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Docs: fix the invalid link (#1315)
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2 changes: 1 addition & 1 deletion docs/advanced/elec_properties/Berry_phase.md
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# Berry Phase Calculation

From version 2.0.0, ABACUS is capable of calculating macroscopic polarization of insulators by using the Berry phase method, known as the ["modern theory of polarization"](https://www.sciencedirect.com/science/article/abs/pii/S0022459612003234). To calculate the polarization, you need first to do a self-consistent calculation to get the converged charge density. Then, do a non-self-consistent calculation with berry_phase setting to 1. You need also to specify the direction of the polarization you want to calculate. An example is given in the directory [examples/berryphase/lcao_PbTiO3](#https://github.com/deepmodeling/abacus-develop/tree/develop/examples/berryphase/lcao_PbTiO3).
From version 2.0.0, ABACUS is capable of calculating macroscopic polarization of insulators by using the Berry phase method, known as the ["modern theory of polarization"](https://www.sciencedirect.com/science/article/abs/pii/S0022459612003234). To calculate the polarization, you need first to do a self-consistent calculation to get the converged charge density. Then, do a non-self-consistent calculation with berry_phase setting to 1. You need also to specify the direction of the polarization you want to calculate. An example is given in the directory [examples/berryphase/lcao_PbTiO3](https://github.com/deepmodeling/abacus-develop/tree/develop/examples/berryphase/lcao_PbTiO3).

To run this example, first do a self-consistent calculation:
```
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2 changes: 1 addition & 1 deletion docs/advanced/elec_properties/Mulliken.md
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# Mulliken Charge Analysis

From version 2.1.0, ABACUS has the function of Mulliken population analysis. The example can be found in [examples/mulliken](#https://github.com/deepmodeling/abacus-develop/tree/develop/examples/mulliken). \
From version 2.1.0, ABACUS has the function of Mulliken population analysis. The example can be found in [examples/mulliken](https://github.com/deepmodeling/abacus-develop/tree/develop/examples/mulliken). \
To use this function, set ‘out_mul’ to ‘1’ in the INPUT file. After calculation, there will be an output file named mulliken.txt in the output directory. In the file, there are contents like:

```
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4 changes: 2 additions & 2 deletions docs/advanced/elec_properties/band.md
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# Extracting Band Structure

ABACUS can calculate the energy band structure, and the exampples can be found in [examples/band](#https://github.com/deepmodeling/abacus-develop/tree/develop/examples/band).\
Similar to the [DOS case](#https://abacus-rtd.readthedocs.io/en/latest/advanced/elec_properties/dos.html), we first, do a ground-state energy calculation ***with one additional keyword "[out_chg](#https://abacus-rtd.readthedocs.io/en/latest/advanced/input_files/input-main.html#out-chg)" in the INPUT file***:
ABACUS can calculate the energy band structure, and the exampples can be found in [examples/band](https://github.com/deepmodeling/abacus-develop/tree/develop/examples/band).\
Similar to the [DOS case](https://abacus-rtd.readthedocs.io/en/latest/advanced/elec_properties/dos.html), we first, do a ground-state energy calculation ***with one additional keyword "[out_chg](https://abacus-rtd.readthedocs.io/en/latest/advanced/input_files/input-main.html#out-chg)" in the INPUT file***:

```
out_chg 1
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16 changes: 8 additions & 8 deletions docs/advanced/elec_properties/dos.md
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## DOS

ABACUS can calculate the density of states (DOS) of the system, and the exampples can be found in [examples/dos](#https://github.com/deepmodeling/abacus-develop/tree/develop/examples/dos).\
We first, do a ground-state energy calculation ***with one additional keyword "[out_chg](#https://abacus-rtd.readthedocs.io/en/latest/advanced/input_files/input-main.html#out-chg)" in the INPUT file***:
ABACUS can calculate the density of states (DOS) of the system, and the exampples can be found in [examples/dos](https://github.com/deepmodeling/abacus-develop/tree/develop/examples/dos).\
We first, do a ground-state energy calculation ***with one additional keyword "[out_chg](https://abacus-rtd.readthedocs.io/en/latest/advanced/input_files/input-main.html#out-chg)" in the INPUT file***:

```
out_chg 1
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- calculation

choose which kind of calculation: scf calculation, nscf calculation, structure relaxation or Molecular Dynamics. Now we need to do one step of nscf calculation.
Attention: This is a main variable of ABACUS, and for its more information please see the [here](#https://abacus-rtd--1282.org.readthedocs.build/en/1282/advanced/input_files/input-main.html#calculation).
Attention: This is a main variable of ABACUS, and for its more information please see the [here](https://abacus-rtd--1282.org.readthedocs.build/en/1282/advanced/input_files/input-main.html#calculation).

- pw_diag_thr

threshold for the CG method which diagonalizes the Hamiltonian to get eigenvalues and eigen wave functions. If one wants to do nscf calculation, pw_diag_thr needs to be changed to a smaller account, typically smaller than 1.0e-3. Note that this parameter only apply to plane-wave calculations that employ the CG or Davidson method to diagonalize the Hamiltonian. For its more information please see the [here](#https://abacus-rtd--1282.org.readthedocs.build/en/1282/advanced/input_files/input-main.html#pw_diag_thr).
threshold for the CG method which diagonalizes the Hamiltonian to get eigenvalues and eigen wave functions. If one wants to do nscf calculation, pw_diag_thr needs to be changed to a smaller account, typically smaller than 1.0e-3. Note that this parameter only apply to plane-wave calculations that employ the CG or Davidson method to diagonalize the Hamiltonian. For its more information please see the [here](https://abacus-rtd--1282.org.readthedocs.build/en/1282/advanced/input_files/input-main.html#pw_diag_thr).

For LCAO calculations, this parameter will be neglected !
- init_chg

the type of starting density. When doing scf calculation, this variable can be set ”atomic”. When doing nscf calculation, the charge density already exists(eg. in SPIN1_CHG), and the variable should be set as ”file”. It means the density will be read from the existing file SPIN1_CHG. For its more information please see the [here](#https://abacus-rtd--1282.org.readthedocs.build/en/1282/advanced/input_files/input-main.html#init_chg).
the type of starting density. When doing scf calculation, this variable can be set ”atomic”. When doing nscf calculation, the charge density already exists(eg. in SPIN1_CHG), and the variable should be set as ”file”. It means the density will be read from the existing file SPIN1_CHG. For its more information please see the [here](https://abacus-rtd--1282.org.readthedocs.build/en/1282/advanced/input_files/input-main.html#init_chg).

- out_dos

output density of state(DOS). The unit of DOS is `(number of states)/(eV * unitcell)`. For its more information please see the [here](#https://abacus-rtd--1282.org.readthedocs.build/en/1282/advanced/input_files/input-main.html#out_dos).
output density of state(DOS). The unit of DOS is `(number of states)/(eV * unitcell)`. For its more information please see the [here](https://abacus-rtd--1282.org.readthedocs.build/en/1282/advanced/input_files/input-main.html#out_dos).

- dos_sigma

the gaussian smearing parameter(DOS), in unit of eV. For its more information please see the [here](#https://abacus-rtd--1282.org.readthedocs.build/en/1282/advanced/input_files/input-main.html#dos_sigma).
the gaussian smearing parameter(DOS), in unit of eV. For its more information please see the [here](https://abacus-rtd--1282.org.readthedocs.build/en/1282/advanced/input_files/input-main.html#dos_sigma).

- read_file_dir

the location of electron density file. For its more information please see the [here](#https://abacus-rtd--1282.org.readthedocs.build/en/1282/advanced/input_files/input-main.html#read_file_dir).
the location of electron density file. For its more information please see the [here](https://abacus-rtd--1282.org.readthedocs.build/en/1282/advanced/input_files/input-main.html#read_file_dir).

To have an accurate DOS, one needs to have a denser k-point mesh. For example, the KPT file can be set as:
```
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2 changes: 1 addition & 1 deletion docs/advanced/elec_properties/potential.md
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# Extracting Electrostatic Potential

From version 2.1.0, ABACUS has the function of outputing electrostatic potential, which consists of Hartree potential and the local pseudopotential. To use this function, set ‘[out_pot](#https://abacus-rtd.readthedocs.io/en/latest/advanced/input_files/input-main.html#out-pot)’ to ‘2’ in the INPUT file. Here is an example for the [Si-111 surface](#https://github.com/deepmodeling/abacus-develop/tree/develop/examples/electrostatic_potential/lcao_Si), and the INPUT file is:
From version 2.1.0, ABACUS has the function of outputing electrostatic potential, which consists of Hartree potential and the local pseudopotential. To use this function, set ‘[out_pot](https://abacus-rtd.readthedocs.io/en/latest/advanced/input_files/input-main.html#out-pot)’ to ‘2’ in the INPUT file. Here is an example for the [Si-111 surface](https://github.com/deepmodeling/abacus-develop/tree/develop/examples/electrostatic_potential/lcao_Si), and the INPUT file is:

```
INPUT_PARAMETERS
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8 changes: 4 additions & 4 deletions docs/advanced/elec_properties/wfc.md
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# Extracting Wave Functions

ABACUS is able to output electron wave functions in both PW and LCAO basis calculations. One can find the examples in [examples/wfc](#https://github.com/deepmodeling/abacus-develop/tree/develop/examples/wfc).
ABACUS is able to output electron wave functions in both PW and LCAO basis calculations. One can find the examples in [examples/wfc](https://github.com/deepmodeling/abacus-develop/tree/develop/examples/wfc).

## wave function in G space
For the wave function in G space, one only needs to do a ground-state energy calculation with one additional keyword in the INPUT file: '***[out_wfc_pw](#https://abacus-rtd.readthedocs.io/en/latest/advanced/input_files/input-main.html#out-wfc-pw)***' for PW basis calculation, and '***[out_wfc_lcao](#https://abacus-rtd.readthedocs.io/en/latest/advanced/input_files/input-main.html#out-wfc-lcao)***' for LCAO basis calculation.
For the wave function in G space, one only needs to do a ground-state energy calculation with one additional keyword in the INPUT file: '***[out_wfc_pw](https://abacus-rtd.readthedocs.io/en/latest/advanced/input_files/input-main.html#out-wfc-pw)***' for PW basis calculation, and '***[out_wfc_lcao](https://abacus-rtd.readthedocs.io/en/latest/advanced/input_files/input-main.html#out-wfc-lcao)***' for LCAO basis calculation.
In the PW basis case, the wave function is output in a file called `WAVEFUNC${k}.txt`, where `${k}` is the index of K point. \
In the LCAO basis case, several `LOWF_K_${k}.dat` files will be output in multi-k calculation and `LOWF_GAMMA_S1.dat` in gamma-only calculation.

## wave function in real space

One can also choose to output real-space wave function in PW basis calculation with the key word ***[out_wfc_r](#https://abacus-rtd.readthedocs.io/en/latest/advanced/input_files/input-main.html#out_wfc_r)***.
One can also choose to output real-space wave function in PW basis calculation with the key word ***[out_wfc_r](https://abacus-rtd.readthedocs.io/en/latest/advanced/input_files/input-main.html#out_wfc_r)***.

After calculation, an additional directory named `wfc_realspace` will appear in the `OUT.${system}` directory.

Notice: when the ***[basis_type](https://abacus-rtd.readthedocs.io/en/latest/advanced/input_files/input-main.html#basis_type)*** is `lcao`, only `ienvelope` ***[calculation](#https://abacus-rtd.readthedocs.io/en/latest/advanced/input_files/input-main.html#calculation)*** is effective. An example is [examples/wfc/lcao_ienvelope_Si2](#https://github.com/deepmodeling/abacus-develop/tree/develop/examples/wfc/lcao_ienvelope_Si2).
Notice: when the ***[basis_type](https://abacus-rtd.readthedocs.io/en/latest/advanced/input_files/input-main.html#basis_type)*** is `lcao`, only `ienvelope` ***[calculation](https://abacus-rtd.readthedocs.io/en/latest/advanced/input_files/input-main.html#calculation)*** is effective. An example is [examples/wfc/lcao_ienvelope_Si2](https://github.com/deepmodeling/abacus-develop/tree/develop/examples/wfc/lcao_ienvelope_Si2).

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