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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. rs-dft: 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\left[- (\mu , r_{12})^2\right]}{2 \sqrt{\pi} \mu} ]

env_type Options

The Jastrow used is multiplied by an envelope v:

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

  • 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} \left(1 - c_a e^{-\alpha_a (\mathbf{r} - \mathbf{R}_a)^2 } \right)

Here, A designates the nuclei, and the coefficients and exponents are defined in the tables enc_coef and env_expo respectively.

j1e_type Options

The Jastrow used is:

\begin{equation} \tau = \sum_i u_{1e}(\mathbf{r}_i) \end{equation}

  • 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}, where the c_p and \alpha_p are defined by the tables j1e_coef and j1e_expo, respectively.

  • if j1e_type is charge-harmonizer: The one-electron Jastrow factor depends on the two-electron Jastrow factor u_{2e} such that the one-electron term is added to compensate for the unfavorable effect of altering the charge density caused by the two-electron factor: \begin{equation} 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), \end{equation}

Feel free to review and let me know if any further adjustments are needed.