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Remove useless and outdated write_psi_r_1 interface and improve related docs and examples (#6345)
* Update docs related to wfc and modify examples * Remove write_psi_r_1 interface from ABACUS
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‎docs/advanced/elec_properties/wfc.md‎

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# Extracting Wave Functions
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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).
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ABACUS is able to output electron wave functions in both PW and LCAO basis calculations. One can find the examples in [examples/11_wfc](https://github.com/deepmodeling/abacus-develop/tree/develop/examples/11_wfc).
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## wave function in G space
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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.
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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. \
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In the LCAO basis case, several `WFC_NAO_K${k}.dat` files will be output in multi-k calculation and `WFC_NAO_GAMMA1.dat` in gamma-only calculation.
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## Wave Function in G-Space
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## wave function in real space
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To output wave functions in G-space, add one of the following keywords to the `INPUT` file while performing SCF calculation:
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- **PW basis**: Set [`out_wfc_pw`](https://abacus-rtd.readthedocs.io/en/latest/advanced/input_files/input-main.html#out-wfc-pw) to `1`. Output file format: `wfs[spin]k[kpoint]_pw.txt`, where `[spin]` is the spin channel index, and `[kpoint]` the k-point index.
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One can also choose to output real-space wave function in PW basis calculation with the key word ***[out_wfc_norm](https://abacus-rtd.readthedocs.io/en/latest/advanced/input_files/input-main.html#out-wfc-norm)***.
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- **LCAO basis**: Set [`out_wfc_lcao`](https://abacus-rtd.readthedocs.io/en/latest/advanced/input_files/input-main.html#out-wfc-lcao) to `1`.
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- **Multi-k calculations**: Generates multiple files `wfs[spin]k[kpoint]_nao.txt`.
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- **Gamma-only calculations**: `wfs[spin]_nao.txt` instead.
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Notice: when the ***[basis_type](https://abacus-rtd.readthedocs.io/en/latest/advanced/input_files/input-main.html#basis_type)*** is `lcao`, only `get_wf` ***[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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## Wave Function in Real Space
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One can also choose to output real-space wave functions with the keyword [`out_wfc_norm`](https://abacus-rtd.readthedocs.io/en/latest/advanced/input_files/input-main.html#out-wfc-norm) or [`out_wfc_re_im`](https://abacus-rtd.readthedocs.io/en/latest/advanced/input_files/input-main.html#out-wfc-re-im).
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Notice: When the [`basis_type`](https://abacus-rtd.readthedocs.io/en/latest/advanced/input_files/input-main.html#basis-type) is `lcao`, only `get_wf` [`calculation`](https://abacus-rtd.readthedocs.io/en/latest/advanced/input_files/input-main.html#calculation) is effective. An example is [examples/11_wfc/lcao_ienvelope_Si2](https://github.com/deepmodeling/abacus-develop/tree/develop/examples/11_wfc/lcao_ienvelope_Si2).

‎docs/advanced/input_files/input-main.md‎

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- **Type**: Boolean
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- **Availability**: Numerical atomic orbital basis (multi-k points)
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- **Description**: Whether to output the density matrix with Bravias lattice vector R index into files in the folder `OUT.${suffix}`. The files are named as `dmr{s}{spin index}{g}{geometry index}{_nao} + {".csr"}`. Here, 's' refers to spin, where s1 means spin up channel while s2 means spin down channel, and the sparse matrix format 'csr' is mentioned in [out_mat_hs2](#out_mat_hs2). Finally, if [out_app_flag](#out_app_flag) is set to false, the file name contains the optinal 'g' index for each ionic step that may have different geometries, and if [out_app_flag](#out_app_flag) is set to true, the density matrix with respect to Bravias lattice vector R accumulates during ionic steps:
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- **Description**: Whether to output the density matrix with Bravias lattice vector R index into files in the folder `OUT.${suffix}`. The files are named as `dmr{s}{spin index}{g}{geometry index}{_nao} + {".csr"}`. Here, 's' refers to spin, where s1 means spin up channel while s2 means spin down channel, and the sparse matrix format 'csr' is mentioned in [out_mat_hs2](#out_mat_hs2). Finally, if [out_app_flag](#out_app_flag) is set to false, the file name contains the optional 'g' index for each ionic step that may have different geometries, and if [out_app_flag](#out_app_flag) is set to true, the density matrix with respect to Bravias lattice vector R accumulates during ionic steps:
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- nspin = 1: `dmrs1_nao.csr`;
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- nspin = 2: `dmrs1_nao.csr` and `dmrs2_nao.csr` for the two spin channels.
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- **Default**: False
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- **Type**: Integer
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- **Availability**: Numerical atomic orbital basis
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- **Description**: Whether to output the electronic wavefunction coefficients into files and store them in the folder `OUT.${suffix}`. The files are named as `wf{s}{spin index}{k(optinal)}{k-point index}{g(optional)}{geometry index1}{_nao} + {".txt"/".dat"}`. Here, 's' refers to spin, where s1 means spin up channel while s2 means spin down channel, and 's12' refer to spinor wave functions that contains both spin channels with spin-orbital coupling or noncollinear calculations enabled. In addition, if 'gamma_only' is set to 0, then the optinoal k-point sampling index appears with the k-point index attached to the electronic wave function file names. Finally, if [out_app_flag](#out_app_flag) is set to false, the file name contains the optinal 'g' index for each ionic step that may have different geometries, and if [out_app_flag](#out_app_flag) is set to true, the wave functions accumulate during ionic steps.
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- **Description**: Whether to output the electronic wavefunction coefficients into files and store them in the folder `OUT.${suffix}`. The files are named as `wf{s}{spin index}{k(optional)}{k-point index}{g(optional)}{geometry index1}{_nao} + {".txt"/".dat"}`. Here, 's' refers to spin, where s1 means spin up channel while s2 means spin down channel, and 's12' refer to spinor wave functions that contains both spin channels with spin-orbital coupling or noncollinear calculations enabled. In addition, if 'gamma_only' is set to 0, then the optinoal k-point sampling index appears with the k-point index attached to the electronic wave function file names. Finally, if [out_app_flag](#out_app_flag) is set to false, the file name contains the optional 'g' index for each ionic step that may have different geometries, and if [out_app_flag](#out_app_flag) is set to true, the wave functions accumulate during ionic steps.
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- 0: no output
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- 1: (txt format)
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- gamma-only: `wfs1_nao.txt` or `wfs2_nao.txt`, ...;

‎examples/08_charge_density/lcao_nspin1_Si2/INPUT‎

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INPUT_PARAMETERS
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#Parameters (General)
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#Parameters (General)
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pseudo_dir ../../../tests/PP_ORB
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orbital_dir ../../../tests/PP_ORB
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calculation scf
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calculation scf
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nbands 8
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#Parameters (Methos)
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#Parameters (Methods)
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basis_type lcao
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symmetry 0
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symmetry 0
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#Parameters (Accuracy)
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ecutwfc 60 ###Energy cutoff needs to be tested to ensure your calculation is reliable.[1]
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ecutwfc 60 ###Energy cutoff needs to be tested to ensure your calculation is reliable.[1]
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scf_thr 1.0e-7 // about iteration
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scf_nmax 100
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scf_nmax 100
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#Parameters (File)
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out_chg 1
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‎examples/08_charge_density/pw_nspin1_Al/INPUT‎

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INPUT_PARAMETERS
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#Parameters (General)
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#Parameters (General)
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pseudo_dir ../../../tests/PP_ORB
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calculation scf
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calculation scf
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symmetry 0
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#Parameters (Methos)
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#Parameters (Methods)
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basis_type pw
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ecutwfc 60 ###Energy cutoff needs to be tested to ensure your calculation is reliable.[1]
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ecutwfc 60 ###Energy cutoff needs to be tested to ensure your calculation is reliable.[1]
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scf_thr 1.0e-8 // about iteration
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scf_nmax 100
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smearing_method gauss
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smearing_sigma 0.01
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scf_nmax 100
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smearing_method gauss
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smearing_sigma 0.01
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#Parameters (File)
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out_chg 1
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‎examples/09_density_matrix/lcao_nspin1_Si2/INPUT‎

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INPUT_PARAMETERS
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#Parameters (General)
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#Parameters (General)
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pseudo_dir ../../../tests/PP_ORB
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orbital_dir ../../../tests/PP_ORB
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calculation scf
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calculation scf
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nbands 16
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#Parameters (Methos)
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#Parameters (Methods)
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basis_type lcao
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symmetry 0
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symmetry 0
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#Parameters (Accuracy)
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ecutwfc 60 ###Energy cutoff needs to be tested to ensure your calculation is reliable.[1]
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ecutwfc 60 ###Energy cutoff needs to be tested to ensure your calculation is reliable.[1]
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scf_thr 1.0e-7 // about iteration
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scf_nmax 100
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scf_nmax 100
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#Parameters (File)
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gamma_only 1
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gamma_only 1
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out_dmk 1
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‎examples/11_wfc/README‎

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These examples show how to output the wavefunction in G space.
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For PW basis:
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- set 'out_wfc_pw' to '1'
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The wave function is output in a file called 'WAVEFUNC1.txt'
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These examples demonstrate how to output wave functions in G-space and real space.
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For LCAO basis:
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- set 'out_wfc_lcao' to '1'
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Several `WFC_NAO_K#.txt` files will be output in multi-k calculation and
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`WFC_NAO_GAMMA1.txt` in gamma-only calculation.
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For Plane-Wave (PW) Basis:
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- Set `out_wfc_pw = 1`.
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The wave functions will be output to a series of files named `wfs[spin]k[kpoint]_pw.txt`.
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For LCAO Basis:
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- Set `out_wfc_lcao = 1`.
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In multi-k calculations, multiple files named `wfs[spin]k[kpoint]_nao.txt` will be generated.
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In gamma-only calculations, `wfs[spin]_nao.txt` instead.
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For the wave functions in Real Space:
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- set 'out_wfc_r' to '1'
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The wave function is output in files OUT.${suffix}/wfc_realspace/wfc_realspace_$K_$B,
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where $K and $B is the index of k point and band respectively.
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Note, it is only used in planewave basis and get_wf calculation in localized orbitals set
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For Wave Functions in Real Space:
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- Set either `out_wfc_norm` or `out_wfc_re_im` to a space-separated string of 0s and 1s.
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- E.g.: `1 0 0 0 0 1 1 1 1 1 0`, or `1 4*0 5*1 0` for short.
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The wave functions will be output to files named `wfi[state]s[spin]k[kpoint][re/im].cube`.
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Note, it is only supported for PW basis and `get_wf` calculation under LCAO basis.

‎examples/11_wfc/lcao_ienvelope_Si2/INPUT1‎

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INPUT_PARAMETERS
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#Parameters (General)
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#Parameters (General)
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pseudo_dir ../../../tests/PP_ORB
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orbital_dir ../../../tests/PP_ORB
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calculation scf
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ntype 1
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nbands 8
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#Parameters (Methos)
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#Parameters (Methods)
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basis_type lcao
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symmetry 0
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#Parameters (Accuracy)
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ecutwfc 50
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scf_thr 1.0e-7 // about iteration
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scf_nmax 100
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scf_nmax 100
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#Parameters (File)
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out_wfc_lcao 1
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out_wfc_lcao 1

‎examples/11_wfc/lcao_ienvelope_Si2/INPUT2‎

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INPUT_PARAMETERS
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#Parameters (General)
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#Parameters (General)
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pseudo_dir ../../../tests/PP_ORB
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orbital_dir ../../../tests/PP_ORB
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calculation get_wf
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nbands 8
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#Parameters (Methos)
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#Parameters (Methods)
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basis_type lcao
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symmetry 0
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#Parameters (Accuracy)
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ecutwfc 50
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#Parameters (File)
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init_wfc file
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out_wfc_r 1
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init_wfc file
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out_wfc_norm 4*1

‎examples/11_wfc/lcao_ienvelope_Si2/run.sh‎

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[[ ! -f get_wf.output ]] ||
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[[ ! -f OUT.ABACUS/running_scf.log ]] ||
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[[ ! -f OUT.ABACUS/running_get_wf.log ]] ||
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[[ ! -f OUT.ABACUS/WFC_NAO_K1.txt ]] ||
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[[ ! -f OUT.ABACUS/WFC_NAO_K36.txt ]] ||
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[[ ! -f OUT.ABACUS/wfs1k1_nao.txt ]] ||
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[[ ! -f OUT.ABACUS/wfs1k36_nao.txt ]] ||
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[[ ! ( "$(tail -1 OUT.ABACUS/running_scf.log)" == " Total Time :"* ) ]] ||
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[[ ! ( "$(tail -1 OUT.ABACUS/running_get_wf.log)" == " Total Time :"* ) ]]
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then

‎examples/11_wfc/lcao_scf_Si2/INPUT‎

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INPUT_PARAMETERS
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#Parameters (General)
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#Parameters (General)
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pseudo_dir ../../../tests/PP_ORB
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orbital_dir ../../../tests/PP_ORB
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calculation scf
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nbands 8
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#Parameters (Methos)
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#Parameters (Methods)
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basis_type lcao
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symmetry 0
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#Parameters (Accuracy)
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ecutwfc 60 ###Energy cutoff needs to be tested to ensure your calculation is reliable.[1]
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ecutwfc 60 ###Energy cutoff needs to be tested to ensure your calculation is reliable.[1]
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scf_thr 1.0e-7 // about iteration
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scf_nmax 100
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scf_nmax 100
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#Parameters (File)
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out_wfc_lcao 1
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out_wfc_lcao 1
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### [1] Energy cutoff determines the quality of numerical quadratures in your calculations.

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