By Will Welch
For Jan Kubelka
CHEM 4560/5560
Fall, 2014
University of Wyoming

– Basic concepts in MD
– GROMACS tutorial, solvated, ionized protein
– Building and Visualization
– Sampling, Equilibrium vs. Non-equilibrium.
– Umbrella Sampling??
– Applications: Research examples

1. Scale: Large collections of interacting particles that cannot
(and should not) be studied by quantum mechanics .
Classical limit?
Quantum
~500,000 atoms
~25 nm
~2,000,000 atoms
2. Dynamics: time dependent behavior and non-equilibrium processes.
Monte Carlo methods can predict many of the same things, but do not provide info on time dependent properties
~115 nm
Still far from bulk material…
Lattice fluids
Continuum models

A Few Theoretical Concepts
𝑄 𝑁, 𝑉, 𝛽 = 𝑒 −𝛽𝐸 𝑖 𝑖
Q is called the
Canonical Partition Function.
A 𝑁, 𝑉, 𝑇 = −𝑘𝑇𝑙𝑛𝑄
𝑆 𝑁, 𝑉, 𝐸 = −𝑘𝑙𝑛𝛺 𝑝𝑉 𝑉, 𝑇, 𝜇 = −𝑘𝑇𝑙𝑛𝛯
𝐺 𝑁, 𝑃, 𝑇 = −𝑘𝑇𝑙𝑛𝛥 microcanonical grand canonical
Isothermal-isobaric
In Equilibrium MD, we want to sample the ensemble as best as possible!

A Few Theoretical Concepts
𝑈 𝑥
1
= 𝑈 ′ 𝑥
1
, 𝑦
1 𝑧
1
+ 𝑓(𝑥
2
… 𝑧 𝑛
) 𝑓 𝑥
2
… 𝑧 𝑛
= ? ? ?

The van Der Waals Equation
Potentials modeling pairwise interactions.
Hard sphere Potential
Lennard-Jones Potential

Molecular Dynamics: Nuts and Bolts
 Particles (atoms and molecules): non-reactive, stable species (generally).
 trajectories determined by solving Newtonian equations of motion
 Forces on particles due to molecular mechanics force fields.
Basic Force Field components
+ other possibilites (implicit solvent, external potentials)

United Atom
OPLS-UA,
TraPPE-UA,
Most atoms uncharged,
Exceptions for
O-H groups etc.
SPC
Includes explicit H atoms
Beads include
H atoms in CH
2
CH
3 etc.
All Atom
Tip4p
( graphic: sklog Wiki
)
Partial charges on most atoms
OPLS-AA, CHARMM, AMBER and many others
Coarse Grain
Beads include large functional groups.
σ/2 http://dx.doi.org/10.1063/1.4863329
1 (nonpolar) Martini water bead represents 4 water molecules…
(http://espressomd.org)

• Force Fields are largely empirical
– You get so many parameters: Make them fit experiment!
• Ab initio calculations can be used
– How does one get charges?
– OPLS obtained dihedrals from QM simulations
• Practical stipulations:
– AMBER—all residues have integer charge
– TraPPE—Carbon hybridization dictates parameters
– CHARMM22—parameterized for tip3P water
• Transferability
– Want to model systems containing mixtures of particles which were parameterized (want parameters to “transfer” to new systems). Possible if all parameters derived in same way…

How do the dynamics happen?
 Forces on each particle are calculated at time t. The forces provide trajectories, which are propagated for a small duration of time, Δt, producing new particle positions at time t+ Δt. Forces due to new positions are then calculated and the process continues:
The **basic** idea…

How do the dynamics happen?
• Verlet algorithm
(http://www.fisica.uniud.it/~ercolessi/md/md/node21.html)
• Velocity Verlet algorithm
• Leap-Frog algorithm (From Wikipedia)

How do the dynamics happen?
 What is a suitably short time step?
Must be significantly shorter than the fastest motion in your simulation:
What is frequency of C-H stretch. O-H stretch?
Adequately
Short Time step
Normal restoring force
Time step
Too long
Huge restoring force: simulation crashes
Minimum time step depends on what you are monitoring. At least, simulation must be stable.
Constraint algorithms: Shake, Rattle, LINCS

Do we use the entire configuration integral?
Cutoff (modified cutoff) radii
For L-J, 2.5σ
Long-range electrostatics
Ewald Sums
Graphic credit: http://beam.acclab.helsinki.fi/~koehenri
How do you keep your particles from drifting out of the cell?
1.Create some type of a wall
2. PERIODIC BOUNDARY CONDITIONS
What’s the maximum cutoff?
Graphic credit: http://server.ccl.net/cca/documents/molecularmodeling/node9.html