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空间群No12：国际空间群表和晶体学数据
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空间群No12：国际空间群表和晶体学数据
美国有个海军，海军有个什么实验室，这个实验室有个晶体学启蒙网站。
在中国，这个网站有时可以打开，有时打不开。也不知道是谁在捣蛋，是老美在捣蛋？还是本拉登在捣蛋？还是什么第三者在捣蛋？咱中国人是不会干这种缺德的事情！
老美财大气粗，特别是老美的海军，更是财大气粗中的财大气粗。他们对于案例中涉及到的晶体结构，都给出了三维动画演示，他们的原子坐标是用矢量法表示的。
我也分析了很多的晶体结构，但是我只能给出数字表示。他们是一帮人，我就我自己。他们财大气粗，有个专门的网站，我只有靠科学网这个平台，才可以把我的结果贴出来。
为什么要贴出来呢？
为了梦中的橄榄树！
老的PDF数据没有给出原子坐标。
这个数据给出了原子坐标，如果没有绿色框之中的信息，数据仍然是不完备的。
这是12号国际空间群表的表头，我喜欢使用No.12和C2h（3）符号。不幸的是，编号为12的空间群有很多种表达方法，这给我们解读晶体学数据（如求键络）带来很多麻烦。
No.12空间群的点群为C2h，有一个C2轴，还有一个镜面m垂直于这个2次轴，还有一个反演中心i，加上单位元素，组成一个4阶点群（C2h）。
这个唯一的对称轴C2就是UNIQUE AXIS。
如果把晶体的对称轴C2给了（置于）b轴（Y轴），就是所谓的UNIQUE AXIS b；
如果把晶体的对称轴C2给了（置于）c轴（Z轴），就是所谓的UNIQUE AXIS c；
当然了，也可以把晶体的对称轴C2给了（置于）a轴（X轴），就是所谓的UNIQUE AXIS a；
除了空间群表的6种表示外，还有其他6种表示符号。
C12/m1，A12/m1，I12/m1；对应选择UNIQUE AXIS b；
A112/m，B112/m，I112/m；对应选择UNIQUE AXIS c；
A2/m,C2/a,C2/m11,C2/m,F2/m,I2/m这也是No.12空间群的表示符号。
教科书上单斜晶系的晶胞参数是：a≠b≠c，α＝γ＝90o，β≠90o。
这种写法是有条件的，即把实际晶体的UNIQUE AXIS给了b。
当然了，也可以把晶体的UNIQUE AXIS给了c，也可以把晶体的UNIQUE AXIS给了a。
相对于晶体来说，a，b，c的安放就相当于参照坐标系的选择，可以是随意的。
国际空间群表只约定了两种：
把晶体的UNIQUE AXIS给了b和把晶体的UNIQUE AXIS给了c。
此外，国际空间群表中的No.12空间群，给出了6种原子坐标，即所谓的CELL CHOICE，这都是由于不同的人的习惯不同，结果弄出6种摆放原子的模式。无论怎么描述原子的摆放，每个原子的环境是不能变的。
如何来描述原子的环境呢？
有点法、线法和面法。各种化学键理论和电子密度理论都需要知道原子的环境。
化合物AlCeCo的原子环境：
"a=",11.098,"b=",4.41,"c=",4.807,"Delta=",.005
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2," ","4i-Al","---","4i-Co"," d===",2.488
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" 配位原子：","4i-Co",": ",.2383,-7.4422,-6.615
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" 配位原子：","4i-Co",": ",.2383,-7.4422,-2.205
" SP coordinates=",-.193,0,.146
"4i-Co",":",.2383,-7.4422,-6.615," Z=",2
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" 配位原子：","4i-Al",": ",.1502,-6.2931,-8.82
" SP coordinates=",-.086,-1.5,.19
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" SP coordinates=",-.086,-.5,.19
3," ","4i-Co","---","4i-Ce"," d===",2.5325
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" 配位原子：","4i-Ce",": ",5.0015,-3.9735,2.205
" SP coordinates=",.13,1,1.325
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" 配位原子：","4i-Co",": ",2.5611,-3.2969,2.205
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4," ","4i-Al","---","4i-Co"," d===",2.574
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5," ","4i-Co","---","4i-Co"," d===",2.7453
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" SP coordinates=",.693,.5,.854
6," ","4i-Al","---","4i-Al"," d===",2.9562
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7," ","4i-Al","---","4i-Al"," d===",3.1074
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" SP coordinates=",.414,0,.19
" 配位原子：","4i-Al",": ",1.2494,.9236,-2.205
" SP coordinates=",.586,0,.81
"4i-Al",":",1.2494,.9236,-2.205," Z=",1
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" 配位原子：","4i-Al",": ",-1.2494,-.9236,-2.205
" SP coordinates=",.414,0,.19
8," ","4i-Al","---","4i-Ce"," d===",3.2007
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" SP coordinates=",1.63,.5,1.325
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" SP coordinates=",1.63,1.5,1.325
"4i-Ce",":",.8025,12.1352,4.41," Z=",2
" SP coordinates=",1.63,1.5,1.325
" 配位原子：","4i-Al",": ",.7582,9.8156,2.205
" SP coordinates=",1.414,1,1.19
" 配位原子：","4i-Al",": ",.7582,9.8156,6.615
" SP coordinates=",1.414,2,1.19
9," ","4i-Ce","---","4i-Co"," d===",3.2115
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" 配位原子：","4i-Co",": ",-5.0453,7.4422,2.205
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" 配位原子：","4i-Co",": ",-5.0453,7.4422,6.615
" SP coordinates=",1.193,2,-.146
"4i-Co",":",-5.0453,7.4422,2.205," Z=",2
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" 配位原子：","4i-Ce",": ",-6.4012,9.3431,0
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10," ","4i-Ce","---","4i-Al"," d===",3.2587
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" 配位原子：","4i-Al",": ",-2.6491,4.446,-4.41
" SP coordinates=",.914,-.5,.19
" 配位原子：","4i-Al",": ",-2.6491,4.446,0
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11," ","4i-Al","---","4i-Ce"," d===",3.3331
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" 配位原子：","4i-Al",": ",-1.2494,-.9236,-2.205
" SP coordinates=",.414,0,.19
" 配位原子：","4i-Al",": ",-1.2494,-.9236,2.205
" SP coordinates=",.414,1,.19
12," ","4i-Ce","---","4i-Al"," d===",3.3744
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" SP coordinates=",.87,2,.675
" 配位原子：","4i-Al",": ",1.2494,.9236,6.615
" SP coordinates=",.586,2,.81
"4i-Al",":",1.2494,.9236,6.615," Z=",1
" SP coordinates=",.586,2,.81
" 配位原子：","4i-Ce",": ",-.1945,3.9735,6.615
" SP coordinates=",.87,2,.675
13," ","4i-Co","---","4i-Ce"," d===",3.469
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" SP coordinates=",-.307,-.5,.854
" 配位原子：","4i-Ce",": ",4.0045,-12.1352,-4.41
" SP coordinates=",-.63,-.5,.675
"4i-Ce",":",4.0045,-12.1352,-4.41," Z=",1
" SP coordinates=",-.63,-.5,.675
" 配位原子：","4i-Co",": ",3.9607,-8.6665,-4.41
" SP coordinates=",-.307,-.5,.854
14," ","4i-Ce","---","4i-Ce"," d===",3.5393
"4i-Ce",":",.8025,12.1352,-4.41," Z=",2
" SP coordinates=",1.63,-.5,1.325
" 配位原子：","4i-Ce",": ",1.8131,14.7126,-6.615
" SP coordinates=",1.87,-1,1.675
" 配位原子：","4i-Ce",": ",1.8131,14.7126,-2.205
" SP coordinates=",1.87,0,1.675
"4i-Ce",":",1.8131,14.7126,-6.615," Z=",2
" SP coordinates=",1.87,-1,1.675
" 配位原子：","4i-Ce",": ",.8025,12.1352,-8.82
" SP coordinates=",1.63,-1.5,1.325
" 配位原子：","4i-Ce",": ",.8025,12.1352,-4.41
" SP coordinates=",1.63,-.5,1.325
15," ","4i-Ce","---","4i-Ce"," d===",3.6797
"4i-Ce",":",-.1945,3.9735,-2.205," Z=",1
" SP coordinates=",.87,0,.675
" 配位原子：","4i-Ce",": ",2.2022,6.7657,-2.205
" SP coordinates=",1.13,0,1.325
"4i-Ce",":",2.2022,6.7657,-2.205," Z=",1
" SP coordinates=",1.13,0,1.325
" 配位原子：","4i-Ce",": ",-.1945,3.9735,-2.205
" SP coordinates=",.87,0,.675
16," ","4i-Ce","---","4i-Ce"," d===",3.6885
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" SP coordinates=",1.63,-.5,1.325
" 配位原子：","4i-Ce",": ",3.2128,9.3431,-4.41
" SP coordinates=",1.37,-.5,1.675
"4i-Ce",":",3.2128,9.3431,-4.41," Z=",1
" SP coordinates=",1.37,-.5,1.675
" 配位原子：","4i-Ce",": ",.8025,12.1352,-4.41
" SP coordinates=",1.63,-.5,1.325
17," ","4i-Al","---","4i-Al"," d===",4.2538
"4i-Al",":",2.6491,-4.446,0," Z=",2
" SP coordinates=",.086,.5,.81
" 配位原子：","4i-Al",": ",3.5576,-.9236,-2.205
" SP coordinates=",.414,0,1.19
" 配位原子：","4i-Al",": ",3.5576,-.9236,2.205
" SP coordinates=",.414,1,1.19
"4i-Al",":",3.5576,-.9236,2.205," Z=",2
" SP coordinates=",.414,1,1.19
" 配位原子：","4i-Al",": ",2.6491,-4.446,0
" SP coordinates=",.086,.5,.81
" 配位原子：","4i-Al",": ",2.6491,-4.446,4.41
" SP coordinates=",.086,1.5,.81
18," ","4i-Ce","---","4i-Ce"," d===",4.41
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" SP coordinates=",.87,1,-.325
" 配位原子：","4i-Ce",": ",-5.0015,3.9735,-2.205
" SP coordinates=",.87,0,-.325
" 配位原子：","4i-Ce",": ",-5.0015,3.9735,6.615
" SP coordinates=",.87,2,-.325
"4i-Ce",":",-5.0015,3.9735,6.615," Z=",2
" SP coordinates=",.87,2,-.325
" 配位原子：","4i-Ce",": ",-5.0015,3.9735,2.205
" SP coordinates=",.87,1,-.325
" 配位原子：","4i-Ce",": ",-5.0015,3.9735,11.025
" SP coordinates=",.87,3,-.325
19," ","4i-Al","---","4i-Al"," d===",4.41
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" SP coordinates=",-.414,1,.81
" 配位原子：","4i-Al",": ",4.0488,-9.8156,-2.205
" SP coordinates=",-.414,0,.81
" 配位原子：","4i-Al",": ",4.0488,-9.8156,6.615
" SP coordinates=",-.414,2,.81
"4i-Al",":",4.0488,-9.8156,6.615," Z=",2
" SP coordinates=",-.414,2,.81
" 配位原子：","4i-Al",": ",4.0488,-9.8156,2.205
" SP coordinates=",-.414,1,.81
" 配位原子：","4i-Al",": ",4.0488,-9.8156,11.025
" SP coordinates=",-.414,3,.81
20," ","4i-Co","---","4i-Co"," d===",4.41
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" 配位原子：","4i-Co",": ",5.3604,-14.0361,-2.205
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21," ","4i-Co","---","4i-Al"," d===",4.4195
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" SP coordinates=",-.086,1.5,1.19
" 配位原子：","4i-Co",": ",2.5611,-3.2969,2.205
" SP coordinates=",.193,1,.854
" 配位原子：","4i-Co",": ",2.5611,-3.2969,6.615
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23," ","4i-Al","---","4i-Co"," d===",4.433
"4i-Al",":",-3.2571,-11.6627,6.615," Z=",2
" SP coordinates=",-.586,2,-.81
" 配位原子：","4i-Co",": ",-.8463,-8.6665,4.41
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" SP coordinates=",-.307,2.5,-.146
"4i-Co",":",-.8463,-8.6665,4.41," Z=",2
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" 配位原子：","4i-Al",": ",-3.2571,-11.6627,2.205
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24," ","4i-Al","---","4i-Co"," d===",4.4891
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" 配位原子：","4i-Co",": ",-3.6456,2.0727,0
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"4i-Co",":",-3.6456,2.0727,0," Z=",1
" SP coordinates=",.693,.5,-.146
" 配位原子：","4i-Al",": ",-7.4561,4.446,0
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25," ","4i-Co","---","4i-Co"," d===",4.4964
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"4i-Co",":",-.8463,-8.6665,4.41," Z=",2
" SP coordinates=",-.307,1.5,-.146
" 配位原子：","4i-Co",": ",-4.5687,-7.4422,2.205
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" 配位原子：","4i-Co",": ",-4.5687,-7.4422,6.615
" SP coordinates=",-.193,2,-.854
26," ","4i-Ce","---","4i-Co"," d===",4.5149
"4i-Ce",":",-6.0121,1.3961,0," Z=",2
" SP coordinates=",.63,.5,-.675
" 配位原子：","4i-Co",": ",-2.5611,3.2969,-2.205
" SP coordinates=",.807,0,.146
" 配位原子：","4i-Co",": ",-2.5611,3.2969,2.205
" SP coordinates=",.807,1,.146
"4i-Co",":",-2.5611,3.2969,-2.205," Z=",2
" SP coordinates=",.807,0,.146
" 配位原子：","4i-Ce",": ",-6.0121,1.3961,-4.41
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" 配位原子：","4i-Ce",": ",-6.0121,1.3961,0
" SP coordinates=",.63,.5,-.675
27," ","4i-Al","---","4i-Ce"," d===",4.54
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" 配位原子：","4i-Ce",": ",6.0121,-1.3961,0
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"4i-Ce",":",6.0121,-1.3961,0," Z=",1
" SP coordinates=",.37,.5,1.675
" 配位原子：","4i-Al",": ",2.6491,-4.446,0
" SP coordinates=",.086,.5,.81
28," ","4i-Co","---","4i-Co"," d===",4.7517
"4i-Co",":",-3.9607,8.6665,0," Z=",1
" SP coordinates=",1.307,.5,.146
" 配位原子：","4i-Co",": ",-1.6379,12.8118,0
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"4i-Co",":",-1.6379,12.8118,0," Z=",1
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" 配位原子：","4i-Co",": ",-3.9607,8.6665,0
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29," ","4i-Ce","---","4i-Ce"," d===",4.807
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