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 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 Can We Predict with Our Continuum Solvation Models?

solvent A

solvent B

ΔGSo(A → B)

gas-phase

pure solution of solute

ΔGSo(self)

gas-phase

liquid solution

ΔGSo

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 model Continuum solvation model

ΔGSo

• 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 EffectsStandard-State free energy of solvation, ,

GEP GCDS[1] GCDS

[2]

GEP

ΔGSo

• 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

GSo GEP GCDS

[1] GCDS[2]

solute

solvent

SASA

GCDS[1] and GCDS

[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

GCDS[1] = Sδ

δ∑ fZk j Z ′ k ,R ′ k ′ ′ k { }( )σZk jδ

[1]

j∑

k∑ Ak(R)

SASA of atom k

GCDS[1]

geometry of solute

The Second CDS term,

Molecular surface tension, a parameter to optimize

GCDS[2] = Sδ

δ∑ σδ

[2] Ak(R)k∑

GCDS[2]

• 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 CO2

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 CO2

– Solvent descriptors that are functions of T and P

• Assume is constant

• = 2.91 Å3 from Bose and Cole1

• Obtain N from equation-of-state for carbon dioxide2

• Use Clausius-Mossotti equation

Dielectric Constant for Supercritical CO2

α =3

4πNε−1ε+2

⎛ ⎝ ⎜

⎞ ⎠ ⎟

Polarizability

Number of molecules per unit volume (density)

1Bose, T. K. and Cole, R. H. J. Chem. Phys. 1970, 52, 140.

2Span, R. and Wagner, W. J. Phys. Chem. Ref. Data 1996, 25, 1509.

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0 10 20 30 40

density from experiment

density from EOS

Density from Equation-of-State (EOS)Density of supercritical carbon dioxide as a function of pressure at 323 K

Den

sity

(g/

cm3 )

Pressure (MPa)

Similar accuracy at other temperatures

1 MPa = 10 atm

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

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-7 TNAZ

RDX CL-20

CM3 dipole moments computed from mPW1PW91/MIDI! comparedto experimental and high-level theoretical dipoles (in debyes)

Compound CM3 Accuratehydrazine 1.71 1.75

nitromethane 3.68 3.46

dimethylnitramine 4.07 4.61

FOX-7 7.62 8.08

TNAZ 0.71 0.53

RDX 6.21 5.65

CL-20 1.23 0.81

Root-mean-square error 0.34

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 Bondi1 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

U = ΔGSo(calc., j)−ΔGS

o(expt., j) +ΔGS

o(calc., j)−ΔGSo(expt., j)j=1

I∑

6j=1N∑

N number of neutral solutesI number of ionic solutes

ΔGEP

ΔGSoΔGEP

• 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

ΔGEP

Results: Using Optimized Radii and Offsets

Mean-unsigned errors (MUEs, in kcal/mol) of the free energies of solvation of varioussolute classes using optimized radii and offsets

mPW1PW91 B3LYP Solute class No. data MIDI! 6-31G(d) 6-31+G(d) 6-31G(d)nitrohydrocarbons 6 0.48 0.28 0.22 0.25

H, C, N, O, F neutrals 170 0.54 0.51 0.62 0.51

H, C, N, O, F ions 32 5.20 5.23 4.86 5.28

P, S, Cl, Br neutrals 86 0.48 0.47 0.80 0.47

P, S, Cl, Br ions 15 3.54 3.17 2.91 3.18

all ions 47 4.67 4.57 4.23 4.61

all neutrals 256 0.52 0.50 0.68 0.49

all compounds 303 1.16 1.13 1.23 1.13

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

1Barone, V. and Cossi, M. J. Phys. Chem. A 1998, 102, 1995.

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 CO2

Problem:

Continuum solvation models developed with absolute free energies of solvation and transfer free energies of solvation

Available experimental solute data in supercritical CO2 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

ΔGSo(self)=RTln

PA•

PoMAl

pure vapor pressure of A

24.45 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

ΔGSo(l→ aq)=−RTln

SA

MAl

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) -->

ΔGSo(self)

ΔGSo(l→ aq)

ΔGSo(aq)

ΔGSo(aq) =ΔGS

o(self)+ΔGSo(l→ aq)

=RTlnPA

•

PoMAl −RTln

SA

MAl

=RTlnPA

•

Po −RTlnSA

+

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

ΔGSo(aq)=RTln

PA•

Po −RTlnSA

• 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)

Solute class No. data MUE GS

o

( )aq

hydrocarbons 17 0.10

C, ,H N compounds 7 0.41

nitr ocompounds 5 0.06

all H, C, ,N O compounds 60 0.21

so lid solutes 15 0.57

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 CO2 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