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 CO 2 along with cosolvents Environmentally problematic Expensive To develop a predictive model for solubilities of high-energy materials in supercritical CO 2 : 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 gas-phase pure solution of solute gas-phase liquid solution Absolute free energy of solvation Solvation energy Free energy of self-solvation Vapor pressure Transfer free energy of solvation Partition coefficient

 G S o (self)  G S o (aq  liq)  G S o (aq) A(liq)A(aq) A(g)  G S o (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  G S o (self ):  G S o (aq  liq)  RTln S A M A l solubility of A molarity of A Similar relationships exist for other liquid solvents or when A is a solid.

The SM5.43R Solvation Model 1,2 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  G S o  G EP  G CDS 1 Thompson, J. D.; Cramer, C. J.; Truhlar, D. G. J. Phys. Chem. A 2004, 108, Thompson, 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 Model 1,2  G S o  G EP  G CDS 1 Thompson, J. D.; Cramer, C. J.; Truhlar, D. G. J. Phys. Chem. A 2004, 108, Thompson, 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? 1 Winget, P.; Thompson, J. D.; Xidos, J. D. Cramer, C. J.; Truhlar, D. G. J. Phys. Chem. A 2002, 106, Thompson, J. D.; Cramer, C. J.; Truhlar, D. G. J. Comput. Chem. 2003, 24, Kelly, C. P.; Cramer, C. J.; Truhlar, D. G. Theor. Chem. Acc. 2004, in press. 4 Thompson, J. D.; Xidos, J. D.; Sonbuchner, T. M.; Cramer, C. J.; Truhlar, D. G. PhysChemComm 2002, 5, 117. SM5.43R Uses CM3 1-3 charges

Accurate, Density, and CM3 Dipole Moments nitramide MUE (density) = 0.30 debyes MUE (CM3) = 0.08 debyes Accurate: mPW0/MG3S density dipole MUE  mean unsigned error: C s C 2v from mPW0/MIDI! Approximate dipoles

Accurate, Density, and CM3 Dipole Moments dimethylnitramine MUE (density) = 0.49 debyes MUE (CM3) = 0.12 debyes Accurate: mPW0/MG3S density dipole MUE  mean unsigned error:

Accurate, Density, and CM3 Dipole Moments : RDX MUE (density) = 0.86 debyes MUE (CM3) = 0.19 debyes Accurate: mPW0/MG3S density dipole MUE  mean unsigned error;

Accurate, Density, and CM3 Dipole Moments : HNIW; CL-20 MUE (density) = 0.32 debyes MUE (CM3) = 0.29 debyes Accurate: mPW1PW91/MG3S density dipole  MUE  mean unsigned error: [hexa-nitrohexaaza-iso-wurtzitane]

CM3 Delivers Consistent Partial Atomic Charges Polarization energies (in nitromethane) calculated using different charge schemes by wave function (kcal/mole): MUD (CM3) = 0.1 MUD (ChElPG) = 5.7 All 14 nitramines (0.2) (2.8) MUD (Löwdin) = 5.9 (2.9) MUD  mean unsigned deviation: 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-PCM Gaussian03 MPW0/6-31+G(d) SM5.43R HONDOPLUS GAMESSPLUS SMXGAUSS mean unsigned error: 257 neutrals in water neutrals in 16 organic solvents neutrals in 74 other org. solvents not available self-solvation energies other self-solvation energies not available 0.55 better density functional better basis universal in solvents broader range of software packages smaller errors, and yet…

SM5.43R for Supercritical CO 2 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

Dielectric Constant Predictions Dielectric constant as a function of pressure at 323 K Pressure (MPa) 1 MPa = 10 atm Dielectric constant,  Similar accuracy at other temperatures

SM5.43R for Supercritical CO 2 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 1 Thompson, 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 logS 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 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 CO 2 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)