Feature: Implementations of Range-Separated Hybrid Functionals

docs/advanced/input_files/input-main.md

@@ -163,9 +163,11 @@
     - [out\_interval](#out_interval)
     - [out\_element\_info](#out_element_info)
     - [restart\_save](#restart_save)
-    - [rpa](#rpa)
+    - [rpa (Under Development Feature)](#rpa-under-development-feature)
     - [nbands\_istate](#nbands_istate)
     - [out\_pchg](#out_pchg)
+    - [out\_wfc\_norm](#out_wfc_norm)
+    - [out\_wfc\_re\_im](#out_wfc_re_im)
     - [if\_separate\_k](#if_separate_k)
     - [out\_elf](#out_elf)
   - [Density of States](#density-of-states)
@@ -261,7 +263,9 @@
     - [block\_height](#block_height)
   - [Exact Exchange (Common)](#exact-exchange-common)
     - [exx\_hybrid\_alpha](#exx_hybrid_alpha)
+    - [exx\_hybrid\_beta](#exx_hybrid_beta)
     - [exx\_hse\_omega](#exx_hse_omega)
+    - [exx\_use\_ewald](#exx_use_ewald)
     - [exx\_separate\_loop](#exx_separate_loop)
   - [Exact Exchange (LCAO/LCAO in PW)](#exact-exchange-lcaolcao-in-pw)
     - [exx\_hybrid\_step](#exx_hybrid_step)
@@ -284,6 +288,8 @@
     - [exx\_opt\_orb\_ecut](#exx_opt_orb_ecut)
     - [exx\_opt\_orb\_tolerence](#exx_opt_orb_tolerence)
     - [exx\_real\_number](#exx_real_number)
+    - [exx\_spencer\_type](#exx_spencer_type)
+    - [exx\_fq\_type](#exx_fq_type)
     - [rpa\_ccp\_rmesh\_times](#rpa_ccp_rmesh_times)
     - [exx\_symmetry\_realspace](#exx_symmetry_realspace)
     - [out\_ri\_cv](#out_ri_cv)
@@ -309,7 +315,6 @@
     - [ref\_cell\_factor](#ref_cell_factor)
     - [md\_pcouple](#md_pcouple)
     - [md\_pfirst, md\_plast](#md_pfirst-md_plast)
-    - [md\_pfreq](#md_pfreq)
     - [md\_pchain](#md_pchain)
     - [lj\_rule](#lj_rule)
     - [lj\_eshift](#lj_eshift)
@@ -476,7 +481,7 @@
     - [abs\_broadening](#abs_broadening)
     - [ri\_hartree\_benchmark](#ri_hartree_benchmark)
     - [aims\_nbasis](#aims_nbasis)
-  - [Reduced Density Matrix Functional Theory](#reduced-density-matrix-functional-theory)
+  - [Reduced Density Matrix Functional Theory (Under Development Feature)](#reduced-density-matrix-functional-theory-under-development-feature)
     - [rdmft](#rdmft)
     - [rdmft\_power\_alpha](#rdmft_power_alpha)
 
@@ -2705,23 +2710,38 @@ These variables are relevant to gate field (compensating charge) [Detailed intro
 These variables are relevant when using hybrid functionals. Currently ABACUS supports hybrid functionals when *[basis_type](#basis_type)==lcao/lcao_in_pw*. 
 Support for hybrid functionals in the *pw [basis_type](#basis_type)* is under active development.
 
-The following parameters apply to *[basis_type](#basis_type)==lcao/lcao_in_pw/pw*. For basis specific parameters, see the sections *[Exact Exchange (LCAO/LCAO in PW)](#exact-exchange-lcaolcao-in-pw)* and *[Exact Exchange (PW)](#exact-exchange-pw)*.
-
-**Availablity**: *[dft_functional](#dft_functional)==hse/hf/pbe0/scan0/opt_orb* or *[rpa](#rpa)==True*. 
+**Availablity**: *[dft_functional](#dft_functional)==hse/hf/pbe0/scan0/opt_orb/...* or *[rpa](#rpa)==True*, and *[basis_type](#basis_type)==lcao/lcao_in_pw*
+
+#### Hybrid Functional Parameters {#hybrid_func_params}
+|[dft_functional](#dft_functional)|[exx_hybrid_alpha](#exx_hybrid_alpha)|[exx_hybrid_beta](#exx_hybrid_beta)|[exx_hse_omega](#exx_hse_omega)|
+|:-:|:-:|:-:|:-:|
+|hf|1|0|0|
+|lc_pbe|1|-1|0.33|
+|lc_wpbe|1|-1|0.4|
+|lrc_wpbe|1|-1|0.3|
+|lrc_wpbeh|1|-0.8|0.2|
+|pbe0|0.25|0|0|
+|hse|0.0|0.25|0.11|
+|scan0|0.25|0|0|
+|cam_pbeh|0.2|0.8|0.7|
 
 ### exx_hybrid_alpha
 
 - **Type**: Real
-- **Description**: fraction of Fock exchange in hybrid functionals, so that $E_{X}=\alpha E_{X}+(1-\alpha)E_{X,\text{LDA/GGA}}$
-- **Default**:
-  - 1: if *[dft_functional](#dft_functional)==hf*
-  - 0.25: else
+- **Description**: fraction of Fock exchange in range-separated hybrid funtionals, so that $E_{X} = \alpha E_{X}^\text{HF-LR}+(\alpha+\beta) E_{X}^\text{HF-SR}+(1-\alpha)E_{X}^\text{KS-LR}+[1-(\alpha+\beta)]E_{X}^\text{KS-SR}$.
+- **Default**: see [hybrid_func_params](#hybrid_func_params)
+
+### exx_hybrid_beta
+
+- **Type**: Real
+- **Description**: fraction of Fock exchange in range-separated hybrid funtionals, so that $E_{X} = \alpha E_{X}^\text{HF-LR}+(\alpha+\beta) E_{X}^\text{HF-SR}+(1-\alpha)E_{X}^\text{KS-LR}+[1-(\alpha+\beta)]E_{X}^\text{KS-SR}$.
+- **Default**: see [hybrid_func_params](#hybrid_func_params)
 
 ### exx_hse_omega
 
 - **Type**: Real
 - **Description**: range-separation parameter in HSE functional, such that $1/r=\text{erfc}(\omega r)/r+\text{erf}(\omega r)/r$
-- **Default**: 0.11
+- **Default**: see [hybrid_func_params](#hybrid_func_params)
 
 ### exx_separate_loop
 
@@ -2731,9 +2751,11 @@ The following parameters apply to *[basis_type](#basis_type)==lcao/lcao_in_pw/pw
   - True: A two-step method is employed, i.e. in the inner iterations, density matrix is updated, while in the outer iterations, $H_{exx}$ is calculated based on density matrix that converges in the inner iteration.
 - **Default**: True
 
-## Exact Exchange (LCAO/LCAO in PW)
+### exx_use_ewald
 
-These variables are relevant when using hybrid functionals with *[basis_type](#basis_type)==lcao/lcao_in_pw*.
+- **Type**: Boolean
+- **Description**: if True, use Ewald method to construct V matrix 
+- **Default**: False
 
 ### exx_hybrid_step
 
@@ -2873,6 +2895,24 @@ These variables are relevant when using hybrid functionals with *[basis_type](#b
   - True: if gamma_only
   - False: else
 
+### exx_spencer_type
+
+- **Type**: Integer
+- **Description**:
+  - 0: see Phys. Rev. B 77, 193110 (2008).
+  - 1: see Phys. Rev. Mater. 5, 013807 (2021).
+  Set Spencer-Alavi scheme type.
+- **Default**: 0
+
+### exx_fq_type
+
+- **Type**: Integer
+- **Description**:
+  - 0: see Phys. Rev. B, 75:205126, May 2007. (In test)
+  - 1: see Phys. Rev. B 48, 5058. August 1993.
+  Auxiliary-function fq used in correction to V(q) at q->0.
+- **Default**: 1
+
 ### rpa_ccp_rmesh_times
 
 - **Type**: Real

examples/hse/pw_Si2/INPUT

@@ -26,7 +26,7 @@ pseudo_rcut            10
 # out_wfc_pw 1
 # out_chg 1
 
-exx_hybrid_alpha        0.25
+exx_hybrid_beta        0.25
 
 cal_stress 1
 # cal_force 1

source/Makefile.Objects

@@ -148,6 +148,7 @@ OBJS_BASE=abfs-vector3_order.o\
     math_ylmreal.o\
     math_bspline.o\
     math_chebyshev.o\
+    math_erf_complex.o\
     math_ylm_op.o\
     math_kernel_op.o\
     math_kernel_op_vec.o\
@@ -642,6 +643,7 @@ OBJS_MODULE_RI=conv_coulomb_pot_k.o\
       Mix_Matrix.o\
       symmetry_rotation.o\
       symmetry_irreducible_sector.o\
+      auxiliary_func.o\
 
 OBJS_PARALLEL=parallel_common.o\
     parallel_global.o\

source/module_base/CMakeLists.txt

@@ -32,6 +32,7 @@ add_library(
     math_ylmreal.cpp
     math_bspline.cpp
     math_chebyshev.cpp
+    math_erf_complex.cpp
     mathzone_add1.cpp
     matrix.cpp
     matrix3.cpp