Supplementary Tables
Solid-State Energetics and Electrostatics:
Madelung Constants and Madelung Energies
Leslie Glasser*
Nanochemistry Research Institute, Department of Chemistry
Curtin University, GPO Box U1987, Perth, WA 6845, Australia
E-mail: [email protected]
Values in italics in the Tables below (for CdI2, BiI3, VF3, and Cr2O3) have been recalculated using the program GULP (Gale, J. D. J. Chem.
Soc., Faraday Trans. 1997, 93).
Table S1: Collated crystal structural information on some ionic solids, and related Madelung constant data.
Ionic Solid
Space Group
Vm
/ nm3
Mr
Z
NaCl
CsCl
TlF
TlI
C
C
O
O
225
221
28
63
0.0472
0.0702
0.0433
0.0777
4
1
4
4
BaBr2
BaI2
BaF2
BaCl2 (CaF2 - type)
BaCl2 (PbCl2 - type)
BeCl2
CaF2 (fluorite)
CaCl2
CaBr2
CaI2
CdCl2
CdI2
CrCl2
O
O
C
C
O
O
C
O
O
H
R
H
O
62
62
225
225
62
72
225
58
58
154
166
156
58
0.1010
0.1260
0.0596
0.0977
0.0878
0.0695
0.5466
0.0840
0.0982
0.1210
0.0747
0.1069
0.0690
4
4
4
4
4
4
4
2
2
1
3
15
2
1.7476
1.7627
ro
/ nm
0.2814
0.3571
0.2590
0.3342
Mr/r
/ nm-1
6.21
4.94
Ma
a
/ nm
3.4951
2.0344
3.2804
2.2290
0.5640
0.4123
0.5180
0.4582
2.4676
2.4676
Ma/a
/ nm-1
0.2017
0.5466
0.2708
20.26
21.29
17.46
4.4890
4.3819
0.2663
0.2988
16.86
14.66
Mv/v1/3
/ nm-1
6.20
4.93
6.33
4.86
0.7311
4.0860
11.6366
4.7276
Mv
11.6366
10.9179
0.4330
0.6240
21.29
17.50
6.3414
6.2330
11.3260
0.3846
0.4240
0.5974
16.49
14.70
18.96
7.0370
7.0220
7.3306
7.3306
7.0400
15.11
14.01
18.77
15.92
15.84
7.3306
7.6730
7.6700
6.2230
21.29
17.52
16.62
12.58
CuF2
HgI2
MgF2
MgCl2
MgBr2
MgI2
PbCl2
PbFCl
SrF2
SrCl2
SrBr2
SrI2
TiCl2
M
T
T
H
H
H
O
T
C
C
T
O
H
14
137
136
166
166
164
62
129
225
225
85
61
164
0.0339
0.1171
0.0326
0.0674
0.0859
0.0511
0.0781
0.0609
0.0488
0.0848
0.0962
0.1243
0.0622
2
2
2
3
3
2
4
2
4
4
10
8
1
AlCI3
AsI3
BiF3
BiI3
FeCl3
IrF3
LaCl3
LaF3
MoF3
PuBr3
ScF3
UD3
VF3
VI3
YF3
YCl3
M
R
C
R
R
R
H
H
R
O
C
C
R
R
C
M
12
148
225
148
166
167
176
165
162
63
221
223
167
0.0883
0.1596
0.0501
0.1695
0.0917
0.0499
0.1059
0.0558
0.1123
0.1184
0.0645
0.0364
0.0517
4
6
4
6
3
6
2
6
6
4
1
8
6
221
12
0.1798
0.1242
1
4
AgO
C
216
0.0279
4
4.7620
0.1942
0.2779
0.1968
24.20
0.3076
0.2511
10.8599
6.5324
11.1886
0.4590
0.4356
14.9869
7.5082
0.9030
0.4106
2.5195
2.5195
4.8441
0.3161
15.33
4.3474
0.2527
17.21
6.1270
8.3030
0.2295
36.17
21.2386
22.3230
22.1220
21.5567
22.2180
23.8340
0.4560
9.1290
9.1190
0.2950
0.2353
30.94
38.75
8.7280
0.2058
42.40
8.2813
8.3130
0.3797
0.2163
0.2585
0.1819
23.66
15.00
7.7320
6.9570
6.8780
6.8520
24.22
17.09
15.59
18.47
7.3306
7.3306
7.1700
20.06
16.68
15.65
16.60
18.29
0.5920
0.8250
35.88
27.06
0.8163
0.6758
0.5418
26.41
32.88
43.99
15.6879
26.3470
36.0270
17.9080
0.4148
0.5666
1.2640
37.82
46.50
28.50
24.4195
3.7970
0.5373
47.25
38.29
32.16
17.4467
SG?
31.41
BaO
BeO
CaO
CdO
CeO
CoO
CuO
CuO
CuO
EuO
FeO
LaO
MgO
NbO
NbO
NdO
NiO
PrO
SnO
SrO
TiO
VO
ZnO
ZnS (sphalerite cubic)
ZnS (wurtzite
hexagonal)
C
H
C
C
C
C
M
M
M
C
C
C
C
C
C
C
C
C
O
C
C
C
H
C
225
186
225
225
225
225
15
15
225
225
225
225
225
225
221
221
225
225
31
225
225
225
186
216
0.0416
0.0138
0.0279
0.0327
0.0329
0.0193
0.0200
0.0201
0.0200
0.0341
0.0200
0.0340
0.0188
0.0249
0.0249
0.0312
0.0183
0.0318
0.0297
0.0343
0.0182
0.0170
0.0239
0.0394
4
2
4
4
6.9823
6.3676
1.7465
1.7469
4
1.7490
2
4
5.9941
6.5522
0.1796
0.2341
33.37
27.99
10.6067
15.1317
0.3250
0.5409
32.64
27.97
H
186
0.0390
8
6.5629
0.2339
28.06
10.7153
0.3811
28.12
α-Al2O3 (corundum)
Ce2O3
Ce2O2S
Cr2O3
Cr2O3
Eu2O3
Fe2O3 - alpha
R
H
H
R
H
H
R
167
164
164
167
167
164
167
0.0425
0.0794
0.0954
0.0480
0.0481
0.0701
0.0499
6
24.2420
0.1848
131.19
67.2580
0.5128
131.16
38.8031
62.2570
62.2217
0.3888
0.5350
0.4952
99.80
116.37
125.65
0.1599
39.83
25.28
39.84
29.12
10.7461
27.44
32.80
4
0.2069
15.7335
0.4653
33.81
33.28
33.45
27.20
32.40
27.20
4
1.7480
28.58
3
0.2105
12.0342
0.4210
28.58
28.00
33.52
27.76
27.04
27.20
38.40
34.40
33.37
103.20
1
6
6
0.2405
0.2485
0.2485
67.3460
0.5414
124.40
125.70
107.40
124.20
Ga2O3 - beta
In2O3 (corundum)
In2O3 (cubic)
La2O3
LaAlO3
M
R
C
H
R
12
167
206
164
167
0.0524
0.0631
0.0647
0.0827
0.0545
Mn2O3 beta
Nd2O3
Pb2O3
Rh2O3
Sc2O3
Ti2O3
V2O3
V2O3
Y2O3
Yb2O3
MgAl2O4
O
H
M
R
C
R
R
R
H
C
C
61
164
14
167
206
167
167
167
164
206
227
0.0522
0.0765
0.0377
0.0526
0.0596
0.0522
0.0495
0.0544
0.0766
0.0710
0.0635
CeO2
CrO2
GeO2 (rutile)
MnO2-beta
MoO2
NbO2
PbO2
PrO2
RhO2
RuO2
SiO2
SiO2 - beta
SnO2
TeO2
C
T
T
T
M
T
O
C
T
T
T
H
T
T
225
136
136
136
14
136
60
225
136
136
136
152
136
92
0.0396
0.0285
0.0276
0.0279
0.0329
0.0352
0.0405
0.0410
0.0311
0.0313
0.0233
0.0394
0.0358
0.0439
-
4
6
16
1
6
4.0740
4.0831
4.0553
24.1787
1
4
4.0215
16
6
4.1784
6
1
4.0583
8.8990
8
114.90
0.2371
101.97
40.1496
44.5550
40.1435
75.3200
0.2253
0.3937
101.97
102.00
124.80
105.00
0.7050
106.84
65.9340
0.5431
121.40
67.9290
0.5647
120.29
39.49
122.15
118.20
121.50
120.30
110.10
111.60
0.1917
4
85.92
100.80
2
44.9300
0.4395
102.23
101.76
93.84
92.88
4
0.2167
43.9557
0.4947
88.85
85.20
98.16
97.68
109.92
3
2
4
17.6094
0.1619
0.2030
108.76
50.9121
44.3844
42.6396
0.5010
0.4737
0.4805
101.62
93.69
88.74
93.60
TiO2 (anatase)
TiO2 (brookite)
TiO2 (rutile)
VO2
VO2
ZrO2
ZrO2
ZrO2
ZrS2
T
O
T
T
O
T
M
C
H
141
61
136
136
62
136
14
225
164
0.0341
0.0322
0.0312
0.0296
0.0337
0.0332
0.0351
0.0338
0.0667
4
8
2
ReO3
WO3
C
T
221
130
0.0527
0.0546
1
4
BaBiO3
BaTiO3
NaTaO3
SrTiO3
C
C
C
C
225
221
221
221
0.0862
0.0683
0.0585
0.0596
8
1
1
1
FeOCl
LaOCl
LaOF - beta
LaOF - gamma
YOF
YOCI
O
T
R
T
R
59
129
166
129
166
0.0495
0.0585
0.0479
0.0489
0.0393
2
2
6
2
6
CuFeO2
CuFeO2
LiCrO2
NaFeO2
R
H
R
R
166
0.0140
BaLiF3
KZnF3
C
C
221
221
0.0638
0.0667
19.0691
18.0660
19.0803
0.1937
0.1842
0.1945
98.42
98.06
98.09
37.2462
90.0560
45.0541
0.3785
0.9184
0.4594
98.40
98.06
98.08
98.16
99.60
4
0.2099
54.8347
0.5743
95.48
91.44
4
4
1
19.7328
0.2030
97.21
46.7065
0.5207
89.70
24.5121
0.3662
66.94
49.5099
58.5355
49.5120
0.3881
0.3905
150.83
126.79
14.6608
0.3750
39.10
13.8672
27.0561
0.4091
33.90
3
36.7040
44.6360
36.6110
42.0570
0.5959
0.3028
0.5100
0.5590
61.59
147.41
71.79
75.24
1
1
10.9177
12.3775
0.3092
71.6318
10.9230
11.4710
11.3914
0.2149
0.2396
0.2419
0.2421
45.58
47.41
47.04
0.2284
BiOBr
BiSCl
T
O
Cu2O
Hg2Cl2
NiAs
SbSI
SiF4
V2O5
a
Complex Oxides
LaCoO3
LaCrO3
LaCuO3
LaFeO3
LaMnO3
LaNiO3
LaRhO3
LaRuO3
LaTiO3
LaVO3
LaYbO3
C
T
H
SrCeO3
SrCoO3
SrCrO3
SrMnO3
SrMoO3
SrSnO3
SrTiO3
SrVO3
0.0760
224
194
0.0396
0.1089
0.0285
0.2723
2
4.4425
2
6.7701
12.4890
4
0.1841
0.2520
0.3632
0.1546
0.1544
24.13
18.1290
29.7134
0.3916
46.29
10.2595
4.6665
10.0455
32.4235
0.4270
0.4478
0.0000
0.8650
24.03
10.42
37.48
80.78
O
62
0.0896
R
R
R
C
R
R
C
C
C
C
167
167
167
62
167
167
62
62
62
62
0.0568
0.0591
0.0577
0.0605
0.0584
0.0576
0.0623
0.0623
0.0621
0.0601
116.70
113.70
115.50
113.40
114.90
116.10
110.70
110.40
113.10
114.00
C
C
C
C
C
C
C
C
62
221
221
221
221
62
221
221
0.0795
0.0566
0.0557
0.0522
0.0628
0.0657
0.0595
0.0567
115.20
128.32
129.60
124.48
124.48
122.56
125.44
128.96
a
La2CoO4
La2CuO4
La2NiO4
LaSrCoO4
LaSrCrO4
LaSrCuO4
LaSrFeO4
LaSrNiO4
O
O
T
T
T
T
T
T
64
64
139
139
139
139
139
139
0.0945
0.0951
0.0944
0.0903
0.0931
0.0951
0.0952
0.0912
134.14
135.28
135.28
143.64
142.88
142.12
140.22
142.12
Sr2MnO4
Sr2MoO4
Sr2RuO4
Sr2SnO4
Sr2TiO4
Sr2VO4
T
T
T
T
T
T
139
139
139
139
139
139
0.0896
0.0980
0.0954
0.1021
0.0949
0.0916
156.80
152.00
153.60
151.20
154.80
155.20
The data for this set of complex oxides has been extracted from Torrance, J. B,Lacorre, P., Asavaroengchai, C., and Metzger, R. M. Physica C,
1991,182, 351-362.
Table S2: Lattice and Madelung (electrostatic) Energies (in kJ mol-1) for materials treated as ionic.
Ionic Solid
NaCl
CsCl
TlF
TlI
BaBr2
BaI2
BaF2
BaCl2 (CaF2 - type)
BaCl2 (PbCl2 - type)
BeCl2
CaF2 (fluorite)
CaCl2
CaBr2
CaI2
CdCl2
CdI2
CrCl2
CuF2
HgI2
MgF2
MgCl2
Madelung
138.94Mr/r 138.94Ma/a 138.94Mv/v1/3
UPOT(BHF)
energy
790
670
850
710
846
686
880
676
863
686
861
686
880
676
1995
1890
2373
2069
3033
2651
2271
2132
2087
2565
2455
2601
3102
2624
2978
2540
2100
1946
2608
2212
2201
2815
2967
2427
2815
2958
2425
2342
2043
2633
3288
2084
3363
2342
2037
3362
2958
2431
2958
2435
2310
1748
2291
2042
2634
3287
2084
3365
2375
MgBr2
MgI2
PbCl2
PbFCl
SrF2
SrCl2
SrBr2
SrI2
TiCl2
AlCI3
AsI3
BiF3
BiI3
FeCl3
IrF3
LaCl3
LaF3
MoF3
PuBr3
ScF3
UD3
VF3
VI3
YF3
YCl3
AgO
BaO
BeO
CaO
2451
2340
2282
2166
2567
2306
2541
2540
2513
2170
1976
2514
5513
5295
3774
5436
6112
4242
4682
6459
3959
5540
5329
5136
4983
4524
2186
2130
2391
2391
5024
3758
5242
3670
4567
6111
4300
5385
6459
3959
6203
5893
6375
5026
4470
5536
4985
3759
3670
4568
6112
4299
5384
5255
6461
3960
5891
6566
5320
4469
4365
3054
4443
3401
2788
2318
2174
5534
4365
3513
5536
4047
CdO
CeO
CoO
CuO
CuO
CuO
EuO
FeO
LaO
MgO
NbO
NbO
NdO
NiO
PrO
SnO
SrO
TiO
VO
ZnO
ZnS (sphalerite cubic)
ZnS (wurtzite hexagonal)
α-Al2O3 (corundum)
Ce2O3
Ce2O2S
Cr2O3
Cr2O3
Eu2O3
Fe2O3 - alpha
Ga2O3 - beta
In2O3 (corundum)
3806
3813
4558
3910
4648
4698
4050
4050
4625
4648
3780
4502
3780
3865
3791
4603
3972
3972
3971
4010
3652
3223
3811
3863
3971
15916
12661
14957
12945
14774
15220
13928
4637
3890
3899
4636
3889
3898
4535
3887
3907
18232
18228
18223
3891
4658
3858
3757
3780
5336
4780
4637
14341
13818
17457
17466
17281
13867
17460
18866
17285
17467
14924
17259
17509
15967
In2O3 (cubic)
La2O3
LaAlO3
Mn2O3 - beta
Nd2O3
Pb2O3
Rh2O3
Sc2O3
Ti2O3
V2O3
V2O3
Y2O3
Yb2O3
MgAl2O4
CeO2
CrO2
GeO2 (rutile)
MnO2-beta
MoO2
NbO2
PbO2
PrO2
RhO2
RuO2
SiO2
SiO2 - beta
SnO2
TeO2
TiO2 (anatase)
TiO2 (brookite)
14169
15035
12736
14841
13708
14149
14520
14168
14168
14174
17342
14591
14841
14844
16864
16868
16708
16713
12705
5487
16974
16425
16884
16717
15299
15508
22814
9627
11939
14007
12828
12970
11648
14201
11217
12347
14204
14141
13040
12907
12345
11839
13640
13574
15274
13125
11807
12150
15114
13015
12331
13678
13627
15111
13675
13624
14119
13018
12330
13672
13624
13007
13640
TiO2 (rutile)
VO2
VO2
ZrO2
ZrO2
ZrO2
ZrS2
13632
13840
11188
12707
12751
12598
9540
26553
26207
BaBiO3
BaTiO3
NaTaO3
SrTiO3
15572
16829
20952
17612
CuFeO2
CuFeO2
LiCrO2
NaFeO2
13627
13266
ReO3
WO3
FeOCl
LaOCl
LaOF - beta
LaOF - gamma
YOF
YOCI
13629
13506
12463
9300
20956
17616
5432
6334
6589
6538
6333
6588
6536
4710
6641
10451
8558
20481
9974
10453
BaLiF3
KZnF3
BiOBr
6432
BiSCl
5302
Cu2O
Hg2Cl2
NiAs
SbSI
SiF4
V2O5
Complex Oxidesa
LaCoO3
LaCrO3
LaCuO3
LaFeO3
LaMnO3
LaNiO3
LaRhO3
LaRuO3
LaTiO3
LaVO3
LaYbO3
3353
1448
3352
3339
1448
5208
11223
39899
16217
15800
16050
15758
15967
16133
15383
15341
15716
15841
SrCeO3
SrCoO3
SrCrO3
SrMnO3
SrMoO3
SrSnO3
SrTiO3
SrVO3
16008
17831
18009
17298
17298
17031
17431
17920
La2CoO4
18640
a
La2CuO4
La2NiO4
LaSrCoO4
LaSrCrO4
LaSrCuO4
LaSrFeO4
LaSrNiO4
18799
18799
19960
19855
19749
19485
19749
Sr2MnO4
Sr2MoO4
Sr2RuO4
Sr2SnO4
Sr2TiO4
Sr2VO4
21789
21122
21344
21011
21511
21567
The data for this set of complex oxides has been extracted from Torrance, J. B,Lacorre, P., Asavaroengchai, C., and Metzger, R. M. Physica C,
1991,182, 351-362.
Table S3: Lattice and Madelung (electrostatic) Energies (in kJ mol-1) for partially-covalent materials with assumed integer charges.
a
Material UPOT
CuH
1196
AuCl
1082
AuBr
1073
c
AuI
1020
LiH
918
NaH
807
KH
713
RbH
684
CsH
653
a
EMb
1299
1069
971
869
1189
995
852
804
760
UPOT = Uvs(calc) – IDE from Glasser, L.; von Szentpály, L. “Born-Haber-Fajans Cycle Generalized: Linear Energy Relation between
Molecules, Crystals and Metals”, J. Am. Chem. Soc., 2006, 128, 12314-12321.
b
The values for EM have been calculated using the program GULP (Gale, J. D. J. Chem. Soc., Faraday Trans. 1997, 93), assuming integer
charges.
c
UPOT(AuI) has been estimated using the correlation in Fig. 2 of the main text.