Joachim Sauer!

Transcription

Joachim Sauer!

IMPRS Block Course!
Schmöckwitz, March 1, 2012!
Quantum chemistry and wavefunction based
methods for electron correlation !
Joachim Sauer!
Institut für Chemie, Humboldt-Universität!
HUMBOLDT-UNIVERSITÄT ZU BERLIN
Wlodzimierz Kolos
1928 - 1996
© Joachim Sauer, HU Berlin, 2012
CO/MgO(001)!
MgO(001)/CO!
O
C
Mg2+
O2-
CO/Mg(001)!
Example: CO/MgO(001) Observed binding energy 15 kJ/mol!
2002
Nygren, Pettersson, J. Chem. Phys. 105 (1996) 9339!
!
!
!
!
!
!
(terrace)!
!
Temperature programmed desorption!
!
!
!
!
!
!
(terrace)!
!
Wichtendahl,... Kuhlenbeck, Freund, Surf. Sci. 423 (1999) 90!
Temperature programmed desorption!
!
29 K peak: multilayer!
! 76 K peak: defects!
!
!
!
Readhead!
57 K Peak: {Mg2+}5c!
(ν=1013 s-1) ! !
0.14 eV (15 kJ/mol)!
!
!
Wichtendahl,... Kuhlenbeck, Freund, Surf. Sci. 423 (1999) 90!
CH4/MgO(100)!
Monolayer,
c 2x 2 R 45 o
(Coulomb et al.)
„dipod configuration (Larese et al.)
Tait, Dohnalek, Campbell, Kay,
JCP 122 (2005) 164708!
12.6 kJ/mol (Θ=1)!
13.1 kJ/mol (40 K) (He scattering)
CH4/MgO(100) - Temperature Programmed Desorption!
(terrace)!
Attractive interaction between molecules!
Cluster formation at low coverage
E0=11.1, γ =1.53
Tait, Dohnalek, Campbell, Kay, JCP 122 (2005) 164708!
CH4/MgO(100) - Arrhenius Barrier vs. Desorption Energy!
EA = Hd + RT!
Hd(T)= Ed + EZPV + ΔH(T)!
EA = Hd + RT!
Arrhenius barrier EA!
T/K!
Hd=EA - RT!
kJ!/mol!
12.6!
13.1!
47!
40!
12.2!
12.8!
ΔH(T)1
1.1!
Hd(0) = Hd - ΔH(T)!
ZPVE1
11.1!
-4.2!
Ed = Hd(0) - ZPVE!
15.3!
1.0!
11.8!
-4.2!
16.0!
15.3± 0.6!
1 Vibrational
contributions from PBE+D slab calculations!
P. Dirac, Proc. Roy. Soc. (London) A123 (1929) 714:!
„The general theory of quantum mechanics is now
almost complete...!
The underlying physical laws necessary for the
mathematical theory of .... the whole of chemistry are
thus completely known, and the difficulty is only that the
exact application of these laws leads to equations that
are much too complicated to be soluble.“!
It therefore becomes desirable that approximate
methods of applying quantum mechanics should be
developed, which can lead to an explanation of the
main features of complex atomic systems without too
much computation.!
The Royal Swedish Academy of Sciences has awarded
The 1998 Nobel Prize in Chemistry in the area of quantum chemistry to
Walter Kohn, University of California at Santa Barbara, USA and
John A. Pople, Northwestern Univ., Evanston, Ill., USA (British citizen).
Citation:
"to Walter Kohn for his development of the density-functional theory and to
John Pople for his development of computational methods in quantum
chemistry."
Quantum chemistry
!
Accuracy · (system size)m ≈ constant(resources)!
!
Coupled cluster expansion of wave function: CCSD(T)!
2nd order Moller-Plesset perturbation theory: MP2!
!
!
!
!
Density functional theory (DFT)!
for full periodic structures feasible!
Dispersion largely missing:!
Van der Waals functional (Langreth & Lundquist)!
Pragmatic solution: DFT+D (e.g. Grimme)!
!
Surface Reaction!
TS
Catalyst-Educt!
Complex!
Catalyst!
+ Educt!
Intrinsic!
Barrier!
Binding!
energy!
Apparent!
Barrier!
Reaction energy!
Catalyst-Product!
Complex!
DFT problems with barriers!
TS
Van der Waals
(dispersion)
Catalyst-Educt!
Complex!
Catalyst!
+ Educt!
SI error
(reaction site)
Intrinsic!
Barrier!
Binding!
energy!
Catalyst-Product!
Complex!
O
Zeolite catalysts: active sites (transitionOmetal
ions, protons)
in a „surface-only Sisilica matrix
!
Al
Si
Si
O
Si
+Al, H
Si
Si
O
Al
O O
O
O
O -Si
O
O
M+
Si
O
O
O
O
O
O
M+
Al
O
O
H
O
O
O
-Si
+Al, H
Si
Al
O
H
O
Zeolite catalysis: Methanol-to-hydrocarbons!
MTG
MTO!
Methanol from
different sources!
CH3OH!
+ CH3OH!
Gasoline!
Olefines!
CH3OCH3!
C-C Formation, induction!
CH2=CH2!
Methylation!
CH2=CH-CH3!
Cyclic Polyens!
Hydrocarbon pool!
mechanism
!
Haw et al, Kolboe et al.
Aromatic HC!
Review: Stöcker, Microp. and Mesop. Mat. 29 (1999) 3-48!
Methylation of ethene, propene, trans-2-butene in H-MFI!
Measured* Apparent Barrier
Ethene
Propene
t-2-Butene
104
64 (-40)
40 (-24)
Transition
structure
MeOH (g)
Alkene (g)
Water (g)
Alkene (g)
MeOH (ads)
Alkene (g)
MeOH (ads)
Alkene (ads)
Water (ads)
Alkene (ads)
*S. Svelle, P.A. Ronning, S. Kolboe, J. Catal. 2004, 224, 115.!
S. Svelle, P.O. Ronning, U. Olsbye, S. Kolboe,J. Catal. 2005, 234, 385.!
Methylation of alkenes in H-MFI - pbc DFT!
Error increases
with chain length
Svelle, Tuma, Rozanska, Kerber, Sauer, JACS 131 (2009) 816!
Pragmatic solution: DFT + Dispersion (DFT+D)!
Many predecessors with DFT, HF+Disp, e.g. Ahlrichs and Scoles!
Many more sophisticated schemes!
E total = E DFT + E disp
E disp = −s
ij
N −1 N
6
6
6
i =1 j =i +1 ij
∑∑
C
fdamp
r
fdamp (R) =
1
1+e-α (R/R0 -1)
s6 = 1.4/1.3/0.7 for BLYP/BP86/PBE
Grimme, J. Comput. Chem., 2004, 25, 1463; 2006, 27, 1787.!
Parameters are as good for solids (condensed systems) as for
molecules
Note, however, Mg2+ very different from Mg, whereas O2- similar to O
Implementation of Ewald sum for 1/r6 for periodic systems
Kerber, Sierka, Sauer, J. Comput. Chem. 29 (2008) 2088.!
Methylation of alkenes in H-MFI - pbc DFT+D!
Dispersion increases
with chain length
Methylation of alkenes in H-MFI - pbc DFT+D!
Dispersion
Too low barrier!
constant SIC error!
Errors on energy barriers (Truhlar et al.)!
kcal/mol
Nucleophilic substitution
Reference data:
CCSD(T) with extrapolation to complete basis set limit(„W1 theory )
Divide and Conquer - Models and Methodsn!
DFT (PBE/plane waves), VASP
20.2x20.5x13.5 Å; 96 +18 atoms
Periodic Boundary Conditions
CCSD(T)/cbs
17+17 Atome
C3O11Si2AlH17
MOLPRO
_
a
MP2/TZVP
123+67Atome
C3O72Si47AlH67
CC2 code
b_
Hybrid high level : low level method!
Hybrid MP2(cluster):PBE+D(pbc) +ΔCCSD(T) method!
Ehybrid (S,C) = EDFT+D(S) + [EMP2(C) - EDFT+D(C)]!
High level correction
Step 0: PBE+D optimization, periodic boundary conditions (pbc)
Frequency calculation for stationary points, ZPVE
Step 1: Hybrid MP2(cluster):PBE+D(pbc) optimization
[Step 2: Basis set extrapolation to CBS limit, single point
Step 3: CCSD(T)-MP2, small cluster model
Tuma, Sauer, CPL 2004, 387, 388; PCCP, 2006, 8, 3955!
Kerber, Sierka, Sauer, J. Comput. Chem. 2008, 29, 2088!
Reuter/Scheffler, PRL 98 (2007) 176103 (CO/Cu(111))!
Stoll, JPC A 113 (2009) 11483 (Be, Mg crystals)!
Energy as functional of orbitals or electron density!
kinet. e-n
e-e
e-e!
en. attract Coulomb exchange/corr
orbital density density !
!
!
EHF = ET + EN +
!
EJ
+
EXFock30 (orbital)!
!
Self-interaction
cancels
EDFT = ET + EN +
EJ +
EXC (density)!
functional of density only!
EXCLDA = EXDirac30 + ECVWN!
functional also of density gradient (Generalized Gradient Approximation)!
EXCBLYP = EXDirac30 + EXB88 + ECLYP!
Self-interaction correction!
Hartree-Fock
EJ
1
2
ρ(x) =
∫∫ ρ(x )
1
1
r12
ρ(x2 )dx1dx2 −
N
∑ i(x)i*(x)
1
2
i =1
EXF30 (orbital)
+
∑ ⎡⎣ ij ij
i, j
1
2
∑ ∫∫ i (x ) j (x )
∗
*
1
2
i, j
1
r12
j (x1 )i (x2 )dx1dx2
− ij ji ⎤⎦
⎡⎣ ii ii − ii ii ⎤⎦ = 0
i= j
Coulomb and exchange terms cancel - self-interaction correction (SIC)!
Kohn-Sham
! EJ
1
2
∫∫ ρ(x )
1
1
r12
+
EXC (density)!
ρ(x2 )dx1dx2 + ∫ dx ρ(x)VXC [ ρ,∇ρ ]
1
2
ii ii
+ i VXC [ ρ,∇ρ ] i ≠ 0
Coulomb and exchange do not cancel - self-interaction error!
* ∫∫ i * (x1 ) j ∗ (x2 ) r121 i (x1 ) j (x2 )dx1dx2 = ij ij
Energy as functional of orbitals or electron density!
kinet. e-n
e-e
e-e!
en. attract Coulomb exchange/corr
orbital density density !
!
!
EHF = ET + EN +
!
EJ
+
EXFock30 (orbital)!
!
Self-interaction
cancels
EDFT = ET + EN +
EJ +
EXC (density)!
functional of density only!
EXCLDA = EXD30 + ECVWN!
functional also of density gradient (Generalized Gradient Approximation)!
EXCBLYP = EXDirac30 + EXB88 + ECLYP!
orbital-density hybrid functional!
EXCB3LYP = a0 EXF30 + (1- a0) EXD30 + aX EXB88 !
Self-interaction
VWN
LYP!
cancels
partially
!
+(1- aC ) EC
+ aC EC
Cluster anions (V2O5)n!-
SOMO
Size-dependent
electron localization
20%
0%
50%
Fock-exchange in functional!
!
CCSD(T) calculations confirm most stable structures!
C s2A
V4O10-
!
!
+ 33!
D2d- 2B1!
- 57 kJ/mol !
C s2A
V6O15-
C2v- 2A2!
!
C s- 2A
!
CCSD(T)//BH-LYP!
B3-LYP!
-10!
BH-LYP!
- 9!
!
- 48 kJ/mol !
Electron hole defects in silica and zeolites
SiO2
Al doped SiO2
electron hole
self-trapped electron hole
[SiO4•]+
- e-
H-Zeolite
-H+
[AlO3•OH]+
[AlO4•]
- e-
- e-H+
[SiO4]
[AlO4-]
[AlO3OH]
The hole is localized at one O site (EPR -quartz)
Solans-Monfort, Branchadell, Sodupe, Sierka, Sauer, J Chem Phys 131 (2004) 6034!
Embedded MFI models (5T, 25T) - QM-Pot!
Energy for electron hole creation (eV)!
BHLYP:Pot.fct.!
5T!
25T//5T!
Hybrid!
7.40!
7.61!
QM//Hybrid!
9.26!
8.81!
-0.45!
LR//Hybrid!
-1.86!
-1.20!
+0.66!
f·LR//Hybrid!
(-1.27)!
-0.82!
(+0.45)!
corrected!
(7.99)!
7.99!
+aperiodic corr.!
Diff.!
8.33!
Systematic error of BHLYP (eV)!
6-31++G(d,p)!
BHLYP, {T5}MFI!
9.26!
BHLYP,
T1// {T5}MFI!
9.47!
CCSD(T), T1// {T5}MFI!
9.60!
cc-pVQZ!
9.91-10.02!
Increment!
0.44-0.55!
f=0.682
Expected rage of IP (eV)!
5T// {25T}MFI!
BHLYP//Hybrid!
8.81!
8.81!
LR//Hybrid!
-1.20!
-0.82!
Hybrid!
7.61!
7.99!
+ aperiodic corr.!
7.95!
8.33!
+ QM error!
0.44!
0.55!
[AlO3•OH]+!
8.4!
8.9!
[SiO2•]+!
9.2!
9.5!
Valence band edge (SiO2): 10.2 - 10.6 eV!
Solans-Monfort, Branchadell, Sodupe, Sierka, Sauer, J Chem Phys 131 (2004) 6034!

Joachim Sauer!

Transcription

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