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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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Page 1: Accuracy of DFT Exchange-Correlation Functionals for H bonds in Small Water Clusters: Benchmarks Approaching the Complete Basis Set Limit Biswawajit Santra,

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

Page 2: Accuracy of DFT Exchange-Correlation Functionals for H bonds in Small Water Clusters: Benchmarks Approaching the Complete Basis Set Limit Biswawajit Santra,

Outline

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

Issue of Global minimum water hexamer structure

Page 3: Accuracy of DFT Exchange-Correlation Functionals for H bonds in Small Water Clusters: Benchmarks Approaching the Complete Basis Set Limit Biswawajit Santra,

Geometries @ Global minima

Dimer Trimer

Tetramer Pentamer

Page 4: Accuracy of DFT Exchange-Correlation Functionals for H bonds in Small Water Clusters: Benchmarks Approaching the Complete Basis Set Limit Biswawajit Santra,

Geometries @ Global minima

Dimer Trimer

Tetramer Pentamer

Page 5: Accuracy of DFT Exchange-Correlation Functionals for H bonds in Small Water Clusters: Benchmarks Approaching the Complete Basis Set Limit Biswawajit Santra,

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.

Page 6: Accuracy of DFT Exchange-Correlation Functionals for H bonds in Small Water Clusters: Benchmarks Approaching the Complete Basis Set Limit Biswawajit Santra,

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).

Page 7: Accuracy of DFT Exchange-Correlation Functionals for H bonds in Small Water Clusters: Benchmarks Approaching the Complete Basis Set Limit Biswawajit Santra,

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.

Page 8: Accuracy of DFT Exchange-Correlation Functionals for H bonds in Small Water Clusters: Benchmarks Approaching the Complete Basis Set Limit Biswawajit Santra,

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)

Page 9: Accuracy of DFT Exchange-Correlation Functionals for H bonds in Small Water Clusters: Benchmarks Approaching the Complete Basis Set Limit Biswawajit Santra,

BSSE and Extrapolation

bondHOHOnHn

e nnEED /)( 22

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

Page 10: Accuracy of DFT Exchange-Correlation Functionals for H bonds in Small Water Clusters: Benchmarks Approaching the Complete Basis Set Limit Biswawajit Santra,

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

Page 11: Accuracy of DFT Exchange-Correlation Functionals for H bonds in Small Water Clusters: Benchmarks Approaching the Complete Basis Set Limit Biswawajit Santra,

Dissociation Energy X3LYPDimer Trimer Tetramer Pentamer ME MAE

X3LYP 213.8 221.9 298.3 316.0 -2.2 2.9

Page 12: Accuracy of DFT Exchange-Correlation Functionals for H bonds in Small Water Clusters: Benchmarks Approaching the Complete Basis Set Limit Biswawajit Santra,

Dissociation Energy PBE0Dimer Trimer Tetramer Pentamer ME MAE

PBE0 214.5 224.6 302.7 320.9 1.0 3.6

Page 13: Accuracy of DFT Exchange-Correlation Functionals for H bonds in Small Water Clusters: Benchmarks Approaching the Complete Basis Set Limit Biswawajit Santra,

Dissociation Energy mPWLYPDimer Trimer Tetramer Pentamer ME MAE

mPWLYP 218.5 226.0 305.4 323.7 3.8 5.0

Page 14: Accuracy of DFT Exchange-Correlation Functionals for H bonds in Small Water Clusters: Benchmarks Approaching the Complete Basis Set Limit Biswawajit Santra,

Dissociation Energy PBE1WDimer Trimer Tetramer Pentamer ME MAE

PBE1W 207.9 216.6 294.9 312.7 -6.6 6.6

Page 15: Accuracy of DFT Exchange-Correlation Functionals for H bonds in Small Water Clusters: Benchmarks Approaching the Complete Basis Set Limit Biswawajit Santra,

Dissociation Energy PBEDimer Trimer Tetramer Pentamer ME MAE

PBE 220.1 233.5 316.4 334.8 11.6 11.6

Page 16: Accuracy of DFT Exchange-Correlation Functionals for H bonds in Small Water Clusters: Benchmarks Approaching the Complete Basis Set Limit Biswawajit Santra,

Dissociation Energy TPSSDimer Trimer Tetramer Pentamer ME MAE

TPSS 196.4 209.4 288.8 307.5 -14.1 14.1

Page 17: Accuracy of DFT Exchange-Correlation Functionals for H bonds in Small Water Clusters: Benchmarks Approaching the Complete Basis Set Limit Biswawajit Santra,

Dissociation Energy B3LYPDimer Trimer Tetramer Pentamer ME MAE

B3LYP 197.4 206.3 280.1 297.2 -20.1 20.1

Page 18: Accuracy of DFT Exchange-Correlation Functionals for H bonds in Small Water Clusters: Benchmarks Approaching the Complete Basis Set Limit Biswawajit Santra,

Dissociation Energy BLYP

Dimer Trimer Tetramer Pentamer ME MAE

BLYP 180.7 191.7 264.9 281.2 -35.0 35.0

Page 19: Accuracy of DFT Exchange-Correlation Functionals for H bonds in Small Water Clusters: Benchmarks Approaching the Complete Basis Set Limit Biswawajit Santra,

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

Page 20: Accuracy of DFT Exchange-Correlation Functionals for H bonds in Small Water Clusters: Benchmarks Approaching the Complete Basis Set Limit Biswawajit Santra,

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)

Page 21: Accuracy of DFT Exchange-Correlation Functionals for H bonds in Small Water Clusters: Benchmarks Approaching the Complete Basis Set Limit Biswawajit Santra,

Hexamers

Prism Cage

Book Cyclic

Page 22: Accuracy of DFT Exchange-Correlation Functionals for H bonds in Small Water Clusters: Benchmarks Approaching the Complete Basis Set Limit Biswawajit Santra,

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.

Page 23: Accuracy of DFT Exchange-Correlation Functionals for H bonds in Small Water Clusters: Benchmarks Approaching the Complete Basis Set Limit Biswawajit Santra,

Acknowledgement

MONETICE groupFHI

THANK YOU !!!!

Page 24: Accuracy of DFT Exchange-Correlation Functionals for H bonds in Small Water Clusters: Benchmarks Approaching the Complete Basis Set Limit Biswawajit Santra,

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


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