【精品文檔】納米結(jié)構(gòu)體系物理化學(xué)性質(zhì)的理論研究方法與實例

1、固體表面化學(xué)的理論研究固體表面化學(xué)的理論研究方法、模型和應(yīng)用方法、模型和應(yīng)用呂鑫呂鑫 State Key Laboratory for Physical Chemistry of Solid Surfaces廈門大學(xué)固體表面物理化學(xué)國家重點實驗室物理體系物理、化學(xué)性質(zhì)（實驗研究）理論模型理論方法表面吸附是固體表面化學(xué)研究的一個中心問題，是一切表面化學(xué)現(xiàn)象的根源固體表面化學(xué)的理論研究固體表面化學(xué)的理論研究 方法、模型與應(yīng)用方法、模型與應(yīng)用分類分類(理論方法、模型方法、物理理論方法、模型方法、物理體系）體系）層板模型方法與應(yīng)用層板模型方法與應(yīng)用（Slab Model and Its Applica

2、tions)3. 簇模型方法及其應(yīng)用簇模型方法及其應(yīng)用（Cluster Model and Its Applications) 分類分類理論方法分類：理論方法分類： 經(jīng)典力學(xué)方法（經(jīng)典力學(xué)方法（MM, MD, MC) 、量子力學(xué)方、量子力學(xué)方法法 (DFT, HF, CI) 、雜交方法（、雜交方法（QM/MM, AIMD) 、其他半經(jīng)驗方法（、其他半經(jīng)驗方法（AM1，PM3等）等）模型分類：模型分類： 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. 應(yīng)用體系分類：應(yīng)用體系分類： 共價體系、離子體系、金屬體系、共價體系、離子體系、金屬體系、HB體系、體系、VDW體系體系

3、2 Slab Model 2.1 First-Principle Method 量子化學(xué)問題均在于求解量子化學(xué)問題均在于求解Schrdinger方程，對方程，對于大塊固體，其于大塊固體，其Schrdinger方程表示為：方程表示為： H (Rm,rn) = E (Rm,rn) (1.1) Problem: H將是無限維的，上式很難求解。將是無限維的，上式很難求解。 Solutions: Introducing some approximations. A. Born-Oppenheimer Approximation: H(Rm) (rn) = E(Rm) (rn) (1.2) (核運動和電子

4、運動分離)B. Single-Particle Approximation for Solving The Wavefunctions of Electrons (電子波函數(shù)的單粒子近似電子波函數(shù)的單粒子近似)C. Energy Band Theory (DFT) and Crystal Orbital Theory (HF) (see A. Gross, Surf. Sci. Rep. 1998, 32, 291)()()()(2)()min(min(22rrrVrVmrHnVnUnTnEEiiiecesiectotrdrnrnnEnnErVecececec3)()()(E Eec(n) e

5、xchange-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 Model for

6、 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 on O 25B

7、onding 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組成的簇來類比表面原子組成的簇來類比表面, 其首要問題其首要問題就是如何消除就是如何消除簇模型的簇模型的“邊界效應(yīng)邊界效應(yīng)” 。()()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內(nèi)的動能與各種相互作用能； 2) VSlr : 環(huán)境S對

8、簇C的長程作用勢，包括簇C與環(huán)境S間的電子電子、電子核、核電子、核核等四種庫侖勢； 3) VSsr : 環(huán)境S對簇C的短程作用勢，包括簇C與環(huán)境S間的電子交換勢，反映出簇C與環(huán)境S間的軌道相互作用。 4) VSsr : 定域化勢（亦稱屏蔽勢）()FVVECSlrSsrSsrCClrCV 3.2 How to reach a successful cluster modeling? 關(guān)鍵問題：關(guān)鍵問題： 怎樣選擇簇模型，使之與環(huán)境的短程作用怎樣選擇簇模型，使之與環(huán)境的短程作用盡可能小盡可能?。ū仨氉⒁猓@并不意味著簇與（必須注意，這并不意味著簇與環(huán)境的相互作用能很?。┉h(huán)境的相互作用能很小）? 怎

9、樣合理地考慮環(huán)境對簇的長程作用怎樣合理地考慮環(huán)境對簇的長程作用? 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 ! Capacity? (ma

10、y 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) Dilemma:

11、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.S. Bagus

12、, 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 atom in a b

13、ulk 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:(4d5sp)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. Slater exponents

14、: 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 a26.4711.094.553.941.40 m

15、26.4610.964.013.351.84UHF/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) 378 Choice of Mul

16、tiplicity Metallic Cr: 3d4s (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: 3d4s/ (3d84s0 - 3d74s1)/(3),1 - 5,3,1

17、 *Co: 3d4s/(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 relative methods Bond-Prepared State Princip

18、le (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 -7.00-5.63-5.30LUMO-4.20-5.63-5.30Te0.01.41Properties of

19、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 19.314.0QNO20.004-0.51Spin of NO20.64-0.13Freqs. (cm-1) (ONO)74280

20、2800 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 principle: 1) fewest dangling bonds at t

21、he 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.C2O32- Surface SpeciesC3O42- Surface Spec

22、ies3.5 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 cluster is embedded into an array of poi

23、nt 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 cluster model for MgO(100) and NiO(100) ( Mg

24、(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:Charge consistency Minimize the short rang

25、e 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 charges and the equivalent in-cluster atoms

26、 is essential and can be readily reached. 自洽條件探討電荷自洽偶極矩自洽電荷密度自洽偶極矩自洽勢自洽SPC Embedded Cluster Model X. Lu et al, J. Phys. Chem. B 103(1999) 2689.SphericalPoint ChargesSelf-consistency of Charge DensityCutout ClusterSPC EmbeddingCoordination Principle Stoichiometry PrincipleNuetrality PrincipleExample:

27、 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 et al., J. Phys. Chem. B, 103(1999) 5657.N

28、xOx+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 solid surfaces, e.g., Silicon, Diamond, Ze

29、olite 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 Reconstruction of X(100) X= C, Si, GeCCCCCCCC

30、CC(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 dideuterioethylene/Si(100) suggested that the ads

31、orption 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., J. Am. Chem. Soc., 2000, 122, 3548.)Contr

32、oversy 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 E = 4.2 = 0.41 E = -3.3 = 1.01 E = -3.1 =

33、 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 -70.7(-72.6) TS2 -24.1(-28.1) LM2 -66.2(-69

34、.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)-2x1CNC1.5021.5431.5971.2791.481CNC1.0961.2241.279172.8109.4CNC1.0951.2221.283163.32.9681.3762.903CN1.1971.246CNN1.0871.0931.397109.91.4671.5001.5941.289Nitrile YlideTS_1LM_1LM_2Nitrile ImineN1

35、69.51.080TS_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 OxideCNN1.2961.146CNN1.1481.317159.22.5372.701CNN1.244112.9

36、1.4701.5241.5891.5081.388DiazomethaneTS_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_5NNN1.4491.4681.5841.3701.261113.51.446NNO112.51.4661.2271.4601.4201.578Example: NH3 on Si(111)-7x7Side View

37、Top Viewa)12346101211137891615145X. Lu et al, Chem. Phys. Lett. 355(2002) 365.Profile of 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 & Si16H1813421.341.461234are) LM2tf) LM3t1.931.961

38、.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 E=-21.5a) TS1b E = 9.2a1.991.491.

39、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) TS3b S = 1.03 S = 1.02 S = 0.35 S =

40、 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 = 0.8634561.372.361.451.221.35167.8123456123456123456122.391.901.311.321.24114.2123.52

41、.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)P2P3P4P5LM13.012.572.272.021.941.

42、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 layerA(set 1)B (set 3)H (set 2)X (set

43、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. Chem. Phys. 3(2001) 2156.) E(kca

44、l/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) ONIOM中最內(nèi)層的中最內(nèi)層的C24簇簇a) SWNT(10,0)

45、片斷片斷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 SWNT by1,3-Dipolar CycloadditionsS

46、WNT(5,5) 片斷片斷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. Chem. Soc., 2003, 125, 10459-10464

47、.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 on the solids to be concerned. A s

48、imulation 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 everywhere nowadays.厗邆篳決欌榕唻煜窫鮇鬼傯畏巺杙

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