1. ONIOM approach to complex and large molecular systems
Modellistica Molecolare (5 CFU)
July 7-11, Torino, Italy
Piero Ugliengo
Dip. Chimica IFM - Via P. Giuria 7
University of Torino
Modellistica Molecolare 2003

2. QM methods vs system size
Hartree-Fock: HF
673 atoms
4000 BF
Møller-Plesset: MP2, MP3, MP4
CI and CC: CI-SD, CCSD, CCSD(T)
Modellistica Molecolare 2003

3. QM methods: relative performance
B3-LYP is close to HF and
scales much better than post-SCF
as a function of basis sets size
Modellistica Molecolare 2003

4. Modeling at different scales
Ab-initio & semiempirical
Molecular mechanics dynamics
Infinite system ??
Modellistica Molecolare 2003

5. Method of the isolated cluster
N° atoms grows fast with cluster size
Large number of terminal H atoms
Hard to enforce crystal memory into the cluster structure
ONIOM or QM/MM type techniques quite effective
Any kind of QM method can be used (MP2, CCSD, DFT)
Modellistica Molecolare 2003

6. Periodic treatment for crystals
Born Von-Karmàn rule:
Bloch theorem:
, g = l a1 + m a2 + n a3
crystalline orbitals g a2
unit cell a1 a3
Modellistica Molecolare 2003

7. One possible strategy: the ONIOM method
The recipy is to divide the molecular system in two levels which are then joined together via fictitious atoms (H atoms) inserted at a given point along pre-existent bonds:
Real level, inclusive of all atoms of the adopted cluster treated with the lowest computational level.
Model level, inclusive of atoms treated at the highest computational level plus link atoms (HL). The memory of the Real level is enforced by the HL positions and forces
F. Maseras and K. Morokuma J. Comput. Chem. 16 (1995) 1170
Modellistica Molecolare 2003

8. The ONIOM machinery
ETOT(High:Low) = E(High, Model) + E; E = E(Low, Real) - E(Low, Model)
If Model  Real, E  0, ETOT(High:Low) = E(High, Real)
If Low  High  ETOT(High: High) = E(High, Real)
All others QM quantities are defined following the same scheme. The link between (High,Model) and (Low,Model) systems is via forces on the common HL atoms.
Modellistica Molecolare 2003

9. Mechanical embedding ONIOM method
Link atoms (H, F,…)
Model cluster
Real system
Two QM methods:
high level for the model cluster
low level for the real system
The two zones are disconnected. Link atoms enforce the structural memory of the real system to the model cluster. Charge transfer occurs only at low level for the real system
Modellistica Molecolare 2003

10. ONIOM energy definition
E(Low level:Real) +
E(High level:Model) –
E(Low level:Model) =
E(High:Low)
Low level: Molecular mechanics, semiempirical, HF, DFT
High level: HF, MP2, CCSDT
IMPORTANT!:
Extension to periodic system: QMPot (J. Sauer & M. Sierka)
Modellistica Molecolare 2003

11. Modeling at different scales: ONIOM method
Real
Model QM
High QM
Low
Sem QM QM MM
Modellistica Molecolare 2003

12. ONIOM applications Bronsted site in HY faujasite O C Mg
NH3 adsorbtion on hydroxylated
silica surfaces (CPL 341 (2001) 625)
Bronsted site in HY faujasite O C Mg O
CO adsorbtion on MgO(001) surface (CPL 366 (2002) 683)
Modellistica Molecolare 2003

13. Surface features of silica based materials
amorphous silica surface
SiO4
isolated
interacting
vicinal
geminal Si O H
External surface of MFI H O
Modellistica Molecolare 2003

14. Experimental evidence of a surface H-bonded complexSi
OH stretching frequency shift:
Dn(OH) = -650 cm-1 (T = 298K)
Dn(OH) = -950 cm-1 (T = 4K)
free OH
Infrared spectroscopy
Heat of adsorption:
isosteric: -37 kJ/mol
microcalorimetric: -45 kJ/mol
Microcalorimetry
Modellistica Molecolare 2003

15. Adopted models and strategiesSi O H N O H Si
C/NH3
High: B3LYP/DZP C
Low: MNDO PM3 AM1
HF/STO-3G
HF/3-21G +
Cm/NH3
Cb/NH3
Cs/NH3
Modellistica Molecolare 2003

16. How to compute physical quantities
Modellistica Molecolare 2003

17. Structural and energetic data
Intermolecular N...H distance (Å) and binding energies (BE) (kJ/mol) for the cluster models in interaction with NH3
Modellistica Molecolare 2003

18. OH vibrational frequency
Harmonic OH frequency wh (cm-1) for the free models
Modellistica Molecolare 2003

19. OH vibrational frequency shift
Harmonic OH frequency red shift, Dwh= wh(Cx)-wh(Cx /NH3) (cm-1) for the cluster models in interaction with NH3
Modellistica Molecolare 2003

20. Modellistica Molecolare 2003
NMR 1H and 29Si data
Chemical shifts d(1H) and [-d(29Si)] (ppm) for the free models. Data relative to B3LYP/DZP shield constants for tetrametilsilane: d(1H)=31.7-s(1H), d(29Si)=403.3-s(29Si)
Modellistica Molecolare 2003

21. Energetic & vibrational internal correlation
Modellistica Molecolare 2003

22. Chemically active sites in zeolites
Powerful solid acid catalyst
Modellistica Molecolare 2003

23. Acidic sites in Faujasite: an overview2 3 1 4
H--O
hexagonal
prism
145 atoms in the UC
Supercage
P1 space group
Four protonation sites
Relative stability
OH frequencies
1dH of acidic protons
b-cage
Modellistica Molecolare 2003

24. Acidic sites in Faujasite: local structureH
O2H O Al
O1H
O3H
O4H
Only O1H and O4H point into the supercage
Modellistica Molecolare 2003

25. Neutron diffraction H-Y (Si/Al=3)
Experimental results on HY
IR H-Y (Si/Al=5) 15 K
Spoto et al. unpublished
NMR H-Y (Si/Al=5)
Janchen et al. Catal. Lett (1996) 147
O3H
3544
O1H
3647
O1H
4.7
O3H
4.1 2 4 6
ppm
Neutron diffraction H-Y (Si/Al=3)
Czjzek et al. J. Phys. Chem (1992) 1535
O1H O2H O3H O4H
Modellistica Molecolare 2003

26. Stoichiometry of the ONIOM model regionsb1
Si12AlO21
Si13AlO22
Si13AlO22 b3 b2
Si16AlO27
Si13AlO23 b5 b4
Si24AlO37
Si21AlO31
Modellistica Molecolare 2003

27. ONIOM clusters at (B3-LYP/SVP:AM1)
Modellistica Molecolare 2003

28. ONIOM(B3LYP/SVP:AM1) OH stabilities4 1 3 2
kJ/mol
Relative stabilities with respect to O1H
Modellistica Molecolare 2003

29. OH numerical harmonic frequenciesb2
w(OH)/cm O1H O2H O3H O4H D(3-1)
ONIOM(B3-LYP/SVP:AM1) s b
Modellistica Molecolare 2003

30. OH harmonic frequencies: a comparison
w(OH) / cm O1H O2H O3H O4H D(3-1)
Measured
Harmonic
Experiment
B3-LYP/SVP:AM1 s
B3-LYP/SVP:AM1 b
Cluster calculation
CRYSTAL B3/GB
DMOL LDA
QMpot B3-LYP
Periodic calculation
Modellistica Molecolare 2003

31. Modellistica Molecolare 2003
1dH chemical shifts
1dH / ppm O1H O3H D(3-1)
1dH = s (H-TMS) - s (OXH)
Experiment / / / 0.7
B3-LYP/SVP:AM1 s
B3-LYP/SVP:AM1 b
Cluster calculation
Modellistica Molecolare 2003

32. Periodic hamiltonians
At the moment HF, LDA, GGA and hybrid functionals (only in CRYSTAL) have been coded in periodic QM codes.
DFT greatly improves HF results, pushing the accuracy close to chemical requests.
A serious drawback of all proposed functionals is that dispersion forces are not taken into account.
J.M. Perez-Jorda and A.D. Becke Chem. Phys. Lett. 229 (1995) 134.
S. Kristyan and P. Pulay Chem. Phys. Lett. 229 (1994) 175.
Q. Wu and W. Yang, J. Chem. Phys. 116 (2002) 515.)
Modellistica Molecolare 2003

33. Dispersive forces in materials modeling
Physisorption
Molecular crystals
Dispersion forces play a major
rôle in the determination of large
molecular structures.
This is particulary
true for crystal structures
Confinement
Modellistica Molecolare 2003

34. Modellistica Molecolare 2003
MgO(001)/CO system
Modellistica Molecolare 2003

35. Computational methods
Periodic HF and B3-LYP calculations using CRYSTAL98
Basis A: 8-511G (Mg); 8-411G(O) G(d)(CO)
Basis B: TZV(p,d) (MgO). VTZ(2d) (CO)
CO and Mg---C fully optimized
Harmonic CO frequency shift
A. Damin, R. Dovesi, A. Zecchina and P. Ugliengo Surf. Science 479 (2001) 255
Modellistica Molecolare 2003

36. Binding energies of MgO(001)/CO
All data in kJ/mol
Electron correlation improves the HF BE
BSSE is very large and almost cancels the BE
Modellistica Molecolare 2003

37. ONIOM method for MgO(001)/CO
Real system: periodic slab
Low level: B3LYP/B
Model system: Mg9O9
High level:
B3LYP/aug-cc-pVXZ (X=D,T,Q) MP2/aug-cc-pVXZ (X=D,T,Q)
Mg2+ C O
O2- CO
Mg2+
O2-
ONIOM (B3LYP/aug-cc-pVXZ:B3LYP/B)
ONIOM (MP2/aug-cc-pVXZ:B3LYP/B)
Modellistica Molecolare 2003

38. ONIOM definition of BE
BE [High:Low] = BE (Mg9O9/CO) - BE (Mg9O9/CO) + BE (Slab/CO)
The use of the correlation consisten basis set allows
for a complete basis set extrapolation of the binding energy
Modellistica Molecolare 2003

39.  = BEC [MP2/Q:B3LYP/B] - BEC [B3LYP/Q:B3LYP/B]
Complete basis set extrapolation of BEs
 = BEC [MP2/Q:B3LYP/B] - BEC [B3LYP/Q:B3LYP/B]
=7.5 kJ/mol  dispersive contribution to the BE plus the intrasystem correlation difference of CO and Mg9O9 at MP2 and B3-LYP respectively
BEC() = a + b / n3
n=4
n=3
exchange repulsion
charge transfer
electrostatic+polarization
dispersion
n=2
Modellistica Molecolare 2003

40. Classical electrostatic binding energy
Using the ONIOM field and the CO multipoles and polarizability the classical BE can be worked out as:
BE = - mzF + 1/2 zzF + 1/6 zzz2F - 1/21 zzzz3F - 1/2 azzF2
intrasystem correlation difference between MP2 and B3-LYP is  1 kJ/mol
the best extrapolated ONIOM MP2 binding energy of 12.7 kJ/mol is in
very good agreement with the experimental values around 13 kJ/mol
the final estimate of the dispersion contribution is then  6.6 ± 1 kJ/mol
Modellistica Molecolare 2003

41. ONIOM hands on tutorial
Substitutional C and B in bulk silicon
Adsorption of NH3 on B-Si surface
Adsorption of NH3 on a Lewis site in silica material
Modellistica Molecolare 2003

42. Chemical reactions in substitutional processes
Energy of reaction as a function of the adopted model region H Si + C H Si Si H Si B + H
ONIOM(AM1:MNDO) H
Modellistica Molecolare 2003

43. ONIOM: adopted model regions
Si-4
Si-1
Si-9
Si-13
Modellistica Molecolare 2003

44. ONIOM: definition of reaction energy
ONIOM(AM1:MNDO) B Si + +
Si-4
Si-B-4
EB(n) = E(Si-B-n) + E(SiH4) – E(BH3) – E(Si-n)
EC(n) = E(Si-B-n) + E(SiH4) – E(CH4) – E(Si-n)
E(BH3), E(SiH4), E(CH4) computed at AM1 level
Modellistica Molecolare 2003

45. E (n) = E(Si-B-n/NH3)– E(NH3) – E(Si-B-n)
Adsorption of NH3 on a B-Si surface
Binding Energy as a function of the adopted model region
ONIOM(AM1:MNDO) Si B H
E (n) = E(Si-B-n/NH3)– E(NH3) – E(Si-B-n)
E(NH3) computed at AM1 level
Modellistica Molecolare 2003

46. E (n) = E(Al-n/NH3)– E(NH3) – E(Al-n)
Adsorption of NH3 on a Lewis site model
Binding Energy as a function of the adopted model region
ONIOM(AM1:MNDO) Al Si N + H O
E (n) = E(Al-n/NH3)– E(NH3) – E(Al-n)
E(NH3) computed at AM1 level
Modellistica Molecolare 2003

47. ONIOM: adopted model regions
Al-1
Al-4
Al-10
Al-24
Modellistica Molecolare 2003

48. Tools and tricks Structure definition and manipulation: MOLDRAW
Export/import XYZ
Add H
MOLDRAW
WebLab viewer Lite
Gaussian-98
Modellistica Molecolare 2003