Is there a way to go from the density directly to the energy without having t...

vitalys

Hi, it's Vitaly
I was searching about the subject of wave function and electron density, when i found a pdf lecture about that, and what confused me is a scheme in the page 17 explaining the process to get the energy,
I always thought that quantum chemistry software use directly the electron density to optimize and get the energy of a system, but I was wrong.
It's a very complicated field, It always make me confused.
I know that the quantum softwares had to solve the schrodinger equation in purpose to access all the other properties, but what's the electron density had to do with that and how the softwares be able to calculated? Is there a specific algorithm?
I hope I could find some clarifications in this forum that remove my confusing.


Lecture:  https://www.southampton.ac.uk/as ... compchem/DFT_L3.pdf

sobereva

According to the first Hohenberg-Kohn theorem, in principle one can exactly evaluate electronic energy (E) of a system based on electron density distribution (ρ) of ground state. However, such an exact functional relationship E[ρ] has not been found in practice. So, you can at most using existing functionals (e.g. PBE, BLYP...) to *approximately* estimate E.

Notice that most quantum chemistry programs like Gaussian and ORCA implement Koha-Sham DFT (KS-DFT) rather than the DFT in original sense (which is often referred to as orbital-free DFT currently). Formally, the KS-DFT equation is an effective one-electron Schrodinger equation, by solving it you will obtain orbital wavefunctions, which will be used in evaluating E in the present SCF cycle and construct effective external potential utilized in the next SCF cycle. The main reason of introducing the orbital wavefunctions in the KS-DFT formalism is to obtain a relatively accurate electronic kinetic energy (T), which is a key component of E and can hardly be evaluated satisfactorily based on existing kinetic energy functional T[ρ] (except for certain metal systems. If you have interest, you may view J. Chem. Phys. 150, 204106 (2019) DOI: 10.1063/1.5095072, which collects almost all already proposed kinetic energy functionals).

Also note exchange-correlation energy Exc is an important part of E, it can be estimated via exchange-correlation (XC) functionals. Many popular XC functionals not only depend on ρ (and its derivatives), but also depend on orbital wavefunctions, these are known as hybrid functionals, such as B3LYP, PBE0, wB97XD, M06-2X.

vitalys

sobereva 发表于 2021-12-5 07:28
According to the first Hohenberg-Kohn theorem, in principle one can exactly evaluate electronic ener ...

That's a pretty detailed wonderful explanation, thank you so much.
I assume that all the information about the wave function are recorded in a specific file with the extension .wfn, and we can calculate all the other properties based on this file, like the electron density, laplacian of electron density, electron spin density, did I asdume TRUE ?
What do you mean by real space functions ?

sobereva

vitalys 发表于 2021-12-5 16:12
That's a pretty detailed wonderful explanation, thank you so much.
I assume that all the informat ...

You are correct.

Real space function means the variable corresponds to a point in three-dimensional space, unlike some functions defined in e.g. momentum space.