1

Structure, Bonding, Relativistic Effects, and Dispersion in the Group 12 Dihalide

(MX2)3 Clusters, with Lessons from the Extended Solids

Kelling J. Donald*, John Stewart, and Matthew Guarino

Department of Chemistry, Gottwald Center for the Sciences, University of Richmond,

28 Westhampton Way, Richmond, VA 23173, United States

* Corresponding Author: Tel.: 804-484-1628; Fax: 804-287-1897; E-mail: kdonald@richmond.edu

Supporting Information

2

Table S1a: Relative energies (Etrimer - E(D2d)trimer) obtained at the B3PW91 level (in kcal·mol-1 units) using the starting geometries in Figure 2. In cases where a system collapsed to a structural isomer from Figure 3 (which do not have assigned columns in this table), the identity [in square brackets] and the relative energy of that isomer are given together. (ii) C2 (iii) C3h (iv) D2h (v) Cs (vi) D3h (vii) D3d (viii) a Cs(2) (ix) D3h(2) (x) C3v(2)

ZnF2 0.0[D2d] 10.6[D3h(2)] 0.0[D2d] 11.9 63.4 60.7 10.6[D3h(2)] 10.6 10.6[D3h(2)]

ZnCl2 0.0[D2d] 14.4[D3h(2)] 11.7 12.9 60.2 0.0[D2d] 14.4 14.4 12.2[Cs(3)] ZnBr2 0.0[D2d] 14.4[D3h(2)] 13.5 11.4 57.0 0.0[D2d] 14.4 14.5 14.4[Cs(2)] ZnI2 0.0[D2d] 12.0[D3h(2)] 139.5 9.9 55.7 0.0[D2d] 10.3[Cs(3)] 12.0 10.2[Cs(3)]

CdF2 0.0[D2d] 12.5[D3h(2)] 0.0[D2d] 6.2[C2v] 49.3 47.9 12.5[D3h(2)] 12.5 12.5[D3h(2)]

CdCl2 0.0[D2d] 15.6[D3h(2)] 6.6 8.1[C2v] 49.6 46.1 10.4[Cs(3)] 15.6 10.4 [Cs(3)]

CdBr2 0.0[D2d] 15.9[D3h(2)] 7.8 7.5[C2v] 47.6 42.9 15.3 15.9 10.1 [Cs(3)]

CdI2 0.0[D2d] 13.8[D3h(2)] 10.4 7.3[C2v] 47.5 0.0[D2d] 13.3 13.8 9.2 [Cs(3)]

HgF2 -16.5 -14.5 -14.6[C2h] -16.5[C2] 71.4 -16.5[C2] -14.5[C3h] 7.8 -14.5[C3h]

HgCl2 -13.4 -9.9 4.5 -13.4[C2] 64.8 -13.0[C2h] 9.1 10.8 -9.9[C3]

HgBr2 -8.1 -4.8 5.8 -8.1[C2] 60.2 -7.8[C2h] 8.8 11.1 -7.6[C3]

HgI2 -2.9 -b -2.6[C2h] 0.5[C2(2)] 58.2 -2.9[C2] 7.3 8.7 -c

a The Cs(2)(chair) structures (with symmetrically unrelated terminal halides bonded to the alternating metal atoms in a chair-shaped (zig-zag) six membered ring) optimizes to a very similar C3v form. The latter keeps the chair shaped ring, but the terminal atoms point in symmetrically identical directions. b This system dissociated into isolated linear HgI2 molecules. c This system dissociated into a dimer fragment and an isolated monomer unit. Table S1b: Number of imaginary frequencies for the optimized structures (see Table S1a) generated using the starting geometries in Figure 3. In cases where a system collapsed to a structural isomer from Figure 3 (which do not have columns in this table), the identity [in square brackets] and the number of imaginary frequency are given together.

(i) D2d (ii) C2 (iii) C3h (iv) D2h (v) Cs (vi) D3h (vii) D3d (viii) a Cs(2) (ix) D3h(2) (x) C3v(2)

ZnF2 0 0[D2d] 0[D3h(2)] 0[D2d] 0[C2v] 3 0 0[D3h(2)] 0 0[D3h(2)] ZnCl2 0 0[D2d] 2[D3h(2)] 1 0 5 0[D2d] 2 2 0[Cs(3)]

ZnBr2 0 0[D2d] 3[D3h(2)] 1 0 5 0[D2d] 2 3 2[Cs(2)]

ZnI2 0 0[D2d] 3[D3h(2)] 1 0 5 0[D2d] 1[Cs(3)] 3 1[Cs(3)]

CdF2 0 0[D2d] 0[D3h(2)] 0[D2d] 0[C2v] 1 0 0[D3h(2)] 0 0[D3h(2)] CdCl2 0 0[D2d] 3[D3h(2)] 1 0[C2v] 3 0 0[Cs(3)] 3 0[Cs(3)] CdBr2 0 0[D2d] 3[D3h(2)] 1 0[C2v] 3 2 2 3 0[Cs(3)] CdI2 0 0[D2d] 3[D3h(2)] 1 1[C2v] 5 0[D2d] 2 3 1[Cs(3)]

HgF2 2 0 0 1[C2h] 0[C2] 3 0[C2] 0[C3h] 3 0[C3h] HgCl2 2 0 2 3 0[C2] 5 1[C2h] 1 4 1[C3] HgBr2 2 0 0 3 0[C2] 5 1[C2h] 1 4 0[C3] HgI2 2 0 -b 1[C2h] 0[C2(2)] 5 0C2] 1 4 -c

a The Cs(2)(chair) structures (with symmetrically unrelated terminal halides bonded to the alternating metal atoms in a chair-shaped (zig-zag) six membered ring) optimizes to a nearly identical C3v form. The latter keeps the chair shaped ring, but the terminal atoms point in symmetrically identical directions. b This system dissociated into isolated linear HgI2 molecules. c This system dissociated into a dimer fragment and an isolated monomer unit.

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Table S1c: A basic summary of relative energies (Etrimer - E(D2d)trimer in kcal·mol-1 units) obtained at the B3PW91 level using the starting geometries in Figure 3. If a starting structure optimized to an alternative form (see Figures 3 and 4) and is a minimum in that latter geometry, the relative energy of that cluster is given under the symmetry label of that preferred isomer. Data are included here only for local minima - cases with no imaginary frequency. a The full slate of structural and frequency data, for all starting structures for all 12 molecules is given in the supporting information in Tables S1a,b.

(ii) C2 (iii) C3h (v) Cs (vii) D3d (x) D3h(2) (xi) Cs(3) (xiii) C3 (xiv) C2v (xv) C2(2) ZnF2 - - 11.9 60.7 10.6 - - - - ZnCl2 - - 12.9 - - 12.2 - - - ZnBr2 - - 11.4 - - - - - - ZnI2 - - 9.9 - - - - - - CdF2 - - - 47.9 12.5 - - 6.2 - CdCl2 - - - 46.1 - 10.4 - 8.1 - CdBr2 - - - - - 10.1 - 7.5 - CdI2 - - - - - - - - - HgF2 -16.5 -14.5 - - - - - - - HgCl2 -13.4 - - - - - - - - HgBr2 -8.1 -4.8 - - - - -7.6 - - HgI2 -2.9 -b - - - - - - -2.5

a A ‘-’ symbol indicates that the optimized structure was not a local minimum or was not located for that geometry. The actual outcome is given in the supporting information in Table S1a. The cases not included here, such as (iv) and (ix), yielded no local minimum. b This system dissociated into isolated linear HgI2 molecules.

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Table S1d: MP2 (unscaled) harmonic vibrational frequencies and force constants in cm-1 and mDynes·Ångstrom-1 units, respectively.

* Doubly degenerate being mode. ν1 (σg) νsymm, ν1 (u) νbend, and ν3 (σu) νasymm. Table S1e: B3PW91 (unscaled) harmonic vibrational frequencies and force constants in cm-1 and mdyne·Ångstrom-1 units, respectively.

* Doubly degenerate being mode. ν1 (σg) νsymm, ν1 (u) νbend, and ν3 (σu) νasymm.

ν1 (σg) ν2 (πu) ν3 (σu) k1 (σg) k2 (πu) k3 (σu) ZnF2 631.0 172.9 816.1 4.457 0.453 10.103 ZnCl2 377.2 112.2 543.2 2.931 0.340 7.965 ZnBr2 233.0 89.2 430.8 2.525 0.317 7.396 ZnI2 240.6 74.9 408.3 4.328 0.235 6.976 CdF2 571.0 142.7 681.4 3.650 0.288 6.565 CdCl2 243.6 121.4 314.3 1.223 0.413 2.764 CdBr2 219.6 68.0 338.8 2.242 0.262 6.495 CdI2 263.7 55.0 315.8 5.201 0.210 6.913 HgF2 618.4 191.0 691.7 4.281 0.477 6.253 HgCl2 382.8 108.4 434.9 3.019 0.308 4.950 HgBr2 238.6 73.2 310.4 2.647 0.340 6.116 HgI2 264.5 56.3 277.3 5.230 0.299 7.249

ν1 (σg) *ν2 (πu) ν3 (σu) k1 (σg) k2 (πu) k3 (σu) ZnF2 615.5 170.0 794.4 4.241 0.438 9.572 ZnCl2 361.1 110.1 521.3 2.686 0.327 7.335 ZnBr2 219.8 83.3 406.7 2.247 0.277 6.593 ZnI2 156.2 67.9 345.2 1.824 0.193 4.985 CdF2 551.8 138.7 659.5 3.408 0.272 6.151 CdCl2 331.0 89.0 425.3 2.257 0.221 5.062 CdBr2 204.3 64.2 316.6 1.940 0.234 5.674 CdI2 146.5 51.3 262.9 1.606 0.183 4.790 HgF2 582.4 177.6 658.8 3.797 0.412 5.672 HgCl2 351.7 99.9 406.2 2.548 0.261 4.318 HgBr2 215.2 67.2 284.7 2.154 0.287 5.143 HgI2 153.9 50.7 228.1 1.771 0.243 4.905

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Table S1f: Sample experimental vibrational frequencies in cm-1 units.a,b,c They are included for comparison with the computed values provided in this work. ν1 (σg) *ν2 (πu) ν3 (σu) ZnF2 595.5 150 758 ZnCl2 361 103 508.5 ZnBr2 230 80 413 ZnI2 168 67.6 337.5 CdF2 555.0(4) 121(5) 661.7(2) CdCl2 329.8 83 427 CdBr2 209.1 60 315 CdI2 153 51 261.3 HgF2 567.6(3) 170(5) 641.7(2) HgCl2 358 108(8) 413 HgBr2 221.8 73(5) 293 HgI2 158.4 63(5) 237 * Doubly degenerate being mode. ν1 (σg) νsymm, ν1 (u) νbend, and ν3 (σu) νasymm. a Experimental results taken largely from a collection of vibrational frequency data from across the literature for

these group 12 dihalides in reported in a review by: (i) Hargittai, M. Chem. Rev. 2000, 100, 2297. The original sources of the data listed here are provided below. (ii) ν1, ν2, and ν3 for ZnF2, CdF2, and HgF2: Givan, A.; Loewenschuss, A. J. Chem. Phys. 1980, 72, 3809; 1976, 64, 1967. (iii) ν1 for ZnX2, for X = Cl, Br, and I: Beattie, I. R.; Horder, J. R. J. Chem. Soc. A 1970, 2433. (iv) ν3 for ZnBr2, CdCl2, CdBr2 and HgI2 Klemperer, W. J. Chem. Phys. 1956, 25, 1066. (v) ν2, and ν3 for ZnX2, for X = Cl, Br, and I: Givan A.; Loewenschuss, A. J. Chem. Phys. 1978, 68, 2228. (vi) ν1 for CdX2, for X = Cl, and Br, Strull, A.; Givan, A.; Loewenschuss, A. J. Mol. Spectrosc. 1976, 62, 283. (vii) ν2, and ν3 for CdI2 Konings, R. J. M.; Booij, A. S.; Cordfunke, E. H. P. Vib. Spectrosc. 1991, 2, 251. (viii) ν1 for HgX2, for X = Cl, Br, and I: Clark, R. J. H.; Rippon, D. M. J. Chem. Soc., Faraday Trans. 2. 1973, 69, 1496. (ix) ν3 for HgX2, for X = Cl, and Br, Klemperer, W.; Lindeman, L. J. Chem. Phys. 1956, 25, 397. b (x) The ν2 values for HgX2, for X = Cl, Br, and I, are from (a) Givan A.; Loewenschuss, A. J. Chem. Phys. 1976, 65, 1851, and (b) Loewenschuss, A.; Ron, A.; Schnepp, O. J. Chem. Phys. 1969, 50, 2502. These three values are not from Hargittai’s review (i) above. The other values, however, are all from that source. c The B3PW91 values appear to be in far better general agreement with experiment than the MP2 values. The MP2 results for the (symmetric and antisymmetric) stretching modes for the iodides and for CdCl2 are especially poor relative to the experimental data.

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Table S2: Optimized D2d structures obtained at the B3PW91 level of theory with the isomer (i) starting geometry. The computed energies for the structures are given in Hartree units.

(ZnF2)3 -1280.8742304 (ZnCl2)3 -3443.0333422 30 -0.003931000 0.000088000 -0.729640000 30 0.002331000 -0.000051000 2.172530000 30 0.009173000 -0.000010000 5.074677000 9 -0.007508000 0.000234000 -2.473065000 9 1.267192000 -0.035342000 0.715981000 9 -1.268624000 0.035310000 0.721080000 9 -0.029777000 -1.268167000 3.626736000 9 0.040882000 1.268120000 3.626535000 9 0.013670000 0.000025000 6.818113000

30 -0.004474365 0.000109158 -0.946061519 30 0.003557065 -0.000133288 2.172856308 30 0.008822323 0.000052201 5.293082377 17 0.016099050 0.000074156 7.395065271 17 0.052612451 1.687486433 3.742034922 17 -0.041396499 -1.687504258 3.742376439 17 -1.688644578 0.047048975 0.605552977 17 1.683315233 -0.046944212 0.596396150 17 -0.004963398 0.000103355 -3.048360044

(ZnBr2)3 -3183.8431854 (ZnI2)3 -2457.0501569 30 -0.004126092 0.000003238 -1.042681090 30 0.003082311 0.000243488 2.171943096 30 0.010783702 0.000021817 5.390260036 35 -0.008655883 -0.000213894 -3.285752539 35 -1.834714515 0.051099263 0.551298092 35 1.830240292 -0.051002845 0.540995945 35 0.059679051 1.832771971 3.796956767 35 -0.042473588 -1.832573427 3.796930566 35 0.011668329 -0.000025804 7.632990976

30 0.000327293 0.000021105 -1.221683275 30 -0.003919377 0.000698258 2.169154607 30 0.012710702 -0.000316277 5.568829990 53 0.025431501 -0.000962979 8.011587258 53 0.058334593 2.017790635 3.895986754 53 -0.054094654 -2.017284742 3.895395265 53 2.015952931 -0.055419900 0.446468365 53 -2.021334057 0.057051092 0.451744401 53 -0.007220647 -0.001213756 -3.664542830

(CdF2)3 -1102.6842473 (CdCl2)3 -3264.8843803 48 -0.002993000 -0.000027000 -1.147290000 48 0.003474000 0.000183000 2.179496000 48 0.007041000 -0.000144000 5.504937000 9 -0.005915000 -0.000144000 -3.092441000 9 0.037125000 -1.336191000 0.512636000 9 -0.037303000 1.336326000 0.512625000 9 -1.329764000 -0.037142000 3.847616000 9 1.341048000 0.037305000 3.843129000 9 0.011166000 -0.000406000 7.450063000

17 -0.443957409 0.004264748 -1.337611247 17 -0.856577418 0.001009208 3.070507384 17 2.509931929 0.000881230 1.963889508 17 1.930450077 1.767844920 5.885896971 17 1.928539424 -1.777162035 5.878153413 17 3.183134663 -0.009200298 9.738106269 48 0.276228618 0.002464010 0.842598080 48 1.379553127 0.000223425 4.198918490 48 2.471817465 -0.012687943 7.554668983

(CdBr2)3 -3005.7111913 (CdI2)3 -2278.937492 35 0.464270504 -0.004163729 1.053632755 35 0.407412759 0.003965779 5.697102479 35 3.926944987 0.004020886 4.140763233 35 3.622068776 1.948579570 8.216484072 35 3.633696395 -1.899569967 8.243150702 35 5.326394509 0.044058107 12.096763851 48 2.899838656 0.008732629 6.573370576 48 4.348893939 0.040519787 9.871764491 48 1.440856360 0.000505006 3.279262680

53 0.514389803 0.005935298 1.169683712 53 0.381943487 -0.005599405 6.115200444 53 4.257216942 -0.005607121 4.411605609 53 3.831469164 -2.142527333 8.696464451 53 3.843129807 2.090582701 8.722677638 53 5.644539814 -0.045986671 12.802833937 48 4.586465727 -0.040293542 10.405502358 48 3.076495107 -0.011613453 6.987279510 48 1.574282355 -0.000453198 3.565700583

(HgF2)3 -1059.7621755 (HgCl2)3 -3222.0137526 80 0.000992212 0.000140049 -0.386532102 80 -0.001817828 -0.000192047 3.118653641 80 0.003043371 -0.000020512 6.623835942 9 -0.000943832 -0.000118147 -2.340428209 9 -1.294208449 -0.162788957 1.363724206 9 1.292836368 0.162684017 1.362718806 9 0.164589216 -1.293475934 4.873956543 9 -0.160932046 1.293561997 4.874213907 9 0.003926366 -0.000141816 8.577733338

17 -0.322415518 0.003299424 -0.697694976 17 -0.165032748 -0.000257249 3.796154991 17 2.998298127 -0.000240045 2.334313249 17 2.965315625 1.739042275 6.416969081 17 2.964783221 -1.745738167 6.415686893 17 4.703789631 -0.006311702 10.179425871 80 3.739653565 -0.002414667 8.092863838 80 2.190950911 -0.003835109 4.740733985 80 0.641898505 0.001453026 1.388783967

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(HgBr2)3 -2962.8604726 (HgI2)3 -2236.1120198 80 0.000927913 0.000170362 -0.642185472 80 -0.001281724 -0.000188503 3.118652262 80 0.002626324 -0.000091532 6.879485731 35 -0.002711250 -0.000295778 -3.077188109 35 -1.878292747 -0.236263702 1.235663650 35 1.877585049 0.236285828 1.235500436 35 0.237591652 -1.877980799 5.001548979 35 -0.234970025 1.877855159 5.001907108 35 0.004223530 -0.000122243 9.314492803

53 0.459631760 -0.002333344 1.032952123 53 0.382695185 -0.001315931 6.037990370 53 4.198714789 -0.001309833 4.366435839 53 3.849917739 -2.107954445 8.750410482 53 3.865142862 2.057976699 8.784545104 53 5.699543088 -0.048714554 12.931738524 80 4.638343673 -0.050133850 10.532717411 80 3.069917949 -0.000776121 6.986806022 80 1.518350309 -0.001841957 3.433213288

Table S3: Optimized C2 structures obtained at the B3PW91 level of theory using the cc-pVTZ basis sets with the isomer (2) starting geometry. For the Zn and Cd systems, these C2 starting structures reverted to the D2d geometry (above). The computed energies for the structures are given in Hartree units.

(HgF2)3 -1059.78856134 (HgCl2)3 -3222.0350296 80 -1.094902000 -1.015950000 0.355490000 80 0.965080000 0.584715000 2.993975000 80 4.674885000 0.558085000 2.909303000 9 -2.512336000 -0.599102000 -0.876592000 9 -0.556620000 1.104232000 1.863446000 9 0.352451000 -1.549263000 1.567642000 9 2.415389000 0.135596000 4.242331000 9 3.215562000 1.103077000 1.716939000 9 6.180423000 0.055445000 3.996365000

80 1.901376010 -0.821141041 5.317454396 80 3.966178408 -4.343987006 6.029732086 80 1.559085355 0.304569917 1.342176853 17 -0.214316202 0.641122445 -0.030276823 17 -0.007144664 -0.362050903 4.129608565 17 3.458139309 0.001571374 2.592597494 17 2.054085345 -4.020788161 4.804411685 17 5.847717134 -4.832724357 7.197122364 17 3.719512868 -1.153255768 6.677099165

(HgBr2)3 -2962.873429 (HgI2)3 -2236.1166922 80 0.260143152 -0.017802381 0.241009990 80 -0.408249586 0.038694709 4.407384815 80 4.214042865 -0.024565379 -1.234252338 35 -1.510070169 1.587030422 5.882650978 35 -1.013599546 1.630921513 1.501567371 35 0.759116102 -1.662998438 3.120989822 35 1.275009935 -1.670447377 -1.231560179 35 3.149792192 1.680619084 0.134360629 35 5.474463300 -1.571753330 -2.577855033

80 0.216613656 -0.088485768 0.228385339 80 -0.463988230 0.129356652 4.589825021 80 4.331800285 -0.046756234 -1.385179854 53 5.719670148 -1.691571325 -2.835627904 53 1.282476935 -1.912406387 -1.329314522 53 3.224391464 1.816152127 0.084656370 53 0.896441156 -1.715804957 3.324148040 53 -1.234022750 1.706660935 1.478416079 53 -1.725146131 1.783510770 6.141935257

Table S4: Optimized C3h structures obtained at the B3PW91 level of theory with the isomer (iii) starting geometry. The computed energies for the structures are given in Hartree units.

(HgF2)3 -1059.7853288 (HgCl2)3 -3222.0295215 9 -0.578936777 -2.080590764 -0.322853956 9 -0.273947709 0.292960736 2.102661219 9 2.396685968 0.327682931 0.305810478 9 5.217104780 2.230661819 0.479479292 9 2.095270004 2.366157388 2.779270641 9 -0.419273850 2.838656610 5.026047615 80 0.862356760 -0.858601391 0.042105683 80 3.639799129 2.247067359 1.582863727 80 -0.284347787 1.600466803 3.559139413

17 -1.663225000 1.097388000 -0.805710000 17 -0.396077000 0.480360000 3.117262000 17 3.998646000 0.766470000 4.242607000 17 2.042898000 -2.893362000 3.813741000 17 2.283099000 -5.410650000 0.036526000 17 -1.037814000 -3.061072000 0.920278000 80 2.094942000 -4.132002000 1.898965000 80 -1.332013000 -0.945000000 0.120736000 80 1.812246000 0.550089000 3.684601000

8

(HgBr2)3 -2962.86812201 (HgI2)3 80 -0.395486000 0.000000000 -0.319411000 80 -0.078784000 0.000000000 5.446837000 80 4.756347000 0.000000000 2.289456000 35 0.479564000 0.000000000 -2.558571000 35 -1.399892000 0.000000000 1.872252000 35 3.360673000 0.000000000 0.323669000 35 6.257928000 0.000000000 4.166905000 35 2.321455000 0.000000000 5.220858000 35 -2.455501000 0.000000000 5.808455000

dissociates to monomers

Table S5: Optimized D2h structures obtained at the B3PW91 level of theory with the isomer (iv) starting geometry. The computed energies for the structures are given in Hartree units.

(ZnF2)3 (ZnCl2)3 -3443.0146347

D2d

30 -0.000151022 0.000086082 -1.086536429 30 0.000164936 0.000054234 2.182399478 30 0.000983488 -0.000027922 5.451336669 17 0.001714162 -0.000257024 7.553464958 17 0.991606938 1.309248817 3.876591215 17 -0.990577640 -1.309106185 3.877008083 17 -0.991168857 -1.309052679 0.488142859 17 0.991013200 1.309303543 0.487855328 17 -0.000283319 -0.000246089 -3.188664944

(ZnBr2)3 -3183.8217489 (ZnI2)3 -2456.8277763 30 -0.000228799 0.000071981 -1.241510651 30 0.000281961 0.000030305 2.182398650 30 0.000995850 0.000001618 5.606311158 35 0.001670868 -0.000268459 7.848459845 35 1.070239298 1.413025293 3.971128015 35 -1.069054517 -1.412869695 3.971495255 35 -1.069706810 -1.412846512 0.393670101 35 1.069590703 1.413043715 0.393304356 35 -0.000401668 -0.000208686 -3.483659527

30 -0.004646362 0.003381090 -1.503577277 30 0.007258712 -0.005504167 2.182401283 30 -0.003302167 0.003338899 5.868379870 53 -0.004588020 0.003141634 -3.943787086 53 -1.166919836 -1.546320656 0.240406170 53 1.171771017 1.542594567 0.240066912 53 1.172327278 1.542747801 4.124287970 53 -1.166012588 -1.546441350 4.124830327 53 -0.002393481 0.003012332 8.308589014

(CdF2)3 (CdCl2)3 -3264.87379210

D2d

17 -0.468511000 0.000600000 -1.424818000 17 -0.850085000 -0.000494000 2.987481000 17 2.455161000 0.000836000 1.906428000 17 3.603186000 -0.001479000 5.417988000 17 0.297903000 -0.000148000 6.498916000 17 3.221547000 -0.002647000 9.830237000 48 2.502935000 -0.001610000 7.648855000 48 1.376621000 -0.000476000 4.202678000 48 0.249973000 0.000358000 0.756607000

(CdBr2)3 -3005.69871194 (CdI2)3 -2278.92096597 35 -0.479148000 0.000141000 -1.530191000 35 -0.996255000 0.000802000 3.090130000 35 2.582043000 0.001613000 1.968907000 35 3.731207000 -0.000245000 5.636061000 35 0.152943000 0.000566000 6.757366000 35 3.214131000 -0.003226000 10.256418000 48 2.487667000 -0.002525000 7.937947000 48 1.367500000 -0.001787000 4.363111000 48 0.247263000 -0.000483000 0.788297000

48 -0.000847000 -0.000440000 -0.338236000 48 0.000161000 -0.000066000 3.625566000 48 0.001120000 0.000540000 7.589367000 53 0.004499000 0.003451000 10.208263000 53 -1.553975000 -1.328341000 5.680601000 53 1.555204000 1.328921000 5.678430000 53 1.551988000 1.331001000 1.570552000 53 -1.552562000 -1.331669000 1.572681000 53 -0.004320000 -0.003536000 -2.957131000

9

(HgF2)3 (HgCl2)3 -3222.00663075

C2h

17 -0.505588000 0.006243000 -1.546476000 17 -0.854923000 -0.003741000 2.932983000 17 2.423999000 -0.001482000 1.858502000 17 3.608255000 -0.004789000 5.472674000 17 0.329205000 -0.002520000 6.546494000 17 3.258137000 0.002951000 9.952084000 80 0.208318000 0.002815000 0.638188000 80 1.376883000 -0.005306000 4.202567000 80 2.544441000 0.000767000 7.767355000

(HgBr2)3 -2962.8512956 (HgI2)3 35 -0.515846000 -0.004527000 -1.648444000 35 -0.994691000 0.002359000 3.043126000 35 2.554091000 0.002313000 1.931814000 35 3.729064000 0.001277000 5.682712000 35 0.180619000 0.001244000 6.795117000 35 3.252121000 -0.007958000 10.374250000 80 0.211807000 -0.000576000 0.673844000 80 1.367013000 0.003410000 4.363260000 80 2.523171000 -0.002686000 8.052369000

C2h

Table S6: Optimized Cs structures obtained at the B3PW91 level of theory with the isomer (v) starting geometry. The computed energies for the structures are given in Hartree units.

(ZnF2)3 -1280.8552906 (ZnCl2)3 -3443.0128285

C2v

30 0.342398000 -0.119511000 0.644626000 30 0.624339000 0.495080000 3.550879000 30 3.334924000 -0.118889000 2.464185000 17 -0.664767000 -0.977070000 -1.001546000 17 -1.072579000 1.081385000 2.338210000 17 1.228307000 -1.547756000 2.557501000 17 2.482033000 1.080772000 4.499738000 17 5.259593000 -0.977220000 2.600357000 17 2.285909000 1.130948000 0.818535000

(ZnBr2)3 -3183.8250819 (ZnI2)3 -2457.0343342 30 0.301754974 -0.127807095 0.587488551 30 0.616348440 0.420803337 3.564256267 30 3.404096552 -0.127824849 2.473825076 35 -0.763897149 -1.026018381 -1.184133122 35 -1.223884506 1.121210957 2.356333930 35 1.240838588 -1.740135292 2.537183463 35 2.364913350 1.208166067 0.688568869 35 2.535572425 1.121196929 4.642176931 35 5.467297427 -1.026237173 2.604686169

30 0.230980925 -0.136301477 0.498996753 30 0.596433878 0.352131738 3.597120382 30 3.515028324 -0.136547384 2.495841218 53 -0.939177385 -1.143497565 -1.413020233 53 -1.401530050 1.242180975 2.359022962 53 1.231250931 -1.981389467 2.553060942 53 2.615075828 1.241995752 4.801304725 53 5.751077068 -1.143689325 2.654899087 53 2.499551528 1.244251390 0.467167492

All the other clusters optimized to either the C2v or the C2 structure. A sample structure for each type is given in the ‘other’ structures table (Table S9) below.

10

Table S7: Optimized D3h structures obtained at the B3PW91 level of theory with the isomer (vi) starting geometry. The computed energies for the structures are given in Hartree units.

(ZnF2)3 -1280.7732084 (ZnCl2)3 -3442.9373467 30 0.000000000 0.000210535 2.525219058 30 0.000000000 -0.000135739 -0.000000004 30 0.000000000 0.000210539 -2.525219072 9 1.339577668 -0.773568190 1.484571829 9 0.000000000 1.546993250 1.484334468 9 -1.339577668 -0.773568190 1.484571829 9 -1.339577655 -0.773568176 -1.484571797 9 1.339577655 -0.773568176 -1.484571797 9 0.000000000 1.546993268 -1.484334513

30 0.000000000 -0.000003855 2.669164882 30 0.000000000 -0.000027105 0.000000000 30 0.000000000 -0.000003855 -2.669164881 17 1.730626618 -0.999127843 1.725420594 17 0.000000000 1.998272545 1.725431505 17 -1.730626617 -0.999127843 1.725420593 17 1.730626618 -0.999127844 -1.725420595 17 0.000000000 1.998272544 -1.725431503 17 -1.730626618 -0.999127844 -1.725420595

(ZnBr2)3 -3183.7523115 (ZnI2)3 -2456.9613645 30 0.000000000 -0.000057059 2.733048490 30 0.000000010 -0.000010748 0.000000003 30 -0.000000004 -0.000057062 -2.733048484 35 1.869138040 -1.079108560 1.824406572 35 0.000000004 2.158278975 1.824450828 35 -1.869138047 -1.079108568 1.824406583 35 -1.869138046 -1.079108567 -1.824406586 35 0.000000003 2.158278989 -1.824450837 35 1.869138040 -1.079108559 -1.824406568

30 0.000000001 0.000024154 2.830204115 30 0.000000001 -0.000056496 -0.000000002 30 -0.000000002 0.000024153 -2.830204115 53 2.063559082 -1.191392007 1.993418694 53 0.000000002 2.382787500 1.993359086 53 -2.063559076 -1.191392006 1.993418684 53 -2.063559081 -1.191392008 -1.993418695 53 -0.000000002 2.382787497 -1.993359082 53 2.063559076 -1.191392006 -1.993418684

(CdF2)3 -1102.6056061 (CdCl2)3 -3264.8053568 48 0.000000001 -0.001438840 2.911381655 48 0.000000000 0.001233834 0.000000000 48 -0.000000001 -0.001438837 -2.911381655 9 1.422472799 -0.820957654 1.642256871 9 -0.000000007 1.642736765 1.645638071 9 -1.422472801 -0.820957656 1.642256876 9 -1.422472797 -0.820957664 -1.642256876 9 0.000000007 1.642736759 -1.645638060 9 1.422472799 -0.820957666 -1.642256882

48 0.000000000 0.001456097 3.035762058 48 0.000000000 -0.000264269 0.000000000 48 0.000000000 0.001456097 -3.035762058 17 1.819985517 -1.051806060 1.820605234 17 0.000000000 2.102287578 1.817883222 17 -1.819985517 -1.051806060 1.820605234 17 -1.819985517 -1.051806060 -1.820605234 17 0.000000000 2.102287578 -1.817883222 17 1.819985517 -1.051806060 -1.820605234

(CdBr2)3 -3005.6353245 (CdI2)3 -2278.8618022 48 -0.000000002 0.000040885 3.085617780 48 0.000000001 -0.000037641 -0.000000003 48 0.000000005 0.000040889 -3.085617780 35 1.958561346 -1.130821964 1.900123810 35 -0.000000005 2.261621234 1.900103817 35 -1.958561364 -1.130821968 1.900123843 35 -1.958561342 -1.130821956 -1.900123808 35 0.000000004 2.261621243 -1.900103833 35 1.958561357 -1.130821960 -1.900123826

48 -0.000000001 -0.000146017 3.170906467 48 0.000000000 0.000022393 0.000000000 48 0.000000000 -0.000146017 -3.170906467 53 2.151332377 -1.241932608 2.047187964 53 0.000000000 2.483999387 2.047323511 53 -2.151332376 -1.241932608 2.047187964 53 0.000000000 2.483999387 -2.047323512 53 -2.151332377 -1.241932608 -2.047187964 53 2.151332377 -1.241932608 -2.047187964

(HgF2)3 -1059.6484072 (HgCl2)3 -3221.9105536 80 -0.000000001 0.000018575 3.033576815 80 0.000000000 0.000011525 0.000000000 80 0.000000001 0.000018572 -3.033576815 9 1.450330260 -0.837333112 1.694657653 9 -0.000000010 1.674641418 1.694555941 9 -1.450330252 -0.837333129 1.694657655 9 1.450330256 -0.837333123 -1.694657652 9 0.000000010 1.674641419 -1.694555946 9 -1.450330264 -0.837333105 -1.694657651

80 0.000000000 0.000006083 3.072226227 80 0.000000000 -0.000010549 0.000000000 80 0.000000000 0.000006083 -3.072226227 17 1.859837894 -1.073790879 1.845673001 17 0.000000001 2.147580368 1.845684892 17 -1.859837894 -1.073790878 1.845673000 17 -1.859837894 -1.073790879 -1.845673000 17 -0.000000001 2.147580368 -1.845684893 17 1.859837894 -1.073790877 -1.845673000

11

(HgBr2)3 -2962.7645274 (HgI2)3 -2236.019194 80 0.000000009 0.000037271 3.100305598 80 0.000000001 -0.000027191 0.000000006 80 -0.000000009 0.000037259 -3.100305593 35 2.000085547 -1.154786684 1.930748278 35 0.000000006 2.309549103 1.930738136 35 -2.000085513 -1.154786669 1.930748221 35 -2.000085557 -1.154786700 -1.930748298 35 -0.000000003 2.309549070 -1.930738097 35 2.000085519 -1.154786680 -1.930748251

80 0.000000001 -0.000059430 3.157234548 80 -0.000000001 -0.000049767 0.000000000 80 0.000000000 -0.000059432 -3.157234548 53 2.193326012 -1.266239094 2.089283638 53 0.000000000 2.532561833 2.089396614 53 -2.193326010 -1.266239093 2.089283635 53 -2.193326012 -1.266239094 -2.089283639 53 -0.000000001 2.532561831 -2.089396610 53 2.193326011 -1.266239095 -2.089283638

Table S8: Optimized D3d structures obtained at the B3PW91 level of theory with the isomer (vii) starting geometry. The computed energies for the structures are given in Hartree units.

The mercury systems optimized to other (C2 and C2h) geometries for which sample structures are included in Table S10.

(ZnF2)3 -1280.777553 (ZnCl2)3 30 0.006394438 0.003221345 1.489949001 30 0.013887981 -0.003130341 3.995375166 30 0.059472939 -0.001151107 6.500347155 9 1.553521928 0.171602984 2.518605544 9 -0.911989978 1.249398946 2.534044825 9 -0.612365951 -1.417503406 2.536649715 9 0.660192755 1.420602569 5.450318758 9 0.961059913 -1.253902160 5.452003912 9 -1.498413116 -0.172873436 5.480346962

D2d

(ZnBr2)3 (ZnI2)3 D2d D2d

(CdF2)3 -1102.6078621 (CdCl2)3 -3264.8108477 48 0.005702865 -0.000814217 1.096652114 48 0.014784336 0.000645916 3.995365800 48 0.059637717 -0.001620459 6.893694975 9 1.649320322 0.175639955 2.352441590 9 -0.658859822 -1.506413713 2.364358431 9 -0.962968322 1.329780414 2.364790022 9 -1.595932879 -0.189341370 5.651361211 9 0.692347613 1.513530699 5.622272129 9 1.022116846 -1.325468354 5.616733162

48 0.002883157 -0.000587941 1.010133440 48 0.010957553 0.000820177 3.995315562 48 0.058805978 -0.001416278 6.980242136 17 2.106419350 0.227232820 2.211590530 17 -0.845753686 -1.928931058 2.232391353 17 -1.238758838 1.701372005 2.233319107 17 -2.054418507 -0.241056208 5.790479427 17 0.876790173 1.936172974 5.754140070 17 1.294842153 -1.698504334 5.750130573

(CdBr2)3 -3005.6428576 (CdI2)3

35 -0.205207452 0.670320078 -0.348711128 35 -0.196832780 0.696763017 3.584913974 35 3.203195172 0.693306930 1.615769548 35 2.064213715 4.359166983 3.547149530 35 -1.349571296 4.325115554 1.599902887 35 2.049099818 4.321641323 -0.384045561 48 0.935299350 -0.502836668 1.621713140 48 0.932324579 2.511109683 1.612024048 48 0.914556619 5.524742164 1.572641135

D2d

12

Table S9: Optimized C3v forms of the Cs(2)(chair) structures obtained at the B3PW91 level with the isomer (viii) starting geometry. The optimized C3v structures are crown type (zig-zag) six-membered rings with a halide bonded to the alternating metal atoms in the ring. The computed energies for the structures are given in Hartree units.

(ZnF2)3 (ZnCl2)3 -3443.0104262

D3h(2)

30 -0.240593980 -0.091177376 -0.416806321 30 -0.240593969 -0.091177384 3.542129550 30 3.187754076 -0.091411574 1.562661615 17 -1.255681452 -0.656858127 -2.174749405 17 1.993918392 0.295503167 -0.328233319 17 -1.281063529 0.295743050 1.562661618 17 -1.255681429 -0.656858134 5.300072642 17 1.993918396 0.295503174 3.453556548 17 5.217851458 -0.656569146 1.562661652

(ZnBr2)3 -3183.8201853 (ZnI2)3 35 -0.137764172 -0.256217175 -0.283884193 35 -0.470256760 -0.067899053 3.760181019 35 3.233921310 -0.066802697 1.974940904 35 2.832196902 1.159840392 5.878578889 35 6.175512878 2.088518345 3.768233146 35 -0.902386833 2.089250315 7.176802943 30 4.136039739 1.142417685 3.852855084 30 0.435566124 1.141985561 5.635919275 30 0.836815197 -0.084295091 1.736468790

Cs(3)

(CdF2)3 (CdCl2)3 D3h(2) Cs(3)

(CdBr2)3 -3005.6868374 (CdI2)3 -2278.9162299 35 -0.240321135 0.285614559 -0.498502974 35 -0.461556970 -0.565204502 3.917692286 35 3.351395242 -0.564963924 2.080561609 35 2.938428442 0.698294741 6.099089590 35 6.123662605 2.648871374 3.584183252 35 -1.013539175 2.648959785 7.022385171 48 4.272525373 1.095522219 3.882272885 48 0.373367200 1.095528834 5.760717957 48 0.795682803 -0.195824805 1.651696079

53 0.425527570 -0.416486364 -0.946787396 53 -0.598209553 -0.797367421 3.729188517 53 2.954395208 -0.416574041 6.937295706 53 -0.055737296 3.200799150 5.981977401 53 -1.467164955 3.200879805 1.581317699 53 1.395501144 6.748518313 3.089368654 48 0.104233242 4.501269642 3.504041101 48 0.949844660 0.613557403 5.591940676 48 -0.422504214 0.613621405 1.313540765

(HgF2)3 (HgCl2)3 -3221.9992511

C3h

17 -0.296598235 0.349924696 -0.568800506 17 -0.180964272 -0.611617575 3.733993835 17 3.165490095 -0.611500941 1.988658854 17 5.932240496 2.619328691 3.153921926 17 2.911049159 0.514741189 5.581931804 17 -0.809026013 2.619373094 6.669666974 80 0.452345348 1.096923221 5.486960810 80 4.240420553 1.096949428 3.511455061 80 0.740295730 -0.178213515 1.419578152

(HgBr2)3 -2962.8464894 (HgI2)3 -2236.1004185 35 -0.191699135 0.602147500 -0.398659702 35 -0.334820054 -0.792537604 4.002169159 35 3.338416094 -0.792773341 2.232661149 35 2.940608766 0.424115653 6.103606743 35 5.874566598 2.855575491 3.493622627 35 -0.928981117 2.855409853 6.771926412 80 4.236037096 1.089049080 3.880506144 80 0.394702147 1.089050255 5.731284456 80 0.810813991 -0.183238604 1.682978867

53 0.702083979 -0.295542273 -0.831602559 53 -0.811444830 -0.739754706 3.797704376 53 3.113156450 -0.294570464 6.681903052 53 -0.281994875 3.157832447 5.993534506 53 -1.657435154 3.158016511 1.702942639 53 1.626603978 6.535549558 3.016227719 80 0.093800613 4.456423773 3.507350002 80 0.924969624 0.635266603 5.559168121 80 -0.423853978 0.634996442 1.354655267

13

Table S10: Optimized D3h(2) structures obtained at the B3PW91 level of theory with the isomer (ix) starting geometry. The computed energies for the structures are given in Hartree units.

(ZnF2)3 -1280.8572627 (ZnCl2)3 -3443.0104472 9 0.271987369 0.000000016 0.643131206 9 0.126579445 -0.000000006 3.974127611 9 2.751829125 -0.000000017 2.870148823 9 2.395562032 -0.000000007 5.694483508 9 5.564591552 0.000000017 4.659886138 9 -0.558659610 0.000000011 7.237496348 30 0.948780054 -0.000000004 2.255804046 30 3.829487041 -0.000000006 4.440572971 30 0.496512670 -0.000000003 5.842597299

30 -0.053983986 0.000000006 -0.093363904 30 -0.053983991 -0.000000002 3.929271329 30 3.430016145 0.000000003 1.917953705 17 -1.108243333 -0.000000011 -1.919473315 17 -1.100153382 0.000000005 1.917953712 17 2.210982961 0.000000001 3.829603316 17 2.210982965 0.000000009 0.006304095 17 -1.108243333 -0.000000003 5.755380743 17 5.538605760 -0.000000007 1.917953713

(ZnBr2)3 -3183.8201544 (ZnI2)3 -2457.0310033 30 -0.097351713 0.000000001 -0.168670764 30 -0.097351713 -0.000000001 4.004578183 30 3.516739686 0.000000001 1.917953711 35 -1.223073271 -0.000000005 5.954306435 35 5.768078764 -0.000000009 1.917953712 35 2.307566749 0.000000007 3.996859966 35 2.307566750 0.000000009 -0.160952545 35 -1.293122172 0.000000004 1.917953712 35 -1.223073278 -0.000000007 -2.118399010

30 -0.178090351 -0.000000001 -0.308479553 30 -0.178090352 -0.000000002 4.144386976 30 3.678171184 0.000000000 1.917953709 53 6.131266033 0.000000003 1.917953710 53 2.420323335 0.000000002 4.192127318 53 -1.404648988 0.000000004 6.268897546 53 -1.518625404 -0.000000008 1.917953712 53 2.420323337 -0.000000007 -0.356219900 53 -1.404648991 0.000000009 -2.432990120

(CdF2)3 -1102.6643657 (CdCl2)3 -3264.8595534 48 -0.065955846 -0.000098419 -0.118242747 48 -0.065955846 -0.000090996 3.954150168 48 3.457963731 -0.000086402 1.917953710 9 -1.049437659 0.000137770 -1.802913718 9 1.984164157 -0.000041659 0.400706958 9 -0.638269875 -0.000043532 1.917953710 9 1.984164158 -0.000039864 3.435200463 9 -1.049437658 0.000132977 5.638821140 9 5.408744644 0.000130125 1.917953710

17 -0.172424127 0.000001990 -0.401146782 17 -0.571609857 -0.000000488 3.817447024 17 2.688369073 -0.000000610 6.248693794 17 3.163240635 -0.000000639 2.211085091 17 -1.165533559 0.000001964 8.011964920 17 6.618653444 0.000002056 4.665001726 48 0.736746739 -0.000001427 1.714205957 48 0.212664132 -0.000001403 6.167042155 48 4.331987262 -0.000001443 4.394951200

(CdBr2)3 -3005.6858134 (CdI2)3 -2278.9154668 35 -0.242004874 0.000000015 -0.419293256 35 -0.242004878 0.000000031 8.394802101 35 -0.259343031 -0.000000060 3.987754427 35 3.583142024 0.000000011 6.206206125 35 3.583142015 0.000000039 1.769302715 35 7.391097549 -0.000000023 3.987754411 48 0.977421652 -0.000000009 6.282534191 48 0.977421640 -0.000000004 1.692974653 48 4.952107699 0.000000001 3.987754412

53 0.386632684 0.000000030 -0.893527524 53 1.018802844 -0.000000035 3.748201771 53 1.464633708 -0.000000072 8.411454015 53 -2.871610552 0.000000161 6.638390821 53 -3.429302114 -0.000000043 1.824047445 53 -7.132996702 -0.000000070 4.692431674 48 -0.104638759 0.000000007 6.299451947 48 -4.519261909 0.000000013 4.389779774 48 -0.658138279 0.000000009 1.521349836

(HgF2)3 -1059.7496784 (HgCl2)3 -3221.9964928 80 -0.180993762 -0.000327593 -0.318205105 80 -0.184957863 -0.000266345 3.930950739 80 3.497562261 -0.000596243 1.811618794 9 -1.162020982 0.000335450 -2.015640492 9 1.874365643 0.002384509 0.370429904 9 -0.617662046 -0.003167863 1.807097973 9 1.874821565 0.000422084 3.247494241 9 -1.161889786 0.001690117 5.630748944 9 5.458075113 -0.002707620 1.801580101

17 -0.213285852 -0.000001301 -0.495786636 17 -0.525805624 0.000000352 3.822535072 17 2.669757244 0.000000428 6.206697556 17 3.136736747 0.000000397 2.247154394 17 -1.226200501 -0.000001313 8.095272578 17 6.720229995 -0.000001199 4.676974104 80 4.427777258 0.000000710 4.406739671 80 0.153972529 0.000000961 6.245006818 80 0.698911946 0.000000965 1.624651528

14

NOTE: All of the C3v(2) structures collapsed to other conformations. See Tables 1 in the main article and table S1 above for the details. Other Structures Considered

Table S11: Sample coordinates for systems optimized in the geometries identified in Figure 4 in the main article. All of these systems were obtained at the B3PW91 level of theory.

(HgBr2)3 -2962.8427872 (HgI2)3 -2236.0980782 35 -0.287370911 0.000000011 -0.497636205 35 -0.287370879 0.000000004 8.473145086 35 -0.235677421 -0.000000056 3.987754421 35 3.571370427 0.000000044 6.185782423 35 3.571370464 0.000000040 1.789726390 35 7.481634039 -0.000000053 3.987754418 80 5.031528764 0.000000020 3.987754422 80 0.937747640 -0.000000001 6.351329542 80 0.937747683 -0.000000010 1.624179298

80 -0.304388932 0.000000001 -0.527194891 80 -0.304388924 -0.000000012 4.363102306 80 3.930732905 0.000000023 1.917953671 53 -1.625821622 -0.000000002 -2.816118828 53 -1.679845278 -0.000000029 1.917953710 53 2.500899787 0.000000029 -0.495803444 53 2.500899791 0.000000015 4.331710795 53 -1.625821568 0.000000011 6.652026268 53 6.573713659 -0.000000035 1.917953808

(xi) Cs(3) ZnI2 (starting with Cs(2)) CdI2 (starting with C3v(2))

53 -0.453503000 0.407686000 -0.793283000 53 1.871957000 -0.475974000 3.067777000 53 -0.127113000 -0.134371000 7.109639000 53 2.141408000 3.266091000 5.176859000 53 -1.359016000 2.111156000 3.281704000 53 -0.063960000 6.376773000 2.614832000 30 0.311002000 4.184584000 3.612080000 30 0.067873000 0.607530000 1.579266000 30 0.897236000 0.904744000 5.133009000

53 -1.145558000 -1.303354000 -1.067487000 53 -0.761166000 -0.630584000 3.728972000 53 3.714708000 0.428076000 5.820265000 53 2.215621000 1.282290000 1.326726000 53 2.246774000 6.080922000 1.745613000 53 -1.700844000 2.990153000 1.143496000 48 -0.704593000 0.285622000 0.991487000 48 0.875797000 3.877649000 1.444575000 48 1.809759000 0.266958000 4.040046000

(xii) C2h HgF2 (starting with D2h) HgBr2 (starting with D3d)

9 1.023409000 1.347791000 4.274163000 9 -0.627575000 -0.895282000 3.806077000 9 -1.077833000 -1.296556000 0.101803000 9 0.784805000 0.792451000 0.554861000 9 -0.341988000 -0.295208000 7.514772000 9 0.241668000 0.341078000 -3.159453000 80 -0.382602000 -0.428076000 -1.510452000 80 0.078548000 -0.051631000 2.180710000 80 0.304636000 0.485501000 5.879114000

35 0.074883000 0.106770000 10.168002000 35 0.362063000 -1.399857000 2.020088000 35 0.074578000 -0.046465000 -2.177545000 35 -0.889839000 2.514183000 1.799020000 35 -0.722208000 1.210820000 5.966283000 35 1.233996000 -2.384583000 6.198160000 80 -0.379866000 1.139128000 -0.134107000 80 -0.152971000 -0.087593000 3.995183000 80 0.604782000 -1.047138000 8.124013000

(xiii) C3 HgCl2 (starting with C3v(2)) HgBr2 (starting with C3v(2))

17 -1.663225000 1.097388000 -0.805710000 17 -0.396077000 0.480360000 3.117262000 17 3.998646000 0.766470000 4.242607000 17 2.042898000 -2.893362000 3.813741000 17 2.283099000 -5.410650000 0.036526000 17 -1.037814000 -3.061072000 0.920278000 80 2.094942000 -4.132002000 1.898965000 80 -1.332013000 -0.945000000 0.120736000 80 1.812246000 0.550089000 3.684601000

35 -1.549495000 1.364368000 -0.546425000 35 -0.334104000 0.684988000 3.742831000 35 4.466805000 0.339921000 3.865983000 35 1.799532000 -3.263048000 4.179350000 35 -1.833195000 -2.934373000 1.604394000 35 1.514253000 -5.308289000 -0.170754000 80 -1.667548000 -0.749111000 0.591233000 80 2.066357000 0.437325000 3.810385000 80 1.579231000 -4.262474000 1.992612000

15

Table S12: MP2 Optimized coordinates for the D2d (ZnX2)3 and (CdX2)3 structures obtained at the MP2 level of theory. This geometry is also preferred at the B3PW91 level. The computed energies for the structures are given in Hartree units.

(xiv) C2v (ZnF2)3 (starting with Cs) (CdF2)3 (starting with Cs)

30 0.364912000 -0.188449000 0.888929000 30 0.744734000 0.894800000 3.352342000 30 3.109447000 -0.182382000 2.556485000 9 -0.180551000 -0.778894000 -0.665270000 9 -0.743447000 0.836364000 2.323683000 9 1.241797000 -1.046698000 2.535985000 9 2.343189000 0.838139000 4.200352000 9 1.867641000 1.071198000 1.507298000 9 4.736558000 -0.783024000 2.325087000

48 0.250370000 -0.241122000 0.715074000 48 0.638812000 0.973844000 3.526249000 48 3.316396000 -0.237066000 2.579425000 9 -0.280409000 -0.912664000 -1.040565000 9 -0.960223000 0.850533000 2.295555000 9 1.215006000 -1.087714000 2.581133000 9 2.467557000 0.852329000 4.379909000 9 5.116027000 -0.915993000 2.239690000 9 1.851817000 1.139566000 1.532849000

(CdI2)3 (starting with Cs) (HgI2)3 (starting with Cs) 48 0.056714000 -0.402818000 0.411279000 48 0.701614000 0.929987000 3.423806000 48 3.673323000 -0.402616000 2.611327000 53 -0.925497000 -1.260029000 -1.871233000 53 -1.745742000 1.124812000 2.320856000 53 1.212768000 -2.032188000 2.583527000 53 2.806959000 1.124855000 5.089422000 53 6.151466000 -1.260439000 2.431082000 53 2.298162000 1.478228000 0.798755000

80 0.385232000 0.611069000 0.115325000 80 0.426542000 -1.134149000 3.877009000 80 3.781575000 0.620752000 2.187096000 53 6.277429000 0.955459000 2.932375000 53 2.651513000 -1.133308000 5.221208000 53 1.463535000 2.291509000 2.169028000 53 2.488216000 -1.291604000 0.487002000 53 -1.789344000 -1.139293000 2.517865000 53 -1.430799000 0.964650000 -1.748485000

(xv) C2(2) at the B3PW91 level of theory (HgBr2)3 (HgI2)3

80 -0.400029000 -0.028592000 -0.299896000 80 0.730035000 0.039263000 3.630857000 80 3.677019000 -0.014925000 0.034783000 35 0.290065000 1.796060000 5.212444000 35 -1.903852000 0.798931000 1.407440000 35 1.287364000 -1.855690000 2.204576000 35 0.993319000 -0.858300000 -2.097501000 35 2.352943000 1.868534000 0.831774000 35 5.173783000 -1.755580000 -0.680178000

80 -0.534074000 -0.146400000 -0.367301000 80 0.796572000 0.120933000 3.714648000 80 3.746142000 0.013410000 0.025915000 53 5.395938000 -1.863217000 -0.672101000 53 0.952653000 -1.027007000 -2.317791000 53 2.343569000 2.091855000 0.794657000 53 1.430178000 -2.016524000 2.333425000 53 -2.186696000 0.721115000 1.451047000 53 0.303955000 2.086490000 5.334744000

(ii) D2d at the MP2 level of theory ZnF2 -1279.2690038 ZnCl2 -3439.272229

30 -0.003880000 0.000088000 -0.711604000 30 0.002347000 -0.000040000 2.172565000 30 0.009139000 -0.000011000 5.056669000 9 -0.007404000 0.000206000 -2.445757000 9 1.261114000 -0.035161000 0.725149000 9 -1.262606000 0.035154000 0.730466000 9 -0.029567000 -1.261924000 3.617410000 9 0.040745000 1.261884000 3.617224000 9 0.013519000 0.000011000 6.790825000

30 -0.004766000 0.000094000 -0.892782000 30 0.004153000 -0.000089000 2.172498000 30 0.008993000 0.000055000 5.237784000 17 0.012400000 0.000125000 7.320817000 17 0.053331000 1.675050000 3.713372000 17 -0.040002000 -1.675084000 3.713653000 17 -1.675265000 0.046662000 0.636089000 17 1.674896000 -0.046707000 0.627287000 17 -0.008812000 0.000187000 -2.975777000

ZnBr2 -3175.6770049 ZnI2 -2450.4043693 30 -0.003898000 0.000003000 -0.966786000 30 0.002890000 0.000148000 2.172485000 30 0.009783000 0.000012000 5.311765000 35 -0.009371000 -0.000178000 -3.178140000 35 -1.810032000 0.050521000 0.594585000 35 1.809203000 -0.050320000 0.586780000 35 0.056847000 1.809699000 3.754489000 35 -0.044009000 -1.809552000 3.754597000 35 0.014069000 -0.000009000 7.523166000

30 -0.002860000 -0.000072000 -1.116657000 30 0.000355000 0.000150000 2.172772000 30 0.011345000 -0.000090000 5.461654000 53 0.019706000 -0.000214000 7.870972000 53 0.060869000 2.004374000 3.837955000 53 -0.050816000 -2.004269000 3.838061000 53 2.002949000 -0.055722000 0.504489000 53 -2.005399000 0.055954000 0.509687000 53 -0.009959000 0.000251000 -3.525994000

16

Table S13: Optimized coordinates for the C2(2) (HgX2)3 structures obtained at the MP2 level of theory starting with the C2 geometry, which is a stable minimum at the B3PW91 level. The computed energies for the structures are given in Hartree units.

CdF2 -1101.2891341 CdCl2 -3261.3450796 48 -0.002864000 -0.000019000 -1.114065000 48 0.003314000 0.000157000 2.178970000 48 0.007157000 -0.000145000 5.472013000 9 -0.006036000 -0.000124000 -3.047071000 9 0.037176000 -1.328571000 0.529019000 9 -0.036836000 1.328704000 0.529030000 9 -1.323378000 -0.036978000 3.830703000 9 1.333903000 0.037084000 3.827154000 9 0.011443000 -0.000348000 7.405018000

48 0.300188000 0.002313000 0.915418000 48 1.376435000 0.000044000 4.199139000 48 2.450616000 -0.010886000 7.483586000 17 -0.408297000 0.003601000 -1.242152000 17 -0.833142000 0.001327000 3.102970000 17 2.508353000 0.001356000 2.007715000 17 1.915491000 1.752884000 5.847594000 17 1.913058000 -1.763445000 5.838836000 17 3.156419000 -0.009557000 9.642020000

CdBr2 -2997.7684951 CdI2 -2272.519673 48 2.899038000 0.010726000 6.573704000 48 4.306611000 0.037813000 9.775083000 48 1.484319000 0.000695000 3.375380000 35 0.521875000 -0.004845000 1.185705000 35 0.453880000 0.004824000 5.739386000 35 3.927352000 0.004832000 4.204535000 35 3.599019000 1.922827000 8.164751000 35 3.609550000 -1.874555000 8.188855000 35 5.268735000 0.044330000 11.964896000

53 0.589109000 0.005979000 1.335947000 53 0.427636000 -0.006125000 6.178872000 53 4.272688000 -0.006181000 4.487727000 53 3.800956000 -2.125506000 8.628173000 53 3.811444000 2.074907000 8.651777000 53 5.571577000 -0.046860000 12.635405000 48 4.529165000 -0.037214000 10.276601000 48 3.077114000 -0.013394000 6.987119000 48 1.630244000 -0.001168000 3.695329000

(xi) C2(2) at the MP2 level of theory HgF2 -1057.9977835574 HgCl2 -3218.1223070440

80 -0.145490000 -0.010443000 -0.093009000 80 0.789984000 0.093189000 3.245897000 80 3.313774000 -0.078032000 0.159339000 9 4.584784000 -1.321921000 -0.505514000 9 1.095891000 -0.404540000 -1.505825000 9 2.071247000 1.230458000 0.877003000 9 1.256410000 -1.221782000 1.895190000 9 -1.288501000 0.385976000 1.399830000 9 0.382291000 1.343448000 4.615329000

80 1.644830000 -0.462831000 5.804278000 80 3.613650000 -3.514674000 4.833681000 80 2.144008000 -0.847711000 2.097869000 17 0.503205000 -1.111515000 0.608424000 17 0.337463000 0.631882000 4.340465000 17 3.917852000 -0.575939000 3.486431000 17 1.461847000 -3.261037000 4.160061000 17 5.728205000 -3.912202000 5.426139000 17 2.933572000 -1.532656000 7.302577000

HgBr2 -2954.5652180856 HgI2 -2229.3407110679 80 -0.285262000 -0.027095000 -0.206069000 80 0.855193000 0.059035000 3.346478000 80 3.423182000 -0.036555000 0.214012000 35 0.459146000 1.795304000 4.894550000 35 -1.784824000 0.662472000 1.502481000 35 1.371920000 -1.851727000 1.989284000 35 1.107644000 -0.718209000 -2.002014000 35 2.158314000 1.862460000 0.958163000 35 4.895334000 -1.755984000 -0.452586000

80 -0.336854000 -0.131236000 -0.211335000 80 0.857667000 0.144417000 3.411990000 80 3.468698000 -0.026423000 0.156954000 53 5.147824000 -1.835545000 -0.473745000 53 1.093053000 -0.902086000 -2.192102000 53 2.139119000 2.072333000 0.872122000 53 1.456962000 -2.010067000 2.114546000 53 -2.021775000 0.620778000 1.565735000 53 0.443542000 2.048485000 5.053077000

17

Influence of Counterpoise Correction on Interatomic Separations and Apparent

Over-Binding at the MP2 Level

Table S14: Differences in the interatomic separations

a,b (including monomer-monomer contacts) for mercury dihalide dimers obtained at the MP2 level of theory by (a) simple geometrical optimization and (b) optimization run with counterpoise correction. The cc-pVTZ basis sets described in the methods section were employed. The Gaussian 09 program was employed as prescribed by one reviewer. All distances are in angstrom units.

r / Optimized Contacts a / Å b / Å c / Å (HgF2)2 2.657 1.900 1.930 (HgCl2)2 3.168 2.232 2.254 (HgBr2)2 3.258 2.360 2.381 (HgI2)2 3.483 2.544 2.562 rcc: Optimized with Counterpoise a / Å b / Å c / Å (HgF2)2 2.736 1.899 1.924 (HgCl2)2 3.256 2.232 2.251 (HgBr2)2 3.383 2.358 2.376 (HgI2)2 3.637 2.542 2.555 r = rcc – r

a / Å b / Å c / Å (HgF2)2 0.079 -0.001 -0.007 (HgCl2)2 0.088 0.000 -0.003 (HgBr2)2 0.125 -0.002 -0.005 (HgI2)2 0.154 -0.002 -0.007 a ‘a’ bond between atoms 1 and 5, ‘b’ between 1 and 3, and ‘c’ between 1 and 2. b A discussion of the effects and limitations of counterpoise corrections is outside the scope of this work. One important observation is that for these HgX2 dimers the inclusion of counterpoise corrections causes a relaxation of the van der Waals type contacts and a very small contraction of the covalent bonds. As the electrostatic (and any small charge transfer) interactions between the monomers become weaker (with the elongation of bond c), the intra-monomer bonding interactions become less perturbed and stronger.

c

b

a

18

Seeking to Account for Dispersion Interactions: B97D3 and M062X

Table S15: Optimized minimum energy C2 (2) structures obtained at the B97D3 level of theory using the cc-pVTZ basis sets with the isomer (2) or C2 starting geometry. The C2 starting structures reverted to the C2(2) geometry. The computed energies for the structures are given in Hartree units.

(HgF2)3 -1060.444911 (HgCl2)3 -3223.1403423 80 0.052465000 -0.891910000 0.502323000 80 0.598739000 0.944457000 3.599069000 80 3.860463000 0.107521000 2.212706000 9 -0.916419000 -0.433192000 -1.114584000 9 -1.079864000 0.835564000 2.583690000 9 1.071463000 -1.430513000 2.112590000 9 2.322791000 1.008744000 4.539403000 9 2.368623000 1.109793000 1.381189000 9 5.361672000 -0.873628000 2.952511000

80 1.591218000 -0.395291000 5.901228000 80 3.719820000 -3.606904000 4.873044000 80 2.088437000 -0.820505000 1.966383000 17 0.385509000 -1.113915000 0.461628000 17 0.202977000 0.666026000 4.394252000 17 3.918012000 -0.518706000 3.378146000 17 1.502860000 -3.371108000 4.194068000 17 5.899394000 -3.975036000 5.476408000 17 2.976407000 -1.451247000 7.414769000

(HgBr2)3 -2968.3014407 (HgI2)3 -2239.0817372 80 -0.436273000 -0.036596000 -0.321699000 80 0.839496000 0.103812000 3.530928000 80 3.594826000 -0.071784000 0.149236000 35 0.408682000 1.971971000 5.033576000 35 -1.925283000 0.788697000 1.439898000 35 1.363251000 -1.898145000 2.173804000 35 1.008031000 -0.863503000 -2.119464000 35 2.323386000 1.914933000 0.898236000 35 5.024531000 -1.919686000 -0.540218000

80 -0.516831000 -0.136123000 -0.367483000 80 0.841464000 0.177380000 3.611151000 80 3.671078000 -0.054036000 0.117927000 53 5.267361000 -2.042079000 -0.531405000 53 1.018352000 -1.055907000 -2.309779000 53 2.322410000 2.131372000 0.831331000 53 1.438816000 -2.061784000 2.294558000 53 -2.166740000 0.777103000 1.481566000 53 0.372328000 2.244729000 5.169379000

(HgF2)3 (HgCl2)3

(HgBr2)3 (HgI2)3

Figure S1: Structures and certain key geometrical parameters (in Å units) of the optimized C2 (2) structures obtained at the B97D3 level of theory using the cc-pVTZ basis sets, starting with the C2 (isomer (2)) starting geometry.

19

Table S16a: Optimized coordinates for the C2 HgF2, and the C2(2) HgCl2, HgBr2, and HgI2 minimum energy structures obtained at the M062X level of theory using the cc-pVTZ basis sets, starting in each case with the with the C2 (i.e. isomer (2)) geometry. The C2 starting structures reverted to the C2(2) geometry in each case except for the fluoride. The computed energies for the structures are in Hartree units.

(HgF2)3 C2 -1059.2081054 (HgCl2)3 C2 (2) -3221.5704918 80 -0.970567000 -0.935321000 0.361533000 80 0.943456000 0.604587000 3.031146000 80 4.565459000 0.463372000 2.876921000 9 -2.382621000 -0.619740000 -0.916989000 9 -0.665801000 1.033192000 1.938148000 9 0.502458000 -1.414574000 1.604256000 9 2.457640000 0.271766000 4.282007000 9 3.045026000 0.977825000 1.707551000 9 6.144880000 -0.004272000 3.884326000

80 1.640872000 -0.459990000 5.810519000 80 3.679216000 -3.504727000 4.898338000 80 2.057014000 -0.826891000 2.074707000 17 0.442110000 -1.049436000 0.478498000 17 0.327800000 0.668430000 4.284759000 17 3.893840000 -0.596742000 3.521224000 17 1.467579000 -3.215548000 4.160613000 17 5.821811000 -4.009406000 5.498360000 17 2.954391000 -1.592374000 7.332908000

(HgBr2)3 C2 (2) -2962.574834 (HgI2)3 C2 (2) -2234.1627244 80 -0.337776000 -0.028569000 -0.247489000 80 0.793103000 0.172083000 3.433004000 80 3.498005000 -0.149632000 0.137579000 35 0.402426000 1.944942000 5.032356000 35 -1.848957000 0.749699000 1.507638000 35 1.343004000 -1.828196000 2.062517000 35 1.100897000 -0.807917000 -2.062144000 35 2.225195000 1.839460000 0.915370000 35 5.024752000 -1.902171000 -0.534534000

80 -0.436052000 -0.146902000 -0.281376000 80 0.810768000 0.211573000 3.539795000 80 3.582514000 -0.080687000 0.073562000 53 5.288727000 -1.928788000 -0.584753000 53 1.065333000 -0.998403000 -2.252333000 53 2.206249000 2.062079000 0.837492000 53 1.456663000 -1.991537000 2.198758000 53 -2.096569000 0.692225000 1.563122000 53 0.370605000 2.161096000 5.202977000

(HgF2)3 C2 (HgCl2)3 C2 (2)

(HgBr2)3 C2 (2) (HgI2)3 C2 (2)

Figure S2: Structures and certain key geometrical parameters (in Å units) of the optimized C2 HgF2, and C2(2) HgCl2, HgBr2, and HgI2 structures obtained at the M062X level of theory using the cc-pVTZ basis sets, starting with the C2 (i.e. isomer (2)) starting geometry.

20

Table S16b: Data for the optimized minimum energy C2(2) HgF2 structure obtained at the the M06-2X level of theory using the cc-pVTZ basis sets, starting in each case with the with the C2(2) geometry. The initial C2 starting structure for the fluoride did not revert to the C2(2) geometry. The computed energy for the structure is in Hartree units.

(HgF2)3 C2 (2) -1059.2111002 (HgF2)3 C2 (2) Geometry 80 0.177352000 -0.741555000 0.599279000 80 0.630007000 0.914121000 3.547896000 80 3.657427000 0.033651000 2.244315000 9 -0.760516000 -0.365778000 -1.046886000 9 -1.027618000 0.649980000 2.522755000 9 1.211175000 -1.283674000 2.232392000 9 2.413488000 1.054715000 4.365118000 9 2.142691000 1.048415000 1.404564000 9 5.195927000 -0.933038000 2.899463000

Geometrical Parameters

Table 17: Optimized (B3PW91) geometrical parameters of the D2d trimer structures with bond distances in Å and bond angles in degree units.a

Structure Bond distances / Å X-M-X bond angle / ˚ a b c α β

Zn3F6 1.929 1.925 1.743 124.6 138.8 Zn3Cl6 2.304 2.290 2.102 117.6 132.4 Zn3Br6 2.450 2.428 2.243 116.1 130.0 Zn3I6 2.655 2.625 2.443 115.0 129.8 Cd3F6 2.137 2.131 1.945 127.5 141.2 Cd3Cl6 2.505 2.499 2.296 119.8 134.9 Cd3Br6 2.641 2.629 2.430 118.1 132.8 Cd3I6 2.833 2.815 2.620 116.2 131.4 Hg3F6 2.188 2.183 1.954 130.2 143.4 Hg3Cl6 2.538 2.539 2.299 122.0 136.7 Hg3Br6 2.671 2.667 2.435 119.9 134.9 Hg3I6 2.851 2.839 2.623 117.8 132.7

a The geometries are given in italics for the mercury dihalides here since the D2d isomer is not a minimum on the potential energy surface for those systems.

21

Table 18: Optimized (B3PW91) geometrical parameters of the HgX2 C2 trimers with bond distances in Å and bond angles in degree units.a

Bond Distances / Å X-M-X bond angle / ˚

d e f γ δ ε

Hg3F6 1.924 1.962 2.642 109.9 109.2 176.6

Hg3Cl6 2.264 2.294 3.266 99.9 98.9 175.6

Hg3Br6 2.406 2.435 3.368 99.2 97.1 174.0

Hg3I6 2.595 2.624 3.572 97.7 96.9 172.1 a The C2 ZnX2 and CdX2 isomers symmetrize during the optimization to the D2d structure. Deformation and Binding (trimerization and dimerization) Energies

Table S19: Computed (B3PW91) deformation energies (Edef),a for the monomer units in the M3X6 clusters. In this case, the trimers are the D2d or C2 trimer structures of the group 12 MX2 compounds. All values are in kcal·mol-1 units.

Trimers Edef

D2d C2 Zn3F6 67.4 Zn3Cl6 64.7 Zn3Br6 60.6 Zn3I6 55.2 Cd3F6 57.4 Cd3Cl6 56.0 Cd3Br6 53.1 Cd3I6 50.4 Hg3F6 98.9 2.6 Hg3Cl6 87.8 1.7 Hg3Br6 65.2 1.8 Hg3I6 70.6 2.0

22

Table S20: Computed (B3PW91 and MP2) counterpoise corrected trimerization energies (ΔEtrim), enthalpies (ΔHtrim), and free energies (ΔGtrim) for each system.a,b A trimer may be viewed as a combination of three monomeric fragments or as a pre-formed dimer plus a monomer. A superscript ( ) is used to distinguish the latter from the former. The thermodynamic data are provided here for both constructions. All values are in kcal·mol-1 units.

ΔQtrim = Qcp(M3X6) - 3 × Q(MX2) ΔQtrim = Qcp(M3X6) – [Q(MX2) + Q(M2X4)] Trimers ΔEtrim (D2d / C2) ΔHtrim (D2d / C2) ΔGtrim (D2d / C2) ΔEtrim (D2d / C2) ΔHtrim (D2d / C2) ΔGtrim (D2d / C2)

B3PW91 MP2 b B3PW91 MP2 b B3PW91 MP2 b B3PW91 MP2 b B3PW91 MP2 b B3PW91 MP2 b Zn3F6 -55.4 -51.7 -45.7 -50.6 -37.4 -33.3 -21.5 -29.1 -23.9 -28.3 -18.3 -19.7 Zn3Cl6 -35.4 -34.7 -33.3 -33.4 -16.4 -16.2 -19.1 -20.3 -18.3 -19.5 -9.7 -10.4 Zn3Br6 -32.5 -32.1 -31.2 -30.8 -14.3 -13.7 -17.3 -18.8 -17.0 -18.0 -8.4 -9.0 Zn3I6 -28.6 -30.1 -27.3 -28.9 -10.5 -12.9 -14.6 -17.5 -14.5 -16.8 -5.6 -8.1 Cd3F6 -55.0 -57.5 -53.8 -56.3 -37.6 -39.9 -21.5 -31.6 -26.4 -30.8 -18.2 -22.6 Cd3Cl6 -33.6 -34.0 -32.4 -32.8 -16.8 -15.0 -17.4 -17.6 -17.8 -17.0 -9.5 -6.2 Cd3Br6 -31.4 -35.7 -30.1 -34.3 -14.4 -18.4 -16.9 -20.9 -16.7 -20.0 -8.7 -11.9 Cd3I6 -28.3 -33.8 -27.0 -32.6 -11.3 -17.8 -15.0 -19.7 -14.8 -18.9 -6.8 -11.0 Hg3F6 -14.5 C2(2) -13.3 C2(2) 1.5 C2(2) -4.8 C2(2) -6.0 C2(2) 1.6 C2(2) Hg3Cl6 -4.4 C2(2) -2.9 C2(2) 9.6 C2(2) -1.4 C2(2) -1.2 C2(2) 5.7 C2(2) Hg3Br6 -3.6 C2(2) -1.8 C2(2) 10.6 C2(2) -1.6 C2(2) -0.7 C2(2) 6.1 C2(2) Hg3I6 -2.0 C2(2) -0.3 C2(2) 11.1 C2(2) -0.8 C2(2) 0.1 C2(2) 5.8 C2(2)

a The trimerization energies, enthalpies, and free energies. A general equation for how the values were obtained is included in the first row of the table, using Q as a general symbol for the various energy terms. The values are given only for the lowest energy structures: D2d for Zn and Cd and C2 for Hg. Counterpoise corrections (cp) have been used to adjust for basis set superposition errors. The enthalpies and Gibbs energies have been obtained for the temperature (T) = 298.15 K. b The C2 (HgX2)3 systems collapse during the optimization to the C2(2) geometry, so no C2 isomer was obtained at that level.

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Charge Distribution

Table 21: NPA charges at the central (c) and terminal (t) M and X sites in the B3PW91 optimized D2d and C2 isomers of Group 12 dihalide trimers. The D2d geometry is the global minimum for M = Zn and Cd; the C2 arrangement is preferred for Hg. The term ‘Central (c)’ refers here to the M atom in the center of the trimer with four symmetrical related and chemically identical X atoms bonded to it. Terminal (t) is used for the other (outer) M and X sites in the trimers.

q/e MX2 qM(c) qM(t) qX(c) qX(t)

Relativistic: D2d Zn3F6 1.67 1.62 -0.83 -0.79 Zn3Cl6 1.36 1.35 -0.68 -0.68 Zn3Br6 1.25 1.25 -0.62 -0.63 Zn3I6 1.08 1.09 -0.54 -0.56 Cd3F6 1.67 1.60 -0.83 -0.77 Cd3Cl6 1.41 1.38 -0.71 -0.67 Cd3Br6 1.27 1.29 -0.64 -0.62 Cd3I6 1.15 1.13 -0.57 -0.56 a Hg3F6 1.53 1.43 -0.76 -0.67 aHg3Cl6 1.25 1.18 -0.63 -0.55 aHg3Br6 1.12 1.07 -0.56 -0.50 aHg3I6 0.24 0.45 -0.16 -0.25

Relativistic: C2 Hg3F6 1.41 1.36 -0.71 -0.65 Hg3Cl6 1.14 1.12 -0.57 -0.54 Hg3Br6 1.04 1.01 -0.52 -0.49 Hg3I6 0.91 0.89 -0.46 -0.43 Non-Relativistic D2d: C2 species that optimized to D2d bHg3F6 1.71 1.63 -0.85 -0.78 bHg3Cl6 1.52 1.47 -0.76 -0.72 bHg3Br6 1.41 1.37 -0.70 -0.67 bHg3I6 0.69 0.84 -0.37 -0.45 a The data for clusters that are not global minima (the D2d mercury species, which are saddle points on the potential surface) when relativistic effects are taken into account are in italics. b The mercury species revert to ‘stable’ the D2d structure if relativistic effects are excluded. The charges for those (non-physical) systems are given at the bottom of the table in italics as well.

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Interaction Diagrams for the Zinc and Mercury Dihalide Trimers

Figure S3: Frontier molecular orbital interaction diagram for (ZnF2)3. The highest energy orbitals shown are the HOMOs for the trimer (center) and the deformed dimer and monomer fragments (left and right respectively).

-11.9

-12.2

-12.5

-12.8

-13.1

-13.4

eV

HOMO

25

Figure S4: Frontier molecular orbital interaction diagram for (ZnI2)3. The highest energy orbitals shown are the HOMOs for the trimer (center) and the deformed dimer and monomer fragments (left and right respectively).

eV

-8.4

-8.5

-8.6

-8.7

-8.8

-8.9

-9.0

-9.1

-9.2

-9.3

26

Figure S5: Frontier molecular orbital interaction diagram for (CdF2)3. The highest energy orbitals shown are the HOMOs for the trimer (center) and the deformed dimer and monomer fragments (left and right respectively).

-11.4

eV

-12.6

-12.4

-12.2

-12.0

-11.6

-11.8

27

Figure S6: Frontier molecular orbital interaction diagram for (CdI2)3. The highest energy orbitals shown are the HOMOs for the trimer (center) and the deformed dimer and monomer fragments (left and right respectively).

28

Figure S7: Frontier molecular orbital interaction diagram for (HgF2)3. The highest energy orbitals shown are the HOMOs for the trimer (center) and the deformed dimer and monomer fragments (left and right respectively).

29

Figure S8: Frontier molecular orbital interaction diagram for (HgI2)3. The highest energy orbitals shown are the HOMOs for the trimer (center) and the deformed dimer and monomer fragments (left and right respectively).

-9.1

-9.0

-8.9

-8.8

-8.7

eV

30

Figure S9: Representation of the SiS2 Structure.