Supplementary Materials Anion Anion (MX3- 2 dimers (M ...Supplementary Materials Anion Anion (MX 3-)...

Supplementary Materials

AnionAnion (MX3-)2 dimers (M = Zn, Cd, Hg; X = Cl, Br, I) in different

environments

Rafał Wysokiński,*1 Wiktor Zierkiewicz,*1 Mariusz Michalczyk,1 and Steve

Scheiner*2

1 Faculty of Chemistry, Wrocław University of Science and Technology, Wybrzeże

Wyspiańskiego 27, 50-370 Wrocław, Poland

2 Department of Chemistry and Biochemistry, Utah State University Logan, Utah 84322-

0300, United States

Table S1. Geometrical parameters (distances in angstroms, angles in degrees) of MX3- monomers

studied calculated at the MP2/aug-cc-pVDZ level of theory.

Isolated molecule Watera Ethanola Gas

R(M-X)/∑∢(X-M-X) R(M-X)/∑∢(X-M-X) R(M-X)/∑∢(X-M-X)

ZnCl3- 2.230/360 2.228/360 2.199/360

ZnBr3- 2.366/359 2.359/360 2.330/360

ZnI3- 2.564/359 2.561/360 2.526/360

CdCl3- 2.499/360 2.492/360 2.398/360

CdBr3- 2.605/360 2.609/359 2.521/360

CdI3- 2.802/360 2.783/360 2.704/360

HgCl3- 2.504/359 2.494/359 2.412/360

HgBr3- 2.619/360 2.600/359 2.531/360

HgI3- 2.792/359 2.787/359 2.705/360

a in the case of complexes in solvents the M-X distance values are averages of three different M-

X distances.

Electronic Supplementary Material (ESI) for Physical Chemistry Chemical Physics.This journal is © the Owner Societies 2021

vacuum ethanol water

(Zn2Cl6)2-

(Zn2Br6)2-

(Zn2I6)2-

(Cd2Cl6)2-

(Cd2Br6)2-

(Cd2I6)2-

(Hg2Cl6)2-

(Hg2Br6)2-

(Hg2I6)2-

Fig. S1. AIM molecular diagrams of MP2/aug-cc-pVDZ optimized bridged structures of

(M2X6)2- complexes. Green dots represent bond critical points. Numbers refers to electron

densities at BCPs (in au)

Table S2. AIM descriptors of the of the bridged dimers. Bond critical point (BCP) properties:

electron density ρ, Laplacian of electron density 2ρ and total electron energy H and potential

electron density energy V as well as kinetic electron density energy G, were obtained at the

MP2/aug-cc-pVDZ level. Data in atomic units.

interaction ρ 2ρ H V G -G/V

vacuum

(Zn2Cl6)2-

Zn – Cla 0.074 +0.247 -0.017 -0.097 0.079 0.814

Zn – Clb 0.054 +0.192 -0.007 -0.061 0.054 0.885

(Zn2Br6)2-

Zn – Bra 0.066 +0.172 -0.015 -0.074 0.059 0.797

Zn – Brb 0.049 +0.139 -0.007 -0.049 0.042 0.857

(Zn2I6)2-

Zn – Ia 0.057 +0.095 -0.014 -0.052 0.038 0.731

Zn – Ib 0.044 +0.084 -0.008 -0.036 0.029 0.806

(Cd2Cl6)2-

Cd – Cla 0.064 +0.204 -0.012 -0.076 0.063 0.829

Cd – Clb 0.047 +0.158 -0.006 -0.051 0.045 0.882

(Cd2Br6)2-

Cd – Bra 0.059 +0.148 -0.013 -0.062 0.050 0.806

Cd – Brb 0.044 +0.121 -0.006 -0.043 0.037 0.860

(Cd2I6)2-

Cd – Ia 0.052 +0.090 -0.012 -0.047 0.035 0.745

Cd – Ib 0.040 +0.081 -0.007 -0.034 0.027 0.794

(Hg2Cl6)2-

Hg – Cla 0.075 +0.206 -0.018 -0.086 0.069 0.802

Hg – Clb 0.051 +0.157 -0.006 -0.051 0.045 0.882

(Hg2Br6)2-

Hg – Bra 0.068 +0.147 -0.017 -0.070 0.053 0.757

Hg – Brb 0.048 +0.123 -0.007 -0.044 0.037 0.841

(Hg2I6)2-

Hg – Ia 0.060 +0.087 -0.016 -0.053 0.037 0.698

Hg – Ib 0.046 +0.083 -0.008 -0.037 0.029 0.784

ethanol

(Zn2Cl6)2-

Zn – Cla 0.074 +0.251 -0.018 -0.098 0.081 0.827

Zn – Cla 0.073 +0.246 -0.017 -0.095 0.078 0.821

Zn – Clb 0.053 +0.192 -0.006 -0.061 0.054 0.885

(Zn2Br6)2-

Zn – Bra 0.065 +0.172 -0.015 -0.072 0.057 0.792

Zn - Brb 0.049 +0.140 -0.007 -0.049 0.042 0.857

(Zn2I6)2-

Zn – Ia 0.057 +0.096 -0.013 -0.051 0.038 0.745

Zn – Ib 0.044 +0.084 -0.007 -0.036 0.028 0.778

(Cd2Cl6)2-

Cd – Cla 0.057 +0.185 -0.009 -0.065 0.056 0.862

Cd – Cla 0.056 +0.184 -0.009 -0.064 0.055 0.859

Cd – Clb 0.043 +0.144 -0.004 -0.044 0.040 0.909

(Cd2Br6)2-

Cd – Bra 0.055 +0.143 -0.011 -0.058 0.047 0.810

Cd – Bra 0.053 +0.136 -0.010 -0.054 0.044 0.815

Cd – Brb 0.039 +0.107 -0.004 -0.035 0.031 0.886

(Cd2I6)2-

Cd – Ia 0.049 +0.087 -0.011 -0.043 0.033 0.767

Cd – Ia 0.047 +0.086 -0.010 -0.042 0.031 0.738

Cd – Ib 0.035 +0.074 -0.005 -0.028 0.023 0.821

(Hg2Cl6)2-

Hg – Cla 0.063 +0.181 -0.011 -0.068 0.057 0.838

Hg – Cla 0.061 +0.176 -0.010 -0.065 0.054 0.831

Hg – Clb 0.043 +0.132 -0.003 -0.040 0.036 0.900

Hg – Clb 0.042 +0.131 -0.003 -0.039 0.036 0.923

(Hg2Br6)2-

Hg – Bra 0.069 +0.143 -0.017 -0.070 0.053 0.757

Hg – Bra 0.063 +0.134 -0.014 -0.061 0.047 0.770

Hg – Brb 0.038 +0.099 -0.003 -0.031 0.028 0.903

(Hg2I6)2-

Hg – Ia 0.055 +0.081 -0.013 -0.046 0.033 0.717

Hg – Ib 0.038 +0.072 -0.005 -0.028 0.023 0.821

water

(Zn2Cl6)2-

Zn – Cla 0.074 +0.251 -0.018 -0.098 0.080 0.816

Zn – Cla 0.073 +0.245 -0.017 -0.095 0.078 0.821

Zn – Clb 0.053 +0.191 -0.006 -0.060 0.054 0.900

(Zn2Br6)2-

Zn – Bra 0.066 +0.174 -0.015 -0.074 0.059 0.797

Zn – Bra 0.065 +0.171 -0.015 -0.073 0.058 0.795

Zn – Brb 0.051 +0.145 -0.008 -0.051 0.044 0.863

Zn – Brb 0.050 +0.142 -0.007 -0.050 0.043 0.860

Zn – Brb 0.048 +0.136 -0.006 -0.046 0.040 0.870

Zn – Brb 0.047 +0.133 -0.006 -0.045 0.039 0.867

(Zn2I6)2-

Zn – Ia 0.057 +0.096 -0.014 -0.052 0.038 0.731

Zn – Ia 0.056 +0.095 -0.013 -0.051 0.037 0.725

Zn – Ib 0.043 +0.083 -0.007 -0.035 0.028 0.800

Zn – Ib 0.042 +0.082 -0.007 -0.035 0.027 0.771

I ··· I 0.003 +0.005 +0.000 -0.001 0.001 1.000

(Cd2Cl6)2-

Cd – Cla 0.058 +0.190 +0.010 -0.067 0.057 0.851

Cd – Cla 0.053 +0.173 -0.008 -0.059 0.051 0.864

Cd – Clb 0.041 +0.138 -0.004 -0.042 0.038 0.905

(Cd2Br6)2-

Cd – Bra 0.048 +0.125 -0.008 -0.047 0.039 0.830

Cd – Brb 0.039 +0.108 -0.004 -0.035 0.031 0.886

(Cd2I6)2-

Cd – Ia 0.047 +0.084 -0.010 -0.041 0.031 0.756

Cd – Ia 0.046 +0.083 -0.009 -0.040 0.030 0.750

Cd – Ia 0.045 +0.082 -0.009 -0.038 0.029 0.763

Cd – Ia 0.044 +0.081 -0.008 -0.037 0.028 0.757

Cd – Ib 0.036 +0.075 -0.005 -0.029 0.024 0.828

Cd – Ib 0.035 +0.074 -0.005 -0.028 0.023 0.821

Cd – Ib 0.034 +0.071 -0.004 -0.026 0.022 0.846

I ··· I 0.002 +0.003 +0.000 -0.001 0.001 1.000

(Hg2Cl6)2-

Hg – Cla 0.072 +0.198 -0.016 -0.081 0.065 0.802

Hg – Cla 0.069 +0.190 -0.015 -0.077 0.062 0.805

Hg – Clb 0.034 +0.104 -0.001 -0.028 0.027 0.964

Hg – Clb 0.033 +0.104 -0.001 -0.028 0.027 0.964

Cl ··· Cl 0.001 +0.004 +0.000 -0.001 0.001 1.000

(Hg2Br6)2-

Hg – Bra 0.063 +0.135 -0.014 -0.061 0.048 0.787

Hg – Bra 0.059 +0.131 -0.011 -0.056 0.044 0.786

Hg – Brb 0.038 +0.098 -0.003 -0.031 0.028 0.903

Hg – Brb 0.037 +0.097 -0.003 -0.030 0.027 0.900

(Hg2I6)2-

Hg – Ia 0.058 +0.084 -0.015 -0.050 0.036 0.720

Hg – Ia 0.051 +0.081 -0.011 -0.042 0.031 0.738

Hg – Ib 0.039 +0.072 -0.006 -0.030 0.024 0.800

Hg – Ib 0.037 +0.071 -0.005 -0.028 0.023 0.821

Hg ··· Hg 0.020 +0.054 -0.001 -0.015 0.014 0.933

ethanol water

(ZnCl3-)2

(ZnBr3-)2

(ZnI3-)2

(CdCl3-)2

(CdBr3-)2

(CdI3-)2

(HgCl3-)2

(HgBr3-)2

(HgI3-)2

Fig. S2. AIM molecular diagrams of optimized stacked structures. Green dots represent bond

critical points. Numbers refers to electron densities at BCPs (in au)

Table S3. AIM descriptors of the of stacked dimers. Bond critical point (BCP) properties:

electron density ρ, Laplacian of electron density 2ρ and total electron energy H and potential

electron density energy V as well as kinetic electron density energy G, were obtained at the

MP2/ aug-cc-pVDZ level. Data in atomic units.

interaction ρ 2ρ H V G -G/V

ethanol

(ZnCl3-)2

Zn-Cl 0.076 +0.255 -0.019 -0.102 0.083 0.814

Zn···Cl 0.003 +0.010 +0.000 -0.002 0.002 1.000

Cl···Cl 0.003 +0.008 +0.000 -0.001 0.002 2.000

(ZnBr3-)2

Zn-Br 0.069 +0.180 -0.017 -0.079 0.062 0.785

Zn-Br 0.068 +0.178 -0.016 -0.077 0.061 0.792

Zn···Br 0.004 +0.011 +0.000 -0.002 0.002 1.000

(ZnI3-)2

Zn-I 0.059 +0.099 -0.015 -0.054 0.040 0.741

Zn-I 0.058 +0.098 -0.014 -0.053 0.039 0.736

Zn···I 0.004 +0.009 +0.000 -0.002 0.002 1.000

(CdCl3-)2

Cd-Cl 0.056 +0.182 -0.009 -0.064 0.055 0.859

Cd-Cl 0.055 +0.181 -0.009 -0.063 0.054 0.857

Cd···Cl 0.004 +0.013 +0.001 -0.002 0.003 1.500

(CdBr3-)2

Cd-Br 0.053 +0.138 -0.010 -0.054 0.044 0.815

Cd-Br 0.052 +0.136 -0.010 -0.053 0.044 0.830

Cd···Br 0.004 +0.012 +0.001 -0.002 0.003 1.500

Br···Br 0.004 +0.009 +0.000 -0.002 0.002 1.000

(CdI3-)2

Cd-I 0.048 +0.087 -0.010 -0.043 0.032 0.744

Cd···I 0.005 +0.011 +0.000 -0.002 0.002 1.000

(HgCl3-)2

Hg-Cl 0.070 +0.196 -0.015 -0.078 0.064 0.821

Hg-Cl 0.069 +0.193 -0.014 -0.076 0.062 0.816

Hg···Cl 0.007 +0.021 +0.001 -0.004 0.004 1.000

(HgBr3-)2

Hg-Br 0.071 +0.147 -0.018 -0.073 0.055 0.753

Hg-Br 0.060 +0.136 -0.012 -0.058 0.046 0.793

Hg-Br 0.059 +0.134 -0.011 -0.056 0.045 0.804

Hg···Br 0.006 +0.018 +0.001 -0.003 0.004 1.333

(HgI3-)2

Hg-I 0.056 +0.084 -0.013 -0.048 0.034 0.708

Hg-I 0.054 +0.078 -0.012 -0.044 0.032 0.727

Hg···I 0.006 +0.016 +0.001 -0.003 0.003 1.000

I···I 0.003 +0.006 +0.000 -0.001 0.001 1.000

water

(ZnCl3-)2 Zn-Cl 0.076 +0.256 -0.019 -0.102 0.083 0.814

Zn-Cl 0.075 +0.253 -0.018 -0.100 0.081 0.810

Zn···Cl 0.003 +0.010 +0.000 -0.002 0.002 1.000

Cl···Cl 0.003 +0.009 +0.000 -0.001 0.002 2.000

(ZnBr3-)2 Zn-Br 0.053 +0.137 -0.010 -0.054 0.044 0.815

Zn-Br 0.050 +0.130 -0.008 -0.049 0.041 0.837

Zn-Br 0.049 +0.127 -0.008 -0.048 0.040 0.833

Zn···Br 0.005 +0.013 +0.001 -0.002 0.003 1.500

(ZnI3-)2 Zn-I 0.058 +0.098 -0.014 -0.053 0.039 0.736

Zn···I 0.004 +0.010 +0.000 -0.002 0.002 1.000

(CdCl3-)2 Cd-Cl 0.055 +0.180 -0.008 -0.062 0.053 0.855

Cd-Cl 0.054 +0.178 -0.008 -0.061 0.053 0.869

Cd···Cl 0.004 +0.013 +0.001 -0.002 0.003 1.500

(CdBr3-)2 Cd-Br 0.053 +0.137 -0.010 -0.054 0.044 0.815

Cd-Br 0.050 +0.130 -0.008 -0.049 0.041 0.837

Cd-Br 0.049 +0.127 -0.008 -0.048 0.040 0.833

Cd···Br 0.005 +0.013 +0.001 -0.002 0.003 1.500

(CdI3-)2 Cd-I 0.048 +0.087 -0.010 -0.043 0.032 0.744

Cd-I 0.047 +0.087 +0.010 -0.042 0.032 0.762

Cd-I 0.045 +0.082 +0.009 -0.038 0.029 0.763

Cd-I 0.044 +0.082 +0.009 -0.038 0.029 0.763

Cd-I 0.043 +0.079 +0.008 -0.035 0.028 0.800

Cd···I 0.004 +0.011 -0.000 -0.002 0.002 1.000

(HgCl3-)2 Hg-Cl 0.069 +0.195 -0.014 -0.077 0.063 0.818

Hg-Cl 0.067 +0.191 -0.013 -0.074 0.061 0.824

Hg-Cl 0.057 +0.168 -0.009 -0.059 0.051 0.864

Hg···Cl 0.007 +0.021 +0.001 -0.004 0.004 1.000

(HgBr3-)2 Hg-Br 0.062 +0.137 -0.013 -0.061 0.047 0.770

Hg-Br 0.061 +0.136 -0.013 -0.059 0.047 0.797

Hg-Br 0.059 +0.132 -0.011 -0.056 0.045 0.804

Hg···Br 0.006 +0.018 +0.001 -0.003 0.004 1.333

(HgI3-)2 Hg-I 0.061 +0.084 -0.016 -0.053 0.037 0.698

Hg-I 0.059 +0.083 -0.015 -0.051 0.036 0.706

Hg-I 0.054 +0.081 -0.012 -0.044 0.032 0.727

Hg-I 0.052 +0.084 -0.011 -0.043 0.031 0.721

Hg···I 0.007 +0.018 +0.001 -0.003 0.004 1.333

Hg···I 0.006 +0.016 +0.001 -0.003 0.003 1.000

Table S4. Coordinates of MX3- (M = Zn, Cd, Hg; X = Cl, Br, I) monomers.

gas ethanol water

ZnCl3-

Zn -0.767316 -1.431088 -0.164654 Cl -2.956310 -1.354537 -0.358896 Cl 0.306252 0.255892 0.750346 Cl 0.344064 -3.186669 -0.882211

Zn -0.771489 -1.429545 -0.142377 Cl -2.989109 -1.365362 -0.374764 Cl 0.335446 0.280552 0.757843 Cl 0.351841 -3.202047 -0.896117

Zn -2.230165 0.001796 0.401117 Cl -2.910445 -1.927341 -0.494825 Cl -2.939659 1.909489 -0.518268 Cl -0.698976 0.014231 2.012212

CdCl3-

Cd -2.215781 -0.002465 -0.365851 Cl -0.588859 0.262970 -2.107043 Cl -3.247705 1.926842 0.614893 Cl -2.810233 -2.197157 0.394681

Cd -2.225232 -0.004586 -0.365905 Cl -0.526730 0.270444 -2.169792 Cl -3.284942 2.012727 0.653004 Cl -2.825674 -2.288395 0.419372

Cd -2.195220 -0.000074 -0.369667 Cl -0.515877 0.265975 -2.204196 Cl -3.232427 2.019153 0.683194 Cl -2.794453 -2.292153 0.414363

HgCl3-

Hg 2.101704 0.038896 0.313986 Cl 0.596573 -0.132917 2.189759 Cl 2.751528 2.204470 -0.527496 Cl 2.966877 -1.955721 -0.732157

Hg 2.029030 -0.042609 0.264815 Cl 0.577092 -0.043697 2.260759 Cl 2.755005 2.271078 -0.490469 Cl 3.055555 -2.030043 -0.791013

Hg 2.000926 -0.040399 0.273412 Cl 0.563314 -0.043413 2.285705 Cl 2.749931 2.275773 -0.513499 Cl 3.027906 -2.032015 -0.791094

ZnBr3-

Zn -2.221433 0.000760 0.486871 Br -3.184050 -1.959501 -0.326372 Br -2.910781 2.064576 -0.345988 Br -0.572769 -0.105896 2.129424

Zn -2.216465 -0.001077 0.481464 Br -3.199824 -1.983328 -0.336814 Br -2.920113 2.088419 -0.353480 Br -0.552632 -0.104074 2.152765

Zn 2.217174 -0.000287 -0.480414 Br 0.554435 -0.106684 -2.155553 Br 3.207125 -1.984746 0.336508 Br 2.915586 2.093859 0.354712

CdBr3-

Cd 2.449425 0.000023 0.484779 Br 3.425633 2.183326 -0.312547 Br 3.427214 -2.182567 -0.312566 Br 0.497003 -0.000690 2.079252

Cd 2.400831 0.000075 0.473722 Br 3.487392 2.231619 -0.346829 Br 3.488983 -2.230839 -0.346818 Br 0.422070 -0.000763 2.158844

Cd -2.198056 0.010030 -0.514785 Br -0.324452 0.300099 -2.366729 Br -3.463891 2.103390 0.401467 Br -2.756010 -2.417191 0.340903

HgBr3-

Hg -2.322909 0.006961 0.444661 Br -0.492876 -0.496600 2.118679 Br -3.580178 -1.890322 -0.663177 Br -2.896344 2.405933 -0.121416

Hg -2.154375 -0.037255 0.499983 Br -0.383316 -0.526038 2.259922 Br -3.702802 -1.742630 -0.747902 Br -3.051815 2.331896 -0.233258

Hg -2.212023 -0.008272 0.425824 Br -0.390842 -0.283988 2.285891 Br -3.397717 -2.120959 -0.541487 Br -2.743082 2.423830 -0.439796

ZnI3-

Zn -2.324398 -0.000408 -0.587952 I -0.537386 0.280374 -2.351086 I -3.515612 2.027444 0.333761 I -2.921390 -2.305604 0.255335

Zn -2.317922 0.002539 -0.581471 I -0.512314 0.285662 -2.380356 I -3.533799 2.049976 0.344426 I -2.934751 -2.336371 0.267459

Zn -0.781245 -1.405335 -0.077140 I -3.317148 -1.363235 -0.461889 I 0.283452 0.555824 1.179270 I 0.613016 -3.431879 -0.810640

CdI3-

Cd -2.319070 0.000509 -0.563334 I -0.370884 0.194546 -2.428218 I -3.592168 2.224927 0.298857 I -2.994376 -2.416794 0.442317

Cd -2.313780 -0.072792 -0.526918 I -0.355869 0.321028 -2.471298 I -3.551426 2.298473 0.240296 I -3.055424 -2.543521 0.507543

Cd 1.174121 -1.660937 -4.335638 I -0.484943 0.497909 -3.721209 I 0.032714 -3.697703 -5.867380 I 3.930755 -1.626787 -3.725233

HgI3-

Hg -0.331633 0.803571 0.000000 I -1.683902 3.145771 -0.000000 I 2.372906 0.803571 -0.000000 I -1.683902 -1.538628 -0.000000

Hg -0.261357 0.803416 0.033524 I -1.792575 3.133579 -0.010591 I 2.520561 0.803608 -0.012682 I -1.793160 -1.526317 -0.010251

Hg -0.757247 -1.418889 -0.164035 I -3.573922 -1.345734 -0.171110 I 0.368392 0.814140 1.113909 I 0.592586 -3.689189 -0.932756

Table S5. Coordinates of (MX3-)2 (M = Zn, Cd, Hg; X = Cl, Br, I). Minima in gas phase. Bridged

complexes.

Zn Cd Hg

(MCl3-)2

Zn 1.661957 0.000015 0.000022 Zn -1.661977 0.000014 -0.000023 Cl 2.870555 1.887468 0.000095 Cl 2.870218 -1.887656 -0.000118 Cl -0.000015 -0.000039 -1.703750 Cl -0.000011 0.000330 1.703748 Cl -2.870501 1.887515 -0.000260 Cl -2.870212 -1.887670 0.000286

Cd 1.832752 0.000053 0.000023 Cd -1.832826 0.000065 -0.000024 Cl 3.150026 2.052114 0.000228 Cl 3.149308 -2.052505 -0.000271 Cl -0.000028 0.000075 -1.808171 Cl -0.000023 0.000786 1.808170 Cl -3.149694 2.052375 -0.000574 Cl -3.149337 -2.052494 0.000621

Hg 1.888286 -0.000013 0.000025 Hg -1.888308 -0.000013 -0.000024 Cl 3.092123 2.120206 -0.000069 Cl 3.092600 -2.119962 -0.000015 Cl -0.000015 -0.000136 -1.823962 Cl 0.000023 -0.000265 1.823963 Cl -3.092048 2.120250 0.000123 Cl -3.092578 -2.119971 -0.000043

(MBr3-)2

Zn -1.723501 0.000000 0.000000 Zn 1.723501 0.000000 0.000000 Br -3.004915 -2.000421 0.000000 Br -3.004915 2.000421 0.000000 Br 0.000000 0.000000 -1.828957 Br 0.000000 0.000000 1.828957 Br 3.004915 -2.000421 0.000000 Br 3.004915 2.000421 0.000000

Cd 1.875573 -0.000040 -0.000009 Cd -1.875574 -0.000040 0.000009 Br 3.256762 -2.158709 -0.000109 Br 3.255800 2.159100 0.000063 Br 0.000012 -0.000415 1.938510 Br -0.000012 -0.000258 -1.938510 Br -3.256761 -2.158710 -0.000068 Br -3.255796 2.159103 0.000111

Hg -1.918960 0.000016 0.000064 Hg 1.918968 0.000016 -0.000063 Br -3.207769 -2.211758 0.000096 Br -3.210341 2.210437 -0.000073 Br -0.000019 0.001898 -1.948318 Br 0.000021 0.002057 1.948318 Br 3.207753 -2.211770 0.000085 Br 3.210331 2.210444 -0.000108

(MI3-)2

Zn -0.743716 -0.645472 -1.231079 Zn 1.203179 -2.048746 -3.985877

Cd -1.955785 0.000121 -0.000007 Cd 1.955802 0.000121 0.000012

Hg -1.973922 0.000061 0.000037 Hg 1.973929 0.000071 -0.000036

I -3.272576 -1.058122 -0.969326 I 0.309757 0.832521 0.596290 I -0.150783 0.280760 -3.706623 I 0.608338 -2.975925 -1.511163 I 0.152175 -3.526860 -5.814737 I 3.731993 -1.634747 -4.245549

I -3.433366 -2.315402 0.000125 I -3.432932 2.316153 -0.000056 I -0.000010 -0.000957 -2.111107 I 0.000011 -0.000781 2.111102 I 3.433371 -2.315400 0.000066 I 3.432910 2.316169 -0.000134

I -3.381903 -2.347346 0.000121 I -3.385942 2.345095 -0.000079 I -0.000022 0.002427 -2.113932 I 0.000027 0.002604 2.113933 I 3.381910 -2.347333 0.000070 I 3.385916 2.345127 -0.000117

Table S6. Coordinates of (MX3-)2 (M = Zn, Cd, Hg; X = Cl, Br, I). Minima in ethanol.

Zn Cd Hg

bridged

(MCl3-)2

Zn -1.625101 0.007745 -0.000064 Zn 1.625036 0.007756 -0.000299 Cl -2.830191 1.902936 0.000752 Cl -2.641197 -1.984743 -0.000318 Cl 0.000632 0.067868 1.740616 Cl 0.000114 0.068966 -1.740801 Cl 2.830239 1.902899 0.000165 Cl 2.640517 -1.985280 0.000226

Cd -1.840207 0.017309 0.000413 Cd 1.840175 0.017351 0.000148 Cl -3.185357 2.110942 -0.000686 Cl -3.401871 -1.927028 -0.000374 Cl 0.000164 -0.232029 1.844427 Cl -0.000116 -0.233128 -1.844145 Cl 3.185752 2.110517 -0.000698 Cl 3.401518 -1.927136 -0.000109

Hg -1.957959 -0.004652 0.000708 Hg 1.958178 -0.005219 -0.000057 Cl -3.334901 2.120095 -0.055197 Cl -3.368155 -2.087953 0.055100 Cl -0.000006 0.117615 1.859182 Cl 0.000054 -0.131036 -1.864190 Cl 3.335747 2.118878 -0.055491 Cl 3.367733 -2.089071 0.054157

(MBr3-)2

Zn -1.687990 0.000079 0.000003 Zn 1.687986 0.000080 -0.000022 Br -2.910679 2.046802 0.000099 Br -2.910527 -2.046812 -0.000088 Br -0.000006 -0.000477 1.862342 Br -0.000015 0.000359 -1.862355 Br 2.910690 2.046830 0.000296 Br 2.910540 -2.046838 -0.000278

Cd 1.880686 0.058234 0.002506 Cd -1.880853 0.058159 -0.002714 Br 3.419144 2.138232 0.003351 Br 2.654077 -2.436244 0.002537 Br 0.002262 0.240278 -2.014883 Br -0.002347 0.240836 2.014728 Br -3.418844 2.138339 -0.002806 Br -2.654127 -2.436144 -0.002767

Hg 2.056396 0.034351 0.000639 Hg -2.056405 0.034810 -0.000641 Br 3.091064 2.371989 0.000285 Br 2.858841 -2.442833 0.000116 Br 0.000021 0.036715 -1.981745 Br -0.000075 0.036137 1.981936 Br -3.090563 2.372728 0.000286 Br -2.859282 -2.442208 -0.000924

(MI3-)2

Zn -1.753970 -0.036199 -0.000134 Zn 1.753957 -0.036225 -0.000025 I -2.732443 2.350201 -0.000328 I -3.418913 -2.004942 0.000206 I -0.000058 -0.324138 2.049086 I 0.000038 -0.324713 -2.049080 I 2.732518 2.350140 -0.000180 I 3.418861 -2.005005 0.000372

Cd 2.011778 0.050974 0.000318 Cd -2.011764 0.051549 0.000318 I 3.546564 2.363545 0.001422 I 3.016438 -2.556146 -0.002058 I 0.000063 0.143251 -2.151212 I 0.000042 0.139697 2.151684 I -3.546479 2.364266 0.001535 I -3.016644 -2.555446 -0.002055

Hg -1.996171 0.000105 -0.000038 Hg 1.996169 -0.000017 0.000047 I -3.382453 2.418484 -0.000406 I -3.382508 -2.418250 0.000204 I -0.000076 0.000095 2.230502 I 0.000072 -0.000067 -2.230490 I 3.382554 2.418287 -0.000415 I 3.382392 -2.418442 0.000601

stacked

(MCl3-)2

Zn -2.214469 0.004219 0.372983 Zn 2.214630 0.004161 -0.373805 Cl -2.903755 -1.938425 -0.471753 Cl -2.960229 1.903883 -0.516570 Cl 0.714358 0.025634 -2.017412 Cl -0.714699 0.026086 2.017616 Cl 2.905597 -1.936765 0.472945 Cl 2.958442 1.904797 0.516625

Cd 2.202027 0.005485 0.346486 Cd -2.202046 0.005451 -0.346502 Cl 3.296532 2.011025 -0.650359 Cl 2.832357 -2.289592 -0.411735 Cl -0.531688 0.263393 -2.178891 Cl 0.531663 0.263415 2.178868 Cl -3.296557 2.010992 0.650363 Cl -2.832287 -2.289646 0.411709

Hg -2.020475 -0.041756 -0.256450 Hg 2.020382 -0.041177 0.256492 Cl -2.757332 2.274619 0.486104 Cl -3.058493 -2.032626 0.789008 Cl 0.580776 -0.045266 2.262766 Cl -0.580722 -0.047373 -2.262556 Cl 2.757669 2.274458 -0.488042 Cl 3.057855 -2.033287 -0.787124

(MBr3-)2

Zn -2.200376 0.001047 0.466770 Zn 2.200719 0.001335 -0.466337 Br -3.204701 -1.982532 -0.331578 Br -2.926287 2.087145 -0.349326 Br 0.558102 -0.105496 -2.157946 Br -0.557670 -0.105720 2.158069 Br 3.204399 -1.983180 0.331172 Br 2.925862 2.087741 0.349236

Cd 2.390040 -0.000038 0.466338 Cd -2.390088 -0.000064 -0.466336 Br 3.495379 2.222917 -0.347952 Br 3.496975 -2.222070 -0.347955 Br -0.416913 -0.000887 -2.168514 Br 0.416882 -0.000717 2.168487 Br -3.495315 2.222980 0.347823 Br -3.496961 -2.222088 0.348082

Hg 2.140545 -0.041852 -0.484453 Hg -2.141208 -0.041822 0.484248 Br 3.714307 -1.743572 0.748684 Br 3.048132 2.330339 0.222549 Br -0.389277 -0.515821 2.265402 Br 0.389031 -0.515293 -2.265869 Br -3.713008 -1.746296 -0.747980 Br -3.048814 2.329912 -0.222924

(MI3-)2

Zn 2.303591 0.003849 0.567566 Zn -2.303744 0.003912 -0.567019 I 3.540517 2.045647 -0.344151 I 2.936741 -2.339287 -0.257488 I -0.517797 0.285158 -2.384509 I 0.517978 0.291451 2.384417 I -3.538253 2.049735 0.339113 I -2.938992 -2.336999 0.262473

Cd 2.290831 -0.070152 0.503545 Cd -2.290772 -0.069882 -0.502818 I 3.557457 2.293924 -0.235807 I 3.063593 -2.552933 -0.494360 I -0.364874 0.324395 -2.478336 I 0.364657 0.329439 2.477402 I -3.555570 2.297709 0.229383 I -3.065282 -2.549034 0.501394

Hg 2.148595 -0.047501 0.424977 Hg -2.148721 -0.045305 -0.424602 I 4.037598 1.891425 -0.206687 I 2.317728 -2.712353 -0.433656 I -0.431376 0.859200 -2.418277 I 0.432371 0.866250 2.415001 I -4.035000 1.898779 0.202402 I -2.321155 -2.707030 0.441244

Table S7. Coordinates of (MX3-)2 (M = Zn, Cd, Hg; X = Cl, Br, I). Minima in water.

Zn Cd Hg

bridged

(MCl3-)2

Zn -1.626401 -0.006701 0.000037 Zn 1.626255 -0.006982 -0.000149 Cl -2.826796 -1.906261 0.000042 Cl -2.629240 1.993114 0.000092 Cl 0.000022 -0.074418 -1.742085 Cl -0.000018 -0.074234 1.741942 Cl 2.826946 -1.906524 0.000205 Cl 2.629438 1.992566 -0.000129

Cd -1.849915 -0.013327 0.000031 Cd 1.849915 -0.013324 -0.000006 Cl -3.361616 -1.974809 0.000075 Cl -2.785329 2.322809 -0.000070 Cl -0.000015 -0.309986 -1.854551 Cl 0.000015 -0.309823 1.854573 Cl 3.361616 -1.974808 0.000028 Cl 2.785330 2.322807 -0.000122

Hg -1.935069 0.031666 -0.000205 Hg 1.935202 0.031831 -0.000044 Cl -3.348539 -1.977283 0.000004 Cl -2.327103 2.473196 0.000745 Cl 0.000063 -0.644465 -1.938964 Cl 0.000220 -0.645637 1.939340 Cl 3.348025 -1.977410 -0.000135 Cl 2.326709 2.472786 0.000183

(MBr3-)2

Zn -0.683580 -0.717026 -1.355892 Zn 1.069620 -1.966251 -3.900510 Br -2.994108 -0.939915 -0.820354 Br 0.749139 0.576324 0.028970 Br -0.414255 0.036580 -3.754545 Br 0.281683 -3.001328 -1.720188 Br 0.472750 -3.377522 -5.714616 Br 3.357119 -1.387453 -3.630931

Cd -1.900896 -0.120981 -0.008851 Cd 1.900922 -0.119022 0.008920 Br -3.785087 -2.000370 -0.008886 Br -2.609139 2.441295 -0.009982 Br 0.008882 -0.302003 -1.993360 Br -0.009128 -0.302250 1.993633 Br 3.786786 -1.996284 0.008257 Br 2.607605 2.443911 0.010253

Hg -2.070981 -0.097630 -0.008030 Hg 2.070375 -0.095894 0.007954 Br -3.582623 -2.216376 -0.011822 Br -2.871110 2.417843 -0.011464 Br 0.003075 -0.085487 -1.973194 Br -0.003363 -0.085709 1.973162 Br 3.585421 -2.212841 0.011372 Br 2.869152 2.420390 0.012005

(MI3-)2

Zn -0.745097 -0.714861 -1.319509 Zn 1.112604 -2.042738 -3.941605 I -3.205410 -0.735831 -0.520305 I 0.922091 0.660612 0.094713 I -0.623384 0.048746 -3.934427 I 0.185600 -3.241888 -1.675909 I 0.658557 -3.509253 -6.009901 I 3.533405 -1.241379 -3.561121

Cd -0.737004 -0.671752 -1.115429 Cd 1.247536 -2.114604 -4.012001 I -3.493113 -0.759786 -0.441005 I 1.069300 1.008572 0.207693 I -0.768418 0.063983 -3.973147 I 0.062607 -3.471490 -1.696159 I 0.593853 -3.613106 -6.318047 I 3.863606 -1.218409 -3.519970

Hg -1.569489 0.065875 -0.054807 Hg 1.570293 0.065920 -0.056882 I -3.211416 -2.235194 0.111096 I -2.954239 2.451977 -0.001495 I -0.000648 -0.415734 -2.528050 I 0.001368 -0.222553 2.477279 I 3.214249 -2.232152 0.107961 I 2.949473 2.454720 0.001797

stacked

(MCl3-)2

Zn -2.218854 0.003017 0.384226 Zn 2.219009 0.002894 -0.383819 Cl -2.912365 -1.930555 -0.487147 Cl -2.943084 1.913115 -0.512130 Cl 0.705097 0.012738 -2.015028 Cl -0.704943 0.012599 2.015286 Cl 2.911382 -1.931443 0.486499 Cl 2.943642 1.913114 0.511802

Cd 2.181181 0.003667 0.360904 Cd -2.181208 0.003664 -0.360938 Cl 3.240205 2.019114 -0.683401 Cl 2.799490 -2.292986 -0.412032 Cl -0.517107 0.263135 -2.210816 Cl 0.517122 0.262884 2.210890 Cl -3.240137 2.019136 0.683514 Cl -2.799525 -2.293034 0.411934

Hg -1.992028 -0.042685 -0.268154 Hg 1.992134 -0.039859 0.267941 Cl -2.755156 2.274197 0.514147 Cl -3.030513 -2.038134 0.787749 Cl 0.565492 -0.044181 2.288664 Cl -0.565436 -0.046215 -2.288846 Cl 2.753191 2.277848 -0.512599 Cl 3.031261 -2.033862 -0.789481

(MBr3-)2

Zn -2.204229 -0.001908 0.469290 Zn 2.205654 -0.000770 -0.468498 Br -3.215430 -1.979733 -0.339204 Br -2.916380 2.094720 -0.344310 Br 0.558998 -0.105566 -2.158736 Br -0.558078 -0.115602 2.159083 Br 3.211161 -1.985080 0.332701 Br 2.918507 2.093558 0.349787

Cd 2.188728 0.011222 0.501667 Cd -2.188712 0.011283 -0.501697 Br 3.463350 2.106051 -0.393513 Br 2.757952 -2.424340 -0.335800 Br -0.332084 0.302454 -2.366954 Br 0.332408 0.302218 2.366803 Br -3.463448 2.106471 0.392902 Br -2.758165 -2.423880 0.336605

Hg 2.212015 -0.008269 -0.425817 Hg -2.212023 -0.008272 0.425824 Br 3.397705 -2.120991 0.541422 Br 2.743118 2.423797 0.439854 Br -0.390842 -0.283988 2.285891 Br 0.390831 -0.283905 -2.285894 Br -3.397717 -2.120959 -0.541487 Br -2.743082 2.423830 -0.439796

(MI3-)2

Zn -0.776133 -1.358177 -0.131983 Zn 1.123176 -1.692226 -4.335787 I -3.325112 -1.401617 -0.456666 I 0.307274 0.542406 1.203515 I -0.243975 0.377265 -3.681427 I 0.592047 -3.427237 -0.785266 I 0.037167 -3.590230 -5.673240 I 3.671277 -1.662741 -4.009362

Cd -0.773509 -1.392013 -0.160415 Cd 1.172890 -1.668490 -4.322701 I -3.602453 -1.417795 -0.177408 I 0.573756 0.806271 1.051025 I -0.483025 0.496171 -3.727443 I 0.535280 -3.721502 -0.933962 I 0.029619 -3.693041 -5.871493 I 3.933164 -1.622158 -3.727822

Hg -0.755292 -1.400788 -0.186084 Hg 1.250332 -1.599744 -4.211385 I -3.577097 -1.357514 -0.167453 I 0.374868 0.808077 1.121589 I -0.558534 0.394605 -3.645618 I 0.587330 -3.689447 -0.922044 I 0.097435 -3.558834 -5.885308 I 3.966680 -1.808912 -3.973915