纳米结构体系物理化学性质的理论研究方法与实例课件

1、固体表面化学的理论研究固体表面化学的理论研究方法、模型和应用方法、模型和应用吕鑫吕鑫 2005.5.19State Key Laboratory for Physical Chemistry of Solid Surfaces厦门大学固体表面物理化学国家重点实验室物理体系物理、化学性质（实验研究）理论模型理论方法表面吸附是固体表面化学研究的一个中心问题，是一切表面化学现象的根源固体表面化学的理论研究固体表面化学的理论研究 方法、模型与应用方法、模型与应用分类分类(理论方法、模型方法、物理理论方法、模型方法、物理体系）体系）层板模型方法与应用层板模型方法与应用（Slab Model and It

2、s Applications)3. 簇模型方法及其应用簇模型方法及其应用（Cluster Model and Its Applications) 分类分类理论方法分类：理论方法分类： 经典力学方法（经典力学方法（MM, MD, MC) 、量子力学方、量子力学方法法 (DFT, HF, CI) 、杂交方法（、杂交方法（QM/MM, AIMD) 、其他半经验方法（、其他半经验方法（AM1，PM3等）等）模型分类：模型分类： 局域模型（簇模型方法）、周期性模型局域模型（簇模型方法）、周期性模型3. 应用体系分类：应用体系分类： 共价体系、离子体系、金属体系、共价体系、离子体系、金属体系、HB体系、体

3、系、VDW体系体系2 Slab Model 2.1 First-Principle Method 量子化学问题均在于求解量子化学问题均在于求解Schrdinger方程，对方程，对于大块固体，其于大块固体，其Schrdinger方程表示为：方程表示为： H (Rm,rn) = E (Rm,rn) (1.1) Problem: H将是无限维的，上式很难求解。将是无限维的，上式很难求解。 Solutions: Introducing some approximations. A. Born-Oppenheimer Approximation: H(Rm) (rn) = E(Rm) (rn) (1.2

4、) (核运动和电子运动分离)B. Single-Particle Approximation for Solving The Wavefunctions of Electrons (电子波函数的单粒子近似电子波函数的单粒子近似)C. Energy Band Theory (DFT) and Crystal Orbital Theory (HF) (see A. Gross, Surf. Sci. Rep. 1998, 32, 291)()()()(2)()min(min(22rrrVrVmrHnVnUnTnEEiiiecesiectotrdrnrnnEnnErVecececec3)()()(E

5、 Eec(n) exchange-correlation functional ec(n) exchange-correlation energy per particle 2.2 Density functional Theory, Kohn-Sham Equation2.3 PSPW and Super Cell Pseudopotentials for inner shells Plane-wave functions for valence shells Periodic Boundary Conditions and Super Cell Method for Solid Slab

6、Model for Solid Surface Car-Parrilleno Molecular Dynamics MethodSlab model: 4 atomic layersQM Method:DFT-GGA, PSPW (see J. A. Rodriguez et al, J. Phys. Chem. B 2000, 104, 7439.)Example 1: SO2 on MgO(100) and CuMgO(100)Eads (kcal/mol)Cu-Free 2-O,O on Mg 8 1-S on O 11 3-S,O,O 21Cu-dopping 2-O,O 28 1-S

7、 on O 25Bonding Modes of SO2 on MgO(100) SurfaceCSI Lbulkbulk()() T其基本思想在于用一小簇其基本思想在于用一小簇原子组成的簇来类比表面原子组成的簇来类比表面, 其首要问题其首要问题就是如何消除就是如何消除簇模型的簇模型的“边界效应边界效应” 。()()HbulkEbulk 定域化 LCSCSbulkT()(,)(,) T3. Cluster Model 3.1 ConceptLocalization: Adams-Gilbert Equation 1) FC: 小簇C的Fock算符，包括簇C内的动能与各种相互作用能； 2) VS

8、lr : 环境S对簇C的长程作用势，包括簇C与环境S间的电子电子、电子核、核电子、核核等四种库仑势； 3) VSsr : 环境S对簇C的短程作用势，包括簇C与环境S间的电子交换势，反映出簇C与环境S间的轨道相互作用。 4) VSsr : 定域化势（亦称屏蔽势）()FVVECSlrSsrSsrCClrCV 3.2 How to reach a successful cluster modeling? 关键问题：关键问题： 怎样选择簇模型，使之与环境的短程作用怎样选择簇模型，使之与环境的短程作用尽可能小尽可能小（必须注意，这并不意味着簇与（必须注意，这并不意味着簇与环境的相互作用能很小）环境的相互

9、作用能很小）? 怎样合理地考虑环境对簇的长程作用怎样合理地考虑环境对簇的长程作用? 3.3 Schemes of Cluster Modeling Simple Cluster Model Embedded Cluster Model (for ionic solids) Saturated Cluster Model (for covalent solids) ONIOM Model (hybrid QM/QM or QM/MM method, readily for covalent solids)3.4 Simple Cluster Model Simple cut-out ! Capa

10、city? (may give qualitatively reasonable simulation results for VDW, HB, metal and ionic solids) How to make a reasonable cut-out? How to determine the electronic state of the cluster? 3.4.1 Cluster Model for Metal SurfaceMLLMMLMMMMML MoleculeL/M ChemisorptionL/M ChemisorptionM M+(a)(a)(b)(b)(c)(c)

11、Dilemma: The larger, the more reasonable, but more expensive; the smaller, the more economical with higher accuracy, but less reasonable. Whats the way out? “Surface molecule” *H/Ni(111): Ni19 (2.75kcal/mol) Ni22(15 kcal/mol) Ni40(46.5kcal/mol) Ni4(55kcal/mol) Expt(63kcal/mol)EanEaexp Examples: 1) P

12、.S. Bagus, et al , J. Chem. Phys., 78 (1983) 1390; 2) C.W. Bauschlicher Jr., Chem. Phys. Lett., 129(1986) 586; 3) P.E.M. Siegbahn et al., Chem. Phys. Lett., 149(1988) 265.* Concept of “Metallic Atom” Two kind of motions of electrons in bulk metal: 1) Localized ; 2) Delocalized-Free electrons. The at

13、om in a bulk metal should be quite different from a simple atom, e.g.a) R(Cr-Cr):1.68 ( Cr2 ), 2.49 (bulk Cr)b) Pd atom: 4d10/ bulk Pd:(4d9.635sp0.37)Metallic Basis Functions The attractive potential of a metallic atom is: m(r) = -(Z*/r)exp(-kSr) vs a(r) = -Z*/r 1/kS - Thomas-Fermi Screening Length.

14、 Slater exponents: m = a + (1) With the help of Free Electron Theory, we have: = - ( a(n)/n (inner shell)(2) = ( a(n-1)/n (outermost valence-shell) (3)( N. Wang et al., J. Mol. Struct. (Theochem), 262(1992) 105.) )(/)(1(1)()(nn kaSaaaSennknnnMetallic m and Atomic a of Co Atom. 1s2sp3sp3d4sp a26.4711

15、.094.553.941.40 m26.4610.964.013.351.84UHF/STO-3G Calculations M-CO cluster CO-likeCo-COCO/CoNi-COCO/Ni MOs a mUPS a mUPS4 21.9916.6816.820.7516.4316.61 16.4613.1013.215.5213.3513.65 18.2712.7013.816.1412.3312.3 4 -15.533.583.0 5 -11.821.021.3X. Xu et al., Surf Sci., 274 (1992)

16、378 Choice of Multiplicity Metallic Cr: 3d5.244s0.76 (3d64s0 - 3d54s1) 3d64s0: 5, 3, 1; 3d54s1: 7, 5, 3,1 Note: UHF wavefunctions of a quintet are mixtures of wavefunctions from quintet and septet, rather than a pure quintet. Multiplicity Dependency in the UHF Calculations of Cr-CO *Fe: 3d7.344s0.61

17、/ (3d84s0 - 3d74s1)/(3),1 - 5,3,1 *Co: 3d8.374s0.63/(3d94s0 - 3d84s1)/(2) - 4,2Multipl.1(3)(5)7CO/Cr4 18.8216.8016.7417.4816.61 14.6612.6612.6013.2312.65 13.9111.6712.0312.68 Metallic State Principle M Mn M Mn MGround State Bulk Metallic StateComposition process Adiabatic decomposition proceSome rel

18、ative methods Bond-Prepared State Principle (P.E. M. Siegbahn et al., Stockholm, 1988) DAM (Dipped Adcluster Model) (H. Nakatsuji, Kyoto, 1991) Many-Electron Embedding Theory (J.L. Whitten, 1980; 1987)Example 2:NO2/Au(111)X. Lu, J.Phys.Chem. A, 103 (1999) 10969.NO2/Au21 g3 uBulkHOMO -7.00-5.63-5.30L

19、UMO-4.20-5.63-5.30Te0.01.41Properties of Au2 cluster and bulk Au (in eV)AuAu2.884 ANOOZNC2V4 g4 u4b26a1NO2Au22A11 g3 uB3LYP calculations of NO2Au2 NO2 (2A1) + Au2 (1 g) NO2Au2 (2A1) NO2 (2A1) + Au2 (3 u) NO2Au2 (2B2)2A12B2NO2/AuEtot (au)-476.02346-475.99512De (kcal/mol) 4.5 19.314.0QNO20.004-0.51Spi

20、n of NO20.64-0.13Freqs. (cm-1) (ONO)742802800 s(NO2)119512001178 as(NO2)14061465More Cluster Models: Au7 and Au12 Results omitted from here3.4.2 Simple cluster model for ionic solidsHow to cut out a cluster? Three Principles: Neutrality, Stoichiometry and Coordination Principles. Coordination number

21、 principle: 1) fewest dangling bonds at the edge of a cut-out; 2) maintain the stronger dative bonds within the cluster. X. Lu et al., 1) Chem. Phys. Lett. 291(1998) 457; 2) Int. J. Quant. Chem. 73 (1999) 377; 3) Theor. Chem. Acc. 102(1999) 179. CO/MgOX. Lu et al., J. Phys. Chem. B, 105(2001) 10024.

22、C2O32- Surface SpeciesC3O42- Surface Species3.5 Embedded Cluster Model for Ionic Solid ()FVVECSlrIsrIsrCClrCV For ionic solid, VSsr can be replaced by VIsr :For ideally ionic solid, VIsr would be negligible:ClrCClrSCEF)V(i.e. Simple embedded cluster model3.5.1 Simple embedded cluster model A cut-out

23、 cluster is embedded into an array of point charges (always in formal charge) to represent the Madelung Potential of the ionic surroundings. E = jC |C+ZZR C+ CZQR S+QQR SExample 4: CO/MgO(100) and NiO(100) See in G. Pacchioni et al. Surf. Sci. 255 (1991) 344.C-+ +-+-+-+zxO OZYXNiOSimple embedded clu

24、ster model for MgO(100) and NiO(100) ( Mg(Ni) +2; O: -2 )Demerits of simple embedded cluster model Most of the ionic solids are not ideally ionic. Hence, the ionic charges are always fractional;the short range interaction between the cut-out cluster and its surrounding is seldom negligible.Way-out:C

25、harge consistency Minimize the short range interaction.Charge Consistence between the Embedded cluster and its PCC surrounding E = jC |C+ZZR C+ CZQR S+QQR SDifferent embedding charge Q gives different C with different charges at the in-cluster atoms. Hence charge consistence between the embedding ch

26、arges and the equivalent in-cluster atoms is essential and can be readily reached. 自洽条件探讨电荷自洽偶极矩自洽电荷密度自洽偶极矩自洽势自洽SPC Embedded Cluster Model X. Lu et al, J. Phys. Chem. B 103(1999) 2689.SphericalPoint ChargesSelf-consistency of Charge DensityCutout ClusterSPC EmbeddingCoordination Principle Stoichiome

27、try PrincipleNuetrality PrincipleExample: SPC Cluster Models for MgOIsland(MgO)8(MgO)4(MgO)6(MgO)6(MgO)4(B)(A)X. Lu et al., J. Phys. Chem. B, 103(1999) 3373.O13O14Mg15Mg16NOR2R1O4O1Mg7Mg8Mg5Mg6O3O2Mg11Mg12O10O9R3R3O9O10Mg12Mg11O2O3Mg6Mg5Mg8Mg7O1O4R1R2ONMgXCOYCMgZCN1O1N2O2 MgXCOYCMgZCN1O1N2O2 X. Lu e

28、t al., J. Phys. Chem. B, 103(1999) 5657.NxOx+12- (X=1,2) Species Formed on MgO 3.6 Saturated Cluster Model for Covalent Solids Saturating the radical-like dangling bonds at the edge of the cut-outs by using suitable saturators (e.g. H or other pseudoatoms). Widely employed in the study of covalent s

29、olid surfaces, e.g., Silicon, Diamond, Zeolite and so on. Examples shown below include Chemical Reactions on Silicon Surfaces.Atomic arrangements of a) X(100)-21 (X= Si, Ge) and b) Si(111)-77 reconstructed surfaces. Side ViewbucklingThree models describing the bonding within a buckled X=X dimer Reco

30、nstruction of X(100) X= C, Si, GeCCCCCCCCCC(100)(100)In the solid state, each atom adopts sp3 hybridization and tetrahedral coordination. Two widely used cluster models for X(100)-2x1 surface X9H12 X15H162+2 addition of Alkene on Si(100) Possible pathways -complex mechanism: FTIR spectra of dideuter

31、ioethylene/Si(100) suggested that the adsorption is stereospecific and stereoselective. (Liu et al., J. Am. Chem. Soc., 1997, 119, 7593.) Radical mechanism: STM images of 2-butene/Si(100) indicates the adsorption is not stereospecific, thought with a high stereoselectivity of 98%. (Lopinski et al.,

32、J. Am. Chem. Soc., 2000, 122, 3548.)Controversy on the Mechanism X. Lu, J. Am. Chem. Soc. 2003, 125, 63843.4841.4811.9442.390124312341.4781.9512.3933.965LM2TS213422.3951.9181.494113.6TS32.4012.4012.3631.364107.8LM11.3842.2882.9412.324113.5TS1114.6109.2LM31.9531.9532.3591.57178.23.946 E = -1.6 = 0.0

33、E = 4.2 = 0.41 E = -3.3 = 1.01 E = -3.1 = 0.95 E = -0.7 = 0.99 E = -42.5 = 0.00C4H4X(X=S,O) on Si(100)-2x1 surfaceX. Lu et al, J. Phys. Chem. B, 105(2001) 10069.C9H121.364Example: HN3 reaction with C(100)-2x1HN3 +C(100)TS1 7.3(5.1)TS1 2.5(1.0) LM1 -62.5(-68.3) TS2 -8.8(-11.1) LM1 -61.0(-64.4) LM2 -7

34、0.7(-72.6) TS2 -24.1(-28.1) LM2 -66.2(-69.1)+ N2(g)+N2(g) 0.0(0.0)X. Lu et al., Chem. Phys. Lett. 343(2001) 212.1,3-Dipolar Cycloadditions on C(100)-2x1CNC1.5021.5431.5971.2791.481CNC1.0961.2241.279172.8109.4CNC1.0951.2221.283163.32.9681.3762.903CN1.1971.246CNN1.0871.0931.397109.91.4671.5001.5941.28

35、9Nitrile YlideTS_1LM_1LM_2Nitrile ImineN169.51.080TS_2CNN1.0801.2021.250160.12.8892.8801.374X. Lu et al., 1) J. Org. Chem. 67(2002) 515; 2) J. Phys. Chem. B, 106(2002) in press.CNO1.0651.1631.212CNO1.2141.187156.92.5722.8241.380CNO1.0861.412110.01.4401.4931.5821.284LM_3TS_3Nitrile OxideCNN1.2961.146

36、CNN1.1481.317159.22.5372.701CNN1.244112.91.4701.5241.5891.5081.388DiazomethaneTS_4LM_4LM_5Methyl AzideNitrous OxideTS_6LM_6NNN1.4751.2341.143173.1NNO1.1331.1952.3272.4751.3931.2171.156149.7NNONNN1.4661.2501.159151.12.4451.3882.580TS_5NNN1.4491.4681.5841.3701.261113.51.446NNO112.51.4661.2271.4601.420

37、1.578Example: NH3 on Si(111)-7x7Side ViewTop Viewa)12346101211137891615145X. Lu et al, Chem. Phys. Lett. 355(2002) 365.Pro Energy SurfaceOrganic functionalization of Si(111)12341234arrac) TS1td) TS2t1.932.011.511.341.583.55b) LM1t4.391.941.491.391.404.79ar12344.40ara) Trans-C4H6 & Si16H1813421.3

38、41.461234are) LM2tf) LM3t1.931.961.501.341.504.471.344.424.161.941.491.391.39ra12341.933.883.201.511.431.37 E = 0.0 E = -16.3 E = -16.1 E = -10.9 E = -59.4 E = -40.2 S = 1.00 S = 1.03 S = 1.02 S = 0.66(X. Lu et al, J. Am. Chem. Soc. 2003, 125, 7923)Benzene/Si(111)b) LM1brc) TS2be) LM2b E= 6.7 E= 7.7

39、 E=-21.5a) TS1b E = 9.2a1.991.491.371.421.421.371.494.381234564.315.58ra1.391.441.441.411.391.412.344.401234561623452.01ar4.394.541.491.371.421.421.371.49123456ra1.982.011.341.511.51ra4.122345611.941.583.542.031.511.351.461.351.52f) LM3b E= -5.7ar1234561.973.003.841.511.411.381.441.361.50 E=12.1d) T

40、S3b S = 1.03 S = 1.02 S = 0.35 S = 1.02Prediction: C4H2 on X(100) Possible pathways E = 1.1 = 0.00TS2 E = -20.3 = 0.901.9261.332.45147.81.911.2851.926LM2 E = -59.8 = 0.00LM1TS1 E =-60.1 = 0.005LM322113344SOSP E = -20.8 = 1.03 E = -19.1 = 0.8634561.372.361.451.221.35167.812345612345612345

41、6122.391.901.311.321.24114.2123.52.381.891.321.341.233.282.391.921.321.341.233.47103.7114.0Is the direct 4+2 pathway realistic? No!The key point P4 on this pathway is indeed diradicaloid! Its UB3LYP wavefunction is 3.4 kcal/mol more stable than the RB3LYP one! Si9H122.22P11.37C4H223411.211.0756(-1.2

42、)P2P3P4P5LM13.012.572.272.021.941.921.922.183.54(-1.6)(-9.6)(-62.3)(-48.6)(-3.0)C4H2/Ge(100)PESIs the direct 4+2 pathway realistic? No!The key point P4b on this pathway is indeed diradicaloid! Its UB3LYP wavefunction is more stable than the RB3LYP one!C4H2/Si(111): PredictionPESouter layerinner laye

43、rA(set 1)B (set 3)H (set 2)X (set 4)Model System = A + HReal System = A + BEONIOM= Ehow(A+H) Elow(A+H) + Elow(A+B)(K. Morokuma et al., J. Mol. Struct. (Theochem) 461-462(1999) 1.)3.7 ONIOM ModelAdsorption of Methanol, Formaldehyde and Formic Acid on Si(100)-2 1 Surface ( see X. Lu et al., Phys. Chem

44、. Chem. Phys. 3(2001) 2156.) E(kcal/mol)0TSReaction CoordinateLM1LM2-67.6(-67.9)-12.6(-14.6)-18.5(-16.9)MethanolCCSD(T):B3LYPSi2H4Si9H12formaldehyde12OC1.7112.3441.4571.9751.09681.5109.2105.370.9C2a)12.367107.31.9581.210126.2121.01.082120.61.081b)OLM1LM2LM3TSLM4COO12OCO12COO1221COOOCO12Formic acidb)

45、 ONIOM中最内层的中最内层的C24簇簇a) SWNT(10,0)片断片断Sidewall functionalization by F and H (Bauschilicher, Chem. Phys. Lett. 322(2000) 237.)ONIOM(B3LYP:UFF) F atoms appear to favor bonding next to existing F atoms. Hydrogenation of the sidewall of SWNT is probably endothermic.Results:Sidewall Functionalization of

46、SWNT by1,3-Dipolar CycloadditionsSWNT(5,5) 片断片断ONIOM(B3LYP/6-31G*:AM1)Predicted Reaction Energies (kcal/mol)123CC+HCNCH2CCHCNCH21,3-DC of nitrile ylide with an olefinSWNTC2H4(1,2)(2,3)HCNCH2-45.2-16.0 -72.1HCNO-20.29.945.9O3-38.7-6.3-56.6X. Lu et al., 1) J. Phys. Chem. B, 106(2002), 2136; 2) J. Am.

47、Chem. Soc., 2003, 125, 10459-10464.33.8 Cluster modeling of electrodes Charged cluster: Cluster Cluster in electric field. More realistic models are required.- - - - - -+ + + + +Liao, M. et al. Int. J. Quant. Chem., 67(1998), 175.Concluding Remarks Methods of simulation vary with and depend largely

48、on the solids to be concerned. A simulation process is meaningless itself, unless certain physical criteria have been introduced to guarantee the consistence between the physical model and the real physical system. More significant is the scientific problem to be concerned. Simulation can be found e

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