Potential Energy Surfaces of SimOn Cluster Formation and Isomerization

Transcription

1 Ames Lbortory Publictions Ames Lbortory Potentil Energy Surfces of SimOn Cluster Formtion nd Isomeriztion Pvel V. Avrmov Iow Stte University Ivn Admovic Iow Stte University Ki-Ming Ho Iow Stte University, C. Z. Wng Iow Stte University W. C. Lu Iow Stte University See next pge for dditionl uthors Follow this nd dditionl works t: Prt of the Chemistry Commons The complete bibliogrphic informtion for this item cn be found t meslb_pubs/329. For informtion on how to cite this item, plese visit howtocite.html. This Article is brought to you for free nd open ccess by the Ames Lbortory t Iow Stte University Digitl Repository. It hs been ccepted for inclusion in Ames Lbortory Publictions by n uthorized dministrtor of Iow Stte University Digitl Repository. For more informtion, plese contct digirep@istte.edu.

2 Potentil Energy Surfces of SimOn Cluster Formtion nd Isomeriztion Abstrct The rection pths for formtion nd isomeriztion of set of silic SimOn (m = 2,3, n = 1 5) nnoclusters hve been investigted using second-order pertubtion theory (MP2) with the 6-31G(d) bsis set. The MP2/ 6-31G(d) clcultions hve predicted singlet ground sttes for ll clusters excluding Si3O2. The totl energies of the most importnt points on the potentil energy surfces (PES) hve been determined using the completely renormlized (CR) singles nd doubles coupled cluster method including perturbtive triples, CR-CCSD(T) with the cc-pvtz bsis set. Although trnsition sttes hve been locted for mny isomeriztion rections, only for Si3O3 nd Si3O4 hve some trnsition sttes been found for the formtion of cluster from the seprted rectnts. In ll other cses, the process of formtion of SimOnclusters ppers to proceed without potentil energy brriers. Disciplines Chemistry Comments Reprinted (dpted) with permission from Journl of Physicl Chemistry A 109 (2005: 6294, doi: / jp058078v. Copyright 2005 Americn Chemicl Society. Authors Pvel V. Avrmov, Ivn Admovic, Ki-Ming Ho, C. Z. Wng, W. C. Lu, nd Mrk S. Gordon This rticle is vilble t Iow Stte University Digitl Repository:

3 6294 J. Phys. Chem. A 2005, 109, Potentil Energy Surfces of Si m O n Cluster Formtion nd Isomeriztion Pvel V. Avrmov,, Ivn Admovic, Ki-Ming Ho, C. Z. Wng, W. C. Lu, nd Mrk S. Gordon*, Ames Ntionl Lbortory/Deprtment of Chemistry, Iow Stte UniVersity, Ames, Iow 50011, nd L.V. Kirensky Institute of Physics SB RAS, Acdemgorodok, , Russi ReceiVed: Mrch 2, 2005; In Finl Form: April 26, 2005 The rection pths for formtion nd isomeriztion of set of silic Si m O n (m ) 2,3, n ) 1-5) nnoclusters hve been investigted using second-order pertubtion theory (MP2) with the 6-31G(d) bsis set. The MP2/ 6-31G(d) clcultions hve predicted singlet ground sttes for ll clusters excluding Si 3 O 2. The totl energies of the most importnt points on the potentil energy surfces (PES) hve been determined using the completely renormlized (CR) singles nd doubles coupled cluster method including perturbtive triples, CR-CCSD(T) with the cc-pvtz bsis set. Although trnsition sttes hve been locted for mny isomeriztion rections, only for Si 3 O 3 nd Si 3 O 4 hve some trnsition sttes been found for the formtion of cluster from the seprted rectnts. In ll other cses, the process of formtion of Si m O n clusters ppers to proceed without potentil energy brriers. I. Introduction Si m O n clusters hve plyed key role in the synthesis of silicon nnostructures. One-dimensionl silicon-silic nd silicon-crbon-silic nnowires nd nnotubes of vrious shpes nd structures hve been synthesized under hightemperture conditions. 1-5 Bulk-quntity Si nnowires 1,2 hve been synthesized by therml evportion of powder mixtures of silicon nd SiO 2 or by therml evportion of silicon monoxide. 3 Initilly, SiO vpor is generted from powder mixture nd condensed on the substrte, with Si nnoprticles nd nnowires surrounded by shells of silicon oxide. The silic content in the strting Si/SiO 2 rection mixture ppers to be key fctor in nnowire growth nd structure. 1,2 Surfce thin Si x O structures function s ctlysts on the tips nd form SiO 2 structures, which retrd the lterl growth of the nnowires. It hs lso been demonstrted 3 tht SiO cn contribute to the formtion of SiC multiwll nnotubes nd nnowires nd SiC- SiO x nnowires in thermochemicl rections with multiwll crbon nnotubes. The structures nd properties of Si m O n clusters hve therefore been studied intensively by photoelectron spectroscopy 6-9 nd by severl theoreticl pproches. 7,9-20 On the bsis of the vibrtionlly resolved PES spectr, Si 3 O 3 nd Si 3 O 4 clusters re proposed to hve closed-shell electronic structures. The experimentl studies hve been ccompnied by theoreticl quntum-chemicl clcultions 7,9 on set of Si m O - n nd Si m O n clusters using second-order perturbtion theory (MP2) 21 nd the G(d) bsis set. 22 This combintion of experiments nd quntum-chemicl clcultions llowed the uthors to interpret the min fetures of the PES spectr nd to extrct the dibtic electron ffinities of neutrl Si m O n clusters. Previous theoreticl studies hve predicted the tomic structures of Si m O - n nd Si m O n clusters 7-10,14-16,18,19 t vrious levels of theory. These include density functionl theory (DFT) 10,14,16,19 nd such correlted b initio pproches s MP2, multireference * Corresponding uthor. E-mil: mrk@si.fi.meslb.gov. Iow Stte University. L.V. Kirensky Institute of Physics SB RAS. second-order perturbtion theory, qudrtic configurtion interction (QCISD(T)), nd coupled cluster (CCSD(T)) methods. 7-9,15,18 Severl differences mong these methods re pprent, even in the lowest-energy spin stte of some Si m O n clusters, s well s in the equilibrium geometry of the complexes. For exmple, recent study 19 predicted singlet electronic ground stte for the pyrmidl globl minimum of Si 3 O 2, in contrst with erlier results 9,18 in which triplet globl minimum ws predicted for the flt pentgon structure. This cn be ttributed to the importnce of electron correltion in correctly predicting the electronic structure of silic clusters. 20 The rectivity nd cohesion energies 13 of set of Si m O n (n,m ) 1-8) clusters nd rection pths for ssembling Si m O n clusters hve lso been studied. 19 Zhng et l. 13 hve used the B3LYP functionl 23 with the 6-31G(d) bsis set, s well s the G2MP2 method. 24 Admovic nd Gordon 20 employed multireference perturbtion theory nd CCSD(T) extrpolted to the complete bsis set limit to study the competing Si + O 2 rections on the singlet nd triplet surfces. All of these studies showed tht dynmic correltion clerly plys n importnt role in such systems. The im of the present pper is to study structures, trnsition sttes, reltive energies, nd formtion rection pths t the MP2 nd CCSD(T) levels of theory for Si 2 O 2,Si 2 O 3, Si 2 O 4,Si 3 O, Si 3 O 2,Si 3 O 3, nd Si 3 O 4 clusters. Although some of the species considered in the present work hve been discussed previously, there hs not been comprehensive study of these systems. Some theoreticl studies 25 considered the structures nd vibrtionl spectr of SiO nd Si 2 O 2. The SiO dimer is postulted to be ring species with D 2h symmetry. 26 Most theoreticl studies on Si 2 O 3 hve been concerned with the high-energy, multiconfigurtionl, propellne-like structure, in which the Si toms re connected by three bridging O toms The globl minimum Si 2 O 3 structure ws found to hve n O tom bound to rhombic Si 2 O 2, both in the experimentl work of Wng et l. 30 nd in recent comprehensive theoreticl study by Lu et l. 19 The geometry, energy, nd vibrtionl frequencies, t the Hrtree-Fock level of theory, were determined for the D 2h globl minimum nd C 2V trnsition /jp058078v CCC: $ Americn Chemicl Society Published on Web 06/28/2005

4 Si m O n Cluster Formtion nd Isomeriztion J. Phys. Chem. A, Vol. 109, No. 28, stte of Si 2 O 4 in study by Ystenes. 31 The D 2h structure ws lso found to be the globl minimum in the recent study by Lu et l. 19 Presented here is systemtic investigtion of the growth rections for the fmily of Si m O n (m ) 2-3, n ) 1-4) species. This study is orgnized s follows: Section II describes the computtionl methods, followed by results nd discussion in Section III. Conclusions re presented in Section IV. II. Computtionl Detils To clculte the electronic structure of silic nnoclusters, the generl tomic nd moleculr electronic structure system (GAMESS) 32 code hs been used. Geometry optimiztions nd trnsition stte serches hve been performed using the MP2/ 6-31G(d) level of theory; for isomer 3 of Si 2 O 3, density functionl theory (DFT) 33 using the B3LYP functionl ws lso employed. 33 Coupled cluster clcultions hve been performed t the MP2/6-31G(d) geometries using the completely renormlized coupled cluster pproch with singles, doubles, nd perturbtive triples (CR-CCSD(T)) 34 with the correltion consistent cc-pvtz bsis set 35,36 to obtin improved energies of ll minim nd trnsition sttes. Becuse isomer 3 of Si 2 O 3 is very configurtionlly mixed, multireference second-order perturbtion theory (MRMP2) 37 ws lso used to obtin energy corrections for this species. All trnsition sttes nd minim hve been confirmed by the clcultion nd digonliztion of the pproprite Hessin mtrix (mtrix of energy second derivtives). For DFT nd MP2, Hessins were obtined by tking finite differences of nlytic grdients. TCSCF nlyticl Hessins cn be obtined using the corresponding generlized vlence bond (GVB) 38 method. The rection enthlpies were corrected for zero-point energy (ZPE) nd temperture effects. The intrinsic rection coordinte (IRC) method hs been employed with the Gonzles-Schlegel second-order integrtion method 39 to ensure tht ech trnsition stte joins two pproprite locl minim long the potentil energy surfce. A useful dignostic to ssess the multireference nture of unusul structures is to exmine the MP2 nturl orbitl occuption numbers (NOON). 40 A closed-shell, single configurtion is indicted by NOON tht re 2.0 nd 0.0 for occupied nd virtul orbitls, respectively. Significnt devitions from these vlues ( 0.1) indicte some degree of multireference chrcter in the wve function. III. Results nd Discussion () SiO + SiO f Si 2 O 2. Since ll molecules involved in this rection re closed-shell (Hrtree-Fock like) systems, single reference methods were used for ll of the clcultions. Optimiztions were ccomplished with MP2/6-31-G(d), nd energy corrections were tken into ccount with CCSD(T)/ cc-pvtz. Figure 1 gives schemtic of rection () nd rectnt nd product structures. The lowest-energy product hs D 2h symmetry, in greement with previous studies. Other isomers were not considered, since they re much higher in energy. An MP2 optimiztion initited with two SiO molecules 3 Å prt, s represented in Figure 1, goes directly into the D 2h isomer of Si 2 O 2, with no intervening brrier. The MP2/ 6-31G(d) rection enthlpy with ZPE nd temperture corrections is H ) kcl/mol, while the CCSD(T)/cc-pVTZ H )-49.5 kcl/mol. The experimentl enthlpy of this dimeriztion rection 43 is H exp )-48.5 kcl/ mol, so the experimentl nd CCSD(T)/cc-pVTZ results re in good greement. The discrepncy between CCSD(T)/cc-pVTZ nd MP2/6-31G(d) Figure 1. A schemtic of rection (): SiO + SiO f Si 2O 2; MP2/ 6-31G(d) structurl prmeters for rection () (Å). TABLE 1: Reltive Energies of the Si 2 O 3 Isomers (kcl/mol) (CCSD(T) nd CR-CCSD(T) with cc-pvtz Bsis Set, All Others with 6-31G(d) Bsis Set HF DFT MP2 MCSCF CCSD(T) (CR-CCSD(T)) 1 (open) (tringle) (56.3) 3 (tricycle) (61.3) 4 (circle) (72.9) 5 (liner) (108.0) 6 (circle1) (220.5) 7 (open1) (229.7) rection enthlpies emphsizes the importnce of triple excittions for proper tretment of dynmicl correltion effects in the silicon-oxygen systems. (b) SiO + SiO 2 f Si 2 O 3. The first step in the investigtion of formtion of Si 2 O 3 ws to find ll possible cndidtes for the ground stte of Si 2 O 3. The propellne-like structure is the only Si 2 O 3 isomer tht hs been extensively exmined previously, primrily due to its high-energy nd multiconfigurtionl chrcter. A systemtic serch for ll possible Si 2 O 3 isomers resulted in the seven structures shown in Figure 2. The globl minimum is isomer 1 (open). This is in greement with Wng et l. 30 nd Lu et l. 19 The reltive energies of ll seven isomers, using vrious levels of theory, re given in Tble 1. Most of these methods give the sme energy ordering, with the open structure being much lower in energy thn ny other isomer. For the most prt, MP2/ 6-31G(d), CCSD(T)/cc-pVTZ, nd CR-CCSD(T)/cc-pVTZ reltive energies re in resonble greement. The bsis set effect (from 6-31G(d) to cc-pvtz) is usully on the order of 3 kcl/ mol. The biggest disgreement between MP2 nd CC methods occurs for isomers 3 nd 5 ( 10 kcl/mol), the two most multiconfigurtionl isomers. For the tricycle isomer, n MRMP2/6-31G(d) single-point energy correction, t the MCSCF optimized geometry, gives reltive energy of 37.7 kcl/mol. This vlue my be too low, on the bsis of the CR-CCSD(T)/ cc-pvtz reltive energy of 61.3 kcl/mol. Anlysis of the Hessin mtrix shows tht the open isomer is minimum on the potentil energy surfce t most levels of theory. Although the TCSCF numericl Hessin hs one imginry frequency of 1422 cm -1, the equivlent nlyticl GVB Hessin hs no imginry frequencies. It is therefore concluded tht the TCSCF Hessin hs numericl errors, nd the GVB nlytic Hessin ws used for ll isomers. All other isomers re minim, except for 6 (circle1), which hs one imginry frequency t ll levels of theory except HF, nd tricycle with one imginry frequency t the HF level of theory. The liner isomer does not exist t the HF level (it dissocites to SiO + SiO 2 ) nd hs 5, 4, 4, nd 2 imginry frequencies t the DFT, MP2, TCSCF, nd GVB levels of theory, respectively. Next, consider the TCSCF nturl orbitl occuption numbers (NOON). Significnt multiconfigurtionl chrcter ws found

5 6296 J. Phys. Chem. A, Vol. 109, No. 28, 2005 Avrmov et l. Figure 2. The lowest-energy Si 2O 3 isomers; MP2/6-31G(d) geometry prmeters (Å). Figure 3. () A schemtic of the prllel pth for rection (5)sformtion of the D 2h isomer; MP2/6-31G(d) geometry prmeters of the Si 2O 4 D 2h isomer (Å). (b) A schemtic of the norml pth for rection (5)sformtion of the C 2V isomer. just for isomers 3 nd 5. The NOONs of the highest occupied moleculr orbitl (HOMO) re nd 1.755, respectively, for isomers 3 nd 5, while corresponding NOONs for the lowest unoccupied moleculr orbitls (LUMO) re nd The rection pth for the formtion of Si 2 O 3 from SiO nd SiO 2 ws determined by inititing n MP2 optimiztion, in C s symmetry, with SiO nd SiO 2 5 Å prt. This leds to the formtion of the isomer 1 (open) with no brrier. The C s rection pth voids the symmetry-forbidden C 2V pth. The MP2/ 6-31G(d) rection enthlpy for the formtion of Si 2 O 3 from SiO nd SiO 2 is H )-70.4 kcl/mol, while the CCSD(T)/ cc-pvtz H )-77.2 kcl/mol. (c) SiO 2 + SiO 2 f Si 2 O 4. Figure 3 gives the MP2/6-31G(d) geometricl prmeters for the Si 2 O 4 D 2h isomer. A C 2V structure lies 79.6 kcl/mol bove the globl minimum, t the MP2/ 6-31G(d) level of theory. The CCSD(T)/cc-pVTZ//MP2/ 6-31G(d) reltive energy is 84.0 kcl/mol. The C 2V structure hs 2 imginry frequencies, so it is second-order sddle point. If the C 2V structure is optimized in C s symmetry (breking C 2V symmetry), it goes directly into D 2h without ny brrier, s found previously. 31 Figure 3,b gives schemtic representtions of two different pths for the formtion of Si 2 O 4. Inititing n MP2/6-31G(d) optimiztion in C s symmetry from the prllel orienttion (Figure 3) leds to the D 2h isomer, with no brrier. Strting from the perpendiculr orienttion (Figure 3b) leds to the C 2V isomer. This pth is lso brrierless. Both pths re highly exothermic. The MP2 (CCSD(T)/cc-pVTZ)) enthlpy of pth () is H MP2/6-31G(d) )-91.5 (-94.1) kcl/mol. The corresponding enthlpies for pth (b) re nd kcl/mol, respectively. Since both rection pths hve no brrier, both C 2V nd D 2h re possible products in the rection of two SiO 2.

6 Si m O n Cluster Formtion nd Isomeriztion J. Phys. Chem. A, Vol. 109, No. 28, TABLE 2: Structures nd Energies of Si 2 O 5 Isomers Figure 4. A schemtic of the Si 2O 5 isomeriztion potentil energy surfce. TABLE 4: Structures nd Energies of Isomers of Si 3 O Nmes of isomers. b V1 nd V2 re two views of ech isomer. c MP2 nturl orbitl occuption numbers. d The structure hs been determined only t the B3LYP level. TABLE 3: Structures, Energies, nd Rection Pths of Trnsition Sttes of Si 2 O 5 d Nmes of structures. b V1 nd V2 re two views of ech trnsition stte. c MP2 nturl orbitl occuption numbers. d GS i nd GS f denote initil nd finl minim on the IRC pth. e Brrier height from GS i / GS f. However, the globl minimum, D 2h, is much lower in energy, nd the C 2V structure is second-order sddle point. So, the C 2V species is dynmiclly unstble, nd vibrtions of this structure should esily led to the globl minimum. (d) Si 2 O 5. Closed- nd open-shell (S ) 1) MP2 6-31G(d) clcultions hve been performed to determine the nture of the ground stte. It is predicted tht the globl minimum Si 2 O 5 structure is singlet. The singlet-triplet splitting for the globl minimum structure GS1 is 23.5 kcl/mol. A set of energy minim nd trnsition sttes hs been determined (Tbles 2 nd 3, Figure 4) for the singlet ground stte. The doubly bridged GS1 isomer ppers to be the globl minimum on both the MP2 nd CR-CCSD(T) potentil energy surfces. The cyclic GS2 isomer is 19.7 (18.7 t the MP2 level) kcl/mol higher in energy thn GS1, with GS3 nd GS4 considerbly higher. Isomers GS1-GS4 hve MP2 NOON for the highest occupied moleculr orbitl (HOMO) in the rnge , resonbly close to the single configurtion vlues of 2.0. It ws not possible to determine the MP2 geometry for GS5 becuse the underlying HF clcultions did not converge. Insted, the geometry of this Nmes of isomers. b V1 nd V2 re two views of ech isomer. c MP2 nturl orbitl occuption numbers. structure ws determined using DFT/B3LYP. The rther high CR-CCSD(T) reltive energy for this species ws then determined t the B3LYP geometry. Trnsition sttes connecting the minim in Tble 2 re listed in Tble 3. TS3 hs the smllest MP2 NOON for the HOMO. This my explin why the reverse brrier for TS3 disppers when single-point CR-CCSD(T) clcultions re performed t the MP2 geometry. Another reson my be the use of the B3LYP GS5 geometry. Note tht ll trnsition sttes listed in Tble 3 correspond to isomeriztion rections. A wide serch for trnsition sttes, intermedites, nd IRC clcultions hs led to the conclusion tht no brriers exist for the formtion of Si 2 O 5 from SiO 2 + SiO 3, even though severl possible pthwys hve been explored. Indeed, n MP2 optimiztion initited with seprted rectnts (SiO 2 + SiO 3 ) 4 Å prt goes directly to the GS1 structure with no brrier. The CR-CCSD(T) E for the rection SiO 2 + SiO 3 f Si 2 O 5 is kcl/mol. The corresponding MP2 vlue is kcl/mol. The globl minimum GS1 cn isomerize to GS2 through trnsition stte TS1, with heights of forwrd nd reverse CR- CCSD(T) brriers of 81.8 nd 62.1 kcl/mol, respectively. GS2 cn isomerize to GS5 nd GS3 vi trnsition sttes TS3 nd TS2, respectively. Breking the O-O bond vi TS3 nd cretion of n equivlent O-O bond from the other side of the molecule genertes n equivlent GS2 structure. (e) Si 3 O. Closed- nd open-shell (S ) 1) MP2 6-31G(d) geometry optimiztions hve been performed to determine the nture of the ground electronic stte. It is predicted tht the Si 3 O globl minimum is singlet, with singlet-triplet splitting of 40.9 kcl/mol. The Si 3 O energy minim nd trnsition sttes for the singlet ground stte re shown in Tbles 4 nd 5, respectively. A schemtic of the potentil energy surfce is given in Figure 5. GS6 is predicted by both MP2 nd CR-CCSD(T) to be the globl minimum on the singlet surfce, with CR-

7 6298 J. Phys. Chem. A, Vol. 109, No. 28, 2005 Avrmov et l. TABLE 5: Structures, Energies, nd Rection Pths of Trnsition Sttes of Si 3 O d TABLE 6: Structures nd Energies of Isomers of Si 3 O 2 Nmes of structures. b V1 nd V2 re two views of ech trnsition stte. c MP2 nturl orbitl occuption numbers. d GS i nd GS f denote initil nd finl minim on the IRC pth. e Brrier height from GS i / GS f. Figure 5. surfce. A schemtic of the Si 3O isomeriztion potentil energy CCSD(T) reltive energies of 12.4 nd 19.7 kcl/mol, respectively, for GS7 nd GS8. All three isomers hve MP2 HOMO NOON greter thn 1.9, suggesting tht they re close to closedshell species. All trnsition sttes listed in Tble 5 hve MP2 NOON greter thn 1.9. The serch for trnsition sttes, intermedites, nd IRC clcultions suggests tht no brriers exist for the rection SiO + Si 2 f Si 3 O. The MP2 optimiztion initited with rectnts Si 2 + SiO 4 Å prt goes directly to the GS6 structure with no brrier. IRC clcultions confirm tht the globl minimum GS6 cn isomerize to GS7 vi TS4, with CR-CCSD(T) brrier of 25.8 kcl/mol. The isomeriztion of GS6 to GS8 vi TS5 hs brrier of 24.1 kcl/mol. (f) Si 3 O 2. Closed- nd open-shell (S ) 1) MP2/6-31G(d) clcultions hve been performed to determine the nture of the ground electronic stte. It hs been predicted tht the globl minimum Si 3 O 2 structure is triplet. Since the CR-CCSD(T) method is currently vilble only for closed shells, the CR- CCSD(T) clcultions were performed only for the singlet sttes. Since the MP2 nd CR-CCSD(T) energy orderings re similr for the other species, MP2 reltive energies re lso expected to be relible here. The Si 3 O 2 singlet nd triplet energy minim nd trnsition sttes re presented in Tbles 6 nd 7, respectively. GS15 (S ) 1) is predicted to be the globl minimum, ) 11.7 kcl/mol lower in energy t the MP2 level of theory thn the corresponding singlet isomer (GS11) nd 4.9 kcl/mol lower in energy thn the lowest-energy singlet, GS9. One other singlet, GS10, nd one other triplet, GS16, hve smll MP2 reltive energies of 11.1 nd 16.9 kcl/mol, respectively. Isomers GS9-GS13 (S ) 0) hve the sme energy order t both the MP2 HOMO nd CR-CCSD(T) levels of theory. All singlet isomers GS9-GS13 hve MP2 NOON in the rnge of , so these re essentilly closed-shell species. The serch for trnsition sttes, intermedites, nd IRC clcultions suggests tht no brriers exist for the formtion rection (SiO + Si 2 O f Si 3 O 2 ) of the singlet GS11 stte. Severl MP2 optimiztions initited with seprted Si 2 O + SiO in the Nmes of the isomers. b V1 nd V2 re two views of ech isomer. c MP2 nturl orbitl occuption numbers. TABLE 7: Structures, Energies, nd Rection Pths of Trnsition Sttes of Si 3 O 2 d Nmes of the structures. b V1 nd V2 re two views of ech trnsition stte. c MP2 nturl orbitl occuption numbers. d GS i nd GS f denote initil nd finl minim on the IRC pth. singlet stte 4 Å prt go directly to the GS11 structure with no brrier. The CR-CCSD(T) (MP2) energy difference for the rection Si 2 O + SiO f Si 3 O 2 )-35.3 (-36.9) kcl/mol. Similrly, GS9 forms with no intervening brrier, strting from SiO + Si 2 O, seprted by 3 Å. The CR-CCSD(T) GS11 f TS6 brrier is negtive. This suggests tht either the loction of the trnsition stte shifts t the higher level of theory or the CR-CCSD(T) brrier does indeed dispper. For the isomeriztion GS11 f GS10, the MP2 brriers in both directions re very smll, 2 kcl/mol. So, there must be very flt potentil energy surfce in this region. For ll singlet Si 3 O 2 trnsition sttes, the MP2 HOMO NOON re in the rnge

8 Si m O n Cluster Formtion nd Isomeriztion J. Phys. Chem. A, Vol. 109, No. 28, TABLE 8: Structures nd Energies of Isomers of the Si 3 O 3 Cluster TABLE 9: Structures, Energies, nd Rection Pths for Si 3 O 3 Trnsition Sttes d Nmes of the structures. b V1 nd V2 re two views of ech trnsition stte. c MP2 nturl orbitl occuption numbers. d GS i nd GS f denote initil nd finl minim on the IRC pth. Nmes of the isomers. b V1 nd V2 re two views of ech isomer. c MP2 nturl orbitl occuption numbers. d IM1 indictes SiO + Si 2O 2 intermedite structure. The MP2 IRC clcultions show tht GS10 cn isomerize to GS11 vi trnsition stte TS6 nd to GS12 through TS7. It is useful to note tht two couples of isomers (GS11 (S ) 0)- GS15 (S ) 1) nd GS12 (S ) 0)-GS17 (S ) 1)) hve similr tomic structures, so tht structures could be connected vi singlet-triplet crossing involving TS8 (S ) 1). (g) Si 3 O 3. The Si 3 O 3 energy minim nd trnsition sttes re presented in Tbles 8 nd 9, respectively. A schemtic of this section of the potentil energy surfce is shown in Figure 6. Singlet GS18 is the lowest-energy isomer on both the MP2 nd CR-CCSD(T) potentil energy surfces, nd ll other isomers re much higher in energy. The singlet-triplet splitting for the lowest-energy singlet nd triplet isomers is 64.2 kcl/mol. All singlet isomers hve MP2 HOMO NOON in the rnge of For severl MP2 trnsition sttes (TS9, TS13-TS17), the CR- CCSD(T) brriers re negtive. This cn men either tht these brriers dispper t the CR-CCSD(T) level of theory or tht Figure 6. A schemtic of the synthesis nd isomeriztion of Si 3O 3. the position of the trnsition stte undergoes significnt shift. For ll TSs, the MP2 HOMO NOON re in the rnge There is n intermedite (IM1) on the rection pth Si 2 O 2 + SiO f Si 3 O 3. IM1 is 4.5 (8.8) kcl/mol lower in energy thn the seprted rectnts t the CR-CCSD(T) (MP2) level of theory. There is no brrier between the rectnts nd IM1. The energy of formtion of the lowest isomer GS18 from rectnts (Si 2 O 2 + SiO) is nd kcl/mol t the CR-CCSD-

9 6300 J. Phys. Chem. A, Vol. 109, No. 28, 2005 Avrmov et l. (T) nd MP2 levels, respectively. This rection occurs with no brrier if the rectnts re seprted by 3 Å. TS9 nd TS17 connect IM1 with GS19 nd GS24, respectively. The energy brrier for the former trnsformtion is very smll (Tble 10), while tht for the ltter is more thn 40 kcl/ mol. So, IM1 is most likely to trnsform to GS19. An dditionl trnsition stte my connect GS19 with globl minimum GS18, but such structure ws not found. There is direct trnsition stte (TS13) for the rection Si 2 O 2 + SiO f Si 3 O 3 (SiO intercts with tringle Si 2 O 2 isomer) tht does not require pssing through n intermedite structure. The CR-CCSD(T) brrier for this rection is only 15.5 kcl/mol, but the product is isomer GS27. Since this isomer is very high in energy, it is probbly not directly involved in the experimentlly observed processes. Two trnsition sttes for the rection 3SiO f Si 3 O 3 (TS16 nd TS18) (Figure 3) connect the rectnts with GS23 nd GS24, respectively. The 3SiO f TS16 CR-CCSD(T) brrier is negtive, nd the CR-CCSD(T) brrier for 3SiO f TS18 is 15.6 kcl/mol. (h) Si 3 O 4. The Si 3 O 4 locl minim nd trnsition sttes re listed in Tbles 10 nd 11, respectively, nd schemtic of the PES is shown in Figure 7. The singlet GS29 is predicted by both MP2 nd CR-CCSD(T)//MP2 to be the lowest-energy isomer. The singlet-triplet splitting for the lowest singlet nd triplet sttes is 64.5 kcl/mol. All isomers except GS36 hve MP2 HOMO NOON in the rnge of For GS36, the HOMO NOON is 1.81, indicting significnt multi-configurtionl chrcter. TS20 is predicted by both MP2 nd CR-CCSD(T)/MP2 to be the lowest-energy trnsition stte. For ll TSs, excluding TS21, the MP2 HOMO NOON re in the rnge TS21 hs the MP2 HOMO NOON ) The serch for intermedites nd trnsition sttes hs shown tht there is n intermedite structure IM2 for the rection Si 2 O 3 + SiO f Si 3 O 4 (GS29, plnr rhombic isomer of Si 2 O 3, Figure 4). The CR-CCSD(T) (MP2) energy of formtion for GS29 is (-11.8) kcl/mol. There re two rection pths for the formtion of the globl minimum isomer GS29. The first of these connects the intermedite IM2 with GS36 through trnsition stte TS19; this is followed by isomeriztion of GS36 to GS29 through TS22. The second route connects IM2 with GS30 through the trnsition stte TS28 nd GS30 with GS29 through TS20. The second route is preferble due to the lower energy brriers on the rection pth. No brrier hs been detected tht connects IM2 with the rectnts. The trnsition sttes TS21, TS23, TS24, TS25, TS26, nd TS27 describe set of isomeriztion rections of Si 3 O 4 clusters. IV. Conclusions Only the lrgest Si 3 O 3 nd Si 3 O 4 clusters pper to hve intermedite structures nd trnsition sttes on the rection pths leding to formtion of these Si m O n clusters. Rections of formtion of smller Si m O n clusters (Si 2 O 2, Si 2 O 3, nd Si 2 O 4 ) re ll brrierless processes. The previous study 20 on the formtion of SiO nd SiO 2 lso showed tht these rections occur with no rection brrier. This leds to the conclusion tht smll Si-O clusters hve strong thermodynmic driving force for growing into bigger clusters. This hs lso been noted in recent pper by Zhng et l. 44 It my be nticipted tht s the vlues of m nd n increse, one will find n incresingly complex energy lndscpe, with intermedites nd trnsition sttes. For most of the species studied here, single configurtion methods pper to be resonble, so methods such s MP2 nd TABLE 10: Structures nd Energies of Isomers of Si 3 O 4 Nmes of the isomers. b V1 nd V2 re two views of ech isomer. c MP2 nturl orbitl occuption numbers. d IM1 indictes SiO + Si 2O 2 intermedite structure.

10 Si m O n Cluster Formtion nd Isomeriztion J. Phys. Chem. A, Vol. 109, No. 28, TABLE 11: Structures, Energies, nd Rection Pths for Si 3 O 4 d B3LYP cn provide resonble geometries, t lest for closedshell species, nd tht the MP2 reltive energies re t lest in qulittive greement with those bsed on coupled cluster methods. Acknowledgment. The uthors re grteful to Professor Piotr Piecuch for invluble discussions. The study hs been supported in prt by grnts from the U.S. Deprtment of Energy vi the Ames Lbortory nd the Air Force Office of Scientific Reserch. References nd Notes Nmes of the structures. b V1 nd V2 re two views of ech trnsition stte. c MP2 nturl orbitl occuption numbers. d GS i nd GS f denote initil nd finl minim on the IRC pth. Figure 7. A schemtic of the synthesis nd isomeriztion of Si 3O 4. CR-CCSD(T) re pproprite. Only few sttionry points my require MCSCF-bsed wve functions. The MP2/6-31G(d) optimiztions of Si m O n cluster geometries presented here hve dded some new low- nd high-energy isomers of Si m O n clusters in comprison with the B3LYP/ 6-31G(d) clcultions of ref 19. However, the reltive energies for the structure of isomers tht re common to both studies re very similr, so the B3LYP geometries for the closed-shell species pper to be relible. The primry new fetures presented here re the explortion of higher spin sttes (importnt for some species) nd n nlysis of the rection pthwys for ech species. It hs, for exmple, been shown tht ll isomers of the Si 2 O 5, Si 3 O, Si 3 O 3, nd Si 3 O 4 clusters hve singlet globl minim, while the Si 3 O 2 cluster hs triplet ground stte. In generl, the Si m O n clusters hve very complex potentil energy surfces, with multiple low-lying spin sttes. So, n dequte level of theory is required to provide quntittively meningful brod picture of their behvior. It ppers tht (1) Wng, N.; Tng, Y. H.; Zhng, Y. F.; Lee, C. 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