Calculation of the Hesse-Matrix

There are two keywords (`HESSE` and `SELHESSE`) which control the
calculation of the cartesian force constant Hesse-Matrix.
Such a Hesse-Matrix can be used later to calculate a IR vibrational spectrum.
The approximation of the Hesse-Matrix
is done by finite differences of the first derivatives of the total energy *E*.
This is either done via a one point approximation

or a two point approximation

, whereas *d* denotes the step-length of each finite differene step in x, y and z
direction.
With the keyword `HESSE` one can select between one of the two modes
and set the step length given in Å. The keyword `SELHESSE` is
manditatory and is used to specify a set of atoms for which the
Hesse-Matrix should be calculated. Example:

`HESSE 2 0.01
SELHESSE A*
`
In that example all atoms are selected for the calculation of the Hesse-Matrix.
The calculation is done by the two point approximation and uses a step length
of 0.01Å.
In the output-directory of EGO the file hesse.out is created with the
corresponding Hesse-Matrix. The dimension of the elements in the Hesse-Matrix is

Note: Features which will affect the proper calculation of the Hesse-Matrix, like, e.g., Minimization, Equilibration or SHAKE are automatically switched off. Furthermore, the number of steps necessary to perform the calculation of the Hesse-Matrix is set automatically.

The Hesse-Matrix is stored in the file hesse.out. The header of that contains the atoms with their masses and positions. So, if you like to investigate isotipoc effects you just have to change the masses here in the file. After the keyword Matrix the hesse-matrix follows. Note: If you choose many atoms for a hesse-calulation the lines in that file get very long and some ASCII editors (like the good old vi will not work properly and will destroy the file).

It is also possible to restart a hesse calculation. Just restart again normally. EGO will look in the hesse.out file and will see how far it is. If it is not completed it will restart at the right point. EGO recognizes the status of the hesse-calcualtion from two numbers in the first line after the number of atoms. If it is not completed there will be for example 3 1 2 The first number specifies the number of atoms for which the hesse matrix should be calulated. The second number specifies the atom which is currently is moved and the third number specifies in which direction it is moved. Once it is completed only the number of atoms will be left.

Example for a completed hesse-matrix for H2O: 3 1 OH2 15.99940 -0.60543 0.00000 0.77339 2 H1 1.00800 0.00000 0.00000 1.54678 3 H2 1.00800 0.00000 0.00000 0.00000 Matrix: 620.76339 0.00555 0.12451 -302.92413 0.00365 -255.71554 -302.90517 0.00985 255.72955 1.34366 -18.29916 -0.03854 -0.53269 -2.53697 -0.13334 -0.52906 -2.54235 0.14224 -0.26595 -3.61815 867.78234 -346.08646 -0.31560 -440.00671 346.51745 -0.77901 -440.35201 -306.01033 0.02860 -349.09602 287.57882 0.00321 300.09174 15.91631 -0.01153 44.18106 4.88112 25.75767 -1.80326 1.59560 3.98306 0.36573 -0.07680 -3.65888 -0.43499 -256.41766 0.18216 -426.99687 301.58252 0.77197 486.95572 -45.46118 -1.13272 -46.69626 -306.92754 0.00193 359.79018 15.84619 0.01383 -43.98345 288.33121 -0.01516 -300.36040 4.50220 23.25857 1.67851 -0.02868 -2.56054 0.52004 1.64183 3.16829 -0.43899 256.58000 1.09238 -426.33925 45.55342 -0.96294 -46.79383 -301.54461 0.63691 487.03730

2000-04-19