Supporting Information

Systematic Estimation and Interpretation of Fractional Free Volume in 1-Alkyl-3-methylimidazolium-based

Ionic Liquids

Takatsugu Endo,* Yuji Nishisaka, Youn Kin, and Yoshifumi Kimura

Department of Molecular Chemistry and Biochemistry, Faculty of Science and Engineering, Doshisha University,

1-3 Tatara Miyakodani, Kyotanabe-shi, Kyoto-fu 610-0394, Japan

Table S1. Experimental IL density (kg m−3) at 298 K used in this study.

Cation Anion

[[BF4]BF4]− [[PF6]PF6]− [[NTf2]NTf2]−

[C1mim]+ - - 1570 ± 2 [1]

[C2mim]+ 1280 ± 1.1 [2] - 1518.5 ± 2.7 [3]

[C3mim]+ 1237.91 ± 0.48 [4] - 1474.44 ± 0.33 [5]

[C4mim]+ 1201.36 ± 0.41 [6] 1367.3 ± 2.9 [7] 1436.3 ± 2.1 [8]

[C5mim]+ 1172 ± 10 [9] 1327.8 ± 0.7 [10] 1403.4 ± 1.1 [11]

[C6mim]+ 1145.4 ± 0.4 [12] 1293.14 ± 0.56 [13] 1372 ± 0.55 [14]

[C7mim]+ - 1262.6 ± 0.6 [10] -

[C8mim]+ 1104.2 ± 0.4 [12] 1235.7 ± 3.2 [15] 1320.59 ± 0.25 [16]

[C9mim]+ 1087.19 ± 0.39 [4] 1212.6 ± 0.93 [17] -

[C10mim]+ 1072 ± 13 [18] - 1278.4 ± 0.23 [19]

[C10mim]+ - - -

[C12mim]+ - - 1244.7 ± 2 [20]

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Table S2. Estimated ion volumes and their differences.

VQCC

(conformer

1a) / Å3

VQCC

(conformer

2b) / Å3

VQCC

(conformer

3c) / Å3

VQCC

(average) /

Å3

VBondi /

Å3

VQCC

(average) –

VBondi / Å3

[C1mim]+ 98.3 ± 0.1 98.3 ± 0.1 99.5 −1.2 ± 0.1

[C2mim]+ 115.2 ± 0.2 113.8 ± 0.2 114.5 ± 0.2 116.5 −2.0 ± 0.2

[C3mim]+ 131.9 ± 0.3 131.1 ± 0.3 130.5 ± 0.3 131.1 ± 0.2 133.5 −2.4 ± 0.2

[C4mim]+ 148.7 ± 0.3 147.2 ± 0.3 147.0 ± 0.4 147.6 ± 0.2 150.5 −2.9 ± 0.2

[C5mim]+ 165.2 ± 0.4 165.3 ± 0.5 163.1 ± 0.4 164.5 ± 0.2 167.5 −3.0 ± 0.2

[C6mim]+ 182.8 ± 0.4 183.4 ± 0.4 183.2 ± 0.5 183.1 ± 0.3 184.5 −1.4 ± 0.3

[C7mim]+ 199.7 ± 0.5 197.1 ± 0.9 200.9 ± 0.5 199.6 ± 0.3 201.5 −1.9 ± 0.3

[C8mim]+ 215.4 ± 0.4 214.4 ± 0.8 217.9 ± 0.5 215.9 ± 0.3 218.5 −2.6 ± 0.3

[C9mim]+ 232.8 ± 0.4 230.7 ± 0.7 230.2 ± 0.8 231.4 ± 0.4 235.5 −4.1 ± 0.4

[C10mim]+ 249.2 ± 0.5 246.9 ± 0.9 251.3 ± 0.9 249.1 ± 0.4 252.5 −3.4 ± 0.4

[C11mim]+ 267.9 ± 0.9 267.4 ± 1.2 268.3 ± 1.2 267.9 ± 0.6 269.5 −1.6 ± 0.6

[C12mim]+ 281.6 ± 0.8 282.1 ± 1.2 286.0 ± 1.0 283.1 ± 0.6 286.5 −3.4 ± 0.6

[BF4]BF4− 52.4 ± 0.2 52.4 ± 0.2 50.5 1.9 ± 0.2

[PF6]PF6− 69.7 ± 0.1 69.7 ± 0.1 74.2 −4.5 ± 0.1

[NTf2]NTf2− 150.6 ± 0.3 150.4 ± 0.4 150.5 ± 0.2 158.7 −8.2 ± 0.2

aConformer 1 represents non-planar for [C2mim]+, trans for [NTf2]NTf2−, and TT for [Cnmim]+ where n = 3 to 12.

bConformer 2 represents planar for [C2mim]+, cis for [NTf2]NTf2−, and GT for [Cnmim]+ where n = 3 to 12.

cConformer 3 represents G’T for [Cnmim]+ where n = 3 to 12.

Table S3. Estimated ion pair volumes.

VQCC (cation +

anion) / Å3

VQCC(IP) / Å3

VBondi /

Å3

[C1mim]BF4 150.8 ± 0.2 143.6 ± 0.2 150.0

[C2mim]BF4 166.9 ± 0.2 161.2 ± 0.2 167.0

[C3mim]BF4 183.6 ± 0.2 178.5 ± 0.3 184.0

[C4mim]BF4 200.0 ± 0.2 196.2 ± 0.3 201.0

[C5mim]BF4 217.0 ± 0.3 213.0 ± 0.4 218.0

[C6mim]BF4 235.5 ± 0.3 230.0 ± 0.4 235.0

[C7mim]BF4 252.1 ± 0.4 248.0 ± 0.5 252.0

[C8mim]BF4 268.4 ± 0.4 263.4 ± 0.6 269.0

[C9mim]BF4 283.8 ± 0.4 282.9 ± 0.7 286.0

[C10mim]BF4 301.5 ± 0.4 297.2 ± 0.8 303.0

[C11mim]BF4 320.3 ± 0.6 316.9 ± 0.7 320.0

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[C12mim]BF4 335.6 ± 0.6 332.0 ± 0.7 337.0

[C1mim]PF6 168.1 ± 0.2 162.9 ± 0.4 173.7

[C2mim]PF6 184.2 ± 0.2 178.9 ± 0.4 190.7

[C3mim]PF6 200.9 ± 0.2 196.3 ± 0.4 207.7

[C4mim]PF6 217.3 ± 0.2 214.9 ± 0.3 224.7

[C5mim]PF6 234.3 ± 0.3 230.4 ± 0.4 241.7

[C6mim]PF6 252.8 ± 0.3 246.2 ± 0.7 258.7

[C7mim]PF6 269.3 ± 0.3 263.4 ± 0.9 275.7

[C8mim]PF6 285.6 ± 0.3 281.9 ± 0.7 292.7

[C9mim]PF6 301.1 ± 0.4 297.0 ± 0.7 309.7

[C10mim]PF6 318.8 ± 0.4 315.5 ± 1.1 326.7

[C11mim]PF6 337.6 ± 0.6 334.3 ± 1.1 343.7

[C12mim]PF6 352.9 ± 0.6 348.0 ± 1.0 360.7

[C1mim]NTf2 248.8 ± 0.3 242.3 ± 0.5 258.2

[C2mim]NTf2 264.9 ± 0.3 259.6 ± 0.5 275.2

[C3mim]NTf2 281.6 ± 0.3 276.7 ± 0.4 292.2

[C4mim]NTf2 298.1 ± 0.3 294.4 ± 0.4 309.2

[C5mim]NTf2 315.0 ± 0.3 311.1 ± 0.6 326.2

[C6mim]NTf2 333.6 ± 0.4 326.8 ± 0.8 343.2

[C7mim]NTf2 350.1 ± 0.4 343.1 ± 0.9 360.2

[C8mim]NTf2 366.4 ± 0.4 362.3 ± 0.9 377.2

[C9mim]NTf2 381.9 ± 0.4 374.9 ± 0.9 394.2

[C10mim]NTf2 399.6 ± 0.5 395.5 ± 1.0 411.2

[C11mim]NTf2 418.3 ± 0.6 412.8 ± 1.5 428.2

[C12mim]NTf2 433.6 ± 0.7 429.5 ± 0.9 445.2

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Figure S1. Histogram of volume calculated by the Gaussian09 program with the Monte-Carlo integration for (a)

[C4mim]+ and (b) [PF6]PF6− as examples. Fitted curves are a Gaussian function.

　　 　　

[C1mim][BF4]BF4, [C1mim][PF6]PF6, [C1mim][NTf2]NTf2

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[C2mim][BF4]BF4, [C2mim][PF6]PF6, [C2mim][NTf2]NTf2

[C3mim][BF4]BF4, [C3mim][PF6]PF6, [C3mim][NTf2]NTf2

[C4mim][BF4]BF4, [C4mim][PF6]PF6, [C4mim][NTf2]NTf2

[C5mim][BF4]BF4, [C5mim][PF6]PF6, [C5mim][NTf2]NTf2

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[C6mim][BF4]BF4, [C6mim][PF6]PF6, [C6mim][NTf2]NTf2

[C7mim][BF4]BF4, [C7mim][PF6]PF6, [C7mim][NTf2]NTf2

[C8mim][BF4]BF4, [C8mim][PF6]PF6, [C8mim][NTf2]NTf2

[C9mim][BF4]BF4, [C9mim][PF6]PF6, [C9mim][NTf2]NTf2

[C10mim][BF4]BF4, [C10mim][PF6]PF6, [C10mim][NTf2]NTf2

[C11mim][BF4]BF4, [C11mim][PF6]PF6, [C11mim][NTf2]NTf2

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[C12mim][BF4]BF4, [C12mim][PF6]PF6, [C12mim][NTf2]NTf2

Figure S2. Optimized ion pair structures for the interaction energy calculation.

Figure S3. FFVQCC versus VQCC. Filled circles, open squares, filled triangles, and open inverted triangles are

[C4mim]X, [C5mim]X, [C6mim]X, and [C8mim]X, respectively. Fitted curves are a function of VQCC−1.

References

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