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Preface: Preface
Dedication: Dedication
Chapter 1: QM/MM with Auxiliary DFT in deMon2k
1.1 Introduction
1.2 Energies and Gradients
1.3 Local Structure Minimization and Transition-state Search
1.4 Molecular Dynamics
1.5 Second-order Energy Derivatives
1.6 QM/MM Magnetic Shielding and Excited-state Calculations
1.6 QM/MM Magnetic Shielding and Excited-state Calculations
1.7 Transformation Program for deMon2k Input Generation
1.7 Transformation Program for deMon2k Input Generation
1.8 Summary
Abbreviations
Acknowledgments
References
Chapter 12: Machine Learning Algorithms for the Analysis of Molecular Dynamics Trajectories
12.1 Introduction
12.2 Underlying Terms and Definitions
12.3 Machine Learning Solutions for Molecular Simulation
12.3 Machine Learning Solutions for Molecular Simulation
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12.3.1 Potential Energy Surfaces (PES)
12.3.2 ML Algorithms for PES
12.3.3 Free Energy Surfaces (FES)
12.3.4 Coarse Graining (CG)
12.3.5 Molecular Kinetics
12.4 MD Descriptor-based ML Models for Drug Discovery Against Different Targets
12.5 Describing the Chemical Space of ERK2 Kinase Inhibitors From MD Trajectories
12.6 ML MD for the Simulation of Infrared Spectra
12.7 The Ligand-binding Mechanism for Purine Nucleoside Phosphorylase Elucidated via MD and ML
12.8 How ML Assists the Interpretation of ABMD Simulations and the Conceptual Understanding of Chemistry
12.9 Conclusion
Abbreviations
Acknowledgments
References
Chapter 2: Computational Enzymology: A Challenge for Multiscale Approaches
2.1 Introduction
2.2 Results and Discussion
2.2.1 The Michaelis-Menten Enzyme-Substrate Complex (ES)
2.2.2 Catalyzed Chemical Reactions
2.2.2.1 Building the PESs
2.2.2.2 The Role of the Metal
2.2.2.3 Enzymatic Promiscuity
2.2.3 Product Release
2.3 Enzymatic Inhibition Mechanisms
2.4 Conclusions and Perspectives
Abbreviations
References
Chapter 3: QM/MM Simulations of Proteins: Is Explicit Inclusion of Polarization on the Horizon?
3.1 Introduction
3.1.1 Importance of Polarizability in Proteins
3.1.2 Need for Polarizable MM in QM/MM
3.1.3 Accurate Description of Potential Energy Alone is not Sufficient
3.1.3 Accurate Description of Potential Energy Alone is not Sufficient
3.2 Overview of Standard QM/MM Methods
3.2.1 QM Methods Summary
3.2.2 Brief Overview of Classical Force-fields
3.2.3 Explicit Treatment for Electronic Degrees of Freedom in Potential Functions
3.2.3.1 Fluctuating Charge Models
3.2.3.2 Induced Dipole Models
3.2.4 Different QM/MM Schemes and Boundary Treatments
3.2.4.1 Electrostatic Embedding
3.2.4.2 Polarizable Embedding
3.3 Challenges and Limitations
3.3.1 Modeling QM/MM Boundaries is Complicated
3.3.1.1 Pseudo Potentials and Link Atoms
3.3.1.2 Other, Less Common Boundary Treatments
3.3.2 Challenges and Limitations in Polarizable Force-fields
3.3.2.1 Simulating Dipole Models is More Time Consuming
3.3.2.2 Accounting for Anisotropy and Multipole Moments
3.3.2.3 Over-polarization Poses a Major Problem
3.3.2.4 Gas-phase Parameter Fitting Strategy Presents a Challenge for Condensed Phase Parameters
3.3.3 Geometry Optimizing Algorithms May Fail
3.4 Sampling is a Challenge in QM or QM/MM
3.4.1 Path-independent Alchemical Free Energy Calculations
3.4.1.1 Sampling in QM/MM for pKa Calculations
3.4.1.2 Multi-stage Calculations for Solvation Free Energy
3.4.2 Path-dependent Free Energy Profile Calculations
3.4.3 Machine Learning Techniques to Improve Free Energy Assessment
3.4.3 Machine Learning Techniques to Improve Free Energy Assessment
3.5 Case Studies
3.5.1 QM/MMPOL in Free Energy Calculations
3.5.2 Substrate-dependent Proton Transport in CLC Transporters
3.5.2 Substrate-dependent Proton Transport in CLC Transporters
3.5.3 Proton Transfer in Carbonic Anhydrase
3.6 Future Outlook and Conclusions
Abbreviations
References
Chapter 4: Electron and Molecular Dynamics Simulations with Polarizable Embedding
4.1 Introduction
4.2 Real-time Time-dependent Auxiliary Density Functional Theory
4.2.1 Numerical Propagation of Electron Densities
4.2.2 On-the-fly Analyses
4.2.3 High-performance Computing Considerations
4.2.4 Benchmarks
4.3 Electron Dynamics in Contact with a Polarizable Environment
4.3 Electron Dynamics in Contact with a Polarizable Environment
4.4 Ehrenfest Molecular Dynamics Simulations
4.4.1 From Born-Oppenheimer to Ehrenfest Molecular Dynamics Simulations
4.4.2 The Gradient Bottleneck
4.5 Some Examples of Applications
4.5.1 Solvent Effect on a Dye Molecule
4.5.2 UV-Visible Spectra with Polarizable Embedding
4.5.3 Irradiation by High-energy Charged Particles
4.6 Conclusion and Future Perspectives
Acknowledgments
References
Chapter 5: DFTB and Hybrid-DFTB Schemes: Application to Metal Nanosystems, Isolated and in Environments
5.1 Introduction
5.2 DFTB: An Approximate DFT Tool for the Simulation of Complex Systems
5.2.1 DFTB Basics and Extensions
5.2.1.1 The DFTB Formalism
5.2.1.2 Hybrid and Extended Schemes with DFTB
5.2.2 Coupling of DFTB with Dynamics and Landscape Exploration
5.2.2 Coupling of DFTB with Dynamics and Landscape Exploration
5.2.2.1 Coupling of DFTB with Dynamics and Extensive Exploration
5.2.2.1 Coupling of DFTB with Dynamics and Extensive Exploration
5.2.2.2 Multi-method Exploration Schemes
5.3 Metal Nanosytems
5.3.1 Isolated Nanoparticles
5.3.1.1 Structural and Energetic Properties
5.3.1.2 Thermodynamical Properties
5.3.2 Nanoparticles, Functionalized and in Environments
5.3.2.1 Functionalized Nanoparticles
5.3.2.2 Nanoparticles in Solvent
5.3.2.3 Nanoparticles Deposited on a Surface
5.4 Perspectives
Abbreviations
References
Chapter 6: From Atomic Orbitals to Nano-scale Charge Transport with Mixed Quantum/Classical Non-adiabatic Dynamics: Method, Implementation and Application
6.1 Introduction
6.2 Coarse-graining of Electronic Structure
6.2.1 Hamiltonian and Basis Set
6.2.2 Site Energies and Electronic Couplings
6.3 FOB-SH: Basic Equations
6.3.1 Electronic Propagation
6.3.2 Non-adiabatic Transitions
6.3.3 Forces and Nuclear Equation of Motion
6.3.4 Adiabatic Populations and Internal Consistency
6.3.5 Mobility Calculation and Inverse Participation Ratio
6.4 FOB-SH: Technical Details
6.4.1 Energy Conservation after a Successful Hop
6.4.2 Stable Electronic Propagation in the Diabatic Basis
6.4.3 Trivial Crossings and State-tracking
6.4.4 Decoherence Correction
6.4.5 Decoherence Correction-induced Spurious Long-range Charge Transfer
6.4.6 Code Speed-up and Cost
6.5 Charge Mobilities in Nano-scale Organic Semiconductors
6.5 Charge Mobilities in Nano-scale Organic Semiconductors
6.6 Conclusion and Outlook
Abbreviations
References
Chapter 7: Modeling Nanocatalytic Reactions with DFTB/MM-MD and DFTB-NMD
7.1 Reactions Catalyzed by Nanoparticles
7.2 Density Functional Tight-binding/Molecular Mechanics Molecular Dynamics (DFTB/MM-MD)
7.2.1 DFTB/MM-MD Methodology
7.2.2 Application to Benzene Hydrogenation on Mo2C Nanoparticles
7.2.2 Application to Benzene Hydrogenation on Mo2C Nanoparticles
7.3 Density Functional Tight-binding Nanoreactor Molecular Dynamics (DFTB-NMD)
7.3.1 DFTB-NMD Methodology
7.3.2 Application to C2H2 Explosion Under Extreme Conditions
7.3.2 Application to C2H2 Explosion Under Extreme Conditions
7.3.3 Application to Fischer-Tropsch Synthesis on Fe Nanoparticles
7.3.3 Application to Fischer-Tropsch Synthesis on Fe Nanoparticles
7.4 Conclusions and Outlook
Abbreviations
References
Chapter 8: Hohenberg-Kohn Theorems as a basis for Multi-scale Simulations: Frozen-density Embedding Theory
8.1 Introduction
8.1.1 Multi-level Simulations Including Quantum-mechanical Descriptor Level
8.1.2 Multi-level Simulation Methods based on eqn (8.1) Seen from the Perspective of the Hohenberg-Kohn Theorems
8.1.2 Multi-level Simulation Methods based on eqn (8.1) Seen from the Perspective of the Hohenberg-Kohn Theorems
8.1.3 Total Energy Functionals Consistent with the Hohenberg-Kohn Theorems for Multi-level Simulations
8.2 Frozen-density Embedding Theory
8.2.1 Definitions and Notation
8.2.2 Total Energy Functional E_\bi v_\bi AB ^\bf FDET \left[ \biPsi _A \rm ,\birho _B \right]
8.2.3 Ground-states from Variational Calculations
8.2.4 FDET with Descriptors of the NA-electron System Other than the Interacting Wavefunction &Psgr;A
8.2.4.1 Embedded Reference System of Non-interacting Electrons
8.2.4.2 Embedded One-particle Reduced Density Matrix ?A(r,r?))
8.2.4.3 Embedded Wavefunction of Reduced Form (Truncated CI or CAS)
8.2.4.4 FDET(SD)+Ec: Ground-states from Non-variational Calculations
8.2.4.4 FDET(SD)+Ec: Ground-states from Non-variational Calculations
8.3 FDET with Enadxct[&rgr;A,&rgr;B]?&E_cmb.tilde;nadxct[&rgr;A,&rgr;B] for Practical Simulations
8.3 FDET with Enadxct[&rgr;A,&rgr;B]?&E_cmb.tilde;nadxct[&rgr;A,&rgr;B] for Practical Simulations
8.3.1 Interpretation of Errors in FDET Results Due to Enadxct[&rgr;A,&rgr;B]?&E_cmb.tilde;nadxct[&rgr;A,&rgr;B]
8.3.2 Approximating Tnads[&rgr;A,&rgr;B] and vnadt[&rgr;A,&rgr;B](r)
8.3.2.1 Exact Relation for the Functional vnadt[&rgr;A,&rgr;B] at Small &rgr;A,&rgr;B Overlaps
8.3.2.2 Approximating Tnads[&rgr;A,&rgr;B]: Where to Start From?
8.3.2.3 GGA97 - Pragmatic Approximation for vnadt[&rgr;A,&rgr;B](r) and Tnads[&rgr;A,&rgr;B]
8.3.3 Approximating Enadxc[&rgr;A,&rgr;B] and vnadxc[&rgr;A,&rgr;B](r)
8.4 FDET with Finite Basis Sets and the Basis Set Localisation
8.4 FDET with Finite Basis Sets and the Basis Set Localisation
8.5 Extensions of Ground-state FDET to Excited States
8.5.1 Other than the Lowest-energy Solutions of the Euler-Lagrange Equation for the Embedded Interacting Wavefunction
8.5.2 Linear-response of Embedded Non-interacting Embedded Wavefunction &PHgr;KSA
8.6 Multi-level Simulations based on FDET
Acknowledgments
References
Chapter 9: 3D-RISM-KH Molecular Solvation Theory
9.1 Introduction
9.1.1 Theoretical Background of the 3D-RISM-KH Molecular Solvation Theory (MST)
9.2 Developments of 3D-RISM-KH Theory in Multiscale Modeling
9.2.1 Multiple Time Step Molecular Dynamics (MTS-MD) Method for Biomolecular Simulations
9.2.2 Dissipative Particle Dynamics (DPD) with an Effective Potential Obtained From DRISM-KH Theory by Coarse-graining
9.2.2 Dissipative Particle Dynamics (DPD) with an Effective Potential Obtained From DRISM-KH Theory by Coarse-graining
9.2.3 Mapping Binding Site(s) on Protein Surfaces
9.2.4 Water Molecules in Active Sites of Proteins
9.2.5 Electric Double Layer in Nanoporous Materials with 3D-RISM-KH-VM
9.2.6 Electrolyte Solutions in Nanopores with the 3D-RISM-KH-VM Theory
9.2.7 Interfacial Problems with the 3D-RISM-KH Theory
9.2.8 Inhomogeneous Solvation From the 3D-RISM-KH Theory
9.2.9 Solvation Free Energy (SFE) Calculations with the 3D-RISM-KH Theory
9.2.10 Machine Learning with the 3D-RISM-KH Theory
9.3 Conclusion
Abbreviations
Acknowledgments
References
Chapter 10: Free Energy Analysis Algorithms along Transition Paths and Transmembrane Ion Permeation
10.1 Introduction
10.2 Illustration of Sampling Errors From Improper RCs
10.2 Illustration of Sampling Errors From Improper RCs
10.3 Free Energy Calculation Methods-WHAM and WELSAM
10.3 Free Energy Calculation Methods-WHAM and WELSAM
10.3.1 The Weighted Histogram Analysis Method (WHAM)
10.3.2 The Weighted Least Squares Analysis Method (WELSAM)
10.3.2 The Weighted Least Squares Analysis Method (WELSAM)
10.3.3 Numerical Results of Data Sampling and PMF Calculation along the Transition Path
10.4 Applications in Transmembrane Ion Permeation
10.4 Applications in Transmembrane Ion Permeation
10.4.1 Free Energy Calculation on the Water-chain-assisted Mechanism of Transmembrane Ion Permeation
10.4.1.1 Reaction Coordinate Design
10.4.2 Umbrella Sampling along the New Reaction Coordinate
10.4.2 Umbrella Sampling along the New Reaction Coordinate
10.4.2.1 Free Energy Calculation based on the New Reaction Coordinate
10.4.2.1 Free Energy Calculation based on the New Reaction Coordinate
10.4.2.2 Free Energy Calculation along the Transition Path
10.4.3 Free Energy Calculation on the Dehydration Mechanism of Transmembrane Ion Permeation
10.4.3.1 Reaction Coordinate Design
10.4.3.2 Umbrella Sampling along the New Reaction Coordinate
10.4.3.3 Phase-plane Analysis and Free Energy Calculations along the Transition Paths
10.4.4 Permeation of Sodium and Chloride Ions through Membranes with Three Different Thicknesses
10.5 Summary
Abbreviations
References
Chapter 11: Pathways in Classification Space: Machine Learning as a Route to Predicting Kinetics of Structural Transitions in Atomic Crystals
11.1 Introduction
11.2 Theoretical Background
11.2.1 Classification Neural Networks for Local Structure Identification
11.2.1 Classification Neural Networks for Local Structure Identification
11.2.1.1 Input Functions
11.2.1.2 Hidden Layers
11.2.1.3 Output Layer
11.2.1.4 Optimizing Weights
11.2.2 Path Collective Variables in Classifier Space
11.2.3 Enhanced Sampling Approaches
11.2.3.1 Driven Adiabatic Free Energy Dynamics
11.2.3.2 Metadynamics
11.3 Application: Solid-Solid Phase Transformation
11.3.1 A15-bcc Interface Setup
11.3.2 Neural Network Setup
11.3.2.1 Selection of Input Functions
11.3.2.2 Producing Training and Test Sets
11.3.2.3 Training the Neural Network
11.3.2.4 Classification Performance of the Neural Networks
11.3.3 Path CV for Phase Fractions
11.3.4 Sampling A15-bcc Phase Transformation
11.3.4.1 dAFED Simulations
11.3.4.2 Metadynamics Simulations
11.4 Concluding Remarks
Abbreviations
Acknowledgments
References