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Accuracy of DFT Exchange-Correlation Functionals for H bonds in Small Water Clusters: Benchmarks Approaching the Complete Basis Set Limit Biswawajit Santra,

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Presentation on theme: "Accuracy of DFT Exchange-Correlation Functionals for H bonds in Small Water Clusters: Benchmarks Approaching the Complete Basis Set Limit Biswawajit Santra,"— Presentation transcript:

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 N 7 (N=number of basis functions).  MP2, less expensive (N 5 ) 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 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” ---------------------- 1 st : LDA

11 Dissociation Energy X3LYP DimerTrimerTetramerPentamerMEMAE X3LYP213.8221.9298.3316.0-2.22.9

12 Dissociation Energy PBE0 DimerTrimerTetramerPentamerMEMAE PBE0214.5224.6302.7320.91.03.6

13 Dissociation Energy mPWLYP DimerTrimerTetramerPentamerMEMAE mPWLYP218.5226.0305.4323.73.85.0

14 Dissociation Energy PBE1W DimerTrimerTetramerPentamerMEMAE PBE1W207.9216.6294.9312.7-6.66.6

15 Dissociation Energy PBE DimerTrimerTetramerPentamerMEMAE PBE220.1233.5316.4334.811.6

16 Dissociation Energy TPSS DimerTrimerTetramerPentamerMEMAE TPSS196.4209.4288.8307.5-14.114.1

17 Dissociation Energy B3LYP DimerTrimerTetramerPentamerMEMAE B3LYP197.4206.3280.1297.2-20.120.1

18 Dissociation Energy BLYP DimerTrimerTetramerPentamerMEMAE BLYP180.7191.7264.9281.2-35.035.0

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. ∆R O-O ∆R hb ∆R O-H ∆Φ∆Φ∆θ∆θ X3LYP-0.002-0.0030.0010.211.04 PBE0-0.024-0.023-0.0010.770.69 Max. from all the xc -0.042-0.0510.0141.461.52

20 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)

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. PrismCageBookCyclic MP2 [CBS]332.8331.1330.4322.9 CCSD(T)* [aug-cc-pVTZ] 347.6345.5338.9332.5 X3LYP43.8844.1745.0845.11 PBE044.6945.0145.7945.76  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 !!!!

24 DimerTrimerTetramerPentamerMEMAE MP2/CBS215.8228.5299.9314.4---- X3LYP213.8221.9298.3316.0-2.22.9 PBE0214.5224.6302.7320.91.03.6 mPWLYP218.5226.0305.4323.73.85.0 B3P86203.5220.0299.4316.5-4.85.9 PBE1W207.9216.6294.9312.7-6.66.6 BH&HLYP213.2219.5291.3308.3-6.66.6 PBE220.1233.5316.4334.811.6 B98205.6211.4285.9303.1-13.213.2 TPSS196.4209.4288.8307.5-14.114.1 B3LYP197.4206.3280.1297.2-19.419.4 MPWB1K199.1210.6276.3292.3-20.120.1 BP86184.4205.7282.5300.8-21.321.3 PW91232.5244.9330.8350.525.0 BLYP180.7191.7264.9281.2-35.035.0

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