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 ... vii 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 viii 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 ix 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 x