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电子理论对话-13：棱形结构和空间群表示约化
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电子理论对话-13：棱形结构和空间群表示约化
余瑞璜EET电子理论的等同键数目（Iα=IM×IS×IK），是其理论的一个专有概念，具有明确的物理内涵，就是为了清点晶体空间中的化学键。
那种持不约化观点的人，对下面的例子就会无所适从。
Fe2O3是一种典型的晶体，空间群为No.176。
176空间群可以选择Hexagonal axes坐标系，对应的原子坐标如下：
12c-Fe和18e-O；
176空间群也可以选择Rhombohedral axes坐标系，对应的原子坐标如下：
4c-Fe和6e-O；
对于前者，不约化观点者取：
IM＝12，对于Fe；IM＝18，对于O；
对于后者，不约化观点者取：
IM＝4，对于Fe；IM＝6，对于O；
显然，两种取法的结果相差3倍！
请问持不约化观点者，对于Fe2O3晶体，其等同键数目究竟等于多少？
余瑞璜的EET电子理论，其计算结果和参照坐标系的选择是没有关系的。
如果把空间群表达式约化到化学式，就会得到相同的结果。
对于Hexagonal axes坐标系:
空间群表达式＝12Fe（12c-Fe）18O（18e-O），约化到化学式，
Fe2O3＝2Fe3O=2Fe（12c-Fe）3（18e-O），得到
IM＝2，对于Fe；IM＝3，对于O.
对于Rhombohedral axes坐标系：
空间群表达式＝4Fe（4c-Fe）6O（6e-O），约化到化学式，就是
Fe2O3＝2Fe3O=2Fe（4c-Fe）3O（6e-O）
IM＝2，对于Fe；IM＝3，对于O.
由此可见，只有把空间群表达式约化到化学式才能使两种情况相等。
凡是没有进行约化的，都是错误的，不符合余瑞璜EET的思想体系。
附录1：Hex坐标系数据（前6条键）
"a=",5.0065,"b=",5.0065,"c=",13.6411,"Delta=",.05 1," The distance of","12c-Fe","and","18e-O"," d===",1.9325 " Coordinates of these two atoms:" " ","12c-Fe",":","Cartesian =",2.5033,10.1197,-2.5782 " SP coordinates=",-.667,1.667,.311 " ","18e-O",":","Cartesian =",3.2642,11.6892,-3.4103 " SP coordinates=",-.696,2,.25 " Neighbors of","12c-Fe","at",2.5033,10.1197,-2.5782,"N=",3,"Is(EET)=",3 " SP coordinates=",-.667,1.667,.311 " Neighbor atom：","18e-O" " Cartesian=",.761,9.9896,-3.4103 " SP coordinates=",-1,1.304,.25 " Neighbor atom：","18e-O" " Cartesian=",3.2642,11.6892,-3.4103 " SP coordinates=",-.696,2,.25 " Neighbor atom：","18e-O" " Cartesian=",3.4845,8.6715,-3.4103 " SP coordinates=",-.304,1.696,.25 " Neighbors of","18e-O","at",3.2642,11.6892,-3.4103,"N=",2,"Is(EET)=",2 " SP coordinates=",-.696,2,.25 " Neighbor atom：","12c-Fe" " Cartesian=",2.5033,10.1197,-2.5782 " SP coordinates=",-.667,1.667,.311 " Neighbor atom：","12c-Fe" " Cartesian=",5.0065,11.5591,-4.2424 " SP coordinates=",-.333,2.333,.189 2," The distance of","18e-O","and","12c-Fe"," d===",2.0899 " Coordinates of these two atoms:" " ","18e-O",":","Cartesian =",1.7423,5.6538,-10.2308 " SP coordinates=",-.304,1,-.25 " ","12c-Fe",":","Cartesian =",2.5032,4.3358,-8.7985 " SP coordinates=",0,1,-.145 " Neighbors of","18e-O","at",1.7423,5.6538,-10.2308,"N=",2,"Is(EET)=",2 " SP coordinates=",-.304,1,-.25 " Neighbor atom：","12c-Fe" " Cartesian=",2.5032,4.3358,-11.6631 " SP coordinates=",0,1,-.355 " Neighbor atom：","12c-Fe" " Cartesian=",2.5032,4.3358,-8.7985 " SP coordinates=",0,1,-.145 " Neighbors of","12c-Fe","at",2.5032,4.3358,-8.7985,"N=",3,"Is(EET)=",3 " SP coordinates=",0,1,-.145 " Neighbor atom：","18e-O" " Cartesian=",1.7423,3.0177,-10.2308 " SP coordinates=",0,.696,-.25 " Neighbor atom：","18e-O" " Cartesian=",1.7423,5.6538,-10.2308 " SP coordinates=",-.304,1,-.25 " Neighbor atom：","18e-O" " Cartesian=",4.0252,4.3358,-10.2308 " SP coordinates=",.304,1.304,-.25 3," The distance of","18e-O","and","18e-O"," d===",2.6361 " Coordinates of these two atoms:" " ","18e-O",":","Cartesian =",3.2642,3.0177,10.2308 " SP coordinates=",.304,1,1.25 " ","18e-O",":","Cartesian =",3.2642,5.6538,10.2308 " SP coordinates=",0,1.304,1.25 " Neighbors of","18e-O","at",3.2642,3.0177,10.2308,"N=",2,"Is(EET)=",2 " SP coordinates=",.304,1,1.25 " Neighbor atom：","18e-O" " Cartesian=",.9813,4.3358,10.2308 " SP coordinates=",-.304,.696,1.25 " Neighbor atom：","18e-O" " Cartesian=",3.2642,5.6538,10.2308 " SP coordinates=",0,1.304,1.25 " Neighbors of","18e-O","at",3.2642,5.6538,10.2308,"N=",2,"Is(EET)=",2 " SP coordinates=",0,1.304,1.25 " Neighbor atom：","18e-O" " Cartesian=",.9813,4.3358,10.2308 " SP coordinates=",-.304,.696,1.25 " Neighbor atom：","18e-O" " Cartesian=",3.2642,3.0177,10.2308 " SP coordinates=",.304,1,1.25 4," The distance of","18e-O","and","18e-O"," d===",2.7427 " Coordinates of these two atoms:" " ","18e-O",":","Cartesian =",1.7398,-8.5458,-1.1322 " SP coordinates=",1.333,-.638,.417 " ","18e-O",":","Cartesian =",3.2667,-8.7972,1.1322 " SP coordinates=",1.667,-.362,.583 " Neighbors of","18e-O","at",1.7398,-8.5458,-1.1322,"N=",2,"Is(EET)=",2 " SP coordinates=",1.333,-.638,.417 " Neighbor atom：","18e-O" " Cartesian=",.761,-7.3534,-3.4103 " SP coordinates=",1,-.696,.25 " Neighbor atom：","18e-O" " Cartesian=",3.2667,-8.7972,1.1322 " SP coordinates=",1.667,-.362,.583 " Neighbors of","18e-O","at",3.2667,-8.7972,1.1322,"N=",2,"Is(EET)=",2 " SP coordinates=",1.667,-.362,.583 " Neighbor atom：","18e-O" " Cartesian=",1.7398,-8.5458,-1.1322 " SP coordinates=",1.333,-.638,.417 " Neighbor atom：","18e-O" " Cartesian=",4.2455,-9.9896,3.4103 " SP coordinates=",2,-.304,.75 5," The distance of","18e-O","and","18e-O"," d===",2.8583 " Coordinates of these two atoms:" " ","18e-O",":","Cartesian =",3.2667,8.5458,14.7733 " SP coordinates=",-.333,1.638,1.583 " ","18e-O",":","Cartesian =",4.0277,10.1153,12.5089 " SP coordinates=",-.362,1.971,1.417 " Neighbors of","18e-O","at",3.2667,8.5458,14.7733,"N=",4,"Is(EET)=",4 " SP coordinates=",-.333,1.638,1.583 " Neighbor atom：","18e-O" " Cartesian=",1.522,8.6715,17.0514 " SP coordinates=",-.696,1.304,1.75 " Neighbor atom：","18e-O" " Cartesian=",4.0277,10.1153,12.5089 " SP coordinates=",-.362,1.971,1.417 " Neighbor atom：","18e-O" " Cartesian=",4.2455,7.102,12.5089 " SP coordinates=",.029,1.667,1.417 " Neighbor atom：","18e-O" " Cartesian=",4.2455,9.9896,17.0514 " SP coordinates=",-.304,2,1.75 " Neighbors of","18e-O","at",4.0277,10.1153,12.5089,"N=",4,"Is(EET)=",4 " SP coordinates=",-.362,1.971,1.417 " Neighbor atom：","18e-O" " Cartesian=",3.2642,11.6892,10.2308 " SP coordinates=",-.696,2,1.25 " Neighbor atom：","18e-O" " Cartesian=",3.2667,8.5458,14.7733 " SP coordinates=",-.333,1.638,1.583 " Neighbor atom：","18e-O" " Cartesian=",5.7675,9.9896,10.2308 " SP coordinates=",0,2.304,1.25 " Neighbor atom：","18e-O" " Cartesian=",5.7675,10.2411,14.7733 " SP coordinates=",-.029,2.333,1.583 6," The distance of","12c-Fe","and","12c-Fe"," d===",2.8646 " Coordinates of these two atoms:" " ","12c-Fe",":","Cartesian =",-5.0065,0,15.6191 " SP coordinates=",-1,-1,1.645 " ","12c-Fe",":","Cartesian =",-5.0065,0,18.4837 " SP coordinates=",-1,-1,1.855 " Neighbors of","12c-Fe","at",-5.0065,0,15.6191,"N=",1,"Is(EET)=",1 " SP coordinates=",-1,-1,1.645 " Neighbor atom：","12c-Fe" " Cartesian=",-5.0065,0,18.4837 " SP coordinates=",-1,-1,1.855 " Neighbors of","12c-Fe","at",-5.0065,0,18.4837,"N=",1,"Is(EET)=",1 " SP coordinates=",-1,-1,1.855 " Neighbor atom：","12c-Fe" " Cartesian=",-5.0065,0,15.6191 " SP coordinates=",-1,-1,1.645 附录2：Rhom坐标系数据（前6条） "a=",5.0065,"b=",5.0065,"c=",13.6411,"Delta=",.05 1," The distance of","6e-O","and","4c-Al"," d===",1.9388 " Coordinates of these two atoms:" " ","6e-O",":","Cartesian =",.761,-1.5724,5.6838 " SP coordinates=",1.25,.554,.946 " ","4c-Al",":","Cartesian =",2.5032,-1.4453,6.525 " SP coordinates=",1.645,.645,.645 " Neighbors of","6e-O","at",.761,-1.5724,5.6838,"N=",2,"Is(EET)=",2 " SP coordinates=",1.25,.554,.946 " Neighbor atom：","4c-Al" " Cartesian=",0,0,4.8426 " SP coordinates=",.855,.855,.855 " Neighbor atom：","4c-Al" " Cartesian=",2.5032,-1.4453,6.525 " SP coordinates=",1.645,.645,.645 " Neighbors of","4c-Al","at",2.5032,-1.4453,6.525,"N=",3,"Is(EET)=",3 " SP coordinates=",1.645,.645,.645 " Neighbor atom：","6e-O" " Cartesian=",.761,-1.5724,5.6838 " SP coordinates=",1.25,.554,.946 " Neighbor atom：","6e-O" " Cartesian=",3.2642,.1272,5.6838 " SP coordinates=",1.554,.946,.25 " Neighbor atom：","6e-O" " Cartesian=",3.4845,-2.8905,5.6838 " SP coordinates=",1.946,.25,.554 2," The distance of","6e-O","and","4c-Al"," d===",2.0899 " Coordinates of these two atoms:" " ","6e-O",":","Cartesian =",1.7423,.1272,-1.1368 " SP coordinates=",.75,.446,.054 " ","4c-Al",":","Cartesian =",2.5032,1.4453,-2.5691 " SP coordinates=",.645,.645,-.355 " Neighbors of","6e-O","at",1.7423,.1272,-1.1368,"N=",2,"Is(EET)=",2 " SP coordinates=",.75,.446,.054 " Neighbor atom：","4c-Al" " Cartesian=",2.5032,1.4453,-2.5691 " SP coordinates=",.645,.645,-.355 " Neighbor atom：","4c-Al" " Cartesian=",2.5032,1.4453,.2956 " SP coordinates=",.855,.855,-.145 " Neighbors of","4c-Al","at",2.5032,1.4453,-2.5691,"N=",3,"Is(EET)=",3 " SP coordinates=",.645,.645,-.355 " Neighbor atom：","6e-O" " Cartesian=",1.7423,.1272,-1.1368 " SP coordinates=",.75,.446,.054 " Neighbor atom：","6e-O" " Cartesian=",1.7423,2.7633,-1.1368 " SP coordinates=",.446,1.054,-.25 " Neighbor atom：","6e-O" " Cartesian=",4.0252,1.4453,-1.1368 " SP coordinates=",1.054,.75,-.554 3," The distance of","6e-O","and","6e-O"," d===",2.636 " Coordinates of these two atoms:" " ","6e-O",":","Cartesian =",.9813,-1.4453,1.1368 " SP coordinates=",.946,.25,.554 " ","6e-O",":","Cartesian =",3.2642,-2.7633,1.1368 " SP coordinates=",1.554,-.054,.25 " Neighbors of","6e-O","at",.9813,-1.4453,1.1368,"N=",2,"Is(EET)=",2 " SP coordinates=",.946,.25,.554 " Neighbor atom：","6e-O" " Cartesian=",3.2642,-2.7633,1.1368 " SP coordinates=",1.554,-.054,.25 " Neighbor atom：","6e-O" " Cartesian=",3.2642,-.1272,1.1368 " SP coordinates=",1.25,.554,-.054 " Neighbors of","6e-O","at",3.2642,-2.7633,1.1368,"N=",2,"Is(EET)=",2 " SP coordinates=",1.554,-.054,.25 " Neighbor atom：","6e-O" " Cartesian=",.9813,-1.4453,1.1368 " SP coordinates=",.946,.25,.554 " Neighbor atom：","6e-O" " Cartesian=",3.2642,-.1272,1.1368 " SP coordinates=",1.25,.554,-.054 4," The distance of","6e-O","and","6e-O"," d===",2.7477 " Coordinates of these two atoms:" " ","6e-O",":","Cartesian =",.9813,-1.4453,1.1368 " SP coordinates=",.946,.25,.554 " ","6e-O",":","Cartesian =",1.522,0,3.4103 " SP coordinates=",1.054,.75,.446 " Neighbors of","6e-O","at",.9813,-1.4453,1.1368,"N=",2,"Is(EET)=",2 " SP coordinates=",.946,.25,.554 " Neighbor atom：","6e-O" " Cartesian=",1.522,-2.8905,-1.1368 " SP coordinates=",1.054,-.25,.446 " Neighbor atom：","6e-O" " Cartesian=",1.522,0,3.4103 " SP coordinates=",1.054,.75,.446 " Neighbors of","6e-O","at",1.522,0,3.4103,"N=",2,"Is(EET)=",2 " SP coordinates=",1.054,.75,.446 " Neighbor atom：","6e-O" " Cartesian=",.9813,-1.4453,1.1368 " SP coordinates=",.946,.25,.554 " Neighbor atom：","6e-O" " Cartesian=",.9813,1.4453,5.6838 " SP coordinates=",.946,1.25,.554 5," The distance of","4c-Al","and","4c-Al"," d===",2.8646 " Coordinates of these two atoms:" " ","4c-Al",":","Cartesian =",2.5032,4.3358,1.978 " SP coordinates=",.645,1.645,-.355 " ","4c-Al",":","Cartesian =",2.5032,4.3358,4.8426 " SP coordinates=",.855,1.855,-.145 " Neighbors of","4c-Al","at",2.5032,4.3358,1.978,"N=",1,"Is(EET)=",1 " SP coordinates=",.645,1.645,-.355 " Neighbor atom：","4c-Al" " Cartesian=",2.5032,4.3358,4.8426 " SP coordinates=",.855,1.855,-.145 " Neighbors of","4c-Al","at",2.5032,4.3358,4.8426,"N=",1,"Is(EET)=",1 " SP coordinates=",.855,1.855,-.145 " Neighbor atom：","4c-Al" " Cartesian=",2.5032,4.3358,1.978 " SP coordinates=",.645,1.645,-.355 6," The distance of","6e-O","and","6e-O"," d===",2.8671 " Coordinates of these two atoms:" " ","6e-O",":","Cartesian =",1.522,0,3.4103 " SP coordinates=",1.054,.75,.446 " ","6e-O",":","Cartesian =",3.2642,.1272,5.6838 " SP coordinates=",1.554,.946,.25 " Neighbors of","6e-O","at",1.522,0,3.4103,"N=",4,"Is(EET)=",4 " SP coordinates=",1.054,.75,.446 " Neighbor atom：","6e-O" " Cartesian=",.761,-1.5724,5.6838 " SP coordinates=",1.25,.554,.946 " Neighbor atom：","6e-O" " Cartesian=",.761,1.5724,1.1368 " SP coordinates=",.554,.946,.25 " Neighbor atom：","6e-O" " Cartesian=",3.2642,-.1272,1.1368 " SP coordinates=",1.25,.554,-.054 " Neighbor atom：","6e-O" " Cartesian=",3.2642,.1272,5.6838 " SP coordinates=",1.554,.946,.25 " Neighbors of","6e-O","at",3.2642,.1272,5.6838,"N=",4,"Is(EET)=",4 " SP coordinates=",1.554,.946,.25 " Neighbor atom：","6e-O" " Cartesian=",1.522,0,3.4103 " SP coordinates=",1.054,.75,.446 " Neighbor atom：","6e-O" " Cartesian=",4.0252,-1.4453,7.9573 " SP coordinates=",2.054,.75,.446 " Neighbor atom：","6e-O" " Cartesian=",4.2455,-1.3181,3.4103 " SP coordinates=",1.75,.446,.054 " Neighbor atom：","6e-O" " Cartesian=",4.2455,1.5724,7.9573 " SP coordinates=",1.75,1.446,.054
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