# [CP2K-user] Using TAMkin with CP2K - how is CP2K diagonalizing the Hessian matrix?

Wed Jun 10 13:56:53 UTC 2020

Dear all,

I would like to use TAMkin (http://molmod.github.io/tamkin/) to compute
thermodynamic properties from the vibrational frequencies computed with
CP2K.
As I have understood it, the way TAMkin works is to read and diagonalize
the Hessian matrix printed in the CP2K output.
When I compare the frequencies obtained with TAMkin with those obtained
with cp2k, the values are not the same (Compare column 2 and 3 in the table
below).

The first task is then to understand how CP2K computes the frequencies. To
investigate this, I copied the Hessian matrix from the CP2K output (printed
below the string "Hessian in cartesian coordinates") and pasted it into
Excel and saved it as a csv file. This file I read into python and
diagonalized the Hessian with numpy. The frequencies I get are different
from those printed in the cp2k output file (compare column 3 and 4 in the
table below).
I have assumed that the units of the Hessian matrix in the cp2k output file
are Ry*bohr-2*kamu-1 (kamu = 1000*amu). This assumption is based on trial
and error; it was what got me closest to the cp2k frequencies.

Table 1: The eight lowest frequencies. There are 48 in total.

frequencies

TAMkin /
cm-1

cp2k /
cm-1

Diag., cp2k Hessian /
cm-1

1

31.1

27.3

32.6

2

38.3

40.8

40.1

3

47.7

51.0

50.2

4

74.7

74.0

78.2

5

82.0

80.0

85.8

6

111.0

109.9

116.3

7

223.7

224.1

234.3

8

245.6

246.3

257.3

What is wrong with my calculation?
What steps should be done to go from the Hessian to the frequencies?

The Hessian in csv format, the python script and the cp2k output file are
attached.

Thanks a lot for your help.

Regards,

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