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Miracle922铜虫 (正式写手)
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【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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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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2楼2010-06-08 03:12:26
quantumor
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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。
3楼2010-06-08 08:01:22
Miracle922
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aylayl08(金币+2):谢谢提示 2010-06-09 16:31:51
aylayl08(金币+2):谢谢提示 2010-06-09 16:31:51
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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 |
4楼2010-06-08 10:36:08
