[Octopus-users] Time propogation problems

[Miguel Marques]

  Hi David,

  Your question is not as simple to answer as it seems (to me, at
least). It is true that if you have the many-body Schrodinger eq. and
you have any state and you propagate it, then the energy is conserved.
Within TDDFT (at least with the functionals I know about) the situation
is trickier. Let's give a practical example: you calculate your
ground-state with the LDA and start propagating with GGA. Now, at the
1st iteration, the wave-functions are the LDA ones, but the Hamiltonian
is the GGA one, so the expectation value of the "new" Hamiltonian has to
be different from the LDA density, yielding some other wave-functions
after the 1st step. Now, for the second step, the density changed, so
the Hamiltonian changes again, and the energy changes again. The
Hamiltonian is intrinsically time-dependent, so the energy is not conserved.

  If, on the other hand, you so an LDA propagation on an LDA GS, the
wave-functions are really eigenfunctions of the LDA Hamiltonian and just
acquire a phase in the propagation, which means that the density is
constant, and so is the Hamiltonian. The energy is stable then.

  What is the deeper meaning of this? I really do not know. It probably
has to do with the initial-state dependence of the xc potential. The
xc-potential should know probably about the starting point (as you don't
start from the GS), and then correct for it... no idea on how it could
possible achieve this, of course...

  Someone there knows something about this?
  Miguel

David Strubbe wrote:
> Alberto,
> 
> Why isn't the energy conserved if you use a different functional? I
> understand that the ground-state energy in GGA will not be the LDA
> energy in the first step of the propagation, but shouldn't the energy
> remain during the propagation as the LDA energy of the GGA ground-state
> density?
> 
> David
> 
> On Wed, Feb 10, 2010 at 1:06 AM, Alberto Castro <acastro at bifi.es
> <mailto:acastro at bifi.es>> wrote:
> 
>     Hi,
> 
>     2010/2/10 Robertson Burgess <Robertson.Burgess at newcastle.edu.au
>     <mailto:Robertson.Burgess at newcastle.edu.au>>:
>     > Thanks Alberto,
>     >
>     > That easily explains why my GGA time propogation was going faster than
>     > my LDA propogation. Am I correct in changing the
>     XCFunctional=gga_x_pbe
>     > + gga_c_pbe to XCFunctional=lda_x + lda_c_pz_mod after the ground
>     state
>     > run if I want TDLDA?
> 
>     If you want to run TDLDA, in principle what you should do is to run
>     the gs with LDA, and the td with LDA. If you want to do the geometry
>     minimization with gga, then I would run the minimization with it, but
>     then I would do a gs LDA calculation at the geometry minimum, and then
>     start the response calculation from there.
> 
>     Thanks for the detailed bug report below. We will try to solve it soon.
> 
>     > When I use a GGA ground state, and a GGA propogation, my energy is
>     > conserved. Likewise when I have an LDA ground state and an LDA
>     > propogation my energy is conserved, but it is not the case for an LDA
>     > propagation based on a GGA ground state.
>     > Thankyou David for confirming that this shouldn't be the case, but I'm
>     > wondering what I'm doing wrong? The only thing I change is my
>     > XCFunctional, and my energy is no longer conserved. I have tried
>     shorter
>     > time steps, that didn't work.
> 
>     I think that is the way it should be, there is nothing that you are
>     doing wrong. The DFT energy is only conserved in a td calculation if
>     the functional you use in the td run is the same that you used in the
>     gs run.
> 
>     Thanks for the detailed info about the bug below. We will try to
>     solve it asap.
> 
>     Cheers, Alberto.
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> 
> 
> 
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-- 
Dr. Miguel A. L. Marques
marques at tddft.org

Laboratoire de Physique de la Matière Condensée et Nanostructures
(LPMCN) - Université Lyon I
Bâtiment Brillouin, Domaine scientifique de la DOUA
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