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better documentation of th ECP block

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q-posev 2021-10-19 15:47:13 +02:00
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@ -118,7 +118,7 @@ arrays are 0-based. Hence, we introduce the ~index~ type which is an
* Effective core potentials (ecp group)
An effective core potential (ECP) $V_A^{\text{ECP}}$ replacing the
core electrons of atom $A$ is expressed as
core electrons of atom $A$ can be expressed as
\[
V_A^{\text{ECP}} =
V_{A \ell_{\max}+1} +
@ -127,6 +127,9 @@ arrays are 0-based. Hence, we introduce the ~index~ type which is an
V_{A \ell} - V_{A \ell_{\max}+1} \right] \langle Y_{\ell m} |
\]
The first term in the equation above is sometimes attributed to the local channel,
while the remaining terms correspond to the non-local channel projections.
The functions $V_{A\ell}$ are parameterized as:
\[
V_{A \ell}(\mathbf{r}) =
@ -135,13 +138,13 @@ arrays are 0-based. Hence, we introduce the ~index~ type which is an
e^{-\alpha_{A q \ell} |\mathbf{r}-\mathbf{R}_{A}|^2 }
\]
See http://dx.doi.org/10.1063/1.4984046 for more info.
See http://dx.doi.org/10.1063/1.4984046 or https://doi.org/10.1063/1.5121006for more info.
#+NAME: ecp
| Variable | Type | Dimensions | Description |
|----------------------+---------+-----------------+----------------------------------------------------------------------------------------|
| ~max_ang_mom_plus_1~ | ~int~ | ~(nucleus.num)~ | $\ell_{\max}+1$, one higher than the max angular momentum in the removed core orbitals |
| ~z_core~ | ~float~ | ~(nucleus.num)~ | Charges to remove |
| ~z_core~ | ~float~ | ~(nucleus.num)~ | Number of core electrons to remove per atom |
| ~num~ | ~dim~ | | Total number of ECP functions for all atoms and all values of $\ell$ |
| ~ang_mom~ | ~int~ | ~(ecp.num)~ | One-to-one correspondence between ECP items and the angular momentum $\ell$ |
| ~nucleus_index~ | ~index~ | ~(ecp.num)~ | One-to-one correspondence between ECP items and the atom index |
@ -150,10 +153,17 @@ arrays are 0-based. Hence, we introduce the ~index~ type which is an
| ~power~ | ~int~ | ~(ecp.num)~ | $n_{A q \ell}$ all ECP powers |
There might be some confusion in the meaning of the $\ell_{\max}$.
It can be attributed to the maximum angular momentum occupied
in the core orbitals, which are removed by the ECP.
On the other hand, it can be attributed to the maximum angular momentum of the
ECP that replaces the core electrons.
*Note*, that the latter $\ell_{\max}$ is always higher by 1 than the former.
*Note for developers*: avoid having variables with similar prefix in their name.
HDF5 back end might cause issues due to the way `find_dataset` function works
in the H5LT module. For example, in the ECP group we use ~max_ang_mom~ and
~ang_mom_max~ due to this.
HDF5 back end might cause issues due to the way `find_dataset` function works.
For example, in the ECP group we use ~max_ang_mom~ and not ~ang_mom_max~.
The latter causes issues when written before ~ang_mom~ in the TREXIO file.
@ -202,19 +212,19 @@ max_ang_mom_plus_1 = [ 1, 1 ]
# number of core electrons to remove per atom
zcore = [ 0, 0 ]
# first 4 ECP elements correspond to the first H atom, same for the second H atom
# first 4 ECP elements correspond to the first H atom; the remaining 4 elements are for the second H atom
nucleus_index = [
0, 0, 0, 0,
1, 1, 1, 1
]
# 3 first ECP elements correspond to l=1 of the first H atom, then 1 ECP for l=0; same for the second H atom
# 3 first ECP elements correspond to the P orbital (l=1), then 1 element for the S orbital (l=0) ; similar for the second H atom
ang_mom = [
1, 1, 1, 0,
1, 1, 1, 0
]
# flat arrays with ECP quantities that can be parsed based on the aforementioned ecp_ang_mom and ecp_nucleus
# ECP quantities that can be attributed to atoms and/or angular momenta based on the aforementioned ecp_nucleus and ecp_ang_mom arrays
coefficient = [
1.00000000000000, 21.24359508259891, -10.85192405303825, 0.00000000000000,
1.00000000000000, 21.24359508259891, -10.85192405303825, 0.00000000000000