Theoretical insights into PF6− and its alkali metal ion pairs: geometries and vibrational frequencies

Electrochimica Acta 50 (2005) 4196–4201

Short communication PF6− and its alkali

Theoretical insights into metal ion pairs: geometries and vibrational frequencies Xiaopeng Xuan a, b , Jianji Wang a, ∗ , Hanqing Wang b b

a Department of Chemistry, Henan Normal University, Xinxiang, Henan 453002, PR China Lanzhou Institute of Chemical Physics, Chinese Academy of Sciences, Lanzhou, Gansu 730000, PR China

Received 29 October 2004; received in revised form 24 January 2005; accepted 25 January 2005 Available online 25 February 2005

Abstract The structures, vibrational frequencies, infrared and Raman intensities of hexafluorophosphate anion (PF6 − ) and M+ PF6 − (M+ = Li+ , Na+ , K , Rb+ and Cs+ ) ion pairs have been studied by ab initio calculations. It is shown that the tridentate coordination of cation by PF6 − is the most stable structure in gas phase. The vibrational spectroscopies of the most stable geometries were calculated and the changes in band position were used to probe the ion associations. © 2005 Elsevier Ltd. All rights reserved. +

Keywords: Ion pair; Hexafluorophosphate; Vibrational frequency; Ab initio calculation

The lithium salts used in liquid electrolytes for lithium battery preferably have large-sized univalent anions with a strongly delocalized charge to reduce viscosity and enhance conductivity of electrolytic solutions. The traditional inorganic (such as ClO4 − , BF4 − , PF6 − , AsF6 − ), and new developed organic anions (CF3 SO3 − and (CF3 SO2 )2 N− ) are most commonly considered [1]. High ionic conductivity for an appropriate lithium salt is the basic requirement. Therefore, the ion pair formation in solutions is undesirable because it reduces the number of effective carriers in the electrolyte, increases the viscosity of electrolyte and affects the ion intercalation into electrode. Unfortunately, ion association often occurs in the commercial electrolyte of lithium battery since its concentration is at least 1 M. It is believed that different types of ionic species make different contributions to the total ionic conductivity and the process of lithium electrochemical intercalation [1]. Knowledge of the extent of association of electrolyte solutions, and the type, structure and the lifetime of the ion pair in solutions used in lithium battery, are relevant information on understanding the mechanism of ion conduc∗

Corresponding author. Tel.: +86 37 3332 6544; fax: +86 37 3332 6544. E-mail address: [email protected] (J. Wang).

0013-4686/$ – see front matter © 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.electacta.2005.01.045

tion at molecular level and on choice and optimization for new liquid electrolytes for electrochemists. Experimentally, vibrational spectroscopies [2–8] and conductivity measurements [9–11] have been proved to be powerful techniques for probing ion associations. As a noted example, Raman spectra of LiClO4 in several organic solvents have been extensively studied [2,3,7], and three bands, at 931, 938 and 945 cm−1 , have been used to fingerprint the free anion, contact ion pair and dimer, respectively. Ab initio calculations have also been an important tool to evaluate interactions between cation and anion [12–18]. Some authors [12,16] have studied the structures and spectral changes of Li+ ClO4 − with different geometries. The bidentate structure was found to be preferred over the monodenate or tridentate structures. Although LiPF6 is now in practical use for lithium ion battery, little structural information is available for the Li+ PF6 − ion pairs [15]. The reason is mainly due to the thermal instability, moisture sensitivity [19] and lower solubility of hexafluorophosphate [1]. For example, Borodin and co-workers have studied interactions between LiPF6 and poly(ethylene-oxide) and the partial information of Li+ PF6 − ion pairs are given. The knowledge of other M+ PF6 − (M = Na+ , K+ , Rb+ and Cs+ ) ion pairs is even absent in literature, which are difficult

X. Xuan et al. / Electrochimica Acta 50 (2005) 4196–4201

to form in the solutions because of the large cation radius, and their structural parameters calculated using electron correlation methods at large basic set is acceptable. In the present paper, we perform a detailed study using ab initio calculations to characterize the structures of PF6 − and its alkaline metal ion pairs M+ PF6 − (M = Li+ , Na+ , K+ , Rb+ and Cs+ ). Furthermore, the vibrational spectra and frequency shifts for ion pairs have been calculated and discussed based on the energetically favorable structure.

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effective core potentials (ECPs) of Hay and Wadt [21], LANL2DZ and SDD, were used for the Rb and Cs atoms, and 6-311 + G(d) for others. It is found that the polarization function is very important for these calculations. Partial atomic charges are obtained from a Mulliken population analysis. The zero-point energies and vibrational frequencies were not corrected. The relative energies are defined as E = E(M+ PF6 − ) − E(M+ ) − E(PF6 − ). 2. Results and discussions

1. Computational methods

2.1. Free PF6 − anion

All the calculations have been carried out using Gaussian98 program suite [20]. Geometry optimization, following the preliminary calculations at HF/6-31G* level, was performed using the tight convergence criterion. Symmetry constrains were applied for each desired coordination geometry in order to minimize the computational cost. Vibrational frequency was calculated at the same computational level with geometry optimization and then used to evaluate the zero-point vibrational energy (ZPVE). The HF and DFT (B3LYP) methods were used for all the systems studied, and MP2 for the selected. For Li+ PF6 − , Na+ PF6 − and K+ PF6 − systems, the calculations were carried out using the following basis sets: D95 + (d), D95 + (2d), 6-31G(d), 6-31 + G(d), 6-311G(d), 6-311 + G(d), 6-311 + G(2d) and 6311 + G(2df). For Rb+ PF6 − and Cs+ PF6 − ion pairs, the

Free PF6 − anion has octahedral symmetry (Oh ) and the bond angle formed by F P F is found to be exactly 90◦ . The optimized P F bond lengths at different basis sets are given in Table 1. Different experimental bond lengths for P F have been reported in literature. Wang et al. [21] cited a value of ˚ arising from the X-ray crystallographic data 1.568–1.592 A ˚ was also obof (CH3 )4 NPF6 , a less value of 1.555–1.556 A tained form P(C6 H5 )4 PF6 crystal [22]. As can be seen in Table 1, the optimized P F bond length is slightly greater than ˚ at the experimental one. The best predicted value is 1.5897 A the HF/6-311 + G(2df) level, and the optimization at B3LYP or MP2 level results in an increase in P F bond length. The greater is the polarization function, the more reasonable is the bond length. On the other hand, the energy follows the order HF > MP2 > B3LYP at the same basis set. It must be

Table 1 Optimized bond lengths, energies and frequencies for free PF6 − aniona Method

HF/d95 + (d) HF/d95 + (2d) HF/6-31g(d) HF/6-31 + g(d) HF/6-311g(d) HF/6-311 + g(d) HF/6-311 + G(2df) B3LYP/d95 + (d) B3LYP/d95 + (2d) B3LYP/6-31g(d) B3LYP/6-31 + g(d) B3LYP/6-311g(d) B3LYP/6-311 + g(d) B3LYP/6-311 + g(2df) MP2/d95 + (2d) MP2/6-31g(d) MP2/6-31 + g(d) MP2/6-311g(d) MP2/6-311 + g(d) Expt. a b c d

F P length

1.6160 1.6006 1.6057 1.6092 1.6005 1.6025 1.5897 1.6588 1.6393 1.6373 1.6485 1.6401 1.6458 1.6292 1.6386 1.6365 1.6481 1.6285 1.6348 1.568–1.592b ; 1.555–1.556c

Energy

−937.7766866 −937.8215483 −937.6027092 −937.6391342 −937.7779926 −937.7968325 −937.8787707 −940.8585456 −940.9025238 −940.6431734 −940.7159646 −940.8657778 −940.896614 −940.9635409 −939.1827519 −938.7668506 −938.8412914 −939.1392923 −939.1807623 –

˚ and frequency in cm−1 . Energy in a.u., bond length in A Ref. [21]. Ref. [22]. Ref. [23].

ZPVE

0.020764 0.020408 0.021101 0.020807 0.020989 0.020801 0.020940 0.018257 0.018187 0.019130 0.018322 0.018675 0.018175 0.018555 0.018300 0.019647 0.018792 0.019521 0.018882 –

Frequency (cm−1 ) t2u

t2g

t1u

eg

a1g

t1u

323.2 323.4 323.6 325.1 331.4 332.9 333.6 283.0 286.9 287.2 283.5 291.3 288.6 295.2 283.9 296.3 289.6 306.3 301.1 –

486.2 497.0 490.1 494.9 502.4 503.9 503.5 428.2 442.7 440.0 435.6 443.9 439.6 447.6 443.1 450.2 445.1 466.0 455.9 470d

594.7 590.5 587.6 596.7 602.6 599.9 604.5 523.9 529.6 528.4 524.5 534.4 526.0 539.5 527.9 540.4 538.8 560.2 547.5 558d

620.0 603.0 643.9 617.2 610.1 602.6 613.8 548.8 538.9 594.1 547.9 553.8 531.8 544.2 546.2 610.6 562.0 572.0 549.3 567d

791.7 790.3 799.5 791.8 790.6 787.2 813.5 684.4 694.2 719.2 689.8 693.0 678.4 706.4 700.9 737.9 708.1 720.2 703.6 741d

956.8 909.8 990.4 952.4 964.5 942.7 941.9 842.1 811.2 907.7 842.1 862.6 824.5 834.4 824.9 934.8 865.4 902.4 857.5 838d

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pointed out that no experimental technique permits study of the isolated free anion in solutions and our calculations are based on the assumption of free anion in gas phase. Thus, the results of MP2 and DFT calculations are more acceptable than those of HF. The free FP6 − anion has 15 vibration modes and can be represented as: Γ = a1g + eg + 2t1u + t2g + t2u Of these modes, ν1 (a1g ), ν2 (eg ) and ν5 (t2g ) are Raman active, ν3 (t1u ) and ν4 (t1u ) are IR active, while the t2u is inactive. The experimental result [23] obtained from the solid PEOLiPF6 gives the vibrational frequencies: ν1 = 741, ν2 = 567, ν3 = 838, ν4 = 558 and ν5 = 470 cm−1 . All of our calculations produce a reasonable frequency corrected by scaling the respective factor. For example, the calculation at B3LYP/6311 + G(2df) level gives the unscaled values: ν1 = 706.4, ν2 = 544.2, ν3 = 834.4, ν4 = 539.5 and ν5 = 447.6 cm−1 (see Table 1). In general, the frequency of PF6 − calculated by MP2 method is closer to the experimental value than those by HF and B3LYP methods. Additionally, all methods predict higher intensity for ν3 and ν4 infrared vibrations and ν1 Raman vibration. This agrees well with the experimental data reported in literature [24]. 2.2. Structures of M+ PF6 − ion pair There are three obvious modes of coordination for Li+ PF6 − ion pairs: monedentate a (C4V ), bidentate b (C2V ), and tridentate c (C3V ) as shown in Fig. 1. Among these coordination modes, the structure c, C3V symmetry, is the global minimum on the potential energy surface. Complex of C4V has one imaginary, indicating a saddle point. The situation for C2V structure is very complicated. The calculation indicates that this structure is a true minimum on potential energy surface at B3LYP/6-311G(d), B3LYP/6-31 + G(d), B3LYP/6311 + G(d), MP2/6-311G(d), MP2/6-311 + G(d) and all the HF levels, and is a saddle point at other levels. The energies of these three structures are collected and compared for further study. It is found that the stability for the Li+ PF6 − ion pairs follows the order C3v > C2v > C4v at all levels of calculations. This is in agreement with the results reported in literature [15,24]. The basis sets and electron correlation ef-

Fig. 1. Coordination geometries of Li+ PF6 − ion pairs: (a) monodentate (C4V ); (b), bidentate (C2V ) and (c) tridentate (C3V ).

fects strongly affect the values of energy, but not the order of stability. Generally, the total energy calculated by HF method is about 3.1 Hartree higher than those by DFT and 1.2 Hartree by MP2. The HF calculation always overestimates the energies. Apparently, the contribution of electron correlation effect to the total energy is large, and there are significant contributions for the core electrons of the valence molecular orbital to the ion pairs. Considering the relative energies, the order follows as: tridentate < bidentate < monodentate, and the relative energies for the bidentate and tridentate structures remain relatively close, and the difference in energy generally at the same level is below 10 kJ/mol. It is also found that basis sets with diffuse function are important for systems, and the lack of this function make a significant error in accuracy. The differences in relative energies for a structure are about 50–100 kJ/mol varied with the basis set. For the M+ PF6 − (M = Na, K, Rb and Cs) systems, the C3V structure is the most stable, the C2V structure is the first-order saddle point on the potential energy surface, and the C4V structure is the second-order saddle point due to the presence of two imaginary frequencies. The reason why the tridentate structure is favored can be explained by population analysis using ChelpG method at MP2/6-311 + G(d) level. For example, the partial charge of Li+ in Li+ PF6 − ion pair with C3V and C2V structures are 0.8945 and 0.9019, respectively. The corresponding values for F atom are −0.4977 and −0.5247, where the superscript  indicates that the atom is the closest to Li+ . The greater difference in charge between Li+ and F atoms (0.3968) in the C3V structure suggests a stronger coordination than in C2V structure (0.3772). In addition, amongst these three structures, the relative energies of structure c is the lowest, indicating the strongest interaction between Li+ and PF6 − anion. It is reported experimentally that the mid-IR active mode, ν(t1u ), of an isolated anion splits into two bands, demonstrating that the symmetry of PF6 − in the coordination is lowered to C3v structure from original Oh point group [25]. In the tridentate structure, the PF6 − is strongly distorted from its original octahedral structure (Table 2). The calculated tendency of the structural parameters is similar for M+ PF6 − ion pairs. For example, the P F bond length in˚ in Li+ PF6 − to 1.6121 A ˚ in Cs+ PF6 − . creases from 1.5760 A The latter value is close to the calculated value of P F in PF6 − ˚ The bond angles decrease for both F P F and (1.6292 A). F P F, but increases for F P F , with increasing cation radius. The structure differences between free PF6 − and PF6 − in M+ PF6 − ion pairs become smaller and smaller from Li+ to Cs+ . This indicates that the greater effect of Li+ on the structure of PF6 − is due to its larger charge/radius ratio. Moreover, the bond lengths of M+ F and M+ P increase from Li+ to Cs+ as expected. Also, the change tendency for the bond lengths of M+ PF6 − ion pairs was similar to the single crystal experimental results of alkaline metals hexafluorophosphate [26]. The calculated bond length for Na+ F , ˚ at HF/6-311G(d) and 2.244 A ˚ at B3LYP/6-311G(d) 2.245 A

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Table 2 Selected geometry parameters for M+ PF6 − ion pairsa PF6 −b M+ –F M+ –P P–F P–F F –Li–F F –P–F F –P–F F–P–F q(M+ ) q(P) q(F ) q(F) ␮ a b c

– – – 1.6292 – – 90 – 0.527716 – −0.2624 0

Li+ PF6 −b

Na+ PF6 −b

K+ PF6 −b

Rb+ PF6 −c

Cs+ PF6 −c

1.8913 2.4432 1.6939 1.5760 73.564 90.515 73.564 94.576 0.501492 0.523872 −0.183162 −0.158626 6.7042

2.2311 2.8385 1.6799 1.5853 61.627 90.175 85.736 93.644 0.705549 0.507303 −0.230140 −0.174144 9.5415

2.5597 3.2141 1.6716 1.5907 53.158 90.087 86.492 93.142 0.886977 0.526568 −0.291862 −0.179320 11.4770

2.7858 3.4759 1.6842 1.6100 48.953 90.167 86.522 92.9641 0.955015 0.593236 −0.342775 −0.173308 13.8155

2.9620 3.6688 1.6814 1.6121 45.899 90.150 86.768 92.775 0.943222 0.583523 −0.337485 −0.171430 14.3509

˚ angle in ◦ , Mulliken charge in e, dipolar moment in D. Energy in a.u., bond length in A, At B3LYP/6-311 + G(2df). At B3LYP/6-311 + G(d) level for P and F atoms and B3LYP/SDD for Rb and Cs atoms.

˚ levels, agrees well with the experimental value (2.262 A) for solid NaPF6 [26]. The other bond lengths for cation–F are slightly smaller than the experimental value. Although ˚ is the shortest among the the Li+ –F bond length (1.8913 A) M+ PF6 − ion pairs, the bond angle for F Li F is the largest (73.564◦ ). This indicates the effect of cation radius. Additionally, the Mulliken charge of cations shows that more charge transferred from Li+ to the anion. Accordingly, the dipolar moment of the M+ PF6 − ion pairs decrease from Li+ to Cs+ . 2.3. Vibrational spectra of M+ PF6 − ion pairs Coordination of a cation to PF6 − will lower the symmetry of PF6 − from Oh to C3V point group. Thus, the 18 vi-

bration modes for M+ PF6 − ion pairs can be represented as Γ = 5A1 + A2 + 6E. The calculated frequencies, infrared and Raman intensities for Li+ PF6 − were collected in Table 3, and assignments were made. It can be seen that all of the modes of Li+ PF6 − , except for the ν(a2 ) band at 275.1 cm−1 , are IR and Raman active. We are interested in the following three bands: ν(a1 ) = 669.5(Raman), ν(a1 ) = 891.2(IR), ν(e) = 891.9(IR) cm−1 , which have high intensities and can be easily determined in the experiments. All of these three bands in ions pairs shift compared with the free PF6 − anion. For instance, the band at about 891 cm−1 upshifts 30–57 cm−1 compared with the free anion. The P F symmetric stretch shifts towards lower wavenumber. This situation was also observed in the calculations of Li+ BF4 − and Li+ ClO4 − ion pairs [3,6,16].

Table 3 Unscaled frequencies, infrared and Raman intensities for free PF6 − and Li+ PF6 − ion pair (C3V ) at B3LYP/6-311 + G(2df) level Position (cm−1 )

Infrared intensity (km mol−1 )

Raman intensity (a4 /amu)

Mode

Assignment

PF6 295.1 447.6 539.5 544.1 706.4 834.43

0.00 0.00 24.56 0.00 0.00 472.22

0.00 0.82 0.00 2.07 12.1 0.00

t2u t2g t1u eg a1g t1u

δ(FP) ρ(FP) δ(FP), νa (FP) νas (FP) νs (FP) νa (FP)

Li+ PF6 − 222.9 275.1 324.2 438.7 444.4 510.0 542.1 545.6 572.1 669.5 891.2 891.9

19.68 0.00 0.01 45.46 6.13 5.94 197.23 97.58 56.02 59.77 295.40 390.16

0.14 0.00 0.05 0.93 0.75 0.63 0.06 0.59 0.04 12.28 1.42 0.75

e a2 e e a1 e a1 e a1 a1 a1 e

δ(LiF3  ) ρ(F3 PF3  ) δ(F3 PF3  ), (LiF ) δ(F3 PF3  ), δ(LiF3  ) δ(F3 PF3  ) δ(FPF ), νa (PF ) νa (FPF ) δ(F3 PF3  ), νa (F3 PF3  ) δ(F3 PF3  ) νs (F3 PF3  ) νa (F3 P) νa (F2 P)

−

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Fig. 2. The calculated infrared (left) and Raman (right) spectra of M+ PF6 − ion pairs. The basis set used is the same as that in Table 2.

Fig. 2 shows the calculated infrared and Raman spectra of PF6 − and M+ PF6 − . In Raman spectra, a strong Raman peak ascribed to P F symmetric stretch is found in the 663–706 cm−1 regions and slightly shifts towards the lower wavenumbers from Li+ to K+ . The first and second strongest  infrared bands, P–F–F and F–P–F asymmetric stretchings, locate in the 845–895 cm−1 region, and they shift toward the lower wavenumber with increasing cation radius. It can be seen from Fig. 2 and Table 3 that the positions of these bands are largely different from these of free PF6 − . Therefore, this difference could be used to probe the presence of ion pairs in solutions as identified by some authors [15,25]. In fact, Perelygin et al. [25] determined experimentally the infrared spectra of NaPF6 and LiPF6 in several organic solvents. They observed three bands in this region. The band at 843 cm−1 was assigned to the free PF6 − , and the other two bands at 852 and 860 cm−1 were assigned to the contact ion pairs. The bands at 844, and 867 cm−1 in LiPF6 /DMC solutions were also ascribed to the free anion and tridentate ion pair, respectively [15]. In summary, this paper reported the possible geometries and vibrational spectra of M+ PF6 − (M+ = Li+ , Na+ , K+ , Rb+ and Cs+ ) ion pairs. The tridentate C3V structure was preferred over the monodentate and bidentate geometry. In the tridentate structure, the symmetry of PF6 − in the coordination is lowered to C3v structure from original Oh point group, and its structural parameters and vibrational modes largely differ from its original octahedral structure. Effect of Li+ on the structure of PF6 − is greater due to its larger charge/radius ratio. The P F symmetric stretch and other typical bands shift to lower wavenumber compared with the free PF6 − anion. The calculated spectra may serve as a basis for identification of the composition and the structure of ion association during experimental studies of particular electrolyte systems.

Acknowledgments Financial support from the National Natural Science Foundation of China (29973009) and Youth Science Foundation of Henan Normal University (2004007) are gratefully acknowledged.

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