[gmx-users] Doubt about hessian matrix in Normal mode analysis

[Varvdekar Bhagyesh Rajendra]

Dear Justin,

I used the following command to print ascii format of the hessian matrix to a file from the default mtx format of gromacs obtained after normal mode analysis.

gmxdump_d -mtx nm.mtx > hessian_matrix.dat

I would like to confirm the way the hessian matrix is written in this new ascii file. Is the following way correct where the x, y, z coordinates of the first atom are considered, then second atom and so on and so forth in each row and column and the matrix elements are the second order derivatives of potential energy with respect to its corresponding row and column coordinates ?

Here x_i = x coordinate of the i_th atom, y_i = y coordinate of the i_th atom, z_i = z coordinate of the i_th atom.
And the matrix elements M are the second order of U (Potential energy) with respect to its corresponding row and column coordinate i.e. M = d^2 U / dx_i d_i

   | x1 | y1 | z1 | x2 | y2 | z2 | ... | x_n | y_n | z_n |
---------------------------------------------------------|
x1 | M  |  M | M  |  M | M  | M  | ...
-----------------------------------
y1 | M  |  M | M  |  M | M  | M  | ...
------------------------------------------
z1 | M  |  M | M  |  M | M  | M  | ...
------------------------------------------
x2 | M  |  M | M  |  M | M  | M  | ...
-------------------------------------------
y2 | M  |  M | M  |  M | M  | M  | ...
------------------------------------------
z2 | M  |  M | M  |  M | M  | M  | ...
------------------------------------------
.
.
.
x_N
y_N
z_N 
------------------------------------------


Thank you,

Bhagyesh