• Two parameters must be created for each ion, ε and Rmin/2. • These two parameters are placed in the Lennard-Jones potential equation

(below) which has a well of depth ε at a distance of Rmin.

• The general scheme we are using is similar to one used by Joung and Cheatham to develop parameters for SPC, TIP3P, and TIP4PEW.

1. Construct all possible cation/anion crystals for ions under study. 2. Search the Rmin space of all ions, holding ε to heuristically minimize the

combined error compared to experimental lattice constants (LC). • This yields Rmin for each ion

3. Determine the RDF peak positions and ΔGhyd for each ion for a range of Rmin and ε values.

4. Using the Rmin found in step 2, search the ε space of each ion to find the minimum combined error of the RDF’s and ΔGhyd.

• This yields ε for each ion 5. Return to step 2 using the new ε for each ion, and iterate until ε

converges.

• MD is used to model the structures and dynamics of large macromolecules. • AMBER is a high performance MD package that is used by many researchers. The

following equation is the energy of any given system in AMBER, using pre-determined parameters and the previous structure:

Molecular Dynamics (MD)

0.5 1.0 1.5 2.0 2.5 3.0

-1.0

-0.5

0.0

0.5

1.0

1.5

Energ

y (

ELJ/

)

Distance (r/Rmin

)

• The Lattice Constant (LC) is the distance between two unit cells in a crystal. For Face Centered Cubic (FCC) crystals the LC is twice the interionic distance. Our method for determining the lattice constant is derived from the one used by Joung and Cheatham. To calculate the lattice constant for a given Rmin, Rmin pair: 1. Build a number of crystals with varying LC’s and calculate the energy of each. 2. Fit a quadratic to the points near the observed minimum. 3. Use the fit curve to find an analytical minimum. This minimum is said to be

the Lattice Constant for that Rmin, Rmin pair.

Convergence Testing: • We initially verified that the default Particle Mesh Ewald settings were converged

with respect to the pure Ewald settings. The energies were slightly different (3 out of 4×107 kcal/mol) but the fit LC’s were the same (5.66042Å vs. 5.66045Å).

• We then looked at the Lennard-Jones cutoff distance and found that a cutoff ≥ 12 was well converged.

Results: • Unlike pairwise LJ interactions, we found that the LC does depend on ε due to the

presence of anion-anion and cation-cation interactions. • Nine surfaces are shown below using Joung & Cheatham TIP4PEW ε parameters.

Lattice Constants

Above: These three images show the same crystal with a lattice constant of 1Å, 3Å, and 5Å respectively. Below: Plots showing the dependence of the potential energy on the lattice constant.

3 4 5 6-1.2x10

6

-1.0x106

-8.0x105

-6.0x105

-4.0x105

LE

(kcal/m

ol)

LC (Å)

Developing monovalent ion parameters for the optimal point charge (OPC) water model Daniel E. Clark, John C. Dood, and Brent P. Krueger*, Department of Chemistry, Hope College, Holland MI 49423.

*kruegerb@hope.edu

Molecular dynamics (MD) simulations are used to model the structure and movement of macromolecules. The gold standard for MD is to explicitly include water molecules using one of several standard models. Recently, a new water model, Optimal Point Charge (OPC), has been developed with simulation performance that compares better to experiment than existing models in its class (Izadi, Anandakrishnan, Onufriev, J. Phys. Chem. Lett., 2014, 5, 3863-3871). For this new water model to be useful, Lennard-Jones (LJ) parameters must be developed for at least a few monovalent ions. In this study MD simulations were used to develop these parameters. Preliminary results are presented including: extensive convergence testing of Hydration Free Energy (ΔGhyd), Lattice Constants (LC), and first peak position of radial distribution functions (RDF’s); as well as surfaces showing the dependence of the RDF and LC on various LJ parameters within the OPC water model.

Abstract

• Finish convergence of remaining TI calculations. • Use converged simulation protocols to develop monovalent ion parameters. • Run lengthy simulations showing correct solubility of ion crystals in water. • Publish parameters and creation procedure . • Add parameters to the AMBER source tree so that anyone can run simulations

using the OPC water model with counter ions.

Future Work

• Simulate water by giving it single van der Waals center with massive and massless point charges.

• Classified by the number of points that are included, typically 3, 4, or 5 points. • Popular 3 point models are TIP3P and SPC. • TIP4PEW is the most popular 4 point model. • OPC is a new 4 point model based on quantum mechanical calculations and

performs better in simulations than previous 4 point models. • Below are representations of 3, 4, and 5 point models.

Water Models

3 point model i.e.. TIP3P or SPC

4 point model i.e.. TIP4PEW or OPC

5 point model i.e.. TIP5P

• Radial Distribution Functions (RDF’s) are a type of histogram showing the density of oxygen (water) around an ion over the course of the simulation. The position of the first peak of the RDF is characteristic for each ion. Neutron diffraction experiments give an experimental known to compare to.

• Positions of the first peaks of the RDFs (seen below) were determined by fitting the points within 0.1Å of the maximum value to a quadratic curve4. Convergence Testing: • We have carefully checked for convergence with equilibration time, sampling time, the period between samples, and the buffer of water around the ion. • To verify the equilibration time we performed 520ps of equilibration before running 210ns of simulation on Na+ with 10ns of sampling at the beginning,

middle, and end. Results from each of these sampling periods were indistinguishable.

• All of the tested buffer sizes (14.3Å, 16Å, 18Å, 20Å, and 25Å) produced a similar RDF showing that the system had converged (STDEV=0.00063Å). There is no

apparent trend in the RDFs as seen above. • We tried shorter sampling times and more frequent sampling with no apparent trend. • Currently our simulations involve 100ns of equilibration followed by 10ns of sampling; we sample every 500fs during the sampling period. • Our simulations use Particle Mesh Ewald with 499 waters (buffer of 15Å). We used constant temperature and pressure with 20ps coupling parameters and a

2fs time step.

Radial Distribution Functions

3 4 5 6 7 80

1

2

3

4

5

Fre

qu

en

cy o

f O

Distance (Å)

K+

Exp: 2.798Å

F−

Exp: 2.63Å Br−

Exp: 3.187Å

15 20 25

2.478

2.480

2.482

2.484

2.486

RD

F (

Å)

Buffer Size (Å)

• The Hydration Free Energy of an ion is the amount of energy gained by solvating the ion in water. Our tests have calculated the dehydration free energy (−ΔGhyd) using a technique called Thermodynamic Integration.

• Thermodynamic integration (TI) is performed by slowly removing the ion from water and calculating the gradient in the free energy at each step. By integrating the free energy with respect to λ we obtain a hydration free energy.

• Our thermodynamic integration is done in two steps. In the first step, charge is eliminated from the ion, and in the second step, the Lennard Jones interaction is removed. The charge elimination part of thermodynamic integration, as seen in the two graphs above, is the largest contribution to the hydration free energy so the bulk of our convergence testing has focused on only this.

Hydration Free Energy (ΔGhyd)

050

100150200

0 0.5 1

∂V/∂λ

λ

Charge ∂V/∂λ

-8

-4

0

4

0 0.2 0.4 0.6 0.8 1

∂V/∂λ

λ

vdW ∂V/∂λ

90.96+0.2360=91.20 kcal/mol

Acknowledgements: Dr. Alexey Onufriev, Saeed Izadi (Virginia Tech) Hope College Department of Chemistry Midwest Undergraduate Computational Chemistry Consortium (MU3C) ambermd.org NSF-MRI award #CHE-1039925 NSF-RUI award #CHE-1058981 References: (1) Salomon-Ferrer et al. J. Chem. Ther. Comp. 2013, 9, 3878 (2) Le Grand et al. Comp. Phys. Comm, 2013, 814, 374 (3) Jenson, K. P.; Jorgenson, W. L. J. Chem. Ther. Comp. 2006, 2, 1499 (4) Joung, I. S.; Cheatam T. E. J. Phys. Chem. B 2008, 112, 9020 (5) Marcus, Y. Chem. Rev. 1988, 88, 1475

Acknowledgements, References

y = -6E-05x + 91.682 R² = 0.0588

91

91.2

91.4

91.6

91.8

92

0.1 1 10 100 1000

Hyd

rati

on

Fre

e

Ene

rgy

(kca

l/m

ol)

NTWX

Parameterization

Convergence Test

Run Test Simulations

Run a large number of LC simulations for different Rmin, Rmin pairs

Pick Rmin’s that minimize error in LC for each crystal

Collect Parameters

Run TI & RDF simulations for a variety of Rmin, ε

Pick ε’s that minimize error in RDF & TI for each crystal

Ion Parameters

Li+

Exp: 2.08Å

0.51.0

1.52.0

2.5

4

6

8

1.52.0

2.53.0

3.5

lif

licl

libr

naf

nacl

nabr

kf

kcl

kbrLC (Å)

Anion Radius (Å)

Cation Radius (Å)

1.0

0.9

0.8

0.7

0.6

1.9

2.0

2.1

2.2

2.3

0.08

0.09

0.10

0.11

0.12

RDF (Å)

(kcal/mol)Rmin

/2 (Å)

-0.006

-0.003

0.000

0.003

0.006

RDF

Error (Å)

3.0

2.8

2.6

2.4

2.2

2.4

2.6

2.8

3.0

0.0014

0.0016

0.0018

RDF (Å)

Rmin

/2 (Å) (kcal/mol)

1.81.7

1.6

1.5

1.4

1.3

2.6

2.7

2.8

2.9

3.0

3.1

0.24

0.26

0.28

0.30

RDF (Å)

Rmin

/2 (Å) (kcal/mol)

3.2

3.0

2.8

2.6

2.4

2.8

3.0

3.2

3.4

3.6

3.8

0.025

0.030

0.035

(kcal/mol)Rmin

/2 (Å)

RDF (Å)

Results: • Using our converged protocol we were able to obtain surfaces showing the dependence of the first peak

position of the RDF on Rmin and ε for all six ions. Some surfaces are presented below. • Analytic fitting of the surfaces was performed with quadric equations of the general form

RDF = ax2 + by2 + cxy + dx +ey + f, where x and y were Rmin and ε respectively.

91.8

91.9

92

92.1

92.2

92.3

92.4

0 20 40 60 80

Hyd

rati

on

Fre

e E

ne

rgy

(kca

l/m

ol)

Time (ns)

Averaged ΔGhyd

15

17.5

20

22.5

25

30

40

50

• We ran simulations for a number of different buffer sizes. Our results (right) suggest that 80-100 ns is adequate simulation time to converge TI, but are inconclusive with respect to buffer size. Experimental ΔGhyd uncertainty ≈ 0.25 kcal/mol.

• We also ran simulations

comparing a number of different output frequencies showing no apparent trend (STDEV=0.0503 kcal/mol)

3.5 4.0-1x10

6

-1x106

-1x106

-9x105

LE

(kcal/m

ol)

LC (Å)