[CPMD-list] Fd and LR in vibrational analysis

[Juerg Hutter]

> 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:
>> >>
>> >>
>> >
>> 
>