Table 1. Bond-length statistics for the transition metal ions bonded to O2− .
Ion | Coordination number | Number of bonds | Number of coordination polyhedra | Mean bond length (Å) | Standard deviation (Å) | Range (Å) | Maximum bond length (Å) | Minimum bond length (Å) | Skewness | Kurtosis |
---|---|---|---|---|---|---|---|---|---|---|
Sc3+ | 6 | 450 | 75 | 2.098 | 0.041 | 0.236 | 2.231 | 1.995 | 0.429 | 0.610 |
7 | 35 | 5 | 2.163 | 0.056 | 0.268 | 2.315 | 2.047 | −0.242 | 0.731 | |
8 | 64 | 8 | 2.234 | 0.101 | 0.497 | 2.554 | 2.057 | 1.352 | 2.513 | |
Ti3+ | 6 | 126 | 21 | 2.037 | 0.051 | 0.263 | 2.167 | 1.904 | −0.115 | 0.160 |
7 | 14 | 2 | 2.108 | 0.022 | 0.077 | 2.134 | 2.057 | −1.113 | 0.575 | |
8 | 8 | 1 | 2.195 | 0.077 | 0.153 | 2.271 | 2.118 | 0.000 | −2.800 | |
Ti4+ | 4 | 16 | 4 | 1.821 | 0.038 | 0.159 | 1.906 | 1.747 | 0.220 | 1.124 |
5 | 85 | 17 | 1.917 | 0.106 | 0.405 | 2.050 | 1.645 | −1.256 | 0.139 | |
6 | 1758 | 293 | 1.971 | 0.107 | 0.826 | 2.474 | 1.648 | 0.124 | 1.531 | |
7 | 7 | 1 | 2.064 | 0.165 | 0.550 | 2.230 | 1.680 | −2.098 | 5.088 | |
V3+ | 6 | 402 | 67 | 2.007 | 0.051 | 0.339 | 2.224 | 1.885 | 0.479 | 0.681 |
V4+ | 5 | 475 | 95 | 1.893 | 0.147 | 0.577 | 2.116 | 1.539 | −1.348 | 0.163 |
6 | 768 | 128 | 1.980 | 0.202 | 1.030 | 2.588 | 1.558 | −0.173 | 0.559 | |
V5+ | 4 | 1380 | 345 | 1.717 | 0.056 | 0.354 | 1.917 | 1.563 | 0.300 | −0.250 |
5 | 325 | 65 | 1.827 | 0.147 | 0.801 | 2.352 | 1.551 | −0.068 | −0.607 | |
6 | 1758 | 293 | 1.924 | 0.213 | 0.993 | 2.547 | 1.554 | 0.324 | −0.519 | |
Cr2+ | 4 | 24 | 6 | 2.004 | 0.010 | 0.028 | 2.025 | 1.997 | 1.441 | 0.378 |
5 | 10 | 2 | 2.113 | 0.144 | 0.432 | 2.426 | 1.994 | 1.637 | 1.313 | |
6 | 54 | 9 | 2.188 | 0.193 | 0.696 | 2.651 | 1.955 | 0.809 | −0.889 | |
Cr3+ | 6 | 624 | 104 | 1.976 | 0.026 | 0.190 | 2.074 | 1.884 | 0.277 | 1.855 |
Cr4+ | 4 | 4 | 1 | 1.784 | 0.035 | 0.086 | 1.844 | 1.758 | 1.825 | 3.332 |
6 | 36 | 6 | 1.950 | 0.032 | 0.094 | 1.988 | 1.894 | −0.362 | −1.336 | |
Cr5+ | 4 | 4 | 1 | 1.693 | 0.006 | 0.012 | 1.699 | 1.687 | 0.000 | −6.000 |
Cr6+ | 4 | 676 | 169 | 1.652 | 0.059 | 0.357 | 1.892 | 1.535 | 1.593 | 2.852 |
Mn2+ | 4 | 40 | 10 | 2.046 | 0.039 | 0.241 | 2.194 | 1.953 | 1.304 | 4.668 |
5 | 120 | 24 | 2.141 | 0.053 | 0.243 | 2.267 | 2.024 | 0.264 | −0.341 | |
6 | 1908 | 318 | 2.199 | 0.085 | 0.830 | 2.798 | 1.968 | 2.070 | 7.951 | |
7 | 14 | 2 | 2.352 | 0.240 | 0.663 | 2.782 | 2.119 | 0.756 | −1.323 | |
8 | 144 | 18 | 2.321 | 0.104 | 0.539 | 2.691 | 2.152 | 0.899 | 0.927 | |
Mn3+ | 4 | 8 | 2 | 1.901 | 0.046 | 0.099 | 1.951 | 1.852 | 0.015 | −2.750 |
5 | 50 | 10 | 1.959 | 0.075 | 0.255 | 2.109 | 1.854 | 0.301 | −1.091 | |
6 | 492 | 82 | 2.031 | 0.149 | 0.755 | 2.598 | 1.843 | 0.841 | −0.500 | |
Mn4+ | 4 | 4 | 1 | 1.750 | 0.000 | 0.000 | 1.750 | 1.750 | − | − |
6 | 120 | 20 | 1.903 | 0.030 | 0.167 | 2.008 | 1.841 | 0.552 | 1.613 | |
Mn5+ | 4 | 32 | 8 | 1.698 | 0.014 | 0.076 | 1.725 | 1.649 | −1.042 | 3.241 |
Mn6+ | 4 | 8 | 2 | 1.662 | 0.012 | 0.034 | 1.687 | 1.653 | 1.599 | 1.380 |
Mn7+ | 4 | 28 | 7 | 1.610 | 0.009 | 0.041 | 1.633 | 1.592 | 0.868 | 1.384 |
Fe2+ | 3 | 24 | 8 | 1.844 | 0.029 | 0.127 | 1.918 | 1.791 | 0.578 | 0.456 |
4 | 24 | 6 | 1.985 | 0.027 | 0.141 | 2.041 | 1.900 | −1.051 | 0.726 | |
5 | 95 | 19 | 2.097 | 0.099 | 0.572 | 2.493 | 1.921 | 1.370 | 3.133 | |
6 | 876 | 146 | 2.147 | 0.089 | 0.713 | 2.646 | 1.933 | 1.440 | 4.840 | |
8 | 40 | 5 | 2.333 | 0.188 | 0.684 | 2.722 | 2.038 | 0.598 | −0.400 | |
Fe3+ | 4 | 260 | 65 | 1.875 | 0.033 | 0.201 | 1.965 | 1.764 | −0.060 | 0.471 |
5 | 105 | 21 | 1.966 | 0.070 | 0.350 | 2.207 | 1.857 | 1.245 | 2.428 | |
6 | 2268 | 378 | 2.015 | 0.064 | 0.539 | 2.391 | 1.852 | 0.971 | 2.078 | |
8 | 16 | 2 | 2.125 | 0.029 | 0.095 | 2.173 | 2.078 | 0.036 | −1.333 | |
Co2+ | 3 | 42 | 14 | 1.854 | 0.058 | 0.223 | 1.980 | 1.757 | 0.457 | −0.754 |
4 | 108 | 27 | 1.967 | 0.022 | 0.189 | 2.081 | 1.892 | 0.502 | 5.715 | |
5 | 80 | 16 | 2.066 | 0.117 | 0.628 | 2.574 | 1.946 | 2.717 | 7.945 | |
6 | 1458 | 243 | 2.108 | 0.062 | 0.571 | 2.516 | 1.945 | 1.612 | 5.825 | |
8 | 8 | 1 | 2.272 | 0.185 | 0.517 | 2.573 | 2.056 | 0.203 | −1.481 | |
Co3+ | 6 | 90 | 15 | 1.908 | 0.021 | 0.108 | 1.969 | 1.861 | 0.717 | 1.335 |
Co4+ | 6 | 6 | 1 | 1.874 | 0.000 | 0.000 | 1.874 | 1.874 | −1.369 | −3.333 |
Ni2+ | 2 | 4 | 2 | 1.686 | 0.001 | 0.002 | 1.687 | 1.685 | 0.000 | −6.000 |
4 | 12 | 3 | 1.950 | 0.039 | 0.092 | 1.982 | 1.890 | −0.800 | −1.573 | |
5 | 40 | 8 | 2.028 | 0.041 | 0.186 | 2.149 | 1.963 | 0.597 | 0.354 | |
6 | 1452 | 242 | 2.070 | 0.054 | 0.589 | 2.462 | 1.873 | 0.874 | 4.880 | |
Ni4+ | 6 | 30 | 5 | 1.870 | 0.012 | 0.067 | 1.906 | 1.839 | 0.446 | 3.019 |
Cu+ | 2 | 84 | 42 | 1.839 | 0.024 | 0.123 | 1.911 | 1.788 | −0.080 | −0.134 |
3 | 6 | 2 | 1.969 | 0.076 | 0.183 | 2.077 | 1.894 | 0.742 | −1.897 | |
4 | 52 | 13 | 2.084 | 0.110 | 0.541 | 2.438 | 1.897 | 0.554 | 0.966 | |
Cu2+ | 4 | 516 | 129 | 1.943 | 0.029 | 0.180 | 2.055 | 1.875 | 0.910 | 2.172 |
5 | 1090 | 218 | 2.037 | 0.155 | 0.865 | 2.700 | 1.835 | 1.784 | 2.494 | |
6 | 2190 | 365 | 2.130 | 0.232 | 0.893 | 2.748 | 1.855 | 0.969 | −0.494 | |
8 | 32 | 4 | 2.302 | 0.304 | 0.794 | 2.743 | 1.949 | 0.052 | −1.973 | |
Cu3+ | 4 | 44 | 11 | 1.850 | 0.029 | 0.135 | 1.946 | 1.811 | 1.485 | 3.710 |
Zn2+ | 4 | 908 | 227 | 1.952 | 0.031 | 0.229 | 2.076 | 1.847 | 0.331 | 0.887 |
5 | 180 | 36 | 2.051 | 0.082 | 0.619 | 2.525 | 1.906 | 1.609 | 5.499 | |
6 | 1158 | 193 | 2.110 | 0.086 | 0.810 | 2.696 | 1.886 | 2.005 | 6.961 | |
Y3+ | 6 | 150 | 25 | 2.264 | 0.041 | 0.226 | 2.400 | 2.174 | 0.695 | 1.020 |
7 | 245 | 35 | 2.332 | 0.082 | 0.499 | 2.661 | 2.162 | 1.248 | 2.181 | |
8 | 800 | 99 | 2.390 | 0.065 | 0.507 | 2.729 | 2.222 | 1.353 | 6.271 | |
9 | 135 | 15 | 2.422 | 0.092 | 0.585 | 2.799 | 2.214 | 1.005 | 3.144 | |
10 | 10 | 1 | 2.496 | 0.187 | 0.604 | 2.857 | 2.253 | 0.715 | −0.598 | |
12 | 12 | 1 | 2.541 | 0.000 | 0.000 | 2.541 | 2.541 | − | − | |
Zr4+ | 6 | 438 | 73 | 2.078 | 0.031 | 0.218 | 2.224 | 2.006 | 1.291 | 3.830 |
7 | 91 | 13 | 2.146 | 0.048 | 0.233 | 2.283 | 2.050 | 0.000 | −0.356 | |
8 | 168 | 21 | 2.199 | 0.053 | 0.313 | 2.407 | 2.094 | 0.536 | 0.471 | |
9 | 27 | 3 | 2.263 | 0.138 | 0.472 | 2.593 | 2.121 | 1.385 | 1.474 | |
10 | 70 | 7 | 2.283 | 0.046 | 0.204 | 2.415 | 2.211 | 1.150 | 0.597 | |
Nb4+ | 6 | 18 | 3 | 2.054 | 0.080 | 0.241 | 2.163 | 1.922 | −0.125 | −1.553 |
Nb5+ | 4 | 8 | 2 | 1.831 | 0.068 | 0.184 | 1.926 | 1.742 | 0.167 | −1.224 |
5 | 20 | 4 | 1.926 | 0.054 | 0.164 | 1.993 | 1.829 | −0.467 | −1.286 | |
6 | 1440 | 240 | 1.993 | 0.115 | 0.742 | 2.444 | 1.702 | 0.646 | 1.077 | |
7 | 21 | 3 | 2.069 | 0.163 | 0.668 | 2.435 | 1.767 | 0.469 | 0.090 | |
8 | 8 | 1 | 2.080 | 0.001 | 0.002 | 2.081 | 2.079 | 0.000 | −2.800 | |
Mo3+ | 6 | 30 | 5 | 2.095 | 0.024 | 0.112 | 2.163 | 2.051 | 0.347 | 1.099 |
Mo4+ | 6 | 54 | 9 | 2.003 | 0.065 | 0.264 | 2.077 | 1.813 | −1.750 | 2.047 |
Mo5+ | 5 | 10 | 2 | 1.916 | 0.122 | 0.328 | 1.981 | 1.653 | −1.799 | 1.552 |
6 | 444 | 74 | 1.992 | 0.167 | 0.806 | 2.429 | 1.623 | −0.627 | 0.085 | |
Mo6+ | 4 | 1736 | 434 | 1.764 | 0.033 | 0.268 | 1.905 | 1.637 | 0.520 | 0.770 |
5 | 75 | 15 | 1.872 | 0.146 | 0.620 | 2.286 | 1.666 | 0.679 | −0.042 | |
6 | 3036 | 506 | 1.972 | 0.232 | 1.005 | 2.608 | 1.603 | 0.431 | −1.027 | |
Tc7+ | 4 | 24 | 6 | 1.705 | 0.019 | 0.068 | 1.740 | 1.672 | −0.044 | −0.591 |
Ru3+ | 6 | 18 | 3 | 2.025 | 0.043 | 0.191 | 2.107 | 1.916 | −1.010 | 2.152 |
Ru4+ | 6 | 48 | 8 | 1.982 | 0.025 | 0.134 | 2.070 | 1.936 | 1.317 | 5.102 |
Ru5+ | 6 | 138 | 23 | 1.964 | 0.076 | 0.273 | 2.113 | 1.840 | 0.384 | −0.755 |
Rh3+ | 6 | 66 | 11 | 2.025 | 0.023 | 0.093 | 2.071 | 1.978 | 0.647 | −0.607 |
Rh4+ | 6 | 18 | 3 | 2.007 | 0.014 | 0.032 | 2.020 | 1.988 | −0.442 | −1.946 |
Pd2+ | 4 | 116 | 29 | 2.011 | 0.024 | 0.104 | 2.060 | 1.956 | 0.347 | −0.596 |
Pd4+ | 6 | 12 | 2 | 2.000 | 0.027 | 0.094 | 2.059 | 1.965 | 0.959 | 0.035 |
Ag+ | 2 | 10 | 5 | 2.136 | 0.018 | 0.053 | 2.164 | 2.111 | 0.435 | −1.386 |
3 | 45 | 15 | 2.278 | 0.112 | 0.391 | 2.535 | 2.144 | 0.888 | −0.181 | |
4 | 148 | 37 | 2.402 | 0.127 | 0.601 | 2.741 | 2.140 | −0.057 | −0.002 | |
5 | 225 | 45 | 2.489 | 0.152 | 0.801 | 2.975 | 2.174 | 0.657 | 0.058 | |
6 | 378 | 63 | 2.537 | 0.135 | 0.652 | 2.894 | 2.242 | 0.330 | −0.288 | |
7 | 63 | 9 | 2.589 | 0.155 | 0.564 | 2.888 | 2.324 | 0.308 | −0.888 | |
8 | 104 | 13 | 2.656 | 0.175 | 0.708 | 3.083 | 2.375 | 0.736 | 0.205 | |
9 | 27 | 3 | 2.704 | 0.143 | 0.402 | 2.863 | 2.461 | −0.894 | −0.873 | |
Cd2+ | 5 | 20 | 4 | 2.257 | 0.078 | 0.342 | 2.486 | 2.144 | 1.352 | 2.401 |
6 | 810 | 135 | 2.302 | 0.069 | 0.591 | 2.754 | 2.163 | 1.472 | 4.484 | |
7 | 42 | 6 | 2.377 | 0.134 | 0.713 | 2.888 | 2.175 | 2.033 | 5.213 | |
8 | 144 | 18 | 2.432 | 0.118 | 0.531 | 2.724 | 2.193 | 0.312 | −0.575 | |
9 | 9 | 1 | 2.530 | 0.214 | 0.500 | 2.826 | 2.326 | 0.688 | −1.714 | |
Hf4+ | 6 | 66 | 11 | 2.082 | 0.051 | 0.322 | 2.241 | 1.919 | 0.195 | 4.551 |
7 | 28 | 4 | 2.128 | 0.019 | 0.072 | 2.167 | 2.095 | 0.016 | −0.842 | |
8 | 56 | 7 | 2.190 | 0.064 | 0.256 | 2.324 | 2.068 | −0.012 | −0.840 | |
Ta5+ | 6 | 828 | 138 | 1.988 | 0.076 | 0.585 | 2.386 | 1.801 | 1.474 | 4.235 |
7 | 98 | 14 | 2.057 | 0.155 | 0.619 | 2.486 | 1.867 | 1.763 | 2.077 | |
W5+ | 6 | 24 | 4 | 1.956 | 0.095 | 0.448 | 2.140 | 1.692 | −0.821 | 1.154 |
W6+ | 4 | 140 | 35 | 1.773 | 0.027 | 0.141 | 1.846 | 1.705 | −0.220 | 0.095 |
5 | 60 | 12 | 1.859 | 0.072 | 0.467 | 2.166 | 1.699 | 0.885 | 4.719 | |
6 | 2178 | 363 | 1.951 | 0.182 | 0.919 | 2.557 | 1.638 | 0.750 | −0.146 | |
Re5+ | 6 | 18 | 3 | 1.940 | 0.068 | 0.183 | 2.027 | 1.844 | 0.045 | −1.764 |
Re7+ | 4 | 164 | 41 | 1.716 | 0.021 | 0.150 | 1.790 | 1.640 | −0.114 | 1.066 |
5 | 40 | 8 | 1.810 | 0.052 | 0.275 | 1.904 | 1.629 | −1.249 | 3.058 | |
6 | 60 | 10 | 1.882 | 0.046 | 0.195 | 1.982 | 1.787 | 0.380 | −0.224 | |
Os5+ | 6 | 24 | 4 | 1.960 | 0.044 | 0.180 | 2.044 | 1.864 | −0.486 | 0.512 |
Os6+ | 6 | 6 | 1 | 1.926 | 0.125 | 0.266 | 2.015 | 1.749 | −0.968 | −1.875 |
Os7+ | 5 | 5 | 1 | 1.825 | 0.034 | 0.092 | 1.855 | 1.763 | −1.448 | 2.287 |
6 | 18 | 3 | 1.887 | 0.021 | 0.058 | 1.923 | 1.865 | 0.864 | −0.668 | |
Os8+ | 4 | 4 | 1 | 1.698 | 0.014 | 0.027 | 1.711 | 1.684 | 0.000 | −6.000 |
5 | 15 | 3 | 1.793 | 0.162 | 0.569 | 2.227 | 1.658 | 2.132 | 3.720 | |
6 | 24 | 4 | 1.880 | 0.170 | 0.442 | 2.169 | 1.727 | 0.747 | −1.167 | |
Ir3+ | 6 | 6 | 1 | 2.042 | 0.000 | 0.000 | 2.042 | 2.042 | − | − |
Ir4+ | 4 | 20 | 5 | 1.909 | 0.008 | 0.032 | 1.929 | 1.897 | 1.151 | 1.194 |
6 | 72 | 12 | 2.015 | 0.024 | 0.176 | 2.096 | 1.920 | −0.698 | 4.820 | |
Ir5+ | 6 | 36 | 6 | 1.990 | 0.013 | 0.039 | 2.010 | 1.971 | −0.237 | −1.358 |
Pt2+ | 4 | 12 | 3 | 2.007 | 0.009 | 0.022 | 2.017 | 1.995 | −0.473 | −1.650 |
Pt4+ | 6 | 198 | 33 | 2.021 | 0.020 | 0.142 | 2.087 | 1.945 | 0.222 | 2.499 |
Au3+ | 4 | 96 | 24 | 1.999 | 0.023 | 0.153 | 2.082 | 1.929 | 0.879 | 2.577 |
Hg2+ | 2 | 2 | 1 | 1.955 | 0.000 | 0.000 | 1.955 | 1.955 | − | − |
4 | 24 | 6 | 2.316 | 0.311 | 0.862 | 2.834 | 1.972 | 0.427 | −1.568 | |
5 | 15 | 3 | 2.380 | 0.271 | 0.688 | 2.726 | 2.038 | −0.031 | −1.928 | |
6 | 150 | 25 | 2.429 | 0.249 | 0.912 | 2.932 | 2.020 | −0.041 | −1.051 | |
7 | 63 | 9 | 2.505 | 0.267 | 0.998 | 2.988 | 1.990 | −0.409 | −1.095 | |
8 | 64 | 8 | 2.502 | 0.163 | 0.685 | 2.906 | 2.221 | 0.493 | −0.182 |