Supporting Information. Accurate prediction of the structure and vibrational spectra of ionic
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1 Electronic Supplementary Material (ESI) for Physical Chemistry Chemical Physics. This journal is the Owner Societies 2018 Supporting Information Accurate prediction of the structure and vibrational spectra of ionic liquid clusters with the generalized energy-based fragmentation approach: critical role of the ion-pair-based fragmentation Yunzhi Li, Dandan Yuan, Qingchun Wang, Wei Li, and Shuhua Li* School of Chemistry and Chemical Engineering, Key Laboratory of Mesoscopic Chemistry of Ministry of Education, Institute of Theoretical and Computational Chemistry, Nanjing University, Nanjing, , P. R. China. Contents (1) Automatic ion-pair-based fragmentation procedure for an IL system. S2 (2) Validation details of the GEBF approach for various IL clusters. S4 (3) Cartesian coordinates of studied IL clusters. S7 S1
2 S2
3 (1) Automatic ion-pair-based fragmentation procedure for an IL system. We will take this IL cluster (with 4 cations and 4 anions) as an example to illustrate the procedure, which contains the following four steps: Step 1: Construct the cation-anion distance matrix of this cluster. Here the distance (in Å) between a cation and an anion is defined as the minimum distance between any atoms of a cation and any atoms of an anion. Anions Cations Step 2: For each cation, label its neighboring anions if the cation-anion distance is less than 4.0 Å. Anions Cations S3
4 List all labelled cation-anion pairs from the above table: , ; , ; , , , ; , ; Step 3: Use the above result to search the optimal pairing scheme. Two conditions should be satisfied in searching the optimal pairing scheme: (1) Each cation (or anion) should be paired with one of its neighboring anions (or cations) to form an ion pair; (2) Any cation or anion in an IL system should be paired. There are four pairing schemes, as listed below: d means the sum of the distances between all cation-anion pairs. Step 4: Obtain the optimal pairing scheme, in which the sum of the distances between all cation-anion pairs is the minimum among all possible pairing schemes. So the assignment 1 denotes the optimal pairing scheme. Å Optimal pairing scheme: , , , ; d = 6.4 With the above procedure, one can easily achieve the automatic pairing scheme for all cations and anions in an IL cluster or crystal. With each ion-pair as a fragment, one S4
5 can achieve the automatic construction of various subsystems in the GEBF approach for a general IL system. S5
6 (2) Validation details of the GEBF approach for various IL clusters Table S1 Ground-state energy deviations (in kcal/mol) between full system calculations and GEBF calculations with different ζ values and two different types of background point charges (with the ion-pair-based fragmentation scheme) for ([EtNH 3 ][Cl]) n (n=10, 20, and 30) at the M06-2X/6-31G** level. ζ (Å) NPA charges ESP charges n=10 n=20 n=30 n=10 n=20 n= Fig. S1 Charge distributions in various cations, anions and ion pair fragments from GEBF-M06-2X/6-31G** calculations for ([EtNH 3 ][Cl]) n, ([EtNH 3 ][NO 3 ]) n, and ([C 1 mim][cl]) n (n=10, 20, and 30) clusters. S6
7 Table S2 Average unsigned errors (AUEs) of the GEBF energies obtained with two different fragmentation schemes (ion-pair-based fragmentation and ion-based fragmentation) at the M06-2X/6-31G** level (relative to the corresponding full system energies) as a function of the γ max value for three IL clusters. a AUEs (kcal/mol) γ max ([EtNH3 ][Cl]) n ([EtNH 3 ][NO 3 ]) n ([C 1 mim][cl]) n (n=10,20,30) (n=10,20,30) (n=10,20,30) (17.93) 1.21 (13.98) 0.88 (0.52) (19.62) 6.93 (8.60) 0.45 (2.27) (22.89) 2.69 (9.49) 0.31 (1.48) (17.27) 0.51 (6.91) 0.28 (1.13) (7.78) 0.44 (6.57) 0.16 (0.82) a The GEBF results obtained with the ion-based fragmentation scheme (with 2.0*γ max ) are displayed in the parenthesis. S7
8 Fig. S2 (a) The root-mean-squared deviations (RMSDs) between energy gradients obtained with conventional calculations and GEBF calculations (with fixed and dynamic ion-pair-based fragmentations) during the optimization of ([EtNH 3 ][NO 3 ]) 10 at the M06-2X/6-31G** level. (b) The corresponding energy deviations obtained from GEBF calculations with fixed and dynamic ion-pair-based fragmentations (relative to the corresponding conventional results). (c) The initial structure of ([EtNH 3 ][NO 3 ]) 10 under study. Fig. S3 Ground-state energy deviations between conventional M06-2X/6-31G** calculations and GEBF-M06-2X/6-31G** calculations (with fixed and dynamic ionpair-based fragments) for ten isomers of ([EtNH 3 ][NO 3 ]) 30, whose geometries were taken out along classical MD trajectories. S8
9 (3) Cartesian coordinates of studied IL clusters. 1) ([EtNH 3 ][Cl]) 10 ([EtNH 3 ][Cl]) 20 ([EtNH 3 ][Cl]) 30 2) ([EtNH 3 ][NO 3 ]) 10 ([EtNH 3 ][NO 3 ]) 20 ([EtNH 3 ][NO 3 ]) ) ([C 1 mim][cl]) 10 ([C 1 mim][cl]) 20 ([C 1 mim][cl]) 30 4) ([C 1 mim][bf 4 ]) 10 ([C 1 mim][bf 4 ]) 20 ([C 1 mim][bf 4 ]) 30 5) ([C 1 mim][no 3 ]) 10 ([C 1 mim][no 3 ]) 20 ([C 1 mim][no 3 ]) 30 6) ([n-c 4 NH 3 ][NO 3 ]) 10 ([n-c 4 NH 3 ][NO 3 ]) 20 ([n-c 4 NH 3 ][NO 3 ]) 30 7) ([n-c 4 mim][bf 4 ]) 10 ([n-c 4 mim][bf 4 ]) 20 ([n-c 4 mim][bf 4 ]) 30 S9
10 ([EtNH 3 ][Cl]) Atomic Atomic Coordinates (Angstroms) Number X Y Z C H H H C H H N H H H Cl C H H H C H H N H H H Cl C H H H C H H N H H H Cl C H H H C H H N H H H Cl C H H H S10
11 C H H N H H H Cl C H H H C H H N H H H Cl C H H H C H H N H H H Cl C H H H C H H N H H H Cl C H H H C H H N H H H Cl C H S11
12 H H C H H N H H H Cl Return S12
13 ([EtNH 3 ][Cl]) Atomic Atomic Coordinates (Angstroms) Number X Y Z C H H H C H H N H H H Cl C H H H C H H N H H H Cl C H H H C H H N H H H Cl C H H H C H H N H H H Cl C H H H S13
14 C H H N H H H Cl C H H H C H H N H H H Cl C H H H C H H N H H H Cl C H H H C H H N H H H Cl C H H H C H H N H H H Cl C H S14
15 H H C H H N H H H Cl C H H H C H H N H H H Cl C H H H C H H N H H H Cl C H H H C H H N H H H Cl C H H H C H H N H H H Cl S15
16 C H H H C H H N H H H Cl C H H H C H H N H H H Cl C H H H C H H N H H H Cl C H H H C H H N H H H Cl C H H H C H H N H H S16
17 H Cl C H H H C H H N H H H Cl Return S17
18 ([EtNH 3 ][Cl]) Atomic Atomic Coordinates (Angstroms) Number X Y Z C H H H C H H N H H H Cl C H H H C H H N H H H Cl C H H H C H H N H H H Cl C H H H C H H N H H H Cl C H H H C H H N H H H Cl C S18
19 H H H C H H N H H H Cl C H H H C H H N H H H Cl C H H H C H H N H H H Cl C H H H C H H N H H H Cl C H H H C H H N H H H Cl C H H H C H H N S19
20 H H H Cl C H H H C H H N H H H Cl C H H H C H H N H H H Cl C H H H C H H N H H H Cl C H H H C H H N H H H Cl C H H H C H H N H H H Cl C H H S20
21 H C H H N H H H Cl C H H H C H H N H H H Cl C H H H C H H N H H H Cl C H H H C H H N H H H Cl C H H H C H H N H H H Cl C H H H C H H N H H S21
22 H Cl C H H H C H H N H H H Cl C H H H C H H N H H H Cl C H H H C H H N H H H Cl C H H H C H H N H H H Cl C H H H C H H N H H H Cl C H H H C S22
23 H H N H H H Cl C H H H C H H N H H H Cl C H H H C H H N H H H Cl Return S23
24 ([EtNH 3 ][NO 3 ]) 10 conformer Atomic Atomic Coordinates (Angstroms) Number X Y Z C H H H C H H N H H H N O O O C H H H C H H N H H H N O O O C H H H C H H N H H H N O O O C H H H C H H N H H H N O O O C S24
25 H H H C H H N H H H N O O O C H H H C H H N H H H N O O O C H H H C H H N H H H N O O O C H H H C H H N H H H N O O O C H H H C H H N S25
26 H H H N O O O C H H H C H H N H H H N O O O Return S26
27 ([EtNH 3 ][NO 3 ]) 10 conformer Atomic Atomic Coordinates (Angstroms) Number X Y Z C H H H C H H N H H H N O O O C H H H C H H N H H H N O O O C H H H C H H N H H H N O O O C H H H C H H N H H H N O O O C S27
28 H H H C H H N H H H N O O O C H H H C H H N H H H N O O O C H H H C H H N H H H N O O O C H H H C H H N H H H N O O O C H H H C H H N S28
29 H H H N O O O C H H H C H H N H H H N O O O Return S29
30 ([EtNH 3 ][NO 3 ]) 10 conformer Atomic Atomic Coordinates (Angstroms) Number X Y Z C H H H C H H N H H H N O O O C H H H C H H N H H H N O O O C H H H C H H N H H H N O O O C H H H C H H N H H H N O O O C S30
31 H H H C H H N H H H N O O O C H H H C H H N H H H N O O O C H H H C H H N H H H N O O O C H H H C H H N H H H N O O O C H H H C H H N S31
32 H H H N O O O C H H H C H H N H H H N O O O Return S32
33 ([EtNH 3 ][NO 3 ]) 10 conformer Atomic Atomic Coordinates (Angstroms) Number X Y Z C H H H C H H N H H H N O O O C H H H C H H N H H H N O O O C H H H C H H N H H H N O O O C H H H C H H N H H H N O O O C S33
34 H H H C H H N H H H N O O O C H H H C H H N H H H N O O O C H H H C H H N H H H N O O O C H H H C H H N H H H N O O O C H H H C H H N S34
35 H H H N O O O C H H H C H H N H H H N O O O Return S35
36 ([EtNH 3 ][NO 3 ]) 10 conformer Atomic Atomic Coordinates (Angstroms) Number X Y Z C H H H C H H N H H H N O O O C H H H C H H N H H H N O O O C H H H C H H N H H H N O O O C H H H C H H N H H H N O O O C S36
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