What do shortrange and longrange corrections mean in DFT methods?
Solution 1
There are many good review articles, but I really like the freely available "The ABC of DFT" by Kieron Burke (and friends) and a recent review article that tries to keep to understandable language.
The problem is treating the Coulomb interactions. Conventional DFT is not "asymptotically correct." That is, at long range, the 1/r behavior is not met, and dispersion interactions (e.g., van der Waals forces) are not properly handled either.
For example, in Neon atom (from ABC of DFT by Burke):
The problem of course is that most DFT methods start from the local density approximation (LDA) which only considers the electron density at a particular (local) point. LDA indicates that the longrange behavior falls off exponentially instead of 1/r:
$$v_{xc}^{\mathrm{LDA}}(\mathbf{r}) = \frac{\delta E^{\mathrm{LDA}}}{\delta\rho(\mathbf{r})} = \epsilon_{xc}(\rho(\mathbf{r})) + \rho(\mathbf{r})\frac{\partial \epsilon_{xc}(\rho(\mathbf{r}))}{\partial\rho(\mathbf{r})}\ $$
So some recent efforts have used "range separated" functionals, e.g.,
$$ \frac{1}{r} = \frac{1g(r)}{r} + \frac{g(r)}{r}$$
The first (shortrange) term can be handled by the generalized gradient approximation (GGA) used by basically all modern functionals. The second term is usually handled by HartreeFock (i.e., exact exchange), and there's some function g(r) which smoothly scales between the two.
I think modern rangeseparated hybrid functionals are quite good, but choosing a functional depends a bit on the property that you want to predict. Thermodynamics? Excitation energies? Oxidation/reduction potentials from orbital eigenvalues? etc.
Solution 2
Geoff basically answers your question. As the tip about choosing a method: if you are looking for an accuracy beyond 1 kcal/mol, then you should consider wavefunction based quantum chemistry methods, e.g. coupledcluster methods. CCSD(T) method would be very appropriate for ground state calculations, while you can use EOMCCSD methods for the excited state calculations. However, these methods have a much worse scaling compared to DFT, so depending on the size of your molecule and the computational sources you have, these methods might be out of reach. You may want to check this review on coupledcluster methods.
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gunakkoc
Updated on August 01, 2022Comments

gunakkoc over 1 year
Currently I am looking for the most accurate calculation method for a simple nonconjugate molecule consist of C, N, O and H. Normally I would try each method for a similar and known molecule then compare them with the experimental results but I don't have anything to compare this time.
So I need to predict a method for ground state and excited state calculations. While I was searching I kept coming across the terms "longrange" and "shortrange". In the original publication of CAMB3LYP for example, the authors claim that CAMB3LYP provides additional longrange corrections, the weak part of B3LYP. What does it suppose to mean to me? I was unable to find any definitions of these terms.
Any additional tips about choosing a method are appreciated, also.

Geoff Hutchison almost 9 yearsI think "choosing a method" would be a separate question, and you'd need to provide a bit more detail on your system.


Geoff Hutchison almost 9 yearsWelcome! There are definitely some CCSD(T) proponents on here. I'd say that many modern DFT functionals, particularly the rangeseparated hybrids do extremely well at a wide range of properties. I do suggest CCSD and CCSD(T) methods, and with modern hardware and F12 implementations, these are much more widely applicable.