Start Learning Density Functional Theory for Beginners

[saray1360]

Hi,

I want to start reading about Density Functional Theory and get through some of its approaches. I have a vey weak back ground of solid state physics.

Please guide me what is the best resource to start reading.

Regards

 

[alxm]

That would depend on whether you want to learn solid-state DFT or atomic/molecular DFT. Obviously, solid-state physicists aren't calculating the same things as quantum chemists. They also use different functionals (and usually different codes).

Many SS textbooks have something on DFT, and many cover a whole introduction (e.g. Patterson and Baily, "Solid-state physics: introduction to the theory"), same goes for practically all (newer) QC textbooks. A very comprehensive and important book is Parr and Yang's "Density functional theory of atoms and molecules", but that's not really a textbook and certainly not for beginners.

The only introductory-level book I can think of that's dedicated specifically to DFT is Koch's "A chemist's guide to density functional theory", (obviously geared towards chemical DFT) which lives up to its name quite well, as it substitutes a more descriptive approach for the details of the derivations of the equations.

Hence, not the best foundation if you intend to delve deeper in the theory, though, but possibly a good complement to the many books which have the opposite proportion of equations-to-text.

 

[cgk]

I can only second alxm's comment. What you need to read depends very much on what you want to achieve.

On another note, I'd recommend you to not spent too much time on the fundamentals of DFT, because they are really quite confusing. Many texts spend lots of time discussing whether or not DFT is a "formally exact theory". But this question is completely irrelevant in practice, and, in the opinion of many QC people, also in theory. If you get some grasp of the approximations applied in practice (and their limits), you are basically set. Knowing how the PBE, BYLP (see Colle-Salvetti) and B3LYP functionals were constructed is much more useful than knowing the Hohenberg-Kohn-"theorems" and their relation to actual real-world DFT.

 

[stone]

I would recommend reading this
http://arxiv.org/abs/cond-mat/0211443
A very nice introduction to DFT (particularly for a physicist).

 

[saray1360]

Thanks for all your replies.

The problem I have with DFT is that I read many papers in which they have done their calculations using DFT with different approximation. I can say I only understand local density approximation but GGA, PAW, GW are all hard for me to comprehend.

I really can not understand the logic behind the codes people are using to do their calculations. As an example a term like cut off energy is always a mystery to me no matter how many textbooks I read about it or for example the k-point grids and so on.

It seems that pseudopotential and its generating is very simple for all the people in the world except me!

I am using different codes for different calculations, but it seems I am swimming in a sea with no boundaries. That was why I thought about restarting my studies and begin from very simple texts to understand what I am doing.

I would be thankful to receive your advice.

 

[cgk]

The problem I have with DFT is that I read many papers in which they have done their calculations using DFT with different approximation. I can say I only understand local density approximation but GGA, PAW, GW are all hard for me to comprehend.

I really can not understand the logic behind the codes people are using to do their calculations. As an example a term like cut off energy is always a mystery to me no matter how many textbooks I read about it or for example the k-point grids and so on.

It seems that pseudopotential and its generating is very simple for all the people in the world except me!

Well, you need to get an overview over the technical details of how these methods are done.
For example: PAW, energy cutoffs and k-point grids are all specifications on the basis functions used to expand the crystal orbitals. In short: the energy cutoff decides how many plane waves you put into the calculation. More plane waves -> more accuracy in representing orbitals. The projectors in PAW are used because plane waves are exceptionally bad at representing atomic cores (because these have spatially very sharp features! Read up on Fourier transformation to see why this is bad). Therefore these cores are represented by something different than the plane waves (e.g., the projectors or ultrasoft pseudopotentials).

GW is not a density functional method, it contains more than self-consistent mean-field correlation. More concretely, it is an approximation to the quasi-particle self-energy in the Dyson equation. It is mentioned in the context of DFT only because the most common way of applying it in practice is as some kind of post-Kohn-Sham method, using lots of approximations and hand-waving (G0W0).

I am using different codes for different calculations, but it seems I am swimming in a sea with no boundaries. That was why I thought about restarting my studies and begin from very simple texts to understand what I am doing.

That is a good idea in general. I would recommend you to first understand how DFT is done in molecules, because there the basis functions are much easier to understand. For that you should read one of the texts alxm recommended (e.g., that Koch book). Afterwards you should learn the relation between Wannier orbitals and Crystal Orbitals (Bloch orbitals). This will give you the formal connection between what is done in molecular DFT programs (local basis functions -> Wannier orbitals, if you interpret the crystal as a big molecule) and what is done in periodic programs (Bloch waves).

There is really no big magic behind it. Just lots of unrelated technical things. Of course you should know these technical things when you apply the methods.

 

[judy lee]

Dear all,

As a beginner, I kind of have an experience similar to that of "saray1360". It is very painful:-)

When we use any codes for calculations, is there any routine procedure for us to follow up?
Like the first step to check the convergence, the second step to optimize geometry and so on? Or what else we need to be concerned about?

Struggling in darkness.

Kind regards

Judy

 

[rick_741]

Try Frank Jensen's book "Introduction to Computational Chemistry". Look for authors Christopher J. Cramer , Szabo (which is a classic) and David Young. You can find the basics in these books, whether you're going to quantum chemistry or solid state physics.

 

[Useful nucleus]

A very recent book that presents DFT from a practical approach for the beginner is:
Density Functional Theory: A Practical Introduction by D. Sholl and J. Steckel.

Reading this book will get you started in doing simulations in a meaningful way. But real understanding requires more knowledge in Solid State Physics and/or Quantum chemistry. I recommend it as a starting point.