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@ -144,8 +144,18 @@
** Electron (electron group) ** Electron (electron group)
We consider wave functions expressed in the spin-free formalism, where The chemical system consists of nuclei and electrons, where the
the number of \uparrow and \downarrow electrons is fixed. nuclei are considered as fixed point charges with Cartesian
coordinates. The wave function is stored in the spin-free
formalism, and therefore, it is necessary for the user to
explicitly store the number of electrons with spin up
($N_\uparrow$) and spin down ($N_\downarrow$). These numbers
correspond to the normalization of the spin-up and spin-down
single-particle reduced density matrices.
We consider wave functions expressed in the spin-free formalism, where
the number of \uparrow and \downarrow electrons is fixed.
#+NAME:electron #+NAME:electron
| Variable | Type | Dimensions | Description | | Variable | Type | Dimensions | Description |
@ -208,9 +218,9 @@
*** Gaussian and Slater-type orbitals *** Gaussian and Slater-type orbitals
We consider here basis functions centered on nuclei. Hence, we enable We consider here basis functions centered on nuclei. Hence, it is
the possibility to define /dummy atoms/ to place basis functions in possibile to define /dummy atoms/ to place basis functions in
random positions. arbitrary positions.
The atomic basis set is defined as a list of shells. Each shell $s$ is The atomic basis set is defined as a list of shells. Each shell $s$ is
centered on a center $A$, possesses a given angular momentum $l$ and a centered on a center $A$, possesses a given angular momentum $l$ and a
@ -553,50 +563,42 @@ power = [
* Orbitals * Orbitals
** Atomic orbitals (ao group) ** Atomic orbitals (ao group)
Going from the atomic basis set to AOs implies a systematic
construction of all the angular functions of each shell. We
consider two cases for the angular functions: the real-valued
spherical harmonics, and the polynomials in Cartesian coordinates.
In the case of real spherical harmonics, the AOs are ordered as
$0, +1, -1, +2, -2, \dots, +m, -m$ (see [[https://en.wikipedia.org/wiki/Table_of_spherical_harmonics#Real_spherical_harmonics][Wikipedia]]).
In the case of polynomials we
impose the canonical (or alphabetical) ordering), i.e
\begin{eqnarray}
p & : & p_x, p_y, p_z \nonumber \\
d & : & d_{xx}, d_{xy}, d_{xz}, d_{yy}, d_{yz}, d_{zz} \nonumber \\
f & : & f_{xxx}, f_{xxy}, f_{xxz}, f_{xyy}, f_{xyz}, f_{xzz}, f_{yyy}, f_{yyz}, f_{yzz}, …f_{zzz} \nonumber \\
{\rm etc.} \nonumber
\end{eqnarray}
Note that there is no exception for $p$ orbitals in spherical
coordinates: the ordering is $0,+1,-1$ which corresponds $p_z, p_x, p_y$.
AOs are defined as AOs are defined as
\[ \[
\chi_i (\mathbf{r}) = \mathcal{N}_i\, P_{\eta(i)}(\mathbf{r})\, R_{s(i)} (\mathbf{r}) \chi_i (\mathbf{r}) = \mathcal{N}_i'\, P_{\eta(i)}(\mathbf{r})\, R_{s(i)} (\mathbf{r})
\] \]
where $i$ is the atomic orbital index, where $i$ is the atomic orbital index, $P$ refers to either
$P$ encodes for either the polynomials or spherical harmonics, and $s(i)$ specifies the shell
polynomials or the spherical harmonics, $s(i)$ returns the on which the AO is expanded.
shell on which the AO is expanded, and $\eta(i)$ denotes which
angular function is chosen. $\eta(i)$ denotes the chosen angular function. The AOs can be
$\mathcal{N}_i$ is a normalization factor that enables the expressed using real spherical harmonics or polynomials in Cartesian
possibility to have different normalization coefficients within a coordinates. In the case of real spherical harmonics, the AOs are
shell, as in the GAMESS convention where ordered as $0, +1, -1, +2, -2, \dots, + m, -m$ (see [[https://en.wikipedia.org/wiki/Table_of_spherical_harmonics#Real_spherical_harmonics][Wikipedia]]). In
$\mathcal{N}_{x^2} \ne \mathcal{N}_{xy}$ because the case of polynomials, the canonical (or alphabetical) ordering is
\[ \left[ \iiint \left(x-X_A \right)^2 R_{s(i)} used,
(\mathbf{r}) dx\, dy\, dz \right]^{-1/2} \ne
\left[ \iiint \left( x-X_A \right) \left( y-Y_A \right) R_{s(i)} | $p$ | $p_x, p_y, p_z$ |
(\mathbf{r}) dx\, dy\, dz \right]^{-1/2}. \] | $d$ | $d_{xx}, d_{xy}, d_{xz}, d_{yy}, d_{yz}, d_{zz}$ |
| $f$ | $f_{xxx}, f_{xxy}, f_{xxz}, f_{xyy}, f_{xyz}$, |
| | $f_{xzz}, f_{yyy}, f_{yyz}, f_{yzz}, f_{zzz}$ |
| $\vdots$ | |
Note that for \(p\) orbitals in spherical coordinates, the ordering
is $0,+1,-1$ which corresponds to $p_z, p_x, p_y$.
$\mathcal{N}_i'$ is a normalization factor that allows for different
normalization coefficients within a single shell, as in the GAMESS
convention where each individual function is unit-normalized.
Using GAMESS convention, the normalization factor of the shell
$\mathcal{N}_d$ in the ~basis~ group is appropriate for instance
for the $d_z^2$ function (i.e.
$\mathcal{N}_{d}\equiv\mathcal{N}_{z^2}$) but not for the $d_{xy}$
AO, so the correction factor $\mathcal{N}_i'$ for $d_{xy}$ in the
~ao~ groups is the ratio $\frac{\mathcal{N}_{xy}}{\mathcal{N}_{z^2}}$.
In such a case, one should set the normalization of the shell (in
the [[Basis set (basis group)][Basis set]] section) to $\mathcal{N}_{z^2}$, which is the
normalization factor of the atomic orbitals in spherical coordinates.
The normalization factor of the $xy$ function which should be
introduced here should be $\frac{\mathcal{N}_{xy}}{\mathcal{N}_{z^2}}$.
#+NAME: ao #+NAME: ao
| Variable | Type | Dimensions | Description | | Variable | Type | Dimensions | Description |
@ -637,18 +639,18 @@ power = [
over atomic orbitals. over atomic orbitals.
#+NAME: ao_1e_int #+NAME: ao_1e_int
| Variable | Type | Dimensions | Description | | Variable | Type | Dimensions | Description |
|-----------------------+---------+--------------------+--------------------------------------------------------------------------| |-----------------------+---------+--------------------+--------------------------------------------------------------------------|
| ~overlap~ | ~float~ | ~(ao.num, ao.num)~ | $\langle p \vert q \rangle$ | | ~overlap~ | ~float~ | ~(ao.num, ao.num)~ | $\langle p \vert q \rangle$ |
| ~kinetic~ | ~float~ | ~(ao.num, ao.num)~ | $\langle p \vert \hat{T}_e \vert q \rangle$ | | ~kinetic~ | ~float~ | ~(ao.num, ao.num)~ | $\langle p \vert \hat{T}_e \vert q \rangle$ |
| ~potential_n_e~ | ~float~ | ~(ao.num, ao.num)~ | $\langle p \vert \hat{V}_{\text{ne}} \vert q \rangle$ | | ~potential_n_e~ | ~float~ | ~(ao.num, ao.num)~ | $\langle p \vert \hat{V}_{\text{ne}} \vert q \rangle$ |
| ~ecp~ | ~float~ | ~(ao.num, ao.num)~ | $\langle p \vert \hat{V}_{\text{ecp}} \vert q \rangle$ | | ~ecp~ | ~float~ | ~(ao.num, ao.num)~ | $\langle p \vert \hat{V}_{\text{ecp}} \vert q \rangle$ |
| ~core_hamiltonian~ | ~float~ | ~(ao.num, ao.num)~ | $\langle p \vert \hat{h} \vert q \rangle$ | | ~core_hamiltonian~ | ~float~ | ~(ao.num, ao.num)~ | $\langle p \vert \hat{h} \vert q \rangle$ |
| ~overlap_im~ | ~float~ | ~(ao.num, ao.num)~ | $\langle p \vert q \rangle$ (imaginary part) | | ~overlap_im~ | ~float~ | ~(ao.num, ao.num)~ | $\langle p \vert q \rangle$ (imaginary part) |
| ~kinetic_im~ | ~float~ | ~(ao.num, ao.num)~ | $\langle p \vert \hat{T}_e \vert q \rangle$ (imaginary part) | | ~kinetic_im~ | ~float~ | ~(ao.num, ao.num)~ | $\langle p \vert \hat{T}_e \vert q \rangle$ (imaginary part) |
| ~potential_n_e_im~ | ~float~ | ~(ao.num, ao.num)~ | $\langle p \vert \hat{V}_{\text{ne}} \vert q \rangle$ (imaginary part) | | ~potential_n_e_im~ | ~float~ | ~(ao.num, ao.num)~ | $\langle p \vert \hat{V}_{\text{ne}} \vert q \rangle$ (imaginary part) |
| ~ecp_im~ | ~float~ | ~(ao.num, ao.num)~ | $\langle p \vert \hat{V}_{\text{ECP}} \vert q \rangle$ (imaginary part) | | ~ecp_im~ | ~float~ | ~(ao.num, ao.num)~ | $\langle p \vert \hat{V}_{\text{ECP}} \vert q \rangle$ (imaginary part) |
| ~core_hamiltonian_im~ | ~float~ | ~(ao.num, ao.num)~ | $\langle p \vert \hat{h} \vert q \rangle$ (imaginary part) | | ~core_hamiltonian_im~ | ~float~ | ~(ao.num, ao.num)~ | $\langle p \vert \hat{h} \vert q \rangle$ (imaginary part) |
#+CALL: json(data=ao_1e_int, title="ao_1e_int") #+CALL: json(data=ao_1e_int, title="ao_1e_int")
@ -679,9 +681,9 @@ power = [
\[ \langle p q \vert \hat{O} \vert r s \rangle \] in physicists \[ \langle p q \vert \hat{O} \vert r s \rangle \] in physicists
notation, where $p,q,r,s$ are indices over atomic orbitals. notation, where $p,q,r,s$ are indices over atomic orbitals.
# TODO: Physicist / Chemist functions # TODO: Physicist / Chemist functions
# Functions are provided to get the indices in physicists or chemists # Functions are provided to get the indices in physicists or chemists
# notation. # notation.
- \[ \hat{W}_{\text{ee}} = \sum_{i=2}^{N_\text{elec}} \sum_{j=1}^{i-1} \frac{1}{\vert \mathbf{r}_i - \mathbf{r}_j \vert} \] : electron-electron repulsive potential operator. - \[ \hat{W}_{\text{ee}} = \sum_{i=2}^{N_\text{elec}} \sum_{j=1}^{i-1} \frac{1}{\vert \mathbf{r}_i - \mathbf{r}_j \vert} \] : electron-electron repulsive potential operator.
- \[ \hat{W}^{lr}_{\text{ee}} = \sum_{i=2}^{N_\text{elec}} - \[ \hat{W}^{lr}_{\text{ee}} = \sum_{i=2}^{N_\text{elec}}
@ -695,14 +697,14 @@ power = [
\] \]
#+NAME: ao_2e_int #+NAME: ao_2e_int
| Variable | Type | Dimensions | Description | | Variable | Type | Dimensions | Description |
|-----------------------+----------------+---------------------------------------------------+-----------------------------------------------| |-----------------------+----------------+---------------------------------------------------+-----------------------------------------------|
| ~eri~ | ~float sparse~ | ~(ao.num, ao.num, ao.num, ao.num)~ | Electron repulsion integrals | | ~eri~ | ~float sparse~ | ~(ao.num, ao.num, ao.num, ao.num)~ | Electron repulsion integrals |
| ~eri_lr~ | ~float sparse~ | ~(ao.num, ao.num, ao.num, ao.num)~ | Long-range electron repulsion integrals | | ~eri_lr~ | ~float sparse~ | ~(ao.num, ao.num, ao.num, ao.num)~ | Long-range electron repulsion integrals |
| ~eri_cholesky_num~ | ~dim~ | | Number of Cholesky vectors for ERI | | ~eri_cholesky_num~ | ~dim~ | | Number of Cholesky vectors for ERI |
| ~eri_cholesky~ | ~float sparse~ | ~(ao.num, ao.num, ao_2e_int.eri_cholesky_num)~ | Cholesky decomposition of the ERI | | ~eri_cholesky~ | ~float sparse~ | ~(ao.num, ao.num, ao_2e_int.eri_cholesky_num)~ | Cholesky decomposition of the ERI |
| ~eri_lr_cholesky_num~ | ~dim~ | | Number of Cholesky vectors for long range ERI | | ~eri_lr_cholesky_num~ | ~dim~ | | Number of Cholesky vectors for long range ERI |
| ~eri_lr_cholesky~ | ~float sparse~ | ~(ao.num, ao.num, ao_2e_int.eri_lr_cholesky_num)~ | Cholesky decomposition of the long range ERI | | ~eri_lr_cholesky~ | ~float sparse~ | ~(ao.num, ao.num, ao_2e_int.eri_lr_cholesky_num)~ | Cholesky decomposition of the long range ERI |
#+CALL: json(data=ao_2e_int, title="ao_2e_int") #+CALL: json(data=ao_2e_int, title="ao_2e_int")
@ -1085,12 +1087,12 @@ power = [
* Correlation factors * Correlation factors
** Jastrow factor (jastrow group) ** Jastrow factor (jastrow group)
The Jastrow factor is an $N$-electron function to which the CI The Jastrow factor is an $N$-electron function which multiplies the CI
expansion is multiplied: $\Psi = \Phi \times \exp(J)$, expansion: $\Psi = \Phi \times \exp(J)$,
In the following, we use the notations $r_{ij} = |\mathbf{r}_i - \mathbf{r}_j|$ and In the following, we use the notations $r_{ij} = |\mathbf{r}_i - \mathbf{r}_j|$ and
$R_{i\alpha} = |\mathbf{r}_i - \mathbf{R}_\alpha|$, where indices $R_{i\alpha} = |\mathbf{r}_i - \mathbf{R}_\alpha|$, where indices
$i$ and $j$ correspond to electrons and $\alpha$ to nuclei. $i$ and $j$ refer to electrons and $\alpha$ to nuclei.
Parameters for multiple forms of Jastrow factors can be saved in Parameters for multiple forms of Jastrow factors can be saved in
TREXIO files, and are described in the following sections. These TREXIO files, and are described in the following sections. These
@ -1109,54 +1111,74 @@ power = [
\] \]
$J_{\text{eN}}$ contains electron-nucleus terms: $J_{\text{eN}}$ contains electron-nucleus terms:
\[ \[
J_{\text{eN}}(\mathbf{r},\mathbf{R}) = \sum_{i=1}^{N_\text{elec}} \sum_{\alpha=1}^{N_\text{nucl}} J_{\text{eN}}(\mathbf{r},\mathbf{R}) = \sum_{i=1}^{N_\text{elec}} \sum_{\alpha=1}^{N_\text{nucl}}\left[
\frac{a_{1,\alpha}\, g_\alpha(R_{i\alpha})}{1+a_{2,\alpha}\, g_\alpha(R_{i\alpha})} + \frac{a_{1,\alpha}\, f_\alpha(R_{i\alpha})}{1+a_{2,\alpha}\,
\sum_{p=2}^{N_\text{ord}^a} a_{p+1,\alpha}\, [g_\alpha(R_{i\alpha})]^p - J_{eN}^\infty f_\alpha(R_{i\alpha})} + \sum_{p=2}^{N_\text{ord}^a} a_{p+1,\alpha}\, [f_\alpha(R_{i\alpha})]^p - J_{\text{eN}}^\infty
\right]
\] \]
$J_{\text{ee}}$ contains electron-electron terms: $J_{\text{ee}}$ contains electron-electron terms:
\[ \[
J_{\text{ee}}(\mathbf{r}) = J_{\text{ee}}(\mathbf{r}) =
\sum_{i=1}^{N_\text{elec}} \sum_{j=1}^{i-1} \sum_{i=1}^{N_\text{elec}} \sum_{j=1}^{i-1}
\frac{b_1\, f(r_{ij})}{1+b_2\, f(r_{ij})} + \left[
\sum_{p=2}^{N_\text{ord}^b} a_{p+1}\, [f(r_{ij})]^p - J_{ee}^\infty \frac{\frac{1}{2}\big(1 + \delta^{\uparrow\downarrow}_{ij}\big)\,b_1\, f_{\text{ee}}(r_{ij})}{1+b_2\, f_{\text{ee}}(r_{ij})} +
\sum_{p=2}^{N_\text{ord}^b} b_{p+1}\, [f_{\text{ee}}(r_{ij})]^p - J_{\text{ee},ij}^\infty
\right]
\] \]
$\delta^{\uparrow\downarrow}_{ij}$ is zero when the electrons $i$ and
$j$ have the same spin, and one otherwise.
and $J_{\text{eeN}}$ contains electron-electron-Nucleus terms: $J_{\text{eeN}}$ contains electron-electron-Nucleus terms:
\[ \[
J_{\text{eeN}}(\mathbf{r},\mathbf{R}) = J_{\text{eeN}}(\mathbf{r},\mathbf{R}) =
\sum_{\alpha=1}^{N_{\text{nucl}}} \sum_{\alpha=1}^{N_{\text{nucl}}}
\sum_{i=1}^{N_{\text{elec}}} \sum_{i=1}^{N_{\text{elec}}}
\sum_{j=1}^{i-1} \sum_{j=1}^{i-1}
\sum_{p=2}^{N_{\text{ord}}} \sum_{p=2}^{N_{\text{ord}}}
\sum_{k=0}^{p-1} \sum_{k=0}^{p-1}
\sum_{l=0}^{p-k-2\delta_{k,0}} \sum_{l=0}^{p-k-2\delta_{k,0}}
c_{lkp\alpha} \left[ f({r}_{ij}) \right]^k c_{lkp\alpha} \left[ g_{\text{ee}}({r}_{ij}) \right]^k \nonumber \\
\left[ \left[ g_\alpha({R}_{i\alpha}) \right]^l + \left[ g_\alpha({R}_{j\alpha}) \right]^l \right] \left[ \left[ g_\alpha({R}_{i\alpha}) \right]^l + \left[ g_\alpha({R}_{j\alpha}) \right]^l \right]
\left[ g_\alpha({R}_{i\,\alpha}) \, g_\alpha({R}_{j\alpha}) \right]^{(p-k-l)/2} \left[ g_\alpha({R}_{i\,\alpha}) \,
g_\alpha({R}_{j\alpha}) \right]^{(p-k-l)/2}
\] \]
$c_{lkp\alpha}$ are non-zero only when $p-k-l$ is even. $c_{lkp\alpha}$ are non-zero only when $p-k-l$ is even.
The terms $J_{\text{ee}}^\infty$ and $J_{\text{eN}}^\infty$ are shifts to ensure that The terms $J_{\text{ee},ij}^\infty$ and $J_{\text{eN}}^\infty$ are shifts to ensure that
$J_{\text{ee}}$ and $J_{\text{eN}}$ have an asymptotic value of zero. $J_{\text{eN}}$ and $J_{\text{ee}}$ have an asymptotic value of zero:
\[
J_{\text{eN}}^{\infty} =
\frac{a_{1,\alpha}\, \kappa_\alpha^{-1}}{1+a_{2,\alpha}\,
\kappa_\alpha^{-1}} + \sum_{p=2}^{N_\text{ord}^a} a_{p+1,\alpha}\, \kappa_\alpha^{-p}
\]
\[
J_{\text{ee},ij}^{\infty} =
\frac{\frac{1}{2}\big(1 + \delta^{\uparrow\downarrow}_{ij}\big)\,b_1\,
\kappa_{\text{ee}}^{-1}}{1+b_2\, \kappa_{\text{ee}}^{-1}} +
\sum_{p=2}^{N_\text{ord}^b} b_{p+1}\, \kappa_{\text{ee}}^{-p}
\]
$f$ and $g$ are scaling function defined as $f$ and $g$ are scaling function defined as
\[ \[
f(r) = \frac{1-e^{-\kappa\, r}}{\kappa} \text{ and } f_\alpha(r) = \frac{1-e^{-\kappa_\alpha\, r}}{\kappa_\alpha} \text{ and }
g_\alpha(r) = e^{-\kappa_\alpha\, r}. g_\alpha(r) = e^{-\kappa_\alpha\, r},
\] \]
*** Mu *** Mu
[[https://aip.scitation.org/doi/10.1063/5.0044683][Mu-Jastrow]] is based on a one-parameter correlation factor that has [[https://aip.scitation.org/doi/10.1063/5.0044683][Mu-Jastrow]] is based on a one-parameter correlation factor that has
been introduced in the context of transcorrelated methods. This been introduced in the context of transcorrelated methods. This
correlation factor imposes the electron-electron cusp and it is correlation factor imposes the electron-electron cusp, and it is
built such that the leading order in $1/r_{12}$ of the effective built such that the leading order in $1/r_{12}$ of the effective
two-electron potential reproduces the long-range interaction of the two-electron potential reproduces the long-range interaction of the
range-separated density functional theory. Its analytical range-separated density functional theory. Its analytical
@ -1167,15 +1189,15 @@ power = [
J_{\text{eN}}(\mathbf{r}, \mathbf{R}) J_{\text{eN}}(\mathbf{r}, \mathbf{R})
\]. \].
The electron-electron cusp is incorporated in the three-body term. The electron-electron cusp is incorporated in the three-body term
\[ \[
J_\text{eeN} (\mathbf{r}, \mathbf{R}) = J_\text{eeN} (\mathbf{r}, \mathbf{R}) =
\sum_{i=1}^{N_\text{elec}} \sum_{j=1}^{i-1} \, u\left(\mu, r_{ij}\right) \, \sum_{i=1}^{N_\text{elec}} \sum_{j=1}^{i-1} \, u\left(\mu, r_{ij}\right) \,
\Pi_{\alpha=1}^{N_{\text{nucl}}} \, E_\alpha({R}_{i\alpha}) \, E_\alpha({R}_{j\alpha}) \Pi_{\alpha=1}^{N_{\text{nucl}}} \, E_\alpha({R}_{i\alpha}) \, E_\alpha({R}_{j\alpha}),
\] \]
$u$ is an electron-electron function given by the symmetric function where ww$u$ is an electron-electron function
\[ \[
u\left(\mu, r\right) = \frac{r}{2} \, \left[ 1 - \text{erf}(\mu\, r) \right] - \frac{1}{2 \, \mu \, \sqrt{\pi}} \exp \left[ -(\mu \, r)^2 \right]. u\left(\mu, r\right) = \frac{r}{2} \, \left[ 1 - \text{erf}(\mu\, r) \right] - \frac{1}{2 \, \mu \, \sqrt{\pi}} \exp \left[ -(\mu \, r)^2 \right].
@ -1186,7 +1208,7 @@ power = [
electrons. electrons.
An envelope function has been introduced to cancel out the Jastrow An envelope function has been introduced to cancel out the Jastrow
effects between two-electrons when they are both close to a nucleus effects between two-electrons when at least one is close to a nucleus
(to perform a frozen-core calculation). The envelope function is (to perform a frozen-core calculation). The envelope function is
given by given by
@ -1223,11 +1245,11 @@ power = [
| Variable | Type | Dimensions | Description | | Variable | Type | Dimensions | Description |
|---------------+----------+---------------------+-----------------------------------------------------------------| |---------------+----------+---------------------+-----------------------------------------------------------------|
| ~type~ | ~string~ | | Type of Jastrow factor: ~CHAMP~ or ~Mu~ | | ~type~ | ~string~ | | Type of Jastrow factor: ~CHAMP~ or ~Mu~ |
| ~ee_num~ | ~dim~ | | Number of Electron-electron parameters |
| ~en_num~ | ~dim~ | | Number of Electron-nucleus parameters | | ~en_num~ | ~dim~ | | Number of Electron-nucleus parameters |
| ~ee_num~ | ~dim~ | | Number of Electron-electron parameters |
| ~een_num~ | ~dim~ | | Number of Electron-electron-nucleus parameters | | ~een_num~ | ~dim~ | | Number of Electron-electron-nucleus parameters |
| ~ee~ | ~float~ | ~(jastrow.ee_num)~ | Electron-electron parameters |
| ~en~ | ~float~ | ~(jastrow.en_num)~ | Electron-nucleus parameters | | ~en~ | ~float~ | ~(jastrow.en_num)~ | Electron-nucleus parameters |
| ~ee~ | ~float~ | ~(jastrow.ee_num)~ | Electron-electron parameters |
| ~een~ | ~float~ | ~(jastrow.een_num)~ | Electron-electron-nucleus parameters | | ~een~ | ~float~ | ~(jastrow.een_num)~ | Electron-electron-nucleus parameters |
| ~en_nucleus~ | ~index~ | ~(jastrow.en_num)~ | Nucleus relative to the eN parameter | | ~en_nucleus~ | ~index~ | ~(jastrow.en_num)~ | Nucleus relative to the eN parameter |
| ~een_nucleus~ | ~index~ | ~(jastrow.een_num)~ | Nucleus relative to the eeN parameter | | ~een_nucleus~ | ~index~ | ~(jastrow.een_num)~ | Nucleus relative to the eeN parameter |
@ -1241,11 +1263,11 @@ power = [
#+begin_src python :tangle trex.json #+begin_src python :tangle trex.json
"jastrow": { "jastrow": {
"type" : [ "string", [] ] "type" : [ "string", [] ]
, "ee_num" : [ "dim" , [] ]
, "en_num" : [ "dim" , [] ] , "en_num" : [ "dim" , [] ]
, "ee_num" : [ "dim" , [] ]
, "een_num" : [ "dim" , [] ] , "een_num" : [ "dim" , [] ]
, "ee" : [ "float" , [ "jastrow.ee_num" ] ]
, "en" : [ "float" , [ "jastrow.en_num" ] ] , "en" : [ "float" , [ "jastrow.en_num" ] ]
, "ee" : [ "float" , [ "jastrow.ee_num" ] ]
, "een" : [ "float" , [ "jastrow.een_num" ] ] , "een" : [ "float" , [ "jastrow.een_num" ] ]
, "en_nucleus" : [ "index" , [ "jastrow.en_num" ] ] , "en_nucleus" : [ "index" , [ "jastrow.en_num" ] ]
, "een_nucleus" : [ "index" , [ "jastrow.een_num" ] ] , "een_nucleus" : [ "index" , [ "jastrow.een_num" ] ]