Cstandardlib · Sep 16, 2026 · Sep 16, 2026 · Sep 16, 2026 · Sep 17, 2026 · Sep 17, 2026
diff --git a/.github/workflows/build_test_cmake.yml b/.github/workflows/build_test_cmake.yml
@@ -24,11 +24,11 @@ jobs:
 
           - tag: gnu
             external_toolchain_args: ""
-            build_args: "-DENABLE_LIBXC=ON -DENABLE_MLALGO=ON -DENABLE_LIBRI=ON -DENABLE_DFTD4=ON -DENABLE_PEXSI=ON"
+            build_args: "-DENABLE_LIBXC=ON -DENABLE_MLALGO=ON -DENABLE_LIBRI=ON -DENABLE_DFTD4=ON -DENABLE_PEXSI=ON -DENABLE_JSON=ON"
             name: "Build extra components with GNU toolchain"
           - tag: intel
             external_toolchain_args: "--with-intel"
-            build_args: "-DENABLE_LIBXC=ON -DENABLE_MLALGO=ON -DENABLE_LIBRI=ON -DENABLE_DFTD4=ON"
+            build_args: "-DENABLE_LIBXC=ON -DENABLE_MLALGO=ON -DENABLE_LIBRI=ON -DENABLE_DFTD4=ON -DENABLE_JSON=ON"
             name: "Build extra components with Intel toolchain"
 
           - tag: cuda

diff --git a/.github/workflows/build_test_makefile.yml b/.github/workflows/build_test_makefile.yml
@@ -22,7 +22,9 @@ jobs:
       - name: Checkout
         uses: actions/checkout@v7.0.1
       - name: Build
+        # TODO: Remove nlohmann-json installation here since Dockerfile will have installed it.
         run: |
+          apt update && apt install -y nlohmann-json3-dev
           export I_MPI_CXX=icpx
           chmod a+x generate_build_info.sh
           cd source

diff --git a/.github/workflows/coverage.yml b/.github/workflows/coverage.yml
@@ -63,7 +63,7 @@ jobs:
           -DENABLE_LIBXC=ON \
           -DENABLE_LIBRI=ON \
           -DENABLE_GOOGLEBENCH=ON \
-          -DENABLE_RAPIDJSON=ON \
+          -DENABLE_JSON=ON \
           -DCMAKE_BUILD_TYPE=Debug \
           -DCMAKE_CXX_FLAGS="--coverage -fprofile-arcs -ftest-coverage" \
           -DCMAKE_EXE_LINKER_FLAGS="--coverage"
@@ -83,7 +83,7 @@ jobs:
 
         lcov --directory . --capture --output-file coverage.info
 
-        lcov --remove coverage.info '/usr/*' '*/test/*' '*/external/*' '*/build/*' --output-file coverage.filtered.info
+        lcov --remove coverage.info '/usr/*' '*/test/*' '*/unittests/*' '*/external/*' '*/build/*' --output-file coverage.filtered.info
 
         genhtml coverage.filtered.info --output-directory coverage-report
 

diff --git a/.github/workflows/test.yml b/.github/workflows/test.yml
@@ -93,7 +93,7 @@ jobs:
             -DENABLE_LIBXC=ON \
             -DENABLE_LIBRI=ON \
             -DENABLE_GOOGLEBENCH=ON \
-            -DENABLE_RAPIDJSON=ON \
+            -DENABLE_JSON=ON \
             -DENABLE_FLOAT_FFTW=ON \
             -DENABLE_DFTD4=ON \
             -DENABLE_PEXSI=ON \
@@ -212,6 +212,13 @@ jobs:
         run: |
           ctest --test-dir build -V --timeout 1700 -R MODULE_ESTATE
 
+      - name: Module_Charge Unittests
+        env:
+          GTEST_COLOR: 'yes'
+          OMP_NUM_THREADS: '2'
+        run: |
+          ctest --test-dir build -V --timeout 1700 -R MODULE_CHARGE
+
       - name: Module_Hamilt Unittests
         env:
           GTEST_COLOR: 'yes'
@@ -343,4 +350,4 @@ jobs:
           GTEST_COLOR: 'yes'
           OMP_NUM_THREADS: '2'
         run: |
-          ctest --test-dir build -V --timeout 1700 -E 'integrate_test|01_PW|02_NAO_Gamma|03_NAO_multik|04_FF|05_rtTDDFT|06_SDFT|07_OFDFT|08_EXX|09_DeePKS|10_others|11_PW_GPU|12_NAO_Gamma_GPU|13_NAO_multik_GPU|15_rtTDDFT_GPU|16_SDFT_GPU|17_DS_DFTU|MODULE_BASE|MODULE_IO|MODULE_HSOLVER|MODULE_CELL|MODULE_MD|MODULE_PSI|MODULE_ESTATE|MODULE_RI|MODULE_HAMILT|MODULE_PW|MODULE_LCAO|MODULE_AO|MODULE_NAO|MODULE_RELAX|MODULE_LR'
+          ctest --test-dir build -V --timeout 1700 -E 'integrate_test|01_PW|02_NAO_Gamma|03_NAO_multik|04_FF|05_rtTDDFT|06_SDFT|07_OFDFT|08_EXX|09_DeePKS|10_others|11_PW_GPU|12_NAO_Gamma_GPU|13_NAO_multik_GPU|15_rtTDDFT_GPU|16_SDFT_GPU|17_DS_DFTU|MODULE_BASE|MODULE_IO|MODULE_HSOLVER|MODULE_CELL|MODULE_MD|MODULE_PSI|MODULE_ESTATE|MODULE_CHARGE|MODULE_RI|MODULE_HAMILT|MODULE_PW|MODULE_LCAO|MODULE_AO|MODULE_NAO|MODULE_RELAX|MODULE_LR'
diff --git a/.readthedocs.yaml b/.readthedocs.yaml
@@ -16,7 +16,7 @@ sphinx:
   # You can configure Sphinx to use a different builder, for instance use the dirhtml builder for simpler URLs
   # builder: "dirhtml"
   # Fail on all warnings to avoid broken references
-  # fail_on_warning: true
+  fail_on_warning: true
 
 # Optionally build your docs in additional formats such as PDF and ePub
 formats: all

diff --git a/AGENTS.md b/AGENTS.md
@@ -50,6 +50,12 @@ rules. Read the complete governance document before making or reviewing changes:
       initializer list to direct parameter passthrough. Perform multi-step
       computations in the constructor body instead, so failures are easy to
       debug and each intermediate result is inspectable.
+  14. Do not write conditional or computed expressions in a function's
+      argument list; first assign the value to a named local variable, then
+      pass that variable. This keeps each argument inspectable and makes the
+      call site self-documenting. For example, prefer
+      `const int isk = (nspin == 2 && isk_ptr) ? isk_ptr[ik] : 0;`
+      followed by `f(..., isk, ...)` over inlining the ternary into the call.
 - Use LF line endings for text files. Only `.bat` and `.cmd` files may use CRLF.
 - Keep source file additions deterministic: update the relevant `CMakeLists.txt`
   or explain why the file is generated or included indirectly.

diff --git a/CMakeLists.txt b/CMakeLists.txt
@@ -61,7 +61,7 @@ option(ENABLE_NATIVE_OPTIMIZATION
 
 option(COMMIT_INFO "Print commit information in log" ON)
 option(ENABLE_GOOGLEBENCH "Enable GOOGLE-benchmark usage" OFF)
-option(ENABLE_RAPIDJSON "Enable rapid-json usage" OFF)
+option(ENABLE_JSON "Enable JSON output" OFF)
 option(ENABLE_CNPY "Enable cnpy usage" OFF)
 
 # Options requiring MPI and LCAO
@@ -110,6 +110,14 @@ abacus_rename_option(USE_OPENMP ENABLE_OPENMP)
 abacus_rename_option(USE_ABACUS_LIBM ENABLE_ABACUS_LIBM)
 abacus_rename_option(INFO MATH_INFO)
 
+if(DEFINED CACHE{ENABLE_RAPIDJSON})
+  message(
+    FATAL_ERROR
+      "ENABLE_RAPIDJSON is no longer supported. "
+      "ABACUS now uses nlohmann-json as its JSON backend; "
+      "please use -DENABLE_JSON=ON instead.")
+endif()
+
 if(DEFINED CACHE{ENABLE_LIBCOMM})
   message(
     DEPRECATION
@@ -139,15 +147,8 @@ if(NOT DEFINED NVHPC_ROOT_DIR AND DEFINED ENV{NVHPC_ROOT})
 endif()
 
 # enable json support
-if(ENABLE_RAPIDJSON)
-  find_package(RapidJSON CONFIG REQUIRED)
-  if(NOT TARGET RapidJSON)
-    message(
-      FATAL_ERROR
-      "RapidJSON was found, but target RapidJSON is missing. "
-      "Check if your RapidJSON installation provides a complete exported CMake configuration."
-    )
-  endif()
+if(ENABLE_JSON)
+  find_package(nlohmann_json REQUIRED)
 endif()
 
 # get commit info
@@ -284,8 +285,8 @@ if(CCACHE)
   set(CMAKE_CUDA_COMPILER_LAUNCHER ${CCACHE} ${CMAKE_CUDA_COMPILER_LAUNCHER})
 endif()
 
-# Choose build type from: Debug Release RelWithDebInfo MinSizeRel Select
-# 'Release' configuration for best performance; this will disable all
+# Choose build type from: Debug Release RelWithDebInfo MinSizeRel
+# Select 'Release' configuration for best performance; this will disable all
 # assertions. Other default configurations are also available, see:
 # https://cmake.org/cmake/help/latest/manual/cmake-buildsystem.7.html#default-and-custom-configurations
 # For default flags, see:

diff --git a/Dockerfile.cuda b/Dockerfile.cuda
@@ -2,7 +2,7 @@ FROM nvidia/cuda:12.2.0-devel-ubuntu22.04
 
 RUN apt update && apt install -y --no-install-recommends \
     libopenblas-openmp-dev liblapack-dev libscalapack-mpi-dev libfftw3-dev libcereal-dev \
-    libxc-dev libgtest-dev libgmock-dev libbenchmark-dev python3-numpy ca-certificates \
+    libxc-dev libgtest-dev libgmock-dev libbenchmark-dev python3-numpy ca-certificates nlohmann-json3-dev \
     bc cmake git g++ make time sudo unzip vim wget libopenmpi-dev gfortran libtool-bin && \
     rm -rf /var/lib/apt/lists/*
 
@@ -25,19 +25,11 @@ RUN cd /tmp && \
     ln -s /usr/local/include/elpa_openmp-$ELPA_VER/elpa /usr/local/include/ && \
     cd /tmp && rm -rf elpa-$ELPA_VER
 
-# RapidJSON
-RUN cd /tmp && \
-    wget --quiet https://codeload.github.com/Tencent/rapidjson/tar.gz/24b5e7a -O rapidjson-24b5e7a.tar.gz && \
-    tar -xzf rapidjson-24b5e7a.tar.gz && cd rapidjson-24b5e7a && \
-    cmake -B build -DRAPIDJSON_BUILD_DOC=OFF -DRAPIDJSON_BUILD_EXAMPLES=OFF -DRAPIDJSON_BUILD_TESTS=OFF && \
-    cmake --build build --target install && \
-    cd /tmp && rm -rf rapidjson-24b5e7a rapidjson-24b5e7a.tar.gz
-
 ADD https://api.github.com/repos/deepmodeling/abacus-develop/git/refs/heads/develop /dev/null
 
 RUN git clone https://github.com/deepmodeling/abacus-develop.git --depth 1 && \
     cd abacus-develop && \
-    cmake -B build -DUSE_CUDA=ON -DENABLE_RAPIDJSON=ON && \
+    cmake -B build -DUSE_CUDA=ON -DENABLE_JSON=ON && \
     cmake --build build -j $(nproc) && \
     cmake --install build && \
     rm -rf build && \

diff --git a/Dockerfile.gnu b/Dockerfile.gnu
@@ -10,7 +10,7 @@
 FROM ubuntu:22.04
 RUN apt update && apt install -y --no-install-recommends \
     libopenblas-openmp-dev liblapack-dev libscalapack-mpi-dev libelpa-dev libfftw3-dev libcereal-dev \
-    libxc-dev libgtest-dev libgmock-dev libbenchmark-dev python3-numpy \
+    libxc-dev libgtest-dev libgmock-dev libbenchmark-dev python3-numpy nlohmann-json3-dev \
     libmetis-dev libparmetis-dev libsuperlu-dist-dev \
     bc cmake git g++ make time sudo unzip vim wget gfortran ca-certificates && \
     rm -rf /var/lib/apt/lists/*
@@ -28,14 +28,6 @@ RUN wget https://download.pytorch.org/libtorch/cpu/libtorch-cxx11-abi-shared-wit
         --quiet -O libtorch.zip && \
     unzip -q libtorch.zip -d /opt && rm libtorch.zip
 
-# RapidJSON
-RUN cd /tmp && \
-    wget --quiet https://codeload.github.com/Tencent/rapidjson/tar.gz/24b5e7a -O rapidjson-24b5e7a.tar.gz && \
-    tar -xzf rapidjson-24b5e7a.tar.gz && cd rapidjson-24b5e7a && \
-    cmake -B build -DRAPIDJSON_BUILD_DOC=OFF -DRAPIDJSON_BUILD_EXAMPLES=OFF -DRAPIDJSON_BUILD_TESTS=OFF && \
-    cmake --build build --target install && \
-    cd /tmp && rm -r rapidjson-24b5e7a rapidjson-24b5e7a.tar.gz
-
 ENV CMAKE_PREFIX_PATH=/opt/libtorch/share/cmake
 
 # PEXSI
@@ -56,7 +48,7 @@ ADD https://api.github.com/repos/deepmodeling/abacus-develop/git/refs/heads/deve
 
 RUN git clone https://github.com/deepmodeling/abacus-develop.git --depth 1 && \
     cd abacus-develop && \
-    cmake -B build -DENABLE_MLALGO=ON -DENABLE_PEXSI=ON -DENABLE_LIBXC=ON -DENABLE_LIBRI=ON -DENABLE_RAPIDJSON=ON && \
+    cmake -B build -DENABLE_MLALGO=ON -DENABLE_PEXSI=ON -DENABLE_LIBXC=ON -DENABLE_LIBRI=ON -DENABLE_JSON=ON && \
     cmake --build build -j $(nproc) && \
     cmake --install build && \
     rm -rf build

diff --git a/Dockerfile.intel b/Dockerfile.intel
@@ -2,7 +2,7 @@ FROM intel/oneapi-hpckit:2025.2.2-0-devel-ubuntu22.04
 
 RUN apt-get update && apt-get install -y \
     bc cmake git gnupg gcc g++ python3-numpy sudo wget vim unzip \
-    libcereal-dev libxc-dev libgtest-dev libgmock-dev libbenchmark-dev \
+    libcereal-dev libxc-dev libgtest-dev libgmock-dev libbenchmark-dev nlohmann-json3-dev \
     pkg-config build-essential autoconf automake libtool ca-certificates && \
     rm -rf /var/lib/apt/lists/*
 
@@ -22,14 +22,6 @@ RUN cd /tmp && \
     ln -s /usr/local/include/elpa_openmp-$ELPA_VER/elpa /usr/local/include/ && \
     cd /tmp && rm -rf elpa-$ELPA_VER
 
-# RapidJSON
-RUN cd /tmp && \
-    wget --quiet https://codeload.github.com/Tencent/rapidjson/tar.gz/24b5e7a -O rapidjson-24b5e7a.tar.gz && \
-    tar -xzf rapidjson-24b5e7a.tar.gz && cd rapidjson-24b5e7a && \
-    cmake -B build -DRAPIDJSON_BUILD_DOC=OFF -DRAPIDJSON_BUILD_EXAMPLES=OFF -DRAPIDJSON_BUILD_TESTS=OFF && \
-    cmake --build build --target install && \
-    cd /tmp && rm -r rapidjson-24b5e7a rapidjson-24b5e7a.tar.gz
-
 # LibTorch (Note: Using pre-built Torch library with MKL might cause issues)
 RUN wget -q https://download.pytorch.org/libtorch/cpu/libtorch-cxx11-abi-shared-with-deps-2.0.0%2Bcpu.zip -O /tmp/libtorch.zip && \
     unzip -q /tmp/libtorch.zip -d /opt && rm -f /tmp/libtorch.zip
@@ -43,7 +35,7 @@ RUN cd /tmp && git clone https://github.com/deepmodeling/abacus-develop.git --de
         -DENABLE_MLALGO=ON \
         -DENABLE_LIBXC=ON \
         -DENABLE_LIBRI=ON \
-        -DENABLE_RAPIDJSON=ON \
+        -DENABLE_JSON=ON \
         -DCMAKE_BUILD_TYPE=Release && \
     cmake --build build -j $(nproc) && \
     cmake --install build && \

diff --git a/cmake/CollectBuildInfoVars.cmake b/cmake/CollectBuildInfoVars.cmake
@@ -155,19 +155,7 @@ else()
     if(FFTW3_VERSION)
       set(ABACUS_FFTW_VERSION "yes (v${FFTW3_VERSION})")
     else()
-      if(FFTW3_INCLUDE_DIR AND EXISTS "${FFTW3_INCLUDE_DIR}/fftw3.h")
-        file(STRINGS "${FFTW3_INCLUDE_DIR}/fftw3.h" _fftw_ver_line
-             REGEX "^#define[\t ]+FFTW_VERSION[\t ]+\"[^\"]+\"")
-        if(_fftw_ver_line)
-          string(REGEX REPLACE "^#define[\t ]+FFTW_VERSION[\t ]+\"([^\"]+)\"" "\\1"
-                 FFTW3_VERSION "${_fftw_ver_line}")
-          set(ABACUS_FFTW_VERSION "yes (v${FFTW3_VERSION})")
-        else()
-          set(ABACUS_FFTW_VERSION "yes (version unknown)")
-        endif()
-      else()
-        set(ABACUS_FFTW_VERSION "yes (version unknown)")
-      endif()
+      set(ABACUS_FFTW_VERSION "yes (version unknown)")
     endif()
   endif()
 endif()
@@ -240,7 +228,7 @@ endif()
 if(ENABLE_NCCL_PARALLEL_DEVICE)
   set(ABACUS_NCCL_PARA "Enabled")
 else()
-  set(ABACUS_NCCL_PARA "Enabled")
+  set(ABACUS_NCCL_PARA "Disabled")
 endif()
 
 # EXX Libraries
@@ -361,12 +349,10 @@ else()
     set(ABACUS_GOOGLEBENCH_VERSION "Disabled")
 endif()
 
-if(DEFINED RapidJSON_DIR AND ENABLE_RAPIDJSON)
-    set(ABACUS_RAPIDJSON_VERSION "yes (path: ${RapidJSON_DIR})")
-elseif(ENABLE_RAPIDJSON)
-    set(ABACUS_RAPIDJSON_VERSION "yes (from git origin/master)")
+if(ENABLE_JSON)
+    set(ABACUS_JSON_VERSION "yes (nlohmann-json v${nlohmann_json_VERSION})")
 else()
-    set(ABACUS_RAPIDJSON_VERSION "no")
+    set(ABACUS_JSON_VERSION "no")
 endif()
 
 if(ENABLE_MLALGO)
@@ -458,7 +444,7 @@ if(ENABLE_EXX_DEV)
   message("                                      (EXX developing features enabled)")
 endif()
 message("                     DFT-D4         = ${ABACUS_DFTD4_VERSION}")
-message("                     RAPIDJSON      = ${ABACUS_RAPIDJSON_VERSION}")
+message("                     JSON           = ${ABACUS_JSON_VERSION}")
 message("                     PEXSI          = ${ABACUS_PEXSI_VERSION}")
 message("                     CNPY           = ${ABACUS_CNPY_VERSION}")
 message(" -------------------------------------------------------------------")

diff --git a/cmake/modules/FindFFTW3.cmake b/cmake/modules/FindFFTW3.cmake
@@ -4,6 +4,7 @@
 #  FFTW3_INCLUDE_DIRS  - Where to find FFTW3 headers.
 #  FFTW3_LIBRARIES     - List of libraries when using FFTW3.
 #  FFTW3_FOUND         - True if FFTW3 is found.
+#  FFTW3_VERSION       - Version from the selected library's pkgconfig/fftw3.pc, if available.
 #
 
 find_path(FFTW3_INCLUDE_DIR
@@ -47,6 +48,7 @@ endif()
 find_package_handle_standard_args(FFTW3 DEFAULT_MSG ${_fftw3_required_vars})
 
 # Copy the results to the output variables and target.
+set(FFTW3_VERSION "")
 if(FFTW3_FOUND)
     set(FFTW3_LIBRARIES ${FFTW3_LIBRARY})
     if (ENABLE_OPENMP)
@@ -55,13 +57,16 @@ if(FFTW3_FOUND)
 
     set(FFTW3_INCLUDE_DIRS ${FFTW3_INCLUDE_DIR})
 
-    # Try to extract FFTW version from header
-    if(FFTW3_INCLUDE_DIR AND EXISTS "${FFTW3_INCLUDE_DIR}/fftw3.h")
-        file(STRINGS "${FFTW3_INCLUDE_DIR}/fftw3.h" _fftw_ver_line REGEX "^#define[\t ]+FFTW_VERSION[\t ]+\"[^\"]+\"")
-        if(_fftw_ver_line)
-            string(REGEX REPLACE "^#define[\t ]+FFTW_VERSION[\t ]+\"([^\"]+)\"" "\\1" FFTW3_VERSION "${_fftw_ver_line}")
-        endif()
+  # Read the literal version from metadata beside the selected library.
+  get_filename_component(_fftw3_library_dir "${FFTW3_LIBRARY}" DIRECTORY)
+  set(_fftw3_pc "${_fftw3_library_dir}/pkgconfig/fftw3.pc")
+  if(EXISTS "${_fftw3_pc}")
+    file(STRINGS "${_fftw3_pc}" _fftw3_version_line REGEX "^Version:[ \t]*[0-9]")
+    if(_fftw3_version_line)
+      string(REGEX REPLACE "^Version:[ \t]*" "" FFTW3_VERSION "${_fftw3_version_line}")
+      string(STRIP "${FFTW3_VERSION}" FFTW3_VERSION)
     endif()
+  endif()
 
     if(NOT TARGET FFTW3::FFTW3)
         add_library(FFTW3::FFTW3 UNKNOWN IMPORTED)

diff --git a/docs/CONTRIBUTING.md b/docs/CONTRIBUTING.md
@@ -95,7 +95,7 @@ To help us reproduce and confirm a bug, please provide a test case and building
 ## Agent governance and automated review
 
 Before coding or requesting review, read the repository governance entry point
-[`AGENTS.md`](../AGENTS.md) and the full
+[`AGENTS.md`](https://github.com/deepmodeling/abacus-develop/blob/develop/AGENTS.md) and the full
 [ABACUS Agent Governance](./developers_guide/agent_governance.md) guide.
 These rules apply to human contributors, AI agents, GitHub CI, and CodeRabbit.
 

diff --git a/docs/Makefile b/docs/Makefile
@@ -3,7 +3,7 @@
 
 # You can set these variables from the command line, and also
 # from the environment for the first two.
-SPHINXOPTS    ?=
+SPHINXOPTS    ?= -W -n --keep-going
 SPHINXBUILD   ?= sphinx-build
 SOURCEDIR     = $(PWD)
 BUILDDIR      = build

diff --git a/docs/advanced/acceleration/cuda.md b/docs/advanced/acceleration/cuda.md
@@ -49,7 +49,7 @@ In `INPUT` file we need to set the input parameter [device](../input_files/input
 - **multi-cards**: ABACUS allows for multi-GPU acceleration. If you have multiple GPU cards, you can run ABACUS with several MPI processes, and each process will utilize one GPU card. For example, the command `mpirun -n 2 abacus` will by default launch two GPUs for computation. If you only have one card, this command will only start one GPU. *note: the number of MPI processes SHOULD be equal to the number of GPU cards, unless you are using MPS in your computer.*
 
 ## Examples
-We provides [examples](https://github.com/deepmodeling/abacus-develop/tree/develop/examples/gpu) of gpu calculations.
+We provides [examples](https://github.com/deepmodeling/abacus-develop/tree/develop/examples/34_gpu) of gpu calculations.
 
 ## Known limitations
 PW basis:

diff --git a/docs/advanced/elec_properties/Berry_phase.md b/docs/advanced/elec_properties/Berry_phase.md
@@ -1,6 +1,6 @@
 # Berry Phase Calculation
 
-From version 2.0.0, ABACUS is capable of calculating macroscopic polarization of insulators by using the Berry phase method, known as the ["modern theory of polarization"](https://www.sciencedirect.com/science/article/abs/pii/S0022459612003234). To calculate the polarization, you need first to do a self-consistent calculation to get the converged charge density. Then, do a non-self-consistent calculation with berry_phase setting to 1. You need also to specify the direction of the polarization you want to calculate. An example is given in the directory [examples/berryphase/lcao_PbTiO3](https://github.com/deepmodeling/abacus-develop/tree/develop/examples/berryphase/lcao_PbTiO3).
+From version 2.0.0, ABACUS is capable of calculating macroscopic polarization of insulators by using the Berry phase method, known as the ["modern theory of polarization"](https://www.sciencedirect.com/science/article/abs/pii/S0022459612003234). To calculate the polarization, you need first to do a self-consistent calculation to get the converged charge density. Then, do a non-self-consistent calculation with berry_phase setting to 1. You need also to specify the direction of the polarization you want to calculate. An example is given in the directory [examples/berryphase/lcao_PbTiO3](https://github.com/deepmodeling/abacus-develop/tree/develop/examples/26_berryphase/02_lcao_PbTiO3).
 
 To run this example, first do a self-consistent calculation:
 ```

diff --git a/docs/advanced/elec_properties/Mulliken.md b/docs/advanced/elec_properties/Mulliken.md
@@ -1,7 +1,7 @@
 # Mulliken Charge Analysis
 
-From version 2.1.0, ABACUS has the function of Mulliken population analysis. The example can be found in [examples/mulliken](https://github.com/deepmodeling/abacus-develop/tree/develop/examples/mulliken). \
-To use this function, set [out_mul](./input-main.md#out_mul) to `1` in the INPUT file. After calculation, there will be an output file named `mulliken.txt` in the output directory. In MD calculations, the output interval is controlled by the keyword [out_freq_ion](./input-main.md#out_freq_ion). In the file, there are contents like (`nspin 1`):
+From version 2.1.0, ABACUS has the function of Mulliken population analysis. The example can be found in [examples/mulliken](https://github.com/deepmodeling/abacus-develop/tree/develop/examples/14_mulliken). \
+To use this function, set [out_mul](../input_files/input-main.md#out_mul) to `1` in the INPUT file. After calculation, there will be an output file named `mulliken.txt` in the output directory. In MD calculations, the output interval is controlled by the keyword [out_freq_ion](../input_files/input-main.md#out_freq_ion). In the file, there are contents like (`nspin 1`):
 
 ```
 STEP: 0