Efficient simulations of water with ab initio accuracy

192 Pages·2015·12.36 MB·English

by  Morawietz, Tobias

RUHR-UNIVERSITA¨T BOCHUM
FAKULTA¨T FU¨R CHEMIE UND BIOCHEMIE
LEHRSTUHL FU¨R THEORETISCHE CHEMIE
Efficient Simulations of Water
with Ab Initio Accuracy:
Development of High-Dimensional Neural Network
Potentials for Water Clusters and Bulk Water
HˆΨ=EΨ
y
1
G
1
y2 E
G
2
y
3
Dissertation
zur Erlangung des Doktorgrades der Naturwissenschaften
Tobias Morawietz

Die vorliegende Dissertation wurde in der Zeit von Januar 2011 bis Mai 2015 am
Lehrstuhl fu¨r Theoretische Chemie an der Fakulta¨t fu¨r Chemie und Biochemie der
Ruhr-Universita¨tBochumangefertigt.
LeiterderArbeit: PDDr. Jo¨rgBehler
1. Referent: PDDr. Jo¨rgBehler
2. Referent: Prof. Dr. DominikMarx
Dekan: Prof. Dr. NilsMetzler-Nolte

Publications
Partoftheworkpresentedinthisthesisisbasedonthefollowingpublications:
• T.MorawietzandJ.Behler,ADensity-FunctionalTheoryBasedNeuralNetwork
PotentialforWaterClustersIncludingvanderWaalsCorrections,J.Phys. Chem.
A117,7356(2013).
• T. Morawietz and J. Behler, A Full-Dimensional Neural Network Potential-
Energy Surface for Water Clusters up to the Hexamer, Z. Phys. Chem. 227,
1559(2013).
• T. Morawietz, V. Sharma, and J. Behler, A Neural Network Potential-Energy
SurfacefortheWaterDimerBasedonEnvironment-DependentAtomicEnergies
andCharges,J.Chem. Phys. 136,064103(2012).
Furthermore,theauthorcontributedtothefollowingpublications:
• S.KondatiNatarajan,T.Morawietz,andJ.Behler,RepresentingthePotential-
Energy Surface of Protonated Water Clusters by High-Dimensional Neural
NetworkPotentials,Phys. Chem. Chem. Phys. 17,8356(2015).
• N. Artrith, T. Morawietz, and J. Behler, High-Dimensional Neural-Network
Potentialsfor MulticomponentSystems: Applicationsto ZincOxide, Phys. Rev.
B83,153101(2011).

For NN ...
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Contents
I. Introduction and State of the Art 1
1. Introduction 3
1.1. OutlineoftheThesis . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2. State of the Art in Simulating Water 5
2.1. EmpiricalWaterModels . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2. AbInitioSimulationsofWater . . . . . . . . . . . . . . . . . . . . . 8
2.3. PotentialsBasedonAbInitioCalculations . . . . . . . . . . . . . . . 10
II. Theoretical Background 13
3. Neural Network Potentials 15
3.1. Feed-ForwardNeuralNetworks . . . . . . . . . . . . . . . . . . . . 15
3.2. High-DimensionalNeuralNetworks . . . . . . . . . . . . . . . . . . 24
3.3. SystematicConstructionoftheReferenceData . . . . . . . . . . . . 31
4. Density-Functional Theory 34
4.1. BasicsofDensity-FunctionalTheory . . . . . . . . . . . . . . . . . . 34
4.2. vanderWaalsCorrections . . . . . . . . . . . . . . . . . . . . . . . 43
4.3. TheFHI-aimscode . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
5. Computational Details 50
5.1. NeuralNetworkPotentials . . . . . . . . . . . . . . . . . . . . . . . 50
5.2. ReferenceCalculations . . . . . . . . . . . . . . . . . . . . . . . . . 50
5.3. MolecularDynamicsSimulations . . . . . . . . . . . . . . . . . . . . 51
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III. Neural Network Potentials for Water Clusters 53
6. The Water Dimer 55
6.1. ExtendingtheReferenceDataSet . . . . . . . . . . . . . . . . . . . 55
6.2. IncorporatingLong-RangeElectrostaticInteractions . . . . . . . . . . 57
6.3. EvaluationofthePotential . . . . . . . . . . . . . . . . . . . . . . . 61
7. Larger Water Clusters 66
7.1. GeneratingtheReferenceDataSet . . . . . . . . . . . . . . . . . . . 66
7.2. LocatingMinimumEnergyConfigurations . . . . . . . . . . . . . . . 73
7.3. ImpactofvanderWaalsInteractions . . . . . . . . . . . . . . . . . . 79
7.4. TransferabilityoftheClusterPotentials . . . . . . . . . . . . . . . . 84
IV. Neural Network Potentials for Bulk Water 89
8. Construction of the Bulk Water Potentials 91
8.1. ReferenceConfigurations . . . . . . . . . . . . . . . . . . . . . . . . 91
8.2. AccuracyoftheReferenceDataSets . . . . . . . . . . . . . . . . . . 96
9. Properties of Crystalline and Liquid Water 98
9.1. PropertiesofCrystallineWater . . . . . . . . . . . . . . . . . . . . . 98
9.2. StructureofLiquidWater . . . . . . . . . . . . . . . . . . . . . . . . 102
9.3. DielectricPropertiesofLiquidWater . . . . . . . . . . . . . . . . . . 106
9.4. DynamicsofLiquidWater . . . . . . . . . . . . . . . . . . . . . . . 108
10.Large-Scale Simulations: The Density Anomalies of Water 111
10.1. DensityIsobars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
10.2. WaterNeighborDistribution . . . . . . . . . . . . . . . . . . . . . . 114
10.3. HydrogenBondStrength . . . . . . . . . . . . . . . . . . . . . . . . 116
V. Summary and Perspectives 121
11.Summary 123
12.Perspectives 126
12.1. NuclearQuantumEffects . . . . . . . . . . . . . . . . . . . . . . . . 126
12.2. ProtonTransferinLiquidWater . . . . . . . . . . . . . . . . . . . . 127
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Appendices 129
A. Neural Network Settings 131
A.1. NeuralNetworkArchitecture . . . . . . . . . . . . . . . . . . . . . . 131
A.2. SymmetryFunctionParameters . . . . . . . . . . . . . . . . . . . . . 131
B. Water Dimer Vibrational Frequencies 138
C. Mininum Energy Configurations for Water Clusters 141
C.1. (H O) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
2 n=2−6
C.2. (H O) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
2 n=2−10
D. Equilibrium Volumes and Energies of Ice Polymorphs 145
Acknowledgements 149
Bibliography 151
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