1. Molecular Simulation at MCSR Brian W. Hopkins Mississippi Center for Supercomputing Research 9 October 2008

2. What We’re Doing Here Talk about molecular simulation procedures. Talk about available simulation programs. Discuss user simulation needs and program options.

3. Why Simulation NOT so we can watch pretty pictures of atoms moving around! Many systems have very large numbers of internal DoF. It’s simply not possible to determine what is “the minimum” or whatever on these surfaces. To get an accurate thermodynamic & kinetic picture of these systems, it’s necessary to sample a medium->large region of phase space.

4. Simulation: Anatomy of A Program Read in sim paramters, atomic coordinates and topology. Begin Timestepping –Apply periodic boundary conditions. –Build neighbor list. –Compute bonded forces. –Compute short-rang nonbonded forces. –Compute electrostatic forces. –Integrate forward in time. Write atomic positions, velocities and forces. Take data for statistical accumulators. –Repeat. End timestepping. Print restart data.

5. Program Anatomy: Read Control nafion #restart temperature 298.00 steps 200000 timestep 0.00050 ps ensemble nve evbconv 1e-6 movlp 1 cutoff 10.0 angstrom rvdw 9.0 angstrom delr 0.00 angstrom

6. Program Anatomy: Read Config hcl in water 2 1 2000000 0.001 21.5518556898 0 0 0 21.5518556898 0 0 0 21.5518556898 …… OW 7 15.994900 -0.820000 4.5231E-01 4.3198E+00 -6.6975E+00 4.7263E+00 3.4690E-01 -6.3309E+00 -1.9170E+04 5.2043E+03 -2.1576E+03 HW 8 1.007800 0.410000 5.1477E-01 5.3695E+00 -6.6887E+00 1.0886E+01 -6.6502E+00 2.6571E+01 -6.1635E+02 -8.2402E+03 2.6958E+03 HW 9 1.007800 0.410000 -5.5940E-01 4.0344E+00 -6.5708E+00 7.6145E+00 -7.4611E-01 -1.0319E+01 1.8438E+04 1.8167E+03 8.6264E+02 …

7. Program Anatomy: Read Topology UNITS kcal MOLECULAR TYPES 4 FLEXIBLE-TIP3P-Water NUMMOLS 332 atoms 3 OW 15.9949 -0.8200 HW 1.0078 0.4100 BONDS 2 harm 1 2 1059.162 1.012 harm 1 3 1059.162 1.012 ANGLES 1 harm 2 1 3 75.900 113.240 FINISH …… vdw 9 OW OW lj 0.155425 3.16549 OT OW lj 0.1238000 3.1420000 HT OW lj 0.0025115 1.5827460

8. Program Anatomy: Set up Cell

10. Program Anatomy: Build Neighbor List Apply PBC to cell Begin at an atom Step out, forming thin shells. When an atom falls within the thin shell, add it to the neighbor list. Continue until cutoff is reached. Move on to the next atom.

11. Pairlisting

12. Bonded Forces Identify atoms that are connected by bonds, angles, dihedrals and impropers. Calculate energies and forces from functions, parameters in input: –Bonds: harmonic, morse –Angles: harmonic –Dihedrals: cosine –Impropers: cosine

13. Short Range Forces Loop over atoms. For each: Loop over pairs Calculate van der Waals potential, force Calculate short-range (real) ES potential, force Scale for 1-4 interactions?

14. Long-Range Forces Because vdW forces obey a 6-12 potential, they fall away very quickly wrt distance. Consequently, as you move away from an atom through a simulation cell you quickly come to a point where including additional vdW terms is irrelevant. Hence, the cutoff. Coulomb forces and energies, however, fall off with r 2 and r respectively. As a result, no reasonable cutoff will be satisfactory; results will always be strange.

16. Solution: Ewald Summation The coulomb equations converged much more quickly in Fourier space. So, we can transform all atomic coordinates to Fourier space, compute ES energies until some convergence criterion is reached, then transform the forces and energies back to real space. This is called an Ewald sum; almost all modern simulations use some form of it.

17. Ewald Sums Are Expensive Ewald sums still require computing interactions between atoms and many layers of periodic images. Fourier transforms are demanding. As much as 80% of a modern simulation is spent in the Ewald routines. –15% in pairlisting/vdw and just 5% everywhere else

18. Speeding up the Ewald sum Computational approaches: –Smarter decompositions –Faster comms –Single precision FFT Physical approximations: –“Multiple timestepping” –Particle mesh approaches

19. The Particle Mesh Ewald Sum Atomic charges are first mapped onto a regular grid. The gridpoints are transformed, worked on, and transformed back. Forces are then decomposed from grid back onto atoms.

20. PME Costs and Benefits Scales with NlogN rather than N 2 Does entail extra cost to map/unmap atomic charges to grid. –Crossover point? Some energetic slop is associated with these methods. Some flavors (PPPM, &c.) may interfere with thermo and barostats.

21. Integration Once a full set of forces has been calculated, the atoms are allowed to move in response to those forces This is done by calculating integral forms of Newton’s Laws. –Verlet, leapfrog, velocity verlet, &c. How far can you integrate forward?

22. Accumulation Recall that the whole point here is to take large scale statistical averages of thermdynamic properties. Some of these properties are a lot easier to calculate inside the program than they will be to calculate from trajectories later. So, every so often, the program needs to take a second and compute –Properties in the current step –Rolling average from the previous steps.

23. Output: Accumulators ------------------------------------------------------------------------------------------------------ ---------------------------- step eng_tot temp_tot eng_cfg eng_vdw eng_cou eng_bnd eng_ang eng_dih eng_tet eng_kin time(ps) eng_pv temp_rot vir_cfg vir_vdw vir_cou vir_bnd vir_ang vir_con vir_tet conserv cpu (s) volume temp_shl eng_shl vir_shl alpha beta gamma vir_pmf press ----------------------------------------------------------------------------------------------------- ----------------------------- 1 8.7047E+01 8.9004E+02 -3.4994E+01 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 1.2204E+02 0.001 8.7047E+01 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 1.98 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 9.0000E+01 9.0000E+01 9.0000E+01 0.0000E+00 0.0000E+00 rolling 8.7047E+01 8.9004E+02 -3.4994E+01 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 1.2204E+02 averages 8.7047E+01 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 9.0000E+01 9.0000E+01 9.0000E+01 0.0000E+00 0.0000E+00 ----------------------------------------------------------------------------------------------------- ----------------------------- step eng_tot temp_tot eng_cfg eng_vdw eng_cou eng_bnd eng_ang eng_dih eng_tet eng_kin time(ps) eng_pv temp_rot vir_cfg vir_vdw vir_cou vir_bnd vir_ang vir_con vir_tet conserv cpu (s) volume temp_shl eng_shl vir_shl alpha beta gamma vir_pmf press ---------------------------------------------------------------------------------------------------------------------------------- 1 8.7047E+01 8.9004E+02 -3.4994E+01 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 1.2204E+02 0.001 8.7047E+01 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 1.98 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 9.0000E+01 9.0000E+01 9.0000E+01 0.0000E+00 0.0000E+00 rolling 8.7047E+01 8.9004E+02 -3.4994E+01 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 1.2204E+02 averages 8.7047E+01 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 9.0000E+01 9.0000E+01 9.0000E+01 0.0000E+00 0.0000E+00 ----------------------------------------------------------------------------------------------------------------------------------

24. Output: Trajectory timestep 1 48 2 0 0.001000 OW 1 15.994900 -0.820000 0.0000E+00 0.0000E+00 0.0000E+00 4.4176E-01 -2.3695E+00 -4.4226E+00 -1.1626E+04 -3.2094E+04 -1.7497E+04 HW 2 1.007800 0.410000 0.0000E+00 0.0000E+00 9.4700E-01 1.7204E-01 1.3940E+01 5.0345E+01 -4.1073E+03 1.5125E+03 3.6299E+04 HW 3 1.007800 0.410000 8.9567E-01 0.0000E+00 -3.1667E-01 7.7140E+01 4.7094E+00 -3.8531E+01 3.2399E+04 -1.4520E+03 -1.4832E+04 OW 4 15.994900 -0.820000 2.4602E+00 -1.0000E-06 -9.0073E-01 -1.1793E+01 -1.9654E-01 -5.1510E-01 -3.5980E+04 7.3873E+02 8.1414E+03 HW 5 1.007800 0.410000 3.0701E+00 -1.0000E-06 -1.7237E-01 9.2834E+00 -2.3632E+00 6.3046E+01 2.2288E+04 -5.2163E+01 2.1425E+04

25. Anatomy of a Simulation Project Identify a problem –Molecular system –Region of phase space Build a system Minimize Equilibrate Run MD Analyze

26. Choosing a Program How intense is your job? Do you need particular features? –Force functions –Thermostats –Barostat –Sampling methods –&c. Ask for help!!

27. Building Your System It’s nontrivial to place 1.5 million atoms in a cubic simulation cell. Biomolecules: PDB, homology modelling, &c. Others: replication of small boxes. Lots of tools for more complicated cases. Sometimes this is the hardest part.

28. Minimization You probably didn’t do a very good job building a box. If anything about your box makes the forcefield angry, it can explode under dynamics. Solution is to run minimization for some time to eliminate bad contacts.

29. Equilibration Minimization brings your box down to ~0K. You need to heat it back up to the intersting temperature. Assign velocities to atoms from a Boltzmann distribution. This will be wacky; temperature and energy will be unstable. To fix, run some “equilibration time” –Don’t take statistics –Periodically scale atomic velocities

30. Run Typical MD runs use a 0.5-2.0 fs timestep and run for 100ps-2ns. This means anywhere from 50,000 to 4 million timesteps. Trajectories are typically output every100-1000 timesteps. Statistics are taken every 100 or so timesteps.

31. How Do I Know My Simulation Doesn’t Suck? Is it conserving what it’s supposed to be conserving? Is it conserving what it’s not really supposed to be conserving? Are you in a region of phase space that interests you? Have you checked for common failures? –Flying icecube, &c.

32. My Simulation is Over. What Now? Now you have large amounts of –thermochemical data –atomistic trajectories From this you can calculate stuff –rates of reactions –diffusion coefficients –structural properties (rdf, sf, &c.)

33. How Do I Do That? Canned analysis programs –VMD! Write your own programs –Everybody does this! We may talk about this another time.

34. What We Can Do For You Help you select simulation software –Almost all MD software is free, so we can get and install most packages you could want. Help you set up your simulation cell. Help you manage your jobs as they run. Help you write, parallelize, and run analysis code.