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docs: add hands-on examples and input keywords for implicit solvation model
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README.md

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20. (subsidiary tool)Generator for second generation numerical orbital basis.
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21. Interface with DPGEN
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22. Interface with phonopy
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23. Implicit solvation model
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[back to top](#readme-top)
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- [BSSE for molecular formation energy](docs/examples/BSSE.md)
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- [ABACUS-DPGEN interface](docs/examples/dpgen.md)
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- [ABACUS-phonopy interface](docs/examples/phonopy.md)
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- [Implicit solvation model](docs/examples/implicit-sol.md)
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[back to top](#readme-top)
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docs/examples/implicit-sol.md

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# Implicit solvation model
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[back to main page](../../README.md)
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Solid-liquid interfaces are ubiquitous in nature and frequently encountered and employed in materials simulation. The solvation effect should be taken into account in accurate first-principles calculations of such systems.
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Implicit solvation model is a well-developed method to deal with solvation effects, which has been widely used in finite and periodic systems. This approach treats the solvent as a continuous medium instead of individual “explicit” solvent molecules, which means that the solute embedded in an implicit solvent and the average over the solvent degrees of freedom becomes implicit in the properties of the solvent bath.
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## Input
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```
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INPUT_PARAMETERS
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imp_sol 1
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eb_k 80
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tau 0.000010798
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sigma_k 0.6
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nc_k 0.00037
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```
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- imp_sol
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If set to 1, an implicit solvation correction is considered. 0:vacuum calculation(default).
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- eb_k
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The relative permittivity of the bulk solvent, 80 for water. Used only if `imp_sol` == true.
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- tau
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The effective surface tension parameter, which describes the cavitation, the dispersion, and the repulsion interaction between the solute and the solvent that are not captured by the electrostatic terms.
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We use the values of `tau`, `sigma_k`, `nc_k` that were obtained by a fit of the model to experimental solvation energies for molecules in water. tau = 0.525 $meV/Å^{2}$ = 1.0798e-05 $Ry/Bohr^{2}$.
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- sigma_k
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We assume a diffuse cavity that is implicitly determined by the electronic structure of the solute.
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`sigma_k` is the parameter that describes the width of the diffuse cavity. The specific value is sigma_k = 0.6.
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- nc_k
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`nc_k` determines at what value of the electron density the dielectric cavity forms.
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The specific value is nc_k = 0.0025 $Å^{-3}$ = 0.00037 $Bohr^{-3}$.
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## Output
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In this example, we calculate the implicit solvation correction for H2O.
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The results of the energy calculation are written in the “running_nscf.log” in the OUT folder.
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```
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Energy Rydberg eV
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E_KohnSham -34.3200995971 -466.948910448
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E_Harris -34.2973698556 -466.639656449
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E_band -7.66026117767 -104.223200184
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E_one_elec -56.9853883251 -775.325983964
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E_Hartree +30.0541108968 +408.907156521
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E_xc -8.32727420734 -113.298378028
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E_Ewald +0.961180728747 +13.0775347188
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E_demet +0 +0
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E_descf +0 +0
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E_efield +0 +0
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E_exx +0 +0
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E_sol_el -0.0250553663339 -0.340895747619
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E_sol_cav +0.00232667606131 +0.031656051834
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E_Fermi -0.499934383866 -6.8019562467
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```
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- E_sol_el: Electrostatic contribution to the solvation energy.
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- E_sol_cav: Cavitation and dispersion contributions to the solvation energy.
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Both `E_sol_el` and `E_sol_cav` corrections are included in `E_KohnSham`.
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[back to top](#implicit-solvation-model)

docs/input-main.md

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[cal_cond](#cal_cond) | [cond_nche](#cond_nche) | [cond_dw](#cond_dw) | [cond_wcut](#cond_wcut) | [cond_wenlarge](#cond_wenlarge) | [cond_fwhm ](#cond_fwhm )
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- [Implicit solvation model](#implicit-solvation-model)
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[imp_sol](#imp_sol) | [eb_k](#eb_k) | [tau](#tau) | [sigma_k](#sigma_k) | [nc_k](#nc_k)
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[back to main page](../README.md)
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## Structure of the file
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- **Type**: Integer
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- **Description**: We use gaussian functions to approxiamte $\delta(E)\approx \frac{1}{\sqrt{2\pi}\Delta E}e^{-\frac{E^2}{2{\Delta E}^2}}$. FWHM for conductivities, $FWHM=2*\sqrt{2\ln2}\cdot \Delta E$. The unit is eV.
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- **Default**: 0.3
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### Implicit solvation model
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This part of variables are used to control the usage of implicit solvation model. This approach treats the solvent as a continuous medium instead of individual “explicit” solvent molecules, which means that the solute embedded in an implicit solvent and the average over the solvent degrees of freedom becomes implicit in the properties of the solvent bath.
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#### imp_sol
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- **Type**: Boolean
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- **Description**: If set to 1, an implicit solvation correction is considered.
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- **Default**: 0
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#### eb_k
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- **Type**: Real
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- **Description**: The relative permittivity of the bulk solvent, 80 for water. Used only if `imp_sol` == true.
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- **Default**: 80
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#### tau
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- **Type**: Real
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- **Description**: The effective surface tension parameter, which describes the cavitation, the dispersion, and the repulsion interaction between the solute and the solvent that are not captured by the electrostatic terms. The unit is $Ry/Bohr^{2}$.
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- **Default**: 1.0798e-05
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#### sigma_k
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- **Type**: Real
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- **Description**: We assume a diffuse cavity that is implicitly determined by the electronic structure of the solute.
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`sigma_k` is the parameter that describes the width of the diffuse cavity.
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- **Default**: 0.6
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#### nc_k
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- **Type**: Real
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- **Description**: It determines at what value of the electron density the dielectric cavity forms.
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The unit is $Bohr^{-3}$.
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- **Default**: 0.00037

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