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xixi1007

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[求助] gaussian计算频率时输出的hessian是那一部分啊

我用水做一例子计算hessian矩阵。以下是输出文件中的一部分，但是不太清楚哪部分是。是最后的 Hessian after L703:后面的吗。是的话，水的话其hessian矩阵是9*9的吗，那么它上三角的内容是什么呢。还有下面出现的D是什么意思啊。是我们平常说的指数e吗？
Hessian from J:
            1          2          3          4          5
   1  0.000000D+00
   2  0.000000D+00  0.000000D+00
   3  0.000000D+00  0.000000D+00  0.000000D+00
   4  0.000000D+00  0.000000D+00  0.000000D+00 -0.441362D+01
   5  0.000000D+00  0.000000D+00  0.000000D+00  0.000000D+00 -0.948350D+00
   6  0.000000D+00  0.000000D+00  0.000000D+00  0.000000D+00  0.000000D+00
   7  0.000000D+00  0.000000D+00  0.000000D+00  0.220681D+01  0.000000D+00
   8  0.000000D+00  0.000000D+00  0.000000D+00  0.000000D+00  0.474175D+00
   9  0.000000D+00  0.000000D+00  0.000000D+00  0.000000D+00  0.121877D+01
   10  0.000000D+00  0.000000D+00  0.000000D+00  0.220681D+01  0.000000D+00
   11  0.000000D+00  0.000000D+00  0.000000D+00  0.000000D+00  0.474175D+00
   12  0.000000D+00  0.000000D+00  0.000000D+00  0.000000D+00 -0.121877D+01
            6          7          8          9          10
   6 -0.273959D+01
   7  0.000000D+00 -0.214794D+01
   8  0.121674D+01  0.000000D+00 -0.602963D+00
   9  0.136980D+01  0.000000D+00 -0.121776D+01 -0.129566D+01
   10  0.000000D+00 -0.588633D-01  0.000000D+00  0.000000D+00 -0.214794D+01
   11 -0.121674D+01  0.000000D+00  0.128788D+00 -0.101712D-02  0.000000D+00
   12  0.136980D+01  0.000000D+00  0.101712D-02 -0.741375D-01  0.000000D+00
            11          12
   11 -0.602963D+00
   12  0.121776D+01 -0.129566D+01
Force constants from FoF:
            1          2          3          4          5
   1  0.000000D+00
   2  0.000000D+00  0.000000D+00
   3  0.000000D+00  0.000000D+00  0.000000D+00
   4  0.000000D+00  0.000000D+00  0.000000D+00 -0.441362D+01
   5  0.000000D+00  0.000000D+00  0.000000D+00  0.000000D+00 -0.948350D+00
   6  0.000000D+00  0.000000D+00  0.000000D+00  0.000000D+00  0.000000D+00
   7  0.000000D+00  0.000000D+00  0.000000D+00  0.220681D+01  0.000000D+00
   8  0.000000D+00  0.000000D+00  0.000000D+00  0.000000D+00  0.474175D+00
   9  0.000000D+00  0.000000D+00  0.000000D+00  0.000000D+00  0.121877D+01
   10  0.000000D+00  0.000000D+00  0.000000D+00  0.220681D+01  0.000000D+00
   11  0.000000D+00  0.000000D+00  0.000000D+00  0.000000D+00  0.474175D+00
   12  0.000000D+00  0.000000D+00  0.000000D+00  0.000000D+00 -0.121877D+01
            6          7          8          9          10
   6 -0.273959D+01
   7  0.000000D+00 -0.214794D+01
   8  0.121674D+01  0.000000D+00 -0.602963D+00
   9  0.136980D+01  0.000000D+00 -0.121776D+01 -0.129566D+01
   10  0.000000D+00 -0.588633D-01  0.000000D+00  0.000000D+00 -0.214794D+01
   11 -0.121674D+01  0.000000D+00  0.128788D+00 -0.101712D-02  0.000000D+00
   12  0.136980D+01  0.000000D+00  0.101712D-02 -0.741375D-01  0.000000D+00
            11          12
   11 -0.602963D+00
   12  0.121776D+01 -0.129566D+01
Second derivatives from L703 IAtSt=0:
            1          2          3          4          5
   1  0.000000D+00
   2  0.000000D+00  0.000000D+00
   3  0.000000D+00  0.000000D+00  0.000000D+00
   4  0.000000D+00  0.000000D+00  0.000000D+00 -0.441362D+01
   5  0.000000D+00  0.000000D+00  0.000000D+00  0.000000D+00 -0.948350D+00
   6  0.000000D+00  0.000000D+00  0.000000D+00  0.000000D+00  0.000000D+00
   7  0.000000D+00  0.000000D+00  0.000000D+00  0.220681D+01  0.000000D+00
   8  0.000000D+00  0.000000D+00  0.000000D+00  0.000000D+00  0.474175D+00
   9  0.000000D+00  0.000000D+00  0.000000D+00  0.000000D+00  0.121877D+01
   10  0.000000D+00  0.000000D+00  0.000000D+00  0.220681D+01  0.000000D+00
   11  0.000000D+00  0.000000D+00  0.000000D+00  0.000000D+00  0.474175D+00
   12  0.000000D+00  0.000000D+00  0.000000D+00  0.000000D+00 -0.121877D+01
            6          7          8          9          10
   6 -0.273959D+01
   7  0.000000D+00 -0.214794D+01
   8  0.121674D+01  0.000000D+00 -0.602963D+00
   9  0.136980D+01  0.000000D+00 -0.121776D+01 -0.129566D+01
   10  0.000000D+00 -0.588633D-01  0.000000D+00  0.000000D+00 -0.214794D+01
   11 -0.121674D+01  0.000000D+00  0.128788D+00 -0.101712D-02  0.000000D+00
   12  0.136980D+01  0.000000D+00  0.101712D-02 -0.741375D-01  0.000000D+00
            11          12
   11 -0.602963D+00
   12  0.121776D+01 -0.129566D+01
Polarizability into L703:
            1          2          3
   1  0.783222D+00
   2  0.000000D+00  0.680812D+01
   3  0.000000D+00  0.000000D+00  0.362564D+01
Polarizability after L703:
            1          2          3
   1  0.783222D+00
   2  0.000000D+00  0.680812D+01
   3  0.000000D+00  0.000000D+00  0.362564D+01
Dipole Derivatives into L703:
               1          2          3          4          5
   1  -0.871467D+00  0.000000D+00  0.000000D+00  0.435734D+00  0.000000D+00
   2 0.000000D+00 -0.387147D+00  0.000000D+00  0.000000D+00  0.193574D+00
   3 0.000000D+00  0.000000D+00 -0.329661D+00  0.000000D+00  0.103814D+00
               6          7          8          9
   1 0.000000D+00  0.435734D+00  0.000000D+00  0.000000D+00
   2 0.176832D+00  0.000000D+00  0.193574D+00 -0.176832D+00
   3 0.164831D+00  0.000000D+00 -0.103814D+00  0.164831D+00
Dipole Derivatives after L703:
               1          2          3          4          5
   1  -0.871467D+00  0.000000D+00  0.000000D+00  0.435734D+00  0.000000D+00
   2 0.000000D+00 -0.387147D+00  0.000000D+00  0.000000D+00  0.193574D+00
   3 0.000000D+00  0.000000D+00 -0.329661D+00  0.000000D+00  0.103814D+00
               6          7          8          9
   1 0.000000D+00  0.435734D+00  0.000000D+00  0.000000D+00
   2 0.176832D+00  0.000000D+00  0.193574D+00 -0.176832D+00
   3 0.164831D+00  0.000000D+00 -0.103814D+00  0.164831D+00
Hessian into L703:
            1          2          3          4          5
   1  0.441373D+01
   2  0.000000D+00  0.166319D+01
   3  0.000000D+00  0.000000D+00  0.317440D+01
   4 -0.220687D+01  0.000000D+00  0.000000D+00  0.214806D+01
   5  0.000000D+00 -0.831595D+00 -0.103436D+01  0.000000D+00  0.997733D+00
   6  0.000000D+00 -0.957818D+00 -0.158720D+01  0.000000D+00  0.996090D+00
   7 -0.220687D+01  0.000000D+00  0.000000D+00  0.588069D-01  0.000000D+00
   8  0.000000D+00 -0.831595D+00  0.103436D+01  0.000000D+00 -0.166139D+00
   9  0.000000D+00  0.957818D+00 -0.158720D+01  0.000000D+00  0.382723D-01
            6          7          8          9
   6  0.149973D+01
   7  0.000000D+00  0.214806D+01
   8 -0.382723D-01  0.000000D+00  0.997733D+00
   9  0.874759D-01  0.000000D+00 -0.996090D+00  0.149973D+01
Hessian after L703:
            1          2          3          4          5
   1  0.117370D-03
   2  0.000000D+00  0.714839D+00
   3  0.000000D+00  0.000000D+00  0.434810D+00
   4 -0.586851D-04  0.000000D+00  0.000000D+00  0.115086D-03
   5  0.000000D+00 -0.357419D+00  0.182376D+00  0.000000D+00  0.394771D+00
   6  0.000000D+00  0.260955D+00 -0.217405D+00  0.000000D+00 -0.221665D+00
   7 -0.586851D-04  0.000000D+00  0.000000D+00 -0.564006D-04  0.000000D+00
   8  0.000000D+00 -0.357419D+00 -0.182376D+00  0.000000D+00 -0.373513D-01
   9  0.000000D+00 -0.260955D+00 -0.217405D+00  0.000000D+00  0.392894D-01
            6          7          8          9
   6  0.204067D+00
   7  0.000000D+00  0.115086D-03
   8 -0.392894D-01  0.000000D+00  0.394771D+00
   9  0.133384D-01  0.000000D+00  0.221665D+00  0.204067D+00

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1楼 2015-04-09 14:49:42

已阅回复此楼关注TA 给TA发消息送TA红花 TA的回帖

xixi1007

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送红花一朵

引用回帖:

9楼: Originally posted by beefly at 2015-04-16 23:54:10
M^1/2 * hessian * M^1/2就是质量加权的hessian。M是原子量矩阵。Matlab语言的写法是
sqrtm(M) * hessian * sqrtm(M)。

有的对角化程序不需要提前计算质量加权的hessian。Matlab命令：
=eig(hessian,M); q=d ...

您好！我以NMA分子为例计算了此分子的振动频率和hessian矩阵，如下图所示，第一列是gaussian计算得到的30个振动模式的频率。第二列是将Hessian after L703后面的矩阵对角化后取其中最后的30个本征值，第二例是将Force constants in Cartesian coordinates后面的矩阵对角化后取其中最后的30个本征值，可以看出这两列的值是非常相近的，但其本证矢量是不一样的。所以我不确定这两个哪一个是质量加权的hessian矩阵。
另外,图中第四列是第一例和第二例的比值，如按您所说5140.48715246*sqrt(q)就是转换成波数单位的振动频率，那这个比值应该是5140.48715246，可这里显然不是啊。
同时，Vibrational analysis in Gussian 中说，将质量加权的hessian矩阵对角化后，其本征值就是基本频率，之后gaussian将其转换成波数的单位cm-1并输出。如果是这样的话，第四列也应该是一个常数啊，起码应该比较相近吧。