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Merge pull request #64 from TREX-CoE/fix-ecp-structure
FIX: more flexible ECP format
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trex.org
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trex.org
@ -118,15 +118,18 @@ arrays are 0-based. Hence, we introduce the ~index~ type which is an
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* Effective core potentials (ecp group)
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An effective core potential (ECP) $V_A^{\text{ECP}}$ replacing the
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core electrons of atom $A$ is expressed as
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core electrons of atom $A$ can be expressed as
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\[
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V_A^{\text{ECP}} =
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V_{A \ell_{\max}} +
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\sum_{\ell=0}^{\ell_{\max} -1}
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V_{A \ell_{\max}+1} +
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\sum_{\ell=0}^{\ell_{\max}}
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\sum_{m=-\ell}^{\ell} | Y_{\ell m} \rangle \left[
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V_{A \ell} - V_{A \ell_{\max}} \right] \langle Y_{\ell m} |
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V_{A \ell} - V_{A \ell_{\max}+1} \right] \langle Y_{\ell m} |
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\]
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The first term in the equation above is sometimes attributed to the local channel,
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while the remaining terms correspond to the non-local channel projections.
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The functions $V_{A\ell}$ are parameterized as:
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\[
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V_{A \ell}(\mathbf{r}) =
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@ -135,23 +138,34 @@ arrays are 0-based. Hence, we introduce the ~index~ type which is an
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e^{-\alpha_{A q \ell} |\mathbf{r}-\mathbf{R}_{A}|^2 }
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\]
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See http://dx.doi.org/10.1063/1.4984046 for more info.
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See http://dx.doi.org/10.1063/1.4984046 or https://doi.org/10.1063/1.5121006for more info.
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#+NAME: ecp
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| Variable | Type | Dimensions | Description |
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|-----------------------+---------+------------------------------------------+----------------------------------------------------------------------------------------------|
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| ~lmax_plus_1~ | ~int~ | ~(nucleus.num)~ | $\ell_{\max} + 1$, one higher than the maximum angular momentum in the removed core orbitals |
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| ~z_core~ | ~float~ | ~(nucleus.num)~ | Charges to remove |
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| ~local_n~ | ~int~ | ~(nucleus.num)~ | Number of local functions $N_{q \ell}$ |
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| ~local_num_n_max~ | ~dim~ | | Maximum value of ~local_n~, used for dimensioning arrays |
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| ~local_exponent~ | ~float~ | ~(ecp.local_num_n_max, nucleus.num)~ | $\alpha_{A q \ell_{\max}}$ |
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| ~local_coef~ | ~float~ | ~(ecp.local_num_n_max, nucleus.num)~ | $\beta_{A q \ell_{\max}}$ |
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| ~local_power~ | ~int~ | ~(ecp.local_num_n_max, nucleus.num)~ | $n_{A q \ell_{\max}}$ |
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| ~non_local_n~ | ~int~ | ~(nucleus.num)~ | $N_{q \ell_{\max}}$ |
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| ~non_local_num_n_max~ | ~dim~ | | Maximum value of ~non_local_n~, used for dimensioning arrays |
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| ~non_local_exponent~ | ~float~ | ~(ecp.non_local_num_n_max, nucleus.num)~ | $\alpha_{A q \ell}$ |
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| ~non_local_coef~ | ~float~ | ~(ecp.non_local_num_n_max, nucleus.num)~ | $\beta_{A q \ell}$ |
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| ~non_local_power~ | ~int~ | ~(ecp.non_local_num_n_max, nucleus.num)~ | $n_{A q \ell}$ |
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| Variable | Type | Dimensions | Description |
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|----------------------+---------+-----------------+----------------------------------------------------------------------------------------|
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| ~max_ang_mom_plus_1~ | ~int~ | ~(nucleus.num)~ | $\ell_{\max}+1$, one higher than the max angular momentum in the removed core orbitals |
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| ~z_core~ | ~int~ | ~(nucleus.num)~ | Number of core electrons to remove per atom |
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| ~num~ | ~dim~ | | Total number of ECP functions for all atoms and all values of $\ell$ |
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| ~ang_mom~ | ~int~ | ~(ecp.num)~ | One-to-one correspondence between ECP items and the angular momentum $\ell$ |
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| ~nucleus_index~ | ~index~ | ~(ecp.num)~ | One-to-one correspondence between ECP items and the atom index |
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| ~exponent~ | ~float~ | ~(ecp.num)~ | $\alpha_{A q \ell}$ all ECP exponents |
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| ~coefficient~ | ~float~ | ~(ecp.num)~ | $\beta_{A q \ell}$ all ECP coefficients |
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| ~power~ | ~int~ | ~(ecp.num)~ | $n_{A q \ell}$ all ECP powers |
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There might be some confusion in the meaning of the $\ell_{\max}$.
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It can be attributed to the maximum angular momentum occupied
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in the core orbitals, which are removed by the ECP.
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On the other hand, it can be attributed to the maximum angular momentum of the
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ECP that replaces the core electrons.
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*Note*, that the latter $\ell_{\max}$ is always higher by 1 than the former.
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*Note for developers*: avoid having variables with similar prefix in their name.
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HDF5 back end might cause issues due to the way `find_dataset` function works.
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For example, in the ECP group we use ~max_ang_mom~ and not ~ang_mom_max~.
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The latter causes issues when written before ~ang_mom~ in the TREXIO file.
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#+CALL: json(data=ecp, title="ecp")
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@ -159,22 +173,74 @@ arrays are 0-based. Hence, we introduce the ~index~ type which is an
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:RESULTS:
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#+begin_src python :tangle trex.json
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"ecp": {
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"lmax_plus_1" : [ "int" , [ "nucleus.num" ] ]
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, "z_core" : [ "float", [ "nucleus.num" ] ]
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, "local_n" : [ "int" , [ "nucleus.num" ] ]
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, "local_num_n_max" : [ "dim" , [] ]
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, "local_exponent" : [ "float", [ "nucleus.num", "ecp.local_num_n_max" ] ]
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, "local_coef" : [ "float", [ "nucleus.num", "ecp.local_num_n_max" ] ]
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, "local_power" : [ "int" , [ "nucleus.num", "ecp.local_num_n_max" ] ]
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, "non_local_n" : [ "int" , [ "nucleus.num" ] ]
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, "non_local_num_n_max" : [ "dim" , [] ]
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, "non_local_exponent" : [ "float", [ "nucleus.num", "ecp.non_local_num_n_max" ] ]
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, "non_local_coef" : [ "float", [ "nucleus.num", "ecp.non_local_num_n_max" ] ]
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, "non_local_power" : [ "int" , [ "nucleus.num", "ecp.non_local_num_n_max" ] ]
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"max_ang_mom_plus_1" : [ "int" , [ "nucleus.num" ] ]
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, "z_core" : [ "int" , [ "nucleus.num" ] ]
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, "num" : [ "dim" , [] ]
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, "ang_mom" : [ "int" , [ "ecp.num" ] ]
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, "nucleus_index" : [ "index", [ "ecp.num" ] ]
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, "exponent" : [ "float", [ "ecp.num" ] ]
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, "coefficient" : [ "float", [ "ecp.num" ] ]
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, "power" : [ "int" , [ "ecp.num" ] ]
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} ,
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#+end_src
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:END:
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** Example
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For example, consider H_2 molecule with the following
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[[https://pseudopotentiallibrary.org/recipes/H/ccECP/H.ccECP.gamess][effective core potential]]
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(in GAMESS input format for the H atom):
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#+BEGIN_EXAMPLE
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H-ccECP GEN 0 1
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3
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1.00000000000000 1 21.24359508259891
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21.24359508259891 3 21.24359508259891
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-10.85192405303825 2 21.77696655044365
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1
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0.00000000000000 2 1.000000000000000
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#+END_EXAMPLE
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In TREXIO representation this would be:
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#+BEGIN_EXAMPLE
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num = 8
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# lmax+1 per atom
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max_ang_mom_plus_1 = [ 1, 1 ]
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# number of core electrons to remove per atom
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zcore = [ 0, 0 ]
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# first 4 ECP elements correspond to the first H atom ; the remaining 4 elements are for the second H atom
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nucleus_index = [
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0, 0, 0, 0,
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1, 1, 1, 1
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]
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# 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
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ang_mom = [
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1, 1, 1, 0,
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1, 1, 1, 0
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]
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# ECP quantities that can be attributed to atoms and/or angular momenta based on the aforementioned ecp_nucleus and ecp_ang_mom arrays
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coefficient = [
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1.00000000000000, 21.24359508259891, -10.85192405303825, 0.00000000000000,
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1.00000000000000, 21.24359508259891, -10.85192405303825, 0.00000000000000
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]
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exponent = [
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21.24359508259891, 21.24359508259891, 21.77696655044365, 1.000000000000000,
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21.24359508259891, 21.24359508259891, 21.77696655044365, 1.000000000000000
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]
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power = [
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-1, 1, 0, 0,
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-1, 1, 0, 0
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]
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#+END_EXAMPLE
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* Basis set (basis group)
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We consider here basis functions centered on nuclei. Hence, we enable
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