update comments

Author: maki49

source/module_lr/potentials/pot_hxc_lrtd.h

@@ -14,6 +14,7 @@ namespace LR
         /// S1: K^Hartree + K^xc
         /// S2_singlet: 2*K^Hartree + K^xc_{upup} + K^xc_{updown}
         /// S2_triplet: K^xc_{upup} - K^xc_{updown}
+        /// S2_updown: K^Hartree + (K^xc_{upup}, K^xc_{updown},  K^xc_{downup} or K^xc_{downdown}), according to `ispin_op` (for spin-polarized systems)
         enum SpinType { S1 = 0, S2_singlet = 1, S2_triplet = 2, S2_updown = 3 };
         enum XCType { None = 0, LDA = 1, GGA = 2, HYB_GGA = 4 };
         /// constructor for exchange-correlation kernel

source/module_lr/potentials/xc_kernel.h

@@ -3,17 +3,19 @@
 
 namespace LR
 {
+    /// @brief Calculate the exchange-correlation (XC) kernel ($f_{xc}=\delta^2E_xc/\delta\rho^2$) and store its components.
     class KernelXC
     {
     public:
         KernelXC(const ModulePW::PW_Basis& rho_basis) : rho_basis_(rho_basis) {};
         ~KernelXC() {};
 
-        // xc kernel for LR-TDDFT
 #ifdef USE_LIBXC
+        /// @brief Calculate the XC kernel using libxc.
         void f_xc_libxc(const int& nspin, const double& omega, const double& tpiba, const double* const* const rho_gs, const double* const rho_core = nullptr);
 #endif
 
+        // Setters and getters for certain components, such as v2rho2, v2rhosigma, v2sigma2,  or other custom combinations.
         void set_kernel(const std::string& name, const std::vector<double>& vec) { this->kernel_set_[name] = vec; }
         void set_kernel(const std::string& name, const std::vector<double>&& vec) { this->kernel_set_[name] = std::move(vec); }
         const std::vector<double>& get_kernel(const std::string& name) { return kernel_set_[name]; }