qp2/plugins/local/jastrow

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

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() = _{a} (1 - e^{-_a ( - _a)^2 } ))

• if env_type is sum-gauss: (v() = 1 - _{a} (1 - c_a e^{-_a ( - _a)^2 } ))

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}() = A {p_A} c_{p_A} e^{-_{p_A} ( - _A)^2}), where the (c_p) and (_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.