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

Outline

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

Issue of Global minimum water hexamer structure

Geometries @ Global minima

Dimer Trimer

Tetramer Pentamer

Geometries @ Global minima

Dimer Trimer

Tetramer Pentamer

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 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

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

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)

BSSE and Extrapolation

bondHOHOnHn

e nnEED /)( 22

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

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

Dissociation Energy X3LYPDimer Trimer Tetramer Pentamer ME MAE

X3LYP 213.8 221.9 298.3 316.0 -2.2 2.9

Dissociation Energy PBE0Dimer Trimer Tetramer Pentamer ME MAE

PBE0 214.5 224.6 302.7 320.9 1.0 3.6

Dissociation Energy mPWLYPDimer Trimer Tetramer Pentamer ME MAE

mPWLYP 218.5 226.0 305.4 323.7 3.8 5.0

Dissociation Energy PBE1WDimer Trimer Tetramer Pentamer ME MAE

PBE1W 207.9 216.6 294.9 312.7 -6.6 6.6

Dissociation Energy PBEDimer Trimer Tetramer Pentamer ME MAE

PBE 220.1 233.5 316.4 334.8 11.6 11.6

Dissociation Energy TPSSDimer Trimer Tetramer Pentamer ME MAE

TPSS 196.4 209.4 288.8 307.5 -14.1 14.1

Dissociation Energy B3LYPDimer Trimer Tetramer Pentamer ME MAE

B3LYP 197.4 206.3 280.1 297.2 -20.1 20.1

Dissociation Energy BLYP

Dimer Trimer Tetramer Pentamer ME MAE

BLYP 180.7 191.7 264.9 281.2 -35.0 35.0

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

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

Prism Cage

Book Cyclic

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.

Acknowledgement

MONETICE groupFHI

THANK YOU !!!!

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