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 h k F exp{ iϕ( h) } =
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1 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 SHELXT P1 図 1 P2 1/c P SHELXT G. M. Sheldrick 1 SHELX 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
2 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 h k F exp{ iϕ( h) } = ±1 8 Fs h 7 s( h) s( k ) s( h k ) 9 F h E h E h 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 h sinθ/λ 図 2. Dual-space methods. 285
3 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 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
4 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) SHELXT Δx 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 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
5 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 (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
6 SHELXT 表 3. Example of phase determination for organoselenium compound. Sheldrick, 1 Fig.2 Try N iter CC R weak CHEM CFOM 表 4. Example of space group determination for organoselenium compound. Sheldrick, 1 Fig.3 R1 Rweak α Flack File Formula P2 1/m _a C28 O4 Se P _b C22 O2 Se 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 Å CFOM combined figure of merit CFOM 0.01CC XR weak X 1 CHEM CFOM CFOM 表 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 Sc SHELXT 表 3 P α 表 1 α 表 4 (6) 実空間精密化ループと電子密度のスケーリング Å a d a C C Å 6 b 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 (9) 空間群の判定 α 0 SFAC α 0 P1 P1 α R1 289
7 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 SHELXT inssfac Br SHELXT α 0 P1 P1 Br R 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 表 1 α 0.3 P2 1 表 5 Formula 2 2 N O C 6.3 直方晶系 P C 13H 15ClN 2O 3 C 13H 15BrN 2O 3 P SHELXT P1 α α 0.3 P 表 5 21Sc SFAC α 0 表 5. Space group determination of chiral organic compounds. R1 Rweak α Flack Formula P C27 F2 N2 O5 S P C13 N3 O2 Cl P C14 N O3 Br
8 SHELXT 表 6. Space group determination of an organic racemate. R1 Rweak α Flack Formula as input Pbam C16 O3 Br as input Pba C11 O Br c, a, b Pmc C27 O9 Br c, b, a Pmc C16 O3 Br as input P 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 P6 3/mmc Ca4 O17 S P6 3mc No Fp Ca O17 S P6m2 No Fp Ca3 Mn O17 S P62c 0.49 Ca4 O17 S P 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 直方晶系 Pba2 C 22H 28Br 2O 2 P Z 2 SHELXT P1 α Br 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 /mmm SHELXS97 P62c. 14 checkcifb SHELXT 21Sc MnSHELXT 表 8 R1 P6m2 P6 3/mmc P62c SHELXT P6m2 表 8 P6m2P6 3/mmc P6m2 Ca Mn R1 SHELXT Sheldrick 7. プログラムの限界 SHELXT X SHELXT. 9 CIF checkcif 291
9 謝辞 SHELXT 文献 1 G. M. Sheldrick: Acta Cryst. A71, , p.111, G. M. Sheldrick, et al.: International Tables for Crystallography, Vol.F, 2nd ed., pp , Chichester, Wiley G. M. Sheldrick: Methods Enzymol. 276, M. C. Burla, B. Carrozzini, G. L. Cascarano, C. Giacovazzo and G. Polidori: J. Appl. Cryst. 33, L. Palatinus and A. van der Lee: J. Appl. Cryst. 41, R. Caliandro, B. Carrozzini, G. L. Cascarano, L. De Caro, C. Giacovazzo and D. Siliqi: Acta Cryst. D61, , X, Bruker AXS Inc.: APEX 3 ver , SHELXL, W. Clegg, K. Harms, G. M. Sheldrick, G. von Kiedrowski and L. -F. Tietze: Acta Cryst. B36, S. Parsons, H. D. Flack and T. Wagner: Acta Cryst. B69, M. C. Barkley, H. Yang, S. H. Evans, R. T. Downs and M. J. Origlieri: Acta Cryst. E67, i プロフィール Shigeru OHBA Research and Education Center for Natural Sciences, Keio University Hiyoshi, Kohoku-ku, Yokohama, Kanagawa , Japan ohba@a3.keio.jp
2004/12/16 texsan/shelx97/kenx Windows XWindows
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