[gmx-users] what do negative eigenvalues imply?

[Chris Neale]

>/> Hello,
/>>/ 
/>>/ I was wondering if anybody can explain why eigenvalues can be negative? 
/>>/ I have found a suggestion on the internet that this is because the 
/>>/ positive eigenvalues have accounted for more than 100% of the motion. 
/>>/ Does this sound accurate?
/>
>No
>
>You normally have six negative eigevalues due to the fact that overall 
>translation and rotation are removed. You have in addition 4 that are 
>very small, maybe you can investigate how many degrees of freedom you 
>have (it says in the md.log file). This should be equal to the umber of 
>non-negative ev.

Thanks for the explanation David.

I have selected only the heavy atoms in the alanine dipeptide for the previously posted analysis. 
Therefore I made a new temperature coupling group composed only of these atoms and ran grompp
in order to get the desired value output:

"Number of degrees of freedom in T-Coupling group Protein_NoH is 23.98"

So 24-6 is 18 and I am positive up to 20. I suppose it is ok that there are more (small) positive values
than 18.

If I re-do the analysis instead using all 22 atoms (include the H's) then grompp indicates:

"Number of degrees of freedom in T-Coupling group Protein is 53.96"

And I am positive up to ev #41 (g_covar eigenval.xvg follows) so 54-6 is 48, but I only have 41 positive.
Nevertheless, the ev 42-48 are very small positive.


# This file was created Mon Oct 29 18:45:06 2007
# by the following command:
# /hpf/data/pomes/cneale/exe/gromacs-3.3.1/exec/fftw-3.1.2/bin/g_covar -s ../adp.tpr -n ../adp.ndx -f ../adp_0-1.56us.xtc -ascii covar.dat -mwa 
#
# /hpf/data/pomes/cneale/exe/gromacs-3.3.1/exec/fftw-3.1.2/bin/g_covar is part of G R O M A C S:
#
# Gnomes, ROck Monsters And Chili Sauce
#
@    title "Eigenvalues of the covariance matrix"
@    xaxis  label "Eigenvector index"
@    yaxis  label "(u nm\S2\N)"
@TYPE xy
         1 0.23291
         2 0.0810199
         3 0.0579589
         4 0.0430226
         5 0.0156911
         6 0.015543
         7 0.0154095
         8 0.0153563
         9 0.0153322
        10 0.0151271
        11 0.0122578
        12 0.00725067
        13 0.00261468
        14 0.00179256
        15 0.00165951
        16 0.00103279
        17 0.000815341
        18 0.000572039
        19 0.000508098
        20 0.000365606
        21 0.000359221
        22 0.000352105
        23 0.00035001
        24 0.000344526
        25 0.000259272
        26 0.000258307
        27 0.000251824
        28 0.000201794
        29 0.000134211
        30 0.0001308
        31 0.00010905
        32 0.000107029
        33 8.21594e-05
        34 7.64162e-05
        35 6.1539e-05
        36 4.31456e-05
        37 3.68485e-05
        38 2.35955e-05
        39 2.11371e-05
        40 1.34103e-05
        41 6.81332e-06
        42 -1.17905e-06
        43 -4.04147e-06
        44 -9.72161e-06
        45 -1.3889e-05
        46 -3.51393e-05
        47 -4.49705e-05
        48 -6.51993e-05
        49 -6.75307e-05
        50 -7.47012e-05
        51 -8.77501e-05
        52 -0.00010138
        53 -0.000103669
        54 -0.000105253
        55 -0.000106886
        56 -0.000110613
        57 -0.000111074
        58 -0.000134431
        59 -0.000166161
        60 -0.000180943
        61 -0.000204832
        62 -0.000298183
        63 -0.000444828
        64 -0.00052514
        65 -0.000592853
        66 -0.00213633


Thanks,
Chris.


>>/ 
/>>/ This system is the alanine dipeptide. I do not find such negative values 
/>>/ when running g_covar on full proteins.
/>>/ 
/>>/ The contents of eigenval.xvg are listed below.
/>>/ 
/>>/ # This file was created Mon Oct 29 16:31:46 2007
/>>/ # by the following command:
/>>/ # /hpf/data/pomes/cneale/exe/gromacs-3.3.1/exec/fftw-3.1.2/bin/g_covar 
/>>/ -s ../adp.tpr -n ../adp.ndx -f ../adp_0-1.56us.xtc -ascii covar.dat -mwa
/>>/ #
/>>/ is part of G R O M A C S:
/>>/ #
/>>/ # Great Red Owns Many ACres of Sand
/>>/ #
/>>/ @    title "Eigenvalues of the covariance matrix"
/>>/ @    xaxis  label "Eigenvector index"
/>>/ @    yaxis  label "(u nm\S2\N)"
/>>/ @TYPE xy
/>>/         1 0.211327
/>>/         2 0.0736961
/>>/         3 0.0522046
/>>/         4 0.04409
/>>/         5 0.0104057
/>>/         6 0.00577603
/>>/         7 0.00198832
/>>/         8 0.00163465
/>>/         9 0.00128302
/>>/        10 0.000735383
/>>/        11 0.000649576
/>>/        12 0.000434795
/>>/        13 0.000376401
/>>/        14 0.000337852
/>>/        15 0.000191994
/>>/        17 8.87514e-05
/>>/        18 7.31975e-05
/>>/        19 5.31939e-05
/>>/        20 4.45637e-05
/>>/        21 -5.03112e-06
/>>/        22 -1.26812e-05
/>>/        23 -2.48763e-05
/>/>        24 -5.90268e-05
/>>/        25 -0.000114215
/>>/        26 -0.000227912
/>>/        27 -0.000355243
/>>/        28 -0.000513052
/>>/        29 -0.000631471
/>>/        30 -0.00178302/