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小木虫论坛-学术科研互动平台 » 计算模拟区 » 量子化学 » Gaussian » 【讨论】深问：原子轨道对分子轨道的贡献，函数如何如何归属到原子轨道里？
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Miracle922

铜虫 (正式写手)

[交流] 【讨论】深问：原子轨道对分子轨道的贡献，函数如何如何归属到原子轨道里？

在6-311+G(d)基组下，用pop=full得到molecular orbital coefficients，如下所示：


1  Al  1S        
2        2S      
3        3S      
4        4S      
5        5S      
6        6S      
7        7PX   
8        7PY   
9        7PZ     
10        8PX   
11        8PY   
12        8PZ   
13        9PX   
14        9PY   
15        9PZ   
16       10PX  
17       10PY  
18       10PZ   
19       11PX  
20       11PY  
21       11PZ   
22       12S     
23       12PX  
24       12PY  
25       12PZ   
26       13D 0  
27       13D+1
28       13D-1
29       13D+2
30       13D-2

91    Ti  1S  
92        2S   
93        3S     
94        4S     
95        5S     
96        6S     
97        7S     
98        8S     
99        9S      
100       10PX  
101       10PY  
102       10PZ  
103       11PX  
104       11PY  
105       11PZ  
106       12PX  
107       12PY  
108       12PZ  
109       13PX  
110       13PY  
111       13PZ  
112       14PX  
113       14PY  
114       14PZ  
115       15D 0
116       15D+1
117       15D-1
118       15D+2
119       15D-2
120       16D 0
121       16D+1
122       16D-1
123       16D+2
124       16D-2
125       17D 0
126       17D+1
127       17D-1
128       17D+2
129       17D-2
130       18S     
131       19PX  
132       19PY  
133       19PZ  
134       20PX  
135       20PY  
136       20PZ  
137       21D 0
138       21D+1
139       21D-1
140       21D+2
141       21D-2
142       22F 0  
143       22F+1
144       22F-1
145       22F+2
146       22F-2
147       22F+3
148       22F-3

这些(s pd f)函数应该是对应于Al（或Ti)的某一院子轨道，比如说2s,3p,3d之类的，但是查了原始的文献，也可能是没有完全明白，最终没法得到确切的归属，也就是说 第二列应该完全可以归属到具体的原子轨道，比如说上面某一行对应哪个原子的哪个轨道。这个归属起来首先是要确定基组含义，可能涉及到很多内容个，不知道哪位对这方面熟悉，可以讨论下；如果有做这块归属的同行讨论那更好了，很想弄明白这个问题。我以前也看到过一位版主给出了相关的文献，但是还是难以捋顺，对6-311+G(d)这个基组或类似的基组还不是很明白，如有哪位虫友对此感兴趣，可以一起讨论




+++++++++++++++++++++++++++++++++++++++++++++++++

以下是Gaussian 技术支持的回复，希望对感兴趣的虫友有所帮助。

Dr. Xu,
      Thank you for giving us a chance to comment.
      The first and probably least satisfying answer is that you really
cannot make a correspondence between the basis functions used in this
calculation and the atomic orbitals of a QM description of an atom.  The
basis set is a mathematical construction which is much less flexible
than the real orbitals and thus many more functions are included in an
attempt to span the space and linear combinations of these functions,
LCAOs, become the MO functions which solve the SCF equations.  The numbers
on these functions (1S,2S,...7Px,...) have no relation to quantum numbers
but rather enumerate the functions on a given atom, 1-N functions.
      The second answer is that the 6-311++G(d) basis set is constructed
with core type functions formed from fixed linear combinations of simple
or primitive gaussians and in the case of Si the first 2 functions are
intended to reproduce 1S and 2S and the first p functions are 2P(x,y,z).
Then the valence 3S and 3P atomic orbitals are represented by 3s and 4s
from the basis set and 2p(x,y,z) and 3p(x,y,z) where I have used lower
case for basis functions and upper case for atomic orbitals.  The additional
s and p functions contribute to a lesser degree to all of the MOs and
the d functions are polarization functions which only contribute to the
occupied MOs indirectly, mixing in with AO functions on other atoms.  A
similar analysis can be applied to V but neither of these is a one to one
correspondence with the atomic orbitals, nor is it intended as such.
      Perhaps a more useful answer in terms of numerical values is to use
the Pop=Orbitals analysis and look in the Mulliken analysis.  It gives a
breakdown of each MO in terms of s, p, d contributions from various atoms.
You don't get a correspondence with atomic orbitals but you do get the
weight of each atom in a given MO.
      Does this help?
On Mon, Jun 07, 2010 at 10:51:40AM -0400

[ Last edited by Miracle922 on 2010-6-8 at 10:36 ]
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1楼2010-06-07 23:54:37
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fooo

金虫 (正式写手)
★
aylayl08(金币+1):谢谢 2010-06-09 16:31:08
NBO已经明确无误地给出这些信息了，仔细看一下。
引用回帖:
Originally posted by Miracle922 at 2010-06-07 23:54:37:
在6-311+G(d)基组下，用pop=full得到molecular orbital coefficients，如下所示：


1  Al  1S        
2        2S      
3        3S      
4        4S      
5        5S      
6        6S      ...

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2楼2010-06-08 03:12:26
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quantumor

金虫 (著名写手)

快乐兔子

1

除了认真学习一点点量子化学中关于基组的基础知识外，没有太好的简单办法确知你的答案。当然，使用NBO的时候，那你需要先知道NBO是怎么一回事，这也需要学习。
另，坛子里以前似有人提出过类似的问题，不妨搜索、参考一下。
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愿好运与快乐伴随你！
3楼2010-06-08 08:01:22
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Miracle922

铜虫 (正式写手)
★ ★
aylayl08(金币+2):谢谢提示 2010-06-09 16:31:51
以下是Gaussian 技术支持的回复，希望对感兴趣的虫友有所帮助。

Dr. Xu,
      Thank you for giving us a chance to comment.
      The first and probably least satisfying answer is that you really
cannot make a correspondence between the basis functions used in this
calculation and the atomic orbitals of a QM description of an atom.  The
basis set is a mathematical construction which is much less flexible
than the real orbitals and thus many more functions are included in an
attempt to span the space and linear combinations of these functions,
LCAOs, become the MO functions which solve the SCF equations.  The numbers
on these functions (1S,2S,...7Px,...) have no relation to quantum numbers
but rather enumerate the functions on a given atom, 1-N functions.
      The second answer is that the 6-311++G(d) basis set is constructed
with core type functions formed from fixed linear combinations of simple
or primitive gaussians and in the case of Si the first 2 functions are
intended to reproduce 1S and 2S and the first p functions are 2P(x,y,z).
Then the valence 3S and 3P atomic orbitals are represented by 3s and 4s
from the basis set and 2p(x,y,z) and 3p(x,y,z) where I have used lower
case for basis functions and upper case for atomic orbitals.  The additional
s and p functions contribute to a lesser degree to all of the MOs and
the d functions are polarization functions which only contribute to the
occupied MOs indirectly, mixing in with AO functions on other atoms.  A
similar analysis can be applied to V but neither of these is a one to one
correspondence with the atomic orbitals, nor is it intended as such.
      Perhaps a more useful answer in terms of numerical values is to use
the Pop=Orbitals analysis and look in the Mulliken analysis.  It gives a
breakdown of each MO in terms of s, p, d contributions from various atoms.
You don't get a correspondence with atomic orbitals but you do get the
weight of each atom in a given MO.
      Does this help?
On Mon, Jun 07, 2010 at 10:51:40AM -0400
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做到极致，做到细处
4楼2010-06-08 10:36:08
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