咪唑氟硼酸類離子液體熔點(diǎn)與分子內(nèi)相互作用能的關(guān)系

李 巍 戚傳松 吳新民 榮 華 龔良發(fā)

(北京石油化工學(xué)院化學(xué)工程學(xué)院,北京102617)

咪唑氟硼酸類離子液體熔點(diǎn)與分子內(nèi)相互作用能的關(guān)系

李 巍*戚傳松 吳新民 榮 華 龔良發(fā)

(北京石油化工學(xué)院化學(xué)工程學(xué)院,北京102617)

運(yùn)用密度泛函理論B3LYP方法及6-311++G(d,p)基組對(duì)11種咪唑氟硼酸離子液體進(jìn)行了研究.選擇相應(yīng)化合物的離子體系{[XIM][BF4]n}(n-1)-(n=2,3)作為研究對(duì)象,即研究體系由一個(gè)烷基咪唑陽(yáng)離子X(jué)IM+和2-3個(gè)BF4-陰離子構(gòu)成,對(duì)其進(jìn)行結(jié)構(gòu)優(yōu)化.在優(yōu)化得到的最低能量構(gòu)型的基礎(chǔ)上計(jì)算了分子內(nèi)陽(yáng)離子與陰離子間的相互作用能,同時(shí)考慮了基組重疊誤差的修正.結(jié)果表明所研究離子體系的離子間相互作用能與離子液體的實(shí)驗(yàn)熔點(diǎn)之間存在明確的線性關(guān)系,并且所得到的線性方程與氨基酸陽(yáng)離子型離子液體中存在的線性關(guān)系相近.我們的工作為今后借助量子化學(xué)方法設(shè)計(jì)功能化離子液體提供了一定的理論基礎(chǔ).

密度泛函理論;咪唑氟硼酸鹽;相互作用能;離子液體;熔點(diǎn)

1 Introduction

Ionic liquids(ILs)are considered a most important new family of green solvents.They have drawn more and more attention from experimentalists and theoreticians for their well known advantages,such as low vapor pressure,excellent solvability,high thermal stability,good recyclability,and wide applications.1-4The possibility of designing ILs with special functions is also an important reason for the tremendous interest in these compounds.Theoretical study of the quantitative structure-property relationships(QSPR)is an ideal way to design ILs according to needs;it also has the advantage of saving materials and energy.In the past decade,QSPR studies have de-veloped quickly.5-9Different QSPR models have been established by introducing constitutional,topological,geometric, electrostatic,and thermodynamic descriptors.These models have been used to predict the common physical properties of ILs such as melting point,viscosity,density,conductivity,and surface tension.Although in most QSPR research,low precision theoretical methods of molecular geometry optimization (such as semiempirical methods)were adopted,effective predictions for some particular series of ILs have been made.

Quantum chemistry calculation is a more reliable way to study the molecular structure,but it is still not efficient enough to be used as a precise method for condensed phase systems, so it can only be used to study the electronic structure of gas phase ion pairs from ILs.Compared with the QSPR work, there is very little quantitative study on the relationship between physical properties and molecular structure just using quantum chemistry methods.Katsyuba and coworkers10have studied several imidazolium(IM)based ILs by investigating their neutral molecules(composed of one cation and one anion)with B3LYP/6-31G*calculations.In their conclusion,no correlation was found between the melting points and the intramolecular interactions.Turner and coworkers11have used ab initio calculations to fully study the ion pair structures of ILs based on 1-alkyl-3-methylimidazolium halides.They found some of the optimized geometries were different from those in the crystal structures.They also tried to explore the interaction energy-melting point relationship,but only gross trends were discovered.Our group12,13has performed a quantum chemistry study on single molecules of some amino acid cation based ILs (AAILs),and we found a linear relationship between the interaction energies and the experimental melting points.In this work,the relationships between the interaction energies and the melting points of imidazolium ILs were investigated with B3LYP/6-311++G(d,p)calculations.Although there have been detailed quantum chemistry research on these kinds of compounds,10,11,14-19the researchers have only studied single molecules composed of one cation and one anion.In this work,ions composed of one imidazolium cation and 2 or 3 anions were studied.Based on these models,the relationship between the interaction energy and the melting point was investigated.

2 Computational details

All the calculations were performed using the Gaussian 03 program package20on a Dawning computer cluster.The hybrid DFT method B3LYP,together with the basis set 6-311++G(d, p),was used throughout the calculations.All stationary geometries have been optimized without constraints,and the convergence criteria of a maximum step size of 0.0018 a.u.and a root mean square(RMS)force of 0.0012 a.u.were adopted.The supermolecular method was used in the calculation of interaction energies between cation and anion,i.e.,the interaction energy is given by ΔE(R)=EAB(R)-EA-EB,in which EAB(R)is the energy of optimized AB molecule,EAand EBrepresent the energies of the optimized cation and anion,respectively.21The basis set superposition error(BSSE)22-24was also considered with the counterpoise(CP)corrections.

In the previous quantum chemistry study of imidazolium tetrafluoroborate,only structures of electrically neutral molecules were investigated.In this work,the ions consisting of one imidazolium cation and two or three BF-4anions were studied.Crystallographic experiments on 1-ethyl-3-methylimidazolium (EMIM)compounds[EMIM]X(X=Cl,Br,I,AlBr4)25have shown that one cation is hydrogen bonded to three anions.The studies based on ion pairs only considered one type of hydrogen bond.Therefore,to consider as much as possible the above-mentioned structural characteristics of IM compounds, we took the ion composed of one cation and multiple anions as the minimal structural unit to be studied.1-ethyl-3-methylimidazolium chloride was studied for testing,its optimized most stable structure{[EMIM]Cl3}2-is shown in Fig.1(l).The distances of Cl-from its three nearest ring carbon atoms are 0.3379, 0.3682,and 0.3657 nm;the average value of the three distances is 0.3573 nm,which is consistent with the experimental value of 0.355 nm.26The three Cl atoms are almost in the plane of the imidazolium ring,which is also consistent with the experimental results.26But in the optimized structures of the electrically neutral ion pair[EMIM]Cl,the Cl atom is not located in the plane of the imidazolium ring.

During the optimizations of the compounds containing side chains with more than two C atoms,different stable conformations probably exist.To make sure that the most stable geometries were obtained,different initial guesses of geometry were considered.Taking 1-n-butyl-3-methylimidazolium cation [BMIM]+as an example,and following the research of Turner et al.,11the optimizations were performed from ten initial geometries.It was found that the{[BMIM][BF4]3}2-structure based on a similar structure to that reported in the literature for“Bmim 5”11is the most stable.

3 Results and discussion

3.1 Optimized geometries

First,we optimized the ion geometries of 11 tetrafluoroborate compounds with alkyl imidazolium type cations,including imidazolium(IM),1-methylimidazolium(MIM),1-methyl-3-methylimidazolium (DMIM), 1-ethyl-3-methylimidazolium (EMIM),1-n-propyl-3-methylimidazolium(PMIM),1-n-butyl-3-methylimidazolium(BMIM),1,3-diethylimidazolium(DEIM),1-ethyl-2,3-dimethylimidazolium(EDMIM),1-n-butyl-2, 3-dimethylimidazolium(BDMIM),1,3-diisopropyl-4,5-dimethylimidazolium(DIP-DMIM),and 1-allyl-3-methylimidazolium (AMIM).The following ions were studied in detail:8 divalent negative ions,including{[IM][BF4]3}2-,{[MIM][BF4]3}2-, {[DMIM][BF4]3}2-,{[EMIM][BF4]3}2-,{[PMIM][BF4]3}2-, {[BMIM][BF4]3}2-,{[DEIM][BF4]3}2-,and{[AMIM][BF4]3}2-; and 3 univalent negative ions,including{[BDMIM][BF4]2}-, {[EDMIM][BF4]2}-,and{[DIP-DMIM][BF4]2}-.In the cations [BDMIM]+or[EDMIM]+,there is a methyl substituent on the C2 atom(where the N ring atom linked to the longer side chain is labeled as N1 and the other N ring atom is labeled as N3)of the imidazolium ring.Because of the steric hindrance of this substituent on the C2 atom,the{[XIM][BF4]2}-structure would be preferred compared with the{[XIM][BF4]3}2-structure for BDMIM and EDMIM compounds.For DIP-DMIM, the interaction energies of{[DIP-DMIM][BF4]},{[DIP-DMIM] [BF4]2}-,and{[DIP-DMIM][BF4]3}2-are-330.62,-429.49, and-355.34 kJ·mol-1,respectively.These energy data indicate that the structure of one cation with three anions was less stable than{[DIP-DMIM][BF4]2}-.

Fig.1 Optimized geometries of imidazolium tetrafluoroborate ILcompounds(a){[IM][BF4]3}2-,(b){[MIM][BF4]3}2-,(c){[DMIM][BF4]3}2-,(d){[EMIM][BF4]3}2-,(e){[PMIM][BF4]3}2-,(f){[BMIM][BF4]3}2-,(g){[DEIM][BF4]3}2-, (h){[AMIM][BF4]3}2-,(i){[DIP-DMIM][BF4]2}-,(j){[EDMIM][BF4]2}-,(k){[BDMIM][BF4]2}-,(l){[EMIM]Cl3}2-;bond length in nm

The choice of the 11 studied compounds was not arbitrary; the approach to IL selection is now presented.First,by searching the data from the Reaxys database27(which integrate data from the Beilstein,Patent,and Gmelin databases),tetrafluorob-orate compounds containing alkyl imidazolium rings with known melting points were collected.Then,from these collected compounds,those contained side chains with more than four carbon atoms were removed,since there would be too many isomers which would need to be considered,and furthermore the effect of side chain on the experimental melting point has already been qualitatively analyzed systematically.28The final determination was made by considering the computational costs and the size of the problem needing to be solved.

The most stable conformations found among the optimization results are shown in Fig.1,and some important structural parameters are also listed on the figure.Fig.1 shows that there are some common characteristics of these most stable geometries.First,compared with the isolated cation structures,the geometries of the cation part are essentially retained.The differences in the values of selected bond lengths(the bond lengths between the five ring atoms and also between the ring atom and its closest side atom)in the isolated cation and in the compound ion are less than 0.0012 nm.It has been reported,based on crystallographic data,that the carbon-nitrogen skeleton structures of[EMIM]+cations do not vary significantly for[EMIM] Br,[EMIM]I,and[EMIM][AlBr4];25our theoretical results are consistent with these experiments.This finding can also be used to simplify searching for the most stable configuration of imidazolium compounds for further quantum chemistry studies.Second,with the exception of{[DIP-DMIM][BF4]2}-,the imidazolium ring atoms and B atoms of the BF4-anions are almost in the same plane,in other words,the cation is in a planar cage of BF4-anions.

Hydrogen bond interactions were found to exist in all the optimized compounds.Hydrogen bonds were classified on the basis of their bond lengths and angles.For X H…Y,if the H…Y bond length is much longer than the normal covalent bond length(H F:0.0918 nm)29and is much shorter than the sum of van der Waals radii of the bonding atoms(the van der Waals radii of H and F are 0.120 nm and 0.135 nm,respectively),and the bond angle is around 180°,then X H…Y can be regarded as a hydrogen bond.Therefore,in Fig.1,only the bond lengths of F…H less than 0.255 nm were listed.

The natural bond orbital(NBO)analysis was also performed to explore the charge distribution of the studied ions.The most important information obtained is that the NBO charges of the F atoms are almost equal to each other(the charge distribution values range from-0.56 a.u.to-0.59 a.u.).Since the B F bond lengths in the compound ions(which range from 0.139 nm to 0.145 nm)are very similar to those(0.142 nm)in the isolated BF4-,it is reasonable to choose the studied ions as the structural unit of the compounds:in the condensed phase structure,layers of cations and anions are interconnected by an extended network of hydrogen bonds;one anion should also be hydrogen bonded with three cations in a symmetric way.

For comparison,the structures of the electrically neutral molecules of each compound were also studied at the same level of theory.The optimized structures are not listed in this article because most of them have been studied before.Apart from [EDMIM][BF4]and[BDMIM][BF4],in the most stable structures,the anion BF4-is close to the ring atom C2,and the B atom is not in the plane of the imidazolium ring.In the most stable structures of[EDMIM][BF4]and[BDMIM][BF4],the BF4-is close to the C5 ring atom,and the B atom is almost in the plane of the imidazolium ring.

3.2 Interaction energies

The interaction energy of each ion was obtained by subtracting the energies of the optimized isolated cation and anion from the energy of the optimized IL ion.The counterpoise corrected energies are also considered and the CP corrections were found to be small(the maximum correction value was 12.3 kJ·mol-1for{[DIP-DMIM][BF4]2}-).The interaction energy results with(ΔECP)and without CP corrections(ΔE)are all listed in Table 1.The interaction energies between the cation and the anion in the electrically neutral molecules of the studied systems(ΔE1-1)are also listed in Table 1.

3.3 Relationship between the interaction energies

and the experimental melting points

We have found a linear relationship between the interaction energies and the experimental melting points for the amino ac-id cation based ILs.Although previous researchers did not find a relationship between interaction energy and melting point for imidazolium ILs,we wondered if this was possibly caused by their improper choice of structural units.

Table 1 Energy data of ILions obtained by the B3LYP/6-311++G(d,p)method and experimental melting points(Tm( exp))

Fig.2 Relationships between the interaction energies ΔE1-1,ΔE,ΔECPand the experimental melting points Tmof 11 imidazolium tetrafluoroborate ILcompounds

Fig.3 Relationships between the interaction energies and the experimental melting points of imidazolium tetrafluoroborate ILcompounds(IM ILs)and amino acid based ILs(AAILs)

The experimental melting point data listed in Table 1 were obtained from the Reaxys database.When different melting points or a melting range were reported,the average value was used in the following discussion.The relationship between the interaction energies ΔE1-1/ΔE/ΔECPand melting points Tmis shown in Fig.2.From Fig.2(a),no clear correlation was found between ΔE1-1and Tm.An obvious linear relation between ΔE and Tmis,however,shown in Fig.2(b).A linear equation was obtained by fitting the 11 data points in Fig.2(b):ΔECP= -336.5-0.2396Tm,with correlation coefficient R=0.84 and standard deviation SD=12.8.With this equation,except for the DEIM-BF4compound,the magnitude of the difference between the predicted Tmand the real Tmis less than 50 K,and the prediction works well.The relationship between ΔECPand Tmcan also be fitted with a linear equation:ΔECP=-322.9-0.2530Tmwith correlation coefficient R=0.84 and standard deviation SD=13.5(Fig.2(c)).

It is interesting that the ΔE-Tmdata in this work also connect up with the linear ΔE-Tmcorrelation for AAILs obtained in our previous work12(Fig.3(a)),but the ΔE1-1-Tmdata do not (Fig.3(b)).Putting the 11 sets of ΔE-Tmdata for imidazolium tetrafluoroborate ILs and the 26 sets of data of AAILs from literature12together,a new linear relationship was obtained: ΔE=-289.3-0.4581Tm,with correlation coefficient R=0.85 and standard deviation SD=19.4.The explanation for this is that during the melting process of ILs,the particles move further away from one another,and the interaction between cations and anions should have an important effect on this,and can be used to predict the melting point.In Fig.3(a),the three points located farthest from the fitted line are{[DEIM][BF4]3}2-, {[DIP-DMIM][BF4]2}-,and{[IM][BF4]3}2-;the common feature of these three compounds is that they all have symmetric cations(4 of the 11 studied compounds have symmetric cations;the other one is DMIM-BF4).One possible explanation for the deviation is that the spatial arrangement of the ions would be more compact for these compounds with symmetric structure,so,in contrast to compounds containing asymmetric cations,the interaction energies calculated in this work would be lower than the real interaction energies.

4 Conclusions

This article reports quantum chemistry studies of 11 types of alkyl imidazolium tetrafluoroborate ILs.Geometry optimizations and interaction energy calculations of the gas-phase ion systems{[XIM][BF4]n}(n-1)-(n=2,3)were performed.It was found that the interaction energy-melting point relationship for{[XIM][BF4]n}(n-1)-(n=2,3)is clearer than that for the neutral molecule[XIM][BF4]systems.It was also found that the ΔE-Tmdata of the studied imidazolium tetrafluoroborate ILs and theAAILs follow a similar linear correlation.The fitted linear ΔE-Tmequation of the two series of ILs could help direct further design of ILs.Compared with the commonly used QSPR method,the advantage of this method is that there is only one structural descriptor(the interaction energy)needed;the melting points can be predicted from the calculated interaction energy and the physical meaning is clear,so it can be used for different categories of compounds directly.The difficulties of this method are the need to choose the proper structural unit and to take into account intermolecular interactions.So,further theoretical work is required.More experimental work to improve the reliability and coverage of the melting point data is also needed.

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April 26,2011;Revised:June 29,2011;Published on Web:July 11,2011.

Relationship between Melting Point and the Interaction Energy of Alkyl Imidazolium Tetrafluoroborate Ionic Liquids

LI Wei*QI Chuan-Song WU Xin-Min RONG Hua GONG Liang-Fa
(College of Chemical Engineering,Beijing Institute of Petro-chemical Technology,Beijing 102617,P.R.China)

Eleven types of alkyl imidazolium tetrafluoroborate ionic liquids(ILs)have been investigated using the density functional theory(DFT)B3LYP method together with basis set 6-311++G(d,p).First,we performed geometry optimization of the ion system{[XIM][BF4]n}(n-1)-(n=2,3),which is composed of one alkyl imidazolium cation XIM+and two or three BF4-anions.Then the intramolecular interaction energies were calculated for those structures with the lowest energies,and the basis set superposition error was corrected by the counterpoise method.The relationship between the experimental melting points and the interaction energies was also investigated.A linear correlation was found for the alkyl imidazolium tetrafluoroborate compounds studied,which was also consistent with the linear correlation previously found for amino acid cation based ILs.Our work shows the possibility of designing ILs with the help of quantum chemistry in the future.

Density functional theory;Imidazolium tetrafluoroborate;Interaction energy; Ionic liquid; Melting point

O641

?Corresponding author.Email:liwei77@bipt.edu.cn;Tel:+86-10-81292127.

The project was supported by the Training Foundation for Backbone Teachers of Beijing Universities,China(PHR201008349).北京市屬高等學(xué)校人才強(qiáng)教深化計(jì)劃(PHR201008349)資助項(xiàng)目