Biswawajit Santra, Angelos Michaelides, and Matthias Scheffler

1. Accuracy of DFT Exchange-Correlation Functionals for H bonds in Small Water Clusters: Benchmarks Approaching the Complete Basis Set Limit Biswawajit Santra, Angelos Michaelides, and Matthias Scheffler Fritz-Haber-Institut der MPG

2. Outline • DFT Exchange-Correlation (xc) benchmark results for the water dimer to pentamer. • Issue of Global minimum water hexamer structure

3. Geometries @ Global minima Dimer Trimer Tetramer Pentamer

4. Geometries @ Global minima Dimer Trimer Tetramer Pentamer

5. Why is this benchmark important? • Small water clusters are implicated in several contemporary problems: • DFT is the most popular theory in electronic structure calculation. • Water clusters are hold together by H bonds and H bonds are crucial in innumerous systems. • Understanding of bulk water and ice properties. • Formation of acid rain. • Anomalous absorption of sunlight by clouds. • Nucleation of water droplets.

6. To choose reliable reference • Dissociation energy of water dimer by experiment: 216.8 +/- 30 meV. • 30 meV is ~15% of total dissociation energy. • Experimental Dissociation energies of other small clusters are not available. • CCSD(T), regarded as the most accurate ab-initio electronic structure theory. • Best dimer dissociation energy: 217.6 +/- 2 meV. • Expensive, scales as N7 (N=number of basis functions). • MP2, less expensive (N5) works very well here. • Dimer dissociation energy : 215.8+/- 3 meV. • For other clusters, MP2 remains always within 3meV of CCSD(T).

7. Benchmark Reference: MP2 • Gaussian-type localized orbitals. • Dunning’s correlation consistent basis sets i.e. aug-cc-pVTZ, aug-cc-pVQZ, aug-cc-pV5Z. • Extrapolated to Complete Basis Set (CBS) limit.

8. Extrapolation - Details 3 == aug-cc-pVTZ (92 basis function/water) 4 == aug-cc-pVQZ (172 basis function/watr) 5 == aug-cc-pV5Z (287 basis function/water)

9. BSSE and Extrapolation • Dissociation energy of ‘n’ water clusters is defined as below:

10. The DFT xc Functionals tested Jacob’s Ladder (J. P. Perdew) “Non-empirical” “Empirical” ---------------------- MPWB1K, PW6B95 5th : hyper-meta-GGA X3LYP, B3LYP, B3P86, B98, BH&HLYP 4th : hyper-GGA PBE0 TPSS ---------------------- 3rd : meta-GGA PW91, PBE, mPWLYP PBE1W, BLYP, XLYP, BP86 2nd : GGA 1st : LDA Hartree Theory

11. Dissociation Energy X3LYP

12. Dissociation Energy PBE0

13. Dissociation Energy mPWLYP

14. Dissociation Energy PBE1W

15. Dissociation Energy PBE

16. Dissociation Energy TPSS

17. Dissociation Energy B3LYP

18. Dissociation Energy BLYP

19. How good are the geometries? • We have compared various bond lengths and angles of the geometries, all optimized with an aug-cc-pVTZ basis set. • All results are quite satisfactory. • X3LYP perform best among all.

20. Summary of 1st part • Hybrid X3LYP and PBE0 perform the best for the energetics of the H bonds considered here, always being within 10 meV/H bond of MP2. • Among the pure GGAs considered mPWLYP and PBE1W perform the best. • PBE and PW91 differ by ~12-14 meV/H bond. • Variable performances with cluster size lead us to conclude the dimer or trimer is not sufficient to give the general abilities of the functional. • All functionals achieve chemical accuracy (1kcal/mol ~ 43 meV). B.Santra, A.Michaelides, and M.Scheffler J. Chem. Phys. (in press)

21. Hexamers Prism Cage Book Cyclic

22. Issue of Global Minimum • All the wave-functional based methods like MP2 and CCSD(T) show “prism” as the lowest energy structure. • Best of the DFT xc functionals for water fail to capture that. * R. M. Olson et al.

23. Acknowledgement • MONET • ICE group • FHI THANK YOU !!!!