Article pubs.acs.org/JPCA
Theoretical Studies on the Electronic States and Liquid Structures of Ferrocenium-Based Ionic Liquids Hiroshi Nakano,*,†,‡ Junki Noguchi,† Tomoyuki Mochida,§ and Hirofumi Sato*,†,‡ †
Department of Molecular Engineering and ‡Elements Strategy Initiative for Catalysts and Batteries, Kyoto University, Kyoto Daigaku Katsura, Kyoto 615-8510, Japan § Department of Chemistry, Kobe University, Rokkodai, Nada, Kobe 657-8501, Japan S Supporting Information *
ABSTRACT: The solvation effects on the electronic structures and magnetic properties were computed for a series of ferrocenium cations in the ferrocenium-based ionic liquids using RISMSCF-SEDD calculations coupled with CASSCF. The spin−orbit coupling was calculated to get insight into the spin anisotropy. The values were on the order of 100 cm−1, exhibiting strong spin anisotropy parallel to the angular momentum. The computed results show that the magnetic properties of the ferrocenium cations are similar both in the isolated state and in ionic liquids. We also carried out molecular dynamics and RISM calculations to investigate the liquid structures. The radial and spatial distribution functions around the cations indicate that the cations are surrounded by about seven TFSA anions above and below the cyclopentadienyl rings and from the side of the ferrocenium cations. The nearest-neighbor cations exist in the oblique directions. The introduction of a butyl group to the ring disturbs the solvation structures, and butyl groups in different cations tend to attract each other like those observed in alkylimidazolium ionic liquids.
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the temperature is lowered under an external magnetic field, these paramagnetic ILs are crystallized to have magnetic anisotropy. The magnitude of magnetic susceptibility parallel to the magnetic field imposed upon the crystallization is increased with increasing magnetic field (∼1 T). A hysteresis of the magnetic susceptibility against temperature is also observed coupled with solid−liquid phase transformation. X-ray diffraction data show that in those crystals, the ferrocenium radical cations are aligned with the two cyclopentadienyl rings normal to the magnetic field.9,11 Although such macroscopic magnetic properties of the materials and microscopic structures of the crystals have been experimentally investigated in detail, microscopic information on the magnetic properties of the constituent ferrocenium cations and liquid structures is still unrevealed. Toward microscopic understanding of these peculiar properties of this ferrocenium-based ILs, here we present the first attempt to study the solvation effect on the ferrocenium cation and its derivatives by means of RISM-SCF-SEDD (reference interaction site model self-consistent field spatial electron density distribution).12 In RISM-SCF-SEDD calculations, the electronic state of a solute molecule is determined under the mean electrostatic potentials (mean field approximation) created by radial distribution functions (RDFs) of solvent, which are obtained from the reference interaction site model (RISM) calculations.14,15 RISM is an integral equation theory
INTRODUCTION
On a conference, you may be frequently asked the following question abour your presentation: “What do you think about the solvation effect?” The importance of the solvation effect has been recognized for a long time, and a realistic, theoretical treatment has become available in the past three decades. The solvation effect is now readily evaluated with a variety of software for quantum chemistry, and our understanding of the electronic structure of a solvated molecule becomes deeper and wider. The polarizable continuum model (PCM) developed by Tomasi and his colleagues1−4 is one of the pioneering works in a class of selfconsistent reaction field methods, and undoubtedly a major contributor to make people aware that the solvation effect is essential in a variety of chemical events including reactions, equilibria, the photoprocess, and so on. Although a wide range of chemical phenomenon in the solution phase can be treated by these solvation theories, there still remain a class of solvents that are not readily treated. Solvation effects in mixed liquid composed of several chemical species is such an example. In particular, computation of molecular property from the first principle is very challenging. Ionic liquids (ILs) are molten salts composed of mostly bulky organic cations and organic or inorganic anions. They exhibit many peculiar properties like low melting points (typically below 100 °C). Various functionalities such as catalytic activity and magnetism can be added through modification of the constituent ions.5,6 Recently, Mochida and co-workers synthesized new ILs composed of ferrocenium cations and some anions.7−10 These ILs exhibit interesting magnetic properties originated from the ferrocenium cation radicals. When © XXXX American Chemical Society
Special Issue: Jacopo Tomasi Festschrift Received: September 29, 2014 Revised: November 28, 2014
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anion (TFSA) were obtained. By utilizing these correlation functions, we then regard the cations as “solutes” in the ILs to compute the solvation effect on the electronic structure using RISM-SCF-SEDD method, especially focused on the magnetic properties.
Table 1. Characteristic Distances (Å) in the Ferrocenium Cation and Neutral Ferrocene with D5h Symmetry at the UB3LYP/DZVP Levela Fe−Cp
Fe−C
C−C
C−H
1.693 1.671
2.086 2.067
1.433 1.431
1.083 1.083
ferrocenium cation neutral ferrocene
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COMPUTATIONAL DETAILS Geometries of the three ferrocenium cations were optimized at the UKS/DZVP level22 with the B3LYP functional (UB3LYP) because this functional was shown to give quantitative results for the optimized structure of the neutral ferrocene.23 We imposed D5h symmetry for the ferrocenium cation as the most stable conformation of the neutral ferrocene.24,25 Cs symmetry was imposed on the butyl derivatives. At the optimized structures, state-averaged (SA) CASSCF/DZVP calculations were performed.15 We examined several sets of active spaces including d orbitals of the iron atom and several π orbitals of the cyclopentadienyl anions as discussed below. The spin−orbit couplings were calculated as the expectation values of full Breit−Pauli Hamiltonian with SA-CASSCF wave functions.26 CASSCF coupled with RISM-SCF-SEDD calculations for the ferrocenium-based ILs were also carried out at the same geometries as the corresponding calculations in the gas phase. In MD and RISM calculations, the ferocenium cations and TFSA anion were modeled with united atoms: The hydrogen atoms in the ferrocenium cations and the fluorine atoms in TFSA anion were fused with the bonded carbon atoms. Although these ions were essentially handled as rigid bodies, the butyl group in nBu-Fc+ was flexible in the MD calculations. All LJ parameters were taken from the literature, namely UFF for the iron atom,27 OPLS-UA for united atoms (CH in cyclopentadienyl anions and CH2 and CH3 in butyl groups),28 and a united atom model for CF3 in the TFSA anion.29 One might be apprehensive about the mixing use of different force field parameters. We have confirmed that the choice of the LJ parameters of the iron atom has little effect on the results shown below. This is probably because the iron atom is inside the rigid-body ferrocenium unit and does not directly contact with atoms of other ions. The intramolecular potential function for bonds, angles, and dihedrals in the flexible n-butyl group were taken from a model of the butylmethylimidazolium cation.30 Although the atomic charges of the ferrocenium cations were
a
Fe−Cp denotes the distance between the iron atom and the center of a cyclopentadienyl ring.
Table 2. Mulliken Charge of Fragments in Ferrocene (Fc), Ferrocenium Cation (Fc+), and its Tertiary Butyl and Normal Butyl Derivatives (tBu-Fc+ and nBu-Fc+) at the UB3LYP/DZVP Level [Unit: Elementary Charge (|e|)] Fc Fc+ tBu-Fc+ nBu-Fc+
Fe
Cp1a
Cp2b
Buc
−0.248 −0.315 −0.401 −0.398
0.124 0.657 0.629 0.633
0.124 0.657 0.691 0.702
0.082 0.062
a Unsubstituted cyclopentadienyl ring. bButyl-substituted cyclopentadienyl ring. cTertiary or normal butyl group.
in statistical mechanics for molecular liquids. The analytical nature and the mean field approximation of the RISM-SCFSEDD method offers an electronic-state computation of a solvated molecule at a reasonable cost. The solvation structures around the ferrocenium cations were analyzed with RDFs and spatial distribution functions (SDFs) computed by molecular dynamics (MD) calculation as well as by RISM theory. Because integral equation theory like RISM can give these functions at significantly lower computational cost than MD calculations, especially for these highly viscous ILs,9 the theory has been applied to study their liquid structures and dynamics including imidazolium-based ionic liquids.16,17 The solvation effects on chemical reactions in ionic liquids were also investigated using the RISM-SCF-SEDD method.18−20 PCM has also been utilized with the SMD model.21 In the present study, the parent ferrocenium cation (Fc+) and its tert-butyl (tBu-Fc+) or n-butyl derivatives (nBu-Fc+) were chosen as the cation in target systems. Using RISM or MD simulation, the liquid structures of ILs composed of one of these ferrocenium cations and the bis[(trifluoromethyl)sulfonyl]amide
Figure 1. Tertiary and normal butyl-substituted ferrocenium cations (green) superimposed on the ferrocenium cation (red). These structures were optimized at the UB3LYP/DZVP level. B
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obtained from natural population analysis (NPA)31,32 calculated at the UB3LYP/DZVP level, those of TFSA anion were taken from the same literature as its LJ parameters. These LJ parameters and atomic charges are listed in the Supporting Information. The MD simulation systems were composed of 256 cation and anion pairs in cubic boxes. The temperatures of the systems were set to 430 K for [Fc+][TFSA], 380 K for [tBu-Fc+][TFSA], and 330 K for [nBu-Fc+][TFSA], which are higher than the melting points (in the case of [nBu-Fc+][TFSA], the cyclopentadienyl rings were octamethylated in the experiment) by about 25 K.7−9 The systems were initially equilibrated in a NPT ensemble for 12 ns followed by 30 ns NVT production runs to obtain the RDFs and SDFs around the ferrocenium cations. The convergence of the results was checked by performing 150 ns production run for the [Fc+][TFSA] ionic liquid. In the RISM calculations, the number densities obtained from the MD calculations in NPT ensemble were adopted. The values were 0.00215 Å−3 for [Fc+][TFSA], 0.00177 Å−3 for [tBu-Fc+][TFSA], and 0.00178 Å−3 for [n-BuFc+][TFSA] IL, respectively.33 The number of the grid points was 4096, and the grid spacing was 0.05 Å. The Kovalenko−Hirata closure was employed.13,14 The obtained correlation functions were used in RISM-SCF-SEDD coupled with the CASSCF calculations. The geometry optimizations and calculations of the NPA charges were carried out with GAMESS34 and Gaussian09 programs.35 The CASSCF calculations in the gas phase and in the ILs with the RISM-SCF-SEDD method were performed by our modified version of the GAMESS program. DL_POLY 2.20 was used for the MD calculations.36
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RESULTS AND DISCUSSION Quantum Mechanical Calculations of the Ferrocenium Cations. Geometries and Atomic Charges. Table 1 lists characteristic distances at the optimized geometry of Fc+ with D5h symmetry together with the neutral ferrocene (Fc) optimized at the same level (B3LYP/DZVP). The calculated geometry of Fc is in good agreement with the experimental one (Fe−Cp, Fe−C, C−C, and C−H distances are 1.66, 2.06, 1.44, and 1.10 Å, respectively) and with the previous calculations at CCSD(T) and B3LYP levels.23 The rather small difference between Fc+ and Fc is observed in the Fe−Cp and Fe−C distances by 0.02 Å. The slightly longer distance between the iron atom and the cyclopentadienyl ring in Fc+ is attributed to an electron removal from a weakly bonding orbital composed of iron dxy or dx2−y2 and from the π orbital of the cyclopentadienyl rings (42nd or 43rd orbitals in Figure 2). The attractive electrostatic interaction between the cyclopentadienyl anions and the iron atom should be weakened, which can be verified from the Mulliken charges in Table 2. It is interesting, however, that the geometries of the cyclopentadienyl rings were hardly changed by ionization. Figure 1 shows superimposed structures of Fc+ and its butyl derivatives (tBu-Fc+ and nBu-Fc+). Substitution with a tertiary or normal butyl group does not introduce large displacement into the ferrocenium unit. Table 2 shows the charge of fragments (iron atom, two cyclopentadienyl rings, and butyl group) calculated by summing up the Mulliken atomic charges. All of the fragments in the neutral ferrocene (Fc) have small charges, implying that electrons are transferred from two cyclopentadienyl anions to the Fe(II) cation through the coordination. The charge of cyclopentadienyl fragment in Fc+ becomes more positive than that of the iron atom, and the total charge (1|e|) resides mostly on the cyclopentadienyl fragments.
Figure 2. Molecular orbitals of the ferrocenium cation relevant to the CASSCF calculations (see the main text). The index refers to the ordering of the molecular orbital, and the SOMO is the 48th orbital at the ROHF/DZVP level.
The butyl substitutions (tBu-Fc+ and nBu-Fc+) introduce small variations in the fragment charges. Because only about 0.1|e| charge is moved from the parent ferrocenium cation unit to the butyl groups, almost all charge is localized on the ferrocenium unit. The butyl groups become nonpolar fragments as in imidazolium-based ionic liquids substituted with long alkyl chains.37 Electronic Structures. Figure 2 illustrates the active orbitals with which a seven state-averaged CASSCF calculation was performed with equal weight (7SA-CASSCF(13e,11o)). The seven states are composed of three sets of doubly degenerate states (−1646.40913, −1646.30827, and −1646.28772 hartree) C
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Figure 3. RDFs obtained from MD calculations: (a) [ferrocenium][TFSA] IL; (b), (d) [tert-butylferrocenium][TFSA] IL; (c), (e) [n-butylferrocenium][TFSA] IL. CH denotes a site of cyclopentadienyl rings. CH3 denotes a methyl unit in the butyl groups (the terminal methyl unit in the tertiary butyl group).
and a remaining state (−1646.26276 hartree). In the first set of degenerate states (ground states), one of the molecular orbitals characterized by dxy or dx2−y2 (corresponding to the 42nd or 43rd orbital in Figure 2) is almost singly occupied and the other is doubly occupied in the main configuration. Other orbitals are doubly occupied or vacant. This result is consistent with previous experimental and theoretical studies.38,39 The π orbital of the cyclopentadienyl anions (corresponding to the 46th or 47th orbital in Figure 2) is almost singly occupied in the second set of the degenerate states. The main configuration in the third set is characterized as a singly occupied dxz or dyz orbital (corresponding to the 44th or 45th orbital in Figure 2). The seventh state in the 7SA-CASSCF calculation is represented as mixed configurations. The natural orbital characterized by iron dz2 (similar to the 48th orbital in Figure 2) is almost fully occupied (occupation number is 1.995), and an energy gap between the most stable degenerate states and the second ones is large (about 60 kcal/mol). Hence, the state-averaged CASSCF(11e,10o) calculation without the dz2 orbital in the active space is enough to properly elucidate the electronic structure. The same calculations were also employed to the butyl-substituted derivatives, namely the active spaces consisting of 11 electrons and ten orbitals. It is noted that the degeneracy of the ground states is resolved due to introduction of asymmetry by the butyl substitutions. The energy difference between the two states are 1.0 kcal/mol for tBu-Fc+ and 3.1 kcal/mol for nBu-Fc+, respectively; both of them are characterized by dxy and dx2−y2 orbitals as in Fc+.
Because the degenerate two ground states are characterized by the dxy and dx2−y2 orbitals, the ferrocenium cation and its butyl derivatives can have a nonzero angular-momentum orbital parallel to the z-axis.40 By diagonalizing the matrix elements of lẑ for the two orbitals (42nd or 43rd orbital in Figure 2), occupied with three electrons, we computed the z-components of the orbital angular momentum to be 1.91 for Fc+, 1.88 for tBu-Fc+, and 1.91 for nBu-Fc+, respectively. Moreover, the electron spin in the ferrocenium radical cations can interact with the orbital angular momentum to align its orientation to the same direction via the spin−orbit coupling, which can also contribute to the anisotropic magnetic moment of the ferrocenium cations. The stabilization energies obtained by aligning spin in the same z direction as the orbital angular momentum were 334 cm−1 for Fc+, 204 cm−1 for tBu-Fc+, and 96 cm−1 for nBu-Fc+, respectively, which were evaluated by using the two state-averaged CASSCF(11e,10o) wave functions. These large spin−orbit couplings indicate that the spin stays in the z-direction even when an external magnetic field (the magnitude is about 1 T in experimental conditions, and the interaction energy between the spin and such an external magnetic field is on the order of 1 cm−1) is imposed in the x or y direction. The butyl substitutions reduce the magnitude of the spin−orbit coupling of the ferrocenium cations because of the relaxation of the degenerate electronic states by substitutions; nevertheless the magnitude of the spin−orbit coupling is large enough to contribute to the magnetic anisotropy. The extent of the reduction seems to correlate with the energy difference D
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between the nearly degenerate electronic states (1.0 kcal/mol for the tertiary butyl derivative and 3.1 kcal/mol for the normal butyl derivative). Because the molecular z-axis of the ferrocenium cations are aligned in almost the same direction in the crystal structures of the ferrocenium-based ILs,9,11 and the magnetic moments of the ferrocenium cations point to the same z direction as described above, the crystals are expected to exhibit magnetic anisotropy observed experimentally.9,11 Liquid Structures of the Ferrocenium-Based Ionic Liquids. Figures 3a and 4a are the RDFs and SDFs of Fc+ and TFSA anions around a ferrocenium cation in [Fc+][TFSA] IL computed with MD simulation. As expected, a ferrocenium cation is surrounded by anions. TFSA anions direct the oxygen atoms to the ferrocenium cations because of the negative charge on these atoms (see the atomic charges listed in the Supporting Information). The first peak in the iron−oxygen RDF corresponds to the population of the oxygen atoms approaching the iron atom from the interstices between the cyclopentadienyl rings. The highest peak position corresponds to the population of TFSA anions above and below the rings. The coordination number of nitrogen atoms of TFSA anions around an iron atom is 7.4 at 9.3 Å, corresponding to the boundary of the first solvation shell. The first peak at 7.6 Å in the iron−iron RDF corresponds to the atoms at oblique directions. The coordination number of iron around an iron atom at 9.3 Å is 6.6. Hence the total numbers of cation and anion in the sphere with the radius of 9.3 Å are 7.6 (=6.6 plus the central cation) and 7.4 respectively, indicating that the local charge neutrality41 is almost satisfied. Figures 3b,c and 4b,c illustrate the RDFs and SDFs in the [t-BuFc+][TFSA] and [n-BuFc+][TFSA] ILs, respectively. The coordination numbers of the nitrogen atoms of TFSA anions around an iron atom at 9.3 Å are 6.4 for the [t-BuFc+][TFSA] and 6.3 for the [n-BuFc+][TFSA], which are smaller by about 1.1 than that for the [Fc+][TFSA]. The oxygen atoms in TFSA anions are directed toward cations, and other cations tend to reside at oblique directions as in the case of the [Fc+][TFSA], but further anisotropy appears in the distribution. The coordination number of iron atoms around an iron atom at 9.3 Å is 5.1 for both the [t-BuFc+][TFSA] and [t-BuFc+][TFSA] ILs, which is smaller by 1.5 than that for the [Fc+][TFSA]. The smaller coordination numbers in these butyl-substituted ILs are due to the larger excluded volume. This can be understood from a slightly different viewpoint that a smaller number of ions is necessary to solvate a cation because the electrostatic potential becomes weaker due to the large distance from the ion. It should be noted that the local charge neutrality is almost satisfied also in these ILs; there are about 6.1 cations and 6.4 anions in the sphere with radius of 9.3 Å centered in the cation. The distributions observed in the [Fc+][TFSA] IL are disturbed by butyl substitutions. The populations of the anion atoms disappear around the butyl group and instead the butyl group in other cations are populated. This is probably because the butyl group has a small positive charge of about 0.1|e| and the nonelectrostatic interaction becomes rather dominant between neighboring butyl groups. This tendency seems to be enhanced in [n-BuFc+][TFSA] than in [t-BuFc+][TFSA] as observed in the RDFs and SDFs; the first peak of CH3−CH3 RDF and the distribution of the methyl unit around the butyl group in [n-BuFc+][TFSA] are distinct and larger than those in [t-BuFc+][TFSA]. The coordination numbers at 7.0 Å are 2.4 for the [n-BuFc+][TFSA] and 1.9 for the [t-BuFc+][TFSA], respectively. Similar behavior has been observed in imidazolium-based
Figure 4. SDFs obtained from MD calculations. Color: (red) oxygen atom, (blue) nitrogen atom, (yellow) sulfur atom, (gray) CF3 group, (cyan) terminal methyl group, and (purple) iron atom. (a) [ferrocenium][TFSA] IL. The values of the isosurfaces are 5 times and 4 times as large as the bulk density for the anion atoms and cation atom. (b) [tertbutylferrocenium][TFSA] and (c) [n-butylferrocenium][TFSA] ILs. The values of the isosurfaces are 5 times as large as the bulk density for the anion atoms and iron atom and 3 times as large as the bulk density for the CH3 methyl group.
ionic liquids in which the cations are substituted with a long alkyl chain.37 Note that the long alkyl chains (≥C6) are experimentally observed to be in contact with each other in the crystals of the ferrocenium-based ILs, though such alignment was not observed in the crystal structure of ([butyloctamethylferrocenium][TFSA] IL with the shorter chain (C4).9 Figure 5 displays the same set of RDFs obtained from the RISM calculations. The overall shapes and peak positions of the RDFs between cations (iron atoms) and anions are in good agreement with those from the MD calculations in Figure 3, though the peak heights are slightly underestimated, as is often E
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Figure 5. RDFs obtained from RISM calculations: (a) [ferrocenium][TFSA] IL; (b), (d) [tert-butylferrocenium][TFSA] IL; (c), (e) [n-butylferrocenium][TFSA] IL. The other things are the same as those in Figure 3.
the case with the Kovalenko−Hirata closure.14 A noticeable difference between the results from the MD and RISM calculations is observed in iron−iron RDF. The position of the rise, where RDFs start to have nonzero values, is at a remarkably short distance in the RISM calculations compared to that in MD. The coordination numbers of the cations shorter than the point (6.0 Å) are, however, less than 1, indicating that the difference in the solvation effect is expected to be not so large. It is interesting to note that the characteristic features of the methyl−methyl RDFs are well reproduced from the RISM calculations. Consequently, the results from RISM and from MD show overall agreement. Considering the significant saving of computational cost, RISM is a useful tool to study the liquid structures and the solvation effect on the ferrocenium cations for the ferrocenium-based ILs. Solvation Effects on the Electronic Structures of the Ferrocenium Cations. Because IL consists of cations and anions, it is often thought that electronic states of molecules in IL are significantly affected by electrostatic interactions between the molecule and surrounding ions. This means that the magnetic properties of the constituent ferrocenium cations could be also changed from those in the isolated state. We thus performed RISM-SCF-SEDD calculations coupled with CASSCF to investigate the solvation effects. The same procedure with the gas phase computation was repeated in RISM-SCF-SEDD calculations for IL environment. Namely, a seven-state-averaged CASSCF(13e,11o) calculation was first carried out for Fc+. Because the obtained seven states in the ILs are essentially similar to those in the gas phase, the same two state-averaged
CASSCF(11e,10o) coupled with RISM-SCF-SEDD calculations was carried out. The degenerate ground states in the parent ferrocenium cation originated from the symmetry remain unchanged because the solvation structure possess also the same symmetry. The near degeneracies of the tertiary and normal butyl derivatives are slightly affected by solvation; the energy differences between the states are changed from those in the gas phase by less than 1 kcal/mol (1.2 kcal/mol for tBu-Fc+ and 2.7 kcal/mol for nBu-Fc+). These results indicate that the magnetic property of the ferrocenium cations in the ILs is not so much affected by solvation. Such a small effect on these states may be understood in terms of the localization of the important orbitals. Because all of the orbitals in the active spaces are essentially localized on the ferrocenium unit, it is likely that the solvation effects on these orbitals become very similar, and consequently their energy differences are not significantly changed by solvation. From a viewpoint of liquid structure, the lower number density due to the bulkiness of the cation gives rise to this moderate solvation effects, similar to other IL system.18 The alteration of the magnetic property may be achieved by the modification of cyclopentadienyl ring. The Mulliken charges of the ferrocenium cations are as shown in Table 3. The small amount of electron is moved to the cyclopentadienyl rings from the iron atom and the butyl groups to enhance the dipole moment (with respect to the center of mass) from 2.34 to 3.45 D for tBu-Fc+ and from 3.86 to 5.05 D for nBu-Fc+, respectively. If a strong electron-withdrawing or electron-donating F
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Table 3. Mulliken Charge of Fragments in Ferrocenium Cation (Fc+) and Its Tertiary Butyl and Normal Butyl Derivatives (tBu-Fc+ and nBu-Fc+) in Ionic Liquid Composed of each Cation and TFSA Anion at the 2SA-CASSCF(11e,10o)/DZVP Levela +
Fc tBu-Fc+ nBu-Fc+
Fe
Cp1b
Cp2c
Bud
−0.325 (−0.376) −0.322 (−0.354) −0.316 (−0.361)
0.663 (0.688) 0.633 (0.630) 0.627 (0.631)
0.663 (0.688) 0.644 (0.660) 0.622 (0.648)
0.045 (0.064) 0.067 (0.082)
a
Values in parentheses refer to those in the gas phase. The unit is elementary charge (|e|). bUnsubstituted cyclopentadienyl ring. cButyl-substituted cyclopentadienyl ring. dTertiary or normal butyl group.
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substituent is introduced instead of the butyl groups, the orbitals in active space and magnetic properties of the ferrocenium cation in the gas phase and in its IL can be rather different from those studied in the present work.
Corresponding Authors
*H. Nakano. E-mail: [email protected]. *H. Sato. E-mail: [email protected].
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Notes
CONCLUDING REMARKS We have investigated the electronic and magnetic properties of the ferrocenium radical cation and its butyl-substituted derivatives from CASSCF calculations in the gas phase and in the ferrocenium-based ionic liquids by using the RISM-SCFSEDD method. The liquid structures of the ionic liquids consisting of those ferrocenium cations and TFSA anions were also studied by molecular dynamics and RISM calculations. The ferrocenium cations have (nearly) degenerate ground states characterized by the dxy and dx2−y2 orbitals of the iron atom. This means that the ferrocenium cations have orbital angular momentum along the line connecting the centers of the cyclopentadienyl rings. The magnitude of the spin−orbit couplings were on the order of 100 cm−1, indicating that the electronic spin tends to be parallel to the orbital angular momentum and contributes to the magnetic anisotropy. Though the butyl substitutions relax the degeneracy of the electronic ground states and reduce the orbital angular momentum and spin−orbit coupling to some extent, the crystals of the ionic liquids composed of these cations are still expected to exhibit magnetic anisotropy. The electronic states of the ferrocenium cations in the ionic liquids were not so much different from those in the gas phase. This is because the (nearly) degenerate states were symmetrical and solvation structures were also symmetric due to the symmetrical structures of the ferrocenium cations. The fact that all of the important orbitals were localized on the ferrocenium unit is also relevant. This result suggests that the magnetic properties of ferrocenium cations in the ionic liquids resemble those in the gas phase. The molecular dynamics calculations showed that the ferrocenium cations are surrounded by seven TFSA anions, which seems to form the first solvation shell. The TFSA anions direct the oxygen atoms to the ferrocenium cations. Neighboring cations reside at oblique directions. The butyl groups perturbed such solvation structures around the ferrocenium cations and attract other butyl groups such as those in alkylmethylimidazolium ionic liquids. Though the distance between the neighboring ferrocenium cations was underestimated, the RISM calculations give RDFs in overall good agreement with those from the MD calculations with significantly lower computational cost.
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AUTHOR INFORMATION
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS The authors are grateful to Mr. K. Hoshihara for the preliminary computation. The work was financially supported in part by Grants-in-Aid for Scientific Research on Innovative Areas “Dynamical ordering of biomolecular systems for creation of integrated functions” (25102002) and Grant-in-Aid for Scientific Research (C) (25410011). A part of this work was performed under a management of “Elements Strategy Initiative for Catalysts & Batteries (ESICB)”. Theoretical computations were partly performed using the Research Center for Computational Science, Okazaki, Japan. The Strategic Programs for Innovative Research (SPIRE), the Computational Materials Science Initiative (CMSI), is also acknowledged. All of them were supported by the Ministry of Education, Culture, Sports, Science and Technology (MEXT) Japan. The manuscript is dedicated to Prof. Jacopo Tomasi.
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REFERENCES
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ASSOCIATED CONTENT
S Supporting Information *
Potential parameters for Fc+, TFSA, tBu-Fc+, and nBu-Fc+. United atom models of tBu-Fc+ and nBu-Fc+. This material is available free of charge via the Internet at http://pubs.acs.org. G
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Mechanics and Molecular Dynamics Simulations. J. Am. Chem. Soc. 1992, 114, 10024−10035. (28) Jorgensen, W. L.; Madura, J. D.; Swenson, C. J. Optimized Intermolecular Potential Functions for Liquid Hydrocarbons. J. Am. Chem. Soc. 1984, 106, 6638−6646. (29) Zhong, X.; Liu, Z.; Cao, D. Improved Classical United-Atom Force Field for Imidazolium-Based Ionic Liquids: Tetrafluoroborate, Hexafluorophosphate, Methylsulfate, Trifluoromethylsulfonate, Acetate, Trifluoroacetate, and Bis(trifluoromethylsulfonyl)amide. J. Phys. Chem. B 2011, 115, 10027−10040. (30) Urahata, S. M.; Ribeiro, M. C. C. Structure of Ionic Liquids of 1Alkyl-3-Methylimidazolium Cations: A Systematic Computer Simulation Study. J. Chem. Phys. 2004, 120, 1855−1863. (31) Foster, J. P.; Weinhold, F. Natural Hybrid Orbitals. J. Am. Chem. Soc. 1980, 120, 7211−7218. (32) Reed, A. E.; Weinstock, R. B.; Weinhold, F. Natural Population Analysis. J. Chem. Phys. 1985, 83, 735−746. (33) In RISM computations, the temperature of ILs was set to 380 K for tBu-Fc+ and 300 K for other systems. (34) Schmidt, M. W.; Baldridge, K. K.; Boatz, J. A.; Elbert, S. T.; Gordon, M. S.; Jensen, J. H.; Koseki, S.; Matsunaga, N.; Nguyen, K. A.; Su, S.; et al. General Atomic and Molecular Electronic Structure System. J. Comput. Chem. 1993, 14, 1347−1363. (35) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A.; et al. Gaussian 09, Revision B.01; Gaussian, Inc.: Wallingford, CT, 2010. (36) Smith, W.; Forester, T. R.; Todorov, I. T. DLPOLY 2.20 User Manual; CCLRC: Daresbury Laboratory: Daresbury, Warrington, U.K., 2009. (37) Canongia Lopes, J. N. A.; Pádua, A. A. H. Nanostructural Organization in Ionic Liquids. J. Phys. Chem. B 2006, 110, 3330−3335. (38) Duggan, D. M.; Hendrickson, D. N. Electronic Structure of Various Ferricenium Systems as Inferred from Raman, Infrared, LowTemperature Electronic Absorption, and Electron Paramagnetic Resonance Measurements. Inorg. Chem. 1975, 14, 955−970. (39) Her, J.; Stephens, P. W.; Ribas-Ariño, J.; Novoa, J. J.; Shum, W. W.; Miller, J. S. Structure and Magnetic Interactions in the OrganicBased Ferromagnet Decamethylferrocenium Tetracyanoethenide, [FeCp*2]·+ [TCNE]·−. Inorg. Chem. 2009, 48, 3296−3307. (40) The dxy and dx2−y2 orbitals can be represented with the eigenstates for angular momentum operator lẑ as dxy = i(1/2)1/2(|−2⟩ − |2⟩) and dx2 − y2 = (1/2)1/2(|−2⟩ + |2⟩), where lẑ |−2⟩ = −2ℏ|−2⟩ and lẑ |2⟩ = 2ℏ|2⟩. (41) Yan, T.; Burnham, C. J.; Pópolo, M. G. D.; Voth, G. A. Molecular Dynamics Simulation of Ionic Liquids: The Effect of Electronic Polarizability. J. Phys. Chem. B 2004, 108, 11877−11881.
(10) Hamada, S.; Mochida, T. Ferrocenium Ionic Liquids Containing 3,4,5-Tri(dodecyloxy) Benzene Sulfonate and Bis(2-ethylhexyl)sulfosuccinate (AOT) Anions. J. Organomet. Chem. 2013, 725, 34−36. (11) Funasako, Y.; Mochida, T.; Inagaki, T.; Sakurai, T.; Ohta, H.; Furukawa, K.; Nakamura, T. Magnetic Memory Based on Magnetic Alignment of a Paramagnetic Ionic Liquid near Room Temperature. Chem. Commun. 2011, 47, 4475−4477. (12) Yokogawa, D.; Sato, H.; Sakaki, S. New Generation of the Reference Interaction Site Model Self-Consistent Field Method: Introduction of Spatial Electron Density Distribution to the Solvation Theory. J. Chem. Phys. 2007, 126, 244504−244509. (13) Kovalenko, A.; Hirata, F. Self-Consistent Description of a MetalWater Interface by the Kohn-Sham Density Functional Theory and the Three-Dimensional Reference Interaction Site Model. J. Chem. Phys. 1991, 110, 10095−10112. (14) Molecular Theory of Solvation; Hirata, F., Ed.; Kluwer: New York, 2004. (15) Roos, B. O.; Taylor, P. R.; Siegbahn, P. E. M. A Complete Active Space SCF Method (CASSCF) Using a Density Matrix Formulated Super-CI Approach. Chem. Phys. 1980, 48, 157−173. (16) Bruzzone, S.; Malvaldi, M.; Chiappe, C. A RISM Approach to the Liquid Structure and Solvation Properties of Ionic Liquids. Phys. Chem. Chem. Phys. 2007, 9, 5576−5581. (17) Yamaguchi, T.; Koda, S. Mode-Coupling Theoretical Analysis of Transport and Relaxation Properties of Liquid Dimethylimidazolium Chloride. J. Chem. Phys. 2010, 132, 114502−114511. (18) Hayaki, S.; Kido, K.; Yokogawa, D.; Sato, H.; Sakaki, S. A Theoretical Analysis of a Diels-Alder Reaction in Ionic Liquids. J. Phys. Chem. B 2009, 113, 8227−8230. (19) Hayaki, S.; Kido, K.; Sato, H.; Sakaki, S. Ab Initio Study on SN2 Reaction of Methyl p-nitrobenzenesulfonate and Chloride Anion in [mmim][PF6]. Phys. Chem. Chem. Phys. 2010, 12, 1822−1826. (20) Hayaki, S.; Kimura, Y.; Sato, H. Ab Initio Study on an ExcitedState Intramolecular Proton-Transfer Reaction in Ionic Liquid. J. Phys. Chem. B 2013, 117, 6759−6767. (21) Bernales, V. S.; Marenich, A. V.; Contreras, R.; Cramer, C. J.; Truhlar, D. G. Quantum Mechanical Continuum Solvation Models for Ionic Liquids. J. Phys. Chem. B 2012, 116, 9122−9129. (22) Godbout, N.; Salahub, D. R.; Andzelm, J.; Wimmer, E. Optimization of Gaussian-Type Basis Sets for Local Spin Density Functional Calculations. Part I. Boron through Neon, Optimization Technique and Validation. Can. J. Chem. 1992, 70, 560−571. (23) Coriani, S.; Haaland, A.; Helgaker, T.; Jørgensen, P. The Equilibrium Structure of Ferrocene. ChemPhysChem 2006, 7, 2454− 249. (24) The symmetry was reduced to Cs symmetry with no imaginary frequency when we carried out geometry optimization without forcing D5h symmetry. Because this symmetry reduction can be artificial due to the unrestricted single reference (UKS) calculation, we determined to force D5h symmetry even though the force constant matrix at the optimized geometry has imaginary frequencies. Note that the difference in the optimized geometries with the D5h and Cs symmetries are rather small and the average difference in the Fe−C distance is 0.02 Å. (25) We also optimized the ferrocenium cation with D5d symmetry at the UB3LYP/DZVP level and calculated a 2SA-CASSCF(11e,10o) wave function and the spin−orbit coupling. The energy difference between the D5h and D5d geometries was less than 1 kcal/mol at both the UB3LYP/DZVP and 2SA-CASSCF(11e,10o) levels. The stabilization energy obtained by the spin−orbit coupling was 334 cm−1 at the geometry with D5d symmetry, which was comparable to 334 cm−1 at the geometry with D5h symmetry. From these results, we concluded that it was reasonable to consider the geometries of the ferrocenium cations with D5h symmetry obtained in the present work. (26) Fedorov, D. G.; Koseki, S.; Shmidt, M. W.; Gordon, M. S. SpinOrbit Coupling in Molecules: Chemistry beyond the Adiabatic Approximation. Int. Rev. Phys. Chem. 2003, 22, 551−592. (27) Rappé, A. K.; Casewit, C. J.; Colwell, K. S.; Goddard, W. A., III; Skiff, W. M. UFF, a Full Periodic Table Force Field for Molecular H
dx.doi.org/10.1021/jp509859f | J. Phys. Chem. A XXXX, XXX, XXX−XXX
Theoretical Studies on the Electronic States and Liquid Structures of Ferrocenium-Based Ionic Liquids Hiroshi Nakano,*,†,‡ Junki Noguchi,† Tomoyuki Mochida,§ and Hirofumi Sato*,†,‡ †
Department of Molecular Engineering and ‡Elements Strategy Initiative for Catalysts and Batteries, Kyoto University, Kyoto Daigaku Katsura, Kyoto 615-8510, Japan § Department of Chemistry, Kobe University, Rokkodai, Nada, Kobe 657-8501, Japan S Supporting Information *
ABSTRACT: The solvation effects on the electronic structures and magnetic properties were computed for a series of ferrocenium cations in the ferrocenium-based ionic liquids using RISMSCF-SEDD calculations coupled with CASSCF. The spin−orbit coupling was calculated to get insight into the spin anisotropy. The values were on the order of 100 cm−1, exhibiting strong spin anisotropy parallel to the angular momentum. The computed results show that the magnetic properties of the ferrocenium cations are similar both in the isolated state and in ionic liquids. We also carried out molecular dynamics and RISM calculations to investigate the liquid structures. The radial and spatial distribution functions around the cations indicate that the cations are surrounded by about seven TFSA anions above and below the cyclopentadienyl rings and from the side of the ferrocenium cations. The nearest-neighbor cations exist in the oblique directions. The introduction of a butyl group to the ring disturbs the solvation structures, and butyl groups in different cations tend to attract each other like those observed in alkylimidazolium ionic liquids.
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the temperature is lowered under an external magnetic field, these paramagnetic ILs are crystallized to have magnetic anisotropy. The magnitude of magnetic susceptibility parallel to the magnetic field imposed upon the crystallization is increased with increasing magnetic field (∼1 T). A hysteresis of the magnetic susceptibility against temperature is also observed coupled with solid−liquid phase transformation. X-ray diffraction data show that in those crystals, the ferrocenium radical cations are aligned with the two cyclopentadienyl rings normal to the magnetic field.9,11 Although such macroscopic magnetic properties of the materials and microscopic structures of the crystals have been experimentally investigated in detail, microscopic information on the magnetic properties of the constituent ferrocenium cations and liquid structures is still unrevealed. Toward microscopic understanding of these peculiar properties of this ferrocenium-based ILs, here we present the first attempt to study the solvation effect on the ferrocenium cation and its derivatives by means of RISM-SCF-SEDD (reference interaction site model self-consistent field spatial electron density distribution).12 In RISM-SCF-SEDD calculations, the electronic state of a solute molecule is determined under the mean electrostatic potentials (mean field approximation) created by radial distribution functions (RDFs) of solvent, which are obtained from the reference interaction site model (RISM) calculations.14,15 RISM is an integral equation theory
INTRODUCTION
On a conference, you may be frequently asked the following question abour your presentation: “What do you think about the solvation effect?” The importance of the solvation effect has been recognized for a long time, and a realistic, theoretical treatment has become available in the past three decades. The solvation effect is now readily evaluated with a variety of software for quantum chemistry, and our understanding of the electronic structure of a solvated molecule becomes deeper and wider. The polarizable continuum model (PCM) developed by Tomasi and his colleagues1−4 is one of the pioneering works in a class of selfconsistent reaction field methods, and undoubtedly a major contributor to make people aware that the solvation effect is essential in a variety of chemical events including reactions, equilibria, the photoprocess, and so on. Although a wide range of chemical phenomenon in the solution phase can be treated by these solvation theories, there still remain a class of solvents that are not readily treated. Solvation effects in mixed liquid composed of several chemical species is such an example. In particular, computation of molecular property from the first principle is very challenging. Ionic liquids (ILs) are molten salts composed of mostly bulky organic cations and organic or inorganic anions. They exhibit many peculiar properties like low melting points (typically below 100 °C). Various functionalities such as catalytic activity and magnetism can be added through modification of the constituent ions.5,6 Recently, Mochida and co-workers synthesized new ILs composed of ferrocenium cations and some anions.7−10 These ILs exhibit interesting magnetic properties originated from the ferrocenium cation radicals. When © XXXX American Chemical Society
Special Issue: Jacopo Tomasi Festschrift Received: September 29, 2014 Revised: November 28, 2014
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anion (TFSA) were obtained. By utilizing these correlation functions, we then regard the cations as “solutes” in the ILs to compute the solvation effect on the electronic structure using RISM-SCF-SEDD method, especially focused on the magnetic properties.
Table 1. Characteristic Distances (Å) in the Ferrocenium Cation and Neutral Ferrocene with D5h Symmetry at the UB3LYP/DZVP Levela Fe−Cp
Fe−C
C−C
C−H
1.693 1.671
2.086 2.067
1.433 1.431
1.083 1.083
ferrocenium cation neutral ferrocene
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COMPUTATIONAL DETAILS Geometries of the three ferrocenium cations were optimized at the UKS/DZVP level22 with the B3LYP functional (UB3LYP) because this functional was shown to give quantitative results for the optimized structure of the neutral ferrocene.23 We imposed D5h symmetry for the ferrocenium cation as the most stable conformation of the neutral ferrocene.24,25 Cs symmetry was imposed on the butyl derivatives. At the optimized structures, state-averaged (SA) CASSCF/DZVP calculations were performed.15 We examined several sets of active spaces including d orbitals of the iron atom and several π orbitals of the cyclopentadienyl anions as discussed below. The spin−orbit couplings were calculated as the expectation values of full Breit−Pauli Hamiltonian with SA-CASSCF wave functions.26 CASSCF coupled with RISM-SCF-SEDD calculations for the ferrocenium-based ILs were also carried out at the same geometries as the corresponding calculations in the gas phase. In MD and RISM calculations, the ferocenium cations and TFSA anion were modeled with united atoms: The hydrogen atoms in the ferrocenium cations and the fluorine atoms in TFSA anion were fused with the bonded carbon atoms. Although these ions were essentially handled as rigid bodies, the butyl group in nBu-Fc+ was flexible in the MD calculations. All LJ parameters were taken from the literature, namely UFF for the iron atom,27 OPLS-UA for united atoms (CH in cyclopentadienyl anions and CH2 and CH3 in butyl groups),28 and a united atom model for CF3 in the TFSA anion.29 One might be apprehensive about the mixing use of different force field parameters. We have confirmed that the choice of the LJ parameters of the iron atom has little effect on the results shown below. This is probably because the iron atom is inside the rigid-body ferrocenium unit and does not directly contact with atoms of other ions. The intramolecular potential function for bonds, angles, and dihedrals in the flexible n-butyl group were taken from a model of the butylmethylimidazolium cation.30 Although the atomic charges of the ferrocenium cations were
a
Fe−Cp denotes the distance between the iron atom and the center of a cyclopentadienyl ring.
Table 2. Mulliken Charge of Fragments in Ferrocene (Fc), Ferrocenium Cation (Fc+), and its Tertiary Butyl and Normal Butyl Derivatives (tBu-Fc+ and nBu-Fc+) at the UB3LYP/DZVP Level [Unit: Elementary Charge (|e|)] Fc Fc+ tBu-Fc+ nBu-Fc+
Fe
Cp1a
Cp2b
Buc
−0.248 −0.315 −0.401 −0.398
0.124 0.657 0.629 0.633
0.124 0.657 0.691 0.702
0.082 0.062
a Unsubstituted cyclopentadienyl ring. bButyl-substituted cyclopentadienyl ring. cTertiary or normal butyl group.
in statistical mechanics for molecular liquids. The analytical nature and the mean field approximation of the RISM-SCFSEDD method offers an electronic-state computation of a solvated molecule at a reasonable cost. The solvation structures around the ferrocenium cations were analyzed with RDFs and spatial distribution functions (SDFs) computed by molecular dynamics (MD) calculation as well as by RISM theory. Because integral equation theory like RISM can give these functions at significantly lower computational cost than MD calculations, especially for these highly viscous ILs,9 the theory has been applied to study their liquid structures and dynamics including imidazolium-based ionic liquids.16,17 The solvation effects on chemical reactions in ionic liquids were also investigated using the RISM-SCF-SEDD method.18−20 PCM has also been utilized with the SMD model.21 In the present study, the parent ferrocenium cation (Fc+) and its tert-butyl (tBu-Fc+) or n-butyl derivatives (nBu-Fc+) were chosen as the cation in target systems. Using RISM or MD simulation, the liquid structures of ILs composed of one of these ferrocenium cations and the bis[(trifluoromethyl)sulfonyl]amide
Figure 1. Tertiary and normal butyl-substituted ferrocenium cations (green) superimposed on the ferrocenium cation (red). These structures were optimized at the UB3LYP/DZVP level. B
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obtained from natural population analysis (NPA)31,32 calculated at the UB3LYP/DZVP level, those of TFSA anion were taken from the same literature as its LJ parameters. These LJ parameters and atomic charges are listed in the Supporting Information. The MD simulation systems were composed of 256 cation and anion pairs in cubic boxes. The temperatures of the systems were set to 430 K for [Fc+][TFSA], 380 K for [tBu-Fc+][TFSA], and 330 K for [nBu-Fc+][TFSA], which are higher than the melting points (in the case of [nBu-Fc+][TFSA], the cyclopentadienyl rings were octamethylated in the experiment) by about 25 K.7−9 The systems were initially equilibrated in a NPT ensemble for 12 ns followed by 30 ns NVT production runs to obtain the RDFs and SDFs around the ferrocenium cations. The convergence of the results was checked by performing 150 ns production run for the [Fc+][TFSA] ionic liquid. In the RISM calculations, the number densities obtained from the MD calculations in NPT ensemble were adopted. The values were 0.00215 Å−3 for [Fc+][TFSA], 0.00177 Å−3 for [tBu-Fc+][TFSA], and 0.00178 Å−3 for [n-BuFc+][TFSA] IL, respectively.33 The number of the grid points was 4096, and the grid spacing was 0.05 Å. The Kovalenko−Hirata closure was employed.13,14 The obtained correlation functions were used in RISM-SCF-SEDD coupled with the CASSCF calculations. The geometry optimizations and calculations of the NPA charges were carried out with GAMESS34 and Gaussian09 programs.35 The CASSCF calculations in the gas phase and in the ILs with the RISM-SCF-SEDD method were performed by our modified version of the GAMESS program. DL_POLY 2.20 was used for the MD calculations.36
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RESULTS AND DISCUSSION Quantum Mechanical Calculations of the Ferrocenium Cations. Geometries and Atomic Charges. Table 1 lists characteristic distances at the optimized geometry of Fc+ with D5h symmetry together with the neutral ferrocene (Fc) optimized at the same level (B3LYP/DZVP). The calculated geometry of Fc is in good agreement with the experimental one (Fe−Cp, Fe−C, C−C, and C−H distances are 1.66, 2.06, 1.44, and 1.10 Å, respectively) and with the previous calculations at CCSD(T) and B3LYP levels.23 The rather small difference between Fc+ and Fc is observed in the Fe−Cp and Fe−C distances by 0.02 Å. The slightly longer distance between the iron atom and the cyclopentadienyl ring in Fc+ is attributed to an electron removal from a weakly bonding orbital composed of iron dxy or dx2−y2 and from the π orbital of the cyclopentadienyl rings (42nd or 43rd orbitals in Figure 2). The attractive electrostatic interaction between the cyclopentadienyl anions and the iron atom should be weakened, which can be verified from the Mulliken charges in Table 2. It is interesting, however, that the geometries of the cyclopentadienyl rings were hardly changed by ionization. Figure 1 shows superimposed structures of Fc+ and its butyl derivatives (tBu-Fc+ and nBu-Fc+). Substitution with a tertiary or normal butyl group does not introduce large displacement into the ferrocenium unit. Table 2 shows the charge of fragments (iron atom, two cyclopentadienyl rings, and butyl group) calculated by summing up the Mulliken atomic charges. All of the fragments in the neutral ferrocene (Fc) have small charges, implying that electrons are transferred from two cyclopentadienyl anions to the Fe(II) cation through the coordination. The charge of cyclopentadienyl fragment in Fc+ becomes more positive than that of the iron atom, and the total charge (1|e|) resides mostly on the cyclopentadienyl fragments.
Figure 2. Molecular orbitals of the ferrocenium cation relevant to the CASSCF calculations (see the main text). The index refers to the ordering of the molecular orbital, and the SOMO is the 48th orbital at the ROHF/DZVP level.
The butyl substitutions (tBu-Fc+ and nBu-Fc+) introduce small variations in the fragment charges. Because only about 0.1|e| charge is moved from the parent ferrocenium cation unit to the butyl groups, almost all charge is localized on the ferrocenium unit. The butyl groups become nonpolar fragments as in imidazolium-based ionic liquids substituted with long alkyl chains.37 Electronic Structures. Figure 2 illustrates the active orbitals with which a seven state-averaged CASSCF calculation was performed with equal weight (7SA-CASSCF(13e,11o)). The seven states are composed of three sets of doubly degenerate states (−1646.40913, −1646.30827, and −1646.28772 hartree) C
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Figure 3. RDFs obtained from MD calculations: (a) [ferrocenium][TFSA] IL; (b), (d) [tert-butylferrocenium][TFSA] IL; (c), (e) [n-butylferrocenium][TFSA] IL. CH denotes a site of cyclopentadienyl rings. CH3 denotes a methyl unit in the butyl groups (the terminal methyl unit in the tertiary butyl group).
and a remaining state (−1646.26276 hartree). In the first set of degenerate states (ground states), one of the molecular orbitals characterized by dxy or dx2−y2 (corresponding to the 42nd or 43rd orbital in Figure 2) is almost singly occupied and the other is doubly occupied in the main configuration. Other orbitals are doubly occupied or vacant. This result is consistent with previous experimental and theoretical studies.38,39 The π orbital of the cyclopentadienyl anions (corresponding to the 46th or 47th orbital in Figure 2) is almost singly occupied in the second set of the degenerate states. The main configuration in the third set is characterized as a singly occupied dxz or dyz orbital (corresponding to the 44th or 45th orbital in Figure 2). The seventh state in the 7SA-CASSCF calculation is represented as mixed configurations. The natural orbital characterized by iron dz2 (similar to the 48th orbital in Figure 2) is almost fully occupied (occupation number is 1.995), and an energy gap between the most stable degenerate states and the second ones is large (about 60 kcal/mol). Hence, the state-averaged CASSCF(11e,10o) calculation without the dz2 orbital in the active space is enough to properly elucidate the electronic structure. The same calculations were also employed to the butyl-substituted derivatives, namely the active spaces consisting of 11 electrons and ten orbitals. It is noted that the degeneracy of the ground states is resolved due to introduction of asymmetry by the butyl substitutions. The energy difference between the two states are 1.0 kcal/mol for tBu-Fc+ and 3.1 kcal/mol for nBu-Fc+, respectively; both of them are characterized by dxy and dx2−y2 orbitals as in Fc+.
Because the degenerate two ground states are characterized by the dxy and dx2−y2 orbitals, the ferrocenium cation and its butyl derivatives can have a nonzero angular-momentum orbital parallel to the z-axis.40 By diagonalizing the matrix elements of lẑ for the two orbitals (42nd or 43rd orbital in Figure 2), occupied with three electrons, we computed the z-components of the orbital angular momentum to be 1.91 for Fc+, 1.88 for tBu-Fc+, and 1.91 for nBu-Fc+, respectively. Moreover, the electron spin in the ferrocenium radical cations can interact with the orbital angular momentum to align its orientation to the same direction via the spin−orbit coupling, which can also contribute to the anisotropic magnetic moment of the ferrocenium cations. The stabilization energies obtained by aligning spin in the same z direction as the orbital angular momentum were 334 cm−1 for Fc+, 204 cm−1 for tBu-Fc+, and 96 cm−1 for nBu-Fc+, respectively, which were evaluated by using the two state-averaged CASSCF(11e,10o) wave functions. These large spin−orbit couplings indicate that the spin stays in the z-direction even when an external magnetic field (the magnitude is about 1 T in experimental conditions, and the interaction energy between the spin and such an external magnetic field is on the order of 1 cm−1) is imposed in the x or y direction. The butyl substitutions reduce the magnitude of the spin−orbit coupling of the ferrocenium cations because of the relaxation of the degenerate electronic states by substitutions; nevertheless the magnitude of the spin−orbit coupling is large enough to contribute to the magnetic anisotropy. The extent of the reduction seems to correlate with the energy difference D
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between the nearly degenerate electronic states (1.0 kcal/mol for the tertiary butyl derivative and 3.1 kcal/mol for the normal butyl derivative). Because the molecular z-axis of the ferrocenium cations are aligned in almost the same direction in the crystal structures of the ferrocenium-based ILs,9,11 and the magnetic moments of the ferrocenium cations point to the same z direction as described above, the crystals are expected to exhibit magnetic anisotropy observed experimentally.9,11 Liquid Structures of the Ferrocenium-Based Ionic Liquids. Figures 3a and 4a are the RDFs and SDFs of Fc+ and TFSA anions around a ferrocenium cation in [Fc+][TFSA] IL computed with MD simulation. As expected, a ferrocenium cation is surrounded by anions. TFSA anions direct the oxygen atoms to the ferrocenium cations because of the negative charge on these atoms (see the atomic charges listed in the Supporting Information). The first peak in the iron−oxygen RDF corresponds to the population of the oxygen atoms approaching the iron atom from the interstices between the cyclopentadienyl rings. The highest peak position corresponds to the population of TFSA anions above and below the rings. The coordination number of nitrogen atoms of TFSA anions around an iron atom is 7.4 at 9.3 Å, corresponding to the boundary of the first solvation shell. The first peak at 7.6 Å in the iron−iron RDF corresponds to the atoms at oblique directions. The coordination number of iron around an iron atom at 9.3 Å is 6.6. Hence the total numbers of cation and anion in the sphere with the radius of 9.3 Å are 7.6 (=6.6 plus the central cation) and 7.4 respectively, indicating that the local charge neutrality41 is almost satisfied. Figures 3b,c and 4b,c illustrate the RDFs and SDFs in the [t-BuFc+][TFSA] and [n-BuFc+][TFSA] ILs, respectively. The coordination numbers of the nitrogen atoms of TFSA anions around an iron atom at 9.3 Å are 6.4 for the [t-BuFc+][TFSA] and 6.3 for the [n-BuFc+][TFSA], which are smaller by about 1.1 than that for the [Fc+][TFSA]. The oxygen atoms in TFSA anions are directed toward cations, and other cations tend to reside at oblique directions as in the case of the [Fc+][TFSA], but further anisotropy appears in the distribution. The coordination number of iron atoms around an iron atom at 9.3 Å is 5.1 for both the [t-BuFc+][TFSA] and [t-BuFc+][TFSA] ILs, which is smaller by 1.5 than that for the [Fc+][TFSA]. The smaller coordination numbers in these butyl-substituted ILs are due to the larger excluded volume. This can be understood from a slightly different viewpoint that a smaller number of ions is necessary to solvate a cation because the electrostatic potential becomes weaker due to the large distance from the ion. It should be noted that the local charge neutrality is almost satisfied also in these ILs; there are about 6.1 cations and 6.4 anions in the sphere with radius of 9.3 Å centered in the cation. The distributions observed in the [Fc+][TFSA] IL are disturbed by butyl substitutions. The populations of the anion atoms disappear around the butyl group and instead the butyl group in other cations are populated. This is probably because the butyl group has a small positive charge of about 0.1|e| and the nonelectrostatic interaction becomes rather dominant between neighboring butyl groups. This tendency seems to be enhanced in [n-BuFc+][TFSA] than in [t-BuFc+][TFSA] as observed in the RDFs and SDFs; the first peak of CH3−CH3 RDF and the distribution of the methyl unit around the butyl group in [n-BuFc+][TFSA] are distinct and larger than those in [t-BuFc+][TFSA]. The coordination numbers at 7.0 Å are 2.4 for the [n-BuFc+][TFSA] and 1.9 for the [t-BuFc+][TFSA], respectively. Similar behavior has been observed in imidazolium-based
Figure 4. SDFs obtained from MD calculations. Color: (red) oxygen atom, (blue) nitrogen atom, (yellow) sulfur atom, (gray) CF3 group, (cyan) terminal methyl group, and (purple) iron atom. (a) [ferrocenium][TFSA] IL. The values of the isosurfaces are 5 times and 4 times as large as the bulk density for the anion atoms and cation atom. (b) [tertbutylferrocenium][TFSA] and (c) [n-butylferrocenium][TFSA] ILs. The values of the isosurfaces are 5 times as large as the bulk density for the anion atoms and iron atom and 3 times as large as the bulk density for the CH3 methyl group.
ionic liquids in which the cations are substituted with a long alkyl chain.37 Note that the long alkyl chains (≥C6) are experimentally observed to be in contact with each other in the crystals of the ferrocenium-based ILs, though such alignment was not observed in the crystal structure of ([butyloctamethylferrocenium][TFSA] IL with the shorter chain (C4).9 Figure 5 displays the same set of RDFs obtained from the RISM calculations. The overall shapes and peak positions of the RDFs between cations (iron atoms) and anions are in good agreement with those from the MD calculations in Figure 3, though the peak heights are slightly underestimated, as is often E
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Figure 5. RDFs obtained from RISM calculations: (a) [ferrocenium][TFSA] IL; (b), (d) [tert-butylferrocenium][TFSA] IL; (c), (e) [n-butylferrocenium][TFSA] IL. The other things are the same as those in Figure 3.
the case with the Kovalenko−Hirata closure.14 A noticeable difference between the results from the MD and RISM calculations is observed in iron−iron RDF. The position of the rise, where RDFs start to have nonzero values, is at a remarkably short distance in the RISM calculations compared to that in MD. The coordination numbers of the cations shorter than the point (6.0 Å) are, however, less than 1, indicating that the difference in the solvation effect is expected to be not so large. It is interesting to note that the characteristic features of the methyl−methyl RDFs are well reproduced from the RISM calculations. Consequently, the results from RISM and from MD show overall agreement. Considering the significant saving of computational cost, RISM is a useful tool to study the liquid structures and the solvation effect on the ferrocenium cations for the ferrocenium-based ILs. Solvation Effects on the Electronic Structures of the Ferrocenium Cations. Because IL consists of cations and anions, it is often thought that electronic states of molecules in IL are significantly affected by electrostatic interactions between the molecule and surrounding ions. This means that the magnetic properties of the constituent ferrocenium cations could be also changed from those in the isolated state. We thus performed RISM-SCF-SEDD calculations coupled with CASSCF to investigate the solvation effects. The same procedure with the gas phase computation was repeated in RISM-SCF-SEDD calculations for IL environment. Namely, a seven-state-averaged CASSCF(13e,11o) calculation was first carried out for Fc+. Because the obtained seven states in the ILs are essentially similar to those in the gas phase, the same two state-averaged
CASSCF(11e,10o) coupled with RISM-SCF-SEDD calculations was carried out. The degenerate ground states in the parent ferrocenium cation originated from the symmetry remain unchanged because the solvation structure possess also the same symmetry. The near degeneracies of the tertiary and normal butyl derivatives are slightly affected by solvation; the energy differences between the states are changed from those in the gas phase by less than 1 kcal/mol (1.2 kcal/mol for tBu-Fc+ and 2.7 kcal/mol for nBu-Fc+). These results indicate that the magnetic property of the ferrocenium cations in the ILs is not so much affected by solvation. Such a small effect on these states may be understood in terms of the localization of the important orbitals. Because all of the orbitals in the active spaces are essentially localized on the ferrocenium unit, it is likely that the solvation effects on these orbitals become very similar, and consequently their energy differences are not significantly changed by solvation. From a viewpoint of liquid structure, the lower number density due to the bulkiness of the cation gives rise to this moderate solvation effects, similar to other IL system.18 The alteration of the magnetic property may be achieved by the modification of cyclopentadienyl ring. The Mulliken charges of the ferrocenium cations are as shown in Table 3. The small amount of electron is moved to the cyclopentadienyl rings from the iron atom and the butyl groups to enhance the dipole moment (with respect to the center of mass) from 2.34 to 3.45 D for tBu-Fc+ and from 3.86 to 5.05 D for nBu-Fc+, respectively. If a strong electron-withdrawing or electron-donating F
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Table 3. Mulliken Charge of Fragments in Ferrocenium Cation (Fc+) and Its Tertiary Butyl and Normal Butyl Derivatives (tBu-Fc+ and nBu-Fc+) in Ionic Liquid Composed of each Cation and TFSA Anion at the 2SA-CASSCF(11e,10o)/DZVP Levela +
Fc tBu-Fc+ nBu-Fc+
Fe
Cp1b
Cp2c
Bud
−0.325 (−0.376) −0.322 (−0.354) −0.316 (−0.361)
0.663 (0.688) 0.633 (0.630) 0.627 (0.631)
0.663 (0.688) 0.644 (0.660) 0.622 (0.648)
0.045 (0.064) 0.067 (0.082)
a
Values in parentheses refer to those in the gas phase. The unit is elementary charge (|e|). bUnsubstituted cyclopentadienyl ring. cButyl-substituted cyclopentadienyl ring. dTertiary or normal butyl group.
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substituent is introduced instead of the butyl groups, the orbitals in active space and magnetic properties of the ferrocenium cation in the gas phase and in its IL can be rather different from those studied in the present work.
Corresponding Authors
*H. Nakano. E-mail: [email protected]. *H. Sato. E-mail: [email protected].
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Notes
CONCLUDING REMARKS We have investigated the electronic and magnetic properties of the ferrocenium radical cation and its butyl-substituted derivatives from CASSCF calculations in the gas phase and in the ferrocenium-based ionic liquids by using the RISM-SCFSEDD method. The liquid structures of the ionic liquids consisting of those ferrocenium cations and TFSA anions were also studied by molecular dynamics and RISM calculations. The ferrocenium cations have (nearly) degenerate ground states characterized by the dxy and dx2−y2 orbitals of the iron atom. This means that the ferrocenium cations have orbital angular momentum along the line connecting the centers of the cyclopentadienyl rings. The magnitude of the spin−orbit couplings were on the order of 100 cm−1, indicating that the electronic spin tends to be parallel to the orbital angular momentum and contributes to the magnetic anisotropy. Though the butyl substitutions relax the degeneracy of the electronic ground states and reduce the orbital angular momentum and spin−orbit coupling to some extent, the crystals of the ionic liquids composed of these cations are still expected to exhibit magnetic anisotropy. The electronic states of the ferrocenium cations in the ionic liquids were not so much different from those in the gas phase. This is because the (nearly) degenerate states were symmetrical and solvation structures were also symmetric due to the symmetrical structures of the ferrocenium cations. The fact that all of the important orbitals were localized on the ferrocenium unit is also relevant. This result suggests that the magnetic properties of ferrocenium cations in the ionic liquids resemble those in the gas phase. The molecular dynamics calculations showed that the ferrocenium cations are surrounded by seven TFSA anions, which seems to form the first solvation shell. The TFSA anions direct the oxygen atoms to the ferrocenium cations. Neighboring cations reside at oblique directions. The butyl groups perturbed such solvation structures around the ferrocenium cations and attract other butyl groups such as those in alkylmethylimidazolium ionic liquids. Though the distance between the neighboring ferrocenium cations was underestimated, the RISM calculations give RDFs in overall good agreement with those from the MD calculations with significantly lower computational cost.
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AUTHOR INFORMATION
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS The authors are grateful to Mr. K. Hoshihara for the preliminary computation. The work was financially supported in part by Grants-in-Aid for Scientific Research on Innovative Areas “Dynamical ordering of biomolecular systems for creation of integrated functions” (25102002) and Grant-in-Aid for Scientific Research (C) (25410011). A part of this work was performed under a management of “Elements Strategy Initiative for Catalysts & Batteries (ESICB)”. Theoretical computations were partly performed using the Research Center for Computational Science, Okazaki, Japan. The Strategic Programs for Innovative Research (SPIRE), the Computational Materials Science Initiative (CMSI), is also acknowledged. All of them were supported by the Ministry of Education, Culture, Sports, Science and Technology (MEXT) Japan. The manuscript is dedicated to Prof. Jacopo Tomasi.
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ASSOCIATED CONTENT
S Supporting Information *
Potential parameters for Fc+, TFSA, tBu-Fc+, and nBu-Fc+. United atom models of tBu-Fc+ and nBu-Fc+. This material is available free of charge via the Internet at http://pubs.acs.org. G
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