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S R Maiti
S R Maiti
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I am new to this field, so there is a chance that I am mixing two entirely different concepts together, but it seems to be that static correlation and finite-temperature smearing in DFT are somehow related.

As I have understood static correlation comes into existence when the HOMO-LUMO gap is small, so that the ground state and the excited state have energies close to each other. This means one configuration (i.e. one slater determinant) is not good enough to describe the system, and multi-configurational methods have to be used.

Finite-temperature smearing (which I have seen mostly in DFT codes) is again used in cases where the HOMO and LUMO levels are close in energy. As they are close in energy they can exchange positions during the SCF iterations, making it difficult to attain convergence. So, the energy levels are allowed to have fractional populations, and the electrons are smeared across orbitals with some scheme like Fermi-Dirac. This fixes the problem (only the SCF convergence or some other problem I am not sure).

Now they both look similar to me in that they are attempting to solve the same problem. Intuitively, the electron-smearing looks like a cheap way to represent the average state of a multi-configuration system.

So, is there any relation between these two? If so, then can electron-smearing return the static correlation energy? If not, then how/why are they different?

Edit: I found this paper by Grimme et. al. (https://onlinelibrary.wiley.com/doi/abs/10.1002/anie.201501887), where finite temperature DFT is used to visualise static correlation in molecules. However, that paper only deals with visualising the fractional orbital density, but does not go into detail about the relation between correlation and temperature smearing, so my question still remains.

I am new to this field, so there is a chance that I am mixing two entirely different concepts together, but it seems to be that static correlation and finite-temperature smearing in DFT are somehow related.

As I have understood static correlation comes into existence when the HOMO-LUMO gap is small, so that the ground state and the excited state have energies close to each other. This means one configuration (i.e. one slater determinant) is not good enough to describe the system, and multi-configurational methods have to be used.

Finite-temperature smearing (which I have seen mostly in DFT codes) is again used in cases where the HOMO and LUMO levels are close in energy. As they are close in energy they can exchange positions during the SCF iterations, making it difficult to attain convergence. So, the energy levels are allowed to have fractional populations, and the electrons are smeared across orbitals with some scheme like Fermi-Dirac. This fixes the problem (only the SCF convergence or some other problem I am not sure).

Now they both look similar to me in that they are attempting to solve the same problem. Intuitively, the electron-smearing looks like a cheap way to represent the average state of a multi-configuration system.

So, is there any relation between these two? If so, then can electron-smearing return the static correlation energy? If not, then how/why are they different?

I am new to this field, so there is a chance that I am mixing two entirely different concepts together, but it seems to be that static correlation and finite-temperature smearing in DFT are somehow related.

As I have understood static correlation comes into existence when the HOMO-LUMO gap is small, so that the ground state and the excited state have energies close to each other. This means one configuration (i.e. one slater determinant) is not good enough to describe the system, and multi-configurational methods have to be used.

Finite-temperature smearing (which I have seen mostly in DFT codes) is again used in cases where the HOMO and LUMO levels are close in energy. As they are close in energy they can exchange positions during the SCF iterations, making it difficult to attain convergence. So, the energy levels are allowed to have fractional populations, and the electrons are smeared across orbitals with some scheme like Fermi-Dirac. This fixes the problem (only the SCF convergence or some other problem I am not sure).

Now they both look similar to me in that they are attempting to solve the same problem. Intuitively, the electron-smearing looks like a cheap way to represent the average state of a multi-configuration system.

So, is there any relation between these two? If so, then can electron-smearing return the static correlation energy? If not, then how/why are they different?

Edit: I found this paper by Grimme et. al. (https://onlinelibrary.wiley.com/doi/abs/10.1002/anie.201501887), where finite temperature DFT is used to visualise static correlation in molecules. However, that paper only deals with visualising the fractional orbital density, but does not go into detail about the relation between correlation and temperature smearing, so my question still remains.

Source Link
S R Maiti
S R Maiti
  • 7.2k
  • 1
  • 13
  • 71

Is there any relation between static correlation and finite-temperature smearing?

I am new to this field, so there is a chance that I am mixing two entirely different concepts together, but it seems to be that static correlation and finite-temperature smearing in DFT are somehow related.

As I have understood static correlation comes into existence when the HOMO-LUMO gap is small, so that the ground state and the excited state have energies close to each other. This means one configuration (i.e. one slater determinant) is not good enough to describe the system, and multi-configurational methods have to be used.

Finite-temperature smearing (which I have seen mostly in DFT codes) is again used in cases where the HOMO and LUMO levels are close in energy. As they are close in energy they can exchange positions during the SCF iterations, making it difficult to attain convergence. So, the energy levels are allowed to have fractional populations, and the electrons are smeared across orbitals with some scheme like Fermi-Dirac. This fixes the problem (only the SCF convergence or some other problem I am not sure).

Now they both look similar to me in that they are attempting to solve the same problem. Intuitively, the electron-smearing looks like a cheap way to represent the average state of a multi-configuration system.

So, is there any relation between these two? If so, then can electron-smearing return the static correlation energy? If not, then how/why are they different?