Docs : add part for XC functionals (#1287)

* doc : update for VdW correction

* doc : fix bug in index.rst

* doc : add another layer in example/vdw

* doc : add link for vdw example

* doc : add part for XC functionals

Co-authored-by: wenfei-li <liwenfei@gmail.com>

docs/advanced/input_files/input-main.md

@@ -206,31 +206,8 @@ This part of variables are used to control general system parameters.
 #### dft_functional
 
 - **Type**: String
-- **Description**: type of exchange-correlation functional used in calculation. If dft_functional is not set, the program will adopt the functional used to generate pseudopotential files, provided all of them are generated using the same functional. For example, we present a few lines in Si’s GGA pseudopotential file Si_ONCV_PBE-1.0.upf:
-        ```
-        ...
-        <PP_HEADER
-        generated="Generated using ONCVPSP code by D. R. Hamann"
-        author="Martin Schlipf and Francois Gygi"
-        date="150105"
-        comment=""
-        element="Si"
-        pseudo_type="NC"
-        relativistic="scalar"
-        is_ultrasoft="F"
-        is_paw="F"
-        is_coulomb="F"
-        has_so="F"
-        has_wfc="F"
-        has_gipaw="F"
-        core_correction="F"
-        functional="PBE"
-        z_valence=" 4.00"
-        total_psenergy=" -3.74274958433E+00"
-        rho_cutoff=" 6.01000000000E+00"
-        ```
-    According to the information above, this pseudopotential is generated using PBE functional.
-    On the other hand, if dft_functional is specified, it will overwrite the functional from pseudopotentials and performs calculation with whichever functional the user prefers. We further offer two ways of supplying exchange-correlation functional. The first is using 'short-hand' names such as 'LDA', 'PBE', 'SCAN'. A complete list of 'short-hand' expressions can be found in [source code](../source/module_xc/xc_functional.cpp). The other way is only available when ***compiling with LIBXC***, and it allows for supplying exchange-correlation functionals as combinations of LIBXC keywords for functional components, joined by plus sign, for example, 'dft_functional='LDA_X_1D_EXPONENTIAL+LDA_C_1D_CSC'. The list of LIBXC keywords can be found on its [website](https://www.tddft.org/programs/libxc/functionals/). In this way, **we support all the LDA,GGA and mGGA functionals provided by LIBXC**.
+- **Description**: In our package, the XC functional can either be set explicitly using the `dft_functional` keyword in `INPUT` file. If `dft_functional` is not specified, ABACUS will use the xc functional indicated in the pseudopotential file. 
+    On the other hand, if dft_functional is specified, it will overwrite the functional from pseudopotentials and performs calculation with whichever functional the user prefers. We further offer two ways of supplying exchange-correlation functional. The first is using 'short-hand' names such as 'LDA', 'PBE', 'SCAN'. A complete list of 'short-hand' expressions can be found in [source code](../../../source/module_xc/xc_functional.cpp). The other way is only available when ***compiling with LIBXC***, and it allows for supplying exchange-correlation functionals as combinations of LIBXC keywords for functional components, joined by plus sign, for example, 'dft_functional='LDA_X_1D_EXPONENTIAL+LDA_C_1D_CSC'. The list of LIBXC keywords can be found on its [website](https://www.tddft.org/programs/libxc/functionals/). In this way, **we support all the LDA,GGA and mGGA functionals provided by LIBXC**.
 
     Furthermore, the old INPUT parameter exx_hybrid_type for hybrid functionals has been absorbed into dft_functional. Options are `hf` (pure Hartree-Fock), `pbe0`(PBE0), `hse` (Note: in order to use HSE functional, LIBXC is required). Note also that HSE has been tested while PBE0 has NOT been fully tested yet, and the maximum parallel cpus for running exx is Nx(N+1)/2, with N being the number of atoms. And forces for hybrid functionals are not supported yet.
 

docs/advanced/scf/construct_H.md

@@ -2,4 +2,82 @@
 
 ## Exchange-Correlation Functionals
 
-## DFT+U
+In our package, the XC functional can either be set explicitly using the `dft_functional` keyword in `INPUT` file. If `dft_functional` is not specified, ABACUS will use the xc functional indicated in the pseudopotential file. 
+
+Several common functionals are implemented in ABACUS, such as PZ and PBE. Users can check out this [file](../../../source/module_xc/xc_funcs.h) for a complete list of functionals implemented in ABACUS. Furthermore, if ABACUS is compiled with LIBXC, we also support all the LDA, GGA and meta-GGA functionals provided therein.
+
+Here, we use a simple [example calculation](https://github.com/deepmodeling/abacus-develop/tree/develop/examples/scf/lcao_Si2) for illustration.
+
+1. **Default setting:**
+
+    In the original `INPUT` file, there is no specification of the `dft_functional` keyword. As a result, we use the default option, that is to use the xc functional in the pseudopotential file, `Si.pz-vbc.UPF`. We can take a look at the first few lines of the `<PP_HEADER>` section from the pseudopotential file:
+
+    ```
+    <PP_HEADER>
+    0                   Version Number
+    Si                   Element
+    NC                  Norm - Conserving pseudopotential
+        F                  Nonlinear Core Correction
+    SLA  PZ   NOGX NOGC   PZ   Exchange-Correlation functional
+    ```
+
+    From the line commented 'Exchange-Correlation functional', we see that this pseudopotential is generated using PZ functional. As a result, if we run ABACUS with the original setting, PZ functional will be used.
+
+    > Note : for systems with multiple elements, if no `dft_functional` is specified, users should make sure that all pseudopotentials are using the same functional. Otherwise, the type of xc functional should be specified explicitly.
+
+2. **Using PBE**
+
+    On the other hand, users might also explicitly specify the xc functional through `dft_functional` parameter. For example, to use PBE functional, add the following line to `INPUT` file and rerun the calculation:
+
+    ```
+    dft_functional PBE
+    ```
+
+3. **More functionals from LIBXC**
+
+    ABACUS has its own implementation of the PBE functional as well as a few others, but our list is far from comprehensive. However, if ABACUS is compiled with LIBXC, we also support all the LDA, GGA and meta-GGA functionals provided therein.
+
+    For this part, users should compile the ABACUS code with LIBXC linked (version 5.1.7 or higher).
+
+    To use SCAN functional, make the following modification to the `INPUT` file:
+
+    ```
+    dft_functional SCAN
+    ```
+
+    Note that in the case of PBE and SCAN, we are using 'short-hand' names to represent the entire functional, which is made up of individual exchange and correlation components. A complete list of 'short-hand' expressions supported by ABACUS can be found in [source code](../source/module_xc/xc_functional.cpp).
+
+    Apart from the 'short-hand' names, ABACUS also allow supplying exchange-correlation functionals as combinations of LIBXC keywords for functional components, joined by plus sign, for example, setting:
+
+    ```
+    dft_functional LDA_X_YUKAWA +LDA_C_1D_CSC
+    ```
+    means we are using the short-range Yukawa attenuated exchange along with the Casula, Sorella & Senatore LDA correlation functional.
+
+    The list of LIBXC keywords can be found on its [website](https://www.tddft.org/programs/libxc/functionals/).
+
+4. **Temperature-dependent functional**
+
+    In ABACUS, we provide temperature-dependent functionals through LIBXC. For such functionals, the keyword `xc_temperature` (unit is Rydberg) is used to specify the temperature, such as the following:
+
+    ```
+    dft_functional LDA_XC_CORRKSDT 
+    xc_temperature 10
+    ```
+
+5. **Hybrid functional**
+
+    The old INPUT parameter exx_hybrid_type for hybrid functionals has been absorbed into `dft_functional`. Options are `hf` (pure Hartree-Fock), `pbe0`(PBE0), `hse` (Note: in order to use HSE functional, LIBXC is required). Note also that HSE has been tested while PBE0 has NOT been fully tested yet, and the maximum parallel cpus for running exx is Nx(N+1)/2, with N being the number of atoms. And forces for hybrid functionals are not supported yet.
+
+    More information on the hybrid functional can be found from the section [Exact Exchange](../input_files/input-main.md#exact-exchange) in the list of input variables for more information.
+
+    An example HSE calculation is provided in this [directory](https://github.com/deepmodeling/abacus-develop/tree/develop/examples/hse/lcao_Si2). Apart from the input files (`INPUT`, `STRU`, `KPT`), we further provide two files: running_scf.log_ref and log_ref, which contains reference for running_scf.log and standard output from the program, respectively.
+
+    In the log_ref file, you will see the repetitive appearance of a piece of warning message:
+    ```
+    The angular momentum larger than 4 (g orbitals) may be error about eggbox.
+    Check file ./module_orbital/ORB_atomic_lm.cpp line 272
+    ```
+    This is normal and it will not affect the results of calculation.
+
+## DFT+U