[CPMD-list] Fd and LR in vibrational analysis

[Yong Zhang]

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?
==================
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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