The coefficients a and b are defined by the equation:
Reference: Z. Su and P. Coppens, Acta Cryst.
A53, 749-762 (1997); P. Macchi and P. Coppens, Acta Cryst.
A57, 656-662 (2001).
Preparation of the table: C. Kim, I. Novozhilova, and P. Coppens.
/
<
2.0 Å-1 range/<
4.0 Å-1 range/<=
6.0 Å-1 range/<
2.0 Å-1 range.Z Atom a1 a2 a3 a4 a5 a6 b1 b2 b3 b4 b5 b6 3 Li+ 0.79375 0.54736 0.46161 0.13918 0.05800 0.00010 2.88678 1.16905 6.18250 0.31715 12.60983 28.15927 4 Be2+ 0.82577 0.73691 0.23557 0.20135 0.00034 0.00010 2.04212 0.80252 4.60157 0.21162 43.68258 103.45510 6 Cv 2.03492 1.64286 0.68060 0.67022 0.51650 0.45488 25.99675 11.77809 0.51013 0.97866 0.16915 57.91874 8 O- 3.56378 2.14950 1.52760 1.47980 0.27065 0.00010 14.10561 5.60491 0.32801 46.88862 0.00980 10.98084 9 F- 3.22684 2.47111 1.59839 1.28490 1.11335 0.30182 4.95997 14.45952 0.17267 11.39653 43.30817 0.96703 11 Na+ 3.69529 3.30459 1.68333 0.69149 0.62431 0.00088 3.24183 7.07179 0.12279 15.45334 1.43664 35.26383 12 Mg2+ 4.30385 2.58390 1.71397 1.39368 0.00470 0.00010 4.02045 1.85304 0.10693 8.78523 58.58712 125.50050 13 Al3+ 4.19367 3.00032 1.71590 1.08840 0.00167 0.00010 3.37134 1.58637 0.09158 6.99679 45.26456 113.97270 14 Si0 5.49488 3.33770 2.38765 1.59864 1.17986 0.00010 2.60802 37.46289 1.09647 0.06439 80.52337 56.27056 14 Si4+ 3.98392 3.53675 1.72808 0.75103 0.00013 0.00010 2.94648 1.39488 0.08069 5.91604 56.23176 79.76580 17 Cl- 7.13932 6.34213 2.29801 1.97826 0.22854 0.00983 1.18073 19.52901 61.04850 0.08057 23.18225 0.09759 19 K+ 8.00372 7.44077 1.42217 1.13491 0.00010 0.00010 12.70476 0.77473 0.00010 32.44270 199.99900 82.98298 20 Ca2+ 8.66803 7.39747 1.38325 0.55348 0.00010 0.00010 10.62955 0.66306 0.00010 30.98476 199.99880 82.97898 21 Sc3+ 9.01395 7.36477 1.32160 0.30179 0.00010 0.00010 8.86658 0.56771 0.00010 29.98133 137.40030 53.69811 22 Ti2+ 9.67607 7.35874 1.66775 1.29681 0.00010 0.00010 7.92858 0.50388 23.88214 0.00010 92.10388 145.58810 22 Ti3+ 9.56376 7.35320 1.26997 0.81496 0.00010 0.00010 7.72729 0.49604 0.00010 22.37931 92.10560 145.58920 22 Ti4+ 9.22395 7.35117 1.23367 0.19305 0.00010 0.00010 7.44634 0.48595 0.00010 28.20512 92.10930 145.59010 23 V2+ 10.14209 7.35015 2.25361 1.23887 0.01533 0.00010 6.90615 0.44224 20.14575 0.00010 120.21700 55.09812 23 V3+ 10.05723 7.34875 1.38759 1.20752 0.00010 0.00010 6.75290 0.43509 18.25122 0.00010 120.22150 55.11062 23 V5+ 9.37695 7.36389 1.11621 0.14450 0.00010 0.00010 6.31625 0.41568 0.00010 25.36044 199.99870 82.97847 24 Cr2+ 10.54130 4.41457 2.93436 2.87024 1.17229 0.06743 6.04009 0.38967 0.38966 16.94938 0.00010 59.98400 24 Cr3+ 10.45597 4.43683 2.92505 2.06149 1.11981 0.00120 5.90641 0.38863 0.37041 15.34221 0.00010 59.68271 25 Mn2+ 10.86580 7.35401 3.49267 1.09987 0.18537 0.00249 5.30450 0.34487 14.15718 0.00010 38.60730 100.13560 25 Mn3+ 11.04414 4.43611 4.06737 2.44502 0.00559 0.00189 5.32462 0.15971 0.47488 13.90108 100.14020 38.59723 25 Mn4+ 10.80739 7.37819 1.80548 1.00948 0.00010 0.00010 5.12031 0.33181 12.46589 0.00010 100.14660 38.60185 26 Fe2+ 11.32394 7.35828 4.08542 1.03934 0.19438 0.00010 4.71611 0.30793 12.87900 0.00024 43.73118 103.91920 26 Fe3+ 11.27641 7.37595 3.32058 0.98461 0.04263 0.00010 4.63894 0.30169 11.63908 0.00010 44.10289 103.92070 27 Co2+ 11.59539 7.37601 4.75131 0.95818 0.31843 0.00010 4.18474 0.27510 11.19206 0.00010 36.27509 93.95933 27 Co3+ 11.58135 7.38964 4.01201 0.91419 0.10353 0.00010 4.13155 0.27012 10.32693 0.00010 35.20369 93.95908 28 Ni2+ 11.83838 5.16446 4.59215 3.72826 0.67719 0.00010 3.76040 9.57707 0.31557 0.11646 25.17286 96.76703 28 Ni3+ 12.08932 7.37051 4.53328 0.89389 0.11440 0.00010 3.73486 0.24588 9.52524 0.00100 36.54998 96.77110 29 Cu+ 11.74994 6.77249 6.21229 1.75552 1.47560 0.03461 3.34714 0.23831 8.32820 23.58346 0.04331 98.01738 29 Cu2+ 11.83187 5.78192 5.77531 2.46041 1.14698 0.00353 3.33965 0.25530 8.03031 0.08201 19.99327 98.02090 30 Zn2+ 12.49609 7.88148 4.99190 2.05602 0.57505 0.00010 3.52509 0.16619 9.20541 1.71372 24.20427 82.21923 31 Ga3+ 10.80193 7.89470 5.30620 3.91136 0.08693 0.00010 3.67800 0.15468 2.08510 9.11568 34.76155 99.34953 32 Ge4+ 8.64238 8.44015 7.88210 2.99985 0.03590 0.00010 3.75852 2.14595 0.14366 8.16207 30.93576 72.31449 35 Br- 14.72809 7.73340 4.08153 3.89920 2.84995 2.70412 1.87781 0.11285 23.45650 3.65207 21.50646 68.50430 37 Rb+ 17.72736 7.70846 6.22707 4.23320 0.10456 0.00010 1.68258 0.09962 13.34713 25.64859 76.90928 199.99860 38 Sr2+ 13.56253 9.15282 7.57461 4.23621 1.47524 0.00010 1.52639 13.37893 0.09009 1.50827 28.97999 162.86130 39 Y3+ 17.83594 10.00061 7.34299 0.76995 0.05161 0.00010 1.37290 11.94201 0.07979 27.59179 0.08311 137.72530 40 Zr4+ 17.88797 10.57832 7.18725 0.34750 0.00010 0.00010 1.24006 10.60035 0.06944 29.00543 131.45550 1.67829 41 Nb3+ 17.94269 11.64938 7.03542 1.17571 0.20353 0.00010 1.13911 10.82291 0.06147 34.40293 1.15832 134.27490 41 Nb5+ 17.35713 10.99074 7.04050 0.57079 0.04542 0.00010 1.13181 9.52278 0.06199 1.11378 134.27980 38.40765 42 Mo3+ 16.70847 11.98967 6.70451 1.98553 1.61267 0.00010 1.02628 9.86398 0.04848 26.23584 1.02613 83.38388 42 Mo6+ 16.84671 11.18317 6.67150 1.21668 0.08306 0.00010 1.01489 8.31776 0.04772 1.01511 36.37142 83.39908 44 Ru3+ 16.20121 13.68489 5.92693 2.62037 2.56751 0.00010 0.83651 8.66621 0.02083 0.83653 22.32915 67.41669 44 Ru4+ 15.97671 13.58921 5.91839 2.79182 1.72564 0.00010 0.83452 8.38679 0.02066 0.83387 21.20783 67.42265 45 Rh3+ 14.55243 14.36520 5.43109 3.60085 2.86567 1.18601 8.09600 0.75250 0.00422 0.75381 21.00325 0.75895 45 Rh4+ 14.57165 14.10996 5.40851 3.65768 1.90013 1.35484 7.90759 0.75012 0.00354 0.75338 19.97214 0.75124 46 Pd2+ 19.27390 15.67787 5.26036 3.78685 0.00010 0.00010 0.69511 7.84482 0.00010 22.21775 60.82368 1.12994 46 Pd4+ 19.16608 15.58248 5.24991 1.97949 0.02452 0.00010 0.69220 7.50980 0.00010 19.35021 0.69139 60.83056 47 Ag+ 19.29333 16.76786 5.18419 4.69146 0.06334 0.00010 0.64534 7.54710 0.00010 23.16034 100.32570 2.35114 47 Ag2+ 19.26038 16.76118 5.17728 3.80102 0.00010 0.00010 0.64383 7.44215 0.00010 21.24567 100.31430 2.43992 48 Cd2+ 19.24328 17.81622 5.07556 3.86538 0.00010 0.00010 0.59548 7.03822 0.00010 20.12238 87.60555 31.88584 49 In3+ 19.15099 19.02664 5.11556 1.72846 1.00259 0.00010 0.55860 6.79490 0.00370 25.60539 8.23095 93.69624 50 Sn2+ 19.14517 19.11002 4.80720 4.48861 0.25075 0.20103 5.86776 0.50516 0.00010 24.33452 87.00222 31.41846 50 Sn4+ 19.71431 19.14550 4.79767 2.34645 0.00010 0.00010 6.04052 0.50506 0.00010 16.17828 87.05909 31.49791 51 Sb3+ 19.06093 12.90928 6.64901 4.63278 4.60732 0.14140 0.46390 5.35884 5.35853 0.00010 21.75129 70.66362 51 Sb5+ 19.55274 19.11016 4.62585 1.75378 0.96170 0.00010 5.57560 0.46433 0.00010 15.08594 5.57571 70.66860 53 I- 18.97534 15.68841 6.74714 4.42194 4.08431 4.06854 0.38165 4.33217 26.51128 4.35007 0.00013 70.73529
/<
4.0 Å-1 range.Z Atom a1 a2 a3 a4 a5 a6 b1 b2 b3 b4 b5 b6 3 Li+ 0.64939 0.57637 0.36786 0.28335 0.10644 0.01659 5.82679 12.88054 0.93928 28.16051 0.36703 0.09916 4 Be2+ 0.66489 0.50696 0.27173 0.25527 0.25503 0.04612 0.87607 4.60157 43.68258 103.45510 0.34369 0.09288 6 Cval 2.10076 1.70870 0.89673 0.61857 0.52072 0.15452 25.99675 11.77809 0.71006 0.28403 57.91874 0.07739 8 O- 3.59296 2.17868 1.50898 1.18959 0.50051 0.02928 14.10561 5.60491 46.88862 0.35181 0.08822 10.98084 9 F- 3.26017 2.50444 1.31823 1.17269 1.14668 0.59779 4.95997 14.45952 11.39653 0.29108 43.30817 0.07573 13 Al3+ 4.99881 1.80939 1.14687 0.72833 0.72266 0.59394 1.73305 6.99679 0.13303 113.97274 45.26456 0.03483 14 Si4+ 4.92503 1.61536 1.10769 0.86417 0.86226 0.62550 1.45168 5.91603 0.11520 56.23176 79.76580 0.03141 14 Si_v 4.56486 3.95794 2.40702 1.34462 1.15279 0.57276 37.46289 1.38921 80.52337 56.27056 0.11110 0.02907 21 Sc3+ 9.21427 6.03182 1.64701 0.50226 0.30232 0.30232 8.86654 0.56076 0.03151 29.97352 199.99871 82.98011 22 Ti3+ 9.42699 7.16666 1.74298 0.67819 0.00010 0.00010 7.72729 0.56044 0.03213 22.37931 145.58919 92.10560 22 Ti4+ 9.18221 6.51384 1.66155 0.24555 0.24555 0.15131 7.44634 0.51731 0.02933 92.10930 145.59014 28.20512 23 V3+ 9.97453 6.75706 1.68229 1.30489 0.14061 0.14061 6.75290 0.47729 0.02763 18.25122 120.22148 55.11062 23 V5+ 9.14230 6.88805 1.67893 0.09691 0.09691 0.09691 6.33388 0.47658 0.02755 32.42055 199.99913 82.98258 24 Cr3+ 9.77901 5.72051 2.12461 1.57723 1.38452 0.41411 5.90642 0.54193 0.30143 0.02191 15.34221 59.68271 25 Mn3+ 10.88285 7.10689 2.28373 1.72558 0.00047 0.00047 5.32462 0.40567 13.90108 0.02496 100.14025 38.59723 25 Mn4+ 10.56403 7.14513 1.72348 1.56212 0.00262 0.00262 5.12031 0.40499 0.02490 12.46589 100.14655 38.60185 26 Fe3+ 11.02091 7.16905 3.06508 1.74465 0.00016 0.00016 4.63894 0.37343 11.63908 0.02375 44.10289 103.92073 27 Co3+ 11.31675 7.17893 3.74741 1.75672 0.00010 0.00010 4.13155 0.34305 10.32693 0.02243 35.20369 93.95908 28 Ni3+ 11.77148 7.14986 4.25928 1.75694 0.03122 0.03122 5.74186 0.31436 9.52524 0.02085 36.54998 96.77110 31 Ga3+ 11.91521 7.01227 5.07480 1.62777 1.25037 1.11958 6.06158 0.23727 9.11568 0.01305 34.76155 99.34953 32 Ge4+ 10.55768 7.01350 4.96667 2.00272 1.95319 1.50624 5.93810 0.21328 8.16207 30.93576 72.31449 0.00841 41 Nb5+ 16.92325 5.97793 4.68218 4.58782 3.40334 0.42549 9.52278 134.27975 0.04739 38.40765 0.16169 4.17449 42 Mo6+ 28.36189 6.77759 0.86023 0.00010 0.00010 0.00010 1.33247 0.08569 0.00010 8.31776 36.37142 83.39908 51 Sb5+ 22.97318 15.99212 7.03439 0.00010 0.00010 0.00010 0.65648 5.57560 0.04056 15.08594 70.66860 5.57571
/<=
6.0 Å-1 range.Z Atom a1 a2 a3 a4 a5 a6 b1 b2 b3 b4 b5 b6 3 Li+ 0.72493 0.65191 0.39790 0.18231 0.03841 0.00455 5.82679 12.88054 0.93892 28.16051 0.19617 0.05039 4 Be2+ 0.70997 0.55216 0.31693 0.30047 0.10651 0.01397 0.87726 4.60157 43.68258 103.45510 0.18990 0.04903 6 Cval 2.19542 1.80336 1.07822 0.61538 0.26206 0.04556 25.99675 11.77809 0.40600 57.91874 0.14572 0.03926 8 O- 3.80720 2.39292 1.72322 0.68630 0.24352 0.14686 14.10561 5.60491 46.88862 0.16162 10.98084 0.04178 9 F- 3.43023 2.67450 1.48829 1.31674 0.87493 0.21529 4.95997 14.45952 11.39653 43.30817 0.15322 0.03970 13 Al3+ 5.03949 1.83267 1.14722 0.74594 0.74437 0.49032 1.69091 6.99679 0.11672 45.26456 113.97274 0.03085 14 Si4+ 2.48739 2.35167 1.73637 1.73634 1.14038 0.54784 5.91604 7.76189 56.23176 79.76580 0.10678 0.02851 14 Si_v 4.22729 4.09970 2.14266 2.06945 1.37270 0.88969 37.46289 1.32268 0.00010 80.52337 0.00010 56.27056 23 V5+ 10.83029 1.78490 1.78490 1.78490 1.43449 0.38052 6.33388 32.42055 199.99913 82.98258 0.02118 0.11185 41 Nb5+ 16.75177 7.09743 5.80645 4.41634 1.67400 0.25401 9.52278 0.12293 134.27975 38.40765 0.00819 4.17449 42 Mo6+ 26.23300 7.08082 1.66319 1.02263 0.00018 0.00018 1.83661 0.11546 0.00763 8.31776 36.37142 83.39908 51 Sb5+ 21.51681 6.71307 5.52857 5.52857 5.52857 1.18443 5.57560 0.06183 15.08594 70.66860 5.57571 0.00010