A new form of finite silica with edge-sharing SiO2 units connected in a ring is proposed. High-level density-functional calculations for (SiO2)(N), N = 4-14, show the rings to be energetically more stable than the corresponding (SiO2)(N) linear chains for N > 11. The rings display frequency modes in remarkable agreement with infrared bands measured on dehydrated silica surfaces indicating their potential as models of strained extended silica systems. Silica rings, if synthesized, may also be useful precursors for new bulk-silica polymorphs with tubular or porous morphologies

Bromley, ST

Maschmeyer, T

Zwijnenburg, MA

English

Bromley, S.T. (author)

Zwijnenburg, M.A. (author)

Maschmeyer, Th. (author)

TU Delft Repository

Fully Coordinated Silica Nanoclusters: (SiO2)N Molecular Rings

Bromley, S.T.

Zwijnenburg, M.A.

Maschmeyer, Th.

NARCIS 

UCL Discovery

Fully Coordinated Silica Nanoclusters: SiO2N Molecular RingsS.T. Bromley, M. A. Zwijnenburg, and Th. MaschmeyerLaboratory of Applied Organic Chemistry and Catalysis, DelftChemTech, Technical University of Delft,Delft 2628 BL, The Netherlands(Received 19 April 2002; published 23 January 2003)A new form of ﬁnite silica with edge-sharing SiO2 units connected in a ring is proposed. High-leveldensity-functional calculations for  SiO2 N, N   4–14, show the rings to be energetically more stablethan the corresponding  SiO2 N linear chains for N>11. The rings display frequency modes inremarkable agreement with infrared bands measured on dehydrated silica surfaces indicating theirpotential as models of strained extended silica systems. Silica rings, if synthesized, may also be usefulprecursors for new bulk-silica polymorphs with tubular or porous morphologies.DOI: 10.1103/PhysRevLett.90.035502 PACS numbers: 61.46.+wPure silica is enormously versatile, exhibiting a largeanddiverse spectrum of naturalpolymorphs.Silica isalsooften deliberately engineered to have speciﬁc propertiessuch as porous or thin ﬁlm topologies and/or particularoptical/electronic characteristics resulting in materialshaving applications ranging from microelectronics tocatalysis. The structural basis for the vast majority ofsilicas is a three-dimensional network of silicon-centeredcorner-sharing SiO4 tetrahedra. In contrast, silica tetra-hedra can also participate in edge sharing, giving rise torings containing two silicon atoms and two oxygenatoms. We propose a new two-ring-based fully coordi-nated,  SiO2 N, structure type, in the form of a molecularring; see Fig. 1.Recent studies have provided a wealth of evidenceconﬁrming that two-rings exist at the surfaces of amor-phous and crystalline silica [1–7]. Two-rings at silicasurfaces form, at temperatures above 900 K, from thecondensation of vicinal hydroxyl groups but are strainedspecies, which are readily reversibly hydrolyzed [1,2]. Athigher temperatures (1400–1700 K), in the absence ofwater, thermodynamic rearrangement of the pure silicastructure favors the formation of two-rings at the surface[3–7].The elevated temperatures of this process cause thesurface to be more ﬂexible and potentially allows formore stable two-rings to form within a relaxed environ-ment. The formation of two-rings via this process isprobably energetically favored over forming reactive non-bridging oxygen (NBO) defect sites, and also entropi-cally, due to the restrictive two-dimensional surfacelayer, making large surface rings unlikely. As with thethermally driven formation of two-rings on the two-dimensional surface of silica, high temperatures canalso be used to synthesize one-dimensional silica struc-tures with edge-sharing units. Combining more than oneSiO2 unit as to only having edge sharing gives rise tochains of two-rings; see Fig. 1. For N   1–6,  SiO2 Nchains are predicted to be the most thermodynamicallystable form of silica, being energetically favored over allother such stoichiometric silica clusters [8,9]. For largerN, two-ring chains of arbitrary length may be formed inthe high temperature synthesis of ﬁbrous silica-w [10].These structures show that the energetic disadvantage ofstrain within two-rings can be outweighed by the energyof their formation and suggests that edge sharing in silicamay be thermodynamically favored in environments ofreduced dimensions.Toinvestigate the effectsofenvironmental strainontheenergetic stability of multi-two-ring silica systems in lowdimensions, we performed high-level density functional(DF) calculations on  SiO2 N edge-sharing chains andrings. Chains are formed by edge-sharing two-rings ter-minated at either end by an NBO group. Our proposedmolecular rings can be thought of as structures resultingfrom joining the NBO end groups of a chain. Unlike thechains, the rings have the novel property of being a fullycoordinated cluster: each oxygen to two silicon atoms andeach silicon to four oxygen atoms.Whereas the strain in alinear chain is not expected to vary signiﬁcantly with N,the interconnectivity of the rings allows us to systemati-cally vary the structural strain bychanging thenumber ofSiO2 units.For all DF calculations the Becke-type three-parameter hybrid exchange-correlation functional,B3LYP [11], was employed. DF calculations have1.511.681.671.6989.5158.689.988.688.889.890.21.68Si OFIG. 1. Structures of the N   12  SiO2 N molecular ring andchain. Bond lengths are in   A, angles in degrees.PHYSICAL REVIEW LETTERS week ending24 JANUARY 2003 VOLUME 90, NUMBER 3035502-1 0031-9007=03=90(3)=035502(4)$20.00  2003 The American Physical Society 035502-1accurately reproduced the properties of silica clustersobtained from both experimental studies and otherhigh-level calculations [8,9]. Cluster geometries were op-timized at the AM1 semiempirical level and then furtherat the B3LYP=6-31G  level, imposing no symmetry con-straints. For the ﬁnal optimizations the basis set includedboth polarization and diffuse functions, 6-311   G d;p ,to accurately account for oxygen polarization effects andstrained bonds. Binding energies (BE) were calculatedfrom the difference between the total energy of a cluster,EN-clus, and the energy of the corresponding isolatedtriplet-state O and Si atoms at the B3LYP=6-311  G d;p  level. Gaussian 98 [12] was used throughout.The SiO2 N chains were all found to consist of planartwo-rings, each having a 90  orientation relative to itsneighbor (all with a similar geometry regardless of N);see Fig. 1. This alternating structure enables the siliconatoms to be as close as possible to the energeticallyfavored SiO4 tetrahedral coordination. At the ends ofthe chains the terminating NBOs cause small distortionsto the peripheral two-rings, with a decreasing effecttowards the center of the chain. For the  SiO2 N ringsstructural distortion is caused by the enhanced internalstrain needed to form a fully coordinated system. Wedeﬁne this ‘‘cyclic strain,’’ Ecyc, to be distinguishedfrom the intrinsic strain possessed by the constituenttwo-rings, as the difference between the energy, E1, con-sumed or released in deforming a chain to form a mo-lecular ring (E1   EN-ring   EN-chain), and the energy, E2,released in forming a chain from two smaller similarlysized subchains (e.g., for even N, E2   EN-chain  2EN=2-chain). The assumption in this Born-Haber cycleestimate isthat theenergy released in forminga localizedtwo-ring when combining two small chains, E2,i ss i m i -lar to that in the corresponding process in joining asuitably bent N-chain. This is supported by examiningthe cyclic strain, which is mainly due, not to the individ-ual two-rings, which stay relatively intact, but in thebending of the links between them. This results in theouter (farthest from the molecular ring center) oxygenatoms being spaced farther from each other relative to thechain oxygens, and the inner (nearest to the molecularring center) oxygens being relatively closer together; seeTable I. The cyclic strain in molecular rings also leads tosome folding of the two-rings along their Si-Si axes withthe pairs of oxygen atoms moving away from the molecu-lar ring center. The folded two-rings open as the molecu-lar ring size increases, being approximately 20  fromplanarity for the14-ring.The cyclic strain of the molecu-lar rings also manifests itself in a mismatch betweenthe inner and outer Si-O-Si internal two-ring angles andSi-O bond lengths. The inner Si-O-Si internal two-ringangles are slightly larger than the outer internal two-ringSi-O-Si angles and the inner Si-O bond lengths areslightly smaller than their outer counterparts. The innerand outer Si-O lengths and Si-O-Si angles of the two-rings quickly converge to constant equal values, like thechains, as N increases. The rings naturally divide into anN-even set, and an N-odd set.The N-even rings consist oflinked structurally equivalent two-rings with a regularalternating orientation pattern and high rotational sym-metry (DN=2d), about an axis through the ring’s radialcenter, perpendicular to the ring plane. The N-odd set,however, has only C2 symmetry about an axis within thering plane through the radial center, with half of the two-rings being structurally nonequivalent. This division isdue to the ability of the rings to mimic the favoredalternating structure found in the chains. For N eventhis is achieved with the opposite orientations of thetwo-rings at the ends of a chain. For N odd there is nosuch match and the ring attempts to distribute this extracyclic strain throughout the ring. The separation of thetwo sets of rings due to this mismatch strain can be seenin the Ecyc values in Table II, the BEs in Fig. 2, and in theenergy gap in Fig. 3, where an oscillation between thelower N-even and higher N-odd ring energy scales isobserved.Spectroscopically, molecular rings possess IR bandscharacteristic of their connectedness distinct from thoseof the chains. Calculated 12-chain harmonic frequenciesgive prominent modes (866, 915, 838 cm 1), and for the12-ring, three main modes (902, 886, 933 cm 1). TheTABLE I. N-even  SiO2 N ring geometric parameters. Two-ring parameters of the 14-chainare given for comparison. Distances are in   A and (interior) two-ring angles in degrees.‘‘Outer’’and ‘‘Inner’’ refer to the distance from the molecular ring center.Si-O Si-O O-O O-O  Si-O-Si  Si-O-Si  O-Si-O  O-Si-Si-OOuter Inner Outer Inner Si-Si Outer Inner Fold4-R 1.78 1.70 3.56 3.03 2.35 82.4 87.5 82.2 126.06-R 1.73 1.67 3.39 2.80 2.35 85.6 89.0 86.2 141.68-R 1.70 1.67 3.26 2.78 2.35 87.0 89.2 87.8 149.610-R 1.69 1.67 3.18 2.79 2.35 87.9 89.6 88.4 154.912-R 1.69 1.67 3.13 2.80 2.36 88.6 89.9 88.7 158.614-R 1.69 1.67 3.10 2.81 2.36 89.0 90.1 88.9 161.314-C 1.67 1.67 2.90 2.90 2.38 90.5 90.5 89.4 180.0PHYSICAL REVIEW LETTERS week ending24 JANUARY 2003 VOLUME 90, NUMBER 3035502-2 035502-212-ring modes are in remarkable agreement with experi-mental IR measurements on dehydrated silica surfaces(908, 888, 932 cm 1) [1,13,14], indicating their potentialuse as models for strained silica surfaces much likemodeling silica defects with terminated silica clusters[15]. This surfacelike signature of the rings contrastswith the chains, which also display NBO modes at1321 cm 1.For  SiO2 3 rings we found that Ecyc was too great andthat the cluster would spontaneously break into the cor-responding chain. For N>3 molecular rings could al-ways be stabilized, due to the greater stabilization fromthe bonding of two terminal NBO groups relative to thecyclic strain induced in the ring. Moving through N  4–14, we observe a monotonic increase in energeticstability of the molecular rings and chains (see Fig. 2),with a corresponding decrease in the cyclic strain in therings (see Table II). For N   4 the rings are much higherin energy than the chains, with Ecyc being over a quarterof the BE per SiO2 unit.With increasing N, however, thestabilization rate is greater for the rings than for thechains, and, eventually for N   12 the energetic stabilityof the rings exceeds that of the chains by 0:024 eV=SiO2,with Ecyc being only 1.6% of the BE per SiO2 unit. Foradditional increases in N, Ecyc continues to drop, alongwith the BE of the rings dropping further below that ofthe corresponding chains.By deﬁnition, Ecyc does not include the intrinsic inter-nal strain of the constituent individual two-rings. Thestrain energy of a relaxed two-ring has been estimatedby numerous high-level calculations in the literature, allgiving similar values. Cluster DF calculations usinghydrogen-terminated two-rings yield relatively high es-timates (0:72e V =SiO2 [16]) but neglect the stabilizingeffect of an extended silica bonding environment [17].Periodic DF calculations on two-rings in a relaxedamorphous silica surface give a value of 0:69 eV=SiO2[6], while similar calculations comparing the energy ofsilica-w to that of  -quartz, yield 0:62 eV=SiO2 [18].Using the latter value, and adding it to the cyclic strainin our molecular rings, gives an estimate of the formationenergy of our rings with respect to  -quartz per SiO2unit, EQ!R; see Table II. Ecyc for the smaller molecularrings is found to be much larger than the intrinsic strainofa two-ringgiving relativelylargeEQ!R values(forN<8 EQ!R > 1:5e V =SiO2). For N>11 Ecyc falls to4 6 8 10 12 14-16.0-15.5-15.0-14.5-14.0-13.5-13.0-12.5Binding energy (eV/SiO2)Number of SiO2 unitsFIG. 2. Variation of the binding energy of the  SiO2 N mo-lecular rings and chains with N.TABLE II. Molecular ring energetics (eV=SiO2).  BE   BEN-chain-BEN-ring, Ecyc  cyclic strain energy, Ecyc=BE   ratio of cyclic strain to binding energy, and EQ!R  formation energy difference between  -quartz and an N-ring.4-R 6-R 8-R 10-R 11-R 12-R 13-R 14-R BE 2.310 0.712 0.229 0.056 0.059  0:024  0:015  0:066Ecyc 3.453 1.474 0.801 0.514 0.473 0.354 0.334 0.260Ecyc=BE 0.274 0.101 0.053 0.033 0.030 0.023 0.021 0.016EQ!R 4.073 2.094 1.421 1.134 1.093 0.974 0.953 0.8804 6 8 10 12 142.0 2.02.53.0 3.03.54.0 4.04.55.0 5.05.56.0 6.06.57.0 7.0HOMO-LUMO gap (eV)Number of SiO2 unitsFIG. 3. Variation of the HOMO-LUMO gap of the  SiO2 Nrings and chains with N.PHYSICAL REVIEW LETTERS week ending24 JANUARY 2003 VOLUME 90, NUMBER 3035502-3 035502-3approximately half the intrinsic two-ring strain yielding,for the 12-ring, EQ!R   0:97eV =SiO2.Although important in assessing the likely formationof a system and the energy released once broken, thestrain tells little about the stability of a ring, as onceformed it is the energy required to break the connected SiO2 N structure (e.g., by external force, or reaction),which is more important. In addition to the energeticstability of N>11 rings, having lower total energiesand BEs over the N>11 chains, due to the similarityof each bonded SiO2 unit throughout a ring or chain, thelower BE (eV=SiO2) also indicates a corresponding ex-cess structural stability. The reactive stability of an SiO2cluster can also be assessed by the size of the energy gapbetween the highest occupied molecular orbital (HOMO)and the lowest unoccupied molecular orbital (LUMO).For increasing  SiO2 N chain lengths this gap remainsalmost constant. For the rings, the HOMO-LUMO gap isinitially smaller than that of the chains but increasesrapidly with increasing N, exceeding that of the chainsby 0.25 eVfor N   12; see Fig. 3.We ﬁnd that the frontierorbitals on the rings and chains have different characters:the chains have both HOMOand LUMO highly localizedon the NBO end groups, while the rings have both orbitalsdistributed regularly over all atomic centers. The chainends also have a dipolar character, making these regionslikely reactive centers. The spatial extent of the electron-accepting LUMO of the rings is radially asymmetric withsigniﬁcant magnitude only around the outer periphery ofthe ring, but an almost total absence towards the center ofthe ring. Our calculations also show that the outer envi-ronment of the rings has a mostly positive electrostaticpotential, whereas towards the center of the rings thepotential is negative, indicating, along with the LUMO,that the ring interiors would be less reactive than theexteriors.Recent DF=B3LYP calculations of the reaction of iso-lated hydrogen-terminated two-rings with water give abarrier of 0.71 eV increasing to 1.11 eV when including amore realistic extended environment [17]. Other studiesfound it necessary to include two-rings in extended sur-face models of annealed silica to reproduce its knownhydrolysis stability [5]. In our silica rings each two-ringis, as on an extended surface, fully coordinated in a con-strained environment, helping to increase its hydrolysisbarrier over isolated two-rings, or terminated two-ringclusters. Experimentally, extended two-ring containingﬁbers of silica-w are structurally stable but susceptible tohydrolysis, although with only isolated bonds being at-tacked leaving intact two-ring  SiO2 N chains estimatedto have 12:5 <N<100 units [10]. To form more stablemulti-two-ring materials we envisage, instead of longﬂexible chains, fully connected small clusters, such asour molecular rings, as material building blocks. If ourproposed silica molecular rings could be successfullysynthesized, then via their mutual interaction, the possi-bility arises for new extended silica polymorphs, whichmay show bulk features reminiscent of its building blockssuch as tubular or porous morphologies. The interiors ofsuch tubes or pores, due to the properties of the rings, arealso likely to be relatively stable to hydrolysis, and thesize of such pores even tailored by the size of the mo-lecular ring employed. Although such ideas are highlyspeculative, we feel that if the synthetic challenge, inher-ent in these studies, could be mastered successfully, fullycoordinated ﬁnite silica clusters and polymorphs basedupon their combination, as proposed here, could provide anew route to the synthesis of novel materials and thefurther fundamental understanding of silica.We acknowledge Stichting Nationale Computerfacil-iteiten (NCF) for computer resources and A. A. Sokolfor useful discussions.[1] A. M. Ferrari, E. Garrone, G. Spoto, P. Ugliengo, andA. Zecchina, Surf. Sci. 323, 151 (1995).[2] B.C. Bunker, D. M. Haaland, T. A. Michalske, and W. L.Smith, Surf. Sci. 222, 95 (1989).[3] C. M. Chaing, B.R. Zegarksi, and L.H. Dubois, J. Phys.Chem. 97, 6948 (1993).[4] A. Roder, W. Kob, and K. Binder, J. Chem. Phys. 114,7602 (2001).[5] V. A. Bakaev and W. A. Steele, J. Chem. Phys. 111, 9803(1999).[6] D. Ceresoli, M. Bernasconi, S. Iarlori, M. Parrinello, andE. Tosatti, Phys. Rev. Lett. 84, 3887 (2000).[7] M. Benoit, S. Ispas, and M. E. Tuckerman, Phys. Rev. B64, 224205 (2001).[8] T.S. Chu, R.Q. Zhang, and H. F. Cheug, J. Phys. Chem. B105, 1705 (2001).[9] S.K. Nayak, B.K. Rao, S. N. Khanna, and P. Jena,J. Chem. Phys. 109, 1245 (1998).[10] A. Weiss, Z. Anorg. Allg. Chem. 276, 95 (1954).[11] A. D. Becke, J. Chem. Phys. 98, 5648 (1993).[12] M.J. Frisch et al., computer code GAUSSIAN 98, Gaussian,Inc., Pittsburgh, PA, 1999.[13] F. Boccuzzi, S. Coluccia, G. Ghiotti, C. Morterra, andA. Zecchina, J. Phys. Chem. 82, 1298 (1978).[14] B. A. Morrow and I. A. Cody, J. Phys. Chem. 80,1 9 9 8(1976).[15] L-S. Wang, J. B. Nicholas, M. Depuis, H. Wu, and S. D.Colson, Phys. Rev. Lett., 78, 4450 (1997).[16] N. Lopez, M.Vitiello, F. Illas, and G. Pacchioni, J. Non-Cryst. Solids 271, 56 (2000).[17] T.R. Walsh, M. Wilson, and A. P. Sutton, J. Chem. Phys.113, 9191 (2000).[18] D.R. Hamann, Phys. Rev. B 55, 14784 (1997).PHYSICAL REVIEW LETTERS week ending24 JANUARY 2003 VOLUME 90, NUMBER 3035502-4 035502-4

Fully coordinated silica nanoclusters: (SiO2)(N) molecular rings

Fully coordinated silica nanoclusters: (SiO2)(N) molecular rings

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