[CPMD-list] Fd and LR in vibrational analysis

[Yong Zhang]

I see finally. Thank you so much for your patience.


On 11/29/06, Juerg Hutter <hutter at pci.unizh.ch> wrote:
>
> > Sorry Juery, I must misunderstand your previous mails. But could you
> please
> > describe the 6N SCF method with more detail again?
> > As you said, with "VIBRATIONAL ANALYSIS FD", the first derivatives are
> > calculated using finite difference (2 points method). Then how is the
> second
> > derivative calculated? Is there a simple formula I can use or a
> reference I
> > can refer to?
>
> One last time - the first derivative of the gradient of the energy IS the
> second derivative of the energy wrt the atomic coordinates == dynamical
> matrix == hessian used in vibrational analysis
>
> regards
>
> Juerg Hutter
>
>
>
> > ==================
> > VIBRATIONAL ANALYSIS FD
> >
> > uses finite difference (2 points) of first derivatives.
> > This way you need 6N SCF calculations to calculate the
> > dynamical matrix.
> > ==================
> >
> > I appreciate your help.
> >
> > Best wishes,
> > Yong
> >
> >
> > On 11/29/06, Juerg Hutter <hutter at pci.unizh.ch> wrote:
> >>
> >> Hi
> >>
> >> > Thanks Bala and Juerg for the clarification.
> >> > For the FD calculation, I understand that 6N is needed for the first
> >> > derivative and 9N**2 for the second derivative. But I still suspect
> that
> >> > CPMD deos not use this exactly for the second derivative: I can find
> the
> >> 6N
> >>
> >> As I tried to explain in my last two mails, CPMD is not using an
> >> algorithm that needs 9N^2 SCF calculations, it uses the
> >> described algorithm using only 6N SCF calculations.
> >>
> >> regards
> >>
> >> Juerg Hutter
> >>
> >>
> >> > SCF in the output file, but I could not find the 9N**2 anywhere. And
> the
> >> > total CPU time seems reasonable only for the 6N SCF. I attached a
> output
> >> > file here.
> >> > I am reading the code, but I am not a good programmer, it will take
> some
> >> > more time for me to figure out the detailed proedure from there. :-(
> >> >
> >> > Best wishes,
> >> > Yong
> >> >
> >> > On 11/29/06, Juerg Hutter <hutter at pci.unizh.ch> wrote:
> >> >>
> >> >> Hi
> >> >>
> >> >> Just to add to my previous mail and the mail by Bala
> >> >>
> >> >> VIBRATIONAL ANALYSIS FD
> >> >>
> >> >> uses finite difference (2 points) of first derivatives.
> >> >> This way you need 6N SCF calculations to calculate the
> >> >> dynamical matrix. Calculating second derivatives by
> >> >> finite differences would require 9N^2 SCF calculations.
> >> >>
> >> >> VIBRATIONAL ANALYSIS LR
> >> >>
> >> >> calculates the dynamical matrix analytically (almost).
> >> >> To do this you need the linear response orbitals
> >> >> that are solutions to the coupled KS equation.
> >> >> There are 3N perturbations, meaning you have to
> >> >> solve 3N CPKS systems iteratively. One iteration
> >> >> of the CPKS iteration is about the same time as
> >> >> an SCF iteration in CPMD. Therefore the two schemes
> >> >> (LR and SD) need about the same total amount of CPU
> >> >> time. The actual relative timings is depending on
> >> >> the convergence of the two schemes and might differ
> >> >> from system to system.
> >> >>
> >> >> regards
> >> >>
> >> >> Juerg Hutter
> >> >>
> >> >> ----------------------------------------------------------
> >> >> Juerg Hutter                   Phone : ++41 44 635 4491
> >> >> Physical Chemistry Institute   FAX   : ++41 44 635 6838
> >> >> University of Zurich           E-mail: hutter at pci.unizh.ch
> >> >> Winterthurerstrasse 190
> >> >> CH-8057 Zurich, Switzerland
> >> >> ----------------------------------------------------------
> >> >>
> >> >>
> >> >> On Tue, 28 Nov 2006, Yong Zhang wrote:
> >> >>
> >> >>
> >> >
> >>
> >
>
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