[CP2K:2654] Looking for zero frequencies

Juerg Hutter hut... at pci.uzh.ch
Fri Apr 9 17:51:15 CEST 2010


Dear An

due to the way cp2k calculates the XC on regular grids,
you will always have these non-zero translational modes.
By increasing the grids etc you will be able to reduce
the frequencies down to a certain value, but this will
still be of the size of other soft modes. However, the
translational modes are typically very well decoupled
from the rest of the modes. You can test this by
calculating the frequencies from a Hessian with
projected out translations. At least in my experience,
the frequencies only change by a fraction of a wavenumber.

best regards

Juerg Hutter

----------------------------------------------------------
Juerg Hutter                   Phone : ++41 44 635 4491
Physical Chemistry Institute   FAX   : ++41 44 635 6838
University of Zurich           E-mail: hut... at pci.uzh.ch
Winterthurerstrasse 190
CH-8057 Zurich, Switzerland
----------------------------------------------------------


On Fri, 9 Apr 2010, An Ghysels wrote:

> Dear forum users,
>
> I am calculating frequencies in periodic structures, from which I'd
> like to derive thermodynamic quantities like the entropy etc.
> Therefore I use the VIBRATIONAL_ANALYSIS keyword, where I have put the
> FULLY_PERIODIC keyword to True, such that rotational motions are not
> projected out.
>
> In principle, the second derivatives matrix should have 3 zero
> eigenvalues (even in non-optimized systems), because the system is
> translational invariant. However, this is not the case in my
> calculations. Even in a small test case like diamond with a cubic cell
> containing 8 atoms, the "zero" frequencies deviate largely from zero.
>
> (Between brackets: I'm much bothered by this bad performance, because
> it signals that the numerical accuracy of the frequencies is poor. I
> aim at studying larger unit cells (eg with 100 to 200 QM atoms) where
> I surely will encounter floppy modes, which are even more sensible to
> numerical errors. And those floppy modes play an essential role in the
> partition function/thermodynamics. Therefore, I wish to improve the
> accuracy of the calculated frequencies.)
>
> So my questions are mainly: why is the accuracy so bad? Is this
> directly related to the eggbox effect, and if so, how to remedy it? Is
> it something with interpolation grids? And what to do to improve it?
>
> I tried decreasing the EPS_DEFAULT (down to 10e-16), increasing the
> E_CUTOFF (up to 1400 Rydberg), increasing the REL_CUTOFF accordingly,
> adding the keyword COMMENSURATE, changing the interpolation grid (to
> spline3), but the improvements still do not get me close to "zero"
> frequencies (still of the order -70 to 50 cm-1).
>
> Looking forward to your comments and remarks,
>
> An
>
> Below: Information on version, input geometry optimization, input
> frequency run, snippets of output
> =====
> Version:
> CP2K| version string:                  CP2K version 2.0.1
> (Development Version)
> CP2K| is freely available from                          http://cp2k.berlios.de/
> CP2K| Program compiled at
> Wed_Sep__9_15:48:59_CEST_2009
> CP2K| Program compiled
> on                                               gengar1
> CP2K| Program compiled for                                   Linux-
> x86-64-intel
> =====
> Input geomery optimization
> &GLOBAL
>  PRINT_LEVEL high
>  PROJECT_NAME vib
>  RUN_TYPE GEO_OPT
>  PREFERRED_FFT_LIBRARY FFTW
> &END GLOBAL
>
> &MOTION
>  &GEO_OPT
>    OPTIMIZER BFGS
>    MAX_ITER 300
>  &END GEO_OPT
> &END MOTION
>
> &VIBRATIONAL_ANALYSIS
>    FULLY_PERIODIC T
> &END VIBRATIONAL_ANALYSIS
>
> &FORCE_EVAL
>
>  METHOD QS
>  &DFT
>    BASIS_SET_FILE_NAME GTH_BASIS_SETS
>    POTENTIAL_FILE_NAME GTH_POTENTIALS
>    &MGRID
>      CUTOFF 100
>      REL_CUTOFF 23
>      COMMENSURATE
>    &END MGRID
>    &QS
>     EPS_DEFAULT 1.0E-10
>    &END QS
>    &SCF
>      EPS_SCF 1.0E-5
>      MAX_SCF 100
>      SCF_GUESS RESTART
>      &OUTER_SCF
>        EPS_SCF 1.0E-5
>        MAX_SCF 20
>      &END
>      &OT
>        ALGORITHM IRAC
>        MINIMIZER CG
>        PRECONDITIONER FULL_ALL
>        ENERGY_GAP 0.001
>      &END OT
>      &PRINT
>        &RESTART
>         BACKUP_COPIES 0
>        &END RESTART
>      &END PRINT
>    &END SCF
>    &XC
>      &XC_FUNCTIONAL PBE
>      &END XC_FUNCTIONAL
>    &END XC
>    &POISSON
>     POISSON_SOLVER PERIODIC
>     PERIODIC XYZ
>     &EWALD
>       EWALD_TYPE EWALD
>       ALPHA 0.3
>       GMAX 11
>       O_SPLINE 6
>     &END EWALD
>   &END POISSON
>  &PRINT
>  &END PRINT
>  &END DFT
>
>  &SUBSYS
>    &CELL
>      ABC 3.567 3.567 3.567
>      PERIODIC XYZ
>    &END CELL
>    &COORD
> C  -0.066491  -0.063731  -0.038851
> C   0.019572   1.759040   1.767428
> C   1.756129   0.023158   1.769616
> C   1.767376   1.770784   0.004363
> C   0.841267   0.843123   0.828198
> C   2.663349   0.903043   2.661920
> C   0.899007   2.665284   2.661387
> C   2.644659   2.648722   0.926362
>  &END COORD
>    &TOPOLOGY
>      &GENERATE
>        CREATE_MOLECULES
>      &END GENERATE
>    &END TOPOLOGY
>
>      &KIND C
>      BASIS_SET DZVP-GTH
>      POTENTIAL GTH-PBE-q4
>    &END KIND
>
>  &END SUBSYS
> &END FORCE_EVAL
> =====
> Input Frequency run
> &GLOBAL
>  PRINT_LEVEL high
>  PROJECT_NAME vib
>  RUN_TYPE VIBRATIONAL_ANALYSIS
>  PREFERRED_FFT_LIBRARY FFTW
> &END GLOBAL
>
> &MOTION
>  &GEO_OPT
>    OPTIMIZER BFGS
>    MAX_ITER 300
>  &END GEO_OPT
> &END MOTION
>
> &VIBRATIONAL_ANALYSIS
>    FULLY_PERIODIC T
> &END VIBRATIONAL_ANALYSIS
>
> &FORCE_EVAL
>
>  METHOD QS
>  &DFT
>    BASIS_SET_FILE_NAME GTH_BASIS_SETS
>    POTENTIAL_FILE_NAME GTH_POTENTIALS
>    &MGRID
>      CUTOFF 100
>      REL_CUTOFF 23
>      COMMENSURATE
>    &END MGRID
>    &QS
>     EPS_DEFAULT 1.0E-10
>    &END QS
>    &SCF
>      EPS_SCF 1.0E-5
>      MAX_SCF 100
>      SCF_GUESS RESTART
>      &OUTER_SCF
>        EPS_SCF 1.0E-5
>        MAX_SCF 20
>      &END
>      &OT
>        ALGORITHM IRAC
>        MINIMIZER CG
>        PRECONDITIONER FULL_ALL
>        ENERGY_GAP 0.001
>      &END OT
>      &PRINT
>        &RESTART
>         BACKUP_COPIES 0
>        &END RESTART
>      &END PRINT
>    &END SCF
>    &XC
>      &XC_FUNCTIONAL PBE
>      &END XC_FUNCTIONAL
>    &END XC
>    &POISSON
>     POISSON_SOLVER PERIODIC
>     PERIODIC XYZ
>     &EWALD
>       EWALD_TYPE EWALD
>       ALPHA 0.3
>       GMAX 11
>       O_SPLINE 6
>     &END EWALD
>   &END POISSON
>  &PRINT
>  &END PRINT
>  &END DFT
>  &SUBSYS
>    &CELL
>      ABC 3.567 3.567 3.567
>      PERIODIC XYZ
>    &END CELL
>    &COORD
>  C        -0.0393192769       -0.0522499977       -0.0007602780
>  C         0.0299677090        1.7769206120        1.7824574256
>  C         1.7642084626        0.0471181783        1.7911208859
>  C         1.7938452241        1.7853211459        0.0053883203
>  C         0.8664406756        0.8762954420        0.8435833733
>  C         2.6939879368        0.9029246308        2.6806928814
>  C         0.9092781460        2.6785011492        2.6771532650
>  C         2.6481574040        2.6661172907        0.9483093511
>  &END COORD
>    &TOPOLOGY
>      &GENERATE
>        CREATE_MOLECULES
>      &END GENERATE
>    &END TOPOLOGY
>
>      &KIND C
>      BASIS_SET DZVP-GTH
>      POTENTIAL GTH-PBE-q4
>    &END KIND
>
>  &END SUBSYS
> &END FORCE_EVAL
> =====
> Snippet output frequency run:
> If I look at the values with the lowest absolute value and I convert
> them to cm-1, it is poor accuracy:
>
> VIB| Cartesian Low frequencies ----0.44072    -0.10876E-01
> 0.12458     0.69806
> VIB| Cartesian Low frequencies --- 0.71490      1.4715
> 2.0898      3.8120
> VIB| Cartesian Low frequencies ---  5.8007
> VIB| Frequencies after removal of the rotations and translations
> VIB| Internal  Low frequencies ----0.14095     0.50894
> 1.4072      2.0559
> VIB| Internal  Low frequencies ---  3.6794      5.7900
> 25.027      25.504
> VIB| Internal  Low frequencies ---  25.855      25.997
> 26.180      26.684
> VIB| Internal  Low frequencies ---  26.818      26.970
> 27.202      27.461
> VIB| Internal  Low frequencies ---  27.643      28.937
> 54.059      54.351
> VIB| Internal  Low frequencies ---  54.817
>
> VIB|                        NORMAL MODES - CARTESIAN DISPLACEMENTS
> VIB|
> VIB|                         1
> 2                    3
> VIB|Frequency (cm^-1)   -82.399299           156.573040
> 260.352529
> ...
>
> -------------------------------------------------------------------------------
> ----                             MULTIGRID
> INFO                            ----
>
> -------------------------------------------------------------------------------
> count for grid        1:            868          cutoff
> [a.u.]           50.00
> count for grid        2:            276          cutoff
> [a.u.]           12.50
> count for grid        3:             80          cutoff
> [a.u.]            3.12
> count for grid        4:              0          cutoff
> [a.u.]            0.78
> total gridlevel count  :           1224
>
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