Feature: Implement ext-WT KEDF for OFDFT (#7231)

* Feature: Implement ext-WT KEDF

* Refactor: Remove useless parameter of_wt_rho0 from KEDF_ExtWT

* Doc: Update doc

* Test: Add an integrate test 07_OFDFT/34_OF_KE_extWT for ext-WT KEDF

* Doc: Update several annotation

* Fix: Enhance the code according to the suggestions of copilot

* Fix: add `delete this->xwm_;` to kedf_manager.h

* Fix: Add check to the denominator.

Author: sunliang98

docs/advanced/input_files/input-main.md

@@ -232,6 +232,7 @@
     - [of\_vw\_weight](#of_vw_weight)
     - [of\_wt\_alpha](#of_wt_alpha)
     - [of\_wt\_beta](#of_wt_beta)
+    - [of\_extwt\_kappa](#of_extwt_kappa)
     - [of\_wt\_rho0](#of_wt_rho0)
     - [of\_hold\_rho0](#of_hold_rho0)
     - [of\_lkt\_a](#of_lkt_a)
@@ -2395,7 +2396,8 @@
   - vw: von Weizsacker (vW) functional
   - tf+: TF + vW functional
   - wt: Wang-Teter (WT) functional
-  - xwm: XWM functional
+  - ext-wt: Extended Wang-Teter (ext-WT) functional
+  - xwm: Xu-Wang-Ma (XWM) functional
   - lkt: Luo-Karasiev-Trickey (LKT) functional
   - ml: Machine learning KEDF
   - mpn: MPN KEDF (automatically sets ml parameters)
@@ -2441,29 +2443,36 @@
 ### of_tf_weight
 
 - **Type**: Real
-- **Availability**: *OFDFT with of_kinetic=tf, tf+, wt, xwm*
+- **Availability**: *OFDFT with of_kinetic=tf, tf+, wt, ext-wt, xwm*
 - **Description**: Weight of TF KEDF (kinetic energy density functional).
 - **Default**: 1.0
 
 ### of_vw_weight
 
 - **Type**: Real
-- **Availability**: *OFDFT with of_kinetic=vw, tf+, wt, lkt, xwm*
+- **Availability**: *OFDFT with of_kinetic=vw, tf+, wt, ext-wt, lkt, xwm*
 - **Description**: Weight of vW KEDF (kinetic energy density functional).
 - **Default**: 1.0
 
 ### of_wt_alpha
 
 - **Type**: Real
-- **Availability**: *OFDFT with of_kinetic=wt*
+- **Availability**: *OFDFT with of_kinetic=wt, ext-wt*
 - **Description**: Parameter alpha of WT KEDF (kinetic energy density functional).
 
 ### of_wt_beta
 
 - **Type**: Real
-- **Availability**: *OFDFT with of_kinetic=wt*
+- **Availability**: *OFDFT with of_kinetic=wt, ext-wt*
 - **Description**: Parameter beta of WT KEDF (kinetic energy density functional).
 
+### of_extwt_kappa
+
+- **Type**: Real
+- **Availability**: *OFDFT with of_kinetic=ext-wt*
+- **Description**: Parameter kappa for EXT-WT KEDF.
+- **Default**: $\dfrac{1}{2(4/3)^{1/3}-1} \approx 0.832$
+
 ### of_wt_rho0
 
 - **Type**: Real

source/source_io/module_parameter/input_parameter.h

@@ -196,6 +196,9 @@ struct Input_para
     double of_vw_weight = 1.0;                   ///< weight of vW KEDF
     double of_wt_alpha = 5. / 6.;                ///< parameter alpha of WT KEDF
     double of_wt_beta = 5. / 6.;                 ///< parameter beta of WT KEDF
+    double of_extwt_kappa = 1.0
+                            / (2.0 * std::pow(4. / 3., 1. / 3.) - 1.0);
+                                                 ///< parameter kappa of EXT-WT KEDF
     double of_wt_rho0 = 0.0;                     ///< set the average density of system, in Bohr^-3
     bool of_hold_rho0 = false;                   ///< If set to 1, the rho0 will be fixed even if the volume of
                                                  ///< system has changed, it will be set to 1 automatically if

source/source_io/module_parameter/read_input_item_ofdft.cpp

@@ -20,6 +20,7 @@ void ReadInput::item_ofdft()
 * vw: von Weizsacker (vW) functional
 * tf+: TF + vW functional
 * wt: Wang-Teter (WT) functional
+* ext-wt: Extended Wang-Teter functional
 * xwm: XWM functional
 * lkt: Luo-Karasiev-Trickey (LKT) functional
 * ml: Machine learning KEDF
@@ -37,10 +38,11 @@ void ReadInput::item_ofdft()
             }
 #endif
             if (para.input.of_kinetic != "tf" && para.input.of_kinetic != "vw" && para.input.of_kinetic != "wt"
+                && para.input.of_kinetic != "ext-wt"
                 && para.input.of_kinetic != "xwm" && para.input.of_kinetic != "lkt" && para.input.of_kinetic != "tf+" 
                 && para.input.of_kinetic != "ml" && para.input.of_kinetic != "mpn" && para.input.of_kinetic != "cpn5")
             {
-                ModuleBase::WARNING_QUIT("ReadInput", "of_kinetic must be tf, vw, tf+, wt, xwm, lkt, ml, mpn, or cpn5");
+                ModuleBase::WARNING_QUIT("ReadInput", "of_kinetic must be tf, vw, tf+, wt, ext-wt, xwm, lkt, ml, mpn, or cpn5");
             }
         };
         item.reset_value = [](const Input_Item& item, Parameter& para) {
@@ -175,7 +177,7 @@ void ReadInput::item_ofdft()
         item.description = "Weight of TF KEDF (kinetic energy density functional).";
         item.default_value = "1.0";
         item.unit = "";
-        item.availability = "OFDFT with of_kinetic=tf, tf+, wt, xwm";
+        item.availability = "OFDFT with of_kinetic=tf, tf+, wt, ext-wt, xwm";
         read_sync_double(input.of_tf_weight);
         this->add_item(item);
     }
@@ -187,7 +189,7 @@ void ReadInput::item_ofdft()
         item.description = "Weight of vW KEDF (kinetic energy density functional).";
         item.default_value = "1.0";
         item.unit = "";
-        item.availability = "OFDFT with of_kinetic=vw, tf+, wt, lkt, xwm";
+        item.availability = "OFDFT with of_kinetic=vw, tf+, wt, ext-wt, lkt, xwm";
         read_sync_double(input.of_vw_weight);
         this->add_item(item);
     }
@@ -199,7 +201,7 @@ void ReadInput::item_ofdft()
         item.description = "Parameter alpha of WT KEDF (kinetic energy density functional).";
         item.default_value = "";
         item.unit = "";
-        item.availability = "OFDFT with of_kinetic=wt";
+        item.availability = "OFDFT with of_kinetic=wt, ext-wt";
         read_sync_double(input.of_wt_alpha);
         this->add_item(item);
     }
@@ -211,10 +213,22 @@ void ReadInput::item_ofdft()
         item.description = "Parameter beta of WT KEDF (kinetic energy density functional).";
         item.default_value = "";
         item.unit = "";
-        item.availability = "OFDFT with of_kinetic=wt";
+        item.availability = "OFDFT with of_kinetic=wt, ext-wt";
         read_sync_double(input.of_wt_beta);
         this->add_item(item);
     }
+    {
+        Input_Item item("of_extwt_kappa");
+        item.annotation = "parameter kappa of EXT-WT KEDF";
+        item.category = "OFDFT: orbital free density functional theory";
+        item.type = "Real";
+        item.description = "Parameter kappa for EXT-WT KEDF.";
+        item.default_value = "1.0 / (2.0 * std::pow(4./3., 1./3.) - 1.0)";
+        item.unit = "";
+        item.availability = "OFDFT with of_kinetic=ext-wt";
+        read_sync_double(input.of_extwt_kappa);
+        this->add_item(item);
+    }
     {
         Input_Item item("of_wt_rho0");
         item.annotation = "the average density of system, used in WT KEDF, in Bohr^-3";

source/source_pw/module_ofdft/CMakeLists.txt

@@ -2,6 +2,7 @@ list(APPEND hamilt_ofdft_srcs
     kedf_tf.cpp
     kedf_vw.cpp
     kedf_wt.cpp
+    kedf_extwt.cpp
     kedf_xwm.cpp
     kedf_lkt.cpp
     kedf_manager.cpp