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...
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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
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 方法、模型与应用
1.分类 (理论方法、模型方法、物理体系）
2.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)
分类1. 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）
2. 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
• 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.
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
[)(
])[][][min(]][min(
22
rrrVrVm
rH
nVnUnTnEE
iiieces
i
ectot
rdrnrnnE
n
nErV
ecec
ecec
3)]([)(][
][)(
ec(n) exchange-correlation functional
ec(n) exchange-correlation energy per particle
2.2 Density functional Theory, Kohn-Sham Equation
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
Slab model:
4 atomic layers
QM 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 21
Cu-dopping
2-O,O 28
1-S on O 25
Bonding Modes of SO2 on MgO(100) Surface
CS
I
L bulk bulk( ) ( )T
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” 。
( ) ( )H bulk E bulk 定域化
L C S C Sbulk T( ) ( , ) ( , ) T
3. Cluster Model 3.1 Concept
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）
( )F V V EC Slr
Ssr
Ssr
C Clr
C V
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
• 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? (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
M
L L
M
M
L
M M M
M
ML Molecule L/M Chemisorption
M+
(a)(b) (c)
• 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 problemConvergence problem
*H/Ni(111):
Ni19 (2.75kcal/mol)
Ni22(15 kcal/mol)
Ni40(46.5kcal/mol)
Ni4(55kcal/mol)
Expt(63kcal/mol)
Ea
n
Eaexp
• 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”
• 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 • 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.)
)(/)
)(1(1)())(( nnk
a
Saa
aSen
nknnn
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
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
X. Xu et al., Surf Sci., 274 (1992) 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 ar
e 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// (3d84s0 - 3d74s1)//(3),1 - 5,3,1• *Co: 3d8.374s0.63//(3d94s0 - 3d84s1)//(2) - 4,2
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
Metallic State Principle
M Mn M Mn MGround State Bulk Metallic StateComposition process Adiabatic decomposition proce
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:NO2/Au(111)X. Lu, J.Phys.Chem. A,
103 (1999) 10969.
NO2/Au21g
3u Bulk
HOMO -7.00 -5.63 -5.30
LUMO -4.20 -5.63 -5.30
Te 0.0 1.41
Properties of Au2 cluster and bulk Au (in eV)
Au Au2.884 A
N
O O
ZN
C2V
4g
4u
4b2
6a1
NO2 Au22A1
1g3u
B3LYP calculations of NO2Au2
• NO2 (2A1) + Au2 (1g) NO2Au2 (2A1)
• NO2 (2A1) + Au2 (3u) NO2Au2 (2B2)2A1
2B2 NO2/Au
Etot (au) -476.02346 -475.99512
De (kcal/mol) 4.5 19.3 ~14.0
QNO2 0.004 -0.51
Spin of NO2 0.64 -0.13
Freqs. (cm-1)
(ONO) 742 802 800
s(NO2) 1195 1200 1178
as(NO2) 1406 1465
More Cluster Models: Au7 and
Au12
• Results omitted from here
3.4.2 Simple cluster model for ionic solidsHow to cut out a cluster?• Three Principles: Neutrality, Stoichiometry
and Coordination Principles. • Coordination number principle: 1) fewest d
angling 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
X. Lu et al., J. Phys. Chem. B, 105(2001) 10024.
C2O32- Surface Species
C3O42- Surface Species
3.5 Embedded Cluster Model for Ionic Solid
( )F V V EC Slr
Isr
Isr
C Clr
C V
For ionic solid, VSsr can be replaced by VI
sr :
For ideally ionic solid, VIsr would be negligible:
ClrCC
lrSC EF )V(
i.e. 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.
E = < C | TiiC
–iC
Zri
C
–iC
Qri
S
+ 1rij
i> jC
|C>
+ZZ
R
>C+
C
ZQ
RS
R
>S
Example 4: CO/MgO(100) and NiO(100)
• See in G. Pacchioni et al. Surf. Sci. 255 (1991) 344.
C
-
-
-
-
+ +
+
++
+
+
+
+
++++
+ +
+++
-
-
-
-
-
-
-
-
-
--
--
+
+
+
-
+
-
--
-
--
- -
++
++
+
+
+
+
+
+
+
z xO
Z
Y
X
Ni
O
Simple embedded cluster 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,
1) the ionic charges are always fractional;
2) the short range interaction between the cut-out cluster and its surrounding is seldom negligible.
Way-out:
1) Charge consistency
2) Minimize the short range interaction.
Charge Consistence between the Embedded cluster and its PCC surrounding
E = < C | TiiC
–iC
Zri
C
–iC
Qri
S
+ 1rij
i> jC
|C>
+ZZ
R
>C+
C
ZQ
RS
R
>S
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.
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 Charges
SphericalPoint Charges
Self-consistency of Charge Density
Self-consistency of Charge Density
Cutout ClusterCutout ClusterSPC EmbeddingSPC Embedding
Coordination Principle
Coordination Principle
Stoichiometry Principle
Stoichiometry Principle
Nuetrality Principle
Nuetrality Principle
Example: SPC Cluster Models for MgO
Island
(MgO)8
(MgO)4
(MgO)6(MgO)6
(MgO)4
(B) (A)
X. Lu et al., J. Phys. Chem. B, 103(1999) 3373.
O13
O14
Mg15
Mg16
NO
R2
R1
O4
O1Mg7
Mg8
Mg5
Mg6
O3
O2
Mg11
Mg12
O10
O9
R3R3
O9
O10
Mg12
Mg11
O2
O3
Mg6
Mg5
Mg8
Mg7 O1
O4
R1R2
O
N
MgXC OYC MgZC
N1O1
N2
O2
MgXC OYC MgZC
N1O1
N2
O2
X. Lu et 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 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)-21 (X= Si, Ge) and b) Si(111)-77 reconstructed surfaces.
Side View
buckling
Three models describing the bonding within a buckled X=X dimer
C
C
CC
C
Reconstruction of X(100) X= C, Si, Ge
C C
C C
C
C C
C C
C
(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 X15H16
[2+2] addition of Alkene on Si(100)
• Possible pathways
• -complex mechanism: FTIR spectra of dideuterioethylene/Si(100) suggested that the adsorption is stereospecific and stereoselective. (Liu et al., J. Am. Chem. Soc., 199
7, 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.)
Controversy on the Mechanism
X. Lu, J. Am. Chem. Soc. 2003, 125, 6384
3.484
1.481
1.944
2.3901 2
4
3
1 2
3
41.478
1.951
2.393
3.965
LM2
TS2
1
3
4
22.395
1.918
1.494
113.6
TS3
2.401
2.401
2.363
1.364
107.8
LM1
1.384
2.288
2.941
2.324
113.5
TS1
114.6
109.2
LM3
1.953 1.953
2.359
1.571
78.23.946
E = -1.6<S2> = 0.0
E = 4.2<S2> = 0.41
E = -3.3<S2> = 1.01
E = -3.1<S2> = 0.95
E = -0.7<S2> = 0.99
E = -42.5<S2> = 0.00
C4H4X(X=S,O) on Si(100)-2x1 surface
X. Lu et al, J. Phys. Chem. B, 105(2001) 10069.
C9H12
1.364
Example: HN3 reaction with C(100)-2x1
HN3 +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(-69.1)
+ 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)-2x1
C
N
C
1.502 1.543
1.597
1.279 1.481
C N C1.096 1.224 1.279
172.8
109.4
C N C1.095 1.222 1.283
163.3
2.968
1.376
2.903
C N1.197 1.246
C
N
N1.0871.093
1.397
109.9
1.4671.500
1.594
1.289
Nitrile Ylide
TS_1
LM_1 LM_2
Nitrile Imine
N169.5
1.080
TS_2
C NN
1.0801.202 1.250
160.1
2.889 2.880
1.374
X. Lu et al., 1) J. Org. Chem. 67(2002) 515; 2) J. Phys. Chem. B, 106(2002) in press.
C N O1.065 1.163 1.212
CN O
1.2141.187
156.9
2.572 2.824
1.380
C
N
O1.0861.412
110.0
1.4401.493
1.582
1.284
LM_3
TS_3
Nitrile Oxide
C N N1.296 1.146
CN N
1.1481.317
159.2
2.537 2.701
C
N
N1.244
112.9
1.4701.524
1.589
1.508
1.388
Diazomethane
TS_4
LM_4 LM_5
Methyl Azide Nitrous Oxide
TS_6
LM_6
N N N1.475 1.234 1.143
173.1
N N O1.133 1.195
2.327 2.475
1.393
1.2171.156
149.7N
N ON NN
1.4661.250 1.159
151.1
2.445
1.388
2.580
TS_5
NN
N1.449 1.468
1.584
1.370 1.261
113.51.446
NN
O112.5
1.4661.227
1.460 1.420
1.578
Example: NH3 on Si(111)-7x7
Side View
Top View
a)
1
2
3
46
1012
11
13
7
8
9
1615
14
5
X. Lu et al, Chem. Phys. Lett. 355(2002) 365.
Profile of Energy Surface
E(kcal/mol)
0
TS1a
Reaction Coordinate
LM1a
LM2a-68.6(-68.1)
-28.6(-28.4)
-30.7(-27.4)
NH3(g)
Si(111)
LM1r
TS1r
LM2r
-39.6(-36.2)
-32.5(-32.6)
-66.5(-65.9)
Organic functionalization of Si(111)
1234
1
23
4a
rr
a
c) TS1t
d) TS2t
1.93
2.01
1.51
1.34
1.58
3.55
b) LM1t
4.39
1.941.49
1.391.40
4.79a
r
1234
4.40 a
r
a) Trans-C4H6 & Si16H18
134
21.34
1.46
123
4 a
r
e) LM2t f) LM3t
1.93
1.96
1.501.34
1.50
4.47
1.34
4.424.16
1.941.49
1.391.39
r
a
12
341.93
3.883.20
1.51
1.431.37
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) LM1b
r
c) TS2be) LM2b
E= 6.7
E= 7.7 E=-21.5
a) TS1b
E = 9.2
a
1.99
1.49
1.371.421.42
1.371.49
4.38
123
4 56
4.315.58
r
a
1.39
1.44
1.44
1.41
1.39
1.41
2.34
4.40
123
4 5 6
16
23
4 5
2.01
a
r
4.394.54
1.491.371.42
1.421.37 1.49 1
234
56
r
a
1.98
2.01
1.34 1.51
1.51
r
a4.12
23
45 6
1 1.941.583.54
2.03
1.51
1.35
1.46 1.35 1.52
f) LM3bE= -5.7
a
r
12
3
45
6
1.97
3.00 3.84
1.511.41
1.38
1.44 1.36
1.50
E=12.1
d) TS3bS = 1.03 S = 1.02 S = 0.35
S = 1.02
Prediction: C4H2 on X(100)
• Possible pathways
E = 1.1<S2> = 0.00
TS2E = -20.3<S2> = 0.90
1.92
6
1.33
2.45
147.8
1.91
1.28 5
1.92
6
LM2 E = -59.8<S2> = 0.00LM1
TS1
E =-60.1<S2> = 0.00
5
LM3
221 1
3
34
4
SOSP
E = -20.8<S2> = 1.03
E = -19.1<S2> = 0.86
3 4
5
6
1.37
2.36
1.42
1.21
3.19
2.25
1.221.35
167.8
1 2
3
4
5
6
1 2
3
4
5
6
1 2
3
45
6
1 22.39
1.90
1.31
1.32
1.24
114.2
123.5
2.38
1.89
1.32
1.34
1.23
3.28
2.39
1.92
1.32
1.341.23
3.47
103.7 114.0
(0.0)
Si9H12
TS2
C4H2
(-19.1)
LM2
LM3
TS1
LM1
+
(-20.8)
(-60.1)
(-20.3)
(-59.8)
E (kcal/mol)
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!!!
Si9H12
2.22
P1
1.37
C4H2
2
3 4
1
1.211.075 6
(-1.2)P2 P3
P4 P5 LM1
3.01 2.57 2.27
2.02 1.941.92 1.922.18
3.54
(-1.6)
(-9.6) (-62.3)(-48.6)
(-3.0)
C4H2/Ge(100)
PES
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!!!
C4H2/Si(111): Prediction
PES
outer layer
inner layer
A(set 1)
B (set 3)H (set 2)
X (set 4)
Model System = A + H
Real System = A + B
EONIOM= Ehow(A+H) – Elow(A+H) + Elow(A+B)
(K. Morokuma et al., J. Mol. Struct. (Theochem) 461-462(1999) 1.)
3.7 ONIOM Model
Adsorption of Methanol, Formaldehyde and Formic Acid on Si(100)-21 Surface
( see X. Lu et al., Phys. Chem. Chem. Phys. 3(2001) 2156.)E(kcal/mol)
0
TS
Reaction Coordinate
LM1
LM2
-67.6(-67.9)
-12.6(-14.6)
-18.5(-16.9)
MethanolCCSD(T):B3LYP
Si2H4@Si9H12
formaldehyde
1 2
O C
1.711
2.344
1.457
1.975
1.096
81.5
109.2
105.370.9
C
2
a)
1 2.367
107.31.958
1.210
126.2
121.01.082
120.61.081
b)
O
LM1' LM2'
LM3'
TS'
LM4'
C
O
O
12
O
C
O
12
C OO
1 2
21
C
O
O
OCO
1 2
Formic acid
b) ONIOM中最内层的 C24
簇a) SWNT(10,0)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 SWNT by1,3-Dipolar Cycloadditions
SWNT(5,5) 片断
ONIOM(B3LYP/6-31G*:AM1)
Predicted Reaction Energies (kcal/mol)
1
2
3
C C + HCNCH2C C
HCN
CH2
1,3-DC of nitrile ylide with an olefin
SWNT C2H4
(1,2) (2,3)
HCNCH2 -45.2 -16.0 -72.1
HCNO -20.2 9.9 45.9
O3 -38.7 -6.3 -56.6
X. Lu et al., 1) J. Phys. Chem. B, 106(2002), 2136; 2) J. Am. Chem. Soc., 2003, 125, 10459-10464.
3
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• 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.