Accessory Publication for
pKa Values of the Prototype Imidazolium Cation
by Magill and Yates

Optimised Cartesian coordinates for all structures studied
Imidazolium cation, 1
B3LYP/6-31G(d)
C     0.000000    0.000000    1.142484
C     0.000000    0.681706   -0.978221
C     0.000000   -0.681706   -0.978221
N     0.000000   -1.074789    0.348785
H     0.000000   -2.033979    0.680267
H     0.000000    0.000000    2.222490
H     0.000000    2.033979    0.680267
H     0.000000    1.391419   -1.791130
H     0.000000   -1.391419   -1.791130
N     0.000000    1.074789    0.348785

G3 (MP2 geometry)
C     0.000000    0.000000    1.145208
C     0.000000    0.684745   -0.974396
C     0.000000   -0.684745   -0.974396
N     0.000000   -1.072379    0.344392
H     0.000000   -2.035166    0.676008
H     0.000000    0.000000    2.225312
H     0.000000    2.035166    0.676008
H     0.000000    1.393535   -1.788656
H     0.000000   -1.393535   -1.788656
N     0.000000    1.072379    0.344392

CBS-QB3
C     0.000000    0.000000    1.141034
C     0.000000    0.679904   -0.977128
C     0.000000   -0.679904   -0.977128
N     0.000000   -1.072714    0.348567
H     0.000000   -2.029907    0.679631
H     0.000000    0.000000    2.218602
H     0.000000    2.029907    0.679631
H     0.000000    1.386376   -1.789234
H     0.000000   -1.386376   -1.789234
N     0.000000    1.072714    0.348567

CPCM/HF/6-31+G(d)
C     0.000000    0.000000    1.120517
C     0.000000    0.671571   -0.971111
C     0.000000   -0.671571   -0.971111
N     0.000000   -1.063436    0.350493
H     0.000000   -2.017268    0.688458
H     0.000000    0.000000    2.193712
H     0.000000    2.017268    0.688458
H     0.000000    1.378955   -1.773655
H     0.000000   -1.378955   -1.773655
N     0.000000    1.063436    0.350493

CPCM/B3LYP/6-31+G(d,p)
C     0.000000    0.000000    1.138835
C     0.000000    0.682628   -0.976964
C     0.000000   -0.682628   -0.976964
N     0.000000   -1.075365    0.347976
H     0.000000   -2.046309    0.687411
H     0.000000    0.000000    2.222618
H     0.000000    2.046309    0.687411
H     0.000000    1.395595   -1.789278
H     0.000000   -1.395595   -1.789278
N     0.000000    1.075365    0.347976

Imidazole, 2
B3LYP/6-31G(d)
C    -1.090715    0.281388    0.000000
C     1.120898    0.300007    0.000000
C     0.635599   -0.983663    0.000000
N    -0.743063   -0.986718    0.000000
H    -2.103497    0.662502    0.000000
H    -0.009303    2.115719    0.000000
H     2.121041    0.706728    0.000000
H     1.198501   -1.907471    0.000000
N     0.000000    1.106165    0.000000

G3 (MP2 geometry)
C    -1.090794    0.283560    0.000000
C     1.118846    0.305441    0.000000
C     0.634799   -0.982968    0.000000
N    -0.740497   -0.992634    0.000000
H    -2.103633    0.663381    0.000000
H    -0.009951    2.115412    0.000000
H     2.118442    0.713771    0.000000
H     1.201518   -1.903976    0.000000
N     0.000000    1.103378    0.000000

CBS-QB3
C    -1.090674    0.281409    0.000000
C     1.119797    0.298397    0.000000
C     0.635108   -0.982770    0.000000
N    -0.741705   -0.983258    0.000000
H    -2.101229    0.661188    0.000000
H    -0.008379    2.111350    0.000000
H     2.118632    0.701176    0.000000
H     1.197524   -1.903378    0.000000
N     0.000000    1.104321    0.000000

CPCM/HF/6-31+G(d)
C    -1.075576    0.289176    0.000000
C     1.109222    0.287921    0.000000
C     0.632864   -0.980635    0.000000
N    -0.743086   -0.967318    0.000000
H    -2.077560    0.672374    0.000000
H    -0.012272    2.096419    0.000000
H     2.104889    0.683769    0.000000
H     1.187491   -1.898375    0.000000
N     0.000000    1.091182    0.000000

CPCM/B3LYP/6-31+G(d,p)
C    -1.091853    0.290908    0.000000
C     1.119267    0.299238    0.000000
C     0.639288   -0.990136    0.000000
N    -0.744743   -0.987828    0.000000
H    -2.103939    0.677308    0.000000
H    -0.010608    2.124476    0.000000
H     2.122040    0.706270    0.000000
H     1.205491   -1.913730    0.000000
N     0.000000    1.102917    0.000000

Imidazol-2-ylidene, 3
B3LYP/6-31G(d)
C     0.000000    0.000000    1.285700
C     0.000000    0.678084   -0.940192
C     0.000000   -0.678084   -0.940192
N     0.000000   -1.049819    0.402542
H     0.000000    2.006561    0.721938
H     0.000000    1.385424   -1.755679
H     0.000000   -1.385424   -1.755679
N     0.000000    1.049819    0.402542
H     0.000000   -2.006561    0.721938

G3 (MP2 geometry)
C     0.000000    0.000000    1.285371
C     0.000000    0.681321   -0.935968
C     0.000000   -0.681321   -0.935968
N     0.000000   -1.045773    0.398585
H     0.000000    2.003976    0.720880
H     0.000000    1.388844   -1.751281
H     0.000000   -1.388844   -1.751281
N     0.000000    1.045773    0.398585
H     0.000000   -2.003976    0.720880

CBS-QB3
C     0.000000    0.000000    1.278055
C     0.000000    0.676601   -0.937896
C     0.000000   -0.676601   -0.937896
N     0.000000   -1.050101    0.403206
H     0.000000    2.003542    0.724433
H     0.000000    1.379315   -1.753659
H     0.000000   -1.379315   -1.753659
N     0.000000    1.050101    0.403206
H     0.000000   -2.003542    0.724433

CPCM/HF/6-31+G(d)
C     0.000000    0.000000    1.250409
C     0.000000    0.669252   -0.927207
C     0.000000   -0.669252   -0.927207
N     0.000000   -1.048827    0.404057
H     0.000000    2.005882    0.716688
H     0.000000    1.373576   -1.733074
H     0.000000   -1.373576   -1.733074
N     0.000000    1.048827    0.404057
H     0.000000   -2.005882    0.716688

CPCM/B3LYP/6-31+G(d,p)
C     0.000000    0.000000    1.270276
C     0.000000    0.680329   -0.934719
C     0.000000   -0.680329   -0.934719
N     0.000000   -1.057874    0.403943
H     0.000000    2.032523    0.719262
H     0.000000    1.390424   -1.749373
H     0.000000   -1.390424   -1.749373
N     0.000000    1.057874    0.403943
H     0.000000   -2.032523    0.719262

Imidazol-4-ylidene, 4
B3LYP/6-31G(d)
C    -1.073576    0.300931    0.000000
C     0.820096   -1.053998    0.000000
C     1.148149    0.295411    0.000000
N     0.000000    1.098213    0.000000
H    -1.195635   -1.765639    0.000000
H     2.117273    0.774708    0.000000
N    -0.590833   -0.955211    0.000000
H    -0.050437    2.109337    0.000000
H    -2.103382    0.626520    0.000000

G3 (MP2 geometry)
C    -1.081514    0.295341    0.000000
C     0.822377   -1.052462    0.000000
C     1.138376    0.306365    0.000000
N     0.000000    1.094727    0.000000
H    -1.176359   -1.774135    0.000000
H     2.108050    0.784863    0.000000
N    -0.578231   -0.955738    0.000000
H    -0.046447    2.107835    0.000000
H    -2.113065    0.613044    0.000000

CBS-QB3
C    -1.070607    0.299389    0.000000
C     0.815464   -1.048758    0.000000
C     1.148023    0.295823    0.000000
N     0.000000    1.096340    0.000000
H    -1.190930   -1.765633    0.000000
H     2.117185    0.767837    0.000000
N    -0.591023   -0.954808    0.000000
H    -0.048104    2.105171    0.000000
H    -2.098277    0.623180    0.000000

CPCM/HF/6-31+G(d)
C     0.000000    1.084062    0.000000
C     0.775204   -1.056529    0.000000
C    -0.591457   -1.024393    0.000000
N    -1.044271    0.295641    0.000000
H     2.010528    0.702494    0.000000
H    -1.304906   -1.822818    0.000000
N     1.075442    0.323408    0.000000
H    -2.000446    0.611874    0.000000
H    -0.025857    2.156274    0.000000

CPCM/B3LYP/6-31+G(d,p)
C    -1.065104    0.293376    0.000000
C     0.815970   -1.041870    0.000000
C     1.151386    0.304564    0.000000
N     0.000000    1.096791    0.000000
H    -1.218734   -1.779287    0.000000
H     2.121582    0.783286    0.000000
N    -0.595272   -0.963854    0.000000
H    -0.049207    2.118804    0.000000
H    -2.100242    0.610222    0.000000

Imidazolate anion, 5
B3LYP/6-31G(d)
C     0.000000    0.000000    1.097317
C     0.000000    0.695537   -0.900047
C     0.000000   -0.695537   -0.900047
N     0.000000   -1.153373    0.394155
H     0.000000    0.000000    2.189204
H     0.000000    1.383835   -1.745358
H     0.000000   -1.383835   -1.745358
N     0.000000    1.153373    0.394155

G3 (MP2 geometry)
C     0.000000    0.000000    1.097939
C     0.000000    0.695399   -0.899741
C     0.000000   -0.695399   -0.899741
N     0.000000   -1.157372    0.393574
H     0.000000    0.000000    2.188248
H     0.000000    1.381912   -1.744520
H     0.000000   -1.381912   -1.744520
N     0.000000    1.157372    0.393574

CBS-QB3
C     0.000000    0.000000    1.098822
C     0.000000    0.695247   -0.899843
C     0.000000   -0.695247   -0.899843
N     0.000000   -1.149502    0.393034
H     0.000000    0.000000    2.186981
H     0.000000    1.381522   -1.742131
H     0.000000   -1.381522   -1.742131
N     0.000000    1.149502    0.393034

CPCM/HF/6-31+G(d)
C     0.000000    0.000000    1.100211
C     0.000000    0.685140   -0.900473
C     0.000000   -0.685140   -0.900473
N     0.000000   -1.124540    0.392576
H     0.000000    0.000000    2.176514
H     0.000000    1.364742   -1.734082
H     0.000000   -1.364742   -1.734082
N     0.000000    1.124540    0.392576

CPCM/B3LYP/6-31+G(d,p)
C     0.000000    0.000000    1.115575
C     0.000000    0.694764   -0.909695
C     0.000000   -0.694764   -0.909695
N     0.000000   -1.143568    0.394373
H     0.000000    0.000000    2.203328
H     0.000000    1.382260   -1.750832
H     0.000000   -1.382260   -1.750832
N     0.000000    1.143568    0.394373

Total energies (Hartree) 
level of theory	1	2	3	4	5	
HF/6-31G(d)	-225.196351	-224.814429	-224.773001	-224.730148	-224.224699	
B3LYP/6-31G(d)	-226.592173	-226.214554	-226.166693	-226.134532	-225.628588	
B3LYP/CBSB7	-226.653480	-226.276907	-226.235176	-226.203520	-225.695084	
B3LYP/CBSB3	-226.670532	-226.297451	-226.255856	-226.225602	-225.726891	
B3LYP/6-311+G(3df,2p)	-226.672564	-226.299695	-226.257898	-226.227745	-225.729144	
MP2/CBSB3	-226.130955	-225.763435	-225.716593	-225.689570	-225.200711	
MP2/GTlarge	-226.350432	-225.982600	-225.935548	-225.908485	-225.419144	
MP4SDQ/CBSB4	-225.966998	-225.592279	-225.551740	-225.518017	-225.021387	
CCSD(T)/6-31+G(d†)	-225.956833	-225.589963	-225.548003	-225.515930	-225.029189	
G1A	-226.210529	-225.855499	-225.812986	-225.782558	-225.303284	
G2MP2A	-226.209630	-225.852853	-225.811096	-225.780777	-225.297299	
G2A	-226.214187	-225.857559	-225.815555	-225.785186	-225.302296	
G3MP2B3A	-226.261279	-225.904554	-225.862691	-225.832910	-225.348797	
G3MP2A	-226.250995	-225.894115	-225.852238	-225.821853	-225.338269	
G3B3A	-226.446742	-226.089594	-226.047297	-226.017248	-225.533319	
G3A	-226.441486	-226.084162	-226.041912	-226.011227	-225.527798	
CBS-4MA	-226.263812	-225.907247	-225.863488	-225.832567	-225.353170	
CBS-QB3A	-226.222929	-225.866795	-225.824125	-225.794197	-225.311741	

A Free energy (includes ZPVE, thermal and entropy corrections)

Sum of zero-point vibrational energy, thermal and entropy corrections (Hartree)
level of theory	1	2	3	4	5	
B3LYP/6-31G(d)	0.059723	0.044961	0.045678	0.044404	0.031984	
CBS-QB3	0.058528	0.043987	0.044875	0.043686	0.031012	
G3	0.056393	0.042510	0.043135	0.042274	0.030269	

Free energies of solvation (kJ mol–1) 
level of theory	1	2	3	4	5	
CPCM/HF/6-31G(d)A	-263.22	-44.06	-50.25	-82.55	-280.87	
CPCM/HF/6-31+G(d)A	-265.47	-47.53	-56.57	-93.01	-276.14	
CPCM/HF/6-311+G(d,p)A	-265.43	-46.82	-56.61	-93.51	-275.81	
CPCM/B3LYP/6-311+G(d,p)B	-264.05	-43.72	-58.62	-82.89	-266.40	
CPCM/HF/6-31G(d)C	-262.46	-43.56	-48.24	-80.37	-278.86	
CPCM/HF/6-31+G(d)C	-264.85	-47.03	-54.18	-90.42	-273.93	
CPCM/HF/6-311+G(d,p)C	-264.76	-46.28	-54.14	-90.88	-273.72	
CPCM/B3LYP/6-311+G(d,p)C	-262.04	-41.92	-54.73	-79.79	-264.72	
CPCM/B3LYP/CBSB7C	-261.08	-39.37	-51.13	-74.43	-269.66	

A Geometry optimised at CPCM/HF/6-31+G(d)
B Geometry optimised at CPCM/B3LYP/6-31+G(d,p)
C Gas-phase geometry optimised at B3LYP/CBSB7

pKa values calculated with different solvation schemesA
	S1	S2	S3	S4	Average	Average deviation	
Reaction 1	7.05	6.83	6.95	7.25	7.02	0.10	
Reaction 2	25.59	24.87	24.86	24.27	24.90	0.28	
Reaction 3	33.69	32.25	32.16	33.78	32.97	0.61	
Reaction 4	18.66	20.10	20.03	21.14	19.98	0.53	

A S1 = CPCM/HF/6-31G(d), S2 = CPCM/HF/6-31+G(d), S3 = CPCM/HF/6-311+G(d,p), S4 = CPCM/B3LYP/6-311+G(d,p)