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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, Angelos Michaelides, and Matthias Scheffler. Fritz-Haber-Institut der MPG. Outline.

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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, Angelos Michaelides, and Matthias Scheffler

Fritz-Haber-Institut der MPG


Outline
Outline in Small Water Clusters: Benchmarks Approaching the Complete Basis Set Limit

  • DFT Exchange-Correlation (xc) benchmark results for the water dimer to pentamer.

  • Issue of Global minimum water hexamer structure


Geometries @ global minima
Geometries @ Global minima in Small Water Clusters: Benchmarks Approaching the Complete Basis Set Limit

Dimer Trimer

Tetramer Pentamer


Geometries @ global minima1
Geometries @ Global minima in Small Water Clusters: Benchmarks Approaching the Complete Basis Set Limit

Dimer Trimer

Tetramer Pentamer


Why is this benchmark important
Why is this benchmark important? in Small Water Clusters: Benchmarks Approaching the Complete Basis Set Limit

  • 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
To choose reliable reference in Small Water Clusters: Benchmarks Approaching the Complete Basis Set Limit

  • 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).


  • Benchmark reference mp2
    Benchmark Reference: MP2 in Small Water Clusters: Benchmarks Approaching the Complete Basis Set Limit

    • 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
    Extrapolation - Details in Small Water Clusters: Benchmarks Approaching the Complete Basis Set Limit

    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
    BSSE and Extrapolation in Small Water Clusters: Benchmarks Approaching the Complete Basis Set Limit

    • Dissociation energy of ‘n’ water clusters is defined as below:


    The dft xc functionals tested
    The DFT xc Functionals tested in Small Water Clusters: Benchmarks Approaching the Complete Basis Set Limit

    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


    Dissociation energy x3lyp
    Dissociation Energy X3LYP in Small Water Clusters: Benchmarks Approaching the Complete Basis Set Limit


    Dissociation energy pbe0
    Dissociation Energy PBE0 in Small Water Clusters: Benchmarks Approaching the Complete Basis Set Limit


    Dissociation energy mpwlyp
    Dissociation Energy mPWLYP in Small Water Clusters: Benchmarks Approaching the Complete Basis Set Limit


    Dissociation energy pbe1w
    Dissociation Energy PBE1W in Small Water Clusters: Benchmarks Approaching the Complete Basis Set Limit


    Dissociation energy pbe
    Dissociation Energy PBE in Small Water Clusters: Benchmarks Approaching the Complete Basis Set Limit


    Dissociation energy tpss
    Dissociation Energy TPSS in Small Water Clusters: Benchmarks Approaching the Complete Basis Set Limit


    Dissociation energy b3lyp
    Dissociation Energy B3LYP in Small Water Clusters: Benchmarks Approaching the Complete Basis Set Limit


    Dissociation energy blyp
    Dissociation Energy BLYP in Small Water Clusters: Benchmarks Approaching the Complete Basis Set Limit


    How good are the geometries
    How good are the geometries? in Small Water Clusters: Benchmarks Approaching the Complete Basis Set Limit

    • 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.


    Summary of 1 st part
    Summary of 1 in Small Water Clusters: Benchmarks Approaching the Complete Basis Set Limitst 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
    Hexamers in Small Water Clusters: Benchmarks Approaching the Complete Basis Set Limit

    Prism Cage

    Book Cyclic


    Issue of global minimum
    Issue of Global Minimum in Small Water Clusters: Benchmarks Approaching the Complete Basis Set Limit

    • 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.


    Acknowledgement
    Acknowledgement in Small Water Clusters: Benchmarks Approaching the Complete Basis Set Limit

    • MONET

    • ICE group

    • FHI

      THANK YOU !!!!


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