The Spacegroup Manual (Version 1.1.4).pdf

The Spacegroup Manual Version 1 1 4 J K Dewhurst S Sharma and L Nordstr om Contents 1Introduction2 2Usage2 3Table of space group symbols3 4Routine Function Prologues15 4 1Fortran Module Interface modmain Source File modmain f90 15 4 2sgsymb Source File sgsymb f90 15 4 3 fi ndprim Source File fi ndprim f90 15 4 4r3frac Source File r3frac f90 16 4 5r3taxi Source File r3taxi f90 16 4 6r3mv Source File r3mv f90 16 4 7r3cross Source File r3cross f90 17 4 8r3minv Source File r3minv f90 17 4 9r3mm Source File r3mm f90 18 1 Source File main f90 Date Fri Apr 24 10 54 31 CEST 20092 1Introduction Spacegroup is a utility which produces crystal geometry for use with the Elk code from the space group defi ned by its Hermann Mauguin symbol and lattice vector lengths and angles Spacegroup recognises all 230 space groups in various coordinate settings giving a total of 530 possible symbols which are tabulated below The code also provides output compatible with the XCrysDen or V Sim packages for visualisation of the crystal structure 2Usage Only one input fi le spacegroup in is required The structure of this fi le is illustrated by the following example for the high Tcsuperconductor La2CuO4 Bmab hrmg 10 0605232 10 060523224 972729 a b c 90 090 090 0 ab ac bc 111 ncell true primcell 3 nspecies La spsymb 1 nwpos 0 00000 00000 3608 wpos Cu Cu in 1 0 00000 00000 0000 O O in 2 0 25000 25000 0000 0 00000 00000 1820 The input parameters are defi ned as follows hrmg The Hermann Mauguin symbol of a space group listed in the table below case sensitive a b c Lattice vector lengths in Bohr i e atomic units NOT Angstroms ab ac bc Angles in degrees between lattice vectors a and b a and c and b and c respectively ncell The number of unit cells required in each direction primcell Set to true if the primitive unit cell should be found nspecies Number of atomic species spsymb The atomic species symbol Source File main f90 Date Fri Apr 24 10 54 31 CEST 20093 nwpos The number of Wyckoff positional coordinates wpos Wyckoff positional coordinates in fractions of the lattice vectors Note that nwpos and wpos are repeated as many times as there are species After creating the input fi le the spacegroup command is run and the fi les GEOMETRY OUT and crystal xsf should be produced The GEOMETRY OUT fi le can simply be appended to an elk in fi le If XCrysDen is available then use the command xcrysden xsf crystal xsf to render the unit cell 3Table of space group symbols We acknowledge Ralf W Grosse Kunstleve http cci lbl gov sginfo for the fol lowing table which associates space group numbers Sch onfl ies symbols Hermann Mauguin symbols and Hall symbols Source File main f90 Date Fri Apr 24 10 54 31 CEST 20094 Number Schoenfl iesHermann MauguinHall 1C1 1 P1P 1 2C1 i P 1 P 1 3 bC1 2 P2 b P121P 2y 3 cC1 2 P2 c P112P 2 3 aC1 2 P2 a P211P 2x 4 bC2 2 P21 b P1211P 2yb 4 cC2 2 P21 c P1121P 2c 4 aC2 2 P21 a P2111P 2xa 5 b1C3 2 C2 b1 C121C 2y 5 b2C3 2 C2 b2 A121A 2y 5 b3C3 2 C2 b3 I121I 2y 5 c1C3 2 C2 c1 A112A 2 5 c2C3 2 C2 c2 B112 B2B 2 5 c3C3 2 C2 c3 I112I 2 5 a1C3 2 C2 a1 B211B 2x 5 a2C3 2 C2 a2 C211C 2x 5 a3C3 2 C2 a3 I211I 2x 6 bC1 s Pm b P1m1P 2y 6 cC1 s Pm c P11mP 2 6 aC1 s Pm a Pm11P 2x 7 b1C2 s Pc b1 P1c1P 2yc 7 b2C2 s Pc b2 P1n1P 2yac 7 b3C2 s Pc b3 P1a1P 2ya 7 c1C2 s Pc c1 P11aP 2a 7 c2C2 s Pc c2 P11nP 2ab 7 c3C2 s Pc c3 P11b PbP 2b 7 a1C2 s Pc a1 Pb11P 2xb 7 a2C2 s Pc a2 Pn11P 2xbc 7 a3C2 s Pc a3 Pc11P 2xc 8 b1C3 s Cm b1 C1m1C 2y 8 b2C3 s Cm b2 A1m1A 2y 8 b3C3 s Cm b3 I1m1I 2y 8 c1C3 s Cm c1 A11mA 2 8 c2C3 s Cm c2 B11m BmB 2 8 c3C3 s Cm c3 I11mI 2 8 a1C3 s Cm a1 Bm11B 2x 8 a2C3 s Cm a2 Cm11C 2x 8 a3C3 s Cm a3 Im11I 2x 9 b1C4 s Cc b1 C1c1C 2yc 9 b2C4 s Cc b2 A1n1A 2yac 9 b3C4 s Cc b3 I1a1I 2ya 9 b1C4 s Cc b1 A1a1A 2ya 9 b2C4 s Cc b2 C1n1C 2ybc 9 b3C4 s Cc b3 I1c1I 2yc 9 c1C4 s Cc c1 A11aA 2a 9 c2C4 s Cc c2 B11nB 2bc 9 c3C4 s Cc c3 I11bI 2b 9 c1C4 s Cc c1 B11b BbB 2b 9 c2C4 s Cc c2 A11nA 2ac 9 c3C4 s Cc c3 I11aI 2a Source File main f90 Date Fri Apr 24 10 54 31 CEST 20095 Number Schoenfl iesHermann MauguinHall 9 a1C4 s Cc a1 Bb11B 2xb 9 a2C4 s Cc a2 Cn11C 2xbc 9 a3C4 s Cc a3 Ic11I 2xc 9 a1C4 s Cc a1 Cc11C 2xc 9 a2C4 s Cc a2 Bn11B 2xbc 9 a3C4 s Cc a3 Ib11I 2xb 10 bC1 2h P2 m b P12 m1 P 2y 10 cC1 2h P2 m c P112 m P 2 10 aC1 2h P2 m a P2 m11 P 2x 11 bC2 2h P21 m b P121 m1 P 2yb 11 cC2 2h P21 m c P1121 m P 2c 11 aC2 2h P21 m a P21 m11 P 2xa 12 b1C3 2h C2 m b1 C12 m1 C 2y 12 b2C3 2h C2 m b2 A12 m1 A 2y 12 b3C3 2h C2 m b3 I12 m1 I 2y 12 c1C3 2h C2 m c1 A112 m A 2 12 c2C3 2h C2 m c2 B112 m B2 m B 2 12 c3C3 2h C2 m c3 I112 m I 2 12 a1C3 2h C2 m a1 B2 m11 B 2x 12 a2C3 2h C2 m a2 C2 m11 C 2x 12 a3C3 2h C2 m a3 I2 m11 I 2x 13 b1C4 2h P2 c b1 P12 c1 P 2yc 13 b2C4 2h P2 c b2 P12 n1 P 2yac 13 b3C4 2h P2 c b3 P12 a1 P 2ya 13 c1C4 2h P2 c c1 P112 a P 2a 13 c2C4 2h P2 c c2 P112 n P 2ab 13 c3C4 2h P2 c c3 P112 b P2 b P 2b 13 a1C4 2h P2 c a1 P2 b11 P 2xb 13 a2C4 2h P2 c a2 P2 n11 P 2xbc 13 a3C4 2h P2 c a3 P2 c11 P 2xc 14 b1C5 2h P21 c b1 P121 c1 P 2ybc 14 b2C5 2h P21 c b2 P121 n1 P 2yn 14 b3C5 2h P21 c b3 P121 a1 P 2yab 14 c1C5 2h P21 c c1 P1121 a P 2ac 14 c2C5 2h P21 c c2 P1121 n P 2n 14 c3C5 2h P21 c c3 P1121 b P21 b P 2bc 14 a1C5 2h P21 c a1 P21 b11 P 2xab 14 a2C5 2h P21 c a2 P21 n11 P 2xn 14 a3C5 2h P21 c a3 P21 c11 P 2xac 15 b1C6 2h C2 c b1 C12 c1 C 2yc 15 b2C6 2h C2 c b2 A12 n1 A 2yac 15 b3C6 2h C2 c b3 I12 a1 I 2ya 15 b1C6 2h C2 c b1 A12 a1 A 2ya 15 b2C6 2h C2 c b2 C12 n1 C 2ybc 15 b3C6 2h C2 c b3 I12 c1 I 2yc 15 c1C6 2h C2 c c1 A112 a A 2a 15 c2C6 2h C2 c c2 B112 n B 2bc 15 c3C6 2h C2 c c3 I112 b I 2b 15 c1C6 2h C2 c c1 B112 b B2 b B 2b 15 c2C6 2h C2 c c2 A112 n A 2ac Source File main f90 Date Fri Apr 24 10 54 31 CEST 20096 Number Schoenfl iesHermann MauguinHall 15 c3C6 2h C2 c c3 I112 a I 2a 15 a1C6 2h C2 c a1 B2 b11 B 2xb 15 a2C6 2h C2 c a2 C2 n11 C 2xbc 15 a3C6 2h C2 c a3 I2 c11 I 2xc 15 a1C6 2h C2 c a1 C2 c11 C 2xc 15 a2C6 2h C2 c a2 B2 n11 B 2xbc 15 a3C6 2h C2 c a3 I2 b11 I 2xb 16D1 2 P222P 2 2 17D2 2 P2221P 2c 2 17 cabD2 2 P2122P 2a 2a 17 bcaD2 2 P2212P 2 2b 18D3 2 P21212P 2 2ab 18 cabD3 2 P22121P 2bc 2 18 bcaD3 2 P21221P 2ac 2ac 19D4 2 P212121P 2ac 2ab 20D5 2 C2221C 2c 2 20 cabD5 2 A2122A 2a 2a 20 bcaD5 2 B2212B 2 2b 21D6 2 C222C 2 2 21 cabD6 2 A222A 2 2 21 bcaD6 2 B222B 2 2 22D7 2 F222F 2 2 23D8 2 I222I 2 2 24D9 2 I212121I 2b 2c 25C1 2v Pmm2P 2 2 25 cabC1 2v P2mmP 2 2 25 bcaC1 2v Pm2mP 2 2 26C2 2v Pmc21P 2c 2 26 ba cC2 2v Pcm21P 2c 2c 26 cabC2 2v P21maP 2a 2a 26 cbaC2 2v P21amP 2 2a 26 bcaC2 2v Pb21mP 2 2b 26 a cbC2 2v Pm21bP 2b 2 27C3 2v Pcc2P 2 2c 27 cabC3 2v P2aaP 2a 2 27 bcaC3 2v Pb2bP 2b 2b 28C4 2v Pma2P 2 2a 28 ba cC4 2v Pbm2P 2 2b 28 cabC4 2v P2mbP 2b 2 28 cbaC4 2v P2cmP 2c 2 28 bcaC4 2v Pc2mP 2c 2c 28 a cbC4 2v Pm2aP 2a 2a 29C5 2v Pca21P 2c 2ac 29 ba cC5 2v Pbc21P 2c 2b 29 cabC5 2v P21abP 2b 2a 29 cbaC5 2v P21caP 2ac 2a 29 bcaC5 2v Pc21bP 2bc 2c 29 a cbC5 2v Pb21aP 2a 2ab 30C6 2v Pnc2P 2 2bc 30 ba cC6 2v Pcn2P 2 2ac Source File main f90 Date Fri Apr 24 10 54 31 CEST 20097 Number Schoenfl iesHermann MauguinHall 30 cabC6 2v P2naP 2ac 2 30 cbaC6 2v P2anP 2ab 2 30 bcaC6 2v Pb2nP 2ab 2ab 30 a cbC6 2v Pn2bP 2bc 2bc 31C7 2v Pmn21P 2ac 2 31 ba cC7 2v Pnm21P 2bc 2bc 31 cabC7 2v P21mnP 2ab 2ab 31 cbaC7 2v P21nmP 2 2ac 31 bcaC7 2v Pn21mP 2 2bc 31 a cbC7 2v Pm21nP 2ab 2 32C8 2v Pba2P 2 2ab 32 cabC8 2v P2cbP 2bc 2 32 bcaC8 2v Pc2aP 2ac 2ac 33C9 2v Pna21P 2c 2n 33 ba cC9 2v Pbn21P 2c 2ab 33 cabC9 2v P21nbP 2bc 2a 33 cbaC9 2v P21cnP 2n 2a 33 bcaC9 2v Pc21nP 2n 2ac 33 a cbC9 2v Pn21aP 2ac 2n 34C10 2v Pnn2P 2 2n 34 cabC10 2v P2nnP 2n 2 34 bcaC10 2v Pn2nP 2n 2n 35C11 2v Cmm2C 2 2 35 cabC11 2v A2mmA 2 2 35 bcaC11 2v Bm2mB 2 2 36C12 2v Cmc21C 2c 2 36 ba cC12 2v Ccm21C 2c 2c 36 cabC12 2v A21maA 2a 2a 36 cbaC12 2v A21amA 2 2a 36 bcaC12 2v Bb21mB 2 2b 36 a cbC12 2v Bm21bB 2b 2 37C13 2v Ccc2C 2 2c 37 cabC13 2v A2aaA 2a 2 37 bcaC13 2v Bb2bB 2b 2b 38C14 2v Amm2A 2 2 38 ba cC14 2v Bmm2B 2 2 38 cabC14 2v B2mmB 2 2 38 cbaC14 2v C2mmC 2 2 38 bcaC14 2v Cm2mC 2 2 38 a cbC14 2v Am2mA 2 2 39C15 2v Abm2A 2 2c 39 ba cC15 2v Bma2B 2 2c 39 cabC15 2v B2cmB 2c 2 39 cbaC15 2v C2mbC 2b 2 39 bcaC15 2v Cm2aC 2b 2b 39 a cbC15 2v Ac2mA 2c 2c 40C16 2v Ama2A 2 2a 40 ba cC16 2v Bbm2B 2 2b 40 cabC16 2v B2mbB 2b 2 40 cbaC16 2v C2cmC 2c 2 Source File main f90 Date Fri Apr 24 10 54 31 CEST 20098 Number Schoenfl iesHermann MauguinHall 40 bcaC16 2v Cc2mC 2c 2c 40 a cbC16 2v Am2aA 2a 2a 41C17 2v Aba2A 2 2ac 41 ba cC17 2v Bba2B 2 2bc 41 cabC17 2v B2cbB 2bc 2 41 cbaC17 2v C2cbC 2bc 2 41 bcaC17 2v Cc2aC 2bc 2bc 41 a cbC17 2v Ac2aA 2ac 2ac 42C18 2v Fmm2F 2 2 42 cabC18 2v F2mmF 2 2 42 bcaC18 2v Fm2mF 2 2 43C19 2v Fdd2F 2 2d 43 cabC19 2v F2ddF 2d 2 43 bcaC19 2v Fd2dF 2d 2d 44C20 2v Imm2I 2 2 44 cabC20 2v I2mmI 2 2 44 bcaC20 2v Im2mI 2 2 45C21 2v Iba2I 2 2c 45 cabC21 2v I2cbI 2a 2 45 bcaC21 2v Ic2aI 2b 2b 46C22 2v Ima2I 2 2a 46 ba cC22 2v Ibm2I 2 2b 46 cabC22 2v I2mbI 2b 2 46 cbaC22 2v I2cmI 2c 2 46 bcaC22 2v Ic2mI 2c 2c 46 a cbC22 2v Im2aI 2a 2a 47D1 2h Pmmm P 2 2 48 1D2 2h Pnnn 1P 2 2 1n 48 2D2 2h Pnnn 2 P 2ab 2bc 49D3 2h Pccm P 2 2c 49 cabD3 2h Pmaa P 2a 2 49 bcaD3 2h Pbmb P 2b 2b 50 1D4 2h Pban 1P 2 2 1ab 50 2D4 2h Pban 2 P 2ab 2b 50 1cabD4 2h Pncb 1P 2 2 1bc 50 2cabD4 2h Pncb 2 P 2b 2bc 50 1bcaD4 2h Pcna 1P 2 2 1ac 50 2bcaD4 2h Pcna 2 P 2a 2c 51D5 2h Pmma P 2a 2a 51 ba cD5 2h Pmmb P 2b 2 51 cabD5 2h Pbmm P 2 2b 51 cbaD5 2h Pcmm P 2c 2c 51 bcaD5 2h Pmcm P 2c 2 51 a cbD5 2h Pmam P 2 2a 52D6 2h Pnna P 2a 2bc 52 ba cD6 2h Pnnb P 2b 2n 52 cabD6 2h Pbnn P 2n 2b 52 cbaD6 2h Pcnn P 2ab 2c 52 bcaD6 2h Pncn P 2ab 2n 52 a cbD6 2h Pnan P 2n 2bc Source File main f90 Date Fri Apr 24 10 54 31 CEST 20099 Number Schoenfl iesHermann MauguinHall 53D7 2h Pmna P 2ac 2 53 ba cD7 2h Pnmb P 2bc 2bc 53 cabD7 2h Pbmn P 2ab 2ab 53 cbaD7 2h Pcnm P 2 2ac 53 bcaD7 2h Pncm P 2 2bc 53 a cbD7 2h Pman P 2ab 2 54D8 2h Pcca P 2a 2ac 54 ba cD8 2h Pccb P 2b 2c 54 cabD8 2h Pbaa P 2a 2b 54 cbaD8 2h Pcaa P 2ac 2c 54 bcaD8 2h Pbcb P 2bc 2b 54 a cbD8 2h Pbab P 2b 2ab 55D9 2h Pbam P 2 2ab 55 cabD9 2h Pmcb P 2bc 2 55 bcaD9 2h Pcma P 2ac 2ac 56D10 2h Pccn P 2ab 2ac 56 cabD10 2h Pnaa P 2ac 2bc 56 bcaD10 2h Pbnb P 2bc 2ab 57D11 2h Pbcm P 2c 2b 57 ba cD11 2h Pcam P 2c 2ac 57 cabD11 2h Pmca P 2ac 2a 57 cbaD11 2h Pmab P 2b 2a 57 bcaD11 2h Pbma P 2a 2ab 57 a cbD11 2h Pcmb P 2bc 2c 58D12 2h Pnnm P 2 2n 58 cabD12 2h Pmnn P 2n 2 58 bcaD12 2h Pnmn P 2n 2n 59 1D13 2h Pmmn 1P 2 2ab 1ab 59 2D13 2h Pmmn 2 P 2ab 2a 59 1cabD13 2h Pnmm 1P 2bc 2 1bc 59 2cabD13 2h Pnmm 2 P 2c 2bc 59 1bcaD13 2h Pmnm 1P 2ac 2ac 1ac 59 2bcaD13 2h Pmnm 2 P 2c 2a 60D14 2h Pbcn P 2n 2ab 60 ba cD14 2h Pcan P 2n 2c 60 cabD14 2h Pnca P 2a 2n 60 cbaD14 2h Pnab P 2bc 2n 60 bcaD14 2h Pbna P 2ac 2b 60 a cbD14 2h Pcnb P 2b 2ac 61D15 2h Pbca P 2ac 2ab 61 ba cD15 2h Pcab P 2bc 2ac 62D16 2h Pnma P 2ac 2n 62 ba cD16 2h Pmnb P 2bc 2a 62 cabD16 2h Pbnm P 2c 2ab 62 cbaD16 2h Pcmn P 2n 2ac 62 bcaD16 2h Pmcn P 2n 2a 62 a cbD16 2h Pnam P 2c 2n 63D17 2h Cmcm C 2c 2 63 ba cD17 2h Ccmm C 2c 2c 63 cabD17 2h Amma A 2a 2a Source File main f90 Date Fri Apr 24 10 54 31 CEST 200910 Number Schoenfl iesHermann MauguinHall 63 cbaD17 2h Amam A 2 2a 63 bcaD17 2h Bbmm B 2 2b 63 a cbD17 2h Bmmb B 2b 2 64D18 2h Cmca C 2bc 2 64 ba cD18 2h Ccmb C 2bc 2bc 64 cabD18 2h Abma A 2ac 2ac 64 cbaD18 2h Acam A 2 2ac 64 bcaD18 2h Bbcm B 2 2bc 64 a cbD18 2h Bmab B 2bc 2 65D19 2h Cmmm C 2 2 65 cabD19 2h Ammm A 2 2 65 bcaD19 2h Bmmm B 2 2 66D20 2h Cccm C 2 2c 66 cabD20 2h Amaa A 2a 2 66 bcaD20 2h Bbmb B 2b 2b 67D21 2h Cmma C 2b 2 67 ba cD21 2h Cmmb C 2b 2b 67 cabD21 2h Abmm A 2c 2c 67 cbaD21 2h Acmm A 2 2c 67 bcaD21 2h Bmcm B 2 2c 67 a cbD21 2h Bmam B 2c 2 68 1D22 2h Ccca 1C 2 2 1bc 68 2D22 2h Ccca 2 C 2b 2bc 68 1ba cD22 2h Cccb 1C 2 2 1bc 68 2ba cD22 2h Cccb 2 C 2b 2c 68 1cabD22 2h Abaa 1A 2 2 1ac 68 2cabD22 2h Abaa 2 A 2a 2c 68 1 cbaD22 2h Acaa 1A 2 2 1ac 68 2 cbaD22 2h Acaa 2 A 2ac 2c 68 1bcaD22 2h Bbcb 1B 2 2 1bc 68 2bcaD22 2h Bbcb 2 B 2bc 2b 68 1a cbD22 2h Bbab 1B 2 2 1bc 68 2a cbD22 2h Bbab 2 B 2b 2bc 69D23 2h Fmmm F 2 2 70 1D24 2h Fddd 1F 2 2 1d 70 2D24 2h Fddd 2 F 2uv 2vw 71D25 2h Immm I 2 2 72D26 2h Ibam I 2 2c 72 cabD26 2h Imcb I 2a 2 72 bcaD26 2h Icma I 2b 2b 73D27 2h Ibca I 2b 2c 73 ba cD27 2h Icab I 2a 2b 74D28 2h Imma I 2b 2 74 ba cD28 2h Immb I 2a 2a 74 cabD28 2h Ibmm I 2c 2c 74 cbaD28 2h Icmm I 2 2b 74 bcaD28 2h Imcm I 2 2a 74 a cbD28 2h Imam I 2c 2 75C1 4 P4P 4 76C2 4 P41P 4w Source File main f90 Date Fri Apr 24 10 54 31 CEST 200911 Number Schoenfl iesHermann MauguinHall 77C3 4 P42P 4c 78C4 4 P43P 4cw 79C5 4 I4I 4 80C6 4 I41I 4bw 81S1 4 P 4P 4 82S2 4 I 4I 4 83C1 4h P4 m P 4 84C2 4h P42 m P 4c 85 1C3 4h P4 n 1P 4ab 1ab 85 2C3 4h P4 n 2 P 4a 86 1C4 4h P42 n 1P 4n 1n 86 2C4 4h P42 n 2 P 4bc 87C5 4h I4 m I 4 88 1C6 4h I41 a 1I 4bw 1bw 88 2C6 4h I41 a 2 I 4ad 89D1 4 P422P 4 2 90D2 4 P4212P 4ab 2ab 91D3 4 P4122P 4w 2c 92D4 4 P41212P 4abw 2nw 93D5 4 P4222P 4c 2 94D6 4 P42212P 4n 2n 95D7 4 P4322P 4cw 2c 96D8 4 P43212P 4nw 2abw 97D9 4 I422I 4 2 98D10 4 I4122I 4bw 2bw 99C1 4v P4mmP 4 2 100C2 4v P4bmP 4 2ab 101C3 4v P42cmP 4c 2c 102C4 4v P42nmP 4n 2n 103C5 4v P4ccP 4 2c 104C6 4v P4ncP 4 2n 105C7 4v P42mcP 4c 2 106C8 4v P42bcP 4c 2ab 107C9 4v I4mmI 4 2 108C10 4v I4cmI 4 2c 109C11 4v I41mdI 4bw 2 110C12 4v I41cdI 4bw 2c 111D1 2d P 42mP 4 2 112D2 2d P 42cP 4 2c 113D3 2d P 421mP 4 2ab 114D4 2d P 421cP 4 2n 115D5 2d P 4m2P 4 2 116D6 2d P 4c2P 4 2c 117D7 2d P 4b2P 4 2ab 118D8 2d P 4n2P 4 2n 119D9 2d I 4m2I 4 2 120D10 2d I 4c2I 4 2c 121D11 2d I 42mI 4 2 122D12 2d I 42dI 4 2bw 123D1 4h P4 mmm P 4 2 Source File main f90 Date Fri Apr 24 10 54 31 CEST 200912 Number Schoenfl iesHermann MauguinHall 124D2 4h P4 mcc P 4 2c 125 1D3 4h P4 nbm 1P 4 2 1ab 125 2D3 4h P4 nbm 2 P 4a 2b 126 1D4 4h P4 nnc 1P 4 2 1n 126 2D4 4h P4 nnc 2 P 4a 2bc 127D5 4h P4 mbm P 4 2ab 128D6 4h P4 mnc P 4 2n 129 1D7 4h P4 nmm 1P 4ab 2ab 1ab 129 2D7 4h P4 nmm 2 P 4a 2a 130 1D8 4h P4 ncc 1P 4ab 2n 1ab 130 2D8 4h P4 ncc 2 P 4a 2ac 131D9 4h P42 mmc P 4c 2 132D10 4h P42 mcm P 4c 2c 133 1D11 4h P42 nbc 1P 4n 2c 1n 133 2D11 4h P42 nbc 2 P 4ac 2b 134 1D12 4h P42 nnm 1P 4n 2 1n 134 2D12 4h P42 nnm 2 P 4ac 2bc 135D13 4h P42 mbc P 4c 2ab 136D14 4h P42 mnm P 4n 2n 137 1D15 4h P42 nmc 1P 4n 2n 1n 137 2D15 4h P42 nmc 2 P 4ac 2a 138 1D16 4h P42 ncm 1P 4n 2ab 1n 138 2D16 4h P42 ncm 2 P 4ac 2ac 139D17 4h I4 mmm I 4 2 140D18 4h I4 mcm I 4 2c 141 1D19 4h I41 amd 1I 4bw 2bw 1bw 141 2D19 4h I41 amd 2 I 4bd 2 142 1D20 4h I41 acd 1I 4bw 2aw 1bw 142 2D20 4h I41 acd 2 I 4bd 2c 143C1 3 P3P 3 144C2 3 P31P 31 145C3 3 P32P 32 146 HC4 3 R3 HR 3 146 RC4 3 R3 RP 3 147C1 3i P 3 P 3 148 HC2 3i R 3 H R 3 148 RC2 3i R 3 R P 3 149D1 3 P312P 3 2 150D2 3 P321P 3 200 151D3 3 P3112P 31 2c 0 0 1 152D4 3 P3121P 31 200 153D5 3 P3212P 32 2c 0 0 1 154D6 3 P3221P 32 200 155 HD7 3 R32 HR 3 200 155 RD7 3 R32 RP 3 2 156C1 3v P3m1P 3 200 157C2 3v P31mP 3 2 158C3 3v P3c1P 3 200c 159C4 3v P31cP 3 2c 160 HC5 3v R3m HR 3 200 Source File main f90 Date Fri Apr 24 10 54 31 CEST 200913 Number Schoenfl iesHermann MauguinHall 160 RC5 3v R3m RP 3 2 161 HC6 3v R3c HR 3 200c 161 RC6 3v R3c RP 3 2n 162D1 3d P 31m P 3 2 163D2 3d P 31c P 3 2c 164D3 3d P 3m1 P 3 200 165D4 3d P 3c1 P 3 200c 166 HD5 3d R 3m H R 3 200 166 RD5 3d R 3m R P 3 2 167 HD6 3d R 3c H R 3 200c 167 RD6 3d R 3c R P 3 2n 168C1 6 P6P 6 169C2 6 P61P 61 170C3 6 P65P 65 171C4 6 P62P 62 172C5 6 P64P 64 173C6 6 P63P 6c 174C1 3h P 6P 6 175C1 6h P6 m P 6 176C2 6h P63 m P 6c 177D1 6 P622P 6 2 178D2 6 P6122P 61 2 0 0 1 179D3 6 P6522P 65 2 0 0 1 180D4 6 P6222P 62 2c 0 0 1 181D5 6 P6422P 64 2c 0 0 1 182D6 6 P6322P 6c 2c 183C1 6v P6mmP 6 2 184C2 6v P6ccP 6 2c 185C3 6v P63cmP 6c 2 186C4 6v P63mcP 6c 2c 187D1 3h P 6m2P 6 2 188D2 3h P 6c2P 6c 2 189D3 3h P 62mP 6 2 190D4 3h P 62cP 6c 2c 191D1 6h P6 mmm P 6 2 192D2 6h P6 mcc P 6 2c 193D3 6h P63 mcm P 6c 2 194D4 6h P63 mmc P 6c 2c 195T1P23P 2 2 3 196T2F23F 2 2 3 197T3I23I 2 2 3 198T4P213P 2ac 2ab 3 199T5I213I 2b 2c 3 200T1 h Pm 3 P 2 2 3 201 1T2 h Pn 3 1P 2 2 3 1n 201 2T2 h Pn 3 2 P 2ab 2bc 3 202T3 h Fm 3 F 2 2 3 203 1T4 h Fd 3 1F 2 2 3 1d 203 2T4 h Fd 3 2 F 2uv 2vw 3 204T5 h Im 3 I 2 2 3 Source File main f90 Date Fri Apr 24 10 54 31 CEST 200914 Number Schoenfl iesHermann MauguinHall 205T6 h Pa 3 P 2ac 2ab 3 206T7 h Ia 3 I 2b 2c 3 207O1P432P 4 2 3 208O2P4232P 4n 2 3 209O3F432F 4 2 3 210O4F4132F 4d 2 3 211O5I432I 4 2 3 212O6P4332P 4acd 2ab 3 213O7P4132P 4bd 2ab 3 214O8I4132I 4bd 2c 3 215T1 d P 43mP 4 2 3 216T2 d F 43mF 4 2 3 217T3 d I 43mI 4 2 3 218T4 d P 43nP 4n 2 3 219T5 d F 43cF 4c 2 3 220T6 d I 43dI 4bd 2c 3 221O1 h Pm 3m P 4 2 3 222 1O2 h Pn 3n 1P 4 2 3 1n 222 2O2 h Pn 3n 2 P 4a 2bc 3 223O3 h Pm 3n P 4n 2 3 224 1O4 h Pn 3m 1P 4n 2 3 1n 224 2O4 h Pn 3m 2 P 4bc 2bc 3 225O5 h Fm 3m F 4 2 3 226O6 h Fm 3c F 4c 2 3 227 1O7 h Fd 3m 1F 4d 2 3 1d 227 2O7 h Fd 3m 2 F 4vw 2vw 3 228 1O8 h Fd 3c 1F 4d 2 3 1cd 228 2O8 h Fd 3c 2 F 4cvw 2vw 3 229O9 h Im 3m I 4 2 3 230O10 h Ia 3d I 4bd 2c 3 Source File modmain f90 Date Fri Apr 24 10 54 31 CEST 200915 4Routine Function Prologues 4 1Fortran Module Interface modmain Source File modmain f90 Contains all the global variables required by the spacegroup code REVISION HISTORY Created October 2006 JKD 4 2sgsymb Source File sgsymb f90 INTERFACE subroutine sgsymb hrmg num schn hall INPUT OUTPUT PARAMETERS hrmg Hermann Mauguin symbol in character 20 num space group number out character 20 schn Schoenflies symbol out character 20 hall Hall symbol out character 20 DESCRIPTION Returns the space group number Schoenfl ies and Hall symbols given the Hermann Mauguin symbol The routine is case sensitive With acknowledgements to Ralf W Grosse Kunstleve and the tables available at http cci lbl gov sginfo REVISION HISTORY Created October 2006 JKD 4 3 fi ndprim Source File fi ndprim f90 INTERFACE subroutine findprim USES use modmain DESCRIPTION This routine fi nds the smallest primitive cell which produces the same crystal structure as the conventional cell This is done by searching through all the vectors which connect atomic positions and fi nding those which leave the crystal structure invariant Of these the three shortest which produce a non zero unit cell volume are chosen