Why does dynamical_matrix return negative values?

Hello,

When following the example for the dynamical_matrix command (here) and turning on the minimization flag, there are substantial negative values. Here are the first six lines of the output file that’s generated when I run it:

5407.73126648 0.60396688 0.00000175
-1276.30761693 -861.92746902 -861.81428983
-193.16889479 0.00650038 -0.00000008
-1276.30761624 -861.92746857 861.81429082
-193.17584859 -0.02457904 0.00000000
-1276.12053965 861.59922389 -861.65460775

This shouldn’t be the case for a minimized configuration, right? Shouldn’t the elements of the Hessian should be positive at a minimum? The matrix’s eigenvalues are negative as well (using this tool). The first 8 are:

8562.748779308313
7914.9129841273425
6797.395660302146
-7513.893638723845
6003.365898566742
-6962.005429797687
-5894.101569206084
-5543.162808769083

I have tried the command on other systems as well, and there have been negative values in every case. I’m not really sure what to make of this.

Perhaps @charlessievers can comment on this.

@jwjeffr try running these python commands on the dynamical matrix produced by the example.

``````python
>>> import numpy as np
>>> dynlen = int(3*np.sqrt(len(dynmat)/3))
>>> dynmat = dynmat.reshape((dynlen, dynlen))
>>> eigvals, eigvecs = np.linalg.eig(dynmat)
>>> print(eigvals)
``````

I would expect the following eigenvalues.

``````[ 1.02087855e+04  1.02086846e+04  1.02086687e+04 -7.02565700e-07
1.09978518e-08 -2.14679921e-07  8.76037508e+03  8.76609157e+03
8.77985671e+03  8.77421085e+03  8.76454125e+03  8.77580396e+03
5.87442129e+03  5.87183508e+03  5.87701407e+03  5.87961102e+03
5.87961998e+03  5.87961593e+03  1.87765175e+03  1.87697734e+03
1.87749573e+03  1.87713498e+03  1.87747312e+03  1.87715744e+03]
``````

Hey Charles,

Thanks for the reply. I’m getting very different values, both with and without minimization.

With minimization off, I’m getting:

``````[18291.47498894  +0.j         16826.16995723  +0.j
15052.74248748  +0.j         13481.35824052  +0.j
11993.33955647  +0.j         11738.41797648  +0.j
10437.00465851  +0.j           -99.24306209 +81.19351375j
-99.24306209 -81.19351375j   239.01553747  +0.j
9301.07339057  +0.j          8703.29381758  +0.j
7672.39998404  +0.j          6490.2455242 +459.03829328j
6490.2455242 -459.03829328j  6425.47294151  +0.j
5512.28512477  +0.j          3875.19846074  +0.j
1830.80372983  +0.j          2556.33288212  +0.j
2155.9857413   +0.j          2262.19726512 +54.13875737j
2262.19726512 -54.13875737j  2268.21773236  +0.j        ]
``````

With minimization (and the dump lines commented out because I don’t have EXTRA-DUMP enabled), I’m getting:

``````[15773.89957411  +0.j         14891.91401907  +0.j
13447.21476291+159.09077261j 13447.21476291-159.09077261j
12330.48643728  +0.j         -1157.881718    +0.j
11130.77015491  +0.j         10679.91571791  +0.j
10360.31082596  +0.j          8573.77137431+649.09068966j
8573.77137431-649.09068966j  7752.65122494  +0.j
6661.62083014  +0.j          6266.26994726  +0.j
-97.62537959  +0.j           220.58766299  +0.j
4499.06141346  +0.j          4198.20182449  +0.j
1423.33929023  +0.j          2582.89660601  +0.j
2392.01937294  +0.j          1997.62990666  +0.j
2197.92664334 +88.48427875j  2197.92664334 -88.48427875j]
``````

I cloned LAMMPS (origin/develop 1ebb60a33f8c13c35d40067cf02e6210b96d86f)
I am on a MacBook 2012, which has an intel chip
Created a lammps executable with BODY, INTERLAYER, KSPACE, MANYBODY, MOLECULE, and PHONON packages.

``````cd examples/PACKAGES/phonon/dynamical_matrix_command/Silicon
../../../../../build/lmp -in in.silicon
python
>>> import numpy as np
>>> dynlen = int(3*np.sqrt(len(dynmat)/3))
>>> dynmat = dynmat.reshape((dynlen, dynlen))
>>> eigvals, eigvecs = np.linalg.eig(dynmat)
>>> print(eigvals)
``````

and this yielded

``````[-6.42091335e-08+7.90277636e-08j -6.42091335e-08-7.90277636e-08j
-1.09533249e-06+0.00000000e+00j  1.02087855e+04+0.00000000e+00j
1.02086846e+04+0.00000000e+00j  1.02086687e+04+0.00000000e+00j
8.76037508e+03+0.00000000e+00j  8.76609157e+03+0.00000000e+00j
8.77985671e+03+0.00000000e+00j  8.77421085e+03+0.00000000e+00j
8.76454125e+03+0.00000000e+00j  8.77580396e+03+0.00000000e+00j
5.87442129e+03+0.00000000e+00j  5.87183508e+03+0.00000000e+00j
5.87701407e+03+0.00000000e+00j  5.87961102e+03+0.00000000e+00j
5.87961998e+03+0.00000000e+00j  5.87961593e+03+0.00000000e+00j
1.87765175e+03+0.00000000e+00j  1.87697734e+03+0.00000000e+00j
1.87749573e+03+0.00000000e+00j  1.87713498e+03+0.00000000e+00j
1.87747312e+03+0.00000000e+00j  1.87715744e+03+0.00000000e+00j]
``````

With energy minimization (I commented out the dump commands)

``````[ 1.02086578e+04+0.00000000e+00j  1.02086513e+04+0.00000000e+00j
1.02086527e+04+0.00000000e+00j -1.16725621e-07+0.00000000e+00j
-1.46634440e-07+3.71726258e-07j -1.46634440e-07-3.71726258e-07j
8.76824945e+03+0.00000000e+00j  8.77207023e+03+0.00000000e+00j
8.76937614e+03+0.00000000e+00j  8.77093843e+03+0.00000000e+00j
8.76903712e+03+0.00000000e+00j  8.77128380e+03+0.00000000e+00j
5.87651234e+03+0.00000000e+00j  5.87601134e+03+0.00000000e+00j
5.87702835e+03+0.00000000e+00j  5.87754508e+03+0.00000000e+00j
5.87754627e+03+0.00000000e+00j  5.87752871e+03+0.00000000e+00j
1.87725025e+03+0.00000000e+00j  1.87738299e+03+0.00000000e+00j
1.87728193e+03+0.00000000e+00j  1.87735103e+03+0.00000000e+00j
1.87728489e+03+0.00000000e+00j  1.87734812e+03+0.00000000e+00j]
``````

If you did the exact same, please let me know what machine/OS and lammps commit you are using.

I just re-cloned and re-built as well and it seems to be working fine now, both w/ and w/o minimization. Really weird. I guess there’s something wrong with my original build.

Thanks Charles!

@charlessievers

I just re-built the executable with the GPU package and it’s returning eigenvalues with large imaginary components again. Using the same executable, but without the -sf gpu flag, I am getting more reasonable values. I attached a screenshot below - these are with minimization on.

@jwjeffr is your lammps compiled with gpu single precision? If so, recompile with double precision and try again.

I was compiling with mixed precision. Switching to double worked, thank you