[CPMD-list] Fd and LR in vibrational analysis

[Yong Zhang]

On 11/28/06, Axel Kohlmeyer <akohlmey at cmm.chem.upenn.edu> wrote:
>
> On 11/28/06, Yong Zhang <zhangymall11 at gmail.com> wrote:
> >
> > I am a little confused.
>
> me too, just to make sure we are on the same page. FD stands for
> finite differences.
> if you compute the energy at point x and x+d and x-d you can approximate
> the
> _second_ derivative of the energy in the direction of d by putting a
> parabola through
> those points and thus you _can_ get the second derivative with respect to
> the displacement (in harmonic approximation, that is).




Thanks Axel.
In this case, the second derivative can be calculated by something like
(V(+d)+V(-d)-2V(0))/d**2. But that is only the one variable case, or say the
diagonal terms in the Hessian matrix. How about the off-diagonal terms?


in linear response you just compute the linear response to a displacement
> operator (without a real displacement and thus you avoid half
> the calculations as the response is symmetric).
> as a result you also get the second derivative in harmonic approximation.


For a molecule of 12 atoms, I actually found that FD is faster than LR.  Is
this reasonable?

> In vibrational analysis, FD is used for first derivative, then how is the
> > second derivative calculated for a job "VIBRATIONAL ANALYSIS FD" ? FD or
> LR?
>
> for more details, please have a look at the code. secder.F and secdpt.F.
>
> note, that there is a second, more generic linear response kernel
> implemented
> into CPMD (job type LINEAR RESPONSE) that also allows to do a vibrational
> analysis via linear response via the PHONON keyword.
>
> axel.
>
> >
> > Best wishes,
> >
> >
> >
> >
> > On 11/28/06, Juerg Hutter <hutter at pci.unizh.ch> wrote:
> > > Hi
> > > > Thanks for the reply. I found the paper, which discussed the LR
> method.
> > > > For the FD method in CPMD, I guess the first order derivative is
> > calculated
> > > > from finite difference method as indicated in the output file. Is
> the
> > second
> > > > order derivative calculated from those first order derivative simply
> > using
> > > > finite difference method one more time? If not, how is the second
> order
> > > > derivative calculated?
> > > > Thanks a lot
> > > >
> > >
> > > You are one off. All first derivatives in CPMD are calculated using
> > > analytic formulas. Linear Response (LR) is needed to calculate
> > > second order derivatives (e.g. dynamical matrix). The finite
> > > difference (FD) method therefore is used on gradients (=first
> > > derivatives) of the energy in the vibrational analysis.
> > >
> > > regards
> > >
> > > Juerg Hutter
> > >
> > >
> > >
> > > > Yong
> > > >
> > > >
> > > > On 11/23/06, Juerg Hutter <hutter at pci.unizh.ch > wrote:
> > > >>
> > > >> Hi
> > > >>
> > > >> >
> > > >> > I am just wondering where I can get detailed description of the
> FD
> > and
> > > >> LR
> > > >> > methods used for vibrational analysis in CPMD, for example, the
> > original
> > > >> > references. Thanks a lot.
> > > >> >
> > > >>
> > > >> See Reference 94 in the manual
> > > >>
> > > >> \bibitem{apdsmp} A. Putrino, D. Sebastiani and M. Parrinello,
> > > >> J. Chem. Phys. {\bf 113}, 7102 (2000)
> > > >>
> > > >>
> > > >> regards
> > > >>
> > > >> Juerg Hutter
> > > >>
> > > >
> > >
> >
> >
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> >
> >
> >
>
>
> --
> =======================================================================
> Axel Kohlmeyer   akohlmey at cmm.chem.upenn.edu   http://www.cmm.upenn.edu
>   Center for Molecular Modeling   --   University of Pennsylvania
> Department of Chemistry, 231 S.34th Street, Philadelphia, PA 19104-6323
> tel: 1-215-898-1582,  fax: 1-215-573-6233,  office-tel: 1-215-898-5425
> =======================================================================
> If you make something idiot-proof, the universe creates a better idiot.
>
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