# Jastrow Information related to the Jastrow factor in trans-correlated calculations. The main keywords are: - `j2e_type` - `j1e_type` - `env_type` ## j2e_type Options 1. **None:** No 2e-Jastrow is used. 2. **Mu:** 2e-Jastrow inspired by Range Separated Density Functional Theory. It has the following shape:

$\tau=\frac{1}{2}\sum_{i,j\neq i}u(\mathbf{r}_i,\mathbf{r}_j)$

with,

$u(\mathbf{r}_1,\mathbf{r}_2)=u(r_{12})=\frac{r_{12}}{2}\left[1-\text{erf}(\mu r_{12})\right]-\frac{\exp[-(\mu r_{12})^2]}{2\sqrt{\pi}\mu}$

3. **Mu_Nu:** A valence and a core correlation terms are used

$u(\mathbf{r}_1,\mathbf{r}_2)=u(\mu;r_{12})\,v(\mathbf{r}_1)\,v(\mathbf{r}_2)+u(\nu;r_{12})[1-v(\mathbf{r}_1)\,v(\mathbf{r}_2)]$

with envelop $v$. ## env_type Options The 2-electron Jastrow is multiplied by an envelope $v$:

$\tau=\frac{1}{2}\sum_{i,j\neq i}u(\mathbf{r}_i,\mathbf{r}_j)\,v(\mathbf{r}_i)\,v(\mathbf{r}_j)$

- if `env_type` is **None**: No envelope is used. - if `env_type` is **Prod_Gauss**:

$v(\mathbf{r})=\prod_{A}\left(1-e^{-\alpha_A(\mathbf{r}-\mathbf{R}_A)^2}\right)$

- if `env_type` is **Sum_Gauss**:

$v(\mathbf{r})=1-\sum_{A}c_A e^{-\alpha_A(\mathbf{r}-\mathbf{R}_A)^2}$

Here, $A$ designates the nuclei, and the coefficients and exponents are defined in the tables `env_coef` and `env_expo` respectively. ## j1e_type Options The 1-electron Jastrow used is:

$\tau=\sum_i u_{1e}(\mathbf{r}_i)$

- if `j1e_type` is **None**: No one-electron Jastrow is used. - if `j1e_type` is **Gauss**: We use

$u_{1e}(\mathbf{r})=\sum_A\sum_{p_A}c_{p_A}e^{-\alpha_{p_A}(\mathbf{r}-\mathbf{R}_A)^2}$

$c_{p_A}\,\text{and}\,\alpha_{p_A}$ are defined by the tables `j1e_coef` and `j1e_expo`, respectively. - if `j1e_type` is **Charge_Harmonizer**: The one-electron Jastrow factor aims to offset the adverse impact of modifying the charge density induced by the two-electron factor

$u_{1e}(\mathbf{r}_1)=-\frac{N-1}{2N}\,\sum_{\sigma}\,\int d\mathbf{r}_2\,\rho^{\sigma}(\mathbf{r}_2)\,u_{2e}(\mathbf{r}_1,\mathbf{r}_2)$

- if `j1e_type` is **Charge_Harmonizer_AO**: The one-electron Jastrow factor **Charge_Harmonizer** is fitted by the product of atomic orbitals:

$u_{1e}(\mathbf{r})=\sum_{\alpha,\beta}C_{\alpha,\beta}\chi_{\alpha}(\mathbf{r})\chi_{\beta}(\mathbf{r})$