# [Octopus-devel] [Octopus-notify] [Octopus] #89: exp_vnlpsi is currently broken

alberto.castro at tddft.org alberto.castro at tddft.org
Sat Dec 22 13:01:19 WET 2007

```Hi,

The formula should be in the Miyamoto  paper about the "Suzuki-trotter":

O. Sugino and Y. Miyamoto, Phys. Rev. B 59, 2579 (1999).

Regards from Ben Gurion airport in Tel Aviv, and merry christmas!

On Fri, 21 Dec 2007, Octopus wrote:

> #89: exp_vnlpsi is currently broken
> ---------------------------+------------------------------------------------
>   Reporter:  marques       |       Owner:  xavier
>       Type:  defect        |      Status:  assigned
>   Priority:  major         |   Milestone:  3.0
>  Component:  octopus-core  |     Version:  trunk
> Resolution:                |    Keywords:
> ---------------------------+------------------------------------------------
> Comment (by marques):
>
>  The formula is, to my knowledge, not written anywhere. It is however easy
>  to derive. We want to calculate
>
>  exp(factor*sum |Vnl><Vnl|/uVu) psi
>
>  First, in the split-operator spirit, we break the sum in the exponent, and
>  write:
>
>  exp(factor|Vnl><Vnl|/uVu) * exp(factor|Vnl><Vnl|/uVu) * ... * psi
>
>  (factor is, obviously i Dt, or -i Dt, I always forget.) I do not remember
>  this very well, but I do remember that sometimes we have to change the
>  order of the exponentials, and that is why the order appears in the
>  subroutine.
>
>  Then we can expand the exponential:
>
>  (1 + factor |Vnl><Vnl|/uVu + factor |Vnl><Vnl|/uVu*factor |Vnl><Vnl|/uVu
>  +...) psi
>
>  if we define norm=<Vnl|Vnl>
>
>  we get
>
>  (1 + factor/uVu |Vnl> exp(factor*norm/uVu) <Vnl|) psi
>
>  I may have gotten something wrong, but from this and the original routine
>  you should be able to find it out.
>
>  Of course that for the local term, you can calculate directly the
>  exponential without expanding...
>
> --
> Ticket URL: <http://www.tddft.org/trac/octopus/ticket/89#comment:2>
> Octopus <http://tddft.org/programs/octopus/>
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>
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======================================================================
Dr. Alberto Castro

Institut fur Theoretisch Physik, Freie Universitat Berlin.
Arnimallee, 14, Berlin 14195 (Deutschland)

Tel:   +49 30 83853028
Fax:   +49 30 83855258
skype: alberto_c_barrigon
email: alberto at physik.fu-berlin.de
======================================================================
```