Molecular Simulation at MCSR
Brian W. Hopkins
Mississippi Center for Supercomputing Research
9 October 2008
What We’re Doing Here
• Talk about molecular simulation
procedures.
• Talk about available simulation
programs.
• Discuss user simulation needs and
program options.
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.
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.
Program Anatomy: Read Control
nafion
#restart
temperature
steps
timestep
298.00
200000
0.00050 ps
ensemble nve
evbconv 1e-6
movlp
1
cutoff
rvdw
delr
10.0 angstrom
9.0 angstrom
0.00 angstrom
Program Anatomy: Read Config
hcl in water
2
1
2000000
21.5518556898
0
0
21.5518556898
0
0
……
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
…
0.001
0
0
21.5518556898
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
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
FINISH
……
vdw 9
OW
OW
lj
0.155425
OT
OW
lj
0.1238000
HT
OW
lj
0.0025115
113.240
3.16549
3.1420000
1.5827460
Program Anatomy: Set up Cell
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.
Pairlisting
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
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?
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 r2 and r respectively.
• As a result, no reasonable cutoff will be
satisfactory; results will always be strange.
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.
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
Speeding up the Ewald sum
• Computational approaches:
– Smarter decompositions
– Faster comms
– Single precision FFT
• Physical approximations:
– “Multiple timestepping”
– Particle mesh approaches
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.
PME Costs and Benefits
• Scales with NlogN rather than N2
• 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.
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?
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.
Output: Accumulators
---------------------------------------------------------------------------------------------------------------------------------step
time(ps)
cpu (s)
eng_tot
eng_pv
volume
temp_tot
temp_rot
temp_shl
eng_cfg
vir_cfg
eng_shl
eng_vdw
vir_vdw
vir_shl
eng_cou
vir_cou
alpha
eng_bnd
vir_bnd
beta
eng_ang
vir_ang
gamma
eng_dih
vir_con
vir_pmf
eng_tet
vir_tet
press
eng_kin
conserv
---------------------------------------------------------------------------------------------------------------------------------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
averages
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
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
----------------------------------------------------------------------------------------------------------------------------------
Output: Trajectory
timestep
OW
0.0000E+00
4.4176E-01
-1.1626E+04
HW
0.0000E+00
1.7204E-01
-4.1073E+03
HW
8.9567E-01
7.7140E+01
3.2399E+04
OW
2.4602E+00
-1.1793E+01
-3.5980E+04
HW
3.0701E+00
9.2834E+00
2.2288E+04
1
48
2
1
15.994900
-0.820000
0.0000E+00 0.0000E+00
-2.3695E+00 -4.4226E+00
-3.2094E+04 -1.7497E+04
2
1.007800
0.410000
0.0000E+00 9.4700E-01
1.3940E+01 5.0345E+01
1.5125E+03 3.6299E+04
3
1.007800
0.410000
0.0000E+00 -3.1667E-01
4.7094E+00 -3.8531E+01
-1.4520E+03 -1.4832E+04
4
15.994900
-0.820000
-1.0000E-06 -9.0073E-01
-1.9654E-01 -5.1510E-01
7.3873E+02 8.1414E+03
5
1.007800
0.410000
-1.0000E-06 -1.7237E-01
-2.3632E+00 6.3046E+01
-5.2163E+01 2.1425E+04
0
0.001000
Anatomy of a Simulation
Project
• Identify a problem
– Molecular system
– Region of phase space
•
•
•
•
•
Build a system
Minimize
Equilibrate
Run MD
Analyze
Choosing a Program
• How intense is your job?
• Do you need particular features?
– Force functions
– Thermostats
– Barostat
– Sampling methods
– &c.
• Ask for help!!
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.
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.
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
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.
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.
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.)
How Do I Do That?
• Canned analysis programs
– VMD!
• Write your own programs
– Everybody does this!
• We may talk about this another time.
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.