59 284-292 2017 SHELXL 入門講座 (5) SHELXT による構造および空間群の決定 Shigeru OHBA: Determination of the Structure and Space Group by SHELXT SHELXT is a revolutionary program which solves the structure assuming space group P1, and determines the space group type based on the assigned Laue group and calculated P1 phase angles. The background and procedures of the computation will be summarized, and important points to check the results will be noted. 1. はじめに SHELXT 2014 3200. 1 SHELXT P1 図 1 P2 1/c P2 12 12 1 2 3 SHELXT G. M. Sheldrick 1 SHELX. 2 2. 位相問題 2.1 構造を解く方法 ( ) F ( k ) = F ( k ) exp iϕ( k ) 1 X I ( k ) = F ( k ) 2 K 2 1 ρ ( r ) = F ( k ) exp( 2πik r ) k 3 V hkl k xyz r3 1 ρ( xyz)= F( hkl) exp 2πi( hx+ky+lz) hkl { } 4 V 1 F k X F k ϕ k 3 (1) パターソン関数 P( nvw)= 1 F( hkl) 2 exp 2πi( hu+kv+lw) 5 V hkl { } 図 1. Difference when the space group is determined. 284 59 6 2017
SHELXT SHELXT (2) 直接法 F ϕ 3 ( ) ( ) + ( ) 6 ϕ h ϕ k ϕ h k exp{ iϕ( h) } exp iϕ( k ) exp iϕ h k { } { ( )} 7 h k 311 101 h k 210 3 6 F exp{ iϕ( h) } = ±1 8 Fs h 7 s( h) s( k ) s( h k ) 9 F h E h E h 2 1 2 K SHELXTsinθ/λ 2.2 古典的な直接法と双対空間法 1 dual-space methods SHELXT 100 図 2. 4 SHELXT 1 v 図 35 F 2 E 3 F v/2 v/2 E ( h) 2 = o F ( h) ε ( h) F 2 2 o ε θ 10 ε h 1 h0l 2 4. 3 10 h sinθ/λ 59 6 2017 図 2. Dual-space methods. 285
図 4 P1. Standard origin of P1. P1 図 3. Patterson superposition minimum function. Ps u. 5 { ( ) ( )} Ps( u) =min P u + v 2, P u v 2 11 N N 2 N 2N 2. 5 2 2 P1 2.3 P1で構造を解く背景 P1. 6 P1 C C1C P1 P1 P1 P1 図 4 P1. 6,7 7 P1 6 SHELXT 2.4 分解能の改善 2 X d min d min = 1 ( 2sin θ λ ) 12 max. 8 free lunchshelxt d min 0.8 Å 2θ max Mo Kα 52.7. 8 286 59 6 2017
SHELXT 3. 構造の対称性 P1 3.1 実空間での対称性 r Rr t ρ( Rr + t ) = ρ( r ) 13 R t. 9 PLATON/ADDSYM 3.2 逆空間での対称性 SHELXT Rr t h Rh. 9 F ( Rh) = F ( h) exp ( 2πih t) 14 ϕ ( Rh) = ϕ( h) 2πih t 15 Δx x ϕ h x = x x 16 ϕ ( Rh)= ϕ ( h) 2πh t 2π ( Rh h) x 17 Δx F h F h F ( h) = F ( h) exp( 2πih x) 18 F ( Rh) = F ( Rh) exp( 2πiRh x) 19 1517 SHELXT Δx 59 6 2017 17 α 3.3 空間群選出の指標 17 h Rh η { } η = ϕ ( Rh) ϕ ( h)+ 2π h t + ( Rh h) x 20 2π 20 modulo 2π η π SHELXT α R t F 2 η 2 α 1 α mean square phase error 3.4 可能な空間群の数 2/mP b 14 表 1 P mmm 120 表 2. 9 56 222 56 8 表 1 Pb. Possible space groups for monoclinic P with unique axis b. m 2 2/m Pm, Pa, Pc, Pn P2, P2/m, P2 1/m, P2/a, P2 1/a, P21 P2/c, P2 1/c, P2/n, P2 1/n 表 2 P. Number of possible space groups for orthorhombic P considering different settings. 222 mm2, m2m, 2mm mmm 8 48 64 56 120 287
4.SHELXTの計算手順 (1) 計算パラメータの設定 SHELXT 図 5 SHELXins hkl SHELXT.ins SHELXT shelxt -m1000 -c -m -c lxt Bruker APEX 3 10 Find Structure SHELXT Intrinsic Phasing Chirality Any Chiral NoncentrosymmetricChiral -c Non-centrosymmetric -n (2) データの読み込み SHELXT.ins LATT SYMM SFAC. 11 UNIT HKLF.hkl ins (3) 双対空間位相改善ループ P1. 4 SHELXT G ( h) = E ( h) q F ( h) 1 q 21 o o o E o h q 0.5 mg o h m 1 G c h ϕ c h m 3 G c h ϕ c h G o h 1 ρ( r)= ( h) ( h) ϕ h h{ 3G } { ( o 2Gc exp i c ) 2πh r} 22 V M rρ r 図 6 3 1 (4) 最善の位相セットの選択 図 5. Input and output files. 図 6 M r. Correction of the electron density with the mask. 288 59 6 2017
SHELXT 表 3. Example of phase determination for organoselenium compound. Sheldrick, 1 Fig.2 Try N iter CC R weak CHEM CFOM 1 100 95.3 0.118 0.974 0.835 2 100 85.0 0.146 0.460 0.704 3 100 82.7 0.126 0.567 0.701 4 100 82.6 0.109 0.689 0.717 表 4. Example of space group determination for organoselenium compound. Sheldrick, 1 Fig.3 R1 Rweak α Flack File Formula 0.21 0.10 0.12 P2 1/m _a C28 O4 Se 0.10 0.05 0.04 P2 1 0.01 _b C22 O2 Se 0.19 0.10 0.14 Pm 0.28 _c C34 O9 Se2 CC G o h G c h R weak E o h 2 10 E c h 2 CHEM 1.1 1.8 Å 95 135 CFOM combined figure of merit CFOM 0.01CC XR weak X 1 CHEM CFOM CFOM 表 3 12. 1 4 R weak CC CFOM CHEM P1 (5) 原点シフトΔxと空間群の候補の選出 SHELXT P1 α α 0 α 0 0.3 21Sc SHELXT 表 3 P α 0 0.175 14 表 1 α0.3 59 6 2017 表 4 (6) 実空間精密化ループと電子密度のスケーリング 10 0.7 Å a d a C C 1.25 1.65 Å 6 b1.65 1.8 Å c d (7) 電子密度ピークへの元素の割り振り SFAC Cl Br I (8) 等方性の精密化 R1 R F 13 0.5 (9) 空間群の判定 α 0 SFAC α 0 P1 P1 α R1 289
表 4 3 P2 1/m P2 1 Pm R1 P2 1 _a _b _c res hkl 図 5 5.lxtファイルの見方 SHELXT lxt lxt Command line parameters.ins.hkl -t3 thread 3 CFOM P1 α 0 lxt Space group determination 1 Formula Cl BrI 6.SHELXTでの計算例 6.1 三斜晶系 P1 C 16H 20O 2 Z 2 SHELXT P1 α 0 0.057 0.3 SHELXT inssfac Br SHELXT α 0 P1 P1 Br R1 0.178 0.182 P1 R1 1 P1 R1 6.2 単斜晶系 P2 1 I C 12H 13FN 2O 3S P Z 4 SHELXT P1 α 0 0.697 0.3 6 表 1 α 0.3 P2 1 表 5 Formula 2 2 N O C 6.3 直方晶系 P2 12 12 1 C 13H 15ClN 2O 3 C 13H 15BrN 2O 3 P SHELXT P1 α 0 0.701 0.3200.3 56α 0.3 P2 12 12 1 表 5 21Sc SFAC α 0 表 5. Space group determination of chiral organic compounds. R1 Rweak α Flack Formula 0.12 0.030 0.002 P2 1 0.13 C27 F2 N2 O5 S2 0.10 0.026 0.001 P2 12 12 1 0.03 C13 N3 O2 Cl 0.07 0.022 0.004 P2 12 12 1 0.04 C14 N O3 Br 290 59 6 2017
SHELXT 表 6. Space group determination of an organic racemate. R1 Rweak α Flack Formula 0.237 0.049 0.069 as input Pbam C16 O3 Br 0.156 0.031 0.040 as input Pba2 0.15 C11 O Br 0.220 0.044 0.060 c, a, b Pmc2 1 0.49 C27 O9 Br2 0.224 0.045 0.066 c, b, a Pmc2 1 0.49 C16 O3 Br 0.242 0.047 0.079 as input P2 12 12 0.49 C12 O5 Br 表 7 表 8. Example of space group determination where caution is needed. Sheldrick, 1 Fig.6 R1 Rweak α Flack Formula 0.073 0.005 0.018 P6 3/mmc Ca4 O17 S2 0.074 0.004 0.016 P6 3mc No Fp Ca O17 S5 0.039 0.004 0.017 P6m2 No Fp Ca3 Mn O17 S2 0.069 0.005 0.017 P62c 0.49 Ca4 O17 S2 0.069 0.004 0.019 P6 322 0.42 Ca4 O17 S2 表 7 Pmc2 1. Non-standard setting of Pmc2 1 and transformation of the axes to the standard setting. P2 1ma c, a, b b, c, a P2 1am c, b, a c, b, a Pm2 1b a, c, b a, c, b Pb2 1m b, c, a c, a, b Pcm2 1 b, a, c b, a, c SHELXT lxt Orientation SHELXT α 0 0.3 6.4 直方晶系 Pba2 C 22H 28Br 2O 2 P Z 2 SHELXT P1 α 0 0.118 0.3 Br 64 56 5 表 6 R1 Pba2 表 6Pmc2 1 No.26 Pmc2 1 a b c 表 7 SHELXT _c.res _d.res _c.hkl _d.hkl 6.5 六方晶系 P6 3/mmc SHELXT Sheldrick 1 59 6 2017 6/mmm SHELXS97 P62c. 14 checkcifb SHELXT 21Sc MnSHELXT 4 12 5 表 8 R1 P6m2 P6 3/mmc P62c SHELXT P6m2 表 8 P6m2P6 3/mmc P6m2 Ca Mn R1 SHELXT 97. 1 100Sheldrick 7. プログラムの限界 SHELXT X SHELXT. 9 CIF checkcif 291
謝辞 SHELXT 文献 1 G. M. Sheldrick: Acta Cryst. A71, 3 2015 2 http://shelx.uni-goettingen.de/ 3 5 11, p.111, 2006 4 G. M. Sheldrick, et al.: International Tables for Crystallography, Vol.F, 2nd ed., pp.413-432, Chichester, Wiley 2012 5 G. M. Sheldrick: Methods Enzymol. 276, 628 1997 6 M. C. Burla, B. Carrozzini, G. L. Cascarano, C. Giacovazzo and G. Polidori: J. Appl. Cryst. 33, 307 2000 7 L. Palatinus and A. van der Lee: J. Appl. Cryst. 41, 975 2008 8 R. Caliandro, B. Carrozzini, G. L. Cascarano, L. De Caro, C. Giacovazzo and D. Siliqi: Acta Cryst. D61, 556 2005 9, X, 2014 10 Bruker AXS Inc.: APEX 3 ver. 2016.1-0 2016 11, SHELXL, 2016 12 W. Clegg, K. Harms, G. M. Sheldrick, G. von Kiedrowski and L. -F. Tietze: Acta Cryst. B36, 3159 1980 13 S. Parsons, H. D. Flack and T. Wagner: Acta Cryst. B69, 249 2013 14 M. C. Barkley, H. Yang, S. H. Evans, R. T. Downs and M. J. Origlieri: Acta Cryst. E67, i47 2011 プロフィール Shigeru OHBA Research and Education Center for Natural Sciences, Keio University 223-8521 4-1-1 4-1-1 Hiyoshi, Kohoku-ku, Yokohama, Kanagawa 223-8521, Japan e-mail: ohba@a3.keio.jp 1981 292 59 6 2017