Awh friction tensor and friction metric relation with two reaction coordinates

User discussions
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1

Hi,

I am trying to understand how the friction metric (last collum in the awh .xvg output file) is calculated from the components of the friction tensor in the optional output file when running awh with two reaction cordinates (e.g. z coordinate and tilt angle). From my understanding, the friction tensor is supposed to be a positive semidefinitive symmetric matrix. My friction tensor output file from gmx awh consists of two collums with the reaction cordinates followed by three collums for the friction tensor (see example below). I assume these three values are the lower half of the tensor. However, if I assume a symmetric matrix (here 2x2) and then calculate the square root of the determinant, I sometimes get negative values which makes no sense when considering the relationship to the diffusion constant. I am at a loss what is the relationship between the diffusion constant and the friction tensor for 2D awh.

Example from the friction tensor .xvg file from gmx awh output:

@ title “Friction tensor”
@ xaxis label “(nm, deg or lambda state)”
@ yaxis label “friction (kJ mol\S-1\Nnm\S-2\Nps, kJ mol\S-1\Nrad\S-2\Nps or kJ mol\S-1\Nps)”
@TYPE xy
@ view 0.15, 0.15, 0.75, 0.85
@ legend on
@ legend box on
@ legend loctype view
@ legend 0.78, 0.8
@ legend length 2
@ s0 legend “dim1”
@ s1 legend “0,0”
@ s2 legend “1,0”
@ s3 legend “1,1”
-3.5000 0.0000 669929 -496770 479707
-3.5000 2.9032 160945 -34161.3 139383
-3.5000 5.8065 15484.4 53557.1 140776
-3.5000 8.7097 61491.4 -39536.7 265344

2

The legend says what the different column represent. The determinant is the product of the third and fifth column, which is always positive for the lines your posted (and is by definition positive).

EDIT: I forgot to subtract the square of the fourth column.

3

What is the fourth column here then? I was thinking the determinant is column3 * column5 - column4 * column4 (assuming a symmetric matrix). Thanks for the answer.

4

Of course (I think I need some coffee).

The correct answer is that the tensor elements fluctuate wildly and you need to average them over time first before computing the determinant.