GROMACS Groningen Machine for Chemical Simulations USER MANUAL Version 4.5 GROMACS USER MANUAL Version 4.5 Written by Emile Apol, Rossen Apostolov, Herman J.C. Berendsen, Aldert van Buuren, Par¨ Bjelkmar, Rudi van Drunen, Anton Feenstra, Gerrit Groenhof, Peter Kasson, Per Larsson, Peiter Meulenhoff, Teemu Murtola, Szilard´ Pall,´ Sander Pronk, Roland Schultz, Michael Shirts, Alfons Sijbers, Peter Tieleman Berk Hess, David van der Spoel, and Erik Lindahl. Additional contributions by Mark Abraham, Christoph Junghans, Carsten Kutzner, Justin A. Lemkul, Erik Marklund, Maarten Wolf. c 1991–2000: Department of Biophysical Chemistry, University of Groningen. Nijenborgh 4, 9747 AG Groningen, The Netherlands. c 2001–2010: The GROMACS development teams at the Royal Institute of Technology and Uppsala University, Sweden. More information can be found on our website: www.gromacs.org. iv Preface & Disclaimer This manual is not complete and has no pretention to be so due to lack of time of the contributors – our first priority is to improve the software. It is worked on continuously, which in some cases might mean the information is not entirely correct. Comments are welcome, please send them by e-mail to [email protected], or to one of the mailing lists (see www.gromacs.org). We try to release an updated version of the manual whenever we release a new version of the soft- ware, so in general it is a good idea to use a manual with the same major and minor release number as your GROMACS installation. Any revision numbers (like 3.1.1) are however independent, to make it possible to implement bug fixes and manual improvements if necessary. On-line Resources You can find more documentation and other material at our homepage www.gromacs.org. Among other things there is an on-line reference, several GROMACS mailing lists with archives and contributed topologies/force fields. Citation information When citing this document in any scientific publication please refer to it as: D. van der Spoel, E. Lindahl, B. Hess, A. R. van Buuren, E. Apol, P. J. Meulenhoff, D. P. Tieleman, A. L. T. M. Sijbers, K. A. Feenstra, R. van Drunen and H. J. C. Berendsen, Gromacs User Manual version 4.5, www.gromacs.org (2010) However, we prefer that you cite (some of) the GROMACS papers [1,2,3,4,5] when you publish your results. Any future development depends on academic research grants, since the package is distributed as free software! Current development GROMACS is a joint effort, with contributions from lots of developers around the world. The core development is currently taking place at • Department of Cellular and Molecular Biology, Uppsala University, Sweden. (David van der Spoel). • Stockholm Bioinformatics Center, Stockholm University, Sweden (Erik Lindahl). • Stockholm Bioinformatics Center, Stockholm University, Sweden (Berk Hess) v GROMACS is Free Software The entire GROMACS package is available under the GNU General Public License. This means it’s free as in free speech, not just that you can use it without paying us money. For details, check the COPYING file in the source code or consult www.gnu.org/copyleft/gpl.html. The GROMACS source code and and selected set of binary packages are available on our home- page, www.gromacs.org. Have fun. vi Contents 1 Introduction1 1.1 Computational Chemistry and Molecular Modeling................1 1.2 Molecular Dynamics Simulations..........................2 1.3 Energy Minimization and Search Methods.....................5 2 Definitions and Units7 2.1 Notation.......................................7 2.2 MD units......................................7 2.3 Reduced units....................................9 3 Algorithms 11 3.1 Introduction..................................... 11 3.2 Periodic boundary conditions............................ 11 3.2.1 Some useful box types........................... 13 3.2.2 Cut-off restrictions............................. 14 3.3 The group concept................................. 14 3.4 Molecular Dynamics................................ 15 3.4.1 Initial conditions.............................. 17 3.4.2 Neighbor searching............................. 18 3.4.3 Compute forces............................... 21 3.4.4 The leap frog integrator.......................... 22 3.4.5 The velocity Verlet integrator....................... 22 3.4.6 Understanding reversible integrators: The Trotter decomposition..... 23 3.4.7 Twin-range cut-offs............................. 25 3.4.8 Temperature coupling........................... 27 3.4.9 Pressure coupling.............................. 31 viii Contents 3.4.10 The complete update algorithm...................... 38 3.4.11 Output step................................. 38 3.5 Shell molecular dynamics.............................. 40 3.5.1 Optimization of the shell positions..................... 40 3.6 Constraint algorithms................................ 40 3.6.1 SHAKE................................... 41 3.6.2 LINCS................................... 41 3.7 Simulated Annealing................................ 44 3.8 Stochastic Dynamics................................ 44 3.9 Brownian Dynamics................................ 45 3.10 Energy Minimization................................ 45 3.10.1 Steepest Descent.............................. 46 3.10.2 Conjugate Gradient............................. 46 3.10.3 L-BFGS................................... 46 3.11 Normal Mode Analysis............................... 47 3.12 Free energy calculations.............................. 48 3.13 Replica exchange.................................. 50 3.14 Essential Dynamics Sampling........................... 51 3.15 Parallelization.................................... 51 3.16 Particle decomposition............................... 52 3.17 Domain decomposition............................... 52 3.17.1 Coordinate and force communication................... 52 3.17.2 Dynamic load balancing.......................... 53 3.17.3 Constraints in parallel........................... 54 3.17.4 Interaction ranges.............................. 54 3.17.5 Multiple-Program, Multiple-Data PME parallelization.......... 56 3.17.6 Domain decomposition flow chart..................... 57 3.18 Implicit solvent................................... 57 4 Interaction function and force field 61 4.1 Non-bonded interactions.............................. 61 4.1.1 The Lennard-Jones interaction....................... 62 4.1.2 Buckingham potential........................... 63 4.1.3 Coulomb interaction............................ 63 Contents ix 4.1.4 Coulomb interaction with reaction field.................. 64 4.1.5 Modified non-bonded interactions..................... 65 4.1.6 Modified short-range interactions with Ewald summation......... 67 4.2 Bonded interactions................................. 68 4.2.1 Bond stretching............................... 68 4.2.2 Morse potential bond stretching...................... 69 4.2.3 Cubic bond stretching potential...................... 70 4.2.4 FENE bond stretching potential...................... 70 4.2.5 Harmonic angle potential.......................... 71 4.2.6 Cosine based angle potential........................ 71 4.2.7 Urey-Bradley potential........................... 72 4.2.8 Bond-Bond cross term........................... 72 4.2.9 Bond-Angle cross term........................... 72 4.2.10 Quartic angle potential........................... 73 4.2.11 Improper dihedrals............................. 73 4.2.12 Proper dihedrals.............................. 73 4.2.13 Tabulated interaction functions....................... 76 4.3 Restraints...................................... 77 4.3.1 Position restraints.............................. 77 4.3.2 Angle restraints............................... 78 4.3.3 Dihedral restraints............................. 78 4.3.4 Distance restraints............................. 79 4.3.5 Orientation restraints............................ 83 4.4 Polarization..................................... 87 4.4.1 Simple polarization............................. 87 4.4.2 Water polarization............................. 87 4.4.3 Thole polarization............................. 87 4.5 Free energy interactions............................... 88 4.5.1 Soft-core interactions............................ 90 4.6 Methods....................................... 92 4.6.1 Exclusions and 1-4 Interactions....................... 92 4.6.2 Charge Groups............................... 92 4.6.3 Treatment of Cut-offs............................ 93 4.7 Virtual interaction-sites............................... 93 x Contents 4.8 Dispersion correction................................ 97 4.8.1 Energy................................... 98 4.8.2 Virial and pressure............................. 99 4.9 Long Range Electrostatics............................. 99 4.9.1 Ewald summation.............................. 99 4.9.2 PME.................................... 100 4.9.3 PPPM.................................... 101 4.9.4 Optimizing Fourier transforms....................... 102 4.10 Force field...................................... 103 4.10.1 GROMOS87................................ 103 4.10.2 GROMOS-96................................ 104 4.10.3 OPLS/AA.................................. 105 4.10.4 AMBER.................................. 105 4.10.5 CHARMM................................. 105 4.10.6 MARTINI.................................. 105 5 Topologies 107 5.1 Introduction..................................... 107 5.2 Particle type..................................... 107 5.2.1 Atom types................................