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

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

Global minima Dimer Trimer Tetramer Pentamer

Global minima Dimer Trimer Tetramer Pentamer

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.

To choose reliable reference  Dissociation energy of water dimer by experiment: /- 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: /- 2 meV.  Expensive, scales as N 7 (N=number of basis functions).  MP2, less expensive (N 5 ) works very well here.  Dimer dissociation energy : /- 3 meV.  For other clusters, MP2 remains always within 3meV of CCSD(T).

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.

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)

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

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

Dissociation Energy X3LYP DimerTrimerTetramerPentamerMEMAE X3LYP

Dissociation Energy PBE0 DimerTrimerTetramerPentamerMEMAE PBE

Dissociation Energy mPWLYP DimerTrimerTetramerPentamerMEMAE mPWLYP

Dissociation Energy PBE1W DimerTrimerTetramerPentamerMEMAE PBE1W

Dissociation Energy PBE DimerTrimerTetramerPentamerMEMAE PBE

Dissociation Energy TPSS DimerTrimerTetramerPentamerMEMAE TPSS

Dissociation Energy B3LYP DimerTrimerTetramerPentamerMEMAE B3LYP

Dissociation Energy BLYP DimerTrimerTetramerPentamerMEMAE BLYP

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. ∆R O-O ∆R hb ∆R O-H ∆Φ∆Φ∆θ∆θ X3LYP PBE Max. from all the xc

Summary of 1 st 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)

Hexamers Prism Cage Book Cyclic

Issue of Global Minimum  All the wave-functional based methods like MP2 and CCSD(T) show “prism” as the lowest energy structure. PrismCageBookCyclic MP2 [CBS] CCSD(T)* [aug-cc-pVTZ] X3LYP PBE  Best of the DFT xc functionals for water fail to capture that. * R. M. Olson et al.

Acknowledgement  MONET  ICE group  FHI THANK YOU !!!!

DimerTrimerTetramerPentamerMEMAE MP2/CBS X3LYP PBE mPWLYP B3P PBE1W BH&HLYP PBE B TPSS B3LYP MPWB1K BP PW BLYP