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shardineblog木虫 (正式写手)
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【求助】谁来帮忙说一下对关联函数的定义。
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突然想要一个有关对关联函数的准确定义了，可是百度了，也google了，竟然没有找到，痛苦啊，。 记得以前我曾经下过一个图，其中有关于对关联函数部分的说明，还是英文的，可惜上次机器硬盘坏了，全丢了。相当的痛苦啊。 现在想找一下定义了，大家来帮帮忙啊。先提前谢谢了。 [ Last edited by freshgirl on 2009-6-28 at 21:54 ] |
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aylayl08
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lei0736(金币+4,VIP+0):谢谢 鼓励新人
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是指交换关联函数吗？Hohenberg和Kohn在非均匀电子气理论基础上提出并证明的两个定理构成了DFT的严格理论基础，其中定理二推导式中有一项为Exc[n],交换关联相互作用项，包括了未包含在无相互作用粒子模型中的所有相互作用，它即是基态电子密度n(r)的泛函。之后Kohn和沈吕九又将HK方程发展为KS方程，它将来自交换和关联的所有多体效应都包括在一个未知泛函中，即交换关联能泛函Exc[n]，其明确物理意义是一个电子在多电子系统中运动时与其它电子间的静电相互作用所产生的能量，被拆成两项处理交换项和关联项；交换项考虑到电子的费米子特性，即自旋相同电子间因泡利不相容原理而产生排斥作用引起的能量。交换关联泛函依赖于整个空间的电子密度分布，求解起来非常困难，因此目前还没有得到准确形式，故有了各种近似方法如LDA、GGA和HDA等 [ Last edited by aylayl08 on 2008-4-6 at 14:33 ] |
2楼2008-04-06 14:29:10
shardineblog
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3楼2008-04-06 14:34:26
shardineblog
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lei0736(金币+3,VIP+0):谢谢详细解答
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刚才找到了。。。 在这里粘一下。。。 This is related to the probability of finding the center of a particle a given distance from the center of another particle. For short distances, this is related to how the particles are packed together. For example, consider hard spheres (like marbles). The spheres can't overlap, so the closest distance two centers can be is equal to the diameter of the spheres. However, several spheres can be touching one sphere; then a few more can form a layer around them, and so on. Further away, these layers get more diffuse, and so for large distances, the probability of finding two spheres with a given separation is essentially constant. In that case, it's related to the density -- a more dense system has more spheres, thus it's more likely to find two of them with a given distance. The pair correlation function g(r) accounts for these factors by normalizing by the density; thus at large values of r it goes to 1, uniform probability. The right picture above shows g(r) calculated for a simple simulation of two-dimensional disks. The function is calculated based on all pairs of particles, but to make it clear I've highlighted one reference particle (black) in the left picture. The surrounding particles are colored based on their distance from the black particle, and correspond to the graph of g(r) on the right. Thus for example about 5 particles are colored purple, and correspond to the prominent peak at a separation of 1 diameter. A couple particles are dark blue, corresponding to the less-likely position about 1.5 diameters away. Several more particles are light blue, corresponding to the 2nd nearest neighbor peak at about 2 diameters. Further away, the green particles form the third nearest neighbors, and the yellow particles form the fourth nearest neighbors. Note of course that this is all a little ambiguous; actually the colors shade continuously just as the distances between particles shade continuously. Nonetheless, there is a lot of structure here that results in the characteristic shape of g(r). All of the particles farther away are colored red, and you can see that g(r) tends toward a uniform value of 1 for large values of r. (Note that this happens even though the number of particles you're finding gets larger, for example, consider the yellow particles in the picture.) |
4楼2008-04-06 14:39:44
aylayl08
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5楼2008-04-06 15:07:26
6楼2008-04-07 08:32:56
cuihang
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7楼2008-04-07 09:14:17