2
$\begingroup$

Why density functional theory (DFT) favors a uniform electron density when we use it to calculate ground state electronic structure self-consistently?

For example, when we use DFT for calculating the (ground state) electron density of two $\text{H}$ atoms with a separation somewhat larger then the bond length of an $\text{H}_2$ molecule, there will still be a non-negligible electron density between the two atoms as if there is still a covalent bond. As a result, the calculated electronic ground state is essentially an excited state of the system.

I cannot remember where did I read this, and I don't understand why DFT has such a problem. I think the problem resides in the fact that we use a local exchange-correlation functional $E_{XC}$ like LDA and GGA. But I don't understand why a local $E_{XC}$ will lead to a uniform electron density.

$\endgroup$
2
$\begingroup$

I think I can see the confusion, and I will do my best to explain.

As an initial attempt to use the electron density, the uniform electron gas (UEG) model was developed. This fictitious model assumes: an infinite number of electrons, a constant non-zero density, an infinite volume, and a uniformly distributed positive charge. IMPORTANT: The electron-electron interactions (correlation and exchange) are fundamentally ignored.

Two main theorems comprise modern DFT: Hohenberg-Kohn (HK) and Kohn-Sham (KS). In principle DFT is exact if we knew the universal HK functional (which contains electron-electron exchange-correlation terms); however, no mathematical description has been developed. As we do not know the exact form of the exchange-correlation term, a number of exchange-correlation functional have been developed. These can be derived from experimental thermochemical date or high-accuracy quantum calculations.

As exchange-correlation functionals are approximations, the electron density is not fully localised to a specific area. I hope this helps.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.