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Molecular Dynamics Simulations with a Quantum-Chemical Core: Methodology and Applications in Photochemistry and Bioinorganic Chemistry

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Molecular Dynamics Simulations with a Quantum-Chemical Core: Methodology and Applications in Photochemistry and Bioinorganic Chemistry Diss. ETH No. 13450 Molecular Dynamics Simulations with a Quantum-Chemical Core: Methodology and Applications in Photochemistry and Bioinorganic Chemistry A dissertation submitted to the SWISS FEDERAL INSTITUTE OF TECHNOLOGY ZURICH for the degree of Doctor of Natural Sciences presented by CHRISTIAN D. BERWEGER Dipl. Chem. ETH born December 28, 1971 citizen of Herisau, Switzerland accepted on the recommendation of Prof. Dr. Wilfred F. van Gunsteren, examiner Prof. Dr. Ursula Rothlisberger,¨ PD Dr. Florian Muller-Plathe,¨ co-examiners 2000 Laß die Molekule¨ rasen was sie auch zusammenknobeln! Laß das Tufteln,¨ laß das Hobeln, heilig halte die Ekstasen! Christian Morgenstern Meinen Eltern Acknowledgments I wish to thank Wilfred van Gunsteren for giving me the opportunity to do my thesis with him. His profound scientific knowledge and unique personal style rendered my four-years stay in his group a pleasant and stimulating period of my life. His indisputable skills in obtaining computer power are amazing and removed any obstacles in terms of computing bottlenecks. I very much enjoyed the freedom in working hours and scientific topics and biomos’ undoubted generosity in providing coffee, borrels and dinners with guests. I thank Florian M¨uller-Plathe, who had the original idea of introducing finite-element inter- polation in molecular dynamics simulation. Collaboration with him has been especially fruitful and motivating. I’m very grateful to Prof. Dr. Walter Thiel, who provided me the source code of the newest version of the MNDO program. Its many features made the development of the zumos program much easier than initially planned. I thank all members of the group for informatikgest¨utzte Chemie at ETH Z¨urich. They all have provided a seething environment both scientifically and personally. I thank Prof. Dr. Kurt Kremer the Max-Planck-Institute f¨ur Polymerforschung who gener- ously made it possible for me to stay at his institute for three months. This was a very intense and productive time. I thank all the members of the AK Kremer for their care in rendering my stay so cordial and pleasant. Much of the work presented here has been enabled by free software. I especially mention Linux and its accompanying software, who established in my home office the same powerful and efficient computer environment as in the lab. Thanks to Linus Torvalds! Thanks also to the mostly unknown people from GNU and the Free Software Foundation. Most of my keystrokes echo in emacs, their ultimate editor, and the fecomd program compiles in their gcc and g++. Their tool gmake greatly facilitated my work and was actually the best way get my projects organised. It and gawk helped many times in my goal to let computers do the work. Many of the graphics in this work are made with xmgr and xfig. Finally, LATEX is probably the only text processor to write publications and theses without horror. Thanks to all who contributed to these programs! I especially thank Salomon Billeter, who was my primary mentor in using the aforementioned programs. Thanks to Walter Scott, Thomas Huber, Philippe H¨unenberger, Harald Bopp, Heiko Sch¨afer, Roland B¨urgi, Alexandre Bonvin, Urs Stocker, Tomas Hansson and Fred Hamprecht for keeping the computers running. Thanks to Prisca Cerutti for keeping most of the administrative concerns away from me. 5 Contents Kurzfassung 11 Summary 13 Publications 14 1 Introduction 17 1.1 ComputersandChemistry . .. 17 1.2 ProblemsAddressed ............................... 19 1.2.1 Photochemistry: Photoisomerisation of cis-Stilbene. 19 1.2.2 BioinorganicChemistry: Metallothionein . ........ 21 1.3 Theory........................................ 22 1.3.1 QuantumChemistry ............................ 22 Ab initio QuantumChemistry . .. .. .. .. .. .. 22 Hartree-FockMethod. 23 ConfigurationInteraction. 24 CalculationofElectronicallyExcitedStates . 25 Semi-EmpiricalQuantumChemistry. 26 MNDO ............................... 26 MNDO/d .............................. 26 1.3.2 ClassicalMolecularDynamics . ... 27 Newton’sEquationsofMotion. 27 ForceFieldBasics ............................. 27 1.3.3 Combining Quantum Chemistry and Classical Molecular Dynamics . 28 Embedding a Quantum-Chemical System into a Classical Environment . 28 ASimpleModel .......................... 28 PolarisingtheQuantum-ChemicalSystem . 29 SplitQuantum-ClassicalMolecules . 29 QuantumTopology. .. .. .. .. .. .. .. 30 SaturationoftheQuantum-ChemicalSystem . 30 DirectlyBondedAtoms . 32 2 Molecular Dynamics Simulation with an ab initio Potential Energy Function and Finite Element Interpolation: Method and Validation 33 2.1 Abstract....................................... 33 2.2 Introduction.................................... 33 2.3 Methods....................................... 34 7 8 Contents 2.3.1 AnAnalog ................................. 34 2.3.2 Finite Element Interpolation for Molecular Dynamics Simulations . 35 2.3.3 AlgorithmOutline ............................. 36 2.3.4 TheRegularGrid.............................. 37 2.3.5 TheInterpolation .............................. 38 2.3.6 TheQuantum/ClassicalCombinationModel . ..... 40 2.3.7 TheQuantumChemistryMethod . 40 2.3.8 ComputationalDetails . 40 StilbeneGeometry ............................. 40 SimulationParameters . 41 2.4 ResultsandDiscussion . ... 42 2.4.1 Preliminary Investigation of the Potential Energy Surface of Photoex- citedStilbene................................ 42 2.4.2 Simulations................................. 42 2.4.3 Accuracyoftheinterpolation. .... 42 2.4.4 Efficiency.................................. 44 2.5 Conclusions..................................... 45 3 The Photoisomerisation of cis-Stilbene Does not Follow the Minimum Energy Path 49 3.1 Summary ...................................... 49 3.2 Introduction.................................... 49 3.3 PotentialEnergySurface . .... 50 3.4 KineticActivation............................... ... 50 3.5 SolventEffect................................... 51 3.6 MolecularShapeChanges . .. 52 3.7 Conclusions..................................... 52 4 Viscosity Dependence and Solvent Effects in the Photoisomerisation of cis-Stilbene 53 4.1 Abstract....................................... 53 4.2 Introduction.................................... 53 4.3 Methods....................................... 55 4.3.1 ComputationalDetails . 55 4.3.2 ActivationEnergies. 56 4.3.3 SolventProperties ............................. 56 4.3.4 EstimationofReactionRateConstants . ..... 57 4.4 ResultsandDiscussion . ... 58 4.4.1 PotentialEnergySurface . .. 58 4.4.2 DependenceonTemperatureandPressure . ..... 62 4.4.3 ViscosityDependence . 64 4.4.4 AverageTrajectories . 68 4.4.5 SomeIndividualDihedralAngleTrajectories . ........ 70 4.4.6 ReasonfortheBarrier-Recrossings . ..... 72 4.4.7 BehaviourontheBarrier . 74 4.4.8 BarrierClose-ups.............................. 74 4.5 Conclusions..................................... 76 Contents 9 5 Simulation of the β DomainofMetallothionein 79 5.1 Summary ...................................... 79 5.2 Introduction.................................... 79 5.3 Methods....................................... 80 5.3.1 ComputationalDetails . 80 5.3.2 Estimation of Van-der-Waals Interaction Parameters forCadmium . 82 5.4 ResultsandDiscussion . ... 83 5.4.1 Comparison of the CdZn2 X-Ray Crystal Structure with the Cd3 NMR SolutionStructure ............................. 83 5.4.2 TheCdZn2 MDcSimulationComparedtotheX-RayStructure . 87 5.4.3 TheCdZn2 MDqSimulationComparedtotheX-Ray Structure . 89 5.4.4 Comparison of the Cd3 MDcSimulationwithNMRData. 92 5.4.5 Comparison of the Cd3 MDqSimulationwithNMRData. 94 5.4.6 Comparison of the Classical MDc and Quantum-Chemical MDq Simu- lations.................................... 95 5.4.7 Comparison of the Simulations of the Cd3, CdZn2 and Zn3 Variants . 96 5.5 Conclusions..................................... 98 6 Outlook 99 6.1 PhotoisomerisationofStilbene . ....... 99 6.1.1 Photoisomerisation of trans-Stilbene.................... 99 6.1.2 QuantumDynamicswithSurfaceHopping . ... 99 6.1.3 InterpolationinMoreDimensions . .... 99 6.1.4 AnotherSystem...............................100 6.2 Metallothionein ................................. 100 6.2.1 Other Metals in the β Domain .......................100 6.2.2 The α Domain ...............................100 6.2.3 OtherProteins ...............................100 A The fecomd Implementation 101 A.1 Features.......................................101 A.2 InputFile ......................................102 A.3 OutputFiles..................................... 103 A.4 AuxiliaryPrograms ............................... 103 B The zumos Implementation 105 B.1 TheQuantumTopology. .. .. .. .. .. .. .. .. 105 B.2 Runningzumos ...................................106 Bibliography 109 Curriculum Vitae 117 10 Contents 11 Kurzfassung Der Einsatz von kombiniert quantenchemisch-klassischen Methoden ist popul¨ar geworden zur Computersimulation von grossen Systemen, die ein reagierendes Molek¨ul enthalten, oder, allgemein gesagt, deren entscheidender Teil mit klassischen Theorien schwierig zu erfassen ist. Typische Anwendungen sind beispielsweise kleinere reagierende Molek¨ule in L¨osung, wobei die reagierenden Molek¨ule quantenchemisch, und das L¨osemittel klassisch beschrieben wird, oder aber Proteine, deren aktives Zentrum quantenchemisch beschrieben wird und der Rest klassisch. Dabei hat das L¨osemittel oder der Rest des Proteins einen entscheidenden Einfluss auf das Zen- trum und kann daher nicht einfach weg gelassen werden.
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