Design of ionic liquids via computational

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Computers and Chemical Engineering 34 (2010) 14761480

Contents lists available atScienceDirect

Computers and Chemical Engineering

j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / c o m p c h e m e n g

Design of ionic liquids via computational molecular design

Samantha E. McLeese, John C. Eslick, Nicholas J. Hoffmann, Aaron M. Scurto, Kyle V. Camarda

Department of Chemical and Petroleum Engineering, University of Kansas, Lawrence, KS 66045, United States

a r t i c l e i n f o

Article history:

Received 1 September 2009

Received in revised form 1 January 2010

Accepted 12 February 2010

Available online 20 February 2010

Keywords:

Molecular product design

Ionic liquids

Optimization

a b s t r a c t

Computational molecular design (CMD) is a methodology which applies optimization techniques to

develop novel lead compounds for a variety of applications. In this work, a CMD methodis applied to the

design of ionic liquids (ILs), which are being considered for use as environmentally benign solvents. The

molecularly tunable nature of ILs yields an extraordinary number of possible cation and anion combi-nations, the majority of which have never been synthesized. The product design framework developed

in this work seeks to accelerate the commonly used experimental trial-and-error approach by searching

through this large molecular space and providing a set of chemical structures likely to match a set of

desired property targets. To predict the physical and chemical properties of an ionic liquid in a specific

system, quantitative structureproperty relations (QSPRs) have been developed. In this work, correla-

tions were created for solubility, diffusivity, and melting temperature. The electronic structure of ionic

liquids is quantified using molecular connectivity indices, whichdescribe bonding environments, charge

distribution, orbital hybridization and other interactions within and between ions. The resulting prop-

erty prediction model is then integrated within a computational molecular design framework, which

combines the QSPRs with structural feasibility constraints in a combinatorial optimization problem. The

problem is reformulated as an MILP after exact linearization of structural constraints. An example is

provided to test theformulationfor thedesign of ionic liquids foruse withina hydrofluorocarbon(refrig-

erant) gas separation system. A second example compares a stochastic optimization algorithm, Tabu

Search, to a standard deterministic solver for the solution of a larger-scale refrigeration design problem.

The computational efficiency and practical implementation of this product design methodology is also

discussed. 2010 Elsevier Ltd. All rights reserved.

1. Introduction

A large portion of the research currently performed today in the

chemical industries is devoted to product design, that is, the search

for new materials with specifically tailored properties. One new

challengewithin product designis in thedesign of environmentally

friendly refrigerants, solvents and mass separating agents. A class

of compounds which are currently being studied for such applica-

tions is ionic liquids: organic salts which are liquid at and around

room temperature. Ionic liquids usually possess negligible vapor

pressure, and thus do not contribute to air pollution (Ren, Scurto,Shiflett & Yokozeki, 2009). These compounds can be molecularly

engineered to match a set of target physio-chemical properties,

including solubility, diffusivity andacidity.It is estimated, however,

thatasmanyas1014 unique cation/anion combinations are possible

for use asionic liquids (Holbrey & Seddon, 1999). Thus the timeand

expense required to perform a true search through this molecular

space to find a novel ionic liquid is prohibitive. Furthermore, mix-

Corresponding author. Tel.: +1 785 864 4965; fax: +1 785 864 4967.

E-mail address:[email protected](K.V. Camarda).

tures of ionic liquids should also be considered, and this certainly

makes a guess-and-test approach intractable. Currently, most new

designs for suchcompounds tendto have similar structuresto those

previously used. In order to discover new ionic liquids which are

far different from those currently used, an efficient computational

screening procedure is required.

Such computational product design strategies are currently

beingimplemented in the chemical and pharmaceutical industries;

a review of industrial applications of CMD is given in Hairston

(1998),and applications to other molecular systems are discussed

in Venkatasubramanian, Chan, and Caruthers (1994).Two majorchallengesarise in the development of sucha computationalmolec-

ular design procedure: the ability to predict the physical and

chemical properties of a given molecule, and the ability to solve

the large optimization problem which is derived from the search

for the best molecule for a given application.

2. Physical property prediction

The simplest form of structureproperty relation links physi-

cal and chemical properties of interest to the number and type

of each functional group within a molecule. This group contribu-

0098-1354/$ see front matter 2010 Elsevier Ltd. All rights reserved.

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S.E. McLeese et al. / Computers and Chemical Engineering34 (2010) 14761480 1477

Table 1

Basic groups and their atomic and valence connectivity indices (andv).

v v

4 4 O 4 6

3 3 O 2 6

CH2 2 2 F 1 7

CH3 1 1 3 5

>C 3 4 N 2 1.333

4 2.667 O 1 7

tion approach is the basis for the well-known UNIFAC property

prediction system. Other structural descriptors take into account

not only the functional group types, but also the topology of those

groups. Bicerano (1996) correlateda largenumber of physical prop-

erties of polymers with topological indices, which are numericaldescriptors based on the electronic structure of the atoms within

a molecule, as well as on the interconnectivity of the atoms within

that molecule. Gonzalez, Abildskov, and Gani (2007) have used

these indices to fill in missing UNIFAC groups to predict physical

properties of small organics. Eike, Brennecke, and Maginn (2004)

have shown thefeasibility of using connectivityindices forthe pre-

diction of activity coefficients of ionic liquids. In this work, Randics

molecular connectivity indices (Randic, 1975) are used to generate

structureproperty correlations for ionic liquids. These descriptors

provide a quantitative assessment of the degree of branching of

molecules, andare based on a setof basic groups, which aredefined

as functional groups containing one non-hydrogen atom in a spe-

cific valence state and a given number of hydrogens. The nth order

simple and valence molecular connectivity indices are given by

nx =

(i0,i1,...,in)n

1i0 , i1 , ..., in

(1)

nxv =

(i0,i1,...,in)n

1v

i0, v

i1, ..., v

in

(2)

where n is the edge set of n consecutive bonds between basic

groupsin a molecule,i0, i1, . . ., in denote the n + 1 basic groupsform-

ing then consecutive bonds,ik ,k = 0,. . .,n are the simple atomic

connectivity indices for those basic groups (the number of bonds

each group can form), and vik

, k = 0, . . ., n are the atomic valency

connectivity indices, which are based on the electronic structure of

the basic group.Table 1shows the basic groups employed in theexample in this paper,along with their atomicconnectivity indices.

These topological indices can then be correlated with vari-

ous physical properties of molecules, given a consistent set of

experimental data for the properties of interest. In this work, six

properties important to the use of an ionic liquid within an absorp-

tionrefrigerationsystem are correlated: solubilityof the compound

in the refrigerants R-32 and R-134A, diffusivity of the ionic liquid

in R-32 and R-134A, Henrys law constant, and melting point. Data

for these correlations was obtained from Shiflett, Harmer, Junk,and

Yokozeki, 2006andShiflett and Yokozeki (2006).The correlations

used in this work (shown below) are preliminary based on 19 com-

monionic liquids, andfurther data is currentlybeing obtained such

thatthe predictivecapabilitiesof the correlations maybe expanded.

Note that the examples given in this paper only allow the introduc-

tion of functional groups present in the 19 ionic liquids evaluated

experimentally by the Shiflett team referenced above. Thus the

example problems cannot design molecules outside of the range of

ionic liquids tested, and thus the application of these correlations

may be considered a form of interpolation in molecular space.In the new correlations developed in this work, zeroth- and

first-order connectivity indices of both the cation and anion are

applied.For thecorrelation ofthe Henrys lawconstant, data atmul-

tiple temperatures was correlated together. Correlations were thus

created which are valid within a given range of temperature, but

since this parameter is assumed to be fixed within a given design

implementation, it is not solved for within the formulation. The cor-

relations employed to predict the physical properties listed above

are as follows:

DR32 = 14.57(P) + 19.971(0cat) + 2.212(

0vcat) + 67.404(1cat)

98.413(1vcat) 43.658(0an) 3.143(

0van)

+107.237(

1

an) 35.885(

1

v

an) 92.735 (3)

DR-134a = 15.12(P) + 3474.68(0cat) + 919.99(

0vcat)

= 3622.20(1cat) 1350(0an) 27.07(

0van) + 1961.14

(4)

100xR-32 = 58.98(P) + 967.05 (0cat) 66.44(

0vcat)

44.37(1 cat) + 30.01(0an) + 15.23(

0van)

57.36(1an) + 29.68(1van) 68.73 (5)

100xR-134a

= 133.31(P)904.57(0 cat

) + 250.37(0vcat

)

+926.35(1cat)+10.27(0an)15.38(

0van)+486.54

(6)

H= 0.01772(T) + 0.22957(0cat) 0.27367(0vcat)

0.01902(0an) + 3.67331 (7)

Tm = 0.01772(T) 52.389 (1an) + 76.389(

0van) 3.934(0an)

23.23(1van) + 69.001 (8)

whereD is the diffusion coefficient (1011 m2/s), Pis the system

pressure,x is the solubility in (mol/L), His the Henrys law constant


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in MPa, andTm is the melting temperature (K). Note that the cor-

relations include topological information about both the anion and

cation, and also involve the operating pressure and temperature. A

largerset of data pointsfroma setof structures which spans a larger

molecularspacewouldallow formore flexibility in thefinal design,

but would not require a different optimization methodology.

3. Problem formulation

The correlations generated in the first phase of this product

designmethodology are then combined with structural constraints

to construct an optimization problem. The solution to this problem

is a candidate ionic liquid (both basic groups and bonds) which is

predicted to have properties matching a set of pre-specified target

values based on the application of interest. The objective function

seeks to minimize thescaleddifference between thephysicalprop-

erty values of the candidate molecule and targets.

Along with the property prediction equations and the expres-

sions defining the molecular connectivity indices, structural

constraints are also included to ensure that a stable, connected

molecule is formed. These include valency and uniqueness con-

straints, which ensure that the valency of each atom is satisfied

and two groups may only bond with one type of bond (single ordouble), charge constraints which insure that the cation and anion

have a charge of +1 or 1, as well as connectedness constraints,

which guarantee that all the basic groups within the molecule are

bonded into one coherent molecule (Camarda & Maranas, 1999;

Lin, Chavali, Camarda, & Miller, 2005).

In order to store the molecular candidates computationally, a

data structure is used which employs binary variables to define

whether two basic groups i and j are bonded with a kth multi-

plicity bond. These binaries form a partitioned adjacency matrix

A which is structured such that the identity of each basic group

is known at each position within the molecule. This ensures that

the square root terms in the connectivity index Eqs. (1) and (2)are

all constants, and thus those equations are linear functions of the

unknown binary variables (Siddhaye, Camarda, Southard, & Topp,2004). The objective function can be reformulated as a set of linear

functions, and all other constraints are formulated linearly as well.

Thus the problem is an MILP, which can be solved to optimality

using standard techniques. The overall formulation may be posed

as:

Min s =

m

1

Pscalem

Pm Ptargetm

s.t. P m =fm()

= gn(aijk, wi)

hc(aijk, wi) 0

Pm, continuous, aijk, wi binary

where Pm is the value of the mth physical of chemical property,Ptargetm is a preselected target value for themth property,P

scalem is a

scaling factor for themth property,fm() are themlinear property

correlations whichare functions of the connectivity indices ,gn are

the (linear) defining equations for the connectivity indices which

are based on the data structure aijkwhich is used to store bonding

and wiwhich storesthe identityof each group i in themolecule, and

hc(aijk, wi) are structural constraints used to ensure that a stable,

connected molecule is designed. Notethat in general,fandgmaybe

nonlinear functions. However, for this and many other molecular

design formulations, the correlations are forced to be linear when

they are created, and the structural feasibility constraints may be

written as linear functions (since no connectivity indices of order

higher than one are employed). Thus the formulation considered

in this work is an MILP.

Table 2

Properties, target values and predicted values for the optimal solution to the first

example problem.

Property Target value Best solution value

Sol. (102 mol/L) 0.80 5.34

D(1011 m2/s) 20.00 20.09

Tm (K) 198.15 199.09

4. Solution methodology

Molecular design problems are often formulated as large MILP

or MINLP problems, and many optimization techniques have been

considered for their solution. When the problem is small or can

be formulated into a very specific form, then deterministic algo-

rithms (combined with integer cuts to obtain multiple solutions)

are often used. However, many molecular design problems, partic-

ularly those including highly nonlinear constraints or constraints

which cannot be written in a closed form, are not well-suited

to deterministic algorithms. In such cases, heuristic methods are

often useful. Heuristic methods are not guaranteed to find the

global optimal solution; however, due to the limited accuracy of

the QSPRs used in molecular design, near-optimal solutions to the

optimization problem are often as useful as global optima in prac-

tice. For example, genetic algorithms have been used in the design

of straight-chain polymers using group contribution methods to

predict properties (Venkatasubramanian et al., 1994),while Tabu

Search has been applied in previous works by this research group

on molecular design (Eslick et al., 2009).

TabuSearch is a heuristicalgorithmdeveloped by Glover (1990a,

1990b). Thismethodkeepsa recordof recentsolutions in a Tabu list,

which prevents cycling near local optima and encourages explo-

ration of the entire search space. Tabu Search has been used in

chemical process optimization (Lin & Miller, 2004a, 2004b),plan-

ning andscheduling (Dowsland, 1998; Gendreau,Laporte,& Semet,

1998; Kimms, 1996),and molecular design (Chavali, Lin, Miller, &

Camarda, 2004; Eslick and Camarda, 2008; Lin et al., 2005; Zhao,

Ralston, Middaugh, & Camarda, 2004. In this work, Tabu Search

is compared to a deterministic branch-and-bound algorithm asimplemented in the CPLEX package within the GAMS optimization

suite.

5. Results

Themethodology is first evaluatedusing anexampleset ofphys-

ical property targets, as shown in Table 2. The targets correspond to

values of solubility, diffusivity, and melting point which would be

reasonable for an ionic liquid used in conjunction with R-32 within

a refrigerant gas separation system. For this preliminary work,

the cation was fixed to be 1-butyl-3-methylimidazolium (BMIM),

which has the structure shown inFig. 1.

The structure of the anion was allowed to vary, but require-

ments were set on the number of total groups and on the existenceof one sulfate group, such that an organic salt would be formed.

The problem wassolved using GAMS/CPLEX,and required less than

300 s to find the optimal solution. The optimal structure found for

this example gave an objective function value of 0.90, which is the

percent scaled deviation from the target property values. While it

is easily possible to weight the importance of the various target

Fig. 1. Structure of 1-butyl-3-methylimidazolium.


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S.E. McLeese et al. / Computers and Chemical Engineering34 (2010) 14761480 1479

Fig. 2. Example ionic liquid designed using optimization methodology.

properties, all three properties in this example were given even

weighting. Properties can instead be given thresholds, which may

be included within the constraint set and require a given prop-

erty to be above or below a set value. The designed structure for

this example is shown inFig. 2,which corresponds to the optimal

solution to the MILP, an ionic liquid which could now be synthe-

sizedand tested. Whilethe solubilityvalue foundexceedsthe target

substantially, this might be valuable for an application such as a

refrigerant gas mixture. However, if such a large deviation in that

property were unacceptable, then the solubility weighting couldbe

increased such that the objective function was skewed in favor of

that property. In that case, it is likely that a feasible solution would

exist corresponding to a lower solubility, but with diffusivity and

melting point deviating farther from the targets.A secondexample uses four property values, andseeksto design

an ionic liquid to be used in an absorbant refrigeration system

in conjunction with the common refrigerant R-134A. While the

important properties of the IL in this system are the same as those

in the previous example, the search space is expanded in this case

by the allowance of more groups in the anion. The cation is still

fixed to be BMIM. The increased size of this problem provides an

opportunity to compare the stochastic algorithm Tabu Search with

CPLEX. In this implementation of Tabu Search, we have defined

moves in terms of thereplacement, addition or subtraction of a sin-

gle functional group, and apply graph isomorphism algorithms to

determine the similarity between two given solutions. These ideas

were developed previously in our research group, and details may

befound in Chavali et al.(2004), Linet al.(2005), and more recentlyEslicket al.(2009). Thetarget valuesfor thefour properties of inter-

est (solubility, diffusivity, melting point and Henrys law constant),

as well as values of these properties for the best candidate IL found

in each case are shown inTable 3.

As can be seen from the property values in the table, the two

optimization algorithms do not find the same solution. Both solu-

tions are of about the same quality, as measured by the scaled

percent deviation (0.0317 for Tabu Search as compared with 0.0244

forCPLEX).Again, equal weightingwas used forall properties, since

the focus is to compare the solution algorithms. Tabu Search pro-

vides a number of alternative solutions, all with similar objective

function values. The structures of the best solutions found via each

algorithm are shown inFig. 3.

While thetwo moleculespresented vary in termsof which prop-erties deviate most strongly from the targets, the key difference

to be considered lies in the computational efficiency of the two

algorithms. The Tabu Search implementation found the solution

presented in the table and numerous alternatives within 5 s, while

CPLEX was run for 20 min to find the one solution presented. Con-

Table 3

Properties, target values andpredicted values for the optimal solutionto the second

example problem, when solved with Tabu Search and CPLEX.

Property Target value Tabu Search CPLEX

Sol. (102 mol/L) 55 39.1 29.3

D(1011 m2/s) 30 117.0 59.5

Tm (K) 198.15 197.5 196.2

Henrys law constant (MPa) 2 2.05 2.06

Fig. 3. Example anions designed using Tabu Search and CPLEX, respectively.

sidering that the overall error in the property prediction equations

may be as high as 10%, one can conclude that the extra computa-

tional effort required to perform bounding calculations and prove

global optimality with a deterministic algorithm is not justified in

this case.

Note the methodology in its current form does not provide

information on how the new candidate structure is to be syn-

thesized, but it does give a researcher a short list of potential

compounds which are likely to match the desired physical prop-

erty targets. Property values may also be bounded (simultaneously

with being optimized) so that maximum and minimum values are

never exceeded for feasible solutions. This method may also be

used to improve a given ionic liquid pair. In this case, one simply

fixes certain groupswithin themolecule, anduses theoptimization

algorithm to suggest useful modifications of a given structure. The

resulting optimization problems have fewer binary variables than

a full design problem, and thus a larger number of modifications

may be considered.

6. Conclusions

In this paper, a molecular design problem for the design of ionic

liquids for use within environmentally friendly refrigeration sys-

tems is considered. The product design problem has been recast as

a mixed-integer linear program, and is solved to provide candidate

structures for synthesis and further testing. Examples are provided

which show theutilityof themethodologyfor designingnovelionic

liquids for use within absorption refrigeration systems. The Tabu

Search algorithm is shown to be more efficient that a determinis-

tic algorithm for the purpose of generating near-optimal solutions

to this molecular design optimization formulation. Further work

will design both the anion and cation within the system, and will

integrate new experimental data to correlate and then design con-

sidering a wider range of properties. Also, new experimental data

is being obtained for mixtures of ionic liquids, and this data will

later be used to develop property correlations for these systems.

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