1. Molecular simulations in chemistry
Adam Liwo
Room B325

2. 30 lecture hours
2 hrs/week; Tuesdays, 8:15 – 10:00 am
Completion requirements
Project
Exam

3. Scope Purpose, time-, and size-scales of molecular simulations.
Energy surfaces of molecules.
All-atom force fields: purpose, derivation, and parameterization
Treatment of solvent in force fields. Models of water.
Metropolis Monte Carlo.
Molecular dynamics.
Calculating ensemble-averages and error estimation in simulations.
Umbrella-sampling simulations and the weighted-histogram analysis method.
Generalized-ensemble simulations.
Enlarging the time- and size-scale of simulations: coarse-grained models. The CABS and UNRES force fields.
Thermodynamics and kinetics of protein folding from simulations.
QM/MM simulations.

4. Literature
Daan Frenkel, Berend Smit, „Understanding Molecular Simulation: From Algorithms to Applications” Academic Press, San Diego, 1996
D.C.A. Rapaport, „The Art of Molecular Dynamics Simulations”, Cambridge University Press, 1998.
A.R. Leach: „Molecular Modeling: Principles and Applications”, Pearson Education EMA, 2001.

5. Learning Nature – how does Science work?
No model
(pysicochemical
tables)
Model
(equations)
Experiment
Exact solution
Simulations

6. Equations (approximate)
– exact solutions
„I am really longing for those good old times when a theorist didn’t need anything but a piece of paper, a pencil, and own brains”.
Quotation from a late Professor of Physical Chemistry.
Not possible anymore…unless we want to consider spherical horses in vacuo to model horse race.
Feynman’s dream that we will be able to ‘see’ the solutions of equations someday does not seem to ever come true.

7. Successful examples of the „exact solution” approach
Chemical Thermodynamics (phenomenological).
Chemical Kinetics.
Modeling electrochemical processess.
Quantum Chemistry.
Kinetic theory of gases.
Application of Statistical Mechanics in Chemistry.

8. What are ‘Simulations’?
‘Das ganze Tschechische Volk ist eine Simulantenbande’
– Dr. Gruenstein of K.u.K military draft office
Modeling (computing) the behavior of complex systems by applying a given description (e.g., Newton’s equations of motion).

9. Where do the ‘molecular simulations’ enter into play?
Condensed systems composed of many particles (e.g., a protein + solvent).
Strong interactions between system’s components. The partition function cannot be separated.
The time evolution has Lyapunov instability depending on the initial conditions.
Therefore, we actually need to compute system’s behavior for given initial/boundary condition rather than analyze the solutions in terms of those.

10. Are simulations another version
of experiment?
No, we do not deal with a real system but with a ‘virtual’ one.
However, the results depend on starting point and are subject to statistical error as the experiemental results.

11. (Pre) History
Lord Kelvin (early 1900’s): hand computations of hard- sphere collisions.
Manhattan Project (Ulam; 1940’s – 1950’s): hand and computer simulations of nuclear fission (ENIAC computer).
J.D. Bernal (1950’s): mechanical models of liquid particles from rubber/styrofoam balls connected with metal rods.
G. Vineyard (1950’s): computer simulation of radiation damage in crystalline Cu.
Rosenbluth, Rosenbluth, Metropolis, Teller (1950’s): Formulation of the Metropolis Monte Carlo algorithm.
Alder and Wainwright (1957): MD simulations of hard- sphere liquids.

12. Types of simulations Monte Carlo (MC): need only energy).
Molecular dynamics (MD): time evolution; need forces).
Combination thereof.

13. What systems do we treat and what are the limits?

14. Description level System level (Networks) Individual components
Fully-detailed QM
Averaging over „less important” degrees of freedom
QM/MM
Averaging over individual components
Individual components
Atomistically-detailed
All-atom
United-atom
Description level
Residue level
Coarse-grained
PDEs to describe reaction/diffusion
Molecule/domain level
System level
(Networks)
Network graphs

15. 10-15 10-12 10-9 10-6 10-3 100 femto pico nano micro milli seconds
sidechain
rotation
helix
formation
protein
folding
10-15
femto
10-12
pico
10-9
nano
10-6
micro
10-3
milli
100
seconds
bond
vibration
loop
closure
folding of
-hairpins
all atom MD step

16. Time step Dt for some standard MD packages
Explicit Solvent
Implicit Solvent
AMBERa
1 fs
2 fs
CHARMMb
3 fs
4-5 fs
TINKERc a b
c dasher.wustl.edu/tinker/

17. Energy surfaces of molecular systems and their properties

18. From Schrödinger equation to analytical all-atom potentials

19. The Born-Oppenheimer approximation
Figure 3b).
The Born-Oppenheimer approximation

20. Conversion of iso-hydrogen cyanide into hydrogen cyainde
HNC®HCN

21. Transition structure
AM1 energy hypersurface of the conversion of iso-hydrogen cyanide into hydrogen cyanide
Energy [kcal/mol]
HNC
HCN

22. Contour plot of the PES
HCN
struktura przejściowa
HNC

23. H
N -C
energy [kcal/mol]
DE╪
HNC
HCN DE
reaction coordinate

24. Jean-Louis David
Napoleon

25. Propane PES as a function of the two dihedral angles

26. Conformational-energy map of terminally-blocked alanine
(degrees)
(degrees)

27. Energy expansion about the stationary point
The derivatives are zero at a stationary point but it need not be a stable point (Coulomb’s egg problem).

28. Matrix H is termed energy Hessian
V – eigenvector matrix

29. Case study: the układu HCN – HNC system
Energy [kcal/mol] x h h x
Neighborhood of the minimum corresponding to the HCN molecule
Neighborhood of the transition point

30. Generalization on n coordinates

32. Summary pf critical points
Minimum: all Hessian eigenvalues > 0
Corresponds to a stable state of a system.
First-order saddle point: l1<0, l2, …, ln >0
Corresponds to the transition state in a reaction. Higher-order transition points are not interesting.
A maximum: all Hessian eigenvalues < 0.