accuracy of dft exchange-correlation functionals for h bonds in small water clusters: benchmarks...
TRANSCRIPT
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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
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Outline
DFT Exchange-Correlation (xc) benchmark results for the water dimer to pentamer.
Issue of Global minimum water hexamer structure
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Geometries @ Global minima
Dimer Trimer
Tetramer Pentamer
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Geometries @ Global minima
Dimer Trimer
Tetramer Pentamer
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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.
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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).
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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.
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Extrapolation - Details
BXHFCBS
HFX AeEE
BXHFCBS
HFX AeEE 53 DXCXEE Corr
CBSCorrX
3 == aug-cc-pVTZ (92 basis function/water)4 == aug-cc-pVQZ (172 basis function/watr)5 == aug-cc-pV5Z (287 basis function/water)
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BSSE and Extrapolation
bondHOHOnHn
e nnEED /)( 22
Dissociation energy of ‘n’ water clusters is defined as below:
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The DFT xc Functionals tested
Hartree Theory
2nd : GGA
3rd : meta-GGA
4th : hyper-GGA
5th : hyper-meta-GGA
X3LYP, B3LYP, B3P86, B98, BH&HLYP
“Empirical”
Jacob’s Ladder (J. P. Perdew)
MPWB1K, PW6B95
PBE1W, BLYP, XLYP, BP86PW91, PBE, mPWLYP
TPSS
PBE0
“Non-empirical”
----------------------
----------------------
1st : LDA
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Dissociation Energy X3LYPDimer Trimer Tetramer Pentamer ME MAE
X3LYP 213.8 221.9 298.3 316.0 -2.2 2.9
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Dissociation Energy PBE0Dimer Trimer Tetramer Pentamer ME MAE
PBE0 214.5 224.6 302.7 320.9 1.0 3.6
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Dissociation Energy mPWLYPDimer Trimer Tetramer Pentamer ME MAE
mPWLYP 218.5 226.0 305.4 323.7 3.8 5.0
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Dissociation Energy PBE1WDimer Trimer Tetramer Pentamer ME MAE
PBE1W 207.9 216.6 294.9 312.7 -6.6 6.6
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Dissociation Energy PBEDimer Trimer Tetramer Pentamer ME MAE
PBE 220.1 233.5 316.4 334.8 11.6 11.6
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Dissociation Energy TPSSDimer Trimer Tetramer Pentamer ME MAE
TPSS 196.4 209.4 288.8 307.5 -14.1 14.1
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Dissociation Energy B3LYPDimer Trimer Tetramer Pentamer ME MAE
B3LYP 197.4 206.3 280.1 297.2 -20.1 20.1
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Dissociation Energy BLYP
Dimer Trimer Tetramer Pentamer ME MAE
BLYP 180.7 191.7 264.9 281.2 -35.0 35.0
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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.
∆RO-O ∆Rhb ∆RO-H ∆Φ ∆θ
X3LYP -0.002 -0.003 0.001 0.21 1.04
PBE0 -0.024 -0.023 -0.001 0.77 0.69
Max. from all the xc
-0.042 -0.051 0.014 1.46 1.52
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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)
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Hexamers
Prism Cage
Book Cyclic
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Issue of Global Minimum All the wave-functional based methods like MP2 and CCSD(T)
show “prism” as the lowest energy structure.
Prism Cage Book Cyclic
MP2 [CBS] 332.8 331.1 330.4 322.9
CCSD(T)*
[aug-cc-pVTZ]
347.6 345.5 338.9 332.5
X3LYP 43.88 44.17 45.08 45.11
PBE0 44.69 45.01 45.79 45.76
Best of the DFT xc functionals for water fail to capture that.
* R. M. Olson et al.
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Acknowledgement
MONETICE groupFHI
THANK YOU !!!!
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Dimer Trimer Tetramer Pentamer ME MAE
MP2/CBS 215.8 228.5 299.9 314.4 ---- ----
X3LYP 213.8 221.9 298.3 316.0 -2.2 2.9
PBE0 214.5 224.6 302.7 320.9 1.0 3.6
mPWLYP 218.5 226.0 305.4 323.7 3.8 5.0
B3P86 203.5 220.0 299.4 316.5 -4.8 5.9
PBE1W 207.9 216.6 294.9 312.7 -6.6 6.6
BH&HLYP 213.2 219.5 291.3 308.3 -6.6 6.6
PBE 220.1 233.5 316.4 334.8 11.6 11.6
B98 205.6 211.4 285.9 303.1 -13.2 13.2
TPSS 196.4 209.4 288.8 307.5 -14.1 14.1
B3LYP 197.4 206.3 280.1 297.2 -19.4 19.4
MPWB1K 199.1 210.6 276.3 292.3 -20.1 20.1
BP86 184.4 205.7 282.5 300.8 -21.3 21.3
PW91 232.5 244.9 330.8 350.5 25.0 25.0
BLYP 180.7 191.7 264.9 281.2 -35.0 35.0