View
2
Download
0
Category
Preview:
Citation preview
Toward Very High Boredom in the Calculation of Adsorption Energies on Ionic Surfaces
Angelos Michaelides
London Centre for Nanotechnology and Department of Chemistry, University College London, London, UK
&&
Fritz-Haber-Institut der Max-Planck-Gesellschaft, Berlin, Germany
IInterfaces:CCatalytic & EEnvironmental
www.chem.ucl.ac.uk/ice
Towards High Precision Adsorption Energies: water/NaCl(001)
The adsorption of atoms and molecules on solid surfaces is important to
many disciplines; essentially an endless list of phenomena
Towards High Precision Adsorption Energies: water/NaCl(001)
many disciplines; essentially an endless list of phenomena…
High accuracy (“chemical accuracy” 1kcal/mol or ~43 meV ) in the
d t i ti f l l d ti i i hi hl d i bl it idetermination of molecular adsorption energies is highly desirable…it is
the accuracy needed to make quantitative predictions of the rates of processes
But let’s just use density functional theory, it’s great isn’t it?
processes
1
DFT is in principle exact in practice approximateDFT is in principle exact, in practice approximate…
Jacob’s Ladder (J P Perdew)Jacob s Ladder (J.P. Perdew)1st -
2nd -
“Non-empirical”(constraint satisfaction)
“Empirical”(property satisfaction)
2
3rd -4th: hyper-GGA
4th - 3rd: meta-GGA
ypB3LYPPBE0
TPSS
1st: LDA
2nd: GGABLYPPBE
TPSS
Hartree-Fock: electron exchange (like spin
interaction treated exactly; electron correlation Hartree Theorybetween electrons of unlike spins ignored)
Towards High Precision Adsorption Energies: water/NaCl(001)
Example: density-functional theory results for water adsorption on salt
(periodic supercell approach fully converged plane-wave basis set)
Towards High Precision Adsorption Energies: water/NaCl(001)
(periodic supercell approach, fully converged plane-wave basis set)
xc functional LDA PBE RPBE
E d (meV/H2O) 611 357 233Eads (meV/H2O) 611 357 233
Eads = ENaCl + Ewater – Ewater/NaCl1 eV ~ 100 kj/mol1 eV ~ 100 kj/mol
2
With this range in adsorption energies the “first principles” prediction of
)
With this range in adsorption energies the first principles prediction of
rates (adsorption/desorption) becomes a waste of time:
V/H
2O)
Tdes (RPBE)Tdes (PBE)
Gad
s(e
V
Tdes (LDA)
Temperature (K) @ 1 atm.p ( ) @
Various solutions are available: (i) guess; (ii) “superior” xc functionals; (iii)
quantum Monte Carlo; and (iv) post Hartree-Fock (quantum chemistry)
Today: work involving quantum chemistry to achieve high accuracy in adsorption energies of molecules on ionic surfaces e g water/salt
quantum Monte Carlo; and (iv) post Hartree Fock (quantum chemistry)
adsorption energies of molecules on ionic surfaces, e.g. water/salt
Total Adsorption Energyp gy
Hartree Fock Correlationcorrads
HFadsads EEE !
contribution contribution
Classical region
(point charge)
Quantum region
(HF)
Quantum region
(MP2,CCSD(T))
Classical region
(point charge)
adsadsads
Cluster embedded in point chargesaCluster embedded in point charges
(and also Periodic HFb calculations)Cluster embedded in point charges
Extrapolation to complete basis set
limit (CBS)
Extrapolation to complete basis set
limit (CBS)limit (CBS) limit (CBS)
Total Adsorption EnergyTotal Adsorption Energy
aS. Humbel, et al., J. Chem. Phys. 105, 1959 (1996); J. A. Mejias et al., Surf. Sci. 327, 59 (1995); P. Sushko, et al., Surf. Sci. 450, 153 (2000). bR. Dovesi et al., CRYSTAL06, , ( ) ,
E. J. Bylaska et al., NWChem
3
The cluster models and adsorption geometryThe cluster models and adsorption geometry
Periodic plane-wave DFT
structure optimizations:
Clusters: 2 layer stoichiometric
with the PBE structurestructure optimizations: with the PBE structure
Na
Cl
Na Cl Na Cl
Na
Na5Cl5 Na9Cl9
DFT: [1] H. Meyer, et al. Surf. Sci. 177, 488 (2001).
[2] J. M. Park, et al. Phys. Rev. B. 69, 233403
(2004).
[3] Y. Yang, et al. Phys. Rev. B. 74, 245409
(2006).
Na13Cl13 Na25Cl25
[4] P. Cabrera-Sanfelix, et al. J. Phys. Chem.
B 110, 24559 (2006).
Helium Scattering: [5] L. W. Bruch et al., J. Chem. Phys. 103,
13 13 25 255109 (1995).
Hartree-Fock Contribution (smallish basis sets)Hartree Fock Contribution (smallish basis sets)
Correlation Contribution (MP2, smallish basis sets, frozen core)
4
Basis Sets Sub Valence correlationBasis Sets
Dunning’s correlation
consistent basis sets
Sub-Valence correlation
Which electrons need to be correlated
to achieve high precision?
cc-pVnZ, aug-cc-pCVnZ
(n = 3, 4, 5)
elements frozen correlated Ecorr (meV)O 1s 2s, 2pCl 1s, 2s, 2p 3s, 3p 244
to achieve high precision?
ads
(n 3, 4, 5)
Extrapolation to CBS
, , p , pNa 1s, 2s, 2p 3sO 1s 2s,2pCl 1s, 2s, 2p 3s, 3p 303N 1 2 2 3Extrapolation to CBS
T. H. Dunning, J. Phys. Chem. A 104, 9062
(2000); B. Santra, A. Michaelides, and M.
Scheffler J Chem Ph s 127 184104 (2007)
Na 1s 2s, 2p, 3sO none 1s,2s,2pCl ” 1s, 2s, 2p, 3s, 3p 306Na ” 1s 2s 2p 3s
Correlations beyond MP2 CCSD(T)
Scheffler, J. Chem. Phys. 127, 184104 (2007) Na 1s, 2s, 2p, 3s
The difference between MP2 and CCSD(T) is evaluated at the 3- level,
i.e., !CCSD(T)a
C ( )P. Jurecka and P. Hobza, Chem. Phys. Lett. 365, 89 (2002)
Fritz Haber Institute of the Max Planck SocietyBringing it all together
Contribution E d (meV)
Bringing it all together
Contribution Eads (meV)
HF/CBS 191
Electron Correlation/CBS/MP2 244
Sub-valence correlation/CBS/MP2 62
CCSD(T) -15
B i (fi d l b) 482Best estimate (fixed slab) 482
Substrate relaxations +30
Best estimate (relaxed slab) 512 47
5
xc Functional PBE RPBE LDA QC
Eads (meV/H2O) 357 233 611 482) Td (PBE)
V/H
2O)
Tdes (RPBE)Tdes (PBE)
Gad
s(e
V
Tdes (LDA)
Temperature (K) @ 1 atm.
Conclusions• Computing accurate adsorption energies for molecules on surfaces is VERY difficult.
Conclusions
• DFT with traditional xc functionals will not always deliver the required accuracy or, at
best, an educated guess of which functional to use is required.
F i i f t H t F k t h i t th d id ibl• For ionic surfaces post Hartree-Fock quantum chemistry methods provide one possible
solution. However, the horrendous scaling with basis set size (>N5) means that at the
moment these methods are not really practical for widespread use...
• The water-salt bond strength on a fixed surface is ~482 meV and on a relaxed surface it
is ~512 meV
Acknowlegements• Bo Li and Matthias Scheffler
www.esf.org/euryi
6
Recommended