Subject: Re: CCL:'electron density' vs 'electronic configurations'...

From: Victor Lua~na <pueyo<<at>>pinon.ccu.uniovi.es>
Date: Thu, 29 May 2003 19:34:01 +0200 (METDST)

> From: Roy Jensen <royj<<at>>uvic.ca>
> Date: Mon, 26 May 2003 00:47:58 -0700
> The following came up recently and we could not come to a conclusion.
>
> One premise behind DFT is that a _single_ electron density completely
> describes each electronic state of a system. In ab initio systems,
> _all_ electronic configurations contribute to the wavefunction for
> each electronic state of a system. Is this an artifact of the
> approximations in ab initio calculations? Alternatively, if described
> exactly, is an exact ab initio wavefunction still composed of all the
> electronic configurations?

I find some confussion in this description, so perhaps I am not
understanding your question. DFT is founded on the Hohenberg-Kohn (HK)
theorem, according to which, for a non-degenerated ground state, the
exact energy can be obtained as a functional of the exact electron
density.  Thus the emphasis on the ground state electron density.
However, every different electronic state has a different electron
density (notice that the Born-Oppenheimer approximation is assumed
here).

>From a full CI perspective, the wavefunction of a given electronic state
will be given as a linear combination of a large number of Slater
determinants, each corresponding to a configuration (i.e. to a
electronic state under the approximation of independent electrons).
Therefore, the single electron density of an electronic state depends
(contains information) on the coupling of all the electron-independent
configurations entering the CI.

> On a second point, would it be correct to say that DFT _variationally_
> optimizes the electron density to determine the minimum energy of the
> system?

There are *many* DFT techniques. Perhaps the most commonly found (at
least in the molecular world) go back to the orbital description and
solve the Kohn-Sham equations. KS equations are not an outcome of the
variational principle. However, they are variational in the sense that,
once an exchange and correlation functional has been fixed, improving
the flexibility of the basis set will diminish the energy and converge
to the best solution that could have been obtained from that basis set.
Notice, however, that in most DFT methods neither the energy nor the
electron density is obtained by solving a variational equation.

    Regards,
                Victor Lua~na

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