Jastrow
Information related to the Jastrow factor in trans-correlated calculations.
The main keywords are:
j2e_type
j1e_type
env_type
j2e_type Options
-
none: No 2e-Jastrow is used.
-
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 useu_{1e}(\mathbf{r}) = \sum_A \sum_{p_A} c_{p_A} e^{-\alpha_{p_A} (\mathbf{r} - \mathbf{R}_A)^2}
, where thec_p
and\alpha_p
are defined by the tablesj1e_coef
andj1e_expo
, respectively. -
if
j1e_type
is charge-harmonizer: The one-electron Jastrow factor depends on the two-electron Jastrow factoru_{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.