22
votes
Accepted
When and Why does Density Functional Theory (DFT) fail?
First, a word of caution: it is hard to generalize since there are so many different approximations to the exact exchange-correlation functional. Nonetheless, in my opinion:
The biggest weakness of ...
- 1,083
21
votes
When and Why does Density Functional Theory (DFT) fail?
It is very important to differentiate between Density Functional Theory (DFT) and Density Functional Approximation (DFA). DFT is an exact theory and if we know the exact formulation for exchange-...
- 9,237
20
votes
Accepted
When do we abandon ab initio methods?
There's three scenarios that come to my mind, for when ab initio methods get abandoned:
The cost becomes prohibitive (e.g. too many electrons)
The insight is lost
It is simply not required for what ...
13
votes
Accepted
What is static correlation, actually?
We know that the many-electron wave function has to be antisymmetric with respect to the exchange of two electrons:
$\Psi (x_1,x_2,\dots,x_i,\dots,x_j,\dots)=-\Psi (x_1,x_2,\dots,x_j,\dots,x_i,\dots)$....
- 20.1k
13
votes
When and Why does Density Functional Theory (DFT) fail?
Known failures of density functional approximations (DFAs) include anions, charge transfer systems and point defects (e.g. vacancy states). These are mainly due to self-interaction error, which can be ...
- 20.1k
11
votes
Is there any relation between static correlation and finite-temperature smearing?
This is a nice thought, but the two are not actually related. In principle, static correlation is completely accounted for in the exchange-correlation functional of Kohn-Sham DFT and there is no need ...
- 8,567
11
votes
Accepted
How should I compare different basis sets for post-Hartree-Fock methods?
First of all, MP2 (for example) is actually guaranteed to converge from above to the basis set limit even though MP2 in one specific basis set can give an energy lower than the FCI energy in that same ...
10
votes
When and Why does Density Functional Theory (DFT) fail?
DFT is single effective correlated particle theory
Problems that can be described by single determinant theory DFT in principle should able to provide a good description given that exact form of xc ...
- 976
10
votes
Accepted
What are the practical limitations of R12/F12 methods?
I will list 5 issues with F12/R12 methods, and then try to explain them the best I can:
Need for an auxiliary basis set
Most (if not all) F12/R12 methods require more than just a standard single-...
10
votes
Accepted
What are Pair Natural Orbitals?
I think Nike has answered to all questions adequately enough. I am sharing my understanding as one of the developers of the PNO-based local coupled-cluster (CC) methods, codes for computing response ...
- 226
10
votes
Accepted
What is the physical meaning of the term "non-local interaction"?
The non-local operator in Hartree Fock is the Exchange operator. Locality is a mathematical property. Look at the Coulomb operator first which acts like this:
$$ \hat v_H\;\varphi_s(r) = \sum_i^{N_\...
- 605
10
votes
How should I compare different basis sets for post-Hartree-Fock methods?
In general, when computing any property with different models (e.g. level of theory, basis set, etc), if you don't have some kind of theoretical bound (like the variational principle) to determine ...
- 15.9k
10
votes
Accepted
Why are Norm-conserving Pseudopotentials considered so important?
I think the best place to start is the original paper¹ proposing norm conserving pseudopotentials (NCPPs). It's very short and gives a nice explanation of why they were developed. I'll just give a ...
- 15.9k
9
votes
How does static correlation differ from Fermi correlation, and how does dynamic correlation differ from Coulomb correlation?
These two terms are quite rigorous in the way they're defined and used:
Fermi correlation: This is the correlation found in the electron exchange term in a Hartree-Fock calculation, describes the ...
9
votes
What are Pair Natural Orbitals?
I'll answer each of your three questions separately, but the one you say is "most important" will go first 😊
And most importantly, why are they used for correlation calculation?
They can ...
7
votes
Accepted
Is it possible to make segmented contracted basis sets for correlated calculations?
Yes, it is perfectly possible. As I've discussed here, it is possible to convert generally contracted basis sets into (somewhat) segmented sets without any formal loss of accuracy; next, one would ...
- 20.1k
7
votes
What are the computational limits of explicitly correlated methods?
Hylleraas' method is special to the case of the helium atom; note that the equation only has a single nucleus. When you go to more electrons, you get more and more interelectronic distances in your ...
- 20.1k
7
votes
Convert ase atoms to pymatgen structure
Try AseAtomsAdaptor.get_structure method from pymatgen.io.ase, it actually serves exactly this purpose.
- 346
7
votes
To what extent can coarse-grained models retain the essential quantum mechanical characteristics of a system?
Generally, in multi-scale modelling, QM characteristics are irrelevant. Most of the processes that we study for these multi-scale modelling are thermodynamics driven. So, I will be very surprised if ...
- 1,416
6
votes
What is the physical meaning of the term "non-local interaction"?
It's all hollow words if no proper definition is given. The definition I know is the following: For a one-body operator $A$, define
$$A(x,x^\prime):=\langle x|A|x^\prime\rangle \tag{1} \quad . $$
We ...
- 757
6
votes
Accepted
What are the computational limits of explicitly correlated methods?
Hylleraas wavefunctions tend only to be used for systems with up to 3 electrons. The reason for this is because the integrals have only been worked out analytically for up to 3 electrons, and they ...
6
votes
Why is electron correlation called the "chemical glue"?
Coincidentially, I recently read Perdew's recent autobiographical article where he also mentions the concept of "chemical glue." His simple image is as follows:
The exchange–correlation ...
- 1,526
5
votes
What correlation effects are included in KS-DFT with LDA and GGA?
LDA only includes local density effects.
GGA also includes dependence on the gradient of the density.
Meta-GGAs include dependence on the Laplacian of the density and/or the local kinetic energy ...
- 20.1k
5
votes
How should I compare different basis sets for post-Hartree-Fock methods?
Well, Nike already answered the point about the variationality: even though methods like MP2, CCSD, and CCSD(T) are non-variational in that they may over- or underestimate the energy of the ground ...
- 20.1k
5
votes
Quantifying electronic overlap?
I recommend the use of Multiwfn package. This software is free with Windows/Linux versions. It uses the wave function calculated from other software.
From the site:
Briefly speaking, Multiwfn can ...
- 24.2k
5
votes
Accepted
Is the one-electron reduced density matrix enough in DFT?
tl;dr
"Well yes, but actually no."
— the Pirate Captain (paraphrased), The Pirates! In an Adventure with Scientists!
The universal 2RDM functional is known (and linear!), but 2RDMs are ...
- 1,116
5
votes
Is the electron-electron interaction to blame, for the added complexity of using "orbitals" for an N-electron system?
Interpreting the question
For a 1-electron system, wavefunctions and orbitals are the same thing. For a 2-electron system, or any N-electron system with N>1, we can use "orbitals" to ...
4
votes
Is there any relation between static correlation and finite-temperature smearing?
You may like to read this 2012 JCP paper to know TAO-DFT:
https://aip.scitation.org/doi/10.1063/1.3703894
Even with the exact exchange-correlation energy functional in KS-DFT, one still needs to ...
- 83
4
votes
Are multiplet free atoms multireference?
Open shell atoms are multireference pretty much by definition. Take fluorine, for example, which has a $1s^2 2s^2 2p^5$ electron configuration and a $^2P$ ground state. We know that the electronic ...
- 20.1k
4
votes
Quantifying electronic overlap?
By the "metal cores", If you're referring to the overlapping of wave functions of electrons of metal ions separated by a distance, then you can in principle use quantum ESPRESSO to get some ...
- 4,536
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