C12 H10 O2 S2 ESPAR96 Example of use of program "PARST96" P2/n R=0.0487 RW=0.0451 Crystal data a = 12.4130(0.0040) alpha= 90.00(0.00) b = 8.5370(0.0020) beta = 116.50(0.02) c = 12.6490(0.0050) gamma= 90.00(0.00) V = 1199.58( 0.70) cubic-Angstrom Niggli reduced cell: 8.537 12.413 12.649 116.50 90.00 90.00 Niggli matrix: 72.8804 154.0826 159.9972 -70.0584 0.0000 0.0000 Transformation matrix: 0.00 1.00 0.00 1.00 0.00 0.00 0.00 0.00 1.00 C 12. H 10. O 2. S 2. M = 250.330 (Atomic weights 1977) Z = 4.00 D(calc.)= 1.3861 Mg/m**3 F(000) = 520.0 mu = 4.246 cm**-1 (Int.Tab. Vol.C, Table 4.2.4.2, p.193) Lambda = 0.7106900 Angstrom Number of atoms: 26 Atomic coordinates Atom X/a Y/b Z/c S1 0.27400( 20) 0.52610( 20) 0.48920( 20) S2 0.35740( 20) 0.68290( 20) 0.42340( 10) O1 0.23480( 40) 0.40340( 60) 0.40380( 50) O2 0.35180( 40) 0.49210( 50) 0.61010( 40) C1 0.14740( 50) 0.62520( 70) 0.48290( 50) C2 0.03750( 60) 0.60660( 100) 0.38570( 70) C3 -0.06190( 80) 0.68550( 130) 0.38500( 100) C4 -0.04830( 120) 0.77750( 130) 0.47710( 140) C5 0.06210( 120) 0.79480( 120) 0.57400( 120) C6 0.16080( 80) 0.72020( 90) 0.57750( 70) C7 0.42450( 50) 0.81510( 80) 0.54370( 50) C8 0.37540( 70) 0.96160( 100) 0.53800( 70) C9 0.43040( 80) 1.06750( 100) 0.62840( 80) C10 0.53780( 70) 1.02810( 100) 0.72380( 60) C11 0.58650( 70) 0.88420( 100) 0.72870( 70) C12 0.53100( 60) 0.77650( 90) 0.63990( 60) H2 0.03380( 680) 0.53650( 930) 0.32810( 680) H3 -0.13270( 660) 0.65440( 870) 0.31980( 630) H4 -0.11320( 670) 0.82870( 870) 0.47480( 650) H5 0.07130( 680) 0.85410( 950) 0.64300( 730) H6 0.24730( 620) 0.72290( 760) 0.64750( 570) H8 0.30670( 460) 0.98290( 660) 0.47580( 470) H9 0.39620( 580) 1.17170( 830) 0.62010( 570) H10 0.57510( 550) 1.11440( 810) 0.78260( 570) H11 0.65980( 420) 0.84980( 560) 0.79430( 420) H12 0.56900( 470) 0.67910( 640) 0.64640( 470) Orthogonal coordinates (Angstrom) Orthogonalization matrix: a b cosgamma c cosbeta 12.41300 0.00000 -5.64396 0 b singamma -c sinbeta cosalpha* 0.00000 8.53700 0.00000 0 0 c sinbeta sinalpha* 0.00000 0.00000 11.32003 Atom X Y Z S1 0.6401(0.0027) 4.4913(0.0017) 5.5378(0.0023) S2 2.0468(0.0026) 5.8299(0.0017) 4.7929(0.0011) O1 0.6355(0.0057) 3.4438(0.0051) 4.5710(0.0057) O2 0.9235(0.0055) 4.2011(0.0043) 6.9063(0.0045) C1 -0.8958(0.0068) 5.3373(0.0060) 5.4664(0.0057) C2 -1.7114(0.0084) 5.1785(0.0085) 4.3661(0.0079) C3 -2.9413(0.0114) 5.8521(0.0111) 4.3582(0.0113) C4 -3.2923(0.0169) 6.6375(0.0111) 5.4008(0.0158) C5 -2.4688(0.0164) 6.7852(0.0102) 6.4977(0.0136) C6 -1.2634(0.0107) 6.1483(0.0077) 6.5373(0.0079) C7 2.2007(0.0068) 6.9585(0.0068) 6.1547(0.0057) C8 1.6234(0.0095) 8.2092(0.0085) 6.0902(0.0079) C9 1.7959(0.0109) 9.1132(0.0085) 7.1135(0.0091) C10 2.5906(0.0093) 8.7769(0.0085) 8.1934(0.0068) C11 3.1675(0.0095) 7.5484(0.0085) 8.2489(0.0079) C12 2.9797(0.0082) 6.6290(0.0077) 7.2437(0.0068) H2 -1.4322(0.0927) 4.5801(0.0794) 3.7141(0.0770) H3 -3.4521(0.0893) 5.5866(0.0743) 3.6201(0.0713) H4 -4.0849(0.0909) 7.0746(0.0743) 5.3747(0.0736) H5 -2.7440(0.0939) 7.2915(0.0811) 7.2788(0.0826) H6 -0.5847(0.0834) 6.1714(0.0649) 7.3297(0.0645) H8 1.1217(0.0630) 8.3910(0.0563) 5.3861(0.0532) H9 1.4182(0.0789) 10.0028(0.0709) 7.0195(0.0645) H10 2.7218(0.0755) 9.5136(0.0691) 8.8591(0.0645) H11 3.7071(0.0573) 7.2547(0.0478) 8.9915(0.0475) H12 3.4147(0.0641) 5.7975(0.0546) 7.3173(0.0532) Displacement parameters, U(I,J)x10**4 exp(-2*pi**2(U11*h**2*(a*)**2+...+2*U12*h*k*(a*)*(b*)+...) Atom U11 U22 U33 U23 U13 U12 S1 537( 11) 496( 11) 700( 12) -100( 11) 221( 9) -22( 10) S2 628( 12) 867( 15) 543( 11) -164( 11) 291( 9) -160( 12) O1 656( 30) 730( 35) 782( 34) 195( 30) 104( 27) 62( 30) O2 867( 38) 662( 33) 1302( 47) -491( 36) 527( 36) -191( 31) C1 505( 39) 398( 40) 472( 39) 39( 35) 223( 34) 0( 34) C2 517( 47) 676( 56) 645( 51) 72( 46) 209( 42) -72( 44) C3 571( 61) 859( 75) 1092( 86) 320( 67) 289( 62) 28( 61) C4 969( 94) 677( 69) 1744( 137) 349( 77) 958( 106) 217( 72) C5 1234( 93) 769( 75) 1367( 100) -163( 72) 906( 85) -182( 71) C6 761( 62) 665( 52) 823( 56) -127( 46) 493( 51) -74( 49) C7 435( 38) 507( 46) 479( 39) 12( 35) 221( 33) -23( 36) C8 434( 45) 702( 55) 581( 50) 139( 49) 161( 41) 86( 47) C9 744( 57) 421( 56) 892( 64) 49( 46) 439( 53) 42( 46) C10 655( 49) 628( 54) 574( 47) -66( 45) 254( 40) -30( 50) C11 489( 48) 602( 59) 613( 53) 38( 45) 166( 44) -17( 43) C12 477( 41) 378( 48) 617( 46) 38( 40) 230( 37) 95( 39) H2 581( 331) H3 918( 306) H4 1133( 318) H5 1363( 318) H6 1005( 262) H8 506( 194) H9 746( 271) H10 642( 243) H11 494( 160) H12 313( 182) Principal axes of the thermal ellipsoids, Uequiv. (x10**4 A**2) and Bequiv.(A**2) Atom R1 R2 R3 Uequiv. Bequiv. Rmax/Rmin S1 796( 18) 545( 13) 453( 11) 598( 8) 4.72(0.06) 1.76 S2 968( 15) 564( 19) 473( 15) 668( 9) 5.28(0.07) 2.05 O1 1170( 60) 761( 41) 478( 28) 803( 23) 6.34(0.18) 2.45 O2 1574( 53) 813( 54) 396( 40) 928( 28) 7.32(0.22) 3.98 C1 505( 44) 487( 60) 377( 49) 456( 30) 3.60(0.23) 1.34 C2 820( 83) 587( 58) 487( 56) 631( 38) 4.98(0.30) 1.68 C3 1404( 117) 641( 97) 568( 61) 871( 55) 6.88(0.43) 2.47 C4 1882( 112) 575( 93) 540( 189) 999( 86) 7.89(0.68) 3.49 C5 1582( 75) 748( 133) 677( 159) 1002( 76) 7.91(0.60) 2.34 C6 946( 51) 625( 65) 522( 113) 698( 47) 5.51(0.37) 1.81 C7 519( 46) 479( 34) 404( 70) 467( 29) 3.69(0.23) 1.28 C8 799( 69) 601( 92) 390( 43) 597( 39) 4.71(0.31) 2.05 C9 906( 55) 653( 110) 415( 56) 658( 44) 5.20(0.35) 2.19 C10 678( 95) 672( 83) 530( 57) 626( 36) 4.95(0.28) 1.28 C11 738( 93) 581( 66) 474( 39) 598( 40) 4.72(0.32) 1.56 C12 635( 64) 533( 50) 320( 55) 496( 34) 3.92(0.27) 1.99 Bond distances (Angstrom) (Corrections following Busing & Levy, Acta Cryst.(1964).17,142) uncorrected lower upper riding non-correlated distance bound bound motion motion S1 - S2 2.0797( 34) 2.0800 2.1971 2.0853 2.1385 S1 - O1 1.4254( 57) 1.4256 1.6194 1.4310 1.5225 S1 - O2 1.4274( 46) 1.4279 1.6000 1.4363 1.5139 S1 - C1 1.7550( 70) 1.7559 1.8750 1.7654 1.8154 S2 - C7 1.7754( 62) 1.7774 1.9083 1.7920 1.8429 C1 - C2 1.3788( 77) 1.3808 1.5386 1.3965 1.4597 C1 - C6 1.3927( 109) 1.3956 1.5613 1.4149 1.4785 C2 - C3 1.4023( 141) 1.4045 1.6142 1.4237 1.5093 C2 - H2 0.9280( 875) C3 - C4 1.3517( 203) 1.3522 1.5505 1.3615 1.4514 C3 - H3 0.9361( 622) C4 - C5 1.3796( 164) 1.3797 1.5951 1.3843 1.4874 C4 - H4 0.9055( 879) C5 - C6 1.3639( 181) 1.3657 1.6175 1.3854 1.4916 C5 - H5 0.9706( 932) C6 - H6 1.0435( 579) C7 - C8 1.3790( 110) 1.3796 1.5267 1.3888 1.4532 C7 - C12 1.3789( 75) 1.3790 1.5193 1.3817 1.4491 C8 - C9 1.3763( 115) 1.3766 1.5408 1.3833 1.4587 C8 - H8 0.8835( 445) C9 - C10 1.3824( 99) 1.3824 1.5571 1.3851 1.4697 C9 - H9 0.9710( 715) C10 - C11 1.3583( 122) 1.3583 1.5357 1.3607 1.4470 C10 - H10 1.0015( 650) C11 - C12 1.3752( 105) 1.3757 1.5285 1.3840 1.4521 C11 - H11 0.9638( 407) C12 - H12 0.9413( 564) Number of bond distances: 27 Bond angles (degrees) (e.s.d. following Cruickshank, Internat. Tables, II, 1959, p.331) Angle e.s.d. O2 - S1 - C1 108.10 0.31 O1 - S1 - C1 108.90 0.31 O1 - S1 - O2 120.10 0.33 S2 - S1 - C1 105.49 0.26 S2 - S1 - O2 109.88 0.22 S2 - S1 - O1 103.43 0.24 S1 - S2 - C7 101.13 0.24 S1 - C1 - C6 118.72 0.55 S1 - C1 - C2 119.64 0.55 C2 - C1 - C6 121.64 0.63 C1 - C2 - H2 117.19 4.92 C1 - C2 - C3 117.90 0.80 C3 - C2 - H2 124.72 5.37 C2 - C3 - H3 110.30 5.36 C2 - C3 - C4 120.17 1.06 C4 - C3 - H3 129.14 4.58 C3 - C4 - H4 119.05 5.09 C3 - C4 - C5 121.37 1.29 C5 - C4 - H4 119.58 5.48 C4 - C5 - H5 121.76 5.10 C4 - C5 - C6 120.04 1.34 C6 - C5 - H5 118.08 5.36 C1 - C6 - C5 118.87 0.85 C5 - C6 - H6 125.91 4.42 C1 - C6 - H6 115.16 3.61 S2 - C7 - C12 120.19 0.48 S2 - C7 - C8 120.29 0.55 C8 - C7 - C12 119.35 0.67 C7 - C8 - H8 117.50 3.83 C7 - C8 - C9 120.56 0.76 C9 - C8 - H8 121.91 3.64 C8 - C9 - H9 118.76 4.15 C8 - C9 - C10 119.54 0.81 C10 - C9 - H9 121.48 4.25 C9 - C10 - H10 114.55 3.89 C9 - C10 - C11 119.74 0.79 C11 - C10 - H10 125.63 4.04 C10 - C11 - H11 123.01 3.09 C10 - C11 - C12 121.12 0.77 C12 - C11 - H11 115.84 2.97 C7 - C12 - C11 119.65 0.66 C11 - C12 - H12 118.06 3.39 C7 - C12 - H12 122.27 3.54 Number of angles: 43 Torsion angles (degrees) (right-hand rule, Klyne & Prelog.(1960). Experientia,16,521) (e.s.d. following Stanford & Waser, Acta Cryst.(1972).A28,213) Angle e.s.d. O2 -S1 -C1 -C2 -148.64 0.58 O1 -S1 -C1 -C2 -16.61 0.68 S2 -S1 -C1 -C2 93.85 0.58 O2 -S1 -C1 -C6 30.84 0.67 O1 -S1 -C1 -C6 162.88 0.59 S2 -S1 -C1 -C6 -86.66 0.59 O1 -S1 -S2 -C7 -171.08 0.33 O2 -S1 -S2 -C7 -41.69 0.33 C1 -S1 -S2 -C7 74.61 0.32 S1 -S2 -C7 -C8 -105.05 0.60 S1 -S2 -C7 -C12 79.70 0.58 S1 -C1 -C6 -H6 -1.36 4.46 S1 -C1 -C6 -C5 -178.64 0.82 S1 -C1 -C2 -C3 178.85 0.69 S1 -C1 -C2 -H2 3.45 5.88 C2 -C1 -C6 -H6 178.12 4.40 C2 -C1 -C6 -C5 0.83 1.29 C6 -C1 -C2 -H2 -176.02 5.83 C6 -C1 -C2 -C3 -0.62 1.19 C1 -C2 -C3 -C4 0.60 1.53 C1 -C2 -C3 -H3 -172.83 5.21 H2 -C2 -C3 -H3 2.19 8.25 H2 -C2 -C3 -C4 175.62 6.36 C2 -C3 -C4 -C5 -0.80 1.99 C2 -C3 -C4 -H4 179.15 5.92 H3 -C3 -C4 -H4 -8.80 8.84 H3 -C3 -C4 -C5 171.24 6.35 C3 -C4 -C5 -C6 1.01 2.10 C3 -C4 -C5 -H5 -175.16 6.12 H4 -C4 -C5 -H5 4.88 8.69 H4 -C4 -C5 -C6 -178.94 5.97 C4 -C5 -C6 -C1 -1.00 1.73 C4 -C5 -C6 -H6 -177.97 4.97 H5 -C5 -C6 -C1 175.31 5.85 H5 -C5 -C6 -H6 -1.65 7.78 S2 -C7 -C12 -H12 -2.77 4.28 S2 -C7 -C12 -C11 175.43 0.61 S2 -C7 -C8 -C9 -176.70 0.67 S2 -C7 -C8 -H8 5.39 4.37 C8 -C7 -C12 -H12 -178.06 4.21 C8 -C7 -C12 -C11 0.13 1.11 C12 -C7 -C8 -H8 -179.32 4.29 C12 -C7 -C8 -C9 -1.41 1.19 C7 -C8 -C9 -C10 2.10 1.34 C7 -C8 -C9 -H9 176.72 4.89 H8 -C8 -C9 -H9 -5.46 6.71 H8 -C8 -C9 -C10 179.92 4.50 C8 -C9 -C10 -C11 -1.51 1.34 C8 -C9 -C10 -H10 175.50 4.47 H9 -C9 -C10 -H10 1.03 6.77 H9 -C9 -C10 -C11 -175.99 5.04 C9 -C10 -C11 -C12 0.25 1.31 C9 -C10 -C11 -H11 -178.04 3.72 H10 -C10 -C11 -H11 5.30 6.30 H10 -C10 -C11 -C12 -176.40 4.98 C10 -C11 -C12 -C7 0.44 1.24 C10 -C11 -C12 -H12 178.71 4.04 H11 -C11 -C12 -C7 178.85 3.45 H11 -C11 -C12 -H12 -2.88 5.36 Number of torsion angles: 59 Weighted least-squares planes through the starred atoms (Nardelli, Musatti, Domiano & Andreetti Ric.Sci.(1965),15(II-A),807). Equation of the plane: m1*X+m2*Y+m3*Z=d Plane 1 m1 = -0.97375(0.00130) m2 = -0.15205(0.00636) m3 = 0.16938(0.00346) D = -0.36826(0.02832) Atom d s d/s (d/s)**2 S1 * 0.0000 0.0027 0.000 0.000 O1 * 0.0000 0.0057 0.000 0.000 O2 * 0.0000 0.0054 0.000 0.000 ============ Sum((d/s)**2) for starred atoms 0.000 Plane 2 m1 = 0.71939(0.00141) m2 = -0.47279(0.00234) m3 = 0.50887(0.00355) D = 1.15504(0.02765) Atom d s d/s (d/s)**2 S2 * 0.0000 0.0021 0.000 0.000 S1 * 0.0000 0.0024 0.000 0.000 O1 * 0.0000 0.0056 0.000 0.000 ============ Sum((d/s)**2) for starred atoms 0.000 Plane 3 m1 = -0.57876(0.00232) m2 = 0.76515(0.00093) m3 = 0.28211(0.00329) D = 4.62830(0.02267) Atom d s d/s (d/s)**2 S2 * 0.0000 0.0020 0.000 0.000 S1 * 0.0000 0.0022 0.000 0.000 O2 * 0.0000 0.0047 0.000 0.000 ============ Sum((d/s)**2) for starred atoms 0.000 Plane 4 m1 = -0.15202(0.00249) m2 = -0.35379(0.00299) m3 = -0.92289(0.00082) D = -6.79702(0.00919) Atom d s d/s (d/s)**2 S2 * 0.0000 0.0013 0.000 0.000 S1 * 0.0000 0.0022 0.000 0.000 C1 * 0.0000 0.0057 0.000 0.000 ============ Sum((d/s)**2) for starred atoms 0.000 Plane 5 m1 = 0.37713(0.00397) m2 = 0.62724(0.00280) m3 = -0.68143(0.00344) D = -0.71505(0.03019) Atom d s d/s (d/s)**2 C1 * 0.0000 0.0060 0.000 0.000 S1 * 0.0000 0.0021 0.000 0.000 O1 * 0.0000 0.0055 0.000 0.000 ============ Sum((d/s)**2) for starred atoms 0.000 Plane 6 m1 = -0.47757(0.00306) m2 = -0.87432(0.00157) m3 = -0.08655(0.00347) D = -4.71182(0.02126) Atom d s d/s (d/s)**2 C1 * 0.0000 0.0062 0.000 0.000 S1 * 0.0000 0.0020 0.000 0.000 O2 * 0.0000 0.0046 0.000 0.000 ============ Sum((d/s)**2) for starred atoms 0.000 Plane 7 m1 = 0.73522(0.00112) m2 = -0.56040(0.00206) m3 = 0.38132(0.00372) D = 0.06536(0.02843) Atom d s d/s (d/s)**2 S1 * 0.0000 0.0024 0.000 0.000 S2 * 0.0000 0.0022 0.000 0.000 C7 * 0.0000 0.0067 0.000 0.000 ============ Sum((d/s)**2) for starred atoms 0.000 Plane 8 m1 = 0.43603(0.00358) m2 = 0.78500(0.00253) m3 = -0.44006(0.00375) D = 1.39542(0.03270) Atom d s d/s (d/s)**2 C1 * -0.0018 0.0061 -0.289 0.083 C2 * 0.0022 0.0084 0.258 0.067 C3 * -0.0019 0.0112 -0.167 0.028 C4 * 0.0028 0.0134 0.212 0.045 C5 * -0.0049 0.0123 -0.395 0.156 C6 * 0.0034 0.0084 0.401 0.161 S1 -0.0276 0.0021 -13.399 179.527 H2 -0.0590 0.0816 -0.722 0.521 H3 -0.1082 0.0768 -1.409 1.986 H4 0.0118 0.0776 0.152 0.023 H5 -0.0712 0.0840 -0.848 0.719 H6 -0.0313 0.0687 -0.456 0.208 ============ Sum((d/s)**2) for starred atoms 0.540 Chi-squared at 95% for 3 degrees of freedom: 7.81 The group of atoms does not deviate significantly from planarity Plane 9 m1 = 0.80711(0.00221) m2 = 0.35655(0.00353) m3 = -0.47057(0.00298) D = 1.36250(0.03656) Atom d s d/s (d/s)**2 C7 * -0.0015 0.0066 -0.220 0.048 C8 * 0.0089 0.0091 0.978 0.957 C9 * -0.0111 0.0102 -1.082 1.170 C10 * 0.0022 0.0087 0.255 0.065 C11 * 0.0037 0.0091 0.407 0.166 C12 * -0.0026 0.0078 -0.335 0.112 S2 0.1127 0.0022 50.739 2574.453 H8 0.0001 0.0601 0.002 0.000 H9 0.0455 0.0749 0.607 0.368 H10 0.0575 0.0724 0.795 0.632 H11 -0.0149 0.0541 -0.276 0.076 H12 0.0174 0.0607 0.286 0.082 ============ Sum((d/s)**2) for starred atoms 2.519 Chi-squared at 95% for 3 degrees of freedom: 7.81 The group of atoms does not deviate significantly from planarity Weighted least-squares lines through the starred atoms (Schoemaker,Waser,Marsh & Bergman,Acta Cryst.(1959).12,600) m1,m2,m3 are the direction cosines referred to the X,Y,Z orthogonal axes. X0,Y0,Z0 are the coordinates of the centroid of the set of atoms. Equation of the line: (X-X0)/m1=(Y-Y0)/m2=(Z-Z0)/m3 Line 1 m1 = 0.87696(0.00337) X0 = -1.90821(0.02319) m2 = -0.47953(0.00618) Y0 = 5.88519(0.01884) m3 = 0.03159(0.00662) Z0 = 5.44493(0.01888) Atom d s d/s (d/s)**2 S1 * 0.0011 0.0030 0.361 0.130 C1 * 0.0157 0.0084 1.872 3.504 C4 * 0.0069 0.0203 0.339 0.115 H4 * 0.0082 0.1075 0.077 0.006 ============ Sum((d/s)**2) for starred atoms 3.755 Chi-squared at 95% for 2 degrees of freedom: 5.99 The group of atoms does not deviate significantly from linearity Line 2 m1 = 0.11701(0.00813) X0 = 2.38996(0.01910) m2 = 0.65596(0.00453) Y0 = 7.76974(0.01751) m3 = 0.74567(0.00429) Z0 = 7.00002(0.01628) Atom d s d/s (d/s)**2 S2 * 0.0033 0.0030 1.104 1.219 C7 * 0.0720 0.0093 7.726 59.688 C10 * 0.0361 0.0122 2.968 8.807 H10 * 0.0873 0.1009 0.865 0.748 ============ Sum((d/s)**2) for starred atoms 70.463 Chi-squared at 95% for 2 degrees of freedom: 5.99 The group of atoms deviates significantly from linearity Dihedral angles formed by LSQ-planes Plane - plane angle (e.s.d.) 1 2 122.85( 0.31) 1 3 60.33( 0.37) 1 4 87.39( 0.26) 1 5 125.31( 0.35) 1 6 54.32( 0.41) 1 7 124.48( 0.35) 1 8 128.20( 0.38) 1 9 156.90( 0.32) 2 3 129.39( 0.26) 2 4 114.31( 0.25) 2 5 111.84( 0.25) 2 6 88.52( 0.22) 2 7 8.92( 0.27) 2 8 106.34( 0.24) 2 9 80.06( 0.22) 3 4 116.30( 0.23) 3 5 86.02( 0.24) 3 6 114.65( 0.19) 3 7 138.31( 0.26) 3 8 77.05( 0.23) 3 9 109.09( 0.24) 4 5 69.53( 0.25) 4 6 62.50( 0.24) 4 7 105.39( 0.25) 4 8 86.44( 0.26) 4 9 79.31( 0.23) 5 6 132.03( 0.29) 5 7 109.52( 0.26) 5 8 16.92( 0.29) 5 9 31.93( 0.27) 6 7 83.92( 0.19) 6 8 148.92( 0.30) 6 9 131.03( 0.27) 7 8 106.69( 0.23) 7 9 77.63( 0.21) 8 9 32.98( 0.28) Angles formed by LSQ-lines Line - line angle (e.s.d.) 1 2 100.86( 0.52) Angles formed by lines and normals to planes Line - plane angle (e.s.d.) 1 1 140.87( 0.46) 1 2 29.11( 0.40) 1 3 149.95( 0.40) 1 4 89.59( 0.37) 1 5 89.52( 0.40) 1 6 90.13( 0.37) 1 7 22.25( 0.40) 1 8 90.46( 0.41) 1 9 58.54( 0.38) 2 1 95.01( 0.52) 2 2 81.17( 0.41) 2 3 49.87( 0.46) 2 4 159.72( 0.30) 2 5 93.01( 0.34) 2 6 133.94( 0.41) 2 7 89.84( 0.41) 2 8 76.24( 0.33) 2 9 91.29( 0.45) Ring puckering coordinates following Cremer D. & Pople J.A., JACS (1975).97,1354 Ring 1 Atom Internal cartesian coordinates X Y Z C1 0.0000(0.0000) 1.3660(0.0078) 0.0022(0.0056) C2 1.2086(0.0084) 0.7024(0.0101) -0.0015(0.0063) C3 1.1875(0.0097) -0.6997(0.0109) 0.0020(0.0076) C4 0.0088(0.0121) -1.3613(0.0140) -0.0034(0.0083) C5 -1.1939(0.0110) -0.6856(0.0145) 0.0041(0.0074) C6 -1.2110(0.0084) 0.6782(0.0117) -0.0036(0.0059) q2 = 0.0023(0.0095) q3 = 0.0069(0.0100) phi2 = -114.56(241.56) Total puckering amplitude: QT = 0.0073(0.0104) Spherical polar angles: Theta2 = 18.64( 72.36) Asymmetry parameters Following Nardelli M., Acta Cryst.(1983). C39, 1141 C1 C2 C3 C4 C5 C6 DS(C1 )=0.0015(0.0049) DS(C1 -C6 )=0.0041(0.0041) D2(C1 )=0.0032(0.0034) D2(C1 -C6 )=0.0014(0.0041) DS(C2 )=0.0001(0.0050) DS(C2 -C1 )=0.0042(0.0044) D2(C2 )=0.0034(0.0035) D2(C2 -C1 )=0.0008(0.0040) DS(C3 )=0.0014(0.0051) DS(C3 -C2 )=0.0043(0.0041) D2(C3 )=0.0033(0.0033) D2(C3 -C2 )=0.0006(0.0042) Ring 2 Atom Internal cartesian coordinates X Y Z C7 0.0000(0.0000) 1.3826(0.0056) 0.0024(0.0051) C8 1.1887(0.0094) 0.6836(0.0094) -0.0092(0.0066) C9 1.1915(0.0094) -0.6926(0.0093) 0.0097(0.0069) C10 -0.0095(0.0096) -1.3769(0.0070) -0.0033(0.0062) C11 -1.1789(0.0081) -0.6859(0.0092) -0.0035(0.0058) C12 -1.1919(0.0088) 0.6892(0.0091) 0.0039(0.0053) q2 = 0.0132(0.0092) q3 = 0.0071(0.0084) phi2 = 93.32( 34.15) Total puckering amplitude: QT = 0.0150(0.0099) Spherical polar angles: Theta2 = 61.78( 29.20) Asymmetry parameters Following Nardelli M., Acta Cryst.(1983). C39, 1141 C7 C8 C9 C10 C11 C12 DS(C7 )=0.0096(0.0045) DS(C7 -C12 )=0.0060(0.0039) D2(C7 )=0.0033(0.0030) D2(C7 -C12 )=0.0065(0.0036) DS(C8 )=0.0053(0.0043) DS(C8 -C7 )=0.0055(0.0035) D2(C8 )=0.0057(0.0028) D2(C8 -C7 )=0.0070(0.0036) DS(C9 )=0.0043(0.0043) DS(C9 -C8 )=0.0089(0.0039) D2(C9 )=0.0060(0.0030) D2(C9 -C8 )=0.0004(0.0035) Cartesian and spherical polar coordinates for stereographic projections Set 1 Atom S1 is at the origin. The Z axis lies along the vector S1 -S2 Atom cartesian coordinates spherical coordinates X Y Z R Phi Theta S1 0.0000 0.0000 0.0000 0.000 0.00 0.00 S2 0.0000 0.0000 2.0797 2.080 0.00 0.00 O1 0.0000 1.3864 -0.3311 1.425 90.00 103.43 O2 1.0375 -0.8518 -0.4853 1.427 -39.39 109.88 C1 -1.5412 -0.6963 -0.4687 1.755 -155.69 105.49 C7 0.2701 -1.7209 2.4225 2.984 -81.08 35.72 Interatomic contacts greater than 0.00 and less than 3.50 Angstrom, involving atoms of the original set. (Corrections following Busing & Levy, Acta Cryst.(1964).17,142) uncorrected lower upper riding non-correlated distance bound bound motion motion S1 ...C2 2.7156( 72) 2.7157 2.8106 2.7171 2.7631 S1 ...C6 2.7144( 105) 2.7148 2.8167 2.7203 2.7657 S1 ...C7 2.9838( 68) 2.9843 3.0583 2.9897 3.0213 S1 ...H2 2.7619( 671) S1 ...H6 2.7448( 772) S2 ...O1 2.7810( 55) 2.7814 2.8874 2.7872 2.8344 S2 ...O2 2.8951( 55) 2.8951 2.9847 2.8953 2.9399 S2 ...C1 3.0586( 77) 3.0597 3.1338 3.0677 3.0968 S2 ...C8 2.7428( 89) 2.7433 2.8273 2.7490 2.7853 S2 ...C12 2.7414( 62) 2.7428 2.8275 2.7524 2.7852 S2 ...H8 2.7869( 587) S2 ...H12 2.8714( 441) O1 ...O2 2.4719( 69) 2.4721 2.6101 2.4772 2.5411 O1 ...C1 2.5946( 90) 2.5956 2.6814 2.6040 2.6385 O1 ...C2 2.9256( 99) 2.9261 3.0202 2.9325 2.9732 O1 ...H2 2.5102( 786) O2 ...C1 2.5835( 67) 2.5858 2.6804 2.5985 2.6331 O2 ...C6 2.9514( 103) 2.9523 3.0650 2.9614 3.0086 O2 ...C7 3.1304( 85) 3.1327 3.2162 3.1444 3.1745 O2 ...C12 3.1995( 90) 3.2028 3.2924 3.2171 3.2476 O2 ...H6 2.5172( 751) O2 ...H12 2.9872( 589) C1 ...C3 2.3827( 105) 2.3879 2.4998 2.4073 2.4438 C1 ...C4 2.7273( 169) 2.7345 2.8421 2.7562 2.7883 C1 ...C5 2.3736( 171) 2.3803 2.4994 2.4026 2.4398 C1 ...H2 1.9829( 692) C1 ...H3 3.1632( 679) C1 ...H5 3.2433( 980) C1 ...H6 2.0650( 608) C2 ...C4 2.3871( 194) 2.3909 2.5189 2.4094 2.4549 C2 ...C5 2.7746( 168) 2.7776 2.8880 2.7929 2.8328 C2 ...C6 2.4198( 104) 2.4198 2.5268 2.4220 2.4733 C2 ...H3 1.9373( 757) C2 ...H4 3.2009( 915) C2 ...H6 3.3223( 573) C3 ...C5 2.3815( 158) 2.3818 2.5161 2.3882 2.4489 C3 ...C6 2.7662( 110) 2.7673 2.8771 2.7773 2.8222 C3 ...H2 2.0761( 947) C3 ...H4 1.9585( 907) C3 ...H5 3.2620( 809) C4 ...C6 2.3764( 156) 2.3784 2.5161 2.3930 2.4473 C4 ...H2 3.2462( 949) C4 ...H3 2.0738( 713) C4 ...H5 2.0628( 740) C4 ...H6 3.3569( 649) C5 ...H3 3.2686( 648) C5 ...H4 1.9891( 705) C5 ...H6 2.1491( 713) C6 ...H2 3.2340( 762) C6 ...H4 3.1891( 774) C6 ...H5 2.0122( 989) C6 ...H8 3.4704( 652) C7 ...C9 2.3929( 113) 2.3944 2.4890 2.4047 2.4417 C7 ...C10 2.7595( 95) 2.7603 2.8403 2.7675 2.8003 C7 ...C11 2.3808( 84) 2.3814 2.4723 2.3879 2.4268 C7 ...H6 3.1239( 885) C7 ...H8 1.9512( 528) C7 ...H9 3.2601( 731) C7 ...H11 3.2256( 398) C7 ...H12 2.0429( 491) C8 ...C10 2.3836( 92) 2.3836 2.4903 2.3854 2.4370 C8 ...C11 2.7351( 95) 2.7351 2.8333 2.7366 2.7842 C8 ...C12 2.3806( 103) 2.3808 2.4848 2.3851 2.4328 C8 ...H6 3.2504( 815) C8 ...H9 2.0305( 715) C8 ...H10 3.2519( 574) C8 ...H12 3.2452( 527) C9 ...C11 2.3705( 113) 2.3705 2.4820 2.3732 2.4263 C9 ...C12 2.7550( 118) 2.7555 2.8521 2.7617 2.8038 C9 ...H8 1.9900( 473) C9 ...H10 2.0161( 540) C9 ...H11 3.2609( 439) C10 ...C12 2.3805( 115) 2.3808 2.4797 2.3857 2.4302 C10 ...H8 3.1919( 444) C10 ...H9 2.0629( 620) C10 ...H11 2.0495( 465) C10 ...H12 3.2131( 576) C11 ...H9 3.2550( 668) C11 ...H10 2.1055( 714) C11 ...H12 1.9987( 566) C12 ...H8 3.1635( 490) C12 ...H10 3.3162( 697) C12 ...H11 1.9939( 414) H2 ...H3 2.2588(1233) H3 ...H4 2.3860(1147) H4 ...H5 2.3389( 902) H5 ...H6 2.4330(1205) H6 ...H8 3.4083(1007) H8 ...H9 2.3139( 837) H9 ...H10 2.3070( 761) H10 ...H11 2.4680( 850) H11 ...H12 2.2388( 686) Number of contacts: 92 Equivalent positions: x,y,z 1/2+x,-y,1/2+z plus the centrosymmetric ones Maximum translation by 1 unit cell Intermolecular contacts less than 3.50 Angstrom Distance e.s.d. S1 ...H9 x,+y-1,+z 3.4576 0.0673 S2 ...H12 -x+1,-y+1,-z+1 3.4474 0.0582 O1 ...C11 x-1/2,-y+1,+z-1/2 3.2686 0.0092 O1 ...H4 -x,-y+1,-z+1 3.2605 0.0912 O1 ...H9 x,+y-1,+z 3.2435 0.0622 O1 ...H11 x-1/2,-y+1,+z-1/2 2.5113 0.0467 O1 ...H12 -x+1,-y+1,-z+1 2.8654 0.0675 O1 ...H12 x-1/2,-y+1,+z-1/2 3.0582 0.0488 O2 ...C2 x+1/2,-y+1,+z+1/2 3.3174 0.0083 O2 ...C3 x+1/2,-y+1,+z+1/2 3.4947 0.0129 O2 ...H2 x+1/2,-y+1,+z+1/2 2.6847 0.0652 O2 ...H3 -x,-y+1,-z+1 3.4495 0.0927 O2 ...H3 x+1/2,-y+1,+z+1/2 2.8603 0.0837 O2 ...H9 x,+y-1,+z 2.7819 0.0710 C2 ...O2 x-1/2,-y+1,+z-1/2 3.3174 0.0083 C3 ...O2 x-1/2,-y+1,+z-1/2 3.4947 0.0129 C11 ...O1 x+1/2,-y+1,+z+1/2 3.2686 0.0092 H2 ...O2 x-1/2,-y+1,+z-1/2 2.6848 0.0652 H2 ...H12 x-1/2,-y+1,+z-1/2 3.1236 0.1118 H3 ...O2 -x,-y+1,-z+1 3.4495 0.0927 H3 ...O2 x-1/2,-y+1,+z-1/2 2.8603 0.0837 H3 ...H3 -x-1/2,+y,-z+1/2 2.6475 0.0951 H4 ...O1 -x,-y+1,-z+1 3.2605 0.0912 H9 ...S1 x,+y+1,+z 3.4576 0.0673 H9 ...O1 x,+y+1,+z 3.2435 0.0622 H9 ...O2 x,+y+1,+z 2.7819 0.0710 H11 ...O1 x+1/2,-y+1,+z+1/2 2.5113 0.0467 H12 ...S2 -x+1,-y+1,-z+1 3.4474 0.0582 H12 ...O1 -x+1,-y+1,-z+1 2.8654 0.0675 H12 ...O1 x+1/2,-y+1,+z+1/2 3.0582 0.0488 H12 ...H2 x+1/2,-y+1,+z+1/2 3.1236 0.1118 Number of contacts: 31 Possible hydrogen bonds Donor-H Donor...Acceptor H...Acceptor Donor-H......Acceptor C2 -H2 C2 ...O1 ( 0) H2 ...O1 ( 0) C2 -H2 ...O1 ( 0) 0.928(.087) 2.926(.010) 2.510(.079) 107.45( 6.24) 1.080 2.469 104.08 (**) C6 -H6 C6 ...O2 ( 0) H6 ...O2 ( 0) C6 -H6 ...O2 ( 0) 1.044(.058) 2.951(.010) 2.517(.075) 104.16( 4.80) 1.080 2.509 103.35 (**) C12 -H12 C12 ...O2 ( 0) H12 ...O2 ( 0) C12 -H12 ...O2 ( 0) 0.941(.056) 3.199(.009) 2.987(.059) 94.35( 3.78) 1.080 2.980 91.69 (**) C2 -H2 C2 ...O2 ( 1) H2 ...O2 ( 1) C2 -H2 ...O2 ( 1) 0.928(.087) 3.317(.008) 2.685(.065) 126.10( 5.93) 1.080 2.598 123.39 (**) C3 -H3 C3 ...O2 ( 1) H3 ...O2 ( 1) C3 -H3 ...O2 ( 1) 0.936(.062) 3.495(.013) 2.860(.084) 126.11( 5.42) 1.080 2.778 123.71 (**) C9 -H9 C9 ...O2 ( 2) H9 ...O2 ( 2) C9 -H9 ...O2 ( 2) 0.971(.072) 3.734(.010) 2.782(.071) 166.88( 5.68) 1.080 2.676 166.35 (**) C11 -H11 C11 ...O1 ( 3) H11 ...O1 ( 3) C11 -H11 ...O1 ( 3) 0.964(.041) 3.269(.009) 2.511(.047) 135.43( 3.80) 1.080 2.430 133.50 (**) C12 -H12 C12 ...O1 ( 4) H12 ...O1 ( 4) C12 -H12 ...O1 ( 4) 0.941(.056) 3.543(.010) 2.865(.068) 129.80( 4.56) 1.080 2.779 127.60 (**) Number of possible hydrogen bonds 8 (**) Values normalized following G.A.Jeffrey & L.Lewis, Carbohydr.Res. (1978).60,179; R.Taylor, O.Kennard, Acta Cryst.(1983).B39,133. Equivalent positions: ( 0) x,y,z ( 1) x-1/2,-y+1,+z-1/2 ( 2) x,+y+1,+z ( 3) x+1/2,-y+1,+z+1/2 ( 4) -x+1,-y+1,-z+1 Comparison of coordinates of atomic subsets Set 1 Set 1' C1 C7 C2 C8 C3 C9 C4 C10 C5 C11 C6 C12 ============================================================ Set 1 in general position, set 1' in x,+y,+z Co-ordinate differences Atom1 Atom2 x1-x2 y1-y2 z1-z2 C1 C7 -0.27710 -0.18990 -0.06080 C2 C8 -0.33790 -0.35500 -0.15230 C3 C9 -0.49230 -0.38200 -0.24340 C4 C10 -0.58610 -0.25060 -0.24670 C5 C11 -0.52440 -0.08940 -0.15470 C6 C12 -0.37020 -0.05630 -0.06240 ----------------------------------------------------- Average -0.38070 -0.20665 -0.11907 e.s.d. 0.10495 0.11672 0.07074 Co-ordinate half-sums Atom1 Atom2 (x1+x2)/2 (y1+y2)/2 (z1+z2)/2 C1 C7 0.28595 0.72015 0.51330 C2 C8 0.20645 0.78410 0.46185 C3 C9 0.18425 0.87650 0.50670 C4 C10 0.24475 0.90280 0.60045 C5 C11 0.32430 0.83950 0.65135 C6 C12 0.34590 0.74835 0.60870 ----------------------------------------------------- Average 0.26685 0.79124 0.54193 e.s.d. 0.05565 0.06641 0.06163 *************************************************************************** There is no direct indication of a symmetry operation between the two sets Look carefully through the results. *************************************************************************** ============================================================ Set 1 in general position, set 1' in x+1/2,-y,+z+1/2 Co-ordinate differences Atom1 Atom2 x1-x2 y1-y2 z1-z2 C1 C7 -0.77710 1.44030 -0.56080 C2 C8 -0.83790 1.56820 -0.65230 C3 C9 -0.99230 1.75300 -0.74340 C4 C10 -1.08610 1.80560 -0.74670 C5 C11 -1.02440 1.67900 -0.65470 C6 C12 -0.87020 1.49670 -0.56240 ----------------------------------------------------- Average -0.88070 1.58247 -0.61907 e.s.d. 0.10495 0.13282 0.07074 Co-ordinate half-sums Atom1 Atom2 (x1+x2)/2 (y1+y2)/2 (z1+z2)/2 C1 C7 0.53595 -0.09495 0.76330 C2 C8 0.45645 -0.17750 0.71185 C3 C9 0.43425 -0.19100 0.75670 C4 C10 0.49475 -0.12530 0.85045 C5 C11 0.57430 -0.04470 0.90135 C6 C12 0.59590 -0.02815 0.85870 ----------------------------------------------------- Average 0.51685 -0.10333 0.79193 e.s.d. 0.05565 0.05836 0.06163 *************************************************************************** There is no direct indication of a symmetry operation between the two sets Look carefully through the results. *************************************************************************** ============================================================ Set 1 in general position, set 1' in -x,-y,-z Co-ordinate differences Atom1 Atom2 x1-x2 y1-y2 z1-z2 C1 C7 0.57190 1.44030 1.02660 C2 C8 0.41290 1.56820 0.92370 C3 C9 0.36850 1.75300 1.01340 C4 C10 0.48950 1.80560 1.20090 C5 C11 0.64860 1.67900 1.30270 C6 C12 0.69180 1.49670 1.21740 ----------------------------------------------------- Average 0.53369 1.58247 1.08387 e.s.d. 0.11130 0.13282 0.12327 Co-ordinate half-sums Atom1 Atom2 (x1+x2)/2 (y1+y2)/2 (z1+z2)/2 C1 C7 -0.13855 -0.09495 -0.03040 C2 C8 -0.16895 -0.17750 -0.07615 C3 C9 -0.24615 -0.19100 -0.12170 C4 C10 -0.29305 -0.12530 -0.12335 C5 C11 -0.26220 -0.04470 -0.07735 C6 C12 -0.18510 -0.02815 -0.03120 ----------------------------------------------------- Average -0.19035 -0.10333 -0.05953 e.s.d. 0.05247 0.05836 0.03537 *************************************************************************** There is no direct indication of a symmetry operation between the two sets Look carefully through the results. *************************************************************************** ============================================================ Set 1 in general position, set 1' in -x-1/2,+y,-z-1/2 Co-ordinate differences Atom1 Atom2 x1-x2 y1-y2 z1-z2 C1 C7 1.07190 -0.18990 1.52660 C2 C8 0.91290 -0.35500 1.42370 C3 C9 0.86850 -0.38200 1.51340 C4 C10 0.98950 -0.25060 1.70090 C5 C11 1.14860 -0.08940 1.80270 C6 C12 1.19180 -0.05630 1.71740 ----------------------------------------------------- Average 1.03369 -0.20665 1.58387 e.s.d. 0.11130 0.11672 0.12327 Co-ordinate half-sums Atom1 Atom2 (x1+x2)/2 (y1+y2)/2 (z1+z2)/2 C1 C7 -0.38855 0.72015 -0.28040 C2 C8 -0.41895 0.78410 -0.32615 C3 C9 -0.49615 0.87650 -0.37170 C4 C10 -0.54305 0.90280 -0.37335 C5 C11 -0.51220 0.83950 -0.32735 C6 C12 -0.43510 0.74835 -0.28120 ----------------------------------------------------- Average -0.44035 0.79124 -0.30953 e.s.d. 0.05247 0.06641 0.03537 *************************************************************************** There is no direct indication of a symmetry operation between the two sets Look carefully through the results. *************************************************************************** Coordinates of the centroids of the two sets referred to the crystallographic axes and to orthogonal axes SET N. 1 X/a = 0.04960(0.00218) X = -2.0955(0.0302) Y/b = 0.70163(0.00267) Y = 5.9898(0.0228) Z/c = 0.48037(0.00237) Z = 5.4378(0.0269) SET N. 1' X/a = 0.48093(0.00165) X = 2.3930(0.0224) Y/b = 0.92217(0.00233) Y = 7.8725(0.0199) Z/c = 0.63375(0.00161) Z = 7.1741(0.0182) Least-squares rotation matrix & translation vector which bring set 1' into set 1 Rotation matrix Transl.vector 0.82123 1.76661 -0.74900 -0.43952 -0.94730 0.16171 -0.44692 1.07038 0.31518 1.56263 -0.58845 -0.19560 Normalized rotation matrix 1/2 Transl.vector 0.39346 0.84641 -0.35886 -0.21976 -0.89381 0.15258 -0.42169 0.53519 0.18548 0.91960 -0.34630 -0.09780 Corrected fractional coordinates for set 1' (The differences with the previous ones are given in parentheses) Atom X/a Y/b Z/c C7 0.42432(-0.00018) 0.81603( 0.00093) 0.54365(-0.00005) C8 0.37401(-0.00139) 0.96057(-0.00103) 0.53714(-0.00086) C9 0.43229( 0.00189) 1.06780( 0.00030) 0.62952( 0.00112) C10 0.53701(-0.00079) 1.02864( 0.00054) 0.72337(-0.00043) C11 0.58566(-0.00084) 0.88354(-0.00066) 0.72818(-0.00052) C12 0.53230( 0.00130) 0.77642(-0.00008) 0.64065( 0.00075) Averaged fractional coordinates (The differences with the previous values are given in parentheses) Atom X/a Y/b Z/c C7 0.42441(-0.00009) 0.81556( 0.00046) 0.54367(-0.00003) C8 0.37471(-0.00069) 0.96108(-0.00051) 0.53757(-0.00043) C9 0.43135( 0.00095) 1.06765( 0.00015) 0.62896( 0.00056) C10 0.53740(-0.00040) 1.02837( 0.00027) 0.72358(-0.00022) C11 0.58608(-0.00042) 0.88387(-0.00033) 0.72844(-0.00026) C12 0.53165( 0.00065) 0.77646(-0.00004) 0.64028( 0.00038) Least-squares rotation matrix & translation vector which bring set 1 into set 1' Rotation matrix Transl.vector 0.77245 -0.53458 -0.94172 0.76790 -1.06649 -0.40915 2.00094 0.32375 -0.52967 -0.79727 1.24711 0.67996 Normalized rotation matrix 1/2 Transl.vector 0.58072 -0.40190 -0.70798 0.38395 -0.46288 -0.17758 0.86845 0.16188 -0.33692 -0.50714 0.79328 0.33998 Corrected fractional coordinates for set 1 (The differences with the previous ones are given in parentheses) Atom X/a Y/b Z/c C1 0.14805( 0.00065) 0.62544( 0.00024) 0.48332( 0.00042) C2 0.03717(-0.00033) 0.60646(-0.00014) 0.38541(-0.00029) C3 -0.06209(-0.00019) 0.68536(-0.00014) 0.38459(-0.00041) C4 -0.04791( 0.00039) 0.77783( 0.00033) 0.47809( 0.00099) C5 0.06202(-0.00008) 0.79457(-0.00023) 0.57313(-0.00087) C6 0.16035(-0.00045) 0.72014(-0.00006) 0.57765( 0.00015) Averaged fractional coordinates (The differences with the previous values are given in parentheses) Atom X/a Y/b Z/c C1 0.14772( 0.00032) 0.62532( 0.00012) 0.48311( 0.00021) C2 0.03734(-0.00016) 0.60653(-0.00007) 0.38556(-0.00014) C3 -0.06199(-0.00009) 0.68543(-0.00007) 0.38480(-0.00020) C4 -0.04810( 0.00020) 0.77766( 0.00016) 0.47760( 0.00050) C5 0.06206(-0.00004) 0.79469(-0.00011) 0.57357(-0.00043) C6 0.16058(-0.00022) 0.72017(-0.00003) 0.57758( 0.00008) Orthogonal internal coordinates of the two sets Atom X' Y' Z' C1 -0.19415( 0.00682) -0.90610( 0.00598) -1.01997( 0.00566) C7 -0.19227( 0.00682) -0.91403( 0.00683) -1.01937( 0.00566) D -0.0019 0.0079 -0.0006 D/S 0.1947 0.8740 0.0756 C2 -0.78192( 0.00844) 0.32785( 0.00854) -1.09361( 0.00793) C8 -0.76958( 0.00955) 0.33664( 0.00854) -1.08389( 0.00793) D -0.0123 -0.0088 -0.0097 D/S 0.9690 0.7283 0.8670 C3 -0.57986( 0.01143) 1.24329( 0.01110) -0.04792( 0.01132) C9 -0.59708( 0.01091) 1.24071( 0.00854) -0.06056( 0.00906) D 0.0172 0.0026 0.0126 D/S 1.0896 0.1845 0.8717 C4 0.19026( 0.01686) 0.90892( 0.01110) 1.01448( 0.01585) C10 0.19765( 0.00933) 0.90435( 0.00854) 1.01937( 0.00679) D -0.0074 0.0046 -0.0049 D/S 0.3834 0.3261 0.2836 C5 0.76699( 0.01637) -0.32972( 0.01024) 1.06890( 0.01359) C11 0.77451( 0.00955) -0.32412( 0.00854) 1.07484( 0.00793) D -0.0075 -0.0056 -0.0059 D/S 0.3964 0.4196 0.3773 C6 0.59868( 0.01069) -1.24425( 0.00768) 0.07813( 0.00793) C12 0.58677( 0.00819) -1.24356( 0.00768) 0.06962( 0.00679) D 0.0119 -0.0007 0.0085 D/S 0.8845 0.0637 0.8153 Sum((d/s)**2) X' 3.2507 Y' 1.6148 Z' 2.4047 Chi-squared at 95% for 6 degrees of freedom: 12.60 Comparison of the two sets by half-normal probability plots S.C. Abrahams & E.T. Keve (1971). Acta Cryst., A27, 157 Comparison of coordinates ========================= P1 P2 S1 S2 D=P1-P2 D/S i D/S(ord) -0.19415-0.19227 0.00682 0.00682 -0.00188 0.00965 0.19466 1 0.06371 -0.90610-0.91403 0.00598 0.00683 0.00793 0.00908 0.87397 2 0.07562 -1.01997-1.01937 0.00566 0.00566 -0.00061 0.00801 0.07562 3 0.18454 -0.78192-0.76958 0.00844 0.00955 -0.01235 0.01274 0.96903 4 0.19466 0.32785 0.33664 0.00854 0.00854 -0.00879 0.01207 0.72829 5 0.28355 -1.09361-1.08389 0.00793 0.00793 -0.00972 0.01121 0.86696 6 0.32613 -0.57986-0.59708 0.01143 0.01091 0.01722 0.01580 1.08964 7 0.37733 1.24329 1.24071 0.01110 0.00854 0.00258 0.01400 0.18454 8 0.38336 -0.04792-0.06056 0.01132 0.00906 0.01264 0.01450 0.87175 9 0.39640 0.19026 0.19765 0.01686 0.00933 -0.00739 0.01927 0.38336 10 0.41963 0.90892 0.90435 0.01110 0.00854 0.00457 0.01400 0.32613 11 0.72829 1.01448 1.01937 0.01585 0.00679 -0.00489 0.01724 0.28355 12 0.81526 0.76699 0.77451 0.01637 0.00955 -0.00751 0.01895 0.39640 13 0.86696 -0.32972-0.32412 0.01024 0.00854 -0.00560 0.01334 0.41963 14 0.87175 1.06890 1.07484 0.01359 0.00793 -0.00593 0.01573 0.37733 15 0.87397 0.59868 0.58677 0.01069 0.00819 0.01191 0.01347 0.88452 16 0.88452 -1.24425-1.24356 0.00768 0.00768 -0.00069 0.01087 0.06371 17 0.96903 0.07813 0.06962 0.00793 0.00679 0.00851 0.01044 0.81526 18 1.08964 Disagreement index: R12=Sum|P1-P2|/Sum[(|P1|+|P2|)/2] = 0.0000 N. delta/sigma > 2 = 0 N. delta/sigma > 2.5 = 0 N. delta/sigma > 3 = 0 delta/sigma max. = 1.0896 i D/S P(X) X D 1 0.064 0.028 0.035 0.399 2 0.076 0.083 0.104 0.397 3 0.185 0.139 0.175 0.393 4 0.195 0.194 0.246 0.387 5 0.284 0.250 0.318 0.379 6 0.326 0.306 0.392 0.369 7 0.377 0.361 0.469 0.357 8 0.383 0.417 0.548 0.343 9 0.396 0.472 0.631 0.327 10 0.420 0.528 0.719 0.308 11 0.728 0.583 0.812 0.287 12 0.815 0.639 0.913 0.263 13 0.867 0.694 1.025 0.236 14 0.872 0.750 1.150 0.206 15 0.874 0.806 1.298 0.172 16 0.885 0.861 1.480 0.133 17 0.969 0.917 1.732 0.089 18 1.090 0.972 2.201 0.035 1.09 -.........!.........!.........!.........!.........!.........!.........!.........!.........!.........* . . . . . . . . 0.98 - . . * . . . . . . . 0.87 - * * * . . * . . . . * . . . 0.76 - . . . D/s(obs.) . * . . . . . 0.65 - . . . . . . . . . 0.54 - . . . . . . . . . 0.44 - . . * . . * . . * * . . . 0.33 - . . * . . * . . . . . 0.22 - . . . . * * . . . . . 0.11 - . . . . * . .* . . . 0.00 -.........!.........!.........!.........!.........!.........!.........!.........!.........!.........! 0.00 0.44 0.88 1.32 1.76 2.20 D/s(expected) Regression line through (delta/sigma)observed vs (delta/sigma)expected (N=number of points, i=intercept, s=slope, r=determination coefficient) N = 18 i = 0.1252(0.0462) s = 0.5300(0.0470) r = 0.9424 Comparison of the distances less than 4.650 ============================================ P1 P2 S1 S2 D=P1-P2 D/S i D/S(ord) 1.36877 1.37899 0.01050 0.01108 -0.01023 0.01526 0.67008 1 0.02672 2.39030 2.39292 0.01263 0.01095 -0.00262 0.01672 0.15679 2 0.14606 2.75337 2.75953 0.01517 0.00986 -0.00616 0.01809 0.34028 3 0.15679 2.37053 2.38083 0.01511 0.01017 -0.01030 0.01821 0.56545 4 0.24213 1.39598 1.37891 0.01078 0.00954 0.01707 0.01440 1.18587 5 0.34028 1.40440 1.37634 0.01391 0.01209 0.02806 0.01843 1.52261 6 0.43519 2.39308 2.38359 0.01772 0.01107 0.00948 0.02089 0.45395 7 0.45395 2.74007 2.73512 0.01651 0.01204 0.00495 0.02043 0.24213 8 0.56545 2.39802 2.38061 0.01217 0.01162 0.01742 0.01683 1.03502 9 0.67008 1.35410 1.38238 0.01956 0.01245 -0.02828 0.02319 1.21946 10 0.81417 2.35280 2.37046 0.01741 0.01293 -0.01765 0.02168 0.81417 11 0.89838 2.75549 2.75500 0.01392 0.01191 0.00049 0.01832 0.02672 12 1.03502 1.36741 1.35830 0.01691 0.01231 0.00910 0.02092 0.43519 13 1.18587 2.38321 2.38054 0.01445 0.01123 0.00267 0.01831 0.14606 14 1.21946 1.35880 1.37516 0.01455 0.01096 -0.01637 0.01822 0.89838 15 1.52261 Disagreement index: R12=Sum|P1-P2|/Sum[(|P1|+|P2|)/2] = -0.0001 N. delta/sigma > 2 = 0 N. delta/sigma > 2.5 = 0 N. delta/sigma > 3 = 0 delta/sigma max. = 1.5226 i D/S P(X) X D 1 0.027 0.033 0.042 0.399 2 0.146 0.100 0.125 0.396 3 0.157 0.167 0.210 0.390 4 0.242 0.233 0.296 0.382 5 0.340 0.300 0.385 0.370 6 0.435 0.367 0.477 0.356 7 0.454 0.433 0.573 0.339 8 0.565 0.500 0.674 0.318 9 0.670 0.567 0.783 0.294 10 0.814 0.633 0.903 0.265 11 0.898 0.700 1.036 0.233 12 1.035 0.767 1.192 0.196 13 1.186 0.833 1.383 0.153 14 1.219 0.900 1.645 0.103 15 1.523 0.967 2.128 0.041 1.52 -.........!.........!.........!.........!.........!.........!.........!.........!.........!.........* . . . . . . . . 1.37 - . . . . . . . . . 1.22 - * . . . . * . . . . . 1.07 - . . . D/s(obs.) . * . . . . . 0.91 - . . * . . . . . . * . 0.76 - . . . . . . * . . . 0.61 - . . . . * . . . . . 0.46 - . . * * . . . . . . * . 0.30 - . . . . . . * . . . 0.15 - * . . * . . . . . . . 0.00 -*........!.........!.........!.........!.........!.........!.........!.........!.........!.........! 0.00 0.43 0.85 1.28 1.70 2.13 D/s(expected) Regression line through (delta/sigma)observed vs (delta/sigma)expected (N=number of points, i=intercept, s=slope, r=determination coefficient) N = 15 i = 0.0580(0.0294) s = 0.7460(0.0300) r = 0.9896 Set 2 Set 2' C1 C7 C2 C12 C3 C11 C4 C10 C5 C9 C6 C8 ============================================================ Set 2 in general position, set 2' in x,+y,+z Co-ordinate differences Atom1 Atom2 x1-x2 y1-y2 z1-z2 C1 C7 -0.27710 -0.18990 -0.06080 C2 C12 -0.49350 -0.16990 -0.25420 C3 C11 -0.64840 -0.19870 -0.34370 C4 C10 -0.58610 -0.25060 -0.24670 C5 C9 -0.36830 -0.27270 -0.05440 C6 C8 -0.21460 -0.24140 0.03950 ----------------------------------------------------- Average -0.40341 -0.21445 -0.12864 e.s.d. 0.15384 0.03567 0.12908 Co-ordinate half-sums Atom1 Atom2 (x1+x2)/2 (y1+y2)/2 (z1+z2)/2 C1 C7 0.28595 0.72015 0.51330 C2 C12 0.28425 0.69155 0.51280 C3 C11 0.26230 0.78485 0.55685 C4 C10 0.24475 0.90280 0.60045 C5 C9 0.24625 0.93115 0.60120 C6 C8 0.26810 0.84090 0.55775 ----------------------------------------------------- Average 0.27304 0.79311 0.53991 e.s.d. 0.01503 0.08734 0.03271 There is a pseudo TWO-FOLD AXIS at x = 0.2730(0.015) and z = 0.5399(0.033) parallel to y with translation -0.2145(0.036) ============================================================ Set 2 in general position, set 2' in x+1/2,-y,+z+1/2 Co-ordinate differences Atom1 Atom2 x1-x2 y1-y2 z1-z2 C1 C7 -0.77710 1.44030 -0.56080 C2 C12 -0.99350 1.38310 -0.75420 C3 C11 -1.14840 1.56970 -0.84370 C4 C10 -1.08610 1.80560 -0.74670 C5 C9 -0.86830 1.86230 -0.55440 C6 C8 -0.71460 1.68180 -0.46050 ----------------------------------------------------- Average -0.90341 1.58622 -0.62864 e.s.d. 0.15384 0.17469 0.12908 Co-ordinate half-sums Atom1 Atom2 (x1+x2)/2 (y1+y2)/2 (z1+z2)/2 C1 C7 0.53595 -0.09495 0.76330 C2 C12 0.53425 -0.08495 0.76280 C3 C11 0.51230 -0.09935 0.80685 C4 C10 0.49475 -0.12530 0.85045 C5 C9 0.49625 -0.13635 0.85120 C6 C8 0.51810 -0.12070 0.80775 ----------------------------------------------------- Average 0.52304 -0.10723 0.78991 e.s.d. 0.01503 0.01784 0.03271 There is a pseudo CENTER OF SYMMETRY at: x = 0.5230(0.015) y =-0.1072(0.018) z = 0.7899(0.033) ============================================================ Set 2 in general position, set 2' in -x,-y,-z Co-ordinate differences Atom1 Atom2 x1-x2 y1-y2 z1-z2 C1 C7 0.57190 1.44030 1.02660 C2 C12 0.56850 1.38310 1.02560 C3 C11 0.52460 1.56970 1.11370 C4 C10 0.48950 1.80560 1.20090 C5 C9 0.49250 1.86230 1.20240 C6 C8 0.53620 1.68180 1.11550 ----------------------------------------------------- Average 0.54607 1.58622 1.07983 e.s.d. 0.03006 0.17469 0.06542 Co-ordinate half-sums Atom1 Atom2 (x1+x2)/2 (y1+y2)/2 (z1+z2)/2 C1 C7 -0.13855 -0.09495 -0.03040 C2 C12 -0.24675 -0.08495 -0.12710 C3 C11 -0.32420 -0.09935 -0.17185 C4 C10 -0.29305 -0.12530 -0.12335 C5 C9 -0.18415 -0.13635 -0.02720 C6 C8 -0.10730 -0.12070 0.01975 ----------------------------------------------------- Average -0.20171 -0.10723 -0.06432 e.s.d. 0.07692 0.01784 0.06454 *************************************************************************** There is no direct indication of a symmetry operation between the two sets Look carefully through the results. *************************************************************************** ============================================================ Set 2 in general position, set 2' in -x-1/2,+y,-z-1/2 Co-ordinate differences Atom1 Atom2 x1-x2 y1-y2 z1-z2 C1 C7 1.07190 -0.18990 1.52660 C2 C12 1.06850 -0.16990 1.52560 C3 C11 1.02460 -0.19870 1.61370 C4 C10 0.98950 -0.25060 1.70090 C5 C9 0.99250 -0.27270 1.70240 C6 C8 1.03620 -0.24140 1.61550 ----------------------------------------------------- Average 1.04607 -0.21445 1.57983 e.s.d. 0.03006 0.03567 0.06542 Co-ordinate half-sums Atom1 Atom2 (x1+x2)/2 (y1+y2)/2 (z1+z2)/2 C1 C7 -0.38855 0.72015 -0.28040 C2 C12 -0.49675 0.69155 -0.37710 C3 C11 -0.57420 0.78485 -0.42185 C4 C10 -0.54305 0.90280 -0.37335 C5 C9 -0.43415 0.93115 -0.27720 C6 C8 -0.35730 0.84090 -0.23025 ----------------------------------------------------- Average -0.45171 0.79311 -0.31432 e.s.d. 0.07692 0.08734 0.06454 *************************************************************************** There is no direct indication of a symmetry operation between the two sets Look carefully through the results. *************************************************************************** Coordinates of the centroids of the two sets referred to the crystallographic axes and to orthogonal axes SET N. 2 X/a = 0.04960(0.00218) X = -2.0955(0.0302) Y/b = 0.70163(0.00267) Y = 5.9898(0.0228) Z/c = 0.48037(0.00237) Z = 5.4378(0.0269) SET N. 2' X/a = 0.48093(0.00165) X = 2.3930(0.0224) Y/b = 0.92217(0.00233) Y = 7.8725(0.0199) Z/c = 0.63375(0.00161) Z = 7.1741(0.0182) Least-squares rotation matrix & translation vector which bring set 2' into set 2 Rotation matrix Transl.vector 0.57902 1.41129 -2.02065 0.43266 -0.14267 1.22428 0.34336 -0.09469 -0.25916 0.81490 -0.83974 0.47823 Normalized rotation matrix 1/2 Transl.vector 0.22870 0.55743 -0.79811 0.21633 -0.11150 0.95684 0.26836 -0.04735 -0.21624 0.67993 -0.70066 0.23911 Corrected fractional coordinates for set 2' (The differences with the previous ones are given in parentheses) Atom X/a Y/b Z/c C7 0.42457( 0.00007) 0.81551( 0.00041) 0.54399( 0.00029) C12 0.53110( 0.00010) 0.77504(-0.00146) 0.63894(-0.00096) C11 0.58631(-0.00019) 0.88558( 0.00138) 0.72958( 0.00088) C10 0.53792( 0.00012) 1.02789(-0.00021) 0.72369(-0.00011) C9 0.43046( 0.00006) 1.06660(-0.00090) 0.62780(-0.00060) C8 0.37525(-0.00015) 0.96238( 0.00078) 0.53849( 0.00049) Averaged fractional coordinates (The differences with the previous values are given in parentheses) Atom X/a Y/b Z/c C7 0.42454( 0.00004) 0.81530( 0.00020) 0.54385( 0.00015) C12 0.53105( 0.00005) 0.77577(-0.00073) 0.63942(-0.00048) C11 0.58640(-0.00010) 0.88489( 0.00069) 0.72914( 0.00044) C10 0.53786( 0.00006) 1.02800(-0.00010) 0.72374(-0.00006) C9 0.43043( 0.00003) 1.06705(-0.00045) 0.62810(-0.00030) C8 0.37533(-0.00007) 0.96199( 0.00039) 0.53825( 0.00025) Least-squares rotation matrix & translation vector which bring set 2 into set 2' Rotation matrix Transl.vector -0.32310 -0.05521 -0.82548 0.77905 0.85113 0.90827 -0.75965 -0.06386 0.06802 0.63714 -0.82730 0.38441 Normalized rotation matrix 1/2 Transl.vector -0.36378 -0.06216 -0.92941 0.38952 0.58367 0.62286 -0.52094 -0.03193 0.06500 0.60888 -0.79060 0.19220 Corrected fractional coordinates for set 2 (The differences with the previous ones are given in parentheses) Atom X/a Y/b Z/c C1 0.14808( 0.00068) 0.62476(-0.00044) 0.48281(-0.00009) C2 0.03639(-0.00111) 0.60727( 0.00067) 0.38587( 0.00017) C3 -0.06079( 0.00111) 0.68487(-0.00063) 0.38480(-0.00020) C4 -0.04896(-0.00066) 0.77784( 0.00034) 0.47723( 0.00013) C5 0.06232( 0.00022) 0.79469(-0.00011) 0.57395(-0.00005) C6 0.16056(-0.00024) 0.72036( 0.00016) 0.57753( 0.00003) Averaged fractional coordinates (The differences with the previous values are given in parentheses) Atom X/a Y/b Z/c C1 0.14774( 0.00034) 0.62498(-0.00022) 0.48285(-0.00005) C2 0.03694(-0.00056) 0.60693( 0.00033) 0.38579( 0.00009) C3 -0.06135( 0.00055) 0.68519(-0.00031) 0.38490(-0.00010) C4 -0.04863(-0.00033) 0.77767( 0.00017) 0.47717( 0.00007) C5 0.06221( 0.00011) 0.79474(-0.00006) 0.57398(-0.00002) C6 0.16068(-0.00012) 0.72028( 0.00008) 0.57751( 0.00001) Orthogonal internal coordinates of the two sets Atom X' Y' Z' C1 -0.19301( 0.00682) -0.91055( 0.00598) -1.01607( 0.00566) C7 -0.19227( 0.00682) -0.91403( 0.00683) -1.01937( 0.00566) D -0.0007 0.0035 0.0033 D/S 0.0773 0.3835 0.4116 C2 0.59337( 0.00844) -1.25601( 0.00854) 0.05874( 0.00793) C12 0.58677( 0.00819) -1.24356( 0.00768) 0.06962( 0.00679) D 0.0066 -0.0125 -0.0109 D/S 0.5620 1.0846 1.0421 C3 0.76712( 0.01143) -0.31236( 0.01110) 1.08483( 0.01132) C11 0.77451( 0.00955) -0.32412( 0.00854) 1.07484( 0.00793) D -0.0074 0.0118 0.0100 D/S 0.4960 0.8398 0.7234 C4 0.19975( 0.01686) 0.90260( 0.01110) 1.01811( 0.01585) C10 0.19765( 0.00933) 0.90435( 0.00854) 1.01937( 0.00679) D 0.0021 -0.0018 -0.0013 D/S 0.1088 0.1254 0.0731 C5 -0.59301( 0.01637) 1.23299( 0.01024) -0.06731( 0.01359) C9 -0.59707( 0.01091) 1.24071( 0.00854) -0.06056( 0.00906) D 0.0041 -0.0077 -0.0068 D/S 0.2067 0.5790 0.4134 C6 -0.77422( 0.01069) 0.34334( 0.00768) -1.07830( 0.00793) C8 -0.76958( 0.00955) 0.33664( 0.00854) -1.08389( 0.00793) D -0.0046 0.0067 0.0056 D/S 0.3238 0.5831 0.4988 Sum((d/s)**2) X' 0.7272 Y' 2.7196 Z' 2.2038 Chi-squared at 95% for 6 degrees of freedom: 12.60 Comparison of the two sets by half-normal probability plots S.C. Abrahams & E.T. Keve (1971). Acta Cryst., A27, 157 Comparison of coordinates ========================= P1 P2 S1 S2 D=P1-P2 D/S i D/S(ord) -0.19301-0.19227 0.00682 0.00682 -0.00075 0.00965 0.07728 1 0.07309 -0.91055-0.91403 0.00598 0.00683 0.00348 0.00908 0.38348 2 0.07728 -1.01607-1.01937 0.00566 0.00566 0.00330 0.00801 0.41159 3 0.10883 0.59337 0.58677 0.00844 0.00819 0.00661 0.01175 0.56201 4 0.12535 -1.25601-1.24356 0.00854 0.00768 -0.01246 0.01149 1.08455 5 0.20669 0.05874 0.06962 0.00793 0.00679 -0.01088 0.01044 1.04210 6 0.32378 0.76712 0.77451 0.01143 0.00955 -0.00739 0.01489 0.49596 7 0.38348 -0.31236-0.32412 0.01110 0.00854 0.01176 0.01400 0.83984 8 0.41159 1.08483 1.07484 0.01132 0.00793 0.01000 0.01382 0.72344 9 0.41342 0.19975 0.19765 0.01686 0.00933 0.00210 0.01927 0.10883 10 0.49596 0.90260 0.90435 0.01110 0.00854 -0.00176 0.01400 0.12535 11 0.49885 1.01811 1.01937 0.01585 0.00679 -0.00126 0.01724 0.07309 12 0.56201 -0.59301-0.59707 0.01637 0.01091 0.00407 0.01967 0.20669 13 0.57899 1.23299 1.24071 0.01024 0.00854 -0.00772 0.01334 0.57899 14 0.58315 -0.06731-0.06056 0.01359 0.00906 -0.00675 0.01633 0.41342 15 0.72344 -0.77422-0.76958 0.01069 0.00955 -0.00464 0.01433 0.32378 16 0.83984 0.34334 0.33664 0.00768 0.00854 0.00670 0.01149 0.58315 17 1.04210 -1.07830-1.08389 0.00793 0.00793 0.00559 0.01121 0.49885 18 1.08455 Disagreement index: R12=Sum|P1-P2|/Sum[(|P1|+|P2|)/2] = 0.0000 N. delta/sigma > 2 = 0 N. delta/sigma > 2.5 = 0 N. delta/sigma > 3 = 0 delta/sigma max. = 1.0846 i D/S P(X) X D 1 0.073 0.028 0.035 0.399 2 0.077 0.083 0.104 0.397 3 0.109 0.139 0.175 0.393 4 0.125 0.194 0.246 0.387 5 0.207 0.250 0.318 0.379 6 0.324 0.306 0.392 0.369 7 0.383 0.361 0.469 0.357 8 0.412 0.417 0.548 0.343 9 0.413 0.472 0.631 0.327 10 0.496 0.528 0.719 0.308 11 0.499 0.583 0.812 0.287 12 0.562 0.639 0.913 0.263 13 0.579 0.694 1.025 0.236 14 0.583 0.750 1.150 0.206 15 0.723 0.806 1.298 0.172 16 0.840 0.861 1.480 0.133 17 1.042 0.917 1.732 0.089 18 1.085 0.972 2.201 0.035 1.08 -.........!.........!.........!.........!.........!.........!.........!.........!.........!.........* . . . * . . . . . 0.98 - . . . . . . . . . 0.87 - . . . . * . . . . . 0.76 - . . . D/s(obs.) . * . . . . . 0.65 - . . . . . . . . * * . 0.54 - * . . . . . . * * . . . 0.43 - . . * . . * . . * . . . 0.33 - . . * . . . . . . . 0.22 - . . * . . . . . . . 0.11 - * * . . . .* * . . . . . 0.00 -.........!.........!.........!.........!.........!.........!.........!.........!.........!.........! 0.00 0.44 0.88 1.32 1.76 2.20 D/s(expected) Regression line through (delta/sigma)observed vs (delta/sigma)expected (N=number of points, i=intercept, s=slope, r=determination coefficient) N = 18 i = 0.0746(0.0229) s = 0.5046(0.0233) r = 0.9834 Comparison of the distances less than 4.650 ============================================ P1 P2 S1 S2 D=P1-P2 D/S i D/S(ord) 1.37585 1.37891 0.01016 0.00954 -0.00305 0.01394 0.21886 1 0.03812 2.38610 2.38083 0.01276 0.01017 0.00528 0.01632 0.32338 2 0.06962 2.75312 2.75953 0.01518 0.00986 -0.00641 0.01810 0.35426 3 0.21886 2.37800 2.39292 0.01256 0.01095 -0.01492 0.01666 0.89540 4 0.25152 1.38344 1.37899 0.01032 0.01108 0.00445 0.01514 0.29372 5 0.27650 1.40483 1.37516 0.01391 0.01096 0.02966 0.01771 1.67514 6 0.29372 2.39477 2.38054 0.01481 0.01123 0.01424 0.01859 0.76586 7 0.32338 2.76017 2.75500 0.01441 0.01191 0.00517 0.01870 0.27650 8 0.35426 2.39188 2.38061 0.01217 0.01162 0.01128 0.01682 0.67025 9 0.52121 1.34257 1.35830 0.01664 0.01231 -0.01573 0.02070 0.76025 10 0.67025 2.35913 2.37046 0.01746 0.01293 -0.01132 0.02173 0.52121 11 0.76025 2.73584 2.73512 0.01441 0.01204 0.00072 0.01877 0.03812 12 0.76586 1.38411 1.38238 0.02150 0.01245 0.00173 0.02484 0.06962 13 0.89540 2.37830 2.38359 0.01791 0.01107 -0.00530 0.02106 0.25152 14 0.92244 1.35883 1.37634 0.01463 0.01209 -0.01751 0.01898 0.92244 15 1.67514 Disagreement index: R12=Sum|P1-P2|/Sum[(|P1|+|P2|)/2] = -0.0001 N. delta/sigma > 2 = 0 N. delta/sigma > 2.5 = 0 N. delta/sigma > 3 = 0 delta/sigma max. = 1.6751 i D/S P(X) X D 1 0.038 0.033 0.042 0.399 2 0.070 0.100 0.125 0.396 3 0.219 0.167 0.210 0.390 4 0.252 0.233 0.296 0.382 5 0.277 0.300 0.385 0.370 6 0.294 0.367 0.477 0.356 7 0.323 0.433 0.573 0.339 8 0.354 0.500 0.674 0.318 9 0.521 0.567 0.783 0.294 10 0.670 0.633 0.903 0.265 11 0.760 0.700 1.036 0.233 12 0.766 0.767 1.192 0.196 13 0.895 0.833 1.383 0.153 14 0.922 0.900 1.645 0.103 15 1.675 0.967 2.128 0.041 1.68 -.........!.........!.........!.........!.........!.........!.........!.........!.........!.........* . . . . . . . . 1.51 - . . . . . . . . . 1.34 - . . . . . . . . . 1.17 - . . . D/s(obs.) . . . . . . 1.01 - . . . . . . * . . * . 0.84 - . . . . . . * * . . . 0.67 - * . . . . . . . . . 0.50 - * . . . . . . . . . 0.34 - * . . * . . * * . . * . . * . 0.17 - . . . . . . * . .* . 0.00 -.........!.........!.........!.........!.........!.........!.........!.........!.........!.........! 0.00 0.43 0.85 1.28 1.70 2.13 D/s(expected) Regression line through (delta/sigma)observed vs (delta/sigma)expected (N=number of points, i=intercept, s=slope, r=determination coefficient) N = 15 i = -0.0136(0.0428) s = 0.6953(0.0437) r = 0.9752 I hope that you succeeded in using this program and that the results of the calculations are useful to have a better understanding of your structure. Best wishes!