Doc: Fix a LaTeX rendering issue of out_current in the doc (deepmodeling#7641)

Author: AsTonyshment

docs/advanced/input_files/input-main.md

@@ -4374,8 +4374,8 @@
 - **Type**: Integer
 - **Description**: Controls the current-density output method for LCAO RT-TDDFT.
   - 0: Do not output current.
-  - 1: Explicitly construct the velocity operator from the momentum, vector-potential, and KB nonlocal-pseudopotential terms using two-center integral / spherical grid integral: $$\hat{v}_{\alpha}=-\mathrm{i}\nabla_{\alpha}+A_{\alpha}(t)+\mathrm{i}\left[\widetilde{V}_{\mathrm{NL}}^{\mathrm{KB}},r_{\alpha}\right],$$ where $\widetilde{V}_{\mathrm{NL}}^{\mathrm{KB}}=\mathrm{e}^{-\mathrm{i}\boldsymbol{A}(t)\cdot\boldsymbol{r}}\hat{V}_{\mathrm{NL}}^{\mathrm{KB}}\mathrm{e}^{\mathrm{i}\boldsymbol{A}(t)\cdot\boldsymbol{r}}$. $\boldsymbol{A}(t)$ is nonzero only for the velocity gauge (td_stype=1); otherwise $\boldsymbol{A}(t)=0$. Other nonlocal Hamiltonian terms (e.g., EXX) are not included explicitly.
-  - 2: Use the full Hamiltonian to construct the generalized velocity matrix in a nonorthogonal NAO basis: $$\widetilde{v}_{\alpha}=\partial_{\alpha}H+\mathrm{i}HS^{-1}\mathcal{R}_{\alpha}-\mathrm{i}\mathcal{R}_{\alpha}S^{-1}H-HS^{-1}\partial_{\alpha}S.$$ This includes all contributions available in the real-space Hamiltonian matrix when enabled. This method is more general but more expensive.
+  - 1: Explicitly construct the velocity operator from the momentum, vector-potential, and KB nonlocal-pseudopotential terms using two-center integral / spherical grid integral: $\hat{v}_{\alpha}=-\mathrm{i}\nabla_{\alpha}+A_{\alpha}(t)+\mathrm{i}\left[\widetilde{V}_{\mathrm{NL}}^{\mathrm{KB}},r_{\alpha}\right]$, where $\widetilde{V}_{\mathrm{NL}}^{\mathrm{KB}}=\mathrm{e}^{-\mathrm{i}\boldsymbol{A}(t)\cdot\boldsymbol{r}}\hat{V}_{\mathrm{NL}}^{\mathrm{KB}}\mathrm{e}^{\mathrm{i}\boldsymbol{A}(t)\cdot\boldsymbol{r}}$. $\boldsymbol{A}(t)$ is nonzero only for the velocity gauge (td_stype=1); otherwise $\boldsymbol{A}(t)=0$. Other nonlocal Hamiltonian terms (e.g., EXX) are not included explicitly.
+  - 2: Use the full Hamiltonian to construct the generalized velocity matrix in a nonorthogonal NAO basis: $\widetilde{v}_{\alpha}=\partial_{\alpha}H+\mathrm{i}HS^{-1}\mathcal{R}_{\alpha}-\mathrm{i}\mathcal{R}_{\alpha}S^{-1}H-HS^{-1}\partial_{\alpha}S$. This includes all contributions available in the real-space Hamiltonian matrix when enabled. This method is more general but more expensive.
 - **Default**: 0
 
 ### out_current_k

docs/parameters.yaml

@@ -3470,8 +3470,8 @@ parameters:
     description: |
       Controls the current-density output method for LCAO RT-TDDFT.
       * 0: Do not output current.
-      * 1: Explicitly construct the velocity operator from the momentum, vector-potential, and KB nonlocal-pseudopotential terms using two-center integral / spherical grid integral: $$\hat{v}_{\alpha}=-\mathrm{i}\nabla_{\alpha}+A_{\alpha}(t)+\mathrm{i}\left[\widetilde{V}_{\mathrm{NL}}^{\mathrm{KB}},r_{\alpha}\right],$$ where $\widetilde{V}_{\mathrm{NL}}^{\mathrm{KB}}=\mathrm{e}^{-\mathrm{i}\boldsymbol{A}(t)\cdot\boldsymbol{r}}\hat{V}_{\mathrm{NL}}^{\mathrm{KB}}\mathrm{e}^{\mathrm{i}\boldsymbol{A}(t)\cdot\boldsymbol{r}}$. $\boldsymbol{A}(t)$ is nonzero only for the velocity gauge (td_stype=1); otherwise $\boldsymbol{A}(t)=0$. Other nonlocal Hamiltonian terms (e.g., EXX) are not included explicitly.
-      * 2: Use the full Hamiltonian to construct the generalized velocity matrix in a nonorthogonal NAO basis: $$\widetilde{v}_{\alpha}=\partial_{\alpha}H+\mathrm{i}HS^{-1}\mathcal{R}_{\alpha}-\mathrm{i}\mathcal{R}_{\alpha}S^{-1}H-HS^{-1}\partial_{\alpha}S.$$ This includes all contributions available in the real-space Hamiltonian matrix when enabled. This method is more general but more expensive.
+      * 1: Explicitly construct the velocity operator from the momentum, vector-potential, and KB nonlocal-pseudopotential terms using two-center integral / spherical grid integral: $\hat{v}_{\alpha}=-\mathrm{i}\nabla_{\alpha}+A_{\alpha}(t)+\mathrm{i}\left[\widetilde{V}_{\mathrm{NL}}^{\mathrm{KB}},r_{\alpha}\right]$, where $\widetilde{V}_{\mathrm{NL}}^{\mathrm{KB}}=\mathrm{e}^{-\mathrm{i}\boldsymbol{A}(t)\cdot\boldsymbol{r}}\hat{V}_{\mathrm{NL}}^{\mathrm{KB}}\mathrm{e}^{\mathrm{i}\boldsymbol{A}(t)\cdot\boldsymbol{r}}$. $\boldsymbol{A}(t)$ is nonzero only for the velocity gauge (td_stype=1); otherwise $\boldsymbol{A}(t)=0$. Other nonlocal Hamiltonian terms (e.g., EXX) are not included explicitly.
+      * 2: Use the full Hamiltonian to construct the generalized velocity matrix in a nonorthogonal NAO basis: $\widetilde{v}_{\alpha}=\partial_{\alpha}H+\mathrm{i}HS^{-1}\mathcal{R}_{\alpha}-\mathrm{i}\mathcal{R}_{\alpha}S^{-1}H-HS^{-1}\partial_{\alpha}S$. This includes all contributions available in the real-space Hamiltonian matrix when enabled. This method is more general but more expensive.
     default_value: "0"
     unit: ""
     availability: ""

source/source_io/module_parameter/read_input_item_output.cpp

@@ -1485,8 +1485,8 @@ In molecular dynamics calculations, the output frequency is controlled by out_fr
         item.type = "Integer";
         item.description = R"(Controls the current-density output method for LCAO RT-TDDFT.
 * 0: Do not output current.
-* 1: Explicitly construct the velocity operator from the momentum, vector-potential, and KB nonlocal-pseudopotential terms using two-center integral / spherical grid integral: $$\hat{v}_{\alpha}=-\mathrm{i}\nabla_{\alpha}+A_{\alpha}(t)+\mathrm{i}\left[\widetilde{V}_{\mathrm{NL}}^{\mathrm{KB}},r_{\alpha}\right],$$ where $\widetilde{V}_{\mathrm{NL}}^{\mathrm{KB}}=\mathrm{e}^{-\mathrm{i}\boldsymbol{A}(t)\cdot\boldsymbol{r}}\hat{V}_{\mathrm{NL}}^{\mathrm{KB}}\mathrm{e}^{\mathrm{i}\boldsymbol{A}(t)\cdot\boldsymbol{r}}$. $\boldsymbol{A}(t)$ is nonzero only for the velocity gauge (td_stype=1); otherwise $\boldsymbol{A}(t)=0$. Other nonlocal Hamiltonian terms (e.g., EXX) are not included explicitly.
-* 2: Use the full Hamiltonian to construct the generalized velocity matrix in a nonorthogonal NAO basis: $$\widetilde{v}_{\alpha}=\partial_{\alpha}H+\mathrm{i}HS^{-1}\mathcal{R}_{\alpha}-\mathrm{i}\mathcal{R}_{\alpha}S^{-1}H-HS^{-1}\partial_{\alpha}S.$$ This includes all contributions available in the real-space Hamiltonian matrix when enabled. This method is more general but more expensive.)";
+* 1: Explicitly construct the velocity operator from the momentum, vector-potential, and KB nonlocal-pseudopotential terms using two-center integral / spherical grid integral: $\hat{v}_{\alpha}=-\mathrm{i}\nabla_{\alpha}+A_{\alpha}(t)+\mathrm{i}\left[\widetilde{V}_{\mathrm{NL}}^{\mathrm{KB}},r_{\alpha}\right]$, where $\widetilde{V}_{\mathrm{NL}}^{\mathrm{KB}}=\mathrm{e}^{-\mathrm{i}\boldsymbol{A}(t)\cdot\boldsymbol{r}}\hat{V}_{\mathrm{NL}}^{\mathrm{KB}}\mathrm{e}^{\mathrm{i}\boldsymbol{A}(t)\cdot\boldsymbol{r}}$. $\boldsymbol{A}(t)$ is nonzero only for the velocity gauge (td_stype=1); otherwise $\boldsymbol{A}(t)=0$. Other nonlocal Hamiltonian terms (e.g., EXX) are not included explicitly.
+* 2: Use the full Hamiltonian to construct the generalized velocity matrix in a nonorthogonal NAO basis: $\widetilde{v}_{\alpha}=\partial_{\alpha}H+\mathrm{i}HS^{-1}\mathcal{R}_{\alpha}-\mathrm{i}\mathcal{R}_{\alpha}S^{-1}H-HS^{-1}\partial_{\alpha}S$. This includes all contributions available in the real-space Hamiltonian matrix when enabled. This method is more general but more expensive.)";
         item.default_value = "0";
         item.unit = "";
         item.availability = "";