固体表面化学的理论研究方法、模型和应用
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固体表面化学的理论研究方法、模型和应用. 吕鑫 2005.5.19. State 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. 理论模型. 理论方法. 物理体系. 物理、化学性质 (实验研究). 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 方法、模型与应用. 分类 ( 理论方法、模型方法、物理体系) 层板模型方法与应用 ( Slab Model and Its Applications)

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固体表面化学的理论研究方法、模型和应用

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5189415

固体表面化学的理论研究方法、模型和应用

吕鑫

2005.5.19

State 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


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理论模型

理论方法

物理体系

物理、化学性质

(实验研究)

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


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固体表面化学的理论研究方法、模型与应用

  • 分类(理论方法、模型方法、物理体系)

  • 层板模型方法与应用(Slab Model and Its Applications)

    3. 簇模型方法及其应用(Cluster Model and Its Applications)


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分类

  • 理论方法分类:

    经典力学方法(MM, MD, MC) 、量子力学方法 (DFT, HF, CI) 、杂交方法(QM/MM, AIMD) 、其他半经验方法(AM1,PM3等)

  • 模型分类:

    局域模型(簇模型方法)、周期性模型

    3. 应用体系分类:

    共价体系、离子体系、金属体系、HB体系、VDW体系


2 slab model 2 1 first principle method

2 Slab Model2.1 First-Principle Method

  • 量子化学问题均在于求解Schrödinger方程,对于大块固体,其Schrödinger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。

    Solutions: Introducing some approximations.


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A. Born-Oppenheimer Approximation:

H({Rm}) '(rn)= E({Rm}) '(rn) (1.2)

(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)

C. Energy Band Theory (DFT) and Crystal Orbital Theory (HF)

(see A. Gross, Surf. Sci. Rep. 1998, 32, 291)


2 2 density functional theory kohn sham equation

2.2 Density functional Theory, Kohn-Sham Equation

Eec(n) exchange-correlation functional

ec(n) exchange-correlation energy per particle


2 3 pspw and super cell

2.3 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 Solid Surface

  • Car-Parrilleno Molecular Dynamics Method


Example 1 so 2 on mgo 100 and cumgo 100

Example 1: SO2 on MgO(100) and CuMgO(100)

Slab model:

4 atomic layers

QM Method:

DFT-GGA, PSPW

(see J. A. Rodriguez et al, J. Phys. Chem. B 2000, 104, 7439.)


Bonding modes of so 2 on mgo 100 surface

Bonding Modes of SO2 on MgO(100) Surface

Eads (kcal/mol)

Cu-Free

2-O,O on Mg 8

1-S on O 11

3-S,O,O 21

Cu-dopping

2-O,O 28

1-S on O 25


3 cluster model 3 1 concept

3. Cluster Model 3.1 Concept

其基本思想在于用一小簇原子组成的簇来类比表面, 其首要问题就是如何消除簇模型的“边界效应” 。

定域化


Localization adams gilbert equation

Localization: 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)     VSlr :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)      ρ VSsr ρ: 定域化势(亦称屏蔽势)


3 2 how to reach a successful cluster modeling

3.2 How to reach a successful cluster modeling?

关键问题:

  • 怎样选择簇模型,使之与环境的短程作用尽可能小(必须注意,这并不意味着簇与环境的相互作用能很小)?

  • 怎样合理地考虑环境对簇的长程作用?


3 3 schemes of cluster modeling

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

3.4 Simple Cluster Model

  • Simple cut-out !!!!!

  • Capacity? (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 surface

3.4.1 Cluster Model for Metal Surface

  • Dilemma: The larger, the more reasonable, but more expensive; the smaller, the more economical with higher accuracy, but less reasonable.

  • What’s the way out?

“Surface molecule”


Convergence problem

Convergence problem

*H/Ni(111):

Ni19 (2.75kcal/mol)

Ni22(15 kcal/mol)

Ni40(46.5kcal/mol)

Ni4(55kcal/mol)

Expt(63kcal/mol)

  • Examples: 1) P.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

Concept of “Metallic Atom”

  • Two kind of motions of electrons in bulk metal: 1) Localized ; 2) Delocalized--Free electrons.

  • The atom in a bulk metal should be quite different from a simple atom, e.g.

    a) R(Cr-Cr):1.68 Å ( Cr2 ), 2.49 Å (bulk Cr)

    b) Pd atom: 4d10// bulk Pd:(4d9.635sp0.37)


Metallic basis functions

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: 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.)


Metallic m and atomic a of co atom

1s

2sp

3sp

3d

4sp

a

26.47

11.09

4.55

3.94

1.40

m

26.46

10.96

4.01

3.35

1.84

Metallic m and Atomic a of Co Atom.


Uhf sto 3g calculations m co cluster

CO-like

Co-CO

CO/Co

Ni-CO

CO/Ni

MO’s

a

m

UPS

a

m

UPS

4

21.99

16.68

16.8

20.75

16.43

16.6

1

16.46

13.10

13.2

15.52

13.35

13.6

5

18.27

12.70

13.8

16.14

12.33

12.3

4-1

5.53

3.58

3.5

5.23

3.08

3.0

5-1

1.81

0.4

0.6

0.62

1.02

1.3

UHF/STO-3G Calculations M-CO cluster

X. Xu et al., Surf Sci., 274 (1992) 378


Choice of multiplicity

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

Multipl.

1

(3)

(5)

7

CO/Cr

4

18.82

16.80

16.74

17.48

16.6

1

14.66

12.66

12.60

13.23

12.6

5

13.91

11.67

12.03

12.68

Multiplicity Dependency in the UHF Calculations of Cr-CO

  • *Fe: 3d7.344s0.61// (3d84s0 - 3d74s1)//(3),1 - 5,3,1

  • *Co: 3d8.374s0.63//(3d94s0 - 3d84s1)//(2) - 4,2


Metallic state principle

Metallic State Principle

M Mn M Mn M

Ground State Bulk Metallic State

Composition process Adiabatic decomposition proce


Some relative methods

Some relative 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 no 2 au 111

Example 2:NO2/Au(111)

X. Lu, J.Phys.Chem. A, 103 (1999) 10969.


No 2 au 2

Properties of Au2 cluster and bulk Au (in eV)

NO2/Au2


B3lyp calculations of no 2 au 2

B3LYP calculations of NO2Au2

  • NO2 (2A1) + Au2 (1g)  NO2Au2 (2A1)

  • NO2 (2A1) + Au2 (3u)  NO2Au2 (2B2)


More cluster models au 7 and au 12

More Cluster Models: Au7 and Au12

  • Results omitted from here


3 4 2 simple cluster model for ionic solids

3.4.2 Simple cluster model for ionic solids

How to cut out a cluster?

  • Three Principles: Neutrality, Stoichiometry and Coordination Principles.

  • Coordination number 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 mgo

CO/MgO

X. Lu et al., J. Phys. Chem. B, 105(2001) 10024.


C 2 o 3 2 surface species

C2O32- Surface Species


C 3 o 4 2 surface species

C3O42- Surface Species


3 5 embedded cluster model for ionic solid

3.5 Embedded Cluster Model for Ionic Solid

For ionic solid, VSsrcan be replaced byVIsr:

For ideally ionic solid, VIsrwould be negligible:

i.e. Simple embedded cluster model


3 5 1 simple embedded cluster model

3.5.1 Simple embedded cluster model

  • A cut-out cluster is embedded into an array of point charges (always in formal charge) to represent the Madelung Potential of the ionic surroundings.


Example 4 co mgo 100 and nio 100

Example 4: CO/MgO(100) and NiO(100)

  • See in G. Pacchioni et al. Surf. Sci. 255 (1991) 344.

Simple embedded cluster model for MgO(100) and NiO(100) ( Mg(Ni) +2; O: -2 )


Demerits of simple embedded cluster model

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 range interaction.


Charge consistence between the embedded cluster and its pcc surrounding

Charge Consistence between the Embedded cluster and its PCC surrounding

Different 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 is essential and can be readily reached.


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自洽条件探讨

电荷自洽

偶极矩自洽

势自洽

电荷密度自洽

偶极矩自洽


Spc embedded cluster model

SPC Embedded Cluster Model

Cutout Cluster

SPC Embedding

Nuetrality Principle

Coordination Principle

Spherical

Point Charges

Self-consistency of Charge Density

Stoichiometry Principle

X. Lu et al, J. Phys. Chem. B 103(1999) 2689.


Example spc cluster models for mgo

Example: SPC Cluster Models for MgO

X. Lu et al., J. Phys. Chem. B, 103(1999) 3373.


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NxOx+12- (X=1,2) Species Formed on MgO

X. Lu et al., J. Phys. Chem. B, 103(1999) 5657.


3 6 saturated cluster model for covalent solids

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, Zeolite and so on.

  • Examples shown below include Chemical Reactions on Silicon Surfaces.


Atomic arrangements of a x 100 2 1 x si ge and b si 111 7 7 reconstructed surfaces

Atomic arrangements of a) X(100)-21 (X= Si, Ge) and b) Si(111)-77 reconstructed surfaces.

buckling


Three models describing the bonding within a buckled x x dimer

Reconstruction of X(100) X= C, Si, Ge

Three models describing the bonding within a buckled X=X dimer

In the solid state, each atom adopts sp3 hybridization and tetrahedral coordination.


Two widely used cluster models for x 100 2x1 surface

Two widely used cluster models for X(100)-2x1 surface

  • X9H12 X15H16


2 2 addition of alkene on si 100

[2+2] addition of Alkene on Si(100)

  • Possible pathways


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Controversy on the Mechanism

  • p-complex mechanism:

  • FTIR spectra of dideuterioethylene/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., J. Am. Chem. Soc., 2000, 122, 3548.)


X lu j am chem soc 2003 125 6384

X. Lu, J. Am. Chem. Soc. 2003, 125, 6384


C 4 h 4 x x s o on si 100 2x1 surface

C4H4X(X=S,O) on Si(100)-2x1 surface

X. Lu et al, J. Phys. Chem. B, 105(2001) 10069.


Example hn 3 reaction with c 100 2x1

Example: HN3 reaction with C(100)-2x1

X. Lu et al., Chem. Phys. Lett. 343(2001) 212.


1 3 dipolar cycloadditions on c 100 2x1

1,3-Dipolar Cycloadditions on C(100)-2x1

X. Lu et al., 1) J. Org. Chem. 67(2002) 515; 2) J. Phys. Chem. B, 106(2002) in press.


Example nh 3 on si 111 7x7

Example: NH3 on Si(111)-7x7

X. Lu et al, Chem. Phys. Lett. 355(2002) 365.


Profile of energy surface

Profile of Energy Surface


Organic functionalization of si 111

Organic functionalization of Si(111)

(X. Lu et al, J. Am. Chem. Soc. 2003, 125, 7923)


Benzene si 111

Benzene/Si(111)


Prediction c 4 h 2 on x 100

Prediction: C4H2 on X(100)

  • Possible pathways


Is the direct 4 2 pathway realistic no

Is 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!!!


C 4 h 2 ge 100

C4H2/Ge(100)

PES


Is the direct 4 2 pathway realistic no1

Is 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!!!


C 4 h 2 si 111 prediction

C4H2/Si(111): Prediction

PES


3 7 oniom model

Model System = A + H

Real System = A + B

outer layer

X (set 4)

inner layer

A(set 1)

H (set 2)

B (set 3)

3.7 ONIOM Model

EONIOM= Ehow(A+H) – Elow(A+H) + Elow(A+B)

(K. Morokuma et al., J. Mol. Struct. (Theochem) 461-462(1999) 1.)


Adsorption of methanol formaldehyde and formic acid on si 100 2 1 surface

Adsorption of Methanol, Formaldehyde and Formic Acid on Si(100)-21 Surface

( see X. Lu et al., Phys. Chem. Chem. Phys. 3(2001) 2156.)

Methanol

[email protected]

CCSD(T):B3LYP


Formaldehyde

formaldehyde


Formic acid

Formic acid


Sidewall functionalization by f and h bauschilicher chem phys lett 322 2000 237

Sidewall functionalization by F and H (Bauschilicher, Chem. Phys. Lett. 322(2000) 237.)

a) SWNT(10,0)片断

b) ONIOM中最内层的C24簇

ONIOM(B3LYP:UFF)

Results:

  • F atoms appear to favor bonding next to existing F atoms.

  • Hydrogenation of the sidewall of SWNT is probably endothermic.


Sidewall functionalization of swnt by1 3 dipolar cycloadditions

Sidewall Functionalization of SWNT by1,3-Dipolar Cycloadditions

ONIOM(B3LYP/6-31G*:AM1)

1,3-DC of nitrile ylide with an olefin

Predicted Reaction Energies (kcal/mol)

1

3

2

3

SWNT(5,5) 片断

X. Lu et al., 1) J. Phys. Chem. B, 106(2002), 2136; 2) J. Am. Chem. Soc., 2003, 125, 10459-10464.


3 8 cluster modeling of electrodes

3.8 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

Concluding Remarks

  • Methods of simulation vary with and depend largely 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 everywhere nowadays.


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