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Chemistry in Parallel Computing
Brian W. Hopkins
Mississippi Center for Supercomputing Research
18 September 2008
What We’re Doing Here
• Discuss the importance of computational
chemistry in the HPC field.
• Define some common terms in computational
chemical sciences.
• Discuss the two major branches of
computational chemistry.
• Discuss the particular needs of various
computational chemistry applications and
methodologies.
Why We’re Doing It
• Computational chemistry is one of the driving
forces for continued investment in HPC
infrastructure.
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Better System Use
More Production
Less Money
More Opportunities
&c.
• Stop me if there are questions!
The Primacy of Computational
Chemistry in HPC
• Nationwide, computational chemistry and molecular
biology consume a very large share of HPC
resources.
Scientific Discipline
%of total Allocation
% of Total Usage
Molecular Biosciences
19
23
Physics
17
23
Astronomical Sciences
14
19
Chemistry
12
21
Materials Research
10
4
Chemical, Thermal Systems
8
6
Atmospheric Sciences
7
7
Advanced Scientific Computing
3
2
All Others
10
109
54% Total
Use!
• Here at UM and MCSR, CC is even more important:
Computational Chemistry at
UM/MCSR
• Quantum programs are the biggest
consumer of resources at MCSR by far:
– Redwood: 99% (98 of 99 jobs)
– Mimosa: 100% (86 of 86 jobs)
– Sweetgum: 100% (24 of 24 jobs)
• The one job in this snapshot that was not a
QC job was an AMBER MD simulation.
• This is typical.
Computational Chemistry: A
Sort-Of Dichotomy
• Quantum chemistry is the attempt to solve the
molecular electronic Schrodinger equation,
and to compute chemical properties
therefrom.
• Molecular dynamics is the attempt to simulate
the motion of atoms and molecules in space
over short (1-10ns) timespans.
• There is actually some overlap between the
two.
Quantum Chemistry: Overview
• The equations that describe chemical behavior
are known:
E  H
• While known, these equations are not solvable
by any analytic approach.
• The basic problem: interdependence of a very
large number of electronic coordinates.
• While analytic solutions are not available,
approximate numerical solutions are.

The Polynomial Scaling Problem
• Because of the complexity of the Schrodinger
equation, the baseline QC method (HF theory)
scales with the system size N as O(N4).
• More accurate methods scale from O(N4) -- O(N8).
• The very best method scales with (get this) O(N!).
• “System size” here is some cooked-up number
generated by hashing the number of electrons, the
number of orbitals, symmetry, &c.
• The polynomial scaling problem applies to every
resource used by a job: CPU time, memory, disk,
everything.
A Word on Alphabet Soup
• Always remember that the Schrodinger
Equation cannot be solved; we’re always
working at some level or approximation
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HF
DFT
MP2
MP4
CCSD, CISD
CCSD(T)
CCSDT, CISDT
CCSDTQ, CISDTQ
…
FCC, FCI
Increasing accuracy
Increasing expense
Decreasing scalability
Decreasing availability
• The fewer approximations we make, the
better the results (and the more the
calculation costs).
Iteration in Quantum Chemistry
• To solve the interdependence of coordinates,
QC programs rely on iteration.
• A guess is made for the location of each
electron; that guess is processed; lather,
rinse, repeat.
• When the solution stops changing, you’re
done.
• The converged solution gives both a total
energy of the molecule and a wavefunction
that decribes its state.
So…What, Exactly, Is This
Program Doing?
• Building a guess wavefunction, represented
by a huge 4D matrix of double-precision
numbers.
• Processing that matrix in a variety of ways
(mostly matrix multiplies and inversions)
• Diagonalizing the matrix.
• Using the resulting eigenvectors to build a
new guess.
• Iterate until self-consistency.
Common Chemical Properties
• Many common chemical properties are
computed by building derivatives of the
molecular electronic wavefunction.
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molecular structures
harmonic vibrational frequencies
polarizabilities
&c.
• These derivatives can be calculated
analytically or numerically.
Geometry Optimization
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One extremely common job type is the geometry optimization.
Procedure:
– Start with a guess set of nuclear coordinates
– Compute the wavefunction for the molecule
– Compute the derivative of the wavefunction with respect to the nuclear
coordinates
– Adjust the nuclear coordinates
– Repeat until the derivative is within tolerance of zero in every dimension
Note that this is a nested iteration: we’re iterating to build a wavefunction,
Requested convergence on RMS density matrix=1.00D-08 within 64 cycles.
Requested convergence on MAX density matrix=1.00D-06.
SCF Done: E(RHF) = -565.830259809
A.U. after
16 cycles
Convg =
0.7301D-08
-V/T = 2.0017
S**2
=
0.0000
•
then we’re iterating again to find a geometry
Item
Maximum Force
RMS
Force
Maximum Displacement
RMS
Displacement
Value
0.000289
0.000078
0.037535
0.006427
Threshold Converged?
0.000015
NO
0.000010
NO
0.000060
NO
0.000040
NO
Analytic vs. Numerical Derivatives
• Computing derivatives can be done two ways:
– analytically, if the relevant functional form is in the
code
• add significant expense relative to the underlying energy
point
• often not as scalable as the corresponding energy point
calculation
– numerically, by finite displacements of the relevant
properties
• always available; just do lots (and lots, and lots) of energy
points (3N-5 internal coordinates)
• embarrassingly parallel
Scaling a Quantum Chemistry App
• QC apps tend not to be very scalable.
• There’s often no really good way to
decompose the problem for workers.
– symmetry blocks excepted
• As a result, these codes are extremely talky
• Talkiness is mitigated somewhat by use of
specialized MP libs (TCGMSG).
• Also, the biggest jobs tend to be I/O intensive,
which murders performance.
• SMP is better than MP, but limited by
machine size (watch out!)
The Scaling Wall
• Gaussian scales to ~8 procs in the very best cases;
many jobs will not scale at all.
• NWChem will scale for most jobs to a few dozen procs;
some jobs to just a handful.
• MPQC will scale to many procs, but functionality is
limited.
• All parallel QC programs show some limited soft
scaling
• Always consult program manuals for scalability of a
new method.
• For most quantum chemists, the principal utility of a
big machine like redwood is for running a large
number of jobs on a few procs each.
Quantum Chemistry and the
Computing Specialist
• User-set parameters:
– the molecule to be studied
– the set of orbitals used to describe the molecule (ie, basis
set)
– the level of approximation used to compute 
• Opportunities for user guidance:
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what program to use?
how to build/optimize that program for a platform
how to effectively run the program on the machine
identification of common pitfalls (and pratfalls, too)
• PARALLEL PROJECTS, SERIAL JOBS
Molecular Simulation Methods
• Basic idea: do a very rudimentary energy
calculation for a very large number of atomic
configurations; translate these energies into
thermodynamic properties via the molecular
partition function
• Configurations can be determined either
deterministically (MD) or stochastically (MC),
but that doesn’t matter.
– we’ll look at MD as an example
The Molecular Dynamics Procedure
• Begin with a set of molecules in a periodic box
– like Asteroids, only geekier
• Compute instantaneous forces on every atom in the
box
– bonds, angles, dihedrals, impropers within molecules
– vdW and coulomb forces for proximal atoms
– kspace electrostatic forces for distal atoms
• Allow the atoms to move for 0.5 -- 2 fs.
• Repeat from 100,000 to 10,000,000 times
• Occasionally print out atomic positions, velocities,
forces, and thermodynamic properties
• Most analysis done post-hoc.
A Snapshot of Computational
Demands
• Bonded forces:
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bonds
angles
dihedrals
impropers
• Short-range pair forces:
– van der Waals forces
– coulomb forces
• Long-range pair forces:
– kspace Ewald sum for elctrostatics
What’s an Ewald Sum?
• The energy of interaction for a van der Waals
pair falls away with r6.
• Consequently there’s a point (~10A) where
these interactions are negligible and can be
excluded
• We set this point as a cutoff and exclude vdW
pairs beyond it.
• By contrast, ES potential falls away with r.
• Over the years, it’s been demonstrated that
imposing even a very long cutoff on the ES part
is an unacceptable approximation.
• The Ewald sum is the current solution.
Electrostatics in Fourier Space
• When transformed into Fourier space (aka kspace),
the ES part converges more rapidly.
• Thus, the Ewald sum:
– Real space ES for pairs within the vdW cutoff
– Fourier (k-)space ES for longer range pairs until
convergence is achieved (usually 5-7 layers of periodic
images).
– Fourier space ES for short range pairs as a correction
against double counting.
• And the particle-mesh Ewald sum:
– Real space as in Ewald
– Fourier space done by projecting atomic forces onto a grid,
computing kspace part, projecting forces from grid back onto
atoms
The Cost of an Ewald Sum
• An ordinary, real-space LRES calculation would
eventually converge, but require >15 periodic images
to do so.
• The kspace LRES of Ewald is similarly pairwise and
similarly scales with N2.
• However, the more rapid convergence means we only
need 5-7 periodic images.
• On the other hand, we now have to do some extra
stuff:
– 3d FFT to generate kspace part
– extra SR calcs for double counting correction
– 3d FFT tp transform Ewald forces back to real space
Particle-Mesh Ewald
• The expense of an Ewald sum can be reduced by mapping atomic
(particle) charges onto a grid (mesh) with far fewer points.
• This grid can be transformed into kspace, the Ewald sum done, and
transformed back.
• The Ewald forces are then reverse-mapped onto the atoms that
made up the grid.
• This is an approximation, of which there are various flavors:
– PME
– SPME
– PPPM
– &c.
• Scales as NlogN rather than N2.
• Reduced scaling + extra mapping expense = crossover point?
• In practice, crossover point is so low as to not matter.
Scaling an MD Simulation
• MD programs lend themselves moderately well to MP
parallelism.
• Typical approach is spatial decomposition; ie, each PE
computes forces & integrates for a region within the
simulation cell.
• Talk points are limited:
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Pairlist builds
3D FFT for Ewald sum
Mapping and unmapping for PME
New atomic positions in integrator
• Thus, the main issue is whether or not there’s enough
work to go around --> soft scaling very pronounced
• I/O can be an issue, esp. for large boxes; should be
limited to once every 100-1000 steps, though.
So, How Do MD Programs Do?
• As usual, there’s a compromise to be made
between “full featured” and “high performance”.
• Old, heavily developed platforms like Amber
have lots of features but only scale moderately
well (to a few dozen procs).
• New, high tech platforms like NAMD scale to
hundreds of procs but lack common features
(NH, &c.)
• Again, all MD programs exhibit pronounced soft
scaling:
– bigger problems more accessible
– smaller problems are no faster.
Moving Between MD Programs
• Trickier than moving between QC programs.
• There are a lot of subtle things that must be
considered:
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available PME approaches
different pairlisting algorithms
trajectory synchronization
scaling of 1-3 and 1-4 interactions
&c.
• It’s almost never possible to build a single research
project on simulations run with two different programs
• Thus, it’s critical to choose the right program for the
whole job at the beginning.
Molecular Simulation and the
Computing Specialist
• User-set parameters:
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the size of the box
the length of the timestep
the number of steps needed
the forcefield features needed
• Opportunities for guidance:
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Which program to use
building/optimizing for a platform
scaling limits for a job of given size
&c.
Summary
• Quantum Chemistry:
– listen to what your users need
– help the user organize jobs into “parallel projects”
– go shopping for the best-scaling program to do individual job
types
– programs are more or less perfectly interchangeable, with a
little care
• Molecular Simulation
– listen to what your users need
– help the user shop for the best program for their sim
– be careful about what you choose, because you’ll be stuck
with it