SlideShare una empresa de Scribd logo

NANO266 - Lecture 13 - Ab initio molecular dyanmics

•
•
University of California, San Diego
University of California, San Diego

UCSD NANO 266 Quantum Mechanical Modelling of Materials and Nanostructures is a graduate class that provides students with a highly practical introduction to the application of first principles quantum mechanical simulations to model, understand and predict the properties of materials and nano-structures. The syllabus includes: a brief introduction to quantum mechanics and the Hartree-Fock and density functional theory (DFT) formulations; practical simulation considerations such as convergence, selection of the appropriate functional and parameters; interpretation of the results from simulations, including the limits of accuracy of each method. Several lab sessions provide students with hands-on experience in the conduct of simulations. A key aspect of the course is in the use of programming to facilitate calculations and analysis.

Educación
1 de 23
Descargar para leer sin conexión
Ab initio molecular dynamics Shyue Ping Ong
What is molecular dynamics (MD)? Moving atomic nuclei by solving Newton’s equation of motion For N nuclei, we have 3N positions and 3N velocities, i.e., a 6N dimensional phase space. NANO266 2 M!!RI = − ∂E ∂RI = FI [{RJ}]
Where do forces come from? Lennard-Jones potential •  OK for rare gases •  No chemistry •  Only pair-wise and no directionality Empirical force-fields •  Fitted parameters based on model function •  Can include many-body terms to incorporate dispersion, polarization, etc. Quantum mechanics! •  Expensive…, and surprisingly, not always the most accurate! NANO266 3 VLJ = 4ε σ r ! " # $ % & 12 − σ r ! " # $ % & 6( ) * * + , - -
2013 Nobel Prize in Chemistry NANO266 4
Computational Experiment NANO266 5 Initialize positions and velocities Compute forces Determine new positions Calculate thermodynamic averages Repeat until time is reached
Initialization 2nd order PDF -> Initial positions and velocities Positions •  Reasonable guess based on structure •  No overlap / short atomic distances Velocities •  Small initial velocity •  Steadily increase temperature (velocity scaling) NANO266 6 M!!RI = − ∂E ∂RI = FI [{RI}]
Maxwell-Boltzmann distribution NANO266 7 f (v) = m 2πkT ! " # $ % & 3 4πv2 e − mv2 2kT
Ensembles Microcanonical – N, V, E Canonical – N, V, T •  Temperature control achieved via thermostats •  Examples: velocity rescaling, Andersen thermostat, Nose-Hoover thermostat, Langevin dynamics, etc. NANO266 8
Integrating equations of motion –Verlet algorithm Key properties of Verlet algorithm •  Errors do not accumulate •  Energy is conserved •  Simulations are stable NANO266 9 M!!RI = FI [{RJ}] !!RI = 1 MI FI [{RJ}] [RI (t + Δt)− RI (t)]−[RI (t)− RI (t − Δt)] (Δt)2 = 1 MI FI [{RJ}] RI (t + Δt) = 2RI (t)+ RI (t − Δt)+ (Δt)2 MI FI [{RJ (t)}]
Flavors of quantum MD Born-Oppenheimer •  Electrons stay in instantaneous ground state as nuclei move •  Perform electronic SCF at each time step •  Compute forces (Hellman-Feynman theorem) •  Move nuclei Car-Parrinello •  Treat ions and electrons as one unified system •  Accomplished with fictitious kinetic energy for electrons NANO266 10 Car, R.; Parrinello, M. Unified approach for molecular dynamics and density-functional theory, Phys. Rev. Lett., 1985, 55, 2471–2474, doi: 10.1103/PhysRevLett.55.2471.
Coupled equations of motion The CP Lagrangian Equations of motion NANO266 11 L = 1 2 (2µ) i=1 N ∑ dr !ψi (r) 2 ∫ + MI I=1 NI ∑ !!RI − E[ψi,r]+ Λij drψi * (r)ψj (r)−δij∫% & ' ( ij ∑ Imposes orthonormality of electronic states µ !!ψi (r,t) = −Hψj (r)+ Λikψk (r,t) k ∑ MI !!RI = − ∂E ∂RI
Comparison of BO vs CP MD NANO266 12 CP Avoids need for costly SCF iteration of electrons at each step Time step required is smaller BO Solves Schrodinger equation at each step Time step can be longer
General procedure for MD simulation NANO266 13
Applications of MD Thermodynamics from ensemble averages Real-time evolution •  Reactions •  Interaction of molecules on surfaces •  Trajectories of ions Ground-state structures •  Geometry optimization is in fact a form of MD. •  For complex structures (e.g., low symmetry systems, interfaces, liquids, amorphous solids, etc.), MD can be used to determine low- energy structures NANO266 14 Nattino, F.; Ueta, H.; Chadwick, H.; Reijzen, M. E. Van; Beck, R. D.; Jackson, B.; Hemert, M. C. Van; Kroes, G. Ab Initio Molecular Dynamics Calculations versus Quantum-State- Resolved Experiments on CHD 3 + Pt(111): New Insights into a Prototypical Gas − Surface Reaction, J. Phys. Chem. Lett., 2014, 5, 1294–1299, doi:10.1021/jz500233n.
Thermodynamic averages Under ergodic hypothesis Examples of averages •  Energy (potential, kinetic, total) •  Temperature •  Pressure •  Mean square displacements (diffusion) •  Radial distribution function NANO266 15 A = Aie−βEi (r,p) i ∑ e−βEi (r,p) i ∑ = lim T→∞ 1 T A(t)dt 0 T ∫
Correlation Functions from MD Pair distribution function Time correlation function NANO266 16 g(r) = V N2 δ(r − rij) j≠i ∑ i ∑ Einstein relation (valid at large t) D = 1 3 dt v(t)v(0) 0 ∞ ∫ Example: Diffusion coefficient D = 1 2dt (r(t)− r(0))22tγ = (A(t)− A(0))2 γ = dt !A(t) !A(0) 0 ∞ ∫
Structure ofAmorphous InP NANO266 17 Lewis, L.; De Vita, A.; Car, R. Structure and electronic properties of amorphous indium phosphide from first principles, Phys. Rev. B, 1998, 57, 1594–1606, doi:10.1103/PhysRevB.57.1594.
Lithium hydroxide phase transition under high pressure NANO266 18 Pagliai, M.; Iannuzzi, M.; Cardini, G.; Parrinello, M.; Schettino, V. Lithium hydroxide phase transition under high pressure: An ab initio molecular dynamics study, ChemPhysChem, 2006, 7, 141–147, doi:10.1002/cphc.200500272.
Dihydrogen oxide NANO266 19 Izvekov, S.; Voth, G. a. Car-Parrinello molecular dynamics simulation of liquid water: New results, J. Chem. Phys., 2002, 116, 10372–10376, doi: 10.1063/1.1473659.
Diffusion in Lithium Superionic Conductors NANO266 20 a c a b 1D conductors would be highly sensitive to blocking defects! X Trace of Li motion at 900K Overall Ea (meV) σ@ 300 K (mS/cm) First principles1 210 13 Experimental 2 240 12 1 S. P. Ong Y. Mo, W. Richards, L. Miara, H. S. Lee, G. Ceder. Energy Environ. Sci., 2013, 6, 148–156. 2 N. Kamaya et al. Nat. Mater. 2011, 10, 682-686
Cation has a small effect on diffusivity of Li10MP2S12 Isovalen t Aliovalen t Ge Si Sn P Al σ @ 300 K (mS/Cm) 13 23 6 4 33 Ea (meV) 210 200 240 260 180 (Aliovalent substitutions are Li+ compensated) S. P. Ong, Y. Mo, W. D. Richards, L. Miara, H. S. Lee, G. Ceder, Phase stability, electrochemical stability and ionic conductivity in the Li10±1MP2X12 family of superionic conductors. Energy Environ. Sci., 2012, doi: 10.1039/C2EE23355J
Phonons from MD NANO266 22 Kim, J.; Yeh, M. L.; Khan, F. S.; Wilkins, J. W. Surface phonons of the Si(111)-7x7 reconstructed surface, Phys. Rev. B, 1995, 52, 14709–14718, doi: 10.1103/PhysRevB.52.14709.
Surface reactions with MD NANO266 23 Arifin, R.; Shibuta, Y.; Shimamura, K.; Shimojo, F.; Yamaguchi, S. Ab Initio Molecular Dynamics Simulation of Ethylene Reaction on Nickel (111) Surface, J. Phys. Chem. C, 2015, 119, 3210–3216, doi:10.1021/jp512148b.

Recomendados

BIOS 203 Lecture 4: Ab initio molecular dynamics
BIOS 203 Lecture 4: Ab initio molecular dynamicsBIOS 203 Lecture 4: Ab initio molecular dynamics
BIOS 203 Lecture 4: Ab initio molecular dynamicsbios203
 
NANO266 - Lecture 2 - The Hartree-Fock Approach
NANO266 - Lecture 2 - The Hartree-Fock ApproachNANO266 - Lecture 2 - The Hartree-Fock Approach
NANO266 - Lecture 2 - The Hartree-Fock ApproachUniversity of California, San Diego
 
Advanced Molecular Dynamics 2016
Advanced Molecular Dynamics 2016Advanced Molecular Dynamics 2016
Advanced Molecular Dynamics 2016Bioinformatics and Computational Biosciences Branch
 
NANO266 - Lecture 4 - Introduction to DFT
NANO266 - Lecture 4 - Introduction to DFTNANO266 - Lecture 4 - Introduction to DFT
NANO266 - Lecture 4 - Introduction to DFTUniversity of California, San Diego
 
Dft calculation by vasp
Dft calculation by vaspDft calculation by vasp
Dft calculation by vaspMIHIR RANJAN SAHOO
 
Molecular Dynamics - review
Molecular Dynamics - review Molecular Dynamics - review
Molecular Dynamics - review Hamed Hoorijani
 
Basics of DFT+U
Basics of DFT+U Basics of DFT+U
Basics of DFT+U Burak Himmetoglu
 
Introduction to DFT Part 2
Introduction to DFT Part 2Introduction to DFT Part 2
Introduction to DFT Part 2Mariana M. Odashima
 

Recomendados

BIOS 203 Lecture 4: Ab initio molecular dynamics
BIOS 203 Lecture 4: Ab initio molecular dynamicsBIOS 203 Lecture 4: Ab initio molecular dynamics
BIOS 203 Lecture 4: Ab initio molecular dynamicsbios203
 
NANO266 - Lecture 2 - The Hartree-Fock Approach
NANO266 - Lecture 2 - The Hartree-Fock ApproachNANO266 - Lecture 2 - The Hartree-Fock Approach
NANO266 - Lecture 2 - The Hartree-Fock ApproachUniversity of California, San Diego
 
Advanced Molecular Dynamics 2016
Advanced Molecular Dynamics 2016Advanced Molecular Dynamics 2016
Advanced Molecular Dynamics 2016Bioinformatics and Computational Biosciences Branch
 
NANO266 - Lecture 4 - Introduction to DFT
NANO266 - Lecture 4 - Introduction to DFTNANO266 - Lecture 4 - Introduction to DFT
NANO266 - Lecture 4 - Introduction to DFTUniversity of California, San Diego
 
Dft calculation by vasp
Dft calculation by vaspDft calculation by vasp
Dft calculation by vaspMIHIR RANJAN SAHOO
 
Molecular Dynamics - review
Molecular Dynamics - review Molecular Dynamics - review
Molecular Dynamics - review Hamed Hoorijani
 
Basics of DFT+U
Basics of DFT+U Basics of DFT+U
Basics of DFT+U Burak Himmetoglu
 
Introduction to DFT Part 2
Introduction to DFT Part 2Introduction to DFT Part 2
Introduction to DFT Part 2Mariana M. Odashima
 
Ab initio md
Ab initio mdAb initio md
Ab initio mdyudhaarman
 
Density Functional Theory
Density Functional TheoryDensity Functional Theory
Density Functional Theorykrishslide
 
Density Functional Theory
Density Functional TheoryDensity Functional Theory
Density Functional TheoryWesley Chen
 
Quantum Chemistry
Quantum ChemistryQuantum Chemistry
Quantum Chemistrybaoilleach
 
Potential Energy Surface Molecular Mechanics ForceField
Potential Energy Surface Molecular Mechanics ForceField Potential Energy Surface Molecular Mechanics ForceField
Potential Energy Surface Molecular Mechanics ForceField Jahan B Ghasemi
 
Dft presentation
Dft presentationDft presentation
Dft presentationSaibalendu Sarkar
 
Density functional theory
Density functional theoryDensity functional theory
Density functional theorysandhya singh
 
Approximations in DFT
Approximations in DFTApproximations in DFT
Approximations in DFTClaudio Attaccalite
 
Density Functional Theory.pptx
Density Functional Theory.pptxDensity Functional Theory.pptx
Density Functional Theory.pptxHassanShah396906
 
Electronic structure of strongly correlated materials
Electronic structure of strongly correlated materialsElectronic structure of strongly correlated materials
Electronic structure of strongly correlated materialsABDERRAHMANE REGGAD
 
Lecture5
Lecture5Lecture5
Lecture5Heather Kulik
 
Ising model
Ising modelIsing model
Ising modelMuhammad Usama Daud
 
Band structure
Band structureBand structure
Band structurenirupam12
 
Applications of Computational Quantum Chemistry
Applications of Computational Quantum ChemistryApplications of Computational Quantum Chemistry
Applications of Computational Quantum ChemistryUniversity of Kerbala, Faculty of Science, Department of Chemistry
 
Introduction to DFT Part 1
Introduction to DFT Part 1 Introduction to DFT Part 1
Introduction to DFT Part 1 Mariana M. Odashima
 
Hartree-Fock Review
Hartree-Fock Review Hartree-Fock Review
Hartree-Fock Review Inon Sharony
 
Exercises with DFT+U
Exercises with DFT+UExercises with DFT+U
Exercises with DFT+UBurak Himmetoglu
 
CHAPTER 6 Quantum Mechanics II
CHAPTER 6 Quantum Mechanics IICHAPTER 6 Quantum Mechanics II
CHAPTER 6 Quantum Mechanics IIThepsatri Rajabhat University
 
Density functional theory (DFT) and the concepts of the augmented-plane-wave ...
Density functional theory (DFT) and the concepts of the augmented-plane-wave ...Density functional theory (DFT) and the concepts of the augmented-plane-wave ...
Density functional theory (DFT) and the concepts of the augmented-plane-wave ...ABDERRAHMANE REGGAD
 
Linear response theory and TDDFT
Linear response theory and TDDFT Linear response theory and TDDFT
Linear response theory and TDDFT Claudio Attaccalite
 
NANO266 - Lecture 12 - High-throughput computational materials design
NANO266 - Lecture 12 - High-throughput computational materials designNANO266 - Lecture 12 - High-throughput computational materials design
NANO266 - Lecture 12 - High-throughput computational materials designUniversity of California, San Diego
 
NANO266 - Lecture 3 - Beyond the Hartree-Fock Approximation
NANO266 - Lecture 3 - Beyond the Hartree-Fock ApproximationNANO266 - Lecture 3 - Beyond the Hartree-Fock Approximation
NANO266 - Lecture 3 - Beyond the Hartree-Fock ApproximationUniversity of California, San Diego
 

Más contenido relacionado

La actualidad más candente

Density Functional Theory
Density Functional TheoryDensity Functional Theory
Density Functional Theorykrishslide
 
Density Functional Theory
Density Functional TheoryDensity Functional Theory
Density Functional TheoryWesley Chen
 
Quantum Chemistry
Quantum ChemistryQuantum Chemistry
Quantum Chemistrybaoilleach
 
Potential Energy Surface Molecular Mechanics ForceField
Potential Energy Surface Molecular Mechanics ForceField Potential Energy Surface Molecular Mechanics ForceField
Potential Energy Surface Molecular Mechanics ForceField Jahan B Ghasemi
 
Density functional theory
Density functional theoryDensity functional theory
Density functional theorysandhya singh
 
Density Functional Theory.pptx
Density Functional Theory.pptxDensity Functional Theory.pptx
Density Functional Theory.pptxHassanShah396906
 
Electronic structure of strongly correlated materials
Electronic structure of strongly correlated materialsElectronic structure of strongly correlated materials
Electronic structure of strongly correlated materialsABDERRAHMANE REGGAD
 
Band structure
Band structureBand structure
Band structurenirupam12
 
Hartree-Fock Review
Hartree-Fock Review Hartree-Fock Review
Hartree-Fock Review Inon Sharony
 
Density functional theory (DFT) and the concepts of the augmented-plane-wave ...
Density functional theory (DFT) and the concepts of the augmented-plane-wave ...Density functional theory (DFT) and the concepts of the augmented-plane-wave ...
Density functional theory (DFT) and the concepts of the augmented-plane-wave ...ABDERRAHMANE REGGAD
 
Linear response theory and TDDFT
Linear response theory and TDDFT Linear response theory and TDDFT
Linear response theory and TDDFT Claudio Attaccalite
 

La actualidad más candente (20)

Ab initio md
Ab initio mdAb initio md
Ab initio md
 
Density Functional Theory
Density Functional TheoryDensity Functional Theory
Density Functional Theory
 
Density Functional Theory
Density Functional TheoryDensity Functional Theory
Density Functional Theory
 
Quantum Chemistry
Quantum ChemistryQuantum Chemistry
Quantum Chemistry
 
Potential Energy Surface Molecular Mechanics ForceField
Potential Energy Surface Molecular Mechanics ForceField Potential Energy Surface Molecular Mechanics ForceField
Potential Energy Surface Molecular Mechanics ForceField
 
Dft presentation
Dft presentationDft presentation
Dft presentation
 
Density functional theory
Density functional theoryDensity functional theory
Density functional theory
 
Approximations in DFT
Approximations in DFTApproximations in DFT
Approximations in DFT
 
Density Functional Theory.pptx
Density Functional Theory.pptxDensity Functional Theory.pptx
Density Functional Theory.pptx
 
Electronic structure of strongly correlated materials
Electronic structure of strongly correlated materialsElectronic structure of strongly correlated materials
Electronic structure of strongly correlated materials
 
Lecture5
Lecture5Lecture5
Lecture5
 
Ising model
Ising modelIsing model
Ising model
 
Band structure
Band structureBand structure
Band structure
 
Applications of Computational Quantum Chemistry
Applications of Computational Quantum ChemistryApplications of Computational Quantum Chemistry
Applications of Computational Quantum Chemistry
 
Introduction to DFT Part 1
Introduction to DFT Part 1 Introduction to DFT Part 1
Introduction to DFT Part 1
 
Hartree-Fock Review
Hartree-Fock Review Hartree-Fock Review
Hartree-Fock Review
 
Exercises with DFT+U
Exercises with DFT+UExercises with DFT+U
Exercises with DFT+U
 
CHAPTER 6 Quantum Mechanics II
CHAPTER 6 Quantum Mechanics IICHAPTER 6 Quantum Mechanics II
CHAPTER 6 Quantum Mechanics II
 
Density functional theory (DFT) and the concepts of the augmented-plane-wave ...
Density functional theory (DFT) and the concepts of the augmented-plane-wave ...Density functional theory (DFT) and the concepts of the augmented-plane-wave ...
Density functional theory (DFT) and the concepts of the augmented-plane-wave ...
 
Linear response theory and TDDFT
Linear response theory and TDDFT Linear response theory and TDDFT
Linear response theory and TDDFT
 

Destacado

NANO266 - Lecture 12 - High-throughput computational materials design
NANO266 - Lecture 12 - High-throughput computational materials designNANO266 - Lecture 12 - High-throughput computational materials design
NANO266 - Lecture 12 - High-throughput computational materials designUniversity of California, San Diego
 
NANO266 - Lecture 6 - Molecule Properties from Quantum Mechanical Modeling
NANO266 - Lecture 6 - Molecule Properties from Quantum Mechanical ModelingNANO266 - Lecture 6 - Molecule Properties from Quantum Mechanical Modeling
NANO266 - Lecture 6 - Molecule Properties from Quantum Mechanical ModelingUniversity of California, San Diego
 
UCSD NANO106 - 13 - Other Diffraction Techniques and Common Crystal Structures
UCSD NANO106 - 13 - Other Diffraction Techniques and Common Crystal StructuresUCSD NANO106 - 13 - Other Diffraction Techniques and Common Crystal Structures
UCSD NANO106 - 13 - Other Diffraction Techniques and Common Crystal StructuresUniversity of California, San Diego
 
Creating It from Bit - Designing Materials by Integrating Quantum Mechanics, ...
Creating It from Bit - Designing Materials by Integrating Quantum Mechanics, ...Creating It from Bit - Designing Materials by Integrating Quantum Mechanics, ...
Creating It from Bit - Designing Materials by Integrating Quantum Mechanics, ...University of California, San Diego
 
SWCNT Growth from Chiral and Achiral Carbon Nanorings: Prediction of Chiralit...
SWCNT Growth from Chiral and Achiral Carbon Nanorings: Prediction of Chiralit...SWCNT Growth from Chiral and Achiral Carbon Nanorings: Prediction of Chiralit...
SWCNT Growth from Chiral and Achiral Carbon Nanorings: Prediction of Chiralit...Stephan Irle
 
Edinburgh | May-16 | Ions that can Hop, Skip and Jump: Lithium Conduction ...
Edinburgh | May-16 | Ions that can Hop, Skip and Jump: Lithium Conduction ... Edinburgh | May-16 | Ions that can Hop, Skip and Jump: Lithium Conduction ...
Edinburgh | May-16 | Ions that can Hop, Skip and Jump: Lithium Conduction ...Smart Villages
 
Intranet 2.0 e Social CRM - BlueKiwi e Lithium
Intranet 2.0 e Social CRM - BlueKiwi e LithiumIntranet 2.0 e Social CRM - BlueKiwi e Lithium
Intranet 2.0 e Social CRM - BlueKiwi e LithiumINSPIRIT BRASIL
 
First Principles Thermodynamics and Kinetic Monte Carlo Simulations: A case s...
First Principles Thermodynamics and Kinetic Monte Carlo Simulations: A case s...First Principles Thermodynamics and Kinetic Monte Carlo Simulations: A case s...
First Principles Thermodynamics and Kinetic Monte Carlo Simulations: A case s...Ghanshyam Pilania
 

Destacado (20)

NANO266 - Lecture 12 - High-throughput computational materials design
NANO266 - Lecture 12 - High-throughput computational materials designNANO266 - Lecture 12 - High-throughput computational materials design
NANO266 - Lecture 12 - High-throughput computational materials design
 
NANO266 - Lecture 3 - Beyond the Hartree-Fock Approximation
NANO266 - Lecture 3 - Beyond the Hartree-Fock ApproximationNANO266 - Lecture 3 - Beyond the Hartree-Fock Approximation
NANO266 - Lecture 3 - Beyond the Hartree-Fock Approximation
 
NANO266 - Lecture 6 - Molecule Properties from Quantum Mechanical Modeling
NANO266 - Lecture 6 - Molecule Properties from Quantum Mechanical ModelingNANO266 - Lecture 6 - Molecule Properties from Quantum Mechanical Modeling
NANO266 - Lecture 6 - Molecule Properties from Quantum Mechanical Modeling
 
NANO266 - Lecture 5 - Exchange-Correlation Functionals
NANO266 - Lecture 5 - Exchange-Correlation FunctionalsNANO266 - Lecture 5 - Exchange-Correlation Functionals
NANO266 - Lecture 5 - Exchange-Correlation Functionals
 
NANO266 - Lecture 9 - Tools of the Modeling Trade
NANO266 - Lecture 9 - Tools of the Modeling TradeNANO266 - Lecture 9 - Tools of the Modeling Trade
NANO266 - Lecture 9 - Tools of the Modeling Trade
 
NANO266 - Lecture 14 - Transition state modeling
NANO266 - Lecture 14 - Transition state modelingNANO266 - Lecture 14 - Transition state modeling
NANO266 - Lecture 14 - Transition state modeling
 
NANO266 - Lecture 7 - QM Modeling of Periodic Structures
NANO266 - Lecture 7 - QM Modeling of Periodic StructuresNANO266 - Lecture 7 - QM Modeling of Periodic Structures
NANO266 - Lecture 7 - QM Modeling of Periodic Structures
 
NANO266 - Lecture 11 - Surfaces and Interfaces
NANO266 - Lecture 11 - Surfaces and InterfacesNANO266 - Lecture 11 - Surfaces and Interfaces
NANO266 - Lecture 11 - Surfaces and Interfaces
 
NANO266 - Lecture 1 - Introduction to Quantum Mechanics
NANO266 - Lecture 1 - Introduction to Quantum MechanicsNANO266 - Lecture 1 - Introduction to Quantum Mechanics
NANO266 - Lecture 1 - Introduction to Quantum Mechanics
 
NANO266 - Lecture 8 - Properties of Periodic Solids
NANO266 - Lecture 8 - Properties of Periodic SolidsNANO266 - Lecture 8 - Properties of Periodic Solids
NANO266 - Lecture 8 - Properties of Periodic Solids
 
04 molecular dynamics
04 molecular dynamics04 molecular dynamics
04 molecular dynamics
 
NANO266 - Lecture 10 - Temperature
NANO266 - Lecture 10 - TemperatureNANO266 - Lecture 10 - Temperature
NANO266 - Lecture 10 - Temperature
 
UCSD NANO106 - 13 - Other Diffraction Techniques and Common Crystal Structures
UCSD NANO106 - 13 - Other Diffraction Techniques and Common Crystal StructuresUCSD NANO106 - 13 - Other Diffraction Techniques and Common Crystal Structures
UCSD NANO106 - 13 - Other Diffraction Techniques and Common Crystal Structures
 
Creating It from Bit - Designing Materials by Integrating Quantum Mechanics, ...
Creating It from Bit - Designing Materials by Integrating Quantum Mechanics, ...Creating It from Bit - Designing Materials by Integrating Quantum Mechanics, ...
Creating It from Bit - Designing Materials by Integrating Quantum Mechanics, ...
 
Ab initio training Ab-initio Architecture
Ab initio training Ab-initio ArchitectureAb initio training Ab-initio Architecture
Ab initio training Ab-initio Architecture
 
SWCNT Growth from Chiral and Achiral Carbon Nanorings: Prediction of Chiralit...
SWCNT Growth from Chiral and Achiral Carbon Nanorings: Prediction of Chiralit...SWCNT Growth from Chiral and Achiral Carbon Nanorings: Prediction of Chiralit...
SWCNT Growth from Chiral and Achiral Carbon Nanorings: Prediction of Chiralit...
 
Edinburgh | May-16 | Ions that can Hop, Skip and Jump: Lithium Conduction ...
Edinburgh | May-16 | Ions that can Hop, Skip and Jump: Lithium Conduction ... Edinburgh | May-16 | Ions that can Hop, Skip and Jump: Lithium Conduction ...
Edinburgh | May-16 | Ions that can Hop, Skip and Jump: Lithium Conduction ...
 
Intranet 2.0 e Social CRM - BlueKiwi e Lithium
Intranet 2.0 e Social CRM - BlueKiwi e LithiumIntranet 2.0 e Social CRM - BlueKiwi e Lithium
Intranet 2.0 e Social CRM - BlueKiwi e Lithium
 
First Principles Thermodynamics and Kinetic Monte Carlo Simulations: A case s...
First Principles Thermodynamics and Kinetic Monte Carlo Simulations: A case s...First Principles Thermodynamics and Kinetic Monte Carlo Simulations: A case s...
First Principles Thermodynamics and Kinetic Monte Carlo Simulations: A case s...
 
UCSD NANO106 - 07 - Material properties and tensors
UCSD NANO106 - 07 - Material properties and tensorsUCSD NANO106 - 07 - Material properties and tensors
UCSD NANO106 - 07 - Material properties and tensors
 

Similar a NANO266 - Lecture 13 - Ab initio molecular dyanmics

Ion-acoustic rogue waves in multi-ion plasmas
Ion-acoustic rogue waves in multi-ion plasmasIon-acoustic rogue waves in multi-ion plasmas
Ion-acoustic rogue waves in multi-ion plasmasMehedi Hassan
 
Complete kinematics studies of fission reactions induced by quasi-free nucleo...
Complete kinematics studies of fission reactions induced by quasi-free nucleo...Complete kinematics studies of fission reactions induced by quasi-free nucleo...
Complete kinematics studies of fission reactions induced by quasi-free nucleo...JoseLuisRodriguezSan16
 
Complete kinematics studies of fission reactions induced by quasi-free nucleo...
Complete kinematics studies of fission reactions induced by quasi-free nucleo...Complete kinematics studies of fission reactions induced by quasi-free nucleo...
Complete kinematics studies of fission reactions induced by quasi-free nucleo...JoseLuisRodriguezSan16
 
Calculation of isotopic dipole moments with spectroscopic accuracy
Calculation of isotopic dipole moments with spectroscopic accuracyCalculation of isotopic dipole moments with spectroscopic accuracy
Calculation of isotopic dipole moments with spectroscopic accuracyAntônio Arapiraca
 
Non linear electron dynamics in solids
Non linear electron dynamics in solidsNon linear electron dynamics in solids
Non linear electron dynamics in solidsClaudio Attaccalite
 
ISFragkopoulos - Seminar on Electrochemical Promotion
ISFragkopoulos - Seminar on Electrochemical PromotionISFragkopoulos - Seminar on Electrochemical Promotion
ISFragkopoulos - Seminar on Electrochemical PromotionIoannis S. Fragkopoulos
 
Resonant Rayleigh Scattering from Collective Molecular Excitations
Resonant Rayleigh Scattering from Collective Molecular ExcitationsResonant Rayleigh Scattering from Collective Molecular Excitations
Resonant Rayleigh Scattering from Collective Molecular ExcitationsbalasubrahmaniyamM
 
Ab-initio real-time spectroscopy: application to non-linear optics
Ab-initio real-time spectroscopy: application to non-linear opticsAb-initio real-time spectroscopy: application to non-linear optics
Ab-initio real-time spectroscopy: application to non-linear opticsClaudio Attaccalite
 
Room Temperature Superconductivity: Dream or Reality?
Room Temperature Superconductivity: Dream or Reality?Room Temperature Superconductivity: Dream or Reality?
Room Temperature Superconductivity: Dream or Reality?ABDERRAHMANE REGGAD
 
Talk device approach to biology march 29 1 2015
Talk device approach to biology march 29 1 2015 Talk device approach to biology march 29 1 2015
Talk device approach to biology march 29 1 2015Bob Eisenberg
 
Non-linear optics by means of dynamical Berry phase
Non-linear optics by means of dynamical Berry phaseNon-linear optics by means of dynamical Berry phase
Non-linear optics by means of dynamical Berry phaseClaudio Attaccalite
 
BVO Research Summary
BVO Research SummaryBVO Research Summary
BVO Research SummaryBernie O'Hare
 
Device approach to biology and engineering
Device approach to biology and engineeringDevice approach to biology and engineering
Device approach to biology and engineeringBob Eisenberg
 
Ion channels poisson fermi for ima july 23 1 2015
Ion channels poisson fermi for ima july 23 1 2015Ion channels poisson fermi for ima july 23 1 2015
Ion channels poisson fermi for ima july 23 1 2015Bob Eisenberg
 

Similar a NANO266 - Lecture 13 - Ab initio molecular dyanmics (20)

Ion-acoustic rogue waves in multi-ion plasmas
Ion-acoustic rogue waves in multi-ion plasmasIon-acoustic rogue waves in multi-ion plasmas
Ion-acoustic rogue waves in multi-ion plasmas
 
Complete kinematics studies of fission reactions induced by quasi-free nucleo...
Complete kinematics studies of fission reactions induced by quasi-free nucleo...Complete kinematics studies of fission reactions induced by quasi-free nucleo...
Complete kinematics studies of fission reactions induced by quasi-free nucleo...
 
Complete kinematics studies of fission reactions induced by quasi-free nucleo...
Complete kinematics studies of fission reactions induced by quasi-free nucleo...Complete kinematics studies of fission reactions induced by quasi-free nucleo...
Complete kinematics studies of fission reactions induced by quasi-free nucleo...
 
Calculation of isotopic dipole moments with spectroscopic accuracy
Calculation of isotopic dipole moments with spectroscopic accuracyCalculation of isotopic dipole moments with spectroscopic accuracy
Calculation of isotopic dipole moments with spectroscopic accuracy
 
Non linear electron dynamics in solids
Non linear electron dynamics in solidsNon linear electron dynamics in solids
Non linear electron dynamics in solids
 
Hybrid quantum systems
Hybrid quantum systemsHybrid quantum systems
Hybrid quantum systems
 
ISFragkopoulos - Seminar on Electrochemical Promotion
ISFragkopoulos - Seminar on Electrochemical PromotionISFragkopoulos - Seminar on Electrochemical Promotion
ISFragkopoulos - Seminar on Electrochemical Promotion
 
Resonant Rayleigh Scattering from Collective Molecular Excitations
Resonant Rayleigh Scattering from Collective Molecular ExcitationsResonant Rayleigh Scattering from Collective Molecular Excitations
Resonant Rayleigh Scattering from Collective Molecular Excitations
 
Ab-initio real-time spectroscopy: application to non-linear optics
Ab-initio real-time spectroscopy: application to non-linear opticsAb-initio real-time spectroscopy: application to non-linear optics
Ab-initio real-time spectroscopy: application to non-linear optics
 
Room Temperature Superconductivity: Dream or Reality?
Room Temperature Superconductivity: Dream or Reality?Room Temperature Superconductivity: Dream or Reality?
Room Temperature Superconductivity: Dream or Reality?
 
final_exam
final_examfinal_exam
final_exam
 
DesiletSpr2013.ppt
DesiletSpr2013.pptDesiletSpr2013.ppt
DesiletSpr2013.ppt
 
Talk device approach to biology march 29 1 2015
Talk device approach to biology march 29 1 2015 Talk device approach to biology march 29 1 2015
Talk device approach to biology march 29 1 2015
 
FinalReport
FinalReportFinalReport
FinalReport
 
Non-linear optics by means of dynamical Berry phase
Non-linear optics by means of dynamical Berry phaseNon-linear optics by means of dynamical Berry phase
Non-linear optics by means of dynamical Berry phase
 
BVO Research Summary
BVO Research SummaryBVO Research Summary
BVO Research Summary
 
Nucleating Nematic Droplets
Nucleating Nematic DropletsNucleating Nematic Droplets
Nucleating Nematic Droplets
 
SNBoseTalk06
SNBoseTalk06SNBoseTalk06
SNBoseTalk06
 
Device approach to biology and engineering
Device approach to biology and engineeringDevice approach to biology and engineering
Device approach to biology and engineering
 
Ion channels poisson fermi for ima july 23 1 2015
Ion channels poisson fermi for ima july 23 1 2015Ion channels poisson fermi for ima july 23 1 2015
Ion channels poisson fermi for ima july 23 1 2015
 

Más de University of California, San Diego

NANO281 Lecture 01 - Introduction to Data Science in Materials Science
NANO281 Lecture 01 - Introduction to Data Science in Materials ScienceNANO281 Lecture 01 - Introduction to Data Science in Materials Science
NANO281 Lecture 01 - Introduction to Data Science in Materials ScienceUniversity of California, San Diego
 
UCSD NANO106 - 08 - Principal Directions and Representation Quadrics
UCSD NANO106 - 08 - Principal Directions and Representation QuadricsUCSD NANO106 - 08 - Principal Directions and Representation Quadrics
UCSD NANO106 - 08 - Principal Directions and Representation QuadricsUniversity of California, San Diego
 
UCSD NANO106 - 03 - Lattice Directions and Planes, Reciprocal Lattice and Coo...
UCSD NANO106 - 03 - Lattice Directions and Planes, Reciprocal Lattice and Coo...UCSD NANO106 - 03 - Lattice Directions and Planes, Reciprocal Lattice and Coo...
UCSD NANO106 - 03 - Lattice Directions and Planes, Reciprocal Lattice and Coo...University of California, San Diego
 
The Materials Project Ecosystem - A Complete Software and Data Platform for M...
The Materials Project Ecosystem - A Complete Software and Data Platform for M...The Materials Project Ecosystem - A Complete Software and Data Platform for M...
The Materials Project Ecosystem - A Complete Software and Data Platform for M...University of California, San Diego
 

Más de University of California, San Diego (14)

A*STAR Webinar on The AI Revolution in Materials Science
A*STAR Webinar on The AI Revolution in Materials ScienceA*STAR Webinar on The AI Revolution in Materials Science
A*STAR Webinar on The AI Revolution in Materials Science
 
NANO281 Lecture 01 - Introduction to Data Science in Materials Science
NANO281 Lecture 01 - Introduction to Data Science in Materials ScienceNANO281 Lecture 01 - Introduction to Data Science in Materials Science
NANO281 Lecture 01 - Introduction to Data Science in Materials Science
 
UCSD NANO106 - 12 - X-ray diffraction
UCSD NANO106 - 12 - X-ray diffractionUCSD NANO106 - 12 - X-ray diffraction
UCSD NANO106 - 12 - X-ray diffraction
 
UCSD NANO106 - 11 - X-rays and their interaction with matter
UCSD NANO106 - 11 - X-rays and their interaction with matterUCSD NANO106 - 11 - X-rays and their interaction with matter
UCSD NANO106 - 11 - X-rays and their interaction with matter
 
UCSD NANO106 - 10 - Bonding in Materials
UCSD NANO106 - 10 - Bonding in MaterialsUCSD NANO106 - 10 - Bonding in Materials
UCSD NANO106 - 10 - Bonding in Materials
 
UCSD NANO106 - 09 - Piezoelectricity and Elasticity
UCSD NANO106 - 09 - Piezoelectricity and ElasticityUCSD NANO106 - 09 - Piezoelectricity and Elasticity
UCSD NANO106 - 09 - Piezoelectricity and Elasticity
 
UCSD NANO106 - 08 - Principal Directions and Representation Quadrics
UCSD NANO106 - 08 - Principal Directions and Representation QuadricsUCSD NANO106 - 08 - Principal Directions and Representation Quadrics
UCSD NANO106 - 08 - Principal Directions and Representation Quadrics
 
UCSD NANO106 - 06 - Plane and Space Groups
UCSD NANO106 - 06 - Plane and Space GroupsUCSD NANO106 - 06 - Plane and Space Groups
UCSD NANO106 - 06 - Plane and Space Groups
 
UCSD NANO106 - 05 - Group Symmetry and the 32 Point Groups
UCSD NANO106 - 05 - Group Symmetry and the 32 Point GroupsUCSD NANO106 - 05 - Group Symmetry and the 32 Point Groups
UCSD NANO106 - 05 - Group Symmetry and the 32 Point Groups
 
UCSD NANO106 - 04 - Symmetry in Crystallography
UCSD NANO106 - 04 - Symmetry in CrystallographyUCSD NANO106 - 04 - Symmetry in Crystallography
UCSD NANO106 - 04 - Symmetry in Crystallography
 
UCSD NANO106 - 03 - Lattice Directions and Planes, Reciprocal Lattice and Coo...
UCSD NANO106 - 03 - Lattice Directions and Planes, Reciprocal Lattice and Coo...UCSD NANO106 - 03 - Lattice Directions and Planes, Reciprocal Lattice and Coo...
UCSD NANO106 - 03 - Lattice Directions and Planes, Reciprocal Lattice and Coo...
 
UCSD NANO106 - 02 - 3D Bravis Lattices and Lattice Computations
UCSD NANO106 - 02 - 3D Bravis Lattices and Lattice ComputationsUCSD NANO106 - 02 - 3D Bravis Lattices and Lattice Computations
UCSD NANO106 - 02 - 3D Bravis Lattices and Lattice Computations
 
UCSD NANO106 - 01 - Introduction to Crystallography
UCSD NANO106 - 01 - Introduction to CrystallographyUCSD NANO106 - 01 - Introduction to Crystallography
UCSD NANO106 - 01 - Introduction to Crystallography
 
The Materials Project Ecosystem - A Complete Software and Data Platform for M...
The Materials Project Ecosystem - A Complete Software and Data Platform for M...The Materials Project Ecosystem - A Complete Software and Data Platform for M...
The Materials Project Ecosystem - A Complete Software and Data Platform for M...
 

Último

microwave assisted reaction. General introduction
microwave assisted reaction. General introductionmicrowave assisted reaction. General introduction
microwave assisted reaction. General introductionMaksud Ahmed
 
2024-NATIONAL-LEARNING-CAMP-AND-OTHER.pptx
2024-NATIONAL-LEARNING-CAMP-AND-OTHER.pptx2024-NATIONAL-LEARNING-CAMP-AND-OTHER.pptx
2024-NATIONAL-LEARNING-CAMP-AND-OTHER.pptxMaritesTamaniVerdade
 
Magic bus Group work1and 2 (Team 3).pptx
Magic bus Group work1and 2 (Team 3).pptxMagic bus Group work1and 2 (Team 3).pptx
Magic bus Group work1and 2 (Team 3).pptxdhanalakshmis0310
 
Sociology 101 Demonstration of Learning Exhibit
Sociology 101 Demonstration of Learning ExhibitSociology 101 Demonstration of Learning Exhibit
Sociology 101 Demonstration of Learning Exhibitjbellavia9
 
psychiatric nursing HISTORY COLLECTION .docx
psychiatric nursing HISTORY COLLECTION .docxpsychiatric nursing HISTORY COLLECTION .docx
psychiatric nursing HISTORY COLLECTION .docxPoojaSen20
 
Key note speaker Neum_Admir Softic_ENG.pdf
Key note speaker Neum_Admir Softic_ENG.pdfKey note speaker Neum_Admir Softic_ENG.pdf
Key note speaker Neum_Admir Softic_ENG.pdfAdmir Softic
 
Kodo Millet PPT made by Ghanshyam bairwa college of Agriculture kumher bhara...
Kodo Millet PPT made by Ghanshyam bairwa college of Agriculture kumher bhara...Kodo Millet PPT made by Ghanshyam bairwa college of Agriculture kumher bhara...
Kodo Millet PPT made by Ghanshyam bairwa college of Agriculture kumher bhara...pradhanghanshyam7136
 
On National Teacher Day, meet the 2024-25 Kenan Fellows
On National Teacher Day, meet the 2024-25 Kenan FellowsOn National Teacher Day, meet the 2024-25 Kenan Fellows
On National Teacher Day, meet the 2024-25 Kenan FellowsMebane Rash
 
Spellings Wk 3 English CAPS CARES Please Practise
Spellings Wk 3 English CAPS CARES Please PractiseSpellings Wk 3 English CAPS CARES Please Practise
Spellings Wk 3 English CAPS CARES Please PractiseAnaAcapella
 
Unit-IV; Professional Sales Representative (PSR).pptx
Unit-IV; Professional Sales Representative (PSR).pptxUnit-IV; Professional Sales Representative (PSR).pptx
Unit-IV; Professional Sales Representative (PSR).pptxVishalSingh1417
 
Food safety_Challenges food safety laboratories_.pdf
Food safety_Challenges food safety laboratories_.pdfFood safety_Challenges food safety laboratories_.pdf
Food safety_Challenges food safety laboratories_.pdfSherif Taha
 
UGC NET Paper 1 Mathematical Reasoning & Aptitude.pdf
UGC NET Paper 1 Mathematical Reasoning & Aptitude.pdfUGC NET Paper 1 Mathematical Reasoning & Aptitude.pdf
UGC NET Paper 1 Mathematical Reasoning & Aptitude.pdfNirmal Dwivedi
 
Mixin Classes in Odoo 17 How to Extend Models Using Mixin Classes
Mixin Classes in Odoo 17 How to Extend Models Using Mixin ClassesMixin Classes in Odoo 17 How to Extend Models Using Mixin Classes
Mixin Classes in Odoo 17 How to Extend Models Using Mixin ClassesCeline George
 
Activity 01 - Artificial Culture (1).pdf
Activity 01 - Artificial Culture (1).pdfActivity 01 - Artificial Culture (1).pdf
Activity 01 - Artificial Culture (1).pdfciinovamais
 
Python Notes for mca i year students osmania university.docx
Python Notes for mca i year students osmania university.docxPython Notes for mca i year students osmania university.docx
Python Notes for mca i year students osmania university.docxRamakrishna Reddy Bijjam
 
Application orientated numerical on hev.ppt
Application orientated numerical on hev.pptApplication orientated numerical on hev.ppt
Application orientated numerical on hev.pptRamjanShidvankar
 
The basics of sentences session 3pptx.pptx
The basics of sentences session 3pptx.pptxThe basics of sentences session 3pptx.pptx
The basics of sentences session 3pptx.pptxheathfieldcps1
 
Making communications land - Are they received and understood as intended? we...
Making communications land - Are they received and understood as intended? we...Making communications land - Are they received and understood as intended? we...
Making communications land - Are they received and understood as intended? we...Association for Project Management
 
Unit-V; Pricing (Pharma Marketing Management).pptx
Unit-V; Pricing (Pharma Marketing Management).pptxUnit-V; Pricing (Pharma Marketing Management).pptx
Unit-V; Pricing (Pharma Marketing Management).pptxVishalSingh1417
 
Introduction to Nonprofit Accounting: The Basics
Introduction to Nonprofit Accounting: The BasicsIntroduction to Nonprofit Accounting: The Basics
Introduction to Nonprofit Accounting: The BasicsTechSoup
 

Último (20)

microwave assisted reaction. General introduction
microwave assisted reaction. General introductionmicrowave assisted reaction. General introduction
microwave assisted reaction. General introduction
 
2024-NATIONAL-LEARNING-CAMP-AND-OTHER.pptx
2024-NATIONAL-LEARNING-CAMP-AND-OTHER.pptx2024-NATIONAL-LEARNING-CAMP-AND-OTHER.pptx
2024-NATIONAL-LEARNING-CAMP-AND-OTHER.pptx
 
Magic bus Group work1and 2 (Team 3).pptx
Magic bus Group work1and 2 (Team 3).pptxMagic bus Group work1and 2 (Team 3).pptx
Magic bus Group work1and 2 (Team 3).pptx
 
Sociology 101 Demonstration of Learning Exhibit
Sociology 101 Demonstration of Learning ExhibitSociology 101 Demonstration of Learning Exhibit
Sociology 101 Demonstration of Learning Exhibit
 
psychiatric nursing HISTORY COLLECTION .docx
psychiatric nursing HISTORY COLLECTION .docxpsychiatric nursing HISTORY COLLECTION .docx
psychiatric nursing HISTORY COLLECTION .docx
 
Key note speaker Neum_Admir Softic_ENG.pdf
Key note speaker Neum_Admir Softic_ENG.pdfKey note speaker Neum_Admir Softic_ENG.pdf
Key note speaker Neum_Admir Softic_ENG.pdf
 
Kodo Millet PPT made by Ghanshyam bairwa college of Agriculture kumher bhara...
Kodo Millet PPT made by Ghanshyam bairwa college of Agriculture kumher bhara...Kodo Millet PPT made by Ghanshyam bairwa college of Agriculture kumher bhara...
Kodo Millet PPT made by Ghanshyam bairwa college of Agriculture kumher bhara...
 
On National Teacher Day, meet the 2024-25 Kenan Fellows
On National Teacher Day, meet the 2024-25 Kenan FellowsOn National Teacher Day, meet the 2024-25 Kenan Fellows
On National Teacher Day, meet the 2024-25 Kenan Fellows
 
Spellings Wk 3 English CAPS CARES Please Practise
Spellings Wk 3 English CAPS CARES Please PractiseSpellings Wk 3 English CAPS CARES Please Practise
Spellings Wk 3 English CAPS CARES Please Practise
 
Unit-IV; Professional Sales Representative (PSR).pptx
Unit-IV; Professional Sales Representative (PSR).pptxUnit-IV; Professional Sales Representative (PSR).pptx
Unit-IV; Professional Sales Representative (PSR).pptx
 
Food safety_Challenges food safety laboratories_.pdf
Food safety_Challenges food safety laboratories_.pdfFood safety_Challenges food safety laboratories_.pdf
Food safety_Challenges food safety laboratories_.pdf
 
UGC NET Paper 1 Mathematical Reasoning & Aptitude.pdf
UGC NET Paper 1 Mathematical Reasoning & Aptitude.pdfUGC NET Paper 1 Mathematical Reasoning & Aptitude.pdf
UGC NET Paper 1 Mathematical Reasoning & Aptitude.pdf
 
Mixin Classes in Odoo 17 How to Extend Models Using Mixin Classes
Mixin Classes in Odoo 17 How to Extend Models Using Mixin ClassesMixin Classes in Odoo 17 How to Extend Models Using Mixin Classes
Mixin Classes in Odoo 17 How to Extend Models Using Mixin Classes
 
Activity 01 - Artificial Culture (1).pdf
Activity 01 - Artificial Culture (1).pdfActivity 01 - Artificial Culture (1).pdf
Activity 01 - Artificial Culture (1).pdf
 
Python Notes for mca i year students osmania university.docx
Python Notes for mca i year students osmania university.docxPython Notes for mca i year students osmania university.docx
Python Notes for mca i year students osmania university.docx
 
Application orientated numerical on hev.ppt
Application orientated numerical on hev.pptApplication orientated numerical on hev.ppt
Application orientated numerical on hev.ppt
 
The basics of sentences session 3pptx.pptx
The basics of sentences session 3pptx.pptxThe basics of sentences session 3pptx.pptx
The basics of sentences session 3pptx.pptx
 
Making communications land - Are they received and understood as intended? we...
Making communications land - Are they received and understood as intended? we...Making communications land - Are they received and understood as intended? we...
Making communications land - Are they received and understood as intended? we...
 
Unit-V; Pricing (Pharma Marketing Management).pptx
Unit-V; Pricing (Pharma Marketing Management).pptxUnit-V; Pricing (Pharma Marketing Management).pptx
Unit-V; Pricing (Pharma Marketing Management).pptx
 
Introduction to Nonprofit Accounting: The Basics
Introduction to Nonprofit Accounting: The BasicsIntroduction to Nonprofit Accounting: The Basics
Introduction to Nonprofit Accounting: The Basics
 

NANO266 - Lecture 13 - Ab initio molecular dyanmics

  • 2. What is molecular dynamics (MD)? Moving atomic nuclei by solving Newton’s equation of motion For N nuclei, we have 3N positions and 3N velocities, i.e., a 6N dimensional phase space. NANO266 2 M!!RI = − ∂E ∂RI = FI [{RJ}]
  • 3. Where do forces come from? Lennard-Jones potential •  OK for rare gases •  No chemistry •  Only pair-wise and no directionality Empirical force-fields •  Fitted parameters based on model function •  Can include many-body terms to incorporate dispersion, polarization, etc. Quantum mechanics! •  Expensive…, and surprisingly, not always the most accurate! NANO266 3 VLJ = 4ε σ r ! " # $ % & 12 − σ r ! " # $ % & 6( ) * * + , - -
  • 4. 2013 Nobel Prize in Chemistry NANO266 4
  • 5. Computational Experiment NANO266 5 Initialize positions and velocities Compute forces Determine new positions Calculate thermodynamic averages Repeat until time is reached
  • 6. Initialization 2nd order PDF -> Initial positions and velocities Positions •  Reasonable guess based on structure •  No overlap / short atomic distances Velocities •  Small initial velocity •  Steadily increase temperature (velocity scaling) NANO266 6 M!!RI = − ∂E ∂RI = FI [{RI}]
  • 7. Maxwell-Boltzmann distribution NANO266 7 f (v) = m 2πkT ! " # $ % & 3 4πv2 e − mv2 2kT
  • 8. Ensembles Microcanonical – N, V, E Canonical – N, V, T •  Temperature control achieved via thermostats •  Examples: velocity rescaling, Andersen thermostat, Nose-Hoover thermostat, Langevin dynamics, etc. NANO266 8
  • 9. Integrating equations of motion –Verlet algorithm Key properties of Verlet algorithm •  Errors do not accumulate •  Energy is conserved •  Simulations are stable NANO266 9 M!!RI = FI [{RJ}] !!RI = 1 MI FI [{RJ}] [RI (t + Δt)− RI (t)]−[RI (t)− RI (t − Δt)] (Δt)2 = 1 MI FI [{RJ}] RI (t + Δt) = 2RI (t)+ RI (t − Δt)+ (Δt)2 MI FI [{RJ (t)}]
  • 10. Flavors of quantum MD Born-Oppenheimer •  Electrons stay in instantaneous ground state as nuclei move •  Perform electronic SCF at each time step •  Compute forces (Hellman-Feynman theorem) •  Move nuclei Car-Parrinello •  Treat ions and electrons as one unified system •  Accomplished with fictitious kinetic energy for electrons NANO266 10 Car, R.; Parrinello, M. Unified approach for molecular dynamics and density-functional theory, Phys. Rev. Lett., 1985, 55, 2471–2474, doi: 10.1103/PhysRevLett.55.2471.
  • 11. Coupled equations of motion The CP Lagrangian Equations of motion NANO266 11 L = 1 2 (2µ) i=1 N ∑ dr !ψi (r) 2 ∫ + MI I=1 NI ∑ !!RI − E[ψi,r]+ Λij drψi * (r)ψj (r)−δij∫% & ' ( ij ∑ Imposes orthonormality of electronic states µ !!ψi (r,t) = −Hψj (r)+ Λikψk (r,t) k ∑ MI !!RI = − ∂E ∂RI
  • 12. Comparison of BO vs CP MD NANO266 12 CP Avoids need for costly SCF iteration of electrons at each step Time step required is smaller BO Solves Schrodinger equation at each step Time step can be longer
  • 13. General procedure for MD simulation NANO266 13
  • 14. Applications of MD Thermodynamics from ensemble averages Real-time evolution •  Reactions •  Interaction of molecules on surfaces •  Trajectories of ions Ground-state structures •  Geometry optimization is in fact a form of MD. •  For complex structures (e.g., low symmetry systems, interfaces, liquids, amorphous solids, etc.), MD can be used to determine low- energy structures NANO266 14 Nattino, F.; Ueta, H.; Chadwick, H.; Reijzen, M. E. Van; Beck, R. D.; Jackson, B.; Hemert, M. C. Van; Kroes, G. Ab Initio Molecular Dynamics Calculations versus Quantum-State- Resolved Experiments on CHD 3 + Pt(111): New Insights into a Prototypical Gas − Surface Reaction, J. Phys. Chem. Lett., 2014, 5, 1294–1299, doi:10.1021/jz500233n.
  • 15. Thermodynamic averages Under ergodic hypothesis Examples of averages •  Energy (potential, kinetic, total) •  Temperature •  Pressure •  Mean square displacements (diffusion) •  Radial distribution function NANO266 15 A = Aie−βEi (r,p) i ∑ e−βEi (r,p) i ∑ = lim T→∞ 1 T A(t)dt 0 T ∫
  • 16. Correlation Functions from MD Pair distribution function Time correlation function NANO266 16 g(r) = V N2 δ(r − rij) j≠i ∑ i ∑ Einstein relation (valid at large t) D = 1 3 dt v(t)v(0) 0 ∞ ∫ Example: Diffusion coefficient D = 1 2dt (r(t)− r(0))22tγ = (A(t)− A(0))2 γ = dt !A(t) !A(0) 0 ∞ ∫
  • 17. Structure ofAmorphous InP NANO266 17 Lewis, L.; De Vita, A.; Car, R. Structure and electronic properties of amorphous indium phosphide from first principles, Phys. Rev. B, 1998, 57, 1594–1606, doi:10.1103/PhysRevB.57.1594.
  • 18. Lithium hydroxide phase transition under high pressure NANO266 18 Pagliai, M.; Iannuzzi, M.; Cardini, G.; Parrinello, M.; Schettino, V. Lithium hydroxide phase transition under high pressure: An ab initio molecular dynamics study, ChemPhysChem, 2006, 7, 141–147, doi:10.1002/cphc.200500272.
  • 19. Dihydrogen oxide NANO266 19 Izvekov, S.; Voth, G. a. Car-Parrinello molecular dynamics simulation of liquid water: New results, J. Chem. Phys., 2002, 116, 10372–10376, doi: 10.1063/1.1473659.
  • 20. Diffusion in Lithium Superionic Conductors NANO266 20 a c a b 1D conductors would be highly sensitive to blocking defects! X Trace of Li motion at 900K Overall Ea (meV) σ@ 300 K (mS/cm) First principles1 210 13 Experimental 2 240 12 1 S. P. Ong Y. Mo, W. Richards, L. Miara, H. S. Lee, G. Ceder. Energy Environ. Sci., 2013, 6, 148–156. 2 N. Kamaya et al. Nat. Mater. 2011, 10, 682-686
  • 21. Cation has a small effect on diffusivity of Li10MP2S12 Isovalen t Aliovalen t Ge Si Sn P Al σ @ 300 K (mS/Cm) 13 23 6 4 33 Ea (meV) 210 200 240 260 180 (Aliovalent substitutions are Li+ compensated) S. P. Ong, Y. Mo, W. D. Richards, L. Miara, H. S. Lee, G. Ceder, Phase stability, electrochemical stability and ionic conductivity in the Li10±1MP2X12 family of superionic conductors. Energy Environ. Sci., 2012, doi: 10.1039/C2EE23355J
  • 22. Phonons from MD NANO266 22 Kim, J.; Yeh, M. L.; Khan, F. S.; Wilkins, J. W. Surface phonons of the Si(111)-7x7 reconstructed surface, Phys. Rev. B, 1995, 52, 14709–14718, doi: 10.1103/PhysRevB.52.14709.
  • 23. Surface reactions with MD NANO266 23 Arifin, R.; Shibuta, Y.; Shimamura, K.; Shimojo, F.; Yamaguchi, S. Ab Initio Molecular Dynamics Simulation of Ethylene Reaction on Nickel (111) Surface, J. Phys. Chem. C, 2015, 119, 3210–3216, doi:10.1021/jp512148b.