CPMD Car-Parrinello Molecular Dynamics An ab initio Electronic Structure and Molecular Dynamics Program The CPMD consortium WWW: http://www.cpmd.org/ Mailing list: [email protected] E-mail: [email protected] June 27, 2008 Send comments and bug reports to [email protected] This manual is for CPMD version 3.13.1 2 CPMD 3.13.1 June 27, 2008 (This page intentionally left blank.) CPMD 3.13.1 Contents 3 Contents I About CPMD8 1 Introduction 8 1.1 Capabilities........................................8 1.2 Citation..........................................8 1.3 Contributions.......................................8 1.4 Mailing list........................................8 1.5 Important constants and conversion factors......................9 1.6 About this manual....................................9 1.7 Recommendations for further reading.......................... 10 1.8 Original Literature.................................... 11 1.9 CPMD Development History.............................. 14 1.10 CPMD License...................................... 17 1.10.1 Definitions.................................... 17 1.10.2 Term and Termination.............................. 17 1.10.3 License Grant................................... 17 1.10.4 Improvements................................... 18 1.10.5 Feedback..................................... 18 1.10.6 No Warranty................................... 18 1.10.7 Limitation of Liability.............................. 18 1.10.8 General...................................... 18 II Installing and Running CPMD 19 2 Installation 19 2.1 Prerequisites....................................... 19 2.1.1 Hardware Requirements............................. 19 2.1.2 Software Requirements.............................. 19 2.1.3 Linux Specific Issues............................... 19 2.2 Compiling CPMD.................................... 20 2.2.1 Optimizing CPMD................................ 21 2.2.2 Preprocessor Flags................................ 22 2.3 Running CPMD..................................... 22 2.3.1 Serial Execution and General Considerations................. 22 2.4 CPMD on Parallel Computers.............................. 23 2.4.1 Distributed Memory Parallelization using MPI................ 23 2.4.2 Shared Memory Parallelization......................... 24 2.4.3 Mixed Shared/Distributed Memory Parallelization.............. 24 2.4.4 Final Remark................................... 24 III Tutorial 25 3 Introduction 25 3.1 Prerequisites....................................... 25 3.2 Pseudopotential Files................................... 25 4 The Basics: Running CPMD, Input and Outputs 26 4.1 Wavefunction Optimization............................... 26 4.1.1 Required Files.................................. 26 4.1.2 Input File Structure............................... 27 4 Contents CPMD 3.13.1 4.1.3 Output File Format............................... 28 4.1.4 Other Output Files................................ 33 4.2 Choosing the Plane Wave Cutoff............................ 33 4.2.1 Relation between Plane Wave Cutoff and Pseudopotential Files....... 34 4.3 Geometry Optimization................................. 34 4.4 Car-Parrinello Molecular Dynamics........................... 36 4.4.1 Converged Wavefunction............................. 36 4.4.2 Input for CP Dynamics............................. 36 4.4.3 CP Dynamics Output.............................. 37 5 Some Commented CPMD Job Examples 39 5.1 Electron Structure and Wavefunction Properties................... 39 5.1.1 Required Files.................................. 39 5.1.2 Single Point Calculation............................. 40 5.1.3 Electron Density, Electrostatic Potential, Electron Localization Function(ELF) 40 5.1.4 Canonical Orbitals, Unoccupied Orbitals.................... 41 5.1.5 Dipole Moment, Atomic Charges........................ 42 5.1.6 Projection on Atomic Orbitals, Population Analysis, etc............ 43 5.1.7 Localized Orbitals, Wannier Centers...................... 45 5.1.8 Methods to Compute the Ground State Wavefunction............ 46 5.2 Vibrational Spectra.................................... 47 5.2.1 Calculation of Vibrational Spectra....................... 47 5.2.2 Prerequisites................................... 48 5.2.3 Finite Differences................................. 48 5.2.4 Point Group Symmetry............................. 49 5.2.5 Linear Response................................. 50 5.2.6 Pre-calculated Hessian.............................. 50 5.2.7 Generic Linear Response Kernel........................ 50 5.3 Further Job Types.................................... 51 IV Theory 52 6 Molecular Dynamics and ab initio Molecular dynamics 52 6.1 Equations of Motion................................... 52 6.2 Microcanonical Ensemble................................ 53 6.3 Numerical Integration.................................. 54 6.4 Extended System Approach............................... 55 6.4.1 Barostats..................................... 55 6.4.2 Thermostats................................... 55 6.5 Ab initio Molecular Dynamics.............................. 56 6.6 Born{Oppenheimer Molecular Dynamics........................ 58 6.6.1 Forces in BOMD................................. 59 6.7 Car{Parrinello Molecular Dynamics.......................... 59 6.7.1 How to Control Adiabaticity ?......................... 61 6.7.2 Forces in CPMD................................. 61 6.7.3 Velocity Verlet Equations for CPMD...................... 62 6.8 Comparing BOMD and CPMD............................. 62 7 Calculating the Electronic Structure from Pseudopotentials and Plane Waves 65 7.1 Unit Cell and Plane Wave Basis............................. 65 7.2 Kinetic Energy and Local Potentials.......................... 66 7.3 Electrostatic Energy................................... 67 7.4 Exchange and Correlation Energy............................ 69 7.5 Car{Parrinello Equations................................ 69 CPMD 3.13.1 Contents 5 7.6 Metals; Free Energy Functional............................. 71 7.7 Charged Systems..................................... 74 7.8 Position Operator in Periodic Systems......................... 76 7.9 Dipole Moments and IR Spectra............................ 77 7.10 Localized Orbitals, Wannier Functions......................... 78 7.11 Pseudopotentials..................................... 82 7.12 Why Pseudopotentials ?................................. 82 7.13 Norm{Conserving Pseudopotentials........................... 83 7.13.1 Hamann{Schl¨uter{Chiang Conditions..................... 83 7.13.2 Bachelet-Hamann-Schl¨uter(BHS) form.................... 85 7.13.3 Kerker Pseudopotentials............................. 85 7.13.4 Troullier{Martins Pseudopotentials....................... 86 7.13.5 Kinetic Energy Optimized Pseudopotentials.................. 86 7.14 Pseudopotentials in the Plane Wave Basis....................... 86 7.14.1 Gauss{Hermit Integration............................ 87 7.14.2 Kleinman{Bylander Scheme........................... 88 7.15 Dual{Space Gaussian (Goedecker-Teter-Hutter) Pseudopotentials.......... 89 7.16 Example: Pseudopotentials for Oxygen......................... 90 7.17 Non-linear Core Correction............................... 90 8 Implementation 93 8.1 Total Energy and Gradients............................... 93 8.1.1 Plane Wave Expansion.............................. 93 8.1.2 Total Energy................................... 93 8.1.3 Wavefunction Gradient............................. 93 8.1.4 Nuclear Gradient................................. 94 8.2 Fast Fourier Transforms................................. 95 8.3 Density and Force Calculations in Practice....................... 96 8.4 Saving Computer Time................................. 96 8.5 Exchange and Correlation Functionals......................... 98 V User's Guide 99 9 Hints and Tricks for setting up CPMD calculations 99 9.1 Pseudopotentials and Plane Wave Cutoff........................ 99 9.2 Wavefunction Initialization............................... 99 9.2.1 Using Vanderbilt Ultrasoft Pseudopotentials.................. 99 9.3 Wavefunction Convergence................................ 100 9.4 Cell Size Requirements for Isolated Systems...................... 101 9.4.1 Choosing Supercell Dimensions and Wavefunction Cutoff in Practice.... 102 9.5 Controlling adiabaticity for CP-dynamics in practice................. 103 9.5.1 Choosing Time Step and the Fictitious Mass................. 104 9.5.2 Additional Considerations and Potential Problems.............. 105 9.6 Geometry Optimization................................. 105 9.7 Molecular Dynamics................................... 106 9.7.1 Choosing the Nos´e-Hoover chain thermostat parameters........... 106 9.8 Restarts.......................................... 107 9.8.1 General information............................... 107 9.8.2 Typical restart scenarios............................. 107 9.8.3 Some special cases................................ 108 9.9 TDDFT.......................................... 108 9.9.1 Electronic spectra................................ 108 9.9.2 Geometry optimizations and molecular dynamics............... 109 9.10 Perturbation Theory / Linear Response........................ 109 6 Contents CPMD 3.13.1 9.10.1 General...................................... 109 9.10.2 &RESP section input.............................. 110 9.10.3 Response output................................. 112 9.10.4 Phonons...................................... 112 9.10.5 Lanczos.....................................