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The first synthesis of 3-deoxyoripavine and its utilization in the preparation of 10-deoxyaporphines and cyprodime

Abstract The synthesis of 3-deoxyoripavine (7) was realized as a novel and promising intermediate towards the synthesis of the important class of dopaminergic and/or serotonergic 10-deoxyaporphines and the special pharmacological tool µ opioid antagonist cyprodime. Generally, the preparation of these valuable biologically active compounds was achieved in remarkable yields.

unknown 3-deoxyoripavine (7). The practical significance of this procedure is even higher due to the fact that the starting derivative of our procedure, oripavine (4), is one of the major industrial poppy alkaloids [10][11][12]. Towards the synthesis of 3-deoxyoripavine (7) we identified in view of literature two potential starting materials; either the 3-O-(trifluoromethyl)sulfonyl-5 or 3-O-(1phenyltetrazoyl)-derivatives 6 of the parent alkaloid 4. The challenge in the preparation of the 3-deoxy derivative was to find an appropriate hydrogenolytic procedure active enough to remove the 3-etheral moiety but keep unaffected the conjugated diene system of ring C known to be especially sensitive to reductive and acidic conditions [11]. The phenyltetrazoyl ether 6 was prepared in excellent yields (94%) from oripavine (4) according to the protocol used for the synthesis of the similar morphine ether [7]. The procedure, in which the free base of 4 and 5-chloro-1-phenyl-1H-tetrazole was refluxed in acetone in the presence of K 2 CO 3 , resulted white crystals allowing us to perform X-ray analysis (Fig. 2, CCDC 860893) of the 3etheral region of the molecule in view of a previous study [13]. The C3-O bond length is 1.413Ǻ, and the C3-O-C bond angle was 116.6 o which are close the average values determined by Johnstone et al. [13] for a series of tetrazoyl ethers used for the removal of phenolic OH function. This study confirmed that compound 6 is a promising starting derivative for the synthesis of 3-deoxyoripavine (7) on the basis of the determining parameters deduced of Johnstone's group [14][15][16][17]. The alternative starting compound of the aimed deoxygenated oripavine 7 was the 3-O-[(trifluoromethyl)sulfonyl]oripavine (5) prepared according to the literature procedure in 75% yield [2]. There were several potential hydrogenolytic conditions identified in the literature, however, as it was referred, finding the appropriate reductive capacity and acidity of the applied conditions was the real task of a complex optimization procedure. This procedure is summarized in Table 1 focusing on the most relevant steps. The hydrogenolysis of the tetrazoyl ethers is usually achieved by catalytic hydrogenation; however this route was ruled out as a potential method on the basis of literature reports [21]. The hydrogenolysis of morphine-3-tetrazoyl ether resulted 3-deoxydihydromorphine and it is well known that the reductive stability of morphine-type alkaloids is considerably higher than the same for oripavine-type diene structures. Therefore, several attempts were made for the selective transfer hydrogenation of tetrazoyl moiety with different hydrogen donors. As it can be concluded from Table 1, these methods gave rise to the expected compound in poor yields (Entries 1 &2). In case of hydrazine the crude reaction mixture contained fully and partially saturated morphinans without 3-OH function besides the aimed compound 7. The application of sodium hypophosphite led to a very complex mixture with partially saturated morphinans. The most promising attempts were made with 1,4-cyclohexadiene as H-donor. Besides 17% of target 3-deoxyoripavine (7) the mixture of partially saturated morphinans with unprotected 3-OH functions were also obtained. Generally the procedures based on 3-O-[(trifluoromethyl)sulfonyl]oripavine (5) proved to be a promising starting compound in view of the Pd-catalyzed deoxygenating methods. The application of formic acid in the presence of Pd(OAc) 2 , triethylamine and triphenylphosphine led to compound 7 in 37% yield (Entry 4), however the use of sterically more demanding dppf resulted higher yield (49%) probably due to a steric hindrance towards ring C of the skeleton. Palladium-on-charcoal with magnesium metal in methanol gave rise to low amount of product besides a mixture of saturated morphinans. It was suggested that the application of ionic additives could improve efficacy and required reaction time [19]. In the course of those experiments ammonium acetate was found to be the best; however in our hands the use of ammonium formate resulted the highest conversion into the desired compound. It is interesting to note that according to the plausible mechanism suggested by Mori et al. methanol is an indirect H-donor interacting with magnesium [19]. The most efficient procedure for the synthesis of targeted product 7 (92%, Entry 8) was the one formic acid and an excess of triethylamine in the presence of Pd(OAc) 2 and dppf. In case of replacing dppf with PPh 3 gave rise to considerably lower yields. In order to further investigate the performance and conformity of our best conditions with different electronic systems in ring C, we synthesized the corresponding triflates of morphine (1), γ-isomorphine (8) and neomorphine (9) according to the method described for the synthesis of (-)-3-O-[-(trifluoromethyl)sulfonylmorphine (2) [1]. On the basis of the difference in the substitution pattern and electronic structure of the ring C of γ-isomorphine (8) [22] and neomorphine (9) [23] these compounds considered as hydroxylated metabolites of morphine (1) itself [24]. The triflate formation of alkaloids 1, 8 and 9 (Scheme 1) was performed in excellent yields (84-91%).

Scheme 1. Synthesis of 3-deoxymorphinans
The previously presented methodology ( Table 1, Entry 8) for the hydrogenolysis of 3-Otriflate function was successfully applied for compounds 2, 10, 11 giving rise to the expected 3-deoxygenated morphinans 12-14 in 85-91% yields. The formation of products with saturated ring C of the morphinan skeleton was not observed. Therefore it can be stated that the substitution pattern and the position of the double bond in ring C are not limiting factors of the application of the 3-deoxygenation of morphinans.
As it was referred previously, one of the main areas for the utilization of new 3deoxyoripavine (7) was the acid-catalyzed rearrangement into 10-deoxyaporphines exploiting all the accumulated knowledge regarding this procedure [25].

Scheme 2.
Synthesis of 2-substituted-11-hydroxyaporphines, the isolated yields for products 15-20 and the literature references for known compounds The data summarized in Scheme 2 suggest that the acid-catalyzed rearrangement could be realized starting from deoxymorphinandiene 7 rather than from morphine (1) or oripavine (4) as in this new method no catechol system is involved. This catechol system often leads to the appearance of oxidized by-products [29]. These side-products make the work-up procedure difficult and contribute to the decrease of isolated yields. In these cases the average isolated yields of three runs were found to be good to excellent. Taking into consideration the high yileding 3-O-triflation of oripavine and 3-deoxygenation of compound 5, the overall yields for this series of 10-deoxyaporphines 15-20 were in the range of 51-62%. Cyprodime [30] is a prototypical, selective µ opioid antagonist which is still the target of intense pharmacological research in part because of the availability of its tritium-labelled derivative [31]. The original synthesis of the cyprodime was based on the preparation of key intermediate 25 from oxymorphone, an expensive semi-synthetic major analgesic, in 6 steps [30,32]. The structure of compound 7 offers the shortening of this procedure as it is presented in Scheme 3.

Scheme 3. New route to key intermediate 25 of the synthesis of cyprodime
All these standard synthetic steps were performed in accordance with a previous report on the alternative synthesis of cyprodime [33]. The overall yield for key intermediate 25 was 32% in the present 5-step study. Interestingly, it was possible to obtain the trimethoxymorphinan 24 in average yield (59%) under usual O-methylation conditions [31] in the presence of 5 equivalents of NaH and (CH 3 ) 2 SO 4 . The position of the double bond in ring C was established on the basis of the coupling constants of H7.

Conclusion
In conclusion, the preparation of 3-deoxyoripavine (7) was achieved starting from both 3-O-(5-phenyltetrazoil)ether and the 3-O-triflate of oripavine. The optimization of the hydrogenolitic conditions resulted in a highly efficient procedure yielding 92% of the desired compound 7. The methodology was extended for morphine (1) and its isomers and found to be a useful route to 3-deoxymorphinans without change in the electronic system of ring C. It was recognized that 3-deoxyoripavine (7) was a valuable starting product towards the synthesis of the important class of dopaminergic and serotonerg 10-deoxyaporphines and the special pharmacological tool µ opioid antagonist cyprodime.

Experimental
Melting points were determined with a Kofler hot-stage apparatus and are uncorrected. Thin layer chromatography was performed on pre-coated Merck 5554 Kieselgel 60 F254 foils using dichloromethane:methanol = 8:2 mobile phase. The spots were visualized with Dragendorff's reagent. 1 H and 13 C NMR spectra were recorded on a Varian Gemini 200 MHz spectrometer; chemical shifts are reported in parts per million (δ) from internal TMS and coupling constants (J) are measured in hertz. Mass spectral measurements were performed with a Bruker micrOTOF-Q instrument in the ESI mode. Elemental analyses (C, H) were obtained on a Carlo Erba EA1108 analyzer.

Procedure for the formation of 3-O-[(trifluoromethyl)sulfonyl]morphinans
A suspension of the alkaloid (9.20 mmol) and Et 3 N (1.92 mL, 13.8 mmol) in CH 2 Cl 2 (150 mL) kept under nitrogen was stirred for 1 h at room temperature. N-Phenyltrifluoromethanesulfonimide (3.94 g, 11.0 mmol) was added, and after being stirred for 48 h, the reaction mixture was extracted with 10% aqueous NaHCO 3 . The organic layer was dried (K 2 CO 3 ), filtered, and concentrated in vacuo. The oily residue was subjected to column chromatography.

Neomorphine (9)
Physical data were fully in agreement with previously published data [23]. Calculated for free base C 17

Acid-catalyzed rearrangement of 3-deoxyoripavine (7) in the presence of alcohols or thiols
A mixture of 7 (200 mg, 0.71 mmol), methanesulfonic acid (1 ml) and alcohol/thiol (200 μl) was stirred for 30 min at 90 o C. Then the reaction mixture was added dropwise, with stirring and external ice-cooling, to a solution of potassium hydrogen carbonate (2 g) in water (10 ml). After extraction with dichloromethane (3x15 ml), the combined extracts were washed with saturated brine, dried (MgSO 4 ), and concentrated under reducer pressure. The purification of 10-deoxyapomorphines was performed by means of column chromatography (Kieselgel 40, dichloromethane:methanol= 8:2).
The characterizations of the novel morphinans related to the synthesis of cyprodime and new aporphines are presented in the supplementary document.


extfieldsofstudy: Chemistry Medicine

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(2,3,5,6-Tetrafluorophenolato)[5,10,15,20-tetrakis(4-methoxyphenyl)porphyrinato]iron(III) cyclohexane monosolvate

The title compound, [Fe(C6HF4O)(C48H36N4O4)]·C6H12, represents a five-coordinate iron(III) porphyrin complex in a square-pyramidal geometry with a tetrafluorophenolate anion as the axial ligand. The FeIII atom is displaced by 0.364 (2) Å from the 24-atom mean plane of the porphyrinate ring towards the tetrafluoro phenolate anion. The average Fe—N distance is 2.053 (2) Å and the Fe—O distance is 1.883 (2) Å. A porphyrin aryl H atom points in the general direction of the phenoxide ring. The mean plane separation between the 24-atom porphyrin planes of two adjacent porphyrin rings is ∼3.7 Å, and the lateral shift is ∼3.5 Å resu, ting in an Fe⋯Fe separation of 5.6167 (14) Å.

The title compound, [Fe(C 6 HF 4 O)(C 48 H 36 N 4 O 4 )]ÁC 6 H 12 , represents a five-coordinate iron(III) porphyrin complex in a square-pyramidal geometry with a tetrafluorophenolate anion as the axial ligand. The Fe III atom is displaced by 0.364 (2) Å from the 24-atom mean plane of the porphyrinate ring towards the tetrafluoro phenolate anion. The average Fe-N distance is 2.053 (2) Å and the Fe-O distance is 1.883 (2) Å . A porphyrin aryl H atom points in the general direction of the phenoxide ring. The mean plane separation between the 24-atom porphyrin planes of two adjacent porphyrin rings is $3.7 Å , and the lateral shift is $3.5 Å resu, ting in an FeÁ Á ÁFe separation of 5.6167 (14) Å .
The authors wish to thank the National Science Foundation (grant CHE-1213674) and the University of Oklahoma for funds to support this research and to acquire the diffractometer and computers used in this work.

Comment
Synthetic metalloporphyrins have been studied intensively due to their potential to act as models for heme enzymes in biological systems. Catalase is a heme enzyme that catalyzes the decomposition of hydrogen peroxide to water and oxygen (Nicholls et al., 2001). Heme catalase contains an active-site tyrosine, a phenolato type ligand, that binds to the heme iron center (Nicholls et al., 2001). A number of iron phenolate porphyrin complexes has been prepared and structurally characterized (Chaudhary et al., 2010, Ueyama et al., 1998, Kanamori et al., 2005. In this paper, we report the structure of (5,10,15,20-tetrakis(4-methoxyphenyl)porphyrinato)(tetrafluorophenolato)iron(III) with a cyclohexane monosolvate.
After stirring for 1 h, the color of the solution changed from green to red. The solution was reduced to 2 ml under reduced pressure, and 10 ml hexane was added. The resulting black precipitation was collected by filtration and dried under vacuum. A suitable prism-shaped crystal was grown by slow evaporation of a CH 2 Cl 2 -cyclohexane (1:1) solution of the complex at room temperature under N 2 .

Refinement
The positions of H atoms bonded to carbons were initially determined by geometry and were refined using a riding model. H atoms bonded to N atoms and O atoms were located on a difference map, and their positions were refined independently. Non-hydrogen atoms were refined with anisotropic displacement parameters. Hydrogen atom displacement parameters were set to 1.2 (1.5 for methyl) times the isotropic equivalent displacement parameters of the bonded atoms. Carbon-bound H atoms were placed in calculated positions (aromatic 0.95, ethyl 0.99, and methyl 0.95 Angstroms) and were refined using a riding model. The C-C bond distances in the cyclohexane were restrained to 1.52 Angstroms and the 1-3 C···C distances were restrained to be equal. Rigid-bond restraints were also applied to the anisotropic displacement parameters of the solvent carbons.

Figure 1
The molecular structure of (T(p-OMe)PP)Fe(OC 6 HF 4 ) . (C 6 H 12 ) with displacement ellipsoids drawn at the 35% probability level. H atoms are omitted for clarity.


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Highly Enantioselective Addition of Phenylethynylzinc to Aldehydes Catalyzed by Chiral Cyclopropane-Based Amino Alcohols

The enantioselective addition of phenylethynylzinc to aldehydes catalyzed by a series of cyclopropane-based amino alcohol ligands 7 was investigated. The reactions afforded chiral propargylic alcohols in high yields (up to 96%) and with excellent enantioselectivities (up to 98% ee) under mild conditions. Furthermore, studies on the structural relationship show that the matching of the chiral center configuration is crucial to obtain the high enantioselectivity.

Introduction
The catalytic enantioselective addition of alkynylzinc to aldehydes is one of the most useful carbon-carbon bond-forming reactions because the resulting propargylic alcohols are versatile, useful building blocks and important precursors for fine chemicals, pharmaceuticals, and natural products [1][2][3][4][5][6][7].

Results and Discussion
The chiral ligands 7 were easily synthesised from commercially available (+)-cis-methyl chrysanthemate and (R) or (S)-prolinol according to a previously reported procedure [44]. The absolute configuration of ligands 7 was (1R, 3S), as confirmed by X-ray crystallography analysis of ligand 7e (Figure 3). This configuration is identical to that of the starting material, (+)-cis-methyl chrysanthemate. An initial study on the structural relationship of the cyclopropane-based ligands 7 in the addition of phenylethynylzinc to benzaldehyde was performed (Table 1). The results indicated that varying the substitution on the pyrrolidine ring of the ligands significantly affected the enantioselectivity of the reaction. The ee value was significantly increased when the hydroxyl group in the prolinol of ligand 7a was protected with a tert-butyldimethylsilyl chloride (TBDMSCl; ligand 7c) or tert-butyldiphenylsilyl chloride (TBDPSCl; ligand 7e) moiety (entry 1 vs. entries 3 and 5). Furthermore, the cyclopropane-based amino alcohol 7d, which was synthesized from (R)-prolinol, afforded the corresponding (S)-propargyl alcohol with only 22% ee, whereas ligand 7c, which was prepared from (S)-prolinol, exhibited a higher ee (80%). This result showed that the match of the cyclopropane configuration with the additional chiral center on the pyrrolidine was crucial to achieve high enantioselectivity. Therefore, the cyclopropane-based amino alcohol 7c was the ligand of choice, providing the propargylic alcohol product with 80% ee (entry 3).
Attempts were made to optimize the reaction conditions by employing the addition of phenylethynylzinc to benzaldehyde. (Table 2). Early optimization showed that temperature significantly affected the ee value. A decrease in the reaction temperature from room temperature to 0 °C increased the ee values (entry 1 vs. entry 2). However, a further decrease in the temperature to −10 and −20 °C reduced both the enantioselectivity and yield (entries 3 and 4). It was interesting to note that the results were almost equally good when the amount of ligand was increased to 20 mol% (entry 6 vs. entry 2). Moreover, both the yield and enantioselectivity of the reaction decreased when the amount of ligand was reduced to 5 mol% (entry 7 vs. entry 2). Although previous studies [47] showed that the addition of polyethylene glycol dimethyl ether (DiMPEG) can significantly promote asymmetric induction, our additive to this reaction only slightly reduced the enantioselectivity (entry 5 vs. entry 2), because the DiMPEG would impact the generation of our unique catalyst system. Finally, the effects of the solvent on this reaction were investigated. Reaction in heptane gave lower enantioselectivity than in toluene (entry 8 vs. entry 2), this may be due to the poor solubility of Zn-amino alcohol complexes. Finally, the optimized reaction conditions were considered as following: 8a (0.5 mmol) with phenylacetylene (1.5 mmol) and Me 2 Zn (1.5 mmol) in toluene at 0 °C for 48 h ( Table 2, entry 2). With the optimal condition in hand, we continued to explore the scope of this reaction. The addition of phenylethynylzinc to various aldehydes was investigated ( Table 3). The results revealed that ligand 7c was a highly enantioselective catalyst for the addition of alkynylzinc to aldehydes. Ortho-, meta-, and para-substituted benzaldehydes containing either electron-donating or electron-withdrawing substituents gave uniformly high ee (90%-98%, entries 1 to 13). In particular, the result (98% ee) obtained from 2-methylbenzaldehyde was remarkable (entry 5). High enantioselectivity was also observed for the addition to other aromatic aldehydes such as 1-naphthaldehyde and 2-naphthaldehyde (entries 14 and 15). A favorable result (entries 16 and 17) was also obtained when the aliphatic aldehydes 8p and 8q were used as substrates.

General Methods and Materials
All reactions were performed under a nitrogen atmosphere. Solvents were dried according to standard procedures and were then distilled prior to use. All reagents were purchased commercially and used without further purification, unless stated otherwise. 1 H-and 13 C-NMR spectra were recorded using a Bruker DP-X300 MHz spectrometer (Bruker, Fallanden, Switzerland), and referenced internally to Me 4 Si. High-resolution mass spectra were obtained on an Agilent MS using the time-of-flight mass spectrometry technique (Agilent Technologies, Waldbroon, Germany). The optical rotations were determined on a Perkin-Elmer PE-341 polarimeter (Perkin-Elmer, Waltham, MA, USA). Crystallographic data were obtained using a Rigaku RAPID-S image plate X-Ray diffractometer (Rigaku Denki Co., Ltd, Tokyo, Japan). Enantiomeric excesses (ee) were determined on an Agilent 1100 HPLC system using a chiral Chiralcel OD-H column (Daicel Chiral Technologies (China) Co., Ltd., Shanghai, China) and isopropanol-hexanes as the eluent.

X-Ray Crystallographic Data of the Ligand 7e
CCDC 808539 contains the supplementary crystallographic data for this paper. These data can be obtained free of charge via http://www.ccdc.cam.ac.uk/conts/retrieving.html (or from the CCDC, 12 Union Road, Cambridge CB2 1EZ, UK; Fax: +44 1223 336033; E-mail: deposit@ccdc.cam.ac.uk). This text may be included in the General subsection of the Experimental or as a suitably referenced endnote.

General Procedure for the Asymmetric Alkynylation of Aldehydes
Phenylacetylene (0.165 mL, 1.5 mmol, 3 equiv) was added to a solution of Me 2 Zn (1.25 mL, 1.2 M in toluene, 1.5 mmol, 3 equiv) in dry toluene (1.75 mL) at room temperature under a nitrogen atmosphere. The mixture was stirred for 30 min, then was transferred via syringe to another Schlenk tube containing neat ligand 7 (0.05 mmol, 0.1 equiv). After stirring for 30 min, an aldehyde (0.5 mmol) was added at 0 °C. The reaction mixture was stirred at 0 °C for 48 h and then quenched with saturated aqueous NH 4 Cl (5 mL). The organic phase was separated, and the aqueous phase was extracted with Et 2 O. The combined organic layers were dried over anhydrous Na 2 SO 4 . The solvents were removed under reduced pressure. Flash chromatography (silica gel, 10% ether in hexanes) afforded the pure propargylic alcohols. The enantiomeric excess was determined by HPLC on a Chiralcel OD-H column. The absolute configurations of the products were assigned by comparing their specific rotations or their HPLC elution order with literature data.

Conclusions
The cyclopropane-based amino alcohol 7c successfully promotes the enantioselective alkynylation of aldehydes and affords chiral propargylic alcohols in high yields and high enantiomeric excess (up to 98% ee) without requiring any additives. In addition, studies on the structural relationship show that the matching of the cyclopropane configuration with the additional chiral center on pyrrolidine is crucial to obtain high enantioselectivity.


The Dynamical Properties on Ionic Liquids: Insights from Molecular Dynamics Study

Ionic liquids (ILs) have attracted many researchers in the areas including physics and chem‐ istry because of their characteristics that are different from conventional molecular liquids and, today, ILs have been one of interesting subjects of scientific study. ILs are consisted of ions and liquids at or near room temperature, and show negligible vapor pressure, thermal and chemical properties, and so on [1-8]. Also, ILs have been widely used as solvents for organic reactions with the expectation of high yields [1]. Most interesting features of ILs can be attributed to remarkable interionic interactions, and these can be an important key factor to study the characteristics of ILs at molecular level. From the results of both experimental and theoretical investigations, it has been recognized that the interionic interaction of ILs could determine physical and chemical properties.

Introduction
Ionic liquids (ILs) have attracted many researchers in the areas including physics and chemistry because of their characteristics that are different from conventional molecular liquids and, today, ILs have been one of interesting subjects of scientific study. ILs are consisted of ions and liquids at or near room temperature, and show negligible vapor pressure, thermal and chemical properties, and so on [1][2][3][4][5][6][7][8]. Also, ILs have been widely used as solvents for organic reactions with the expectation of high yields [1]. Most interesting features of ILs can be attributed to remarkable interionic interactions, and these can be an important key factor to study the characteristics of ILs at molecular level. From the results of both experimental and theoretical investigations, it has been recognized that the interionic interaction of ILs could determine physical and chemical properties.
From an experimental side, both femtosecond optically heterodyne-detected Raman-induced Kerr effect spectroscopy (OHD-RIKES) [3,9,10] and THz time-domain spectroscopy (THz-TDS) [11,12] have been applied to investigate the intermolecular vibrational dynamics in ILs. In particular, with OHD-RIKES studies, the possibility to control a property such as shear viscosity by substituting an atomic element in an ionic unit has been reported [13,14]. On the other hand, from theoretical and computational viewpoints in recent years, ILs have been chosen to study static properties such as structural and thermophysical properties [15][16][17][18] and novel interionic dynamics under solvation dynamics [19][20][21], dynamical properties [22][23][24][25][26], and Kerr spectra analyses [14,27]. It has been suggested from the simulation studies by Ishida et al. [14] that interionic properties in ILs could be effectively adjustable by substituting an atomic unit in an ion unit in addition to a combination of cations and anions. Also, it has been pointed out that the interplay of motions between cation and anion species could play an important role in specific interionic interactions of ILs. [28] Now, we can consider two factors important to understand specific interionic interactions in ILs. One is the interionic interaction depending on specific correlations such as cross-correlation terms between cations and anions, and the other is polarization effects due to manybody interactions caused by cations and anions in ILs. While a large number of experimental approaches have been applied to investigate these subjects, molecular-level understanding of many specific properties of ILs has been left unresolved. Obviously, theoretical researches are suitable to tackle these problems to which experimental procedures are not accessible. Thus, it is expected that such computational method as molecular dynamics (MD) simulations enables us to obtain significant information of ILs, utilizing the force field with wellparameterized potential functions and partial charges [29].
With the MD simulation procedures, it is possible to study the effects of the cross-correlations on dynamic collective motions of ions in ILs which are considered to govern the strength and behavior of couplings between ionic motions through interionic interactions [28]. The computation of the time correlations of velocity and momentum between a tagged ion and other unlike ions at different distances provides cross-correlation and momentum correlation functions [28,30,31]. Utilizing these calculated functions, we can investigate not only interionic interactions at molecular level but also how collective motions in ILs can proceed accompanied by the momentum transfer between ions in the target IL system.
On the other hand, electrostatic interactions between ions in ILs could be modulated due to many-body interactions and, then, it could emerge as polarization effects caused by the distortion of electron densities under anisotropic environment in ILs. It has been pointed out that the inclusion of polarization effects is significant to investigate the characteristics of ILs in structural and dynamical properties [23,24]. Therefore, it is required for us to carry out the MD simulation, introducing such procedures as a point dipole model and a polarization energy term into the total potential energy representation of the system [32]. In addition to electrostatic interactions, describing the variation and relaxation of the polarizability anisotropy of ILs is important to investigate dynamics in ILs. For achieving this, we need to compute time-dependent polarization effects on a target system due to environmental effects in ILs. Theoretically, when we would take polarizability anisotropy into account, to track the change of molecular polarizability tensor partly dependent on molecular orientations such as rotational motions would be required. With the calculation of the time correlation function (TCF) of off-diagonal elements of the total polarizability of the system, we can investigate collective properties with the result of the polarizability anisotropy relaxation of the system. ]. Below, we start from the explanation for the velocity cross-correlations of a central atom with neighboring atoms. Then, we show how to evaluate both cross-correlation and momentum correlation functions of the target IL. In addition, we describe the introduction of a polarization energy term and the procedure to calculate induced dipole moments and the polarization energy. Following those, the theoretical background of polarization TCFs is given. Computational details are also summarized. In later sections, we discuss polarization effects on interionic interactions and specific properties related to those based on the MD simulation results. We show computation results obtained from performing MD simulation and computing the polarization TCF with the dipole-dipole (DID) approximation [4,5]. Also, we examine the relation between the anisotropic polarizability relaxation and collective motions of ionic species. Lastly, we discuss relaxation processes of ILs including an explanation of important points in studying dynamical properties on ILs. ] + , the Y direction is along the line connecting two nitrogen (blue colored) atoms in the ring, and the Z direction is set perpendicular to the ring plane and the Y direction axis. The X directionis set in the ring plane orthogonal to both the Y and the Z axes. In [PF6] -, the X, Y, and Z direction axes are set equivalently. In [NTf 2 ] -, the Y axis is along the line connecting two sulfurs (dark yellow colored), and the Z axis is set perpendicular the S-N-S plane and the X axis. The X axis is set in the S-N-S plane orthogonal to both the Y and Z axes.

Tracking Ionic Motions Through Interionic Interactions: Cross-Correlation, Polarization Effects, and Dynamical Properties
As mentioned in the previous section, for many problems of ILs to which experimental procedures are not accessible, theoretical investigations with computer simulation procedures are promising and suitable to obtain detailed information at molecular level. In particular, specific correlations such as cross-correlations between cations and anions seem not to be feasible to detect experimentally, but the MD simulations enable us to evaluate those. Also, for tracing dynamics in ILs such as librational and reorientational dynamics of ionic species, cross-correlated ionic motions, and the influence of polarization coming from many-body effects caused by cations and anions in ILs from a microscopic point of view, the MD simulations are considered to be one of useful and powerful tools. In this chapter, we will show and explain the dynamical properties on ILs based on MD simulation results taking into consideration mainly following points: The items 1 and 2 are main parts in this chapter, including the key results mentioned above. The item 3 is considered to be important for suggesting (or notifying) attention to researchers who are working on analyzing the dynamical properties on ILs. The item 4 includes future perspectives. In particular, we will show and discuss new aspects of ILs in each section related to the items 1, 2, and 3. Also, some of theoretical backgrounds and computational procedures for studying the dynamical properties of ILs are given in each related section, below.
At first, let us consider following points: 1. how can the collective dynamics through interionic interactions cause the unique physical and chemical properties of ILs ?
2. how can interionic dynamics be modified by electronic polarizability effects ?
The former includes the investigation of the contribution of ionic motions due to Coulombic interactions to velocity cross-correlation functions. In particular, through the analysis of the longitudinal and nonlongitudinal contributions to the velocity cross-correlation function in ILs, we will be able to investigate interionic interactions in detail. Also, important properties for physical and chemical interests such as case effects seems to be within the scope of unique collective dynamics in ILs. The later covers the relation between polarizability correlation functions and interionic interactions for ILs. To investigate these points, we can utilize useful information for static properties obtained from computer simulations, but those are not often enough to extract the details of specific interactions.
Here, we give an example that it is difficult for us to find the importance of the interactions between cation and anion species only from static properties. Figure 2 displays the computed radial distribution functions, g(r), comparing non-polarizable model with polarizable model [28]. As shown in the figure, we can observe only small difference in RDFs between two models, except that the g(r) of cation-anion is different from those of cation-cation and anion-anion as easily deduced. But, obviously, it is not feasible for us to observe information other than strong spatial correlations and sequential ordering of cation and anion pairs. In addition, the analysis of averaged static structures such as RDFs is not enough to investigate remarkable polarization effects such as screening effects influenced by polarization. Below, we give a schematic explanation and discuss that to consider interionic interactions with cross-correlation analyses is important to investigate the interplay between cation and anion species in ILs, and it is shown that the cross-correlation analyses provide contrastive features. Different from a usual velocity autocorrelation functions (VACF), cross-correlation functions describe interactions between unlike (ionic) species (that is, between a cation and an anion in ILs) and show opposite features to VACFs. In Figure 3, these features are explained schematically. Here, it should be emphasized that cross-correlation functions provide more information on interionic interactions than that static properties such as RDFs include. As seen in Figure 3 ((a) and (b)), the variation of cross-correlation function correlates with the alteration of the VACF. In particular, the cross-correlation function shows the increasing toward the maximum peak where the VACF approaches a minimum point.
These features indicate that it is possible for us to track the time evolution of cross-correlations (between cation and anion species in ILs) as collective dynamics. In addition, it is observed in Figure 3 ((c)) that a particle (ionic species) is bouncing back and forth between like and unlike particles (ions). This implies collective (ionic) motions between coordination shells, thus, it is indicated that not only interionic interactions but also momentum transferring among ionic species could be extracted by analyzing cross-correlation functions. Also, considering that these cross-correlation functions could be modulated by the strength of interionic interactions and the coupling between cation and anion motions, cross-correlation functions would be largely influenced by polarization effects. On the other hand, as another type of the appearance of interplay between cross-correlation and polarization effects, we consider the polarizability anisotropy and its relaxation of an IL system. These correspond to the variation of the sum of molecular polarizability depending on time. Therefore, it is required to compute the change of molecular polarizablity on each molecule due to interionic interactions and interaction-induced multipole effects. Obviously, it is expected that molecular polarizabilites are influenced by interionic cross-correlations. In later sections, we introduce the theoretical background of polarizability TCF and its application to the study of ILs, and show how degree these are effective and discuss the importance of considering cross-correlations.

Theoretical Background
Here, we introduce cross-correlation functions, and then, give an explanation of a polarizable model and polarizability time correlation function. Computational details are also given.

Cross-Correlation Function
A velocity autocorrelation function (VACF) is defined for calculating the velocity correlation of a same particle as follows, where v i (t) is the velocity of i-th species. Different from the VACF, the time cross-correlation functions between the velocity of a central species i and the velocity of a neighboring species j different from the particle i is defined as follows [30,31], where v i (t) is the velocity of the species i and v j (t) is the velocity of the species j. v i 2 and v j 2 represent the mean square velocities. Here, it should be noted that n represents a restricted statistical average [30,31], where θ represents the step function. a n and b n are set as the positions of the nth minima of the radial distribution function of the system, g(r). The N n in Eqs. (2) and (3) is the coordination number in the region between r = a n and b n . as follows,  (4) where ρ is the number density of the system.
Here, we can define the cross-correlation in ILs as that between a centered cation and the total contribution of other anions [28,30], where "C" and "A" in super-and subscript represent cation and anion, respectively. By interchanging "C" and "A" in super-and subscript in the above equation, we can easily derive the formulation for the cross-correlation between a centered anion and other cations.
Also, with the computation of the cross-correlation functions between the velocity of a central ion and velocities of neighboring distinct ions, we can analyze the momentum transfer between distinct ions in ILs. Introducing the momentum correlation function [28,31], the transfer of the momentum of a cation to distinct cations and anions is defined as follows, where p + and pmean the momentums of cation and anion, respectively. The transference of momentum of an anion to distinct anions and cations, P n A(total) (t), is also given as follows,

A Polarizable Model
Here, we introduce a polarizable model considering induced dipole moments and explain the procedure for computing induced dipole moments and the many-body polarization energy [33][34][35].
The total potential energy of the system under the resulting polarizable force field is defined as follows, where the terms V bond and V nonbond are intra-and intermolecular interaction energies. The polarization energy, V pol , is decomposed into the three terms as follows, where the charge-dipole contribution, V charge-dipole , the dipole-dipole contribution, V dipole-dipole , and the self-polarizability term, V self , are defined, respectively, as In the above equations, E i is the electric field on atom i, produced by the partial charges of all other surrounding atoms, and μ i represents the induced dipole moment on atom i. Also, α i means the isotropic atomic polarizability of atom i. In Eq. (11), the T ij , is the dipole field tensor element defined as follows, where r ij = r i -r j . The induced dipole moment on atom i is given by With Eqs. (10), (11), and (12), the polarization energy, E pol , is summarized as follows,

Polarizability Time-Correlation Function (TCF)
The polarizability anisotropy of the system can be tractable by calculating the TCF of offdiagonal elements of the total polarizability. Here, the theoretical background of the polarizability TCF is summarized briefly.
At first, we define the total polarizability of the system, Π(t), that is the sum of the molecular polarizability, Π M (t), and the interaction-induced polarizability, Π II (t), as follows, where t represents the time dependence, and subscripts M and II mean the molecular part and the interaction-induced part, respectively. The molecular part is given by the sum of the polarizability tensors of isolated gas phase molecular polarizability in the laboratory frame, = å (17) where N is the number of molecules, and α i is the polarizability tensor of molecule i. For the formulation of the interaction-induced part, we employ the dipole-induced-dipole (DID) model approximation [36,37], which assumes that the molecular polarizabilities are modified due to a dipolar coupling with the influence of higher order unconsidered. The interaction-induced polarizability in the DID approximation is given as follows, where T ij means the dipole interaction tensor between molecules i and j. α i (t)is the effective polarizability for molecule i defined by the following equation including the interaction-induced effects, Equation (19) can be solved by the calculation procedure that is called the all-orders DID approximation [37]. It should be noted that the DID model employed here assumes a centercenter DID model, where it recognizes the polarizability as concentrated in the center of mass of the molecule.
Here, we give the representation of the total system polarizability including the cationic and anionic components [14,27], where the superscripts C and A represent cation and anion species, respectively. Referring to Equations. (16), (17), and (18), the Π C (t) and Π A (t) defined as follows, t t a a = P = + å (22) where the indices k and l go over all cations and anions, respectively. Then, the total polarizability of the system, Π(t), can be rewritten, as follows, Where β C (t) = { Π C (t) − 1 3 Tr ( Π C (t) ) I } and β A (t) = { Π A (t) − 1 3 Tr ( Π A (t) ) I } and I is the unit tensor. Finally, the polarizability TCF, ϕ(t), can be rewritten as follows, where The nuclear response function, R(t), is represented as the time derivative of the polarizability TCF,

Computational Details
Utilizing  [45,46], we adopted 1.152, 0.705 and 0.0885 Å 3 for the C, N, and H atoms of the cation, respectively, and 0.121 and 3.630 Å 3 for the F and P atoms of the anion, respectively. We considered the distance and vector between the atomic sites of distinct molecules in the dipole interaction tensor, T = (I − 3rr) / r 3 , wherer = r / rThen, the range of the attenuation of dipolar interactions at short distances, s, was evaluated with the Thole's definition [47], s = 1.662(α i α j ) 1/6 with atomic polarizabilities, α i andα j . Also, the dipole interaction tensor we used is given by [47] 3T ( 3 ) / ( ) r r s = -> I rr where a = r/s. Equation (14) is solved with an iterative procedure at each time step, and then, the criterion value of iterative solution for induced dipole moment was set to 0.001 D.  Figure 2. For more computational procedures in detail, interested readers should refer to references [14] and [28].

Cross-Correlation, Momentum Correlation, and Polarization Effects
The computed velocity cross-correlation functions [28]  With these values, the first (C 1 (t)) and second (C 2 (t)) coordination shells were specified. It should be noted that the C 1 (t) between the center anion and distinct anions is not shown in Figure 5 because the C 1 (t) is almost zero corresponding to the result that the anion-anion RDF result is almost zero at the region of the specified first coordination shell (see RDFs in Figure 2(b)). Also, it should be noted that the initial values, C n (0), are negative since the system size is finite as have been pointed out [30].  Figures 4 and 5, the VACFs are also displayed for comparison. As briefly explained in Section 2 with Figure 3, the initial rise of the cross-correlation function, C 1 (t), appears toward the maximum for both models, corresponding to the decay of the VACF to the minimum (see the (a) and (b) in Figure 3). These results indicate that the initial momentum of the central ion is gained by neighboring ions immediately after t = 0. In addition, following decay profiles (see the (c) in Figure 3) are seen. These are ascribed to the spread of transferred momentum to the outer coordination shells. The peak height of the C 1 (t) in the polarizable model is larger than that in the nonpolarizable model. These significant results indicate that the momentum transfer can be intensified from the more distant coordination shells to the first ones due to both the charge-dipole and dipole-dipole interactions by polarization effects in addition to charge-charge Coulomb interactions. As the characteristics of the VACF profile, it is noted that the minima of the VACF are located at the positions later than those of the maxima of the velocity cross-correlation functions for the first coordination shell. These features imply that the momentum transmitted to the neighbors at the first shell is regained partly by the central cation or anion, bounc-ing back and forth for some time, as have been pointed out in the literature on the computer simulations of simple liquid binary mixtures [28,31]. On the other hand, an interesting feature is seen in the C 1 (t) between distinct cations (or the C 2 (t) for distinct anions). As indicated in Figures 4 and 5, the cross-correlation function for distinct ions reaches the maximum point earlier than the C 1 (t) for the cation-anion cross-correlation, even though the peak height is smaller than that in the cation-anion cross-correlation function. On these results, it is considered that the alteration of cage effects increases the probability that a cation (or an anion) meets a distinct cation (or anion) at early time region.

As shown in
Also, in Figures 4 and 5, it is clearly observed that the cross-correlation function between distinct like ions is influenced by the modulation of cage effects due to polarization effects and that its peak height is enhanced in the polarizable model [28]. As shown in Figures 4  and 5, when VACFs pass the value of zero to negative, the cross-correlation functions reach the maximum point. Thus, this implies that the central cation (or anion) is likely to lose its initial momentum. In addition, as seen in Figure 5, the peak position of C 2 (t) is shifted to the time region later than that of C 1 (t). This is consistent with the consideration that the momentum of the central ion is transferred from the first coordination shell to the second.
Here, we examine the characteristics of the cross-correlation functions. As shown in Figure  6, we consider the decomposition of a cross-correlation function into the longitudinal (denoted as L in the figure), C n L (t), and nonlogitudinal (denoted as NL in the figure), C n NL (t), contributions as follows [28,31,49], where CR n L (t) is represented as the velocity cross-correlation along the direction designated by the center of masses of distinct ions at t = 0. We can compute CR n L (t) with the following equation [28,31,49], where v i and v i (t) is the velocity of the ionic species i. Also, r ij (0) means the direction vector between the center of masses of the distinct ions i and j. v i 2 and v j 2 represent the mean square velocities. CR n NL (t) can be computed with CR n (t) and CR n L (t). Figure 7 shows the computed C n L (t) and C n NL (t) functions for a centered cation at the first coordination shell (n = 1) both for the nonpolarizable and polarizable models [28]. All the results indicate that the velocity cross-correlations at the short time region up to 0.4 ps are predominantly governed by the longitudinal function, C n L (t). These results clearly indicate that the Coulomb interactions between neighboring ions are mainly effective on the ionic motions as "driving forces" at the short time. In addition, the magnitude of the longitudinal correlation of ions in the polarizable model is larger than that in the nonpolarizable model. Therefore, it is considered that the longitudinal motions are strongly affected by polarization effects. On the decay behavior, similar features are obtained in both models. These indicate that polarization effects on the longitudinal motion complete mostly at the short time region. Next, the computed results of momentum correlation functions [28] are displayed in Figures  8 and 9. As shown in Figures 8 and 9 in common, the initial momentum of the cation (or anion) is mainly transferred to the close anions (or cations) while the momentum correlation with distinct cations (or anions) is smaller. These results are consistent with the consideration that strong Coulomb interactions between the cations and the anions enhance the possibility of approaching or attracting each other. Also, while the contribution of the momentum correlation between distinct cations, P 1 CC (t), is smaller than that between the cation and anion molecules, P 1 CA (t), the peak height of the P 1 CA (t) in the polarizable model is larger than that in the nonpolarizable model. These results indicate that the transference of the momentum between distinct cations could be intensified by both charge-dipole and dipole-dipole interactions coming from polarization effects. As we could observe in the cross-correlation functions (see Figures 4 and 5), the maxima of the momentum correlation functions between distinct cations emerge at earlier time region in comparison with those of the momentum correlations between cation and anion species. Based on these results, obviously, it is indicated that the variation of cage effects promotes the transfer of the initial momentum of the central cation to distinct cations rather than anions. Then, the cage effects is considered to be weakened by polarization effects, though the degree of this effect is likely to be relatively small as deduced from the figures.
On the other hand, the momentum correlations for the center anion in Figure 9 show distinct features from those for the center cation. The momentum correlation function between distinct anions, P 1 AA (t), indicates much smaller contributions to the total momentum correlations, P 1 (t), in both the nonpolarizable and polarizable models, compared with the P 1 AC (t). Therefore, these indicate that the initial momentum of the center anion is mainly transferred to neighboring cations, and the transference between distinct anions is not enhanced. These are consistent with the consideration that the cation-anion interactions promote the propagation of the momentum one after another, as mentioned in the cation case. In addition, Figure 9 shows more interesting features. Compared with the results for the central cation in Figure 8, while the P 1 AA (t) does not contribute negligibly to the total momentum correlation in the nonpolarizable model, it indicates characteristic oscillating behavior in the short time region up to 0.4 ps in the polarizable model, and the latter has a relatively larger contribution to the P 1 (t) up to 0.1 ps than in the nonpolarizable model. This clearly indicates the decrease of cage effects through polarization effects and implies that the interionic interactions between distinct anions could become effective by the charge-charge and dipole-dipole interactions [28].

Relaxation Processes and Dynamical Properties
Firstly, the relaxation feature of IL system is examined with the computed polarizability TCF and its time derivative, and then, we discuss dynamical behavior of cations and anions in ILs, and consider what kinds of properties with simulation data we have to check and care in the study of dynamical properties of ILs.   Figure 10(a), the relaxation of the polarizability TCFs seems to be slower than in usual liquids. In particular, the relaxation of the anion shows faster decay than that of the cation. Also, for each component, it takes about 2~3 ns to approach toward zero. Thus, this indicates that it is required for us to perform a production MD simulation run for, at least, a few ns to study the relaxation behavior of the polarizability TCF. Also, as seen in Figure 10(a), the cation-anion cross-correlation indicates similar variation to the total polarizability TCF. Therefore, the relaxation behavior of the system strongly correlates with the cation-anion cross-correlation, and it is emphasized that tracking cross-correlation terms is very important. On the other hand, cor-responding to this result, the time derivative of the polarizability TCF shows long-decay feature extending up to the nanosecond times, as seen in Figure 10(b). Considering that the time derivative of the polarizability TCF is directly related to optical Kerr effect (OKE) response, [14] these results are indicative of how long a MD simulation has to be carried out to examine the relaxation of the total system polarizability and the OKE response.
The relaxation process of ILs implies long-time dynamics of ILs. In particular, it has been known that diffusive motion of each ion in ILs at room temperature is usually much slower than in usual liquids. [1,16] Therefore, a MD simulation would need to be run for a few ns or more. Then, we are able to use a procedure to check whether a system is in the diffusive regime. The procedure is to compute β(t) = dlog(MSD)/dlog(t), [16] where MSD means the meansquared displacement (MSD) of the center of mass of ions, ∑ i=1 N r i (t) − r(0) 2 . In the case that β(t) = 1, the system is in the diffusive regime, while when b(t) < 1, the system is in the sub-diffusive regime. In Figure 11, computed β(t)s for [BMIm][NTf 2 ] are shown. These results indicate that both the cation and the anion reach the β(t) region between 0.8 and 1 (the shadowed area in Figure 11) after about 16 ns. This β(t) region is considered to be almost in the diffusive regime. Therefore, Figure 11 obviously indicates that, for confirming reliable self-diffusivities carefully, we need to perform a longer MD simulation than about 15 ~ 20 ns.
where r(t) is the displacement of an ion at time t with respect to its position at t = 0. In Figure  12, the MSDs of [PMIm] + and [NTf 2 ] -indicate three typical dynamic ranges (regions), respec-tively. Also, the behavior of the short-and long-time regimes of MSD for both the cation and the anion is similar to each other. For [BMIm] + , first region is a microscopic regime until about 10 ps. Second is a crossover regime (the shadowed area in the Figure 12) until about 3-5 ns, and third regime is a sublinear time dependence (sub-diffusive region) toward 20 ns. Also, α(t) has a double peak structure. One is at about 0.5 ps and the other at about 800 ps. In addition, a small shoulder structure emerges at between two peaks. As clearly seen in Figure 12, the shorttime maximum peak corresponds to the microscopic region of the MSD, while the longtime maximum is located at around the center of the crossover regime of the MSD. On the other hand, for the anion, [NTf 2 ] -, α(t) has a double peak structure similar to that of the cation. In particular, the long-time maximum peak is slightly shifted to about 300 ps, while the short-time maximum is locacted at the almost same time region as the cation. The time regime where the long-time maximum appear, is in good accord with those of [BMIm] + , as shown in Figure 12. Therefore, considering that the magnitude of the deviation from the Gaussian behavior is remarkably larger for [BMIm] + than for [NTf 2 ] -as shown in Figure 12, it is expected that the relaxation behavior of the cation in perturbed [BMIm][NTf 2 ] IL might be largely different from that of the anion. This consideration implies the possibility for us to find a distinct relaxation process in the OKE response (compare Figure 10 with Figure 12). Also, it should be noticed that the diffusive regime (linear time-dependence region) after about 10 ns in Figure 12 coincides with the diffusive region in Figure 11 (after about 16 ns) for both the cation and the anion.
In particular, the shadowed area in Figure 12 covers the time range of the full width at half maximum (FWHM) of the second peak of α(t). As pointed out previously, [52] this FWHM range is likely to include a slow decay region usually known as the α relaxation which is characteristic of glass-forming supercooled liquids in general. Also, recently, it has been reported that similar behavior could appear for ILs at room temperature. [51,53,54] Therefore, we had better study the α relaxation in ILs with the observations of the non-Gaussian parameter in addition to information on spatial relaxation such as intermediate scattering function. Also, it is suggested that, when we investigate dynamical properties of ILs, the crossover, the sub-diffusive, and the diffusive regimes have to be carefully examined, as one of criterions for reliable research. Thus, only with a long-time MD simulation, it is considered that we are able to investigate dynamical properties of ILs to which experimental procedures are not accessible.

Conclusion
In this chapter, we introduced cross-correlation function analyses with a polarizable model, polarizability TCFs for investigating the relaxation behavior of ILs, and some of procedures for studying dynamical properties. We showed the importance of considering cross-correlation functions and related properties, showing some of examples. Firstly, we employed the polarizable model based on point dipole treatment to the investigation of the polarization effect on the target IL, [BMIm] [PF 6 ]. With the MD simulation data for both the nonpolarizable and polarizable models, velocity cross-correlation analyses were shown, and we presented the momentum correlation functions between the cation and anion species in the IL. Next, we computed polarizability TCFs of [BMIm][NTf 2 ] and discussed their relaxation behavior. In addition, we investigated dynamical properties of ILs such MSDs and non-Gaussian parameters and considered what kinds of properties with simulation data we have to check and care in the study of dynamical properties of ILs. This chapter is summarized as follows: 1. In the study and discussion of velocity cross-correlation functions, it was shown that polarization effects could enhance the cross-correlations between [BMIm] + and [PF 6 ]in the polarizable model in comparison with that in the nonpolarizable model. These features are ascribed to interionic interactions through attractive forces coming from the charge-dipole and dipole-dipole interactions caused by polarization effects in addition to charge-charge Coulomb interactions. Based on the results of computed cross-correlation between distinct cations (or anions), it was shown that, at early time region, the modulation of cage effects through polarization effects could improve the probability of approach between like ions. Also, by decomposing the cross-correlation function into the longitudinal and nonlongitudinal components, it was indicated that, at the short time region, the velocity cross-correlation is predominantly controlled by the longitudinal contribution. In addition, it was indicated that, compared with the longitudinal correlation in the nonpolarizable model, the longitudinal component is further modified in the polarizable model. 6 ] -, it was exhibited that the correlation between [BMIm] + and [PF 6 ] -plays a important role. Also, it was shown that the contribution of the cross-correlation between distinct anions could be enhanced in the polarizable model. This result indicates that cage effects could be diminished with polarization effects, implying that the interionic interactions between distinct anions could be intensified by the charge-charge and dipole-dipole interactions related to polarization effects. Therefore, as has been pointed out in the literature [23,24,29], it is considered that the cage effect in ILs could be reduced by many-body polarization effects.

3.
Both the computed polarizability TCF for each component and the time derivative of the total polarizability TCF for [BMIm][NTf 2 ] showed long-time decay behavior. It was indicated that those took about 2~3 ns to approach toward zero. Therefore, this indicates that it is required for us to perform a production MD simulation run. Also, the relaxation behavior of ILs was investigated with the calculation of β(t) = dlog(MSD)/ dlog(t) as an indicator of the diffusive region. Our results suggested that long-time dynamics of ILs has to be studied with a longer MD simulation than about 15 ~ 20 ns for confirming reliable self-diffusivities in ILs, carefully. Furthermore, we examined MSDs and non-Gaussian parameters for [BMIm][NTf 2 ]. From our studies, it was exhibited that the magnitude of the deviation from the Gaussian behavior is remarkably larger for [BMIm] + than for [NTf 2 ] -, and that, comparing with corresponding MSDs, it is possible to study diffusive motion of the cation and the anion. In addition, it was suggested that these studies imply the possibility for us to find a distinct relaxation process in the OKE response. Therefore, it is suggested that we had better study the α relaxation in ILs with the observations of the non-Gaussian parameter in addition to information on spatial relaxation such as intermediate scattering function. Lastly, it is concluded, only with a long-time MD simulation (> 15 ~ 20 ns), that we are able to investigate the dynamical properties of ILs to which experimental procedures are not accessible.