Development of Methods for Predicting Solvation and Separation of Energetic Materials in Supercritical Fluids Jason D. Thompson, Benjamin J. Lynch, Casey P. Kelly, 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 Can We 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

What is a Continuum Solvation Model? Solvent molecules replaced with continuous, homogeneous medium of bulk dielectric constant,  Solvent molecules in near vicinity of solvent represented by a set of solvent descriptors, n, , , , , and  Can treat solute quantum mechanically (one can use neglect-of- differential-overlap molecular orbital theory, ab initio molecular orbital theory, density-functional theory (DFT), and hybrid-DFT) Explicit solvation modelContinuum solvation model

Bulk-electrostatic contribution, –Electronic distortion energy of solute –Work required to put solute’s charge distribution in solvent Solute-solvent polarization energy Generalized Born approximation –Approximate solution to Poisson equation –Solute is collection of atom-centered spheres with empirical Coulomb radii and atom-centered point charges Elements of Our Continuum Solvation Model: Bulk-electrostatic Effects Standard-State free energy of solvation,,  G EP  G CDS [1]  G CDS [2]  G EP

Nonbulk-electrostatic contributions, –Inner solvation-shell effects, short-range interactions Cavitation, dispersion, solvent-structural rearrangement Modeled as proportional to solvent-accessible surface area (SASA) of the atoms in solute Elements of Our Continuum Solvation Model: Nonbulk Electrostatic Effects  G S o  G EP  G CDS [1]  G CDS [2] solute solvent SASA G CDS [1] andG CDS [2]

Semiempirical Depends on –Characteristics of solvent Index of refraction, n Abraham’s acidity and basicity parameters,  and  –SASAs of the atoms Recognizes functional groups in solute The First CDS term, value of solvent descriptor,  atomic surface tension, a parameter to optimize “chemical environment” term SASA of atom k geometry of solute

The Second CDS term, Molecular surface tension, a parameter to optimize Semiempirical Depends on –Characteristics of solvent Macroscopic surface tension,  Square of Abraham’s basicity parameter,  Square of aromaticity factor,  Square of electronegative halogenicity factor,  –Total SASA of solute

Toward an Accurate Solvation Model for Supercritical CO 2 We have: We want: Dielectric constant as a function of T and P Universal continuum solvation model, SM5.43R –Accurate charge distributions using our newest charge model, CM3 Validate CM3 for high-energy materials (HEMs) –Optimize Coulomb radii to use in generalized Born method –Optimize atomic and molecular surface tension parameters Reliable experimental solubilities in supercritical carbon dioxide –Validate relationship between solubility, free energy of solvation and vapor pressure Continuum solvation model for supercritical CO 2 –Solvent descriptors that are functions of T and P

Assume  is constant  = 2.91 Å 3 from Bose and Cole 1 Obtain N from equation-of-state for carbon dioxide 2 Use Clausius-Mossotti equation Dielectric Constant for Supercritical CO 2 Polarizability Number of molecules per unit volume (density) 1 Bose, T. K. and Cole, R. H. J. Chem. Phys. 1970, 52, Span, R. and Wagner, W. J. Phys. Chem. Ref. Data 1996, 25, 1509.

Density from Equation-of-State (EOS) Density of supercritical carbon dioxide as a function of pressure at 323 K Density (g/cm 3 ) Pressure (MPa) Similar accuracy at other temperatures 1 MPa = 10 atm

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

CM3 Charge Model for High-Energy Materials (HEMs) CM3 trained on large, diverse training set of data (398 data for 382 compounds) –Training set did not include high-energy materials of interest –Do we need to include dipole moment data of high-energy materials in CM3 training set? Considered –hydrazine, nitromethane, dimethylnitramine (DMNA), 1,1-diamino-2,2-dinitroethylene (FOX-7), 1,3,3-trinitroazetidine (TNAZ), 1,3,5-trinitro-s-triazine (RDX), and hexanitrohexaazaisowurtzitane (CL-20) We are interested in CM3 charge distributions from the following wave functions: –mPW1PW91/MIDI!, mPW1PW91/6-31G(d), mPW1PW91/6-31+G(d), B3LYP/6-31G(d), and B3LYP/6-31+G(d)

CM3 Dipoles vs. High-level Dipoles FOX-7TNAZ RDXCL-20

CM3 Results, Part 1

CM3 Results, Part 2

Solvation Model, SM5.43R Now calibrate the universal solvation model –Next several slides will go through steps –In each step, treat solutes as follows Use CM3 charges Hybrid density-functional theory (HDFT) –mPW1PW91, B3LYP Polarized double-zeta basis sets –MIDI!, 6-31G(d), 6-31+G(d)

Training set –47 ionic solutes containing H, C, N, O, F, P, S, Cl, and Br in water –256 neutral solutes containing H, C, N, O, F, P, S, Cl, and Br in water Optimize the following parameters with these aqueous data –Specific Coulomb radii for H, S, and P –Common offset from van der Waals of Bondi 1 radii for C, N, O, and F (first row offset) and an offset from radii for Cl and Br Coulomb Radii for Generalized Born Method 1 Bondi, A. J. Phys. Chem. 1964, 68, 441.

Optimize H radius and first row offset first and simultaneously Then optimize Cl and Br offset Then optimize S radius, then P radius For a given set of Coulomb radii, –Calculate electrostatic term ( ) for all neutral and ionic solutes –Optimize atomic surface tensions by minimizing root-mean square error (RMSE) between calculated and exptl. using only neutrals –Evaluate unfitness function, U, Parameter Optimization N  number of neutral solutes I  number of ionic solutes

Parameters to optimize –Atomic and molecular surface tensions for general organic solvents –Atomic surface tensions for water Coulomb radii are fixed Training set consists of compounds containing H, C, N, O, F, P, S, Cl, and Br –1856 absolute solvation energies in 90 organic solvents and 75 transfer free energies between 12 organic solvents and water for 285 neutral solutes –256 aqueous free energies of solvation for 256 neutral solutes Predict absolute and transfer free energies of solvation –Need , n, , , , , and  of solvent Universal Continuum Solvation Model

Minimize RMSE between calculated and exptl. solvation free energies with respect to the atomic and molecular surface tension parameters –First for H, C, N, and O –Then for F, S, Cl, and Br –Finally for P Parameter Optimization

Results: Using Optimized Radii and Offsets

Comparison of SM5.43R to Other Continuum Solvation Models SM54.3R vs. C-PCM, 1 as it is implemented in Gaussian98, for our aqueous training set of data in terms of MUEs 1 Barone, V. and Cossi, M. J. Phys. Chem. A 1998, 102, C-PCM  Conductor-like-screening-based Polarized Continuum Model

Comparisons to Popular and Generally Available Continuum Solvation Model (C-PCM) for Free Energies of Solvation in Water

Results: SM5.43R

SM5.43R vs. C-PCM for Free Energies of Solvation in Organic Solvents

Reliable Solute Data in Supercritical CO 2 Problem: Continuum solvation models developed with absolute free energies of solvation and transfer free energies of solvation Available experimental solute data in supercritical CO 2 in the form of solubility Solution: Relate solubility to free energy of solvation and vapor pressure of solute Use test set of compounds with known aqueous free energies of solvation, pure-substance vapor pressures, and solubilities

Relationship Between Solubility and Free Energy of Solvation, Part 1 A(g)  A(l) Consider the equilibrium between a pure solution of substance A and its vapor Use a 1 molar standard-state at 298 K and assume ideal behavior in both phases pure vapor pressure of A atm molarity of pure liquid A

Relationship Between Solubility and Free Energy of Solvation, Part 2 A(l)  A(aq) Now consider the equilibrium between a pure solution of A and a saturated aqueous solution of A Use a 1 molar standard-state at 298 K and assume ideal behavior in both phases equilibrium aqueous solubility of A in units of molarity

Relationship Between Solubility and Free Energy of Solvation, Part 3 A(g)  A(l) --> A(l)  A(aq) --> A(g)  A(aq) --> + A similar argument can be made for solids

Validation of Relationship: Test Set 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

Error of 0.20 kcal/mol is within exptl. uncertainty of free energy measurement We can also predict solubility –From SM5.43R free energies of solvation and experimental vapor pressures –From SM5.43R free energies of solvation and vapor pressures (C-PCM cannot) Mean-Unsigned Errors (MUE in kcal/mol) MUEs (kcal/mol) of the aqueous free energies of solvation calculated using exptl. vapor pressures and solubilities for various classes of the test set

Summary of Progress We can obtain  for supercritical CO 2 at various temperatures and pressures CM3 is reliable method for obtaining accurate charge distributions of high-energy materials We have optimized atomic radii based on CM3 charges We have robust and accurate atomic and molecular surface tensions for organic solvents and water –Predict free energies of solvation in water and organic solvents –Predict vapor pressures –Predict solubilities We have begun obtaining and organizing solubility data in supercritical carbon dioxide, which we can relate to free energy of solvation

Future Work Solvent descriptors for supercritical carbon dioxide –  as function of T and P Reliable solute-vapor pressure data as a function of T Account for potential clustering effects –spatial inhomogeneities in solvent Continuum solvation models for supercritical carbon dioxide with various cosolvents

Acknowledgments Department of Defense Multidisciplinary University Research Initiative (MURI) Christopher J. Cramer and Donald G. Truhlar Casey P. Kelly and Benjamin J. Lynch Chris Kinsinger, Bethany Kormos, John Lewin, Joe Scanlon Minnesota Supercomputing Institute