ISIS Neutron training course.
6th March 2014
Molecular Dynamics
Lecture 3: Analysis of the results, some examples.
David J. Willock
Cardiff University, U.K.
1
Water Models
1040
TIP4P/2005
1020
Density (kg m-3)
SPC/E
1000
Experiment [6]
980
960
940
920
900
200
225
250
275
300
325
350
Temperature (K)
375
400
425
450
• TIP4P/2005 provides a much more accurate description of liquid water
than SPC/E
• SPC/E underestimates the temperature at which the density of water has its
maximum, so the water structure will be affected.
[6] G. S. Kell, J. Chem. Eng. Data, 20, 97, (1975)
Water/Methanol mixtures.
Density (kg m-3)
1000
Pure Water
900
Pure Methanol
800
10%
20%
700
30%
600
40%
90%
500
200
225
250
275 300 325
Temperature (K)
350
375
400
• Even a small amount of methanol alters the properties of the
solution by disrupting the hydrogen bonding network.
Radial Distribution Functions
g(r)
Water Oxygen - Water Oxygen RDF
5
4
3
2
1
0
200 K
300 K
0
2
4
6
8
400 K
r
Methanol Oxygen - Methanol
Oxygen RDF
4
g(r)
3
2
200 K
1
300 K
0
400 K
0
2
4
6
r
8
• Peaks show the
distances of the first,
second etc. neighbours
• Narrow peaks indicate
that the system is more
ordered
• Integrating the radial
distribution functions to
their first minima allow
us to calculate the
average number of
hydrogen bonds formed
by each molecule.
Moment of Inertia of molecules
The moment of inertia of a molecule is a matrix which pays the role of mass in
rotational motion. It is defined as:

z
Origin :
Centre of Mass
x
r
y

2
  m r  rx2
 atoms
I    mrx ry
 atoms

  mrx rz
 atoms

 mrx ry

atoms
2
m
r

r

y
2
atoms
 mr r
y z
atoms



atoms

mry rz 


atoms
2
2 
m
r

r

z 
atoms

 mrx rz


mass, m
e2
e2
If we diagonalise this matrix we
get the three principle axes of
rotation. Which give a frame of
reference in which I is diagonal.
By comparing these we can see
how elongated the molecule is.
3 similar values tells us the
molecule is near spherical.
el
e3
el
e3
MoI in Analysis of Results
500
Average sMoI ((amu)Å2)
Average sMoI against
coverage for 3-GPMS on the
(111), (110) and (100)
surfaces of iron (with torsion
angles).
600
400
300
200
100
(111)
(110)
(100)
0
0
60
120
180
240
2
300
360
420
-1
Coverage (Å mol )
(111)
(110)
(100)
o
Average Inclination Angle ()
90
Average inclination angle
against coverage for 3GPMS on the (111), (110)
and (100) surfaces of iron
(with torsion angles).
80
70
60
50
40
0
60
120
180
240
2
300
-1
Coverage (Å mol )
360
420
RDF for Oepoxide-Oepoxide at ½ AA
and ½ AB surface coverages.
1 /2 A A
1 /2 A B
3
g (r)
a) ½ AA
starting
structure;
4
2
1
0
0
1
2
3
4
5
6
r (Å )
b) ½ AB
starting
structure.
RDF for Halcohol-Halcohol at ½ AA
and ½ AB surface coverages.
1 /2 A A
1 /2 A B
1/2 AA
9
g (r)
½ AB is trapped: none ergodic.
12
1/2 AB
6
3
0
0
1
2
r (Å )
3
4
SANS data
 N-(2-hydroxypropil) methacryleamide (HPMA) is a polymer used
as carrier in drug delivery systems.
 MD compared with small angle neutron scattering (SANS) data. O
Log (I(Q) / cm-1)
Log (Q / Å-1)
HO
NH
Flory power law approximation
Flory used self avoiding random walks to show that a polymer conformation should
be expected to lead to a radius of gyration that depends on monomer number via a
power law:
With ν = 0.6 for a “good” solvent
90
80
minimisation
explicit water, Rg(265)= 66 Å
70
Rg, nm
60
50
40
React. field, Rg(265)= 62 Å
30
20
10
Dist. dielectric, Rg(265)= 27 Å
0
50
100
150
200
250
N (number of HPMA monomers)
SANS: HPMA-265, R g = 75 ± 3 Å
Shape Information: Moments of inertia
Ellipsoid
dimensions:
RX / RZ = 0.36
RY / RZ = 0.43
RZ / RZ = 1.00
RX / RZ = 0.02
RY / RZ = 0.02
RZ / RZ = 1.00
Neutron scattering is controlled by the
scattering length density:
To describe the observed “shape” we can
use the scattering factors, bi, in place of
mass in the moment of inertia matrix.
This allows us to define a set of axes and
determine the dimensions of an ellipsoid
that represents the shape using the
furthest atom distance in each direction
at each frame of the MD trajectory.
HPMA-50 comparison of starting points
R/Å
HPMA-50, MOE built
Etot 56.4 kcal mol-1, (monomer)
RZ
RX, RY
NVT ensemble, 310 K,
AMBER99 forcefield
Reaction field implicit water (ε = 80.1).
MOE start point eventually gives more
spherical polymer shape.
t / ns
R/Å
Zebedde start point rapidly achieves
constant shape parameters.
HPMA-50, Zebedde start point
Etot 57.7 kcal mol-1, (monomer)
RZ
RX, RY
t / ns
MD runs comparing elongated (MOE)
and Zebedde generated start points.
Comparison with SANS data
Conjugate
Vol. Calc.
/ 105 Å3
Vol. SANS
/ 105 Å3
Vcalc/VSANS
Aspect
ratio calc.
Aspect ratio
SANS
HPMA-C6-F-10
1.275
1.024
0.803
2.56
4.83
HPMA-C8-OH-10
1.232
1.024
0.831
1.95
4.83
HPMA-C6-OH-10
1.122
1.125
1.003
1.70
4.38
HPMA-C6-10
1.052
2.658
1.975
1.43
3.48
HPMA-C12-5
1.196
7.654
6.397
1.54
7.80
The volume from the MD ellipsoids and cylinders fitted to SANS measurements
show reasonable agreement for first three cases.
For HPMA-C6-10 and HPMA-C12-5 cases data suggests that there is
agglomeration of polymer in the experimental case.
Aspect ratios for single chains show more elongated structures than would be
expected from the simulations.