Simplify code for deepks_bandgap labels.

Author: ErjieWu

docs/advanced/input_files/input-main.md

@@ -195,7 +195,7 @@
     - [bessel\_descriptor\_smooth](#bessel_descriptor_smooth)
     - [bessel\_descriptor\_sigma](#bessel_descriptor_sigma)
     - [deepks\_bandgap](#deepks_bandgap)
-    - [deepks\_bandgap\_range](#deepks_bandgap_range)
+    - [deepks\_band\_range](#deepks_band_range)
     - [deepks\_v\_delta](#deepks_v_delta)
     - [deepks\_out\_unittest](#deepks_out_unittest)
   - [OFDFT: orbital free density functional theory](#ofdft-orbital-free-density-functional-theory)
@@ -2150,20 +2150,20 @@ Warning: this function is not robust enough for the current version. Please try
 - **Availability**: numerical atomic orbital basis and `deepks_scf` is true
 - **Description**: include bandgap label for DeePKS training
   - 0: Don't include bandgap label
-  - 1: Include HOMO and LOMO for bandgap label
-  - 2: Include multiple bandgap label (see [deepks\_bandgap\_range](#deepks_bandgap_range) for more details)
-  - 3: Include target bandgap label (see [deepks\_bandgap\_range](#deepks_bandgap_range) for more details)
-  - 4: For systems containing H atoms only, HOMO is defined as the max occupation expect H atoms and the bandgap label is the energy between (HOMO, HOMO + 1)
+  - 1: Include HOMO and LUMO for bandgap label
+  - 2: Include multiple bandgap label (see [deepks\_bandgap\_range](#deepks_band_range) for more details)
+  - 3: Include target bandgap label (see [deepks\_bandgap\_range](#deepks_band_range) for more details)
+  - 4: For systems containing H atoms only, HOMO is defined as the max occupation expect H atoms and the bandgap label is the energy between HOMO and (HOMO + 1)
 - **Default**: 0
 
-### deepks_bandgap_range
+### deepks_band_range
 
 - **Type**: Int*2
 - **Availability**: numerical atomic orbital basis, `deepks_scf` is true, and `deepks_bandgap` is 2 or 3
-- **Description**: 
-  - `deepks_bandgap` is 2: Bandgap labels are energies between (LUMO + deepks_bandgap_range[0], HOMO), (LUMO + deepks_bandgap_range[0] + 1, HOMO), ..., (LUMO + deepks_bandgap_range[1], HOMO) except (HOMO, HOMO)
-  - `deepks_bandgap` is 3: Bandgap label is the energy between (LUMO + deepks_bandgap_range[0], LUMO + deepks_bandgap_range[1])
-- **Default**: 0 0
+- **Description**: The first value should not be larger than the second one and the meaning differs in different cases below
+  - `deepks_bandgap` is 2: Bandgap labels are energies between HOMO and all states in range [`LUMO + deepks_band_range[0]`, `LUMO + deepks_band_range[1]`] (Thus there are `deepks_band_range[1] - deepks_band_range[0] + 1` bandgaps in total). If HOMO is included in the setting range, it will be ignored since it will always be zero and has no valuable messages (`deepks_band_range[1] - deepks_band_range[0]` bandgaps in this case). *NOTICE: The set range can be greater than, less than, or include the value of HOMO. In the bandgap label, we always calculate the energy of the state in the set range minus the energy of HOMO state, so the bandgap can be negative if the state is lower than HOMO.*
+  - `deepks_bandgap` is 3: Bandgap label is the energy between `LUMO + deepks_band_range[0]` and `LUMO + deepks_band_range[1]`.
+- **Default**: 0 1 (for deepks_bandgap=3), or 0 0 (for other cases)
 
 ### deepks_v_delta