博文
对话电子理论-2：分子和晶体
|||
对话余瑞璜电子理论-2：分子和晶体
余瑞璜的EET电子理论里，有一个重要的概念，等同键数（Iα）。
为了清点晶体空间的化学键数目，余瑞璜给出一个公式：
Iα=IM×IS×IK
余瑞璜定义：
如果键两边的原子在空间群占位相同，而且原子序数也相同，则IK＝1；
如果键两边的原子在空间群占位不同，不管原子序数是否相同，则IK＝2；
余瑞璜（张瑞林书）没有论述这么定义的理由和根据。实际上，要回答这个问题，涉及到很复杂的空间理论。对于晶体，现在还没有清点化学键数目的方法，因此，也就没有办法检验余瑞璜的公式是否正确。
不过，上面公式中的IM×IS部分是可检验的，具有明确的物理意义。
对于IK，反正不是1就是2，这是晶体的情况。
余瑞璜先生称自己的理论为“固体与分子经验电子理论”，这也表明，这个理论也可以用于分子。无论多大的分子，其原子数目总是有限的，因此，分子中的键也是有限的，可以一条一条地数出来。
例如，水分子H2O共有3条键，2条H-O键，1条H-H键，除此之外，再没有任何的化学键，如图所示。
对于d1键，一边是O原子，一边是H原子：O原子的（配对）配位数是2，H原子的（配对）配位数是1。注意，水分子的化学式是H2O，写成系数的形式就是H2O＝2H1O，2个H，1个O。
对于d1键，用上面余瑞璜的公式计算，结果如下：
以O为参考原子，Iα=IM×IS×IK＝1×2×2＝4；
以H为参考原子，Iα=IM×IS×IK＝2×1×2＝4；
对于d2键，结果如下：
以左边H为参考原子，Iα=IM×IS×IK＝2×1×1＝2；
以右边H为参考原子，Iα=IM×IS×IK＝2×1×1＝2；
需要强调的是，配位数的概念是针对原子定义的，键没有配位数的概念。键的两边有两个原子，这两个原子的配位数不一定相同，但是，两边的原子都可以是参考原子，求出的键数应该是一样的。自圆其说是任何理论都必须要具备的第一条件。余瑞璜的“等同键数”公式满足这个条件，但是余瑞璜先生把实际情况扩大了2倍，因为4＋2＝6。
有没有一个公式，能求出水分子的键是3条呢？
或者说，如何修改余瑞璜的公式，能求出水分子的等同键数等于3呢？
如果（网友）你认为自己比余瑞璜聪明，就去试试吧！
下面再看一个例子：
足球C60共有90条键，其中，60条d56（五边形/六边形），30条d66（六边形/六边形）。C60的60个原子坐标的对称性都是一样的，完全可以用Ih点群（120个矩阵）一次操作出来。
参考阅读：
http://www.sciencenet.cn/blog/user_content.aspx?id=222885
http://www.sciencenet.cn/blog/user_content.aspx?id=223462
C60的第1键d66=1.39，第2键d56＝1.45。
对于第1键d66，两边C原子（配对）配位数是1；对于第2键d56，两边C原子的（配对）配位数是2。
如果按照余瑞璜的公式，得到的键数是（60＋120）＝180，正好是数出来（90）的2倍。
由此可见，余瑞璜的“等同键数”是实际的键数目的2倍，最少对分子是这样。
这对EET电子理论有什么影响吗？
应该没有什么影响，相当于量子力学波函数的一个归一化因子。
对于晶体的情况，是不是也扩大了2倍？
这是个非常困难的问题，问题的关键是如何清点晶体空间的化学键？
这个问题可以先放一放，就当是个“归一化”因子。
不过，上面公式中的IM×IS部分是可检验的，具有明确的物理意义。
我确定IM×IS的方法和余瑞璜的不同，我的方法具有某种自洽特征。这种自洽特征是建立在“完备性和正确性”的基础之上。我的计算程序能保证所考察的晶体空间中不多一个原子，也不少一个原子，只要实验数据正确，我就能做到每一个原子的坐标正确无误。在这种情况下，扫描计算足够大（如27个晶胞）的晶体空间的原子间距和每一个原子周围的空间配位原子，同时要标记出这些原子的笛卡尔坐标和晶体学坐标。
需要提醒的是，IS是配对配位数，而我的计算程序要给出每一个原子的空间配位数。一般来说，空间配位数大于配对配位数。配对配位数和空间配位数的差别如下图所示：
成键原子的空间配位数：
原子A和原子B被一条键（红线）连结着，A的周围有4个原子，因此，A的空间配位数是4，1个D原子和3个B原子。B的周围有5个原子，因此，B的空间配位数是5，1个C原子和4个A原子。
成键原子的配对配位数：
A和B配对成键，A的周围有3个B原子，因此，A的配对配位数是3；B的周围有4个A原子，因此，B的配对配位数是4。
实际上，空间配位数反映了化学键的“多原子体系”特性，而配对配位数相当于进行了简化，只考虑化学键的“二原子体系”特性。
对于IM，则要根据空间群的原子占位来确定，先举一个例子。
对于Nd2Fe14B晶体，空间群占位如下：
8Nd=4Nd(4f)4Nd(4g)；
4B=4B(4g)；
56Fe=4Fe(4c)4Fe(4e)8Fe(8j1)8Fe(8j2)16Fe(16k1)16Fe(16k2)；
这说明一个晶胞里有4个Nd2Fe14B，即68个原子。
约化之后（除以公因子4），把原子数约化回Nd2Fe14B：
2Nd=1Nd(4f)1Nd(4g)
1B=1B(4g)
14Fe=1Fe(4c)1Fe(4e)2Fe(8j1)2Fe(8j2)4Fe(16k1)4Fe(16k2)
上面3个表达式中，化学元素前面的数字，就是IM的取值。
一条键（A-B）的IM×IS值，无论以A为参考原子，还是以B为参考原子，求得的IM×IS值应该是一样的。这就是一个自洽条件，也是对称性条件。
本次对话文章如下：
TiC和TiN都是NaCl结构，并不是很复杂，但是这篇文章还是漏掉了2条键，如Table 1中红色注释所示。这对EET的计算究竟有多大影响？这需要重新计算才能知道。
下面是TiC的键络数据（7条键）。
"a=",4.24,"b=",4.24,"c=",4.24,"Delta=",.005
1," ","4a-Ti","---","4b-C"," d===",2.12
"4a-Ti",":",-2.12,-2.12,-2.12," Z=",6
" SP coordinates=",0,0,0
" 配位原子：","4b-C",": ",-4.24,-2.12,-2.12
" SP coordinates=",-.5,0,0
" 配位原子：","4b-C",": ",-2.12,-4.24,-2.12
" SP coordinates=",0,-.5,0
" 配位原子：","4b-C",": ",-2.12,-2.12,-4.24
" SP coordinates=",0,0,-.5
" 配位原子：","4b-C",": ",-2.12,-2.12,0
" SP coordinates=",0,0,.5
" 配位原子：","4b-C",": ",-2.12,0,-2.12
" SP coordinates=",0,.5,0
" 配位原子：","4b-C",": ",0,-2.12,-2.12
" SP coordinates=",.5,0,0
"4b-C",":",-2.12,-2.12,0," Z=",6
" SP coordinates=",0,0,.5
" 配位原子：","4a-Ti",": ",-4.24,-2.12,0
" SP coordinates=",-.5,0,.5
" 配位原子：","4a-Ti",": ",-2.12,-4.24,0
" SP coordinates=",0,-.5,.5
" 配位原子：","4a-Ti",": ",-2.12,-2.12,-2.12
" SP coordinates=",0,0,0
" 配位原子：","4a-Ti",": ",-2.12,-2.12,2.12
" SP coordinates=",0,0,1
" 配位原子：","4a-Ti",": ",-2.12,0,0
" SP coordinates=",0,.5,.5
" 配位原子：","4a-Ti",": ",0,-2.12,0
" SP coordinates=",.5,0,.5
2," ","4b-C","---","4b-C"," d===",2.9981
"4b-C",":",-2.12,0,2.12," Z=",12
" SP coordinates=",0,.5,1
" 配位原子：","4b-C",": ",-4.24,-2.12,2.12
" SP coordinates=",-.5,0,1
" 配位原子：","4b-C",": ",-4.24,0,0
" SP coordinates=",-.5,.5,.5
" 配位原子：","4b-C",": ",-4.24,0,4.24
" SP coordinates=",-.5,.5,1.5
" 配位原子：","4b-C",": ",-4.24,2.12,2.12
" SP coordinates=",-.5,1,1
" 配位原子：","4b-C",": ",-2.12,-2.12,0
" SP coordinates=",0,0,.5
" 配位原子：","4b-C",": ",-2.12,-2.12,4.24
" SP coordinates=",0,0,1.5
" 配位原子：","4b-C",": ",-2.12,2.12,0
" SP coordinates=",0,1,.5
" 配位原子：","4b-C",": ",-2.12,2.12,4.24
" SP coordinates=",0,1,1.5
" 配位原子：","4b-C",": ",0,-2.12,2.12
" SP coordinates=",.5,0,1
" 配位原子：","4b-C",": ",0,0,0
" SP coordinates=",.5,.5,.5
" 配位原子：","4b-C",": ",0,0,4.24
" SP coordinates=",.5,.5,1.5
" 配位原子：","4b-C",": ",0,2.12,2.12
" SP coordinates=",.5,1,1
"4b-C",":",0,0,0," Z=",12
" SP coordinates=",.5,.5,.5
" 配位原子：","4b-C",": ",-2.12,-2.12,0
" SP coordinates=",0,0,.5
" 配位原子：","4b-C",": ",-2.12,0,-2.12
" SP coordinates=",0,.5,0
" 配位原子：","4b-C",": ",-2.12,0,2.12
" SP coordinates=",0,.5,1
" 配位原子：","4b-C",": ",-2.12,2.12,0
" SP coordinates=",0,1,.5
" 配位原子：","4b-C",": ",0,-2.12,-2.12
" SP coordinates=",.5,0,0
" 配位原子：","4b-C",": ",0,-2.12,2.12
" SP coordinates=",.5,0,1
" 配位原子：","4b-C",": ",0,2.12,-2.12
" SP coordinates=",.5,1,0
" 配位原子：","4b-C",": ",0,2.12,2.12
" SP coordinates=",.5,1,1
" 配位原子：","4b-C",": ",2.12,-2.12,0
" SP coordinates=",1,0,.5
" 配位原子：","4b-C",": ",2.12,0,-2.12
" SP coordinates=",1,.5,0
" 配位原子：","4b-C",": ",2.12,0,2.12
" SP coordinates=",1,.5,1
" 配位原子：","4b-C",": ",2.12,2.12,0
" SP coordinates=",1,1,.5
3," ","4a-Ti","---","4a-Ti"," d===",2.9981
"4a-Ti",":",-2.12,-2.12,-2.12," Z=",12
" SP coordinates=",0,0,0
" 配位原子：","4a-Ti",": ",-4.24,-4.24,-2.12
" SP coordinates=",-.5,-.5,0
" 配位原子：","4a-Ti",": ",-4.24,-2.12,-4.24
" SP coordinates=",-.5,0,-.5
" 配位原子：","4a-Ti",": ",-4.24,-2.12,0
" SP coordinates=",-.5,0,.5
" 配位原子：","4a-Ti",": ",-4.24,0,-2.12
" SP coordinates=",-.5,.5,0
" 配位原子：","4a-Ti",": ",-2.12,-4.24,-4.24
" SP coordinates=",0,-.5,-.5
" 配位原子：","4a-Ti",": ",-2.12,-4.24,0
" SP coordinates=",0,-.5,.5
" 配位原子：","4a-Ti",": ",-2.12,0,-4.24
" SP coordinates=",0,.5,-.5
" 配位原子：","4a-Ti",": ",-2.12,0,0
" SP coordinates=",0,.5,.5
" 配位原子：","4a-Ti",": ",0,-4.24,-2.12
" SP coordinates=",.5,-.5,0
" 配位原子：","4a-Ti",": ",0,-2.12,-4.24
" SP coordinates=",.5,0,-.5
" 配位原子：","4a-Ti",": ",0,-2.12,0
" SP coordinates=",.5,0,.5
" 配位原子：","4a-Ti",": ",0,0,-2.12
" SP coordinates=",.5,.5,0
"4a-Ti",":",-2.12,0,0," Z=",12
" SP coordinates=",0,.5,.5
" 配位原子：","4a-Ti",": ",-4.24,-2.12,0
" SP coordinates=",-.5,0,.5
" 配位原子：","4a-Ti",": ",-4.24,0,-2.12
" SP coordinates=",-.5,.5,0
" 配位原子：","4a-Ti",": ",-4.24,0,2.12
" SP coordinates=",-.5,.5,1
" 配位原子：","4a-Ti",": ",-4.24,2.12,0
" SP coordinates=",-.5,1,.5
" 配位原子：","4a-Ti",": ",-2.12,-2.12,-2.12
" SP coordinates=",0,0,0
" 配位原子：","4a-Ti",": ",-2.12,-2.12,2.12
" SP coordinates=",0,0,1
" 配位原子：","4a-Ti",": ",-2.12,2.12,-2.12
" SP coordinates=",0,1,0
" 配位原子：","4a-Ti",": ",-2.12,2.12,2.12
" SP coordinates=",0,1,1
" 配位原子：","4a-Ti",": ",0,-2.12,0
" SP coordinates=",.5,0,.5
" 配位原子：","4a-Ti",": ",0,0,-2.12
" SP coordinates=",.5,.5,0
" 配位原子：","4a-Ti",": ",0,0,2.12
" SP coordinates=",.5,.5,1
" 配位原子：","4a-Ti",": ",0,2.12,0
" SP coordinates=",.5,1,.5
4," ","4a-Ti","---","4b-C"," d===",3.6719
"4a-Ti",":",2.12,0,0," Z=",8
" SP coordinates=",1,.5,.5
" 配位原子：","4b-C",": ",0,-2.12,-2.12
" SP coordinates=",.5,0,0
" 配位原子：","4b-C",": ",0,-2.12,2.12
" SP coordinates=",.5,0,1
" 配位原子：","4b-C",": ",0,2.12,-2.12
" SP coordinates=",.5,1,0
" 配位原子：","4b-C",": ",0,2.12,2.12
" SP coordinates=",.5,1,1
" 配位原子：","4b-C",": ",4.24,-2.12,-2.12
" SP coordinates=",1.5,0,0
" 配位原子：","4b-C",": ",4.24,-2.12,2.12
" SP coordinates=",1.5,0,1
" 配位原子：","4b-C",": ",4.24,2.12,-2.12
" SP coordinates=",1.5,1,0
" 配位原子：","4b-C",": ",4.24,2.12,2.12
" SP coordinates=",1.5,1,1
"4b-C",":",4.24,2.12,-2.12," Z=",8
" SP coordinates=",1.5,1,0
" 配位原子：","4a-Ti",": ",2.12,0,-4.24
" SP coordinates=",1,.5,-.5
" 配位原子：","4a-Ti",": ",2.12,0,0
" SP coordinates=",1,.5,.5
" 配位原子：","4a-Ti",": ",2.12,4.24,-4.24
" SP coordinates=",1,1.5,-.5
" 配位原子：","4a-Ti",": ",2.12,4.24,0
" SP coordinates=",1,1.5,.5
" 配位原子：","4a-Ti",": ",6.36,0,-4.24
" SP coordinates=",2,.5,-.5
" 配位原子：","4a-Ti",": ",6.36,0,0
" SP coordinates=",2,.5,.5
" 配位原子：","4a-Ti",": ",6.36,4.24,-4.24
" SP coordinates=",2,1.5,-.5
" 配位原子：","4a-Ti",": ",6.36,4.24,0
" SP coordinates=",2,1.5,.5
5," ","4b-C","---","4b-C"," d===",4.24
"4b-C",":",2.12,2.12,0," Z=",6
" SP coordinates=",1,1,.5
" 配位原子：","4b-C",": ",-2.12,2.12,0
" SP coordinates=",0,1,.5
" 配位原子：","4b-C",": ",2.12,-2.12,0
" SP coordinates=",1,0,.5
" 配位原子：","4b-C",": ",2.12,2.12,-4.24
" SP coordinates=",1,1,-.5
" 配位原子：","4b-C",": ",2.12,2.12,4.24
" SP coordinates=",1,1,1.5
" 配位原子：","4b-C",": ",2.12,6.36,0
" SP coordinates=",1,2,.5
" 配位原子：","4b-C",": ",6.36,2.12,0
" SP coordinates=",2,1,.5
"4b-C",":",6.36,2.12,0," Z=",6
" SP coordinates=",2,1,.5
" 配位原子：","4b-C",": ",2.12,2.12,0
" SP coordinates=",1,1,.5
" 配位原子：","4b-C",": ",6.36,-2.12,0
" SP coordinates=",2,0,.5
" 配位原子：","4b-C",": ",6.36,2.12,-4.24
" SP coordinates=",2,1,-.5
" 配位原子：","4b-C",": ",6.36,2.12,4.24
" SP coordinates=",2,1,1.5
" 配位原子：","4b-C",": ",6.36,6.36,0
" SP coordinates=",2,2,.5
" 配位原子：","4b-C",": ",10.6,2.12,0
" SP coordinates=",3,1,.5
6," ","4a-Ti","---","4a-Ti"," d===",4.24
"4a-Ti",":",-2.12,-2.12,-2.12," Z=",6
" SP coordinates=",0,0,0
" 配位原子：","4a-Ti",": ",-6.36,-2.12,-2.12
" SP coordinates=",-1,0,0
" 配位原子：","4a-Ti",": ",-2.12,-6.36,-2.12
" SP coordinates=",0,-1,0
" 配位原子：","4a-Ti",": ",-2.12,-2.12,-6.36
" SP coordinates=",0,0,-1
" 配位原子：","4a-Ti",": ",-2.12,-2.12,2.12
" SP coordinates=",0,0,1
" 配位原子：","4a-Ti",": ",-2.12,2.12,-2.12
" SP coordinates=",0,1,0
" 配位原子：","4a-Ti",": ",2.12,-2.12,-2.12
" SP coordinates=",1,0,0
"4a-Ti",":",-2.12,2.12,-2.12," Z=",6
" SP coordinates=",0,1,0
" 配位原子：","4a-Ti",": ",-6.36,2.12,-2.12
" SP coordinates=",-1,1,0
" 配位原子：","4a-Ti",": ",-2.12,-2.12,-2.12
" SP coordinates=",0,0,0
" 配位原子：","4a-Ti",": ",-2.12,2.12,-6.36
" SP coordinates=",0,1,-1
" 配位原子：","4a-Ti",": ",-2.12,2.12,2.12
" SP coordinates=",0,1,1
" 配位原子：","4a-Ti",": ",-2.12,6.36,-2.12
" SP coordinates=",0,2,0
" 配位原子：","4a-Ti",": ",2.12,2.12,-2.12
" SP coordinates=",1,1,0
7," ","4b-C","---","4a-Ti"," d===",4.7405
"4b-C",":",-2.12,-2.12,0," Z=",24
" SP coordinates=",0,0,.5
" 配位原子：","4a-Ti",": ",-6.36,-4.24,0
" SP coordinates=",-1,-.5,.5
" 配位原子：","4a-Ti",": ",-6.36,-2.12,-2.12
" SP coordinates=",-1,0,0
" 配位原子：","4a-Ti",": ",-6.36,-2.12,2.12
" SP coordinates=",-1,0,1
" 配位原子：","4a-Ti",": ",-6.36,0,0
" SP coordinates=",-1,.5,.5
" 配位原子：","4a-Ti",": ",-4.24,-6.36,0
" SP coordinates=",-.5,-1,.5
" 配位原子：","4a-Ti",": ",-4.24,-2.12,-4.24
" SP coordinates=",-.5,0,-.5
" 配位原子：","4a-Ti",": ",-4.24,-2.12,4.24
" SP coordinates=",-.5,0,1.5
" 配位原子：","4a-Ti",": ",-4.24,2.12,0
" SP coordinates=",-.5,1,.5
" 配位原子：","4a-Ti",": ",-2.12,-6.36,-2.12
" SP coordinates=",0,-1,0
" 配位原子：","4a-Ti",": ",-2.12,-6.36,2.12
" SP coordinates=",0,-1,1
" 配位原子：","4a-Ti",": ",-2.12,-4.24,-4.24
" SP coordinates=",0,-.5,-.5
" 配位原子：","4a-Ti",": ",-2.12,-4.24,4.24
" SP coordinates=",0,-.5,1.5
" 配位原子：","4a-Ti",": ",-2.12,0,-4.24
" SP coordinates=",0,.5,-.5
" 配位原子：","4a-Ti",": ",-2.12,0,4.24
" SP coordinates=",0,.5,1.5
" 配位原子：","4a-Ti",": ",-2.12,2.12,-2.12
" SP coordinates=",0,1,0
" 配位原子：","4a-Ti",": ",-2.12,2.12,2.12
" SP coordinates=",0,1,1
" 配位原子：","4a-Ti",": ",0,-6.36,0
" SP coordinates=",.5,-1,.5
" 配位原子：","4a-Ti",": ",0,-2.12,-4.24
" SP coordinates=",.5,0,-.5
" 配位原子：","4a-Ti",": ",0,-2.12,4.24
" SP coordinates=",.5,0,1.5
" 配位原子：","4a-Ti",": ",0,2.12,0
" SP coordinates=",.5,1,.5
" 配位原子：","4a-Ti",": ",2.12,-4.24,0
" SP coordinates=",1,-.5,.5
" 配位原子：","4a-Ti",": ",2.12,-2.12,-2.12
" SP coordinates=",1,0,0
" 配位原子：","4a-Ti",": ",2.12,-2.12,2.12
" SP coordinates=",1,0,1
" 配位原子：","4a-Ti",": ",2.12,0,0
" SP coordinates=",1,.5,.5
"4a-Ti",":",0,2.12,0," Z=",24
" SP coordinates=",.5,1,.5
" 配位原子：","4b-C",": ",-4.24,0,0
" SP coordinates=",-.5,.5,.5
" 配位原子：","4b-C",": ",-4.24,2.12,-2.12
" SP coordinates=",-.5,1,0
" 配位原子：","4b-C",": ",-4.24,2.12,2.12
" SP coordinates=",-.5,1,1
" 配位原子：","4b-C",": ",-4.24,4.24,0
" SP coordinates=",-.5,1.5,.5
" 配位原子：","4b-C",": ",-2.12,-2.12,0
" SP coordinates=",0,0,.5
" 配位原子：","4b-C",": ",-2.12,2.12,-4.24
" SP coordinates=",0,1,-.5
" 配位原子：","4b-C",": ",-2.12,2.12,4.24
" SP coordinates=",0,1,1.5
" 配位原子：","4b-C",": ",-2.12,6.36,0
" SP coordinates=",0,2,.5
" 配位原子：","4b-C",": ",0,-2.12,-2.12
" SP coordinates=",.5,0,0
" 配位原子：","4b-C",": ",0,-2.12,2.12
" SP coordinates=",.5,0,1
" 配位原子：","4b-C",": ",0,0,-4.24
" SP coordinates=",.5,.5,-.5
" 配位原子：","4b-C",": ",0,0,4.24
" SP coordinates=",.5,.5,1.5
" 配位原子：","4b-C",": ",0,4.24,-4.24
" SP coordinates=",.5,1.5,-.5
" 配位原子：","4b-C",": ",0,4.24,4.24
" SP coordinates=",.5,1.5,1.5
" 配位原子：","4b-C",": ",0,6.36,-2.12
" SP coordinates=",.5,2,0
" 配位原子：","4b-C",": ",0,6.36,2.12
" SP coordinates=",.5,2,1
" 配位原子：","4b-C",": ",2.12,-2.12,0
" SP coordinates=",1,0,.5
" 配位原子：","4b-C",": ",2.12,2.12,-4.24
" SP coordinates=",1,1,-.5
" 配位原子：","4b-C",": ",2.12,2.12,4.24
" SP coordinates=",1,1,1.5
" 配位原子：","4b-C",": ",2.12,6.36,0
" SP coordinates=",1,2,.5
" 配位原子：","4b-C",": ",4.24,0,0
" SP coordinates=",1.5,.5,.5
" 配位原子：","4b-C",": ",4.24,2.12,-2.12
" SP coordinates=",1.5,1,0
" 配位原子：","4b-C",": ",4.24,2.12,2.12
" SP coordinates=",1.5,1,1
" 配位原子：","4b-C",": ",4.24,4.24,0
" SP coordinates=",1.5,1.5,.5
https://blog.sciencenet.cn/blog-2321-269664.html
上一篇：干女儿：权势老男人的性福番号
下一篇：对话电子理论-3：老外的刊物VS刊物的老外
