Guohui Zhou,Kun Jiang,Zhenlei Wang,Xiaomin Liu*

School of Chemistry and Chemical Engineering,Qingdao University,Qingdao 266071,China

Keywords:Ionic liquid Molecular simulation Interface Hygroscopicity Cluster

ABSTRACT How to completely remove the water from ionic liquids (ILs) is difficult for researchers because of the hygroscopicity of ILs.In order to study the hygroscopicity of ILs,two kinds of ILs,1-Butyl-3-methylimidazolium hexafluorophosphate ([Bmim][PF6 ]) and 1-Butyl-3-methylimidazolium Bis(trifluoromethanesulfonyl) ([Bmim][NTf2 ]) were investigated by molecular dynamics simulations.Although[Bmim][PF6 ]and [Bmim][NTf2 ]are hydrophobic,both of the ILs could absorb water molecules from the vapor.In this work,the process of absorbing water from the vapor phase was studied,and the water molecules could disperse into the IL.Aggregation was observed with increasing the water concentration.Although the absorbed water increases obviously,the amount of free water and small cluster in the ILs does not change significantly and always stays at a certain level.The amount of free water and small cluster in [Bmim][PF6 ]is more than that in [Bmim][NTf2 ],which is consistent with their hydrophobicity.In addition,the liquid-vacuum and liquid–liquid interfaces of the ILs were simulated and analyzed in detail.The number density distribution and angle distribution indicated that[Bmim]+cations arrangement regularly at the IL-vacuum interface.The butyl chain point to the vacuum,while the imidazlium ring is close to the IL phase region and perpendicular to the interface.While at the IL-water interface,the cations and anions are disordered.

1.Introduction

Room temperature ionic liquids (ILs) are salts consisting of asymmetric organic cations and almost any type of anions,usually present as liquids at temperatures below 100 °C or at room temperature.ILs have excellent properties such as low volatility,low flammability,wide stability temperature range,ability to dissolve organic compounds,and high electrical conductivity[1–3],making them widely used in electrochemical studies [4,5],gas capture[6–8],green solvents,phase separation,catalysis and metal ion extraction [9–11].

The presence of water will cause certain changes in the physical and chemical properties of ILs,such as viscosity,polarity,surface tension and electrical conductivity [5,11–13].Many ILs are hydrophilic and can thoroughly mixed with water;some ILs are hydrophobic and begin phase separation when mixed with water.When paired with 1-butyl-3-methylimidazole cations ([Bmim]+),tetrafluoroborate ([BF4]-) and hexafluorophosphate ([PF6]-) form hydrophilic and hydrophobic ILs,respectively.Although incompatible with water,hydrophobic ILs still have significant hygroscopicity,e.g.one mole [Bmim][PF6]can absorb 0.37 mole of water at 298 K [9,14].ILs composed by cations with short alkyl chains are usually uniformly distributed in solution,while cations with longer alkyl chains especially at high concentration will form clusters[15–18].

Fig.1.Molecular structures and atom types of anions and water.

Molecular dynamics (MD) simulation is a powerful tool to obtain understanding of the atomic structure and properties[17–21].Sieffert and Wipff [22]performed molecular dynamics simulation for the aqueous interface of hydrophobic IL ([Bmim][NTf2]),found that the water is in the form of monomers and dimers in the weakly humid IL phase,and as higher aggregates when the IL phase is more humid.Koishi [23]found that in the aqueous solution of imidazolium-based ILs,composed by [PF6]-and [NTf2]-anions,water molecules form large clusters.Hantal et al.[24]found that the surface of phase rich in [Bmim][PF6]is more susceptible to water than the surface rich in [Bmim][NTf2].Konieczny and Szefczyk[19]studied the structures of alkyl imidazolidine ILs at the vacuum and water interfaces by molecular dynamics simulations,results show that the ILs with short alkyl chains have an unfixed orientation at the surface,while the alkyl chain extends into the air at interface for ILs with longer chains.However,at the IL-water interface,the chain enters the IL phase,anions and water tend to bind to polar imidazole groups.Zhao et al.[25]found that pure [Emim][Dmp]absorbs water easily.Water molecules are distributed in the inner layer of the interface,and the two OH vectors (from atom O to atom H) are tilted outward.McDaniel et al.[26]found that [Bmim][FSI]had relative hydrophilicity without water,but its hydrophobicity increased rapidly when preferential absorption sites of the IL become saturated.Lynden Bell et al.[27]used MD simulation to study the interface structures of dimethylimidazole ammonium chloride([Dmim]Cl) and different Lennard-Jones fluids and water.Ramya et al.[28]studied the aggregation process of[Hmim][NTf2]from the perspective of energy and structure by changing water concentration.They reported phase separation between IL and water,which was due to the hydrophobicity of the two ILs and micelle formation at high water concentrations.

At present,a great deal of researches have devoted to the structures and properties of ILs.As many important applications depend on the properties of ILs at the interface with other solvents,such as extraction,polyphase synthesis,and catalysis,lots of interfacial studies have been reported.However,most of them are on liquid/-vapor interfaces [20,25,29,30],studies on liquid/liquid interfaces involving ILs are relatively few.Banerjee [31]reported the liquid–liquid extraction theory of cesium extraction (Cs+),verified the phase separation of [Bmim][NTf2]and water,he found that[Bmim]+cations were distributed into the aqueous phase and exchanged with Cs+ions.Mohebbi et al.[32]studied the potential of [Hmim][PF6]as a heavy metal cadmium ion extractor and performed MD simulation for a two-phase system of IL and water,and found that[CdCl4]2-ions tended to be distributed at the interface.Iwahashi et al.[33]studied the interface of water/[Cnmim][NTf2](n=4,8) and found that SO2group of anions preferred toward the aqueous phase,and polarity orientation of [NTf2]-anions was derived from the ordered structure of [Cnmim]+cationic alkyl chain.

In order to study the existing form of water molecules in the process of absorption,eight systems with different water contents were simulated for [Bmim][PF6]and [Bmim][NTf2].When a small amount of water is absorbed,the water molecules are free,and with the water molecular number increase,clusters could be observed,but the amount of free water and small cluster remains relatively constant.In addition,the IL-vacuum and IL-water interfaces of the two hydrophobic ILs was investigated,and the structure of ILs at the interfaces was analyzed and compared in detail.

2.Simulation Detail

2.1.Molecular structure and force filed

All-atom force fields were used in the simulations [34].The parameters of the ILs involved in this paper were derived from OPLS Force Field[35].In consideration of the effect of charge transfer and polarizability,the charges were uniformly scaled by 0.8.The SPC model [36]was adopted for the water molecule.The OH bond in water molecule is flexible,as SPC model water has been used in previous work[37–39]for IL aquoues system,and the simulation results are verified by experiments,we also used the SPC model in this work.The molecular structures and atom types of cation and anion and water are shown in Fig.1.

2.2.Simulation detail

The number of ILs is 400 in all simulation systems,and the simulations were performed at 298 K by Gromacs program[40].Tables 1 and 2 show the details of the system.For IL-vapor system,the pure phase of ILs were firstly simulated.Then the Z direction of the box was doubled to create a vacuum area,and then NVT simulation was carried out.After equilibrium,the water molecules were placed in the vacuum area,some of them were absorbed into the IL,and sampling were performed more than 100 ns.For the IL-water system,the different strategy was used,and the pure phases of IL and water are simulated separately.After stabilization,we extended the box by twice in the Z direction,and ILs were placed at the center of box,the water phase was placed at both sides of the box,then continued with NPT simulation.For the IL-vacuum system,the simulation strategy is similar with the IL-vapor system.The pure phase of ILs were firstly simulated,and then doubled the Z direction of the box and created the vacuum area.

The simulation of pure phase was carried out in the following steps:first,the initial configuration was generated using Packmol[41],then energy was minimized,followed by NVT and NPT simulation,and finally the temperature reached at 298 K.Thecutoff distance between LJ and Coulomb interaction is 1.2 nm.Temperature control using Nosé-Hoover thermostat [42]with a coupling time of 0.2 ps,and pressure (1.0 bar,1 bar=105Pa) controlled by Parrinello-Rahman constant [43]with a coupling time of 2.0 ps.

Table 1 Simulation details for IL-vapor systems

Table 2 Simulation details for IL-vacuum and IL-water systems

3.Results and Discussion

3.1.Mass density

Firstly,the mass density was analyzed.In order to verify the rationality of the force field model and simulation method,the density of IL in the volume phase was counted and compared with the experimental values.The results are shown in Table 3.The error of [Bmim][NTf2]is less than 2%,and that of [Bmim][PF6]is less than 5%,which are all within the reasonable range.

3.2.The hygroscopicity of two ILs

ILs are easy to absorb water from the air,even hydrophobic ILs,which brings a lot of inconvenience to the storage and application of ILs.To analyze the hygroscopicity of the hydrophobic ILs,we performed simulations of several systems,in which include 400 ILs and 10,20,50,100,200,400,800 and 1600 water molecules,respectively.The results of the two ILs are analyzed and compared.As very high water content would produce a phase split,similar with the IL-water case,and we didn’t discuss it in this work.According to the results of statistical analysis,we define as follows:one or two water molecules are free water,3–20 water molecules are small clusters,and more than 20 water molecules are large clusters.

Table 3 Comparison of simulated and experimental densities of ILs

3.2.1.[Bmim][NTf2]

Fig.2 is the final snapshots of 8 simulation systems for[Bmim][NTf2].From these snapshots,we can see that in NV10 and NV20 systems,water is mainly in the form of free water,and large clusters have appeared since NV50.From system NV100 to NV1600,the water clusters grew up gradually.Because water molecules were absorbed into the bulk phase from the two interfaces,there are usually two clusters distributed near the interfaces.

In order to further reveal the shape and size of the clusters,we carried out statistical analysis of the equilibrium configurations.It is reported that hydrogen bond length between water molecules is 1.95 ? (1 ?=0.1 nm) [46],which is used to judge whether two water molecules are connected together or not,and all water molecules connected together are taken as a cluster.According to this standard,the size distribution of water molecular clusters were counted,and the results are shown in Fig.3.In NV10 and NV20,most of the water molecules are free water.Big clusters appeared in NV50 and NV100 systems.The big clusters contain 70 water molecules could be observed,but clusters composed of 20–60 molecules are absent.With the increase of water,the volume of clusters gradually increased.Starting with NV200,each system contains two large clusters with slightly different volumes,except for NV400.In other cases,two clusters can be clearly seen,and no cluster merger phenomenon is found when the simulation time exceeds 300 ns.

Fig.2.Snapshots of[Bmim][NTf2 ]absorbing different numbers of water molecules.Red is oxygen,white is hydrogen,and light blue translucent part stands for ILs.(a)NV10,(b) NV20,(c) NV50,(d) NV100,(e) NV200,(f) NV400,(g) NV800,(h) NV1600.

There is a clear boundary between the small cluster and the large cluster in Fig.3(d)–(h).Therefore,we calculated the proportion of free water/small cluster water and big cluster water,as shown in Fig.4.It is found that when water molecules are relatively little,they mainly exist in the form of free water and small cluster.When there are 50 water molecules in the ILs phase,proportion of free water/small cluster is equivalent to big cluster.In NV100,about three-quarters of water is in big clusters.In NV200 to NV1600,the percentage increased to more than 90%.Based on the above study,it is found that the hydrophobic IL could absorb a large amount of water from the vapor phase,but most of the water molecules were concentrated and distributed near the interface.

3.2.2.[Bmim][PF6]

In order to comparison,we also analyzed the results of [Bmim][PF6].Fig.5 shows the simulation results for systems with different water contents.We can see that when the number of water molecules is less than 50,there is no obvious big cluster formation,big clusters begin to appear in PV100 system,and clusters become bigger in the order of PV200 ＜PV400 ＜PV800 ＜PV1600.

Fig.6 shows the distribution of water clusters in the system.Clusters do not separate significantly in PV10,PV20,PV50 and PV100 systems.This phenomenon has already appeared in[Bmim][NTf2].They are identical and both exist two water clusters with slightly different volumes.

Fig.7 shows the proportion of free water/small cluster and big cluster.It can be found that the proportion of free water and small cluster water is significantly higher than that of [Bmim][NTf2]at the same water content.The free water and small cluster ratio in PV200 is similar to NV100.When a small amount of water is absorbed by the hydrophilic IL,the water will be uniformly dispersed into the IL without forming a cluster.In contrast,when water is absorbed by the hydrophobic IL,most of the water molecules are clustered and a few are free.The greater the hydrophobicity,the more the water tends to be clumped rather than free.Therefore,simulation results show that [Bmim][NTf2]has a stronger hydrophobicity than [Bmim][PF6].

3.2.3.Free/small cluster water

We believe that the amount of free water and small cluster has an important influence on properties of ILs,and make the IL purification difficultly.In order to investigate the microstructures,statistics are made on the amount of free water for these systems,and the results are shown in Fig.8.At the beginning it increases,followed by decreases,and then slowly rises.With the increase of the total water,the free water and small cluster maintains a relatively stable amount.

3.3.Interface structure and properties

In this part,IL-vacuum and IL-water were studied,their snapshot were shown in Figs.9 and 10.We analyze the structure and properties of the interface in detail from three aspects:mass density distribution,number density distribution and angle distribution.

3.3.1.Mass density distribution

IL-vacuum.Fig.11 shows the density distribution along the Zaxis of the two ILs.A peak at the interface is observed for the density of [Bmim][PF6].The average peak value on the left and right sides is 1.388 g·cm-3,7.4% higher than the average body density(1.304 g·cm-3).In contrast,the density of[Bmim][NTf2]has almost no peak at the interface,and it is very close to the average density of the body phase,less than 3%,and not much different from the body phase density.

Through the density analysis of cations and anions,it can be seen that in[Bmim][NTf2],the peak position of anions and cations does not overlap.The peak position of cations is close to the interface,while the anions are close to the body phase,with a difference of 0.4 nm,which reduces the overall density of IL.The peak position of cation and anion in [Bmim][PF6]is relatively close at the interface,so it forms a peak higher than the average density of body phase.

IL-water.The density distribution is shown in Fig.12.Compared with IL-vacuum(Fig.11),the IL density peak at the interface for[Bmim][PF6]disappears,and the interface is very smooth without any peaks.There are small peaks for [Bmim][NTf2]because many anions are distributed at the interface.This is opposite of ILvacuum (Fig.11(b)).

Fig.3.The distribution of water after the absorption by [Bmim][NTf2 ].(a) NV10,(b) NV20,(c) NV50,(d) NV100,(e) NV200,(f) NV400,(g) NV800,(h) NV1600.

Fig.4.The proportion of free water/small cluster and big cluster in[Bmim][NTf2 ]+-vapor system.

Interface thickness.In order to compare the IL-water interface and the IL-vacuum interface,we firstly compared thickness of the interfaces to understand the impact of water.The interface thickness is defined as the interval where the density of the IL from 90% to 10% of the bulk density [47],and the results are shown in Table 4.In the IL-vacuum system,the interface thickness difference between [Bmim][PF6]and [Bmim][NTf2]is relatively small,both are about 0.6 nm,and in [Bmim][NTf2]it is slightly thicker.In the IL-water system,the interface thickness of[Bmim][PF6]almost doubled while the that of[Bmim][NTf2]increased slightly.As more water molecules entered the interface and the thickness of the interface increased,the ions distribution became disordered,so the density changes became much smoother.

From the aqueous phase to the IL phase,the number density of water decreased sharply along the Z axis at the interface.According to the interface definition (10%–90% IL density),the number density of water molecules in the[Bmim][PF6]-water system interface decreases from 33.7 N·nm-3to 4.45 N·nm-3,and the number density of water molecules in the [Bmim][NTf2]-water system interface decreases from 33.7 N·nm-3to 4.51 N·nm-3.

In addition to the above results,we also analyzed the number of water molecules in IL phase.We calculated the water content in IL phase at the cut-off point where the rate of decrease of water molecules number density along Z-axis was less than 0.5 N·nm-4.Table 5 is the statistical results.For the [Bmim][NTf2]system,the mole fraction of water in IL phase is 0.018.For the[Bmim][PF6]system,the mole fraction of water in IL phase is 0.009.Compared with the two ILs,the solubility of [Bmim][PF6]is better than [Bmim][NTf2].

3.3.2.Number density distribution

In order to further analyze the detailed structure of ILs at the interface,we investigated the number density distribution of heavier atoms in the cation and anion of ILs.IL-vacuum and IL-water are discussed and compared respectively.

IL-vacuum.Fig.13 shows the atomic number density distribution of [Bmim][PF6]at the IL-vacuum interface.The symmetry is very well for the left and right interfaces,as shown in Fig.13(a).The number density distribution of IL-water and IL-vacuum systems also show similar laws.Therefore,only the left interface is analyzed in detail.Fig.13(b) is number density distribution of atoms in [Bmim]+cations.The outermost atom of the interface is the terminal carbon atom CT of the butyl chain,and the following order is along the alkyl chain to the imidazlium ring,CS,C2,and C1a.The methyl carbon,C1m,is on the innermost side of the interface.The five atoms on the imidazlium ring overlapped to some extent,NAa and its adjacent atoms CWa and CR are close to vacuum,NAm and its adjacent atoms CWm are close to body phase.[Bmim]+structure diagram is also shown in Fig.13(b),and the atoms distribution has a good consistency with the peak position of the atom.It can be seen that [Bmim]+cations exhibit excellent regular arrangement at the interface,alkyl chain points to vacuum,and imidazlium ring is in the body phase.

However,[PF6]-anions show less regularity,with a relatively gentle peak near the atoms in the imidazlium ring.This is because most of the positive charge distributes on the imidazolium ring.The high density anion and imidazole ring peak at the same position,which is the reason for the mass density peak of IL at the interface.

Fig.5.Snapshots of[Bmim][PF6 ]absorbing different numbers of water molecules.Red is oxygen,white is hydrogen,and light blue translucent part stands for ILs.(a)PV10,(b)PV20,(c) PV50,(d) PV100,(e) PV200,(f) PV400,(g) PV800,(h) PV1600.

Fig.6.The distribution of water clusters after the absorption of water by[Bmim][PF6 ].(a) PV10,(b) PV20,(c) PV50,(d) PV100,(e) PV200,(f)PV400,(g)PV800,(h) PV1600.

The atomic number density results of [Bmim][NTf2]are shown in Fig.14.[Bmim]+results are highly consistent in [Bmim][PF6]and [Bmim][NTf2],and the number density values are generally low.In[Bmim][PF6],the number density of imidazlium ring is similar to that of alkyl chain,which is lower than methyl.In [Bmim][NTf2],the number density of imidazlium ring is higher than that of alkyl chain,and close to methyl group.The C and F atoms in anions distributed at the outside,while N,S and O atoms are at the inside.The peaks of N,S and O atoms are close to C and N atoms on the imidazlium ring,because there are strong interactions between them.

Fig.7.The proportion of free water/small cluster and big cluster in [Bmim][PF6 ]-vapor system.

Fig.8.The amount of free water and small cluster in different systems.

IL-water.Compared to IL-vacuum,the orientation of [Bmim]+in the two ILs became disordered in IL-water,as shown in Figs.15 and 16.The distribution of the atoms is very similar to each other,and the number density curve changes gently at the interface.There is a peak at the interface for [NTf2]-anion.

3.3.3.Angle distribution

In this part,we analyzed the angle distribution between cation and the interface.Since anions have high symmetry,we don’t analysis the angle distribution of anion in this work.

Angle of the alkyl chain.From the results of the number density for cations discussed in 3.2,we can see that the alkyl chain of cation points to the vacuum.C1a-CT line stand for the direction of the alkyl chain,and the angle distribution between the alkyl chain and the Z axis was calculated,as shown in Fig.17.Fig.17(a) and (c) are the results of [Bmim][NTf2]and [Bmim][PF6]for IL-vacuum system,respectively.We can see that an obvious peak appears at the interfaces,the acute angle is on the left and the obtuse angle is on the right.Therefore,the alkyl chain is parallel to the normal of interface,pointing to the vacuum.Yang et al.[48,49]have studied the liquid-vacuum interface of [Bmim][PF6].Those works demonstrated that the alkyl chains in both protic and aprotic ILs prefer pointing to the vacuum phase due to the hydrophobic interactions.Our result is consistent with their findings.In IL body phase,the angular distribution of alkyl chain is irregular.Fig.17(b) and (d) are the results of [Bmim][NTf2]and[Bmim][PF6]for IL-water systems,respectively.Compared with IL-vacuum,the most obvious difference is that no peak appears at the interface,the orientation of alkyl chain at the interface is relatively free.

Fig.9.The snapshot of IL-vacuum system at 100 ns.(a) [Bmim][NTf2 ],(b) [Bmim][PF6 ].

Fig.10.The snapshot of IL-water system at 100 ns.(a) [Bmim][NTf2 ],(b) [Bmim][PF6 ].

Fig.11.The distribution of the mass density along the Z axis for IL-vacuum system.(a) [Bmim][PF6 ],(b) [Bmim][NTf2 ].

Fig.12.The distribution of the mass density along the Z axis for IL-water system.(a) [Bmim][PF6 ],(b) [Bmim][NTf2 ].

Table 4 Interface thickness of ILs

Table 5 The number of water molecules in IL phase

Angle of the imidazlium ring.Three atoms,CR and two CW atoms on the imidazlium ring are selected to represent the plane of imidazlium ring.The angle between the imidazlium ring plane and the XY plane is counted and shown in Fig.18.Fig.18(a) and(c) are results of[Bmim][NTf2]and [Bmim][PF6]in IL-vacuum system,respectively.Although there are also two peaks at the interface,they are different from the peaks of the alkyl chain.In addition to peak height,there is no greater difference in the distribution between the interface and the bulk phase.Therefore,the peak of imidazole ring at the interface is caused by its high local number density and appear at the same position (Figs.13(b) and 14(b)).Fig.18(a) and (c) are results of [Bmim][NTf2]and [Bmim][PF6]in IL-water system,respectively.They are very similar to the result of alkyl chain,and no peak appearing at the interface.Both IL-vacuum and IL-water,most of the imidazlium ring are perpendicular to the XY plane,and parallel to each other as a result of π-π interaction.

4.Conclusions

Fig.13.The distribution of atomic density along the Z axis of[Bmim][PF6 ]-vacuum system.(a)Cation,(b)Cation at the left interface,(c)Anion,(d)Anion at the left interface.

Fig.14.The distribution of atomic density along the Z axis of[Bmim][NTf2 ]-vacuum system.(a)Cation,(b)Cation at the left interface,(c)Anion,(d)Anion at the left interface.

Fig.15.The distribution of atomic density along the Z axis of[Bmim][PF6 ]-water system.(a)Cation,(b)Cation at the left interface,(c) Anion,(d)Anion at the left interface.

Fig.16.The distribution of atomic density along the Z axis of[Bmim][NTf2 ]-water system.(a)Cation,(b)Cation at the left interface,(c)Anion,(d)Anion at the left interface.

Fig.17.The angle distribution between the alkyl chain and the Z axis.(a) [Bmim][NTf2 ]-vacuum,(b) [Bmim][NTf2 ]-water,(c) [Bmim][PF6 ]-vacuum,(d) [Bmim][PF6 ]-water.

Fig.18.The angle distribution between the imidazlium ring and XY plane.(a) [Bmim][NTf2 ]-vacuum,(b) [Bmim][NTf2 ]-water,(c) [Bmim][PF6 ]-vacuum,(d) [Bmim][PF6 ]-water.

In this work,we studied the hygroscopicity of two kinds of ILs by ing absorbing different numbers of water molecules.When a small amount of water were absorbed,the water molecules were free.With increasing of water amount,clusters appeared and distributed near the interface.In [Bmim][NTf2],when 100 water was absorbed,small cluster and large cluster separated.In[Bmim][PF6],when 200 water was absorbed,small cluster and large cluster separated.The amount of free water/small cluster remains relatively constant with increasing the number of total water molecules.We believe that the free/small cluster water plays a key role in drying of ILs.Then,the interfaces of[Bmim][PF6]and[Bmim][NTf2]with vacuum and water were simulated and analyzed in detail by means of number density distribution and angle distribution.In the IL-vacuum system,[Bmim]+ions were excellent regular at the interface,with the alkyl chain pointing outwards and the imidazlium ring in body phase.After replacing the vacuum with water,the interface for two ILs became thicker.The interface for [Bmim][PF6]almost doubled,while that for [Bmim][NTf2]increased only a little.At the same time,cation and anion were completely disordered at the interface.The above studies will provide insight into the hygroscopicity of the ILs,and boost further exploration of IL applications.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

The authors thank the financial support from the National Science Fund for Excellent Young Scholars(21722610)and Taishan Scholars Program of Shandong Province (tsqn201909091).The work was carried out at National Supercomputer Center in Tianjin,and the calculations were performed on TianHe-1(A).

Supplementary Material

Supplementary data to this article can be found online at https://doi.org/10.1016/j.cjche.2020.09.047.