Skip to content

Commit

Permalink
Update hsolver.md (#1305)
Browse files Browse the repository at this point in the history
  • Loading branch information
wenfei-li committed Sep 26, 2022
1 parent f0a577e commit 9f88a50
Showing 1 changed file with 2 additions and 2 deletions.
4 changes: 2 additions & 2 deletions docs/advanced/scf/hsolver.md
Original file line number Diff line number Diff line change
Expand Up @@ -10,11 +10,11 @@
#### blablabla

## Stochasic DFT
We support stochastic DFT calculation (SDFT) or mixed stochastic-deterministic DFT (MDFT) with plane-wave basis [[Phys. Rev. B 106, 125132 (2022)](https://doi.org/10.1103/PhysRevB.106.125132)]. Different from traditional KSDFT with the explicit diagonalization method, SDFT and MDFT caluclate physics quantities with trace. The advanges of SDFT and MDFT compared to the traditional KSDFT are the ability to simulate larger sizes and higher temperatures. In our package, SDFT and MDFT can be used when setting the `calculation` parameter to `sto-scf` or `sto-md` for SCF calculations or MD calculations. To start it, you can refer to an easy [example](../../examples/stochastic.md) and [INPUT](../../input-main.md#electronic-structure-sdft).
We support stochastic DFT calculation (SDFT) or mixed stochastic-deterministic DFT (MDFT) with plane-wave basis [[Phys. Rev. B 106, 125132 (2022)](https://doi.org/10.1103/PhysRevB.106.125132)]. Different from traditional KSDFT with the explicit diagonalization method, SDFT and MDFT calculate physical quantities with trace of the corresponding operators. The advantages of SDFT and MDFT compared to the traditional KSDFT are the ability to simulate larger sizes and higher temperatures. In our package, SDFT and MDFT can be used by setting the `calculation` parameter to `sto-scf` or `sto-md` for SCF calculations or MD calculations. To start with, you can refer to an easy [example](../../examples/stochastic.md) and an explanation of the [input variables](../../input-main.md#electronic-structure-sdft).

When we have a hamiltonian, the electronic density can be calculated with
$$\rho(\mathbf{r})={\rm Tr}[f(\hat{H})\ket{\mathbf{r}}\bra{\mathbf{r}}],$$
where the Fermi-Dirac function $f(\hat{H})=\frac{1}{1+\exp(\frac{\hat{H}-\mu}{kT})}$ and it can be calculated with the Chebyshev expansion. Here we only support the "fd" or "fermi-dirac" `smearing_method`, the parameter `smearing_sigma` is equal the temperature $T$ (in Ry) and `nche_sto` represents the orders of the expansion.
where the Fermi-Dirac function $f(\hat{H})=\frac{1}{1+\exp(\frac{\hat{H}-\mu}{kT})}$ and it can be calculated with the Chebyshev expansion. Here we only support the "fd" or "fermi-dirac" `smearing_method`, the parameter `smearing_sigma` is equal the temperature $T$ (in Ry) and `nche_sto` represents the order of the expansion.
SDFT calculates the trace with
$${\rm Tr}[\hat{O}]=\sum_{i=1}^{N_\chi}{\bra{\chi_i}\hat{O}\ket{\chi_i}},$$
while MDFT calculates the trace with
Expand Down

0 comments on commit 9f88a50

Please sign in to comment.