures2 for most mono-alkene adducts. Preference for the uncommon perpendicbinding of NBE is predicted to arise from unfavorable inteactions within the silicon lattice when parallel binding occuon adjacent rows, a binding motif that is observed for othe simplest monoalkene, ethylene, and only at hcoverage.2,7

The primary reaction products of NBE are not those pdicted by the@212# cycloaddition reaction between CvCand SivSi double bonds, suggesting that, in general, thisnot the mechanism for chemisorption of alkenes on Si~001!.Rather, the reaction products are those expected on thethat the silicon dimer bond is biradical in nature. Carestructural, polarization, and band-structure analyses ofreconstructed surface are also shown to provide no evidefor the existence for a doubly bonded silicon dimer.

Provided that NBE does fully bind to the surface vboth alkene groups, its structure is such that the apex ahas a flagpolelike binding topology with fixed azimuthangles. Its two hydrogen atoms, for example, rise in a plthat is vertical to the surface and parallel to the C–C bothat bind to the surface. Substituted NBE derivativeswhich these two hydrogens are replaced with other mothus present orientationally controlled attachments. Anample of such a substitution is the fusion of a spiro ringpossibly a planar geometry such as cyclopentadiene.

However, one disadvantage of such a linker is the obserorientational disorder in the binding of NBE, a disorder thwould be passed on to the orientation of the attached splane. Substitution of asp2 center at position 7 such as thketone

would eliminate this difficulty by introducing cylindricasymmetry. Hence, despite the presence of unwanted variity in the attachment of norbornadiene to silicon, its funtionalized derivatives may prove useful as controlled attament points to silicon~001!. Specifically, we have considerea variant of NBE in which a 7-aza group is attachedtrimethylsilane.4


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As silylation of nitrogen favorssp2 over sp3 hybridization,this structure could stand erect on the surface and hencea flexible anchor point for nanomolecular structures abothe surface.

SUPPORTING INFORMATION

Provided in supporting information are the optimized cordinates for structures1–18.56

ACKNOWLEDGMENTS

The work was supported by the Australian ReseaCouncil. The use of supercomputer facilities at the AustralPartnership for Advanced Computing~APAC! is gratefullyacknowledged.

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