The Spacegroup Manual
Version 1.1.2
J. K. Dewhurst, S. Sharma and C. Ambrosch-Draxl
Contents
1 Introduction
2
2 Usage
2
3 Table of space group symbols
3
4 Routine/Function Prologues
4.1 Fortran: Module Interface modmain (Source
4.2 sgsymb (Source File: sgsymb.f90) . . . . . .
4.3 findprim (Source File: findprim.f90) . . . .
4.4 r3frac (Source File: r3frac.f90) . . . . . . .
4.5 r3taxi (Source File: r3taxi.f90) . . . . . . .
4.6 r3mv (Source File: r3mv.f90) . . . . . . . .
4.7 r3cross (Source File: r3cross.f90) . . . . . .
4.8 r3minv (Source File: r3minv.f90) . . . . . .
4.9 r3mm (Source File: r3mm.f90) . . . . . . .
4.10 r3dot (Source File: r3dot.f90) . . . . . . . .
1
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modmain.f90)
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16
16
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17
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18
18
Source File: main.f90, Date: Mon Dec 15 14:37:08 CET 2008
1
2
Introduction
Spacegroup is a utility which produces crystal geometry for use with the EXCITING code,
from the space group defined 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.
2
Usage
Only one input file, spacegroup.in, is required. The structure of this file is illustrated by
the following example for the high Tc superconductor La2 CuO4 :
’Bmab’
10.0605232 10.0605232 24.972729
90.0
90.0
90.0
1 1 1
.true.
3
’La’ ’La.in’
1
0.0000
0.0000
0.3608
’Cu’ ’Cu.in’
1
0.0000
0.0000
0.0000
’O’ ’O.in’
2
0.2500
0.2500
0.0000
0.0000
0.0000
0.1820
:
:
:
:
:
:
:
:
:
hrmg
a, b, c
ab, ac, bc
ncell
primcell
nspecies
spsymb, spfname
nwpos
wpos
The input parameters are defined 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 Ångstroms)
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, spfname
The species symbol and the species filename required by EXCITING
Source File: main.f90, Date: Mon Dec 15 14:37:08 CET 2008
3
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 file, the spacegroup command is run and the files GEOMETRY.OUT and crystal.xsf
should be produced. The GEOMETRY.OUT file can simply be appended to an exciting.in
file. If XCrysDen is available, then use the command
xcrysden --xsf crystal.xsf
to render the unit cell.
3
Table of space group symbols
We acknowledge Ralf W. Grosse-Kunstleve (http://cci.lbl.gov/sginfo/) for the following table which associates space group numbers, Schönflies symbols, Hermann-Mauguin
symbols, and Hall symbols.
4
Source File: main.f90, Date: Mon Dec 15 14:37:08 CET 2008
Number
1
2
3:b
3:c
3:a
4:b
4:c
4:a
5:b1
5:b2
5:b3
5:c1
5:c2
5:c3
5:a1
5:a2
5:a3
6:b
6:c
6:a
7:b1
7:b2
7:b3
7:c1
7:c2
7:c3
7:a1
7:a2
7:a3
8:b1
8:b2
8:b3
8:c1
8:c2
8:c3
8:a1
8:a2
8:a3
9:b1
9:b2
9:b3
9:-b1
9:-b2
9:-b3
9:c1
9:c2
9:c3
9:-c1
9:-c2
9:-c3
Schoenflies
C11
C1i
C12
C12
C12
C22
C22
C22
C32
C32
C32
C32
C32
C32
C32
C32
C32
C1s
C1s
C1s
C2s
C2s
C2s
C2s
C2s
C2s
C2s
C2s
C2s
C3s
C3s
C3s
C3s
C3s
C3s
C3s
C3s
C3s
C4s
C4s
C4s
C4s
C4s
C4s
C4s
C4s
C4s
C4s
C4s
C4s
Hermann-Mauguin
P1
P-1
P2:b = P121
P2:c = P112
P2:a = P211
P21:b = P1211
P21:c = P1121
P21:a = P2111
C2:b1 = C121
C2:b2 = A121
C2:b3 = I121
C2:c1 = A112
C2:c2 = B112 = B2
C2:c3 = I112
C2:a1 = B211
C2:a2 = C211
C2:a3 = I211
Pm:b = P1m1
Pm:c = P11m
Pm:a = Pm11
Pc:b1 = P1c1
Pc:b2 = P1n1
Pc:b3 = P1a1
Pc:c1 = P11a
Pc:c2 = P11n
Pc:c3 = P11b = Pb
Pc:a1 = Pb11
Pc:a2 = Pn11
Pc:a3 = Pc11
Cm:b1 = C1m1
Cm:b2 = A1m1
Cm:b3 = I1m1
Cm:c1 = A11m
Cm:c2 = B11m = Bm
Cm:c3 = I11m
Cm:a1 = Bm11
Cm:a2 = Cm11
Cm:a3 = Im11
Cc:b1 = C1c1
Cc:b2 = A1n1
Cc:b3 = I1a1
Cc:-b1 = A1a1
Cc:-b2 = C1n1
Cc:-b3 = I1c1
Cc:c1 = A11a
Cc:c2 = B11n
Cc:c3 = I11b
Cc:-c1 = B11b = Bb
Cc:-c2 = A11n
Cc:-c3 = I11a
Hall
P1
-P 1
P 2y
P2
P 2x
P 2yb
P 2c
P 2xa
C 2y
A 2y
I 2y
A2
B2
I2
B 2x
C 2x
I 2x
P -2y
P -2
P -2x
P -2yc
P -2yac
P -2ya
P -2a
P -2ab
P -2b
P -2xb
P -2xbc
P -2xc
C -2y
A -2y
I -2y
A -2
B -2
I -2
B -2x
C -2x
I -2x
C -2yc
A -2yac
I -2ya
A -2ya
C -2ybc
I -2yc
A -2a
B -2bc
I -2b
B -2b
A -2ac
I -2a
5
Source File: main.f90, Date: Mon Dec 15 14:37:08 CET 2008
Number
9:a1
9:a2
9:a3
9:-a1
9:-a2
9:-a3
10:b
10:c
10:a
11:b
11:c
11:a
12:b1
12:b2
12:b3
12:c1
12:c2
12:c3
12:a1
12:a2
12:a3
13:b1
13:b2
13:b3
13:c1
13:c2
13:c3
13:a1
13:a2
13:a3
14:b1
14:b2
14:b3
14:c1
14:c2
14:c3
14:a1
14:a2
14:a3
15:b1
15:b2
15:b3
15:-b1
15:-b2
15:-b3
15:c1
15:c2
15:c3
15:-c1
15:-c2
Schoenflies
C4s
C4s
C4s
C4s
C4s
C4s
C12h
C12h
C12h
C22h
C22h
C22h
C32h
C32h
C32h
C32h
C32h
C32h
C32h
C32h
C32h
C42h
C42h
C42h
C42h
C42h
C42h
C42h
C42h
C42h
C52h
C52h
C52h
C52h
C52h
C52h
C52h
C52h
C52h
C62h
C62h
C62h
C62h
C62h
C62h
C62h
C62h
C62h
C62h
C62h
Hermann-Mauguin
Cc:a1 = Bb11
Cc:a2 = Cn11
Cc:a3 = Ic11
Cc:-a1 = Cc11
Cc:-a2 = Bn11
Cc:-a3 = Ib11
P2/m:b = P12/m1
P2/m:c = P112/m
P2/m:a = P2/m11
P21/m:b = P121/m1
P21/m:c = P1121/m
P21/m:a = P21/m11
C2/m:b1 = C12/m1
C2/m:b2 = A12/m1
C2/m:b3 = I12/m1
C2/m:c1 = A112/m
C2/m:c2 = B112/m = B2/m
C2/m:c3 = I112/m
C2/m:a1 = B2/m11
C2/m:a2 = C2/m11
C2/m:a3 = I2/m11
P2/c:b1 = P12/c1
P2/c:b2 = P12/n1
P2/c:b3 = P12/a1
P2/c:c1 = P112/a
P2/c:c2 = P112/n
P2/c:c3 = P112/b = P2/b
P2/c:a1 = P2/b11
P2/c:a2 = P2/n11
P2/c:a3 = P2/c11
P21/c:b1 = P121/c1
P21/c:b2 = P121/n1
P21/c:b3 = P121/a1
P21/c:c1 = P1121/a
P21/c:c2 = P1121/n
P21/c:c3 = P1121/b = P21/b
P21/c:a1 = P21/b11
P21/c:a2 = P21/n11
P21/c:a3 = P21/c11
C2/c:b1 = C12/c1
C2/c:b2 = A12/n1
C2/c:b3 = I12/a1
C2/c:-b1 = A12/a1
C2/c:-b2 = C12/n1
C2/c:-b3 = I12/c1
C2/c:c1 = A112/a
C2/c:c2 = B112/n
C2/c:c3 = I112/b
C2/c:-c1 = B112/b = B2/b
C2/c:-c2 = A112/n
Hall
B -2xb
C -2xbc
I -2xc
C -2xc
B -2xbc
I -2xb
-P 2y
-P 2
-P 2x
-P 2yb
-P 2c
-P 2xa
-C 2y
-A 2y
-I 2y
-A 2
-B 2
-I 2
-B 2x
-C 2x
-I 2x
-P 2yc
-P 2yac
-P 2ya
-P 2a
-P 2ab
-P 2b
-P 2xb
-P 2xbc
-P 2xc
-P 2ybc
-P 2yn
-P 2yab
-P 2ac
-P 2n
-P 2bc
-P 2xab
-P 2xn
-P 2xac
-C 2yc
-A 2yac
-I 2ya
-A 2ya
-C 2ybc
-I 2yc
-A 2a
-B 2bc
-I 2b
-B 2b
-A 2ac
6
Source File: main.f90, Date: Mon Dec 15 14:37:08 CET 2008
Number
15:-c3
15:a1
15:a2
15:a3
15:-a1
15:-a2
15:-a3
16
17
17:cab
17:bca
18
18:cab
18:bca
19
20
20:cab
20:bca
21
21:cab
21:bca
22
23
24
25
25:cab
25:bca
26
26:ba-c
26:cab
26:-cba
26:bca
26:a-cb
27
27:cab
27:bca
28
28:ba-c
28:cab
28:-cba
28:bca
28:a-cb
29
29:ba-c
29:cab
29:-cba
29:bca
29:a-cb
30
30:ba-c
Schoenflies
C62h
C62h
C62h
C62h
C62h
C62h
C62h
D12
D22
D22
D22
D32
D32
D32
D42
D52
D52
D52
D62
D62
D62
D72
D82
D92
C12v
C12v
C12v
C22v
C22v
C22v
C22v
C22v
C22v
C32v
C32v
C32v
C42v
C42v
C42v
C42v
C42v
C42v
C52v
C52v
C52v
C52v
C52v
C52v
C62v
C62v
Hermann-Mauguin
C2/c:-c3 = I112/a
C2/c:a1 = B2/b11
C2/c:a2 = C2/n11
C2/c:a3 = I2/c11
C2/c:-a1 = C2/c11
C2/c:-a2 = B2/n11
C2/c:-a3 = I2/b11
P222
P2221
P2122
P2212
P21212
P22121
P21221
P212121
C2221
A2122
B2212
C222
A222
B222
F222
I222
I212121
Pmm2
P2mm
Pm2m
Pmc21
Pcm21
P21ma
P21am
Pb21m
Pm21b
Pcc2
P2aa
Pb2b
Pma2
Pbm2
P2mb
P2cm
Pc2m
Pm2a
Pca21
Pbc21
P21ab
P21ca
Pc21b
Pb21a
Pnc2
Pcn2
Hall
-I 2a
-B 2xb
-C 2xbc
-I 2xc
-C 2xc
-B 2xbc
-I 2xb
P22
P 2c 2
P 2a 2a
P 2 2b
P 2 2ab
P 2bc 2
P 2ac 2ac
P 2ac 2ab
C 2c 2
A 2a 2a
B 2 2b
C22
A22
B22
F22
I22
I 2b 2c
P 2 -2
P -2 2
P -2 -2
P 2c -2
P 2c -2c
P -2a 2a
P -2 2a
P -2 -2b
P -2b -2
P 2 -2c
P -2a 2
P -2b -2b
P 2 -2a
P 2 -2b
P -2b 2
P -2c 2
P -2c -2c
P -2a -2a
P 2c -2ac
P 2c -2b
P -2b 2a
P -2ac 2a
P -2bc -2c
P -2a -2ab
P 2 -2bc
P 2 -2ac
7
Source File: main.f90, Date: Mon Dec 15 14:37:08 CET 2008
Number
30:cab
30:-cba
30:bca
30:a-cb
31
31:ba-c
31:cab
31:-cba
31:bca
31:a-cb
32
32:cab
32:bca
33
33:ba-c
33:cab
33:-cba
33:bca
33:a-cb
34
34:cab
34:bca
35
35:cab
35:bca
36
36:ba-c
36:cab
36:-cba
36:bca
36:a-cb
37
37:cab
37:bca
38
38:ba-c
38:cab
38:-cba
38:bca
38:a-cb
39
39:ba-c
39:cab
39:-cba
39:bca
39:a-cb
40
40:ba-c
40:cab
40:-cba
Schoenflies
C62v
C62v
C62v
C62v
C72v
C72v
C72v
C72v
C72v
C72v
C82v
C82v
C82v
C92v
C92v
C92v
C92v
C92v
C92v
C10
2v
C10
2v
C10
2v
C11
2v
C11
2v
C11
2v
C12
2v
C12
2v
C12
2v
C12
2v
C12
2v
C12
2v
C13
2v
C13
2v
C13
2v
C14
2v
C14
2v
C14
2v
C14
2v
C14
2v
C14
2v
C15
2v
C15
2v
C15
2v
C15
2v
C15
2v
C15
2v
C16
2v
C16
2v
C16
2v
C16
2v
Hermann-Mauguin
P2na
P2an
Pb2n
Pn2b
Pmn21
Pnm21
P21mn
P21nm
Pn21m
Pm21n
Pba2
P2cb
Pc2a
Pna21
Pbn21
P21nb
P21cn
Pc21n
Pn21a
Pnn2
P2nn
Pn2n
Cmm2
A2mm
Bm2m
Cmc21
Ccm21
A21ma
A21am
Bb21m
Bm21b
Ccc2
A2aa
Bb2b
Amm2
Bmm2
B2mm
C2mm
Cm2m
Am2m
Abm2
Bma2
B2cm
C2mb
Cm2a
Ac2m
Ama2
Bbm2
B2mb
C2cm
Hall
P -2ac 2
P -2ab 2
P -2ab -2ab
P -2bc -2bc
P 2ac -2
P 2bc -2bc
P -2ab 2ab
P -2 2ac
P -2 -2bc
P -2ab -2
P 2 -2ab
P -2bc 2
P -2ac -2ac
P 2c -2n
P 2c -2ab
P -2bc 2a
P -2n 2a
P -2n -2ac
P -2ac -2n
P 2 -2n
P -2n 2
P -2n -2n
C 2 -2
A -2 2
B -2 -2
C 2c -2
C 2c -2c
A -2a 2a
A -2 2a
B -2 -2b
B -2b -2
C 2 -2c
A -2a 2
B -2b -2b
A 2 -2
B 2 -2
B -2 2
C -2 2
C -2 -2
A -2 -2
A 2 -2c
B 2 -2c
B -2c 2
C -2b 2
C -2b -2b
A -2c -2c
A 2 -2a
B 2 -2b
B -2b 2
C -2c 2
8
Source File: main.f90, Date: Mon Dec 15 14:37:08 CET 2008
Number
40:bca
40:a-cb
41
41:ba-c
41:cab
41:-cba
41:bca
41:a-cb
42
42:cab
42:bca
43
43:cab
43:bca
44
44:cab
44:bca
45
45:cab
45:bca
46
46:ba-c
46:cab
46:-cba
46:bca
46:a-cb
47
48:1
48:2
49
49:cab
49:bca
50:1
50:2
50:1cab
50:2cab
50:1bca
50:2bca
51
51:ba-c
51:cab
51:-cba
51:bca
51:a-cb
52
52:ba-c
52:cab
52:-cba
52:bca
52:a-cb
Schoenflies
C16
2v
C16
2v
C17
2v
C17
2v
C17
2v
C17
2v
C17
2v
C17
2v
C18
2v
C18
2v
C18
2v
C19
2v
C19
2v
C19
2v
C20
2v
C20
2v
C20
2v
C21
2v
C21
2v
C21
2v
C22
2v
C22
2v
C22
2v
C22
2v
C22
2v
C22
2v
D12h
D22h
D22h
D32h
D32h
D32h
D42h
D42h
D42h
D42h
D42h
D42h
D52h
D52h
D52h
D52h
D52h
D52h
D62h
D62h
D62h
D62h
D62h
D62h
Hermann-Mauguin
Cc2m
Am2a
Aba2
Bba2
B2cb
C2cb
Cc2a
Ac2a
Fmm2
F2mm
Fm2m
Fdd2
F2dd
Fd2d
Imm2
I2mm
Im2m
Iba2
I2cb
Ic2a
Ima2
Ibm2
I2mb
I2cm
Ic2m
Im2a
Pmmm
Pnnn:1
Pnnn:2
Pccm
Pmaa
Pbmb
Pban:1
Pban:2
Pncb:1
Pncb:2
Pcna:1
Pcna:2
Pmma
Pmmb
Pbmm
Pcmm
Pmcm
Pmam
Pnna
Pnnb
Pbnn
Pcnn
Pncn
Pnan
Hall
C -2c -2c
A -2a -2a
A 2 -2ac
B 2 -2bc
B -2bc 2
C -2bc 2
C -2bc -2bc
A -2ac -2ac
F 2 -2
F -2 2
F -2 -2
F 2 -2d
F -2d 2
F -2d -2d
I 2 -2
I -2 2
I -2 -2
I 2 -2c
I -2a 2
I -2b -2b
I 2 -2a
I 2 -2b
I -2b 2
I -2c 2
I -2c -2c
I -2a -2a
-P 2 2
P 2 2 -1n
-P 2ab 2bc
-P 2 2c
-P 2a 2
-P 2b 2b
P 2 2 -1ab
-P 2ab 2b
P 2 2 -1bc
-P 2b 2bc
P 2 2 -1ac
-P 2a 2c
-P 2a 2a
-P 2b 2
-P 2 2b
-P 2c 2c
-P 2c 2
-P 2 2a
-P 2a 2bc
-P 2b 2n
-P 2n 2b
-P 2ab 2c
-P 2ab 2n
-P 2n 2bc
Source File: main.f90, Date: Mon Dec 15 14:37:08 CET 2008
Number
53
53:ba-c
53:cab
53:-cba
53:bca
53:a-cb
54
54:ba-c
54:cab
54:-cba
54:bca
54:a-cb
55
55:cab
55:bca
56
56:cab
56:bca
57
57:ba-c
57:cab
57:-cba
57:bca
57:a-cb
58
58:cab
58:bca
59:1
59:2
59:1cab
59:2cab
59:1bca
59:2bca
60
60:ba-c
60:cab
60:-cba
60:bca
60:a-cb
61
61:ba-c
62
62:ba-c
62:cab
62:-cba
62:bca
62:a-cb
63
63:ba-c
63:cab
Schoenflies
D72h
D72h
D72h
D72h
D72h
D72h
D82h
D82h
D82h
D82h
D82h
D82h
D92h
D92h
D92h
D10
2h
D10
2h
D10
2h
D11
2h
D11
2h
D11
2h
D11
2h
D11
2h
D11
2h
D12
2h
D12
2h
D12
2h
D13
2h
D13
2h
D13
2h
D13
2h
D13
2h
D13
2h
D14
2h
D14
2h
D14
2h
D14
2h
D14
2h
D14
2h
D15
2h
D15
2h
D16
2h
D16
2h
D16
2h
D16
2h
D16
2h
D16
2h
D17
2h
D17
2h
D17
2h
Hermann-Mauguin
Pmna
Pnmb
Pbmn
Pcnm
Pncm
Pman
Pcca
Pccb
Pbaa
Pcaa
Pbcb
Pbab
Pbam
Pmcb
Pcma
Pccn
Pnaa
Pbnb
Pbcm
Pcam
Pmca
Pmab
Pbma
Pcmb
Pnnm
Pmnn
Pnmn
Pmmn:1
Pmmn:2
Pnmm:1
Pnmm:2
Pmnm:1
Pmnm:2
Pbcn
Pcan
Pnca
Pnab
Pbna
Pcnb
Pbca
Pcab
Pnma
Pmnb
Pbnm
Pcmn
Pmcn
Pnam
Cmcm
Ccmm
Amma
Hall
-P 2ac 2
-P 2bc 2bc
-P 2ab 2ab
-P 2 2ac
-P 2 2bc
-P 2ab 2
-P 2a 2ac
-P 2b 2c
-P 2a 2b
-P 2ac 2c
-P 2bc 2b
-P 2b 2ab
-P 2 2ab
-P 2bc 2
-P 2ac 2ac
-P 2ab 2ac
-P 2ac 2bc
-P 2bc 2ab
-P 2c 2b
-P 2c 2ac
-P 2ac 2a
-P 2b 2a
-P 2a 2ab
-P 2bc 2c
-P 2 2n
-P 2n 2
-P 2n 2n
P 2 2ab -1ab
-P 2ab 2a
P 2bc 2 -1bc
-P 2c 2bc
P 2ac 2ac -1ac
-P 2c 2a
-P 2n 2ab
-P 2n 2c
-P 2a 2n
-P 2bc 2n
-P 2ac 2b
-P 2b 2ac
-P 2ac 2ab
-P 2bc 2ac
-P 2ac 2n
-P 2bc 2a
-P 2c 2ab
-P 2n 2ac
-P 2n 2a
-P 2c 2n
-C 2c 2
-C 2c 2c
-A 2a 2a
9
10
Source File: main.f90, Date: Mon Dec 15 14:37:08 CET 2008
Number
63:-cba
63:bca
63:a-cb
64
64:ba-c
64:cab
64:-cba
64:bca
64:a-cb
65
65:cab
65:bca
66
66:cab
66:bca
67
67:ba-c
67:cab
67:-cba
67:bca
67:a-cb
68:1
68:2
68:1ba-c
68:2ba-c
68:1cab
68:2cab
68:1-cba
68:2-cba
68:1bca
68:2bca
68:1a-cb
68:2a-cb
69
70:1
70:2
71
72
72:cab
72:bca
73
73:ba-c
74
74:ba-c
74:cab
74:-cba
74:bca
74:a-cb
75
76
Schoenflies
D17
2h
D17
2h
D17
2h
D18
2h
D18
2h
D18
2h
D18
2h
D18
2h
D18
2h
D19
2h
D19
2h
D19
2h
D20
2h
D20
2h
D20
2h
D21
2h
D21
2h
D21
2h
D21
2h
D21
2h
D21
2h
D22
2h
D22
2h
D22
2h
D22
2h
D22
2h
D22
2h
D22
2h
D22
2h
D22
2h
D22
2h
D22
2h
D22
2h
D23
2h
D24
2h
D24
2h
D25
2h
D26
2h
D26
2h
D26
2h
D27
2h
D27
2h
D28
2h
D28
2h
D28
2h
D28
2h
D28
2h
D28
2h
C14
C24
Hermann-Mauguin
Amam
Bbmm
Bmmb
Cmca
Ccmb
Abma
Acam
Bbcm
Bmab
Cmmm
Ammm
Bmmm
Cccm
Amaa
Bbmb
Cmma
Cmmb
Abmm
Acmm
Bmcm
Bmam
Ccca:1
Ccca:2
Cccb:1
Cccb:2
Abaa:1
Abaa:2
Acaa:1
Acaa:2
Bbcb:1
Bbcb:2
Bbab:1
Bbab:2
Fmmm
Fddd:1
Fddd:2
Immm
Ibam
Imcb
Icma
Ibca
Icab
Imma
Immb
Ibmm
Icmm
Imcm
Imam
P4
P41
Hall
-A 2 2a
-B 2 2b
-B 2b 2
-C 2bc 2
-C 2bc 2bc
-A 2ac 2ac
-A 2 2ac
-B 2 2bc
-B 2bc 2
-C 2 2
-A 2 2
-B 2 2
-C 2 2c
-A 2a 2
-B 2b 2b
-C 2b 2
-C 2b 2b
-A 2c 2c
-A 2 2c
-B 2 2c
-B 2c 2
C 2 2 -1bc
-C 2b 2bc
C 2 2 -1bc
-C 2b 2c
A 2 2 -1ac
-A 2a 2c
A 2 2 -1ac
-A 2ac 2c
B 2 2 -1bc
-B 2bc 2b
B 2 2 -1bc
-B 2b 2bc
-F 2 2
F 2 2 -1d
-F 2uv 2vw
-I 2 2
-I 2 2c
-I 2a 2
-I 2b 2b
-I 2b 2c
-I 2a 2b
-I 2b 2
-I 2a 2a
-I 2c 2c
-I 2 2b
-I 2 2a
-I 2c 2
P4
P 4w
11
Source File: main.f90, Date: Mon Dec 15 14:37:08 CET 2008
Number
77
78
79
80
81
82
83
84
85:1
85:2
86:1
86:2
87
88:1
88:2
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
Schoenflies
C34
C44
C54
C64
S14
S24
C14h
C24h
C34h
C34h
C44h
C44h
C54h
C64h
C64h
D14
D24
D34
D44
D54
D64
D74
D84
D94
D10
4
C14v
C24v
C34v
C44v
C54v
C64v
C74v
C84v
C94v
C10
4v
C11
4v
C12
4v
D12d
D22d
D32d
D42d
D52d
D62d
D72d
D82d
D92d
D10
2d
D11
2d
D12
2d
D14h
Hermann-Mauguin
P42
P43
I4
I41
P-4
I-4
P4/m
P42/m
P4/n:1
P4/n:2
P42/n:1
P42/n:2
I4/m
I41/a:1
I41/a:2
P422
P4212
P4122
P41212
P4222
P42212
P4322
P43212
I422
I4122
P4mm
P4bm
P42cm
P42nm
P4cc
P4nc
P42mc
P42bc
I4mm
I4cm
I41md
I41cd
P-42m
P-42c
P-421m
P-421c
P-4m2
P-4c2
P-4b2
P-4n2
I-4m2
I-4c2
I-42m
I-42d
P4/mmm
Hall
P 4c
P 4cw
I4
I 4bw
P -4
I -4
-P 4
-P 4c
P 4ab -1ab
-P 4a
P 4n -1n
-P 4bc
-I 4
I 4bw -1bw
-I 4ad
P42
P 4ab 2ab
P 4w 2c
P 4abw 2nw
P 4c 2
P 4n 2n
P 4cw 2c
P 4nw 2abw
I42
I 4bw 2bw
P 4 -2
P 4 -2ab
P 4c -2c
P 4n -2n
P 4 -2c
P 4 -2n
P 4c -2
P 4c -2ab
I 4 -2
I 4 -2c
I 4bw -2
I 4bw -2c
P -4 2
P -4 2c
P -4 2ab
P -4 2n
P -4 -2
P -4 -2c
P -4 -2ab
P -4 -2n
I -4 -2
I -4 -2c
I -4 2
I -4 2bw
-P 4 2
Source File: main.f90, Date: Mon Dec 15 14:37:08 CET 2008
Number
124
125:1
125:2
126:1
126:2
127
128
129:1
129:2
130:1
130:2
131
132
133:1
133:2
134:1
134:2
135
136
137:1
137:2
138:1
138:2
139
140
141:1
141:2
142:1
142:2
143
144
145
146:H
146:R
147
148:H
148:R
149
150
151
152
153
154
155:H
155:R
156
157
158
159
160:H
Schoenflies
D24h
D34h
D34h
D44h
D44h
D54h
D64h
D74h
D74h
D84h
D84h
D94h
D10
4h
D11
4h
D11
4h
D12
4h
D12
4h
D13
4h
D14
4h
D15
4h
D15
4h
D16
4h
D16
4h
D17
4h
D18
4h
D19
4h
D19
4h
D20
4h
D20
4h
C13
C23
C33
C43
C43
C13i
C23i
C23i
D13
D23
D33
D43
D53
D63
D73
D73
C13v
C23v
C33v
C43v
C53v
Hermann-Mauguin
P4/mcc
P4/nbm:1
P4/nbm:2
P4/nnc:1
P4/nnc:2
P4/mbm
P4/mnc
P4/nmm:1
P4/nmm:2
P4/ncc:1
P4/ncc:2
P42/mmc
P42/mcm
P42/nbc:1
P42/nbc:2
P42/nnm:1
P42/nnm:2
P42/mbc
P42/mnm
P42/nmc:1
P42/nmc:2
P42/ncm:1
P42/ncm:2
I4/mmm
I4/mcm
I41/amd:1
I41/amd:2
I41/acd:1
I41/acd:2
P3
P31
P32
R3:H
R3:R
P-3
R-3:H
R-3:R
P312
P321
P3112
P3121
P3212
P3221
R32:H
R32:R
P3m1
P31m
P3c1
P31c
R3m:H
Hall
-P 4 2c
P 4 2 -1ab
-P 4a 2b
P 4 2 -1n
-P 4a 2bc
-P 4 2ab
-P 4 2n
P 4ab 2ab -1ab
-P 4a 2a
P 4ab 2n -1ab
-P 4a 2ac
-P 4c 2
-P 4c 2c
P 4n 2c -1n
-P 4ac 2b
P 4n 2 -1n
-P 4ac 2bc
-P 4c 2ab
-P 4n 2n
P 4n 2n -1n
-P 4ac 2a
P 4n 2ab -1n
-P 4ac 2ac
-I 4 2
-I 4 2c
I 4bw 2bw -1bw
-I 4bd 2
I 4bw 2aw -1bw
-I 4bd 2c
P3
P 31
P 32
R3
P 3*
-P 3
-R 3
-P 3*
P32
P 3 2′′
P 31 2c (0 0 1)
P 31 2′′
P 32 2c (0 0 -1)
P 32 2′′
R 3 2′′
P 3* 2
P 3 -2′′
P 3 -2
P 3 -2′′ c
P 3 -2c
R 3 -2′′
12
Source File: main.f90, Date: Mon Dec 15 14:37:08 CET 2008
Number
160:R
161:H
161:R
162
163
164
165
166:H
166:R
167:H
167:R
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201:1
201:2
202
203:1
203:2
204
Schoenflies
C53v
C63v
C63v
D13d
D23d
D33d
D43d
D53d
D53d
D63d
D63d
C16
C26
C36
C46
C56
C66
C13h
C16h
C26h
D16
D26
D36
D46
D56
D66
C16v
C26v
C36v
C46v
D13h
D23h
D33h
D43h
D16h
D26h
D36h
D46h
T1
T2
T3
T4
T5
T1h
T2h
T2h
T3h
T4h
T4h
T5h
Hermann-Mauguin
R3m:R
R3c:H
R3c:R
P-31m
P-31c
P-3m1
P-3c1
R-3m:H
R-3m:R
R-3c:H
R-3c:R
P6
P61
P65
P62
P64
P63
P-6
P6/m
P63/m
P622
P6122
P6522
P6222
P6422
P6322
P6mm
P6cc
P63cm
P63mc
P-6m2
P-6c2
P-62m
P-62c
P6/mmm
P6/mcc
P63/mcm
P63/mmc
P23
F23
I23
P213
I213
Pm-3
Pn-3:1
Pn-3:2
Fm-3
Fd-3:1
Fd-3:2
Im-3
Hall
P 3* -2
R 3 -2′′ c
P 3* -2n
-P 3 2
-P 3 2c
-P 3 2′′
-P 3 2′′ c
-R 3 2′′
-P 3* 2
-R 3 2′′ c
-P 3* 2n
P6
P 61
P 65
P 62
P 64
P 6c
P -6
-P 6
-P 6c
P62
P 61 2 (0 0 -1)
P 65 2 (0 0 1)
P 62 2c (0 0 1)
P 64 2c (0 0 -1)
P 6c 2c
P 6 -2
P 6 -2c
P 6c -2
P 6c -2c
P -6 2
P -6c 2
P -6 -2
P -6c -2c
-P 6 2
-P 6 2c
-P 6c 2
-P 6c 2c
P223
F223
I223
P 2ac 2ab 3
I 2b 2c 3
-P 2 2 3
P 2 2 3 -1n
-P 2ab 2bc 3
-F 2 2 3
F 2 2 3 -1d
-F 2uv 2vw 3
-I 2 2 3
13
Source File: main.f90, Date: Mon Dec 15 14:37:08 CET 2008
Number
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222:1
222:2
223
224:1
224:2
225
226
227:1
227:2
228:1
228:2
229
230
Schoenflies
T6h
T7h
O1
O2
O3
O4
O5
O6
O7
O8
T1d
T2d
T3d
T4d
T5d
T6d
O1h
O2h
O2h
O3h
O4h
O4h
O5h
O6h
O7h
O7h
O8h
O8h
O9h
O10
h
Hermann-Mauguin
Pa-3
Ia-3
P432
P4232
F432
F4132
I432
P4332
P4132
I4132
P-43m
F-43m
I-43m
P-43n
F-43c
I-43d
Pm-3m
Pn-3n:1
Pn-3n:2
Pm-3n
Pn-3m:1
Pn-3m:2
Fm-3m
Fm-3c
Fd-3m:1
Fd-3m:2
Fd-3c:1
Fd-3c:2
Im-3m
Ia-3d
Hall
-P 2ac 2ab 3
-I 2b 2c 3
P423
P 4n 2 3
F423
F 4d 2 3
I423
P 4acd 2ab 3
P 4bd 2ab 3
I 4bd 2c 3
P -4 2 3
F -4 2 3
I -4 2 3
P -4n 2 3
F -4c 2 3
I -4bd 2c 3
-P 4 2 3
P 4 2 3 -1n
-P 4a 2bc 3
-P 4n 2 3
P 4n 2 3 -1n
-P 4bc 2bc 3
-F 4 2 3
-F 4c 2 3
F 4d 2 3 -1d
-F 4vw 2vw 3
F 4d 2 3 -1cd
-F 4cvw 2vw 3
-I 4 2 3
-I 4bd 2c 3
14
Source File: modmain.f90, Date: Mon Dec 15 14:37:08 CET 2008
4
4.1
15
Routine/Function Prologues
Fortran: Module Interface modmain (Source File: modmain.f90)
Contains all the global variables required by the spacegroup code.
REVISION HISTORY:
Created October 2006 (JKD)
4.2
sgsymb (Source File: sgsymb.f90)
INTERFACE:
subroutine sgsymb(hrmg,num,schn,hall)
INPUT/OUTPUT PARAMETERS:
hrmg
num
schn
hall
:
:
:
:
Hermann-Mauguin symbol (in,character(20))
space group number (out,character(20))
Schoenflies symbol (out,character(20))
Hall symbol (out,character(20))
DESCRIPTION:
Returns the space group number, Schoenflies 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
findprim (Source File: findprim.f90)
INTERFACE:
subroutine findprim
USES:
use modmain
DESCRIPTION:
This routine finds 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 finding those which leave the crystal structure invariant. Of these, the
three shortest which produce a non-zero unit cell volume are chosen.
REVISION HISTORY:
Created April 2007 (JKD)
Source File: r3taxi.f90, Date: Mon Dec 15 14:37:08 CET 2008
4.4
16
r3frac (Source File: r3frac.f90)
INTERFACE:
subroutine r3frac(eps,v,iv)
INPUT/OUTPUT PARAMETERS:
eps : zero component tolerance (in,real)
v
: input vector (inout,real(3))
iv : integer parts of v (out,integer(3))
DESCRIPTION:
Finds the fractional part of each component of a real 3-vector using the function frac (x) =
x − ⌊x⌋. A component is taken to be zero if it lies within the intervals [0, ǫ) or (1 − ǫ, 1].
The integer components of v are returned in the variable iv.
REVISION HISTORY:
Created January 2003 (JKD)
4.5
r3taxi (Source File: r3taxi.f90)
INTERFACE:
real(8) function r3taxi(x,y)
INPUT/OUTPUT PARAMETERS:
x : input vector 1 (in,real(3))
y : input vector 2 (in,real(3))
DESCRIPTION:
Returns the taxi-cab distance between two real 3-vectors: d = |x1 −y1 |+|x2 −y2 |+|x3 −y3 |.
REVISION HISTORY:
Created March 2006 (JKD)
4.6
r3mv (Source File: r3mv.f90)
INTERFACE:
subroutine r3mv(a,x,y)
INPUT/OUTPUT PARAMETERS:
Source File: r3cross.f90, Date: Mon Dec 15 14:37:08 CET 2008
a : input matrix (in,real(3,3))
x : input vector (in,real(3))
y : output vector (out,real(3))
DESCRIPTION:
Multiplies a real 3 × 3 matrix with a vector.
REVISION HISTORY:
Created January 2003 (JKD)
4.7
r3cross (Source File: r3cross.f90)
INTERFACE:
subroutine r3cross(x,y,z)
INPUT/OUTPUT PARAMETERS:
x : input vector 1 (in,real(3))
y : input vector 2 (in,real(3))
z : output cross-product (out,real(3))
DESCRIPTION:
Returns the cross product of two real 3-vectors.
REVISION HISTORY:
Created September 2002 (JKD)
4.8
r3minv (Source File: r3minv.f90)
INTERFACE:
subroutine r3minv(a,b)
INPUT/OUTPUT PARAMETERS:
a : input matrix (in,real(3,3))
b : output matrix (in,real(3,3))
DESCRIPTION:
Computes the inverse of a real 3 × 3 matrix.
REVISION HISTORY:
Created April 2003 (JKD)
17
Source File: r3dot.f90, Date: Mon Dec 15 14:37:08 CET 2008
4.9
r3mm (Source File: r3mm.f90)
INTERFACE:
subroutine r3mm(a,b,c)
INPUT/OUTPUT PARAMETERS:
a : input matrix 1 (in,real(3,3))
b : input matrix 2 (in,real(3,3))
c : output matrix (out,real(3,3))
DESCRIPTION:
Multiplies two real 3 × 3 matrices.
REVISION HISTORY:
Created April 2003 (JKD)
4.10
r3dot (Source File: r3dot.f90)
INTERFACE:
real(8) function r3dot(x,y)
INPUT/OUTPUT PARAMETERS:
x : input vector 1 (in,real(3))
y : input vector 2 (in,real(3))
DESCRIPTION:
Returns the dot-product of two real 3-vectors.
REVISION HISTORY:
Created January 2003 (JKD)
18