S1

Supplementary Information: A Characterization of Composition-Dependent Maxwell-Stefan Diffusivities in Mixtures of Polydimethylsiloxane, Nerve Agent VX, and Methanol Stefan A. Bringuier,1 Mark J. Varady,1,† Thomas P. Pearl,1 and Brent A. Mantooth 2,*

1 DCS Corporation, 100 Walter Ward Boulevard, Suite 100, Abingdon, Maryland 21009, U.S.A

2 U.S Army Edgewood Chemical Biological Center, 5183 Blackhawk Road, Aberdeen Proving Ground, Maryland 21010-5424, U.S.A.

_____________________________

* Author to whom correspondence should be addressed. Electronic mail: brent.a.mantooth.civ@mail.mil.

† Mark Varady is now affiliated with US Army, Edgewood Chemical Biological Center.

S2

SI. ELECTRONIC STRUCTURE CALCULATION DETAILS

All calculations have been performed using density functional theory (DFT) calculations with the Quickstep module within the CP2K

program.1 The exchange and correlation energies were calculated within the generalized gradient approximation (GGA) using the Perdew-

Burke-Emzerhof (PBE) functional. The TZV2P dual basis sets of Gaussian and plane waves was employed alongside the Goedecker-Teter-

Hutter (GTH) pseudopotentials for treatment of core electrons. A plane wave cutoff energy of 250 Ha (i.e., 500 Rydbergs) was used to ensure

sufficient energy convergence. The VX structure was geometrically minimized using the Quickstep module and the final structure was utilized

for all subsequent calculations. In Fig. S1 the ground state structure for VX is shown with a total energy of -136.790 Ha was found. The

bond lengths and angles for bonds associated with the phosphorus and sulfur displayed in Fig. S1

Figure S1. Geometry optimized VX molecule with bonds (in Ångstroms) and angles (in degrees and highlighted by arrows) shown for pairs which are relevant to the force field (FF) parameterization process.

SII. SULFUR AND PHOSPHORUS IN VX FORCE FIELD PARAMETRIZATION

The purpose of these calculations is to determine the force field (FF) parameters of the 𝐸𝐸𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏 terms in Eq. S1 for species bonded to S and

P that are found to result in unphysical geometries and forces when using the default values available in the COMPASS FF.2, 3 For all other

interactions the COMPASS FF parameters were utilized.

𝐸𝐸 = 𝐸𝐸𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏 + 𝐸𝐸𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏

𝐸𝐸𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏 = 𝐸𝐸𝑠𝑠𝑠𝑠𝑠𝑠𝑏𝑏𝑠𝑠𝑠𝑠ℎ + 𝐸𝐸𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏 + 𝐸𝐸𝑠𝑠𝑏𝑏𝑠𝑠𝑠𝑠𝑡𝑡𝑏𝑏𝑏𝑏 + 𝐸𝐸𝑠𝑠𝑠𝑠𝑏𝑏𝑠𝑠𝑠𝑠

𝐸𝐸𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏 = 𝐸𝐸𝑉𝑉𝑏𝑏𝑉𝑉 + 𝐸𝐸𝑠𝑠𝑏𝑏𝑐𝑐𝑐𝑐𝑏𝑏𝑐𝑐𝑏𝑏 .

(S1)

S3

The 𝐸𝐸𝑠𝑠𝑠𝑠𝑠𝑠𝑏𝑏𝑠𝑠𝑠𝑠ℎ and 𝐸𝐸𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏 terms in Eq. S1 are given as: 2, 3

𝐸𝐸𝑠𝑠𝑠𝑠𝑠𝑠𝑏𝑏𝑠𝑠𝑠𝑠ℎ = �𝑘𝑘𝑏𝑏(𝑟𝑟 − 𝑟𝑟𝑏𝑏)𝑏𝑏𝑁𝑁=4

𝑏𝑏=2

(S2)

𝐸𝐸𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏 = �𝑘𝑘𝑏𝑏(𝜃𝜃 − 𝜃𝜃𝑏𝑏)𝑏𝑏𝑁𝑁=4

𝑏𝑏=2

(S3)

The list of stretch and bend pairs are shown in Table S1. The procedure for determining the FF parameters was carried out by performing

a series of single point energy calculations for different stretching and bending displacements along the respective pair. This produces a curve

associated with the change in the molecular energy as a function of deformed bond length or angle. Subsequently the best fit parameters for

Eqs. (S2-S3) are determined through a least-squares fitting procedure. The results from the DFT calculations and least-squares fitting are

shown in Figs. S2-S3 and the final parameters are provided in Tables S2-S3. We note that in many cases, the generic COMPASS FF

angle parameters for the angles were P is the central atom produces good agreement with the DFT data; hence the COMPASS angle

parameters for pairs of where P was the central atom were utilized alongside the bonded parameters determined here. The torsion and cross-

bonded terms associated with P and S were not parameterized and are set to zero.

Table S1. List of bond stretching and bending pairs to be parameterized. Bond pairs Angle Pairs

P-S ∠ P-S-C

P-C ∠ C-P-S

S-C ∠ O-P=O

P-O ∠ C-O-P

P=O ∠ O-P-S

---- ∠ O=P-S

S4

Figure S2. DFT and Eq. (S2) least-squares fit results for change in energy as function of bond length.

S5

Figure S3. DFT and Eq. (S3) least-squares fit results for change in energy as function of bending of the bond angle. In some cases the COMPASS FF parameters reproduced the DFT results; these parameters were than used.

S6

Table S2. Final COMPASS FF stretching parameters for species bonded to P and S from fitting DFT data. Bond Stretching Pairs ro [Å] k2 k3 k4

P-S 2.123 151.846 -258.962 260.629

P-C 1.816 211.809 -387.069 444.545

S-C 1.850 187.259 -334.552 373.658

P-O 1.629 316.179 -724.574 965.559

P=O 1.490 642.981 -1427.246 1794.916

Table S3. Final COMPASS FF bending parameters for species bonded to P and S from fitting DFT data. Bond Bending Pairs θo [Å] k2 k3 k4

∠ P-S-C 95.513 0.027 -0.001 0.000

∠ C-O-P 118.283 48.110 -10.360 7.870

∠ C-P-S* 109.500 45.000 0.000 0.000

∠ O=P-O* 109.500 45.000 0.000 0.000

∠ O-P-S* 109.500 45.000 0.000 0.0000

∠ O=P-S 107.500 43.150 0.000 0.000

*It was found that the generic ∠X-P-X COMPASS FF parameters provided good reproduction of the DFT results.

References

(1) VandeVondele, J.; Krack, M.; Mohamed, F.; Parrinello, M.; Chassaing, T.; Hutter, J., Quickstep: Fast and accurate density functional calculations using a mixed Gaussian and plane waves approach. Comput. Phys. Commun. 2005, 167, 103-128. (2) Sun, H., COMPASS:  An ab Initio Force-Field Optimized for Condensed-Phase ApplicationsOverview with Details on Alkane and Benzene Compounds. J. Phys. Chem. B 1998, 102, 7338-7364. (3) Sun, H.; Ren, P.; Fried, J. R., The COMPASS force field: parameterization and validation for phosphazenes. Comput. Theor. Polym. Sci. 1998, 8, 229-246.