London Centre for Nanotechnology and Department of ...th.fhi-berlin.mpg.de/th/Meetings/MarieCuriePsik2008/...Toward Very High Boredom in the Calculation of Adsorption Energies on Ionic

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


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)


Example: density-functional theory results for water adsorption on salt

(periodic supercell approach fully converged plane-wave basis set)


(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

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London Centre for Nanotechnology and Department of ...th.fhi-berlin.mpg.de/th/Meetings/MarieCuriePsik2008/...Toward Very High Boredom in the Calculation of Adsorption Energies on Ionic