Accuracy of DFT Exchange-Correlation Functionals for H bonds in Small Water Clusters: Benchmarks App...
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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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Biswawajit Santra, Angelos Michaelides, and Matthias Scheffler

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Biswawajit santra angelos michaelides and matthias scheffler

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

  • 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

Dimer Trimer

Tetramer Pentamer


Geometries @ global minima1

Geometries @ Global minima

Dimer Trimer

Tetramer Pentamer


Why is this benchmark important

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

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).


  • Benchmark reference mp2

    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

    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

    BSSE and Extrapolation

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


    The dft xc functionals tested

    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


    Dissociation energy x3lyp

    Dissociation Energy X3LYP


    Dissociation energy pbe0

    Dissociation Energy PBE0


    Dissociation energy mpwlyp

    Dissociation Energy mPWLYP


    Dissociation energy pbe1w

    Dissociation Energy PBE1W


    Dissociation energy pbe

    Dissociation Energy PBE


    Dissociation energy tpss

    Dissociation Energy TPSS


    Dissociation energy b3lyp

    Dissociation Energy B3LYP


    Dissociation energy blyp

    Dissociation Energy BLYP


    How good are the geometries

    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.


    Summary of 1 st part

    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)


    Hexamers

    Hexamers

    Prism Cage

    Book Cyclic


    Issue of global minimum

    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.


    Acknowledgement

    Acknowledgement

    • MONET

    • ICE group

    • FHI

      THANK YOU !!!!


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