Development of Methods for Predicting Solvation and Separation of Energetic

Materials in Supercritical Fluids

Jason Thompson, Casey Kelly, Benjamin Lynch,

Christopher J. Cramer and Donald G. Truhlar

Department of Chemistry and Supercomputing Institute

University of Minnesota

Minneapolis, MN 55455

Methods for the demilitarization of excess stockpiles

containing high-energy materials

• burning

• detonation

• recycling explosive materials by extraction using

supercritical CO2 along with cosolvents

• Environmentally problematic• Expensive

To develop a predictive model for solubilities of high-energy materials

in supercritical CO2: cosolvent mixtures.

What cosolvent? What conditions?

The goal of this work

What Do We Usually Predict with Our Continuum Solvation Models?

solvent A

solvent B

GSo(A B)

gas-phase

pure solution of solute

GSo(self )

gas-phase

liquid solution

GSo

Absolute free energy of solvation

Solvation energy

Free energy of self-solvation

Vapor pressure

Transfer free energy of solvation

Partition coefficient

GSo (self)

GSo (aqliq)

GSo (aq)

A(liq)A(aq)

A(g)

GSo (aq):

equilibrium standard-state aqueous free energy of solvation

can be calculated or obtained from expt.

equilibrium standard-state free energy of self-solvation

can be calculated or obtained from expt.

defines pure-solute vapor pressure of A

GSo (self ):

GSo (aq liq) RT ln

SA

MAl

solubility of A

molarity of A

Similar relationships exist for other liquid solvents or when A is a solid.

The SM5.43R Solvation Model1,2

• Bulk-electrostatic contribution to free energy of solvation

– Solute-solvent polarization energy

– Electronic distortion energy of solute and solvent cost

• Generalized Born approximation

– Solute is collection of atom-centered spheres with empirical Coulomb radii and atom-centered point charges

• Need accurate charges

• Need dielectric constant of solvent

GSo GEP GCDS

1Thompson, J. D.; Cramer, C. J.; Truhlar, D. G. J. Phys. Chem. A 2004, 108, 6532.

2Thompson, J. D.; Cramer, C. J.; Truhlar, D. G. Theor. Chem. Acc. 2004, in press.

• Non-bulk-electrostatic contribution to free energy of solvation

– Cavitation, dispersion, solvent structure, and other effects

• Model: proportional to solvent-accessible surface areas of atoms in solute

– Constants of proportionality are surface tension coefficients

• Need index of refraction, Abraham and parameters, and macroscopic surface tension of solvent

The SM5.43R Solvation Model1,2

GSo GEP GCDS

1Thompson, J. D.; Cramer, C. J.; Truhlar, D. G. J. Phys. Chem. A 2004, 108, 6532.

2Thompson, J. D.; Cramer, C. J.; Truhlar, D. G. Theor. Chem. Acc. 2004, in press.

H bond acidity, basicity

• CM3 charge model

– Maps lower level charges to improved charges as trained on dipole moments

– Uses a larger training set than previous charge models

– Is less sensitive to basis set size than previous charge models

– Uses redistributed Löwdin population analysis (RLPA)4 charges when diffuse functions are used

– Is available for many combinations of hybrid-density functional theory and basis set

• How accurate is CM3 for high-energy materials?

1Winget, P.; Thompson, J. D.; Xidos, J. D. Cramer, C. J.; Truhlar, D. G. J. Phys. Chem. A 2002, 106, 10707.

2Thompson, J. D.; Cramer, C. J.; Truhlar, D. G. J. Comput. Chem. 2003, 24, 1291.

3Kelly, C. P.; Cramer, C. J.; Truhlar, D. G. Theor. Chem. Acc. 2004, in press.

4Thompson, J. D.; Xidos, J. D.; Sonbuchner, T. M.; Cramer, C. J.; Truhlar, D. G. PhysChemComm 2002, 5, 117.

SM5.43R Uses CM31-3 charges

Accurate, Density, and CM3 Dipole Moments

N NO

OH

HN N

H

H

O

ON N

HH

O

ON N

H

H

O

O

3.943.593.84

4.313.93 4.19

2.972.71 2.89

3.283.07 3.27

nitramide

MUE (density) = 0.30 debyes MUE (CM3) = 0.08 debyes

Accurate: mPW0/MG3S density dipole

MUE mean unsigned error:

Cs C2v Cs C2v

from mPW0/MIDI!

Approximate dipoles

Accurate, Density, and CM3 Dipole Moments

4.814.21 4.67

5.044.43 4.87

3.432.99 3.33

3.693.38 3.77

dimethylnitramine

MUE (density) = 0.49 debyes MUE (CM3) = 0.12 debyes

Accurate: mPW0/MG3S density dipole

N NO

OMe

MeN N

Me

Me

O

ON N

MeMe

O

ON N

Me

Me

O

O

MUE mean unsigned error:

Accurate, Density, and CM3 Dipole Moments

5.975.22 6.20

7.196.227.34

: RDX

MUE (density) = 0.86 debyes MUE (CM3) = 0.19 debyes

Accurate: mPW0/MG3S density dipole

N N

N

NO2

O2N NO2

MUE mean unsigned error;

Accurate, Density, and CM3 Dipole Moments

1.561.321.80

0.310.42 0.79

: HNIW; CL-20

MUE (density) = 0.32 debyes MUE (CM3) = 0.29 debyes

Accurate: mPW1PW91/MG3S density dipole

2.561.95 2.41

N N

N N

NNNO2O2N

NO2

NO2O2N

O2N

MUE mean unsigned error:

[hexa-nitrohexaaza-iso-wurtzitane]

CM3 Delivers Consistent Partial Atomic Charges

Conformer CM3 ChElPG CM3 ChElPG-HNIW -12.6 -13.4 -12.4 -19.1-HNIW -13.2 -13.6 -13.0 -19.2-HNIW -13.7 -13.9 -13.7 -19.6

mPW1PW91/MIDI! HF/MIDI!

Polarization energies (in nitromethane) calculated using different charge schemes by wave function (kcal/mole):

MUD (CM3) = 0.1MUD (ChElPG) = 5.7

All 14 nitramines(0.2)(2.8)

MUD (Löwdin) = 5.9 (2.9)

MUD mean unsigned deviation:

GP 1

2

1

qk q k k k

k , k

electrostatic fitting

population analysis

The new CDS Term for SM5.43R

• Parameters in surface tension coefficients optimized using a large training set of solvation data

– 2237 experimental free energies of solvation in water and 90 organic solvents, partition coefficients between water and 12 organic solvents, and free energies of self-solvation

• Parameters are universal

– Parameters optimized for specific wave functions are similar to one another

• 2–8 times more accurate than the polarizable-continuum models (PCMs) in Gaussian 03, such as IEF-PCM

Mean-Unsigned Errors (MUEs) of Free Energies of Solvation

B3LYP/6-31G(d)IEF-PCMGaussian03

MPW0/6-31+G(d)SM5.43RHONDOPLUSGAMESSPLUSSMXGAUSS

mean unsigned error: 257 neutrals in water 1.24 0.54 621 neutrals in 16 organic solvents 3.96 0.511359 neutrals in 74 other org. solvents not available 0.53 16 self-solvation energies 3.93 0.56 74 other self-solvation energies not available 0.55

better density functionalbetter basisuniversal in solventsbroader range of software packages

smaller errors, and yet…

SM5.43R for Supercritical CO2

with and without cosolvents

• Need to develop solvent descriptors as a function of T and P

– Dielectric constant, index of refraction, Abraham’s hydrogen bond parameters, macroscopic surface tension, possibly others

1.00

1.10

1.20

1.30

1.40

1.50

1.60

0 10 20 30 40

dielectric constant fromexperimentdielectric constant fromClausius-Mossotti eq.

Dielectric Constant Predictions

Dielectric constant as a function of pressure at 323 K

Pressure (MPa)

1 MPa = 10 atm

Die

lect

ric

cons

tant

,

Similar accuracy at other temperatures

SM5.43R for Supercritical CO2

with and without Cosolvents

• Develop solvent descriptors as a function of T and P

– Dielectric constant, index of refraction, Abraham’s hydrogen bond parameters, macroscopic surface tension, possibly others

• Need training set of solvation data

– Mostly solubility data

• Relate free energies of solvation to solubility?1

1Thompson, J. D.; Cramer, C. J.; Truhlar, D. G. J. Chem. Phys. 2003, 119, 1661.

Test Relationship

• Use a test set of 75 liquid solutes and 15 solid solutes

– Compounds composed of H, C, N, O, F, and Cl• Each solute has a known experimental aqueous free energy of solvation, pure

vapor pressure, and aqueous solubility

• Predict using experimental quantities

• Predict using experimental vapor pressures and calculated aqueous free energies of solvation

• Predict using calculated vapor pressures and aqueous free energies of solvation

solubility of A SA PA

Po

exp

GSo(aq)

RT

log Slog S

log S

Mean-Unsigned Errors of the Logarithm of Solubility

calculated from experimental values, from theoretical free energies and experimental vapor pressures, and from theoretical values

Solute class No.data

Expt1.GS

o (aq) and PCalc. GS

o (aq)

Exptl. PCalc.

GSo (aq) and P

nitro compounds 5 0.04 0.25 0.35

all H, C, N, Ocompounds

60 0.15 0.32 0.35

all liquid solutes 75 0.15 0.32 0.34

solid solutes 15 (7) 0.42 0.47 (0.66)

requires “solvent” descriptors for solutes;we have the required solvent descriptors for only 7

Other Progress

• Optimized electronic structure computer programs for hybrid density functional methods– Up to 4 times faster

• Assembling training set of solubility data in supercritical CO2

• New theoretical models to estimate solvent descriptors for free energy of self-solvation calculations

Acknowledgments

Department of Defense Multidisciplinary University Research Initiative (MURI)

Minnesota Supercomputing Institute (MSI)

Casey P. Kelly (grad. student)

Dr. Benjamin J. Lynch (postdoctoral associate)

Jason D. Thompson (graduate student; Ph. D. completed summer ’04)

Christopher J. Cramer (co-PI)