Development of Methods for Predicting Solvation and Separation of Energetic Materials in...
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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 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
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
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