TREX/trexio
1
0
Fork 0
mirror of https://github.com/TREX-CoE/trexio.git synced 2025-01-03 18:16:22 +01:00
Code Issues Projects Releases Wiki Activity

Merge pull request #64 from TREX-CoE/fix-ecp-structure

Browse Source 
FIX: more flexible ECP format
This commit is contained in:
Anthony Scemama 2021-10-21 19:40:50 +02:00 committed by GitHub
commit 94d00fc697
No known key found for this signature in database
GPG Key ID: 4AEE18F83AFDEB23
1 changed files with 97 additions and 31 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

128
trex.org
View File

@ -118,15 +118,18 @@ arrays are 0-based. Hence, we introduce the ~index~ type which is an
* Effective core potentials (ecp group) * Effective core potentials (ecp group)
An effective core potential (ECP) $V_A^{\text{ECP}}$ replacing the 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
\[ \[
V_A^{\text{ECP}} = V_A^{\text{ECP}} =
V_{A \ell_{\max}} + V_{A \ell_{\max}+1} +
\sum_{\ell=0}^{\ell_{\max} -1} \sum_{\ell=0}^{\ell_{\max}}
\sum_{m=-\ell}^{\ell} | Y_{\ell m} \rangle \left[ \sum_{m=-\ell}^{\ell} | Y_{\ell m} \rangle \left[
V_{A \ell} - V_{A \ell_{\max}} \right] \langle Y_{\ell m} | V_{A \ell} - V_{A \ell_{\max}+1} \right] \langle Y_{\ell m} |
\] \]
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: The functions $V_{A\ell}$ are parameterized as:
\[ \[
V_{A \ell}(\mathbf{r}) = V_{A \ell}(\mathbf{r}) =
@ -135,23 +138,34 @@ arrays are 0-based. Hence, we introduce the ~index~ type which is an
e^{-\alpha_{A q \ell} |\mathbf{r}-\mathbf{R}_{A}|^2 } e^{-\alpha_{A q \ell} |\mathbf{r}-\mathbf{R}_{A}|^2 }
\] \]
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 #+NAME: ecp
| Variable | Type | Dimensions | Description | | Variable | Type | Dimensions | Description |
|-----------------------+---------+------------------------------------------+----------------------------------------------------------------------------------------------| |----------------------+---------+-----------------+----------------------------------------------------------------------------------------|
| ~lmax_plus_1~ | ~int~ | ~(nucleus.num)~ | $\ell_{\max} + 1$, one higher than the maximum angular momentum in the removed core orbitals | | ~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~ | ~int~ | ~(nucleus.num)~ | Number of core electrons to remove per atom |
| ~local_n~ | ~int~ | ~(nucleus.num)~ | Number of local functions $N_{q \ell}$ | | ~num~ | ~dim~ | | Total number of ECP functions for all atoms and all values of $\ell$ |
| ~local_num_n_max~ | ~dim~ | | Maximum value of ~local_n~, used for dimensioning arrays | | ~ang_mom~ | ~int~ | ~(ecp.num)~ | One-to-one correspondence between ECP items and the angular momentum $\ell$ |
| ~local_exponent~ | ~float~ | ~(ecp.local_num_n_max, nucleus.num)~ | $\alpha_{A q \ell_{\max}}$ | | ~nucleus_index~ | ~index~ | ~(ecp.num)~ | One-to-one correspondence between ECP items and the atom index |
| ~local_coef~ | ~float~ | ~(ecp.local_num_n_max, nucleus.num)~ | $\beta_{A q \ell_{\max}}$ | | ~exponent~ | ~float~ | ~(ecp.num)~ | $\alpha_{A q \ell}$ all ECP exponents |
| ~local_power~ | ~int~ | ~(ecp.local_num_n_max, nucleus.num)~ | $n_{A q \ell_{\max}}$ | | ~coefficient~ | ~float~ | ~(ecp.num)~ | $\beta_{A q \ell}$ all ECP coefficients |
| ~non_local_n~ | ~int~ | ~(nucleus.num)~ | $N_{q \ell_{\max}}$ | | ~power~ | ~int~ | ~(ecp.num)~ | $n_{A q \ell}$ all ECP powers |
| ~non_local_num_n_max~ | ~dim~ | | Maximum value of ~non_local_n~, used for dimensioning arrays |
| ~non_local_exponent~ | ~float~ | ~(ecp.non_local_num_n_max, nucleus.num)~ | $\alpha_{A q \ell}$ |
| ~non_local_coef~ | ~float~ | ~(ecp.non_local_num_n_max, nucleus.num)~ | $\beta_{A q \ell}$ | There might be some confusion in the meaning of the $\ell_{\max}$.
| ~non_local_power~ | ~int~ | ~(ecp.non_local_num_n_max, nucleus.num)~ | $n_{A q \ell}$ | 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.
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.
#+CALL: json(data=ecp, title="ecp") #+CALL: json(data=ecp, title="ecp")
@ -159,22 +173,74 @@ arrays are 0-based. Hence, we introduce the ~index~ type which is an
:RESULTS: :RESULTS:
#+begin_src python :tangle trex.json #+begin_src python :tangle trex.json
"ecp": { "ecp": {
"lmax_plus_1" : [ "int" , [ "nucleus.num" ] ] "max_ang_mom_plus_1" : [ "int" , [ "nucleus.num" ] ]
, "z_core" : [ "float", [ "nucleus.num" ] ] , "z_core" : [ "int" , [ "nucleus.num" ] ]
, "local_n" : [ "int" , [ "nucleus.num" ] ] , "num" : [ "dim" , [] ]
, "local_num_n_max" : [ "dim" , [] ] , "ang_mom" : [ "int" , [ "ecp.num" ] ]
, "local_exponent" : [ "float", [ "nucleus.num", "ecp.local_num_n_max" ] ] , "nucleus_index" : [ "index", [ "ecp.num" ] ]
, "local_coef" : [ "float", [ "nucleus.num", "ecp.local_num_n_max" ] ] , "exponent" : [ "float", [ "ecp.num" ] ]
, "local_power" : [ "int" , [ "nucleus.num", "ecp.local_num_n_max" ] ] , "coefficient" : [ "float", [ "ecp.num" ] ]
, "non_local_n" : [ "int" , [ "nucleus.num" ] ] , "power" : [ "int" , [ "ecp.num" ] ]
, "non_local_num_n_max" : [ "dim" , [] ]
, "non_local_exponent" : [ "float", [ "nucleus.num", "ecp.non_local_num_n_max" ] ]
, "non_local_coef" : [ "float", [ "nucleus.num", "ecp.non_local_num_n_max" ] ]
, "non_local_power" : [ "int" , [ "nucleus.num", "ecp.non_local_num_n_max" ] ]
} , } ,
#+end_src #+end_src
:END: :END:
** Example
For example, consider H_2 molecule with the following
[[https://pseudopotentiallibrary.org/recipes/H/ccECP/H.ccECP.gamess][effective core potential]]
(in GAMESS input format for the H atom):
#+BEGIN_EXAMPLE
H-ccECP GEN 0 1
3
1.00000000000000 1 21.24359508259891
21.24359508259891 3 21.24359508259891
-10.85192405303825 2 21.77696655044365
1
0.00000000000000 2 1.000000000000000
#+END_EXAMPLE
In TREXIO representation this would be:
#+BEGIN_EXAMPLE
num = 8
# lmax+1 per atom
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 ; 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 potential of 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
]
# 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
]
exponent = [
21.24359508259891, 21.24359508259891, 21.77696655044365, 1.000000000000000,
21.24359508259891, 21.24359508259891, 21.77696655044365, 1.000000000000000
]
power = [
-1, 1, 0, 0,
-1, 1, 0, 0
]
#+END_EXAMPLE
* Basis set (basis group) * Basis set (basis group)
We consider here basis functions centered on nuclei. Hence, we enable We consider here basis functions centered on nuclei. Hence, we enable