Chemical Physics Letters 457 (2008) 263–266

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Chemical Physics Letters

journal homepage: www.elsevier .com/locate /cplet t

An application of the consistent charge equilibration (CQEq) method toguanidinium ionic liquid systems

Masato Tanaka, Hans-Ullrich Siehl *

Institute of Organic Chemistry I, University of Ulm, Albert-Einstein-Allee 11, Ulm D-89069, Germany

a r t i c l e i n f o a b s t r a c t

Article history:Received 12 December 2007In final form 31 March 2008Available online 7 April 2008

0009-2614/$ - see front matter � 2008 Elsevier B.V. Adoi:10.1016/j.cplett.2008.03.087

* Corresponding author. Fax: +49 731 502 2787.E-mail address: ullrich.siehl@uni-ulm.de (H.-U. Sie

The consistent charge equilibration (CQEq) method is applied to guanidinium chloride ionic liquid sys-tems. The QEq parameters are optimized for methyl substituted guanidinium chlorides to represent theatomic charges by quantum chemical calculations with six atom types for H, C, N and Cl atoms. The atomiccharges and optimized structural parameters are compared with quantum chemical calculations.

� 2008 Elsevier B.V. All rights reserved.

1. Introduction

Despite the widespread applications of ionic liquids (IL’s) inchemistry, chemical engineering and various other areas, theirphysical and chemical properties are quite often not well known.To understand the properties of IL’s, molecular simulations withmolecular mechanics (MM) and quantum mechanics (QM) meth-ods have been performed [1–3]. Molecular dynamics (MD) simula-tion studies of IL’s have demonstrated that the polarization effect isimportant to correctly describe the dynamical properties, e.g., theself-diffusion coefficients, of these systems [2]. Generally fixedatomic charges are used in MM calculations, and the polarizationeffect often is taken into account by adding a polarization termwith fixed atomic charges [2]. The molecular polarization in realityhowever results from the distortion of the electron density in themolecule. If the molecules are treated with QM methods, thecharge distribution of molecules varies reflecting the differenceof the chemical environment of located molecules [4] and themolecular polarization is included simultaneously. However, be-cause of high computational costs, the size of systems to be studiedand the simulation time for molecular simulations with QM meth-ods are limited to relatively small systems and short times [3], thusit is difficult to obtain the ensemble average of a large system. Asan alternative way to treat the molecular polarization in MM calcu-lations, several methods have been developed which can treatcharge variations reflecting the difference of the chemical environ-ment for the atoms. One of them is the charge equilibration (QEq)method, which treats the atomic charge variation through theequilibration of electronegativities at atomic sites [5].

In this study, the QEq method has been applied to one of the io-nic liquid systems, the guanidinium salts, in order to include thepolarization effect in MM calculations. The QEq parameters havebeen optimized for guanidinium chlorides to reproduce the

ll rights reserved.

hl).

charges obtained by a QM method. Then the results of QEq calcu-lations were compared to those of QM calculations.

2. Computational details

The consistent QEq (CQEq) method [6] is used in this study, andwe implemented it to the TINKER program package [7]. The Rappéand Goddard’s QEq parameters [5], atomic electronegativity (v0),atomic hardness (g0) and atomic radius (R0), are used. The OPLS-AA force field [8,9] is used for the MM potential function. TheQEq parameters, v0 and g0, are optimized to reproduce the chargesobtained by QM calculations. The natural charge scheme [10] isused as the definition of atomic charge for the QM calculations.The QM calculations are performed with the GAUSSIAN 03 programsuite [11] at the B3LYP/6-31++G** level of theory.

Nine structures, seven m-methyl (m = 0–6) substituted guanid-inium chlorides and two additional structures, the parent guanid-inium chloride (m = 0) and N-dimethyl guanidinium chloride(m = 2) which differ in the position of the chloride anion, are usedas test molecules for the data set. In the QEq parameter optimiza-tion, the six atom types, H3, HC, CA, CT, N2, and Cl�, are adopted forthe H, C, N, and Cl atoms which include two different atom typesfor the H atom, which is bonded to the alkyl carbon (HC) or thenitrogen atom (H3) and the C atom, which is the central carbon(CA) or the alkyl carbon (CT) (Fig. 1).

The QEq parameters are optimized to reduce the root-mean-square deviation (RMSD) of charges between the CQEq methodand the QM method. In the optimization, the Powell method [12]is used to minimize the following objective function f.

f ¼ RMSDþ CXMatom type

i

ðv0i � v0;original

i Þ2 þXMatom type

i

ðg0i � g0;original

i Þ2 !

RMSD ¼XMatom type

i

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1Ni

XNi

j

ðqQMj � qCQEq

j Þ2vuut

-1.0

-0.5

0.0

0.5

1.0

-1.0 -0.5 0.0 0.5 1.0

q (CQEq)

q(N

atur

al C

harg

e)

Fig. 2. Comparison of atomic charges by the CQEq method and QM method (naturalcharge) for the nine structures of m-methyl (m = 0–6) substituted guanidinium c-hlorides. Data points include charges for all H, C, O and Cl atoms; (�) using originalQEq parameter [5] and (d) using optimized QEq parameter.

Table 2Comparison of atomic charges between CQEq and QM methods

a b c d

C

C

N

N

N

H

H

H

H

HH

H

ClCA

CT

N2

HC

H3

Cl -

Fig. 1. Six atom types for guanidinium chlorides.

264 M. Tanaka, H.-U. Siehl / Chemical Physics Letters 457 (2008) 263–266

The second term is added to avoid QEq parameters to becomefar from the original parameters [5], and C = 2.721 � 10�3 is used[13]. Here Matom_type, Ni and qj are the number of atom types, thenumber of atoms treated as the atom type i and the charge of atomj, respectively.

The atomic charges derived by the CQEq method are then com-pared to those obtained by QM calculations. The optimized geom-etries obtained by the CQEq method are also compared to thoseobtained by using the OPLS-AA force field and QM calculations.

3. Results and discussions

3.1. QEq parameter optimization

From test calculations for the guanidinium chlorides, we foundthat the charge separation in CQEq method calculations is smallerthan in QM calculations. To obtain a charge separation similar tothose of QM calculations by using the CQEq method, the QEqparameters have been optimized. The optimized QEq parametersfor the six atom types are listed in Table 1. As shown in Table 1,we obtained different parameters for two different atom typesfor the H atoms (H3,HC) and also for the C atoms (CA,CT). TheQEq parameters for the hydrogen bonded to the hetero atoms(H3) are smaller than those of hydrogen bonded to the carbonatoms (HC). The QEq parameters for biomolecules such as DNAbase pairs and amino acids, have been optimized by Ogawa et al.[13,14]. They defined two types of the QEq parameters for thehydrogen atoms which are bond to the hetero atoms (N,O) andto the carbon atoms of amino acids, and obtained v0 = 1.824 eV,g0 = 6.170 eV and v0 = 4.220 eV, g0 = 8.121 eV, respectively [14].Our results show for the guanidinium ions the same tendency.The parameter optimization for the C atom parameters shows thatthe hardness of CA, the carbon of the cation center is larger thanthat of CT, the alkyl carbons. This is in accord with chemical intu-ition. On the other hand, despite the order of atomic electronega-tivity is expected to be CA (sp2) > CT (sp3), the parameteroptimization led to an opposite order CA < CT.

The correlation of charges for all atoms obtained using the CQEqmethod and QM calculated charges show that the CQEq chargesobtained with optimized QEq parameters are significantly im-proved compared to the original QEq parameter (Fig. 2).

Table 1Comparison of the original and optimized QEq parameters, atomic electronegativity(v0) and atomic hardness (g0)

Atom type v0/eV g0/eV

Originala Optimized Originala Optimized

H3 4.528 3.910 6.947 5.641HC 4.448 6.619CA 5.343 4.321 5.063 5.923CT 6.468 5.454N2 6.899 7.852 5.880 5.878Cl� 8.564 10.125 4.946 4.375

a QEq parameters in [5].

3.2. Comparison of charges derived by CQEq method and QMcalculation

Table 2 shows the comparison of charges obtained using theCQEq method with original [5] (CQEq_orig) and with optimizedQEq parameters (CQEq_opt), and the QM calculated charges forthe QM optimized geometry of the parent guanidinium chloride(Fig. 3). The atomic charge parameters in OPLS-AA force field arealso listed in the table. The variation of the atomic charges calcu-lated by the CQEq method reflects the difference of the chemicalenvironments of atoms. The tendency is agreement with the QMcalculated charges. The CQEq charges calculated with the originalQEq parameters are smaller in absolute values than those fromQM calculations. In other words, the charge separation obtainedfrom the CQEq model is smaller than that obtained from the QMcalculation. By using optimized QEq parameters, this small chargeseparation is modified and becomes closer to the values obtainedfrom QM calculations (Table 2). Although the atomic charges inthe OPLS-AA force field are much closer to those obtained by QMcalculations, these atomic charges are fixed. The advantage of theQEq method however is the ability to treat the variation of charges.

In order to show how the charge distribution of the guanidi-nium cation is changed by the chloride anion, the atomic chargesof the guanidinium cation are also calculated with the same geom-etry as in the guanidinium chloride ion pair (Fig. 3). Table 3 showsthe atomic charges of the guanidinium cation and the charge dif-

Atom OPLS-AA CQEq_orig CQEq_opt QM

C1 0.640 0.357 0.563 0.659N2 �0.800 �0.522 �0.914 �0.849N3 �0.800 �0.412 �0.712 �0.828N4 �0.800 �0.412 �0.713 �0.827H5 0.460 0.220 0.396 0.434H6 0.460 0.220 0.396 0.434H7 0.460 0.207 0.374 0.424H8 0.460 0.245 0.438 0.449H9 0.460 0.245 0.437 0.449H10 0.460 0.207 0.375 0.424Cl11 �1.000 �0.356 �0.641 �0.768

a Subscriptions in the atoms are related to Fig. 3.b Original QEq parameters [5].c Optimized QEq parameters.d QM calculation, natural charges (B3LYP/6-31++G**).

H8

H9

N4

N3

N2

H6

H5

H10

H7

C1 Cl11

Fig. 3. Optimized geometry of guanidinium chloride.

Table 3Atomic charges for the guanidinium cation and charge differences between the barecation and the cation in the ion pair

Atoma Atomic charge Charge differencee

CQEq_origb CQEq_optc QMd CQEq_origb CQEq_optc QMd

C1 0.444 0.636 0.672 �0.087 �0.073 �0.013N2 �0.359 �0.750 �0.811 �0.163 �0.164 �0.038N3 �0.361 �0.750 �0.805 �0.051 0.038 �0.023N4 �0.361 �0.750 �0.805 �0.051 0.037 �0.022H5 0.275 0.438 0.456 �0.055 �0.042 �0.022H6 0.275 0.438 0.456 �0.055 �0.042 �0.022H7 0.278 0.443 0.462 �0.071 �0.069 �0.038H8 0.266 0.426 0.457 �0.021 0.012 �0.009H9 0.266 0.425 0.457 �0.021 0.012 �0.008H10 0.278 0.443 0.462 �0.071 �0.068 �0.038

a Subscripts of atoms are related to Fig. 3.b Original QEq parameters [5].c Optimized QEq parameters.d QM calculation, natural charges (B3LYP/6-31++G**).e Charge difference showing charges for cation in the ion pair (Table 2) minus

charges for the bare cation.

Table 4Atomic distances, bond angles and dihedral anglesa in optimized geometries obtainedby the OPLS-AA force field, the CQEq methods and QM

OPLS-AA CQEq_origb,c CQEq_optb,d QMe

C1–N2 1.34 1.34 1.32 1.36C1–N3 1.33 1.33 1.37 1.33N2–H5 1.01 1.00 1.01 1.01N3–H7 1.01 1.00 0.98 1.01N3–H8 1.05 1.02 1.02 1.05C1���Cl11 3.55 3.64 3.60 3.46N2–C1–N3 120.88 120.25 121.09 120.49N3–C1–N4 118.20 119.32 117.80 118.95H5–N2–C1 121.18 118.92 120.92 120.94H7–N3–C1 128.07 121.93 120.34 120.93H8–N3–C1 115.34 116.76 115.67 115.90H5–N2–H6 117.58 121.70 118.08 118.05H7–N3–H8 116.63 120.14 122.63 121.02N2–C1–N3–H9 179.93 175.65 175.53 –179.94N2–C1–N3–H10 0.10 �14.25 �14.35 �16.99N2–C1–N4–H7 �0.05 �4.30 �2.04 �16.85N2–C1–N4–H8 �179.92 178.76 178.64 179.75N3–C1–N2–H5 �0.04 �14.37 �13.22 �9.80N3–C1–N2–H6 179.93 176.90 177.22 172.14N3–C1–N4–H7 �179.95 174.76 175.41 163.25N3–C1–N4–H8 0.17 �2.18 �3.91 �0.15N4–C1–N2–H5 �179.94 164.68 164.18 170.30N4–C1–N2–H6 0.03 �4.05 �5.38 �7.76N4–C1–N3–H9 �0.17 �3.41 �2.06 �0.04N4–C1–N3–H10 �180.00 166.69 168.06 162.92

a Atomic distance in Å, bond angle and dihedral angle in degree.b OPLS-AA force field parameters are used except for atomic charges [8].c Original QEq parameters [5].d Optimized QEq parameters.e QM calculation (B3LYP/6-31++G**).

M. Tanaka, H.-U. Siehl / Chemical Physics Letters 457 (2008) 263–266 265

ferences between the cation in the ion pair and the bare cation. Theatomic charges of the bare cation are not completely symmetricbecause of its distorted geometry taken from the ion pair. The ten-dency of charge differences obtained with CQEq_orig calculationsagrees with that of the QM calculation. The results of CQEq_opt cal-culations are somewhat different. The tendency of the CQEq_optcalculated charge differences of the amino groups however alsoagrees with QM calculations. The charge differences for the aminogroups N3 and N4 (CQEq_orig: –0.143, CQEq_opt: –0.019, and QM:–0.069) are somewhat less to the negative direction than that forthe amino group N2 (CQEq_orig: –0.272, CQEq_opt: –0.249, andQM: –0.082). Thus the amino groups N3 and N4 which are locatednear the chloride anion have more positive than the amino groupN2 (Table 2). The charges of the amino groups are CQEq_orig: –0.082 and 0.040, CQEq_opt: –0.122 and 0.100, and QM: 0.019and 0.045 for N2 and N3, respectively. This clearly shows the polar-ization of the guanidinium cation caused by the chloride anion, andagrees with chemical expectation.

The tendency for the charge differences obtained using the CQE-q_orig parameters appears to be closer to the results of QM calcu-lations than those obtained using the CQEq_opt parameters. Theabsolute atomic charges from CQEq_opt calculations however arecloser to those calculated by a QM method than those obtainedfrom CQEq_orig calculations. It is to be expected that the optimizedQEq parameters will improve the results of molecular simulationsof ionic liquids systems, because reasonable atomic charges areneeded to describe the interactions between ions. However theabsolute value of charges calculated by the QM method dependson the level of theory and this is only one criteria and the differ-ence of atomic charges has also to be taken into account in theevaluation of QEq parameters.

3.3. Comparison of optimized structures

The structural parameters of the optimized structures of theguanidinium chlorides calculated using the OPLS-AA force field,the CQEq method, with the original and the optimized QEq param-eters, and the QM method are listed in Table 4. The structuralparameters of the guanidinium cation are quite similar for allmethods except for the flexible dihedral angles. The cation-aniondistances (C���Cl), measured as the distances between the centralcarbon atom and the chloride anion are calculated slightly longerwith the CQEq method compared to QM calculation. The same ten-dencies, the slightly longer cation–anion distance, are also ob-served for the other methyl substituted guanidinium chlorides.On the other hand, the cation-anion distance in the polarizablemodel is slightly shorter than in the non-polarizable model inthe radial distribution function obtained by MD simulations foran imidazolium-based ionic liquid system [2]. Ogawa et al. re-ported that they obtained too short hydrogen-bond distances inDNA base pairs by geometry optimization with their optimizedQEq parameters, thus they optimized the van der Waals (vdW)parameter for hydrogen to obtain reasonable results [13]. Similarlythe slightly longer cation-anion distance we have observed for theguanidinium chlorides may result from a mismatch of the Len-nard–Jones potential parameters in the OPLS-AA force field [8]for the CQEq method, which means that the vdW interaction andthe electrostatic interaction are somewhat unbalanced.

4. Conclusions

We have applied the consistent charge equilibration (CQEq)method to guanidinium chlorides, one of the ionic liquid systems,and obtained reasonable charge variations reflecting the differenceof the chemical environment. We found that small charge separa-tions compared with the QM calculations are obtained with the

266 M. Tanaka, H.-U. Siehl / Chemical Physics Letters 457 (2008) 263–266

CQEq method for the guanidinium chlorides system using the ori-ginal QEq parameters [5]. The QEq parameters were optimized forguanidinium chlorides with six atom types. The charge separationwas improved significantly and a similar charge distribution aswith QM calculations was obtained.

It is shown that the QEq method is applicable to the guanidi-nium-based ionic liquid systems. The advantage of the QEq methodis that the polarization effect in MM is taken into account by var-iation of the charge distribution in the molecules. The atomiccharge variation relates to the intramolecular geometrical changesas well as to the intermolecular configurational changes of molec-ular species. The results of molecular simulations which accom-pany such geometrical and configurational changes for ionicliquid systems thus can be improved significantly by includingthe charge equilibration (QEq) method into the simulation of thissystems.

Acknowledgement

This work was supported financially by the Bundesministeriumfür Bildung und Forschung (BMBF).

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