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better documentation of th ECP block
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trex.org
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trex.org
@ -118,7 +118,7 @@ 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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\[
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V_A^{\text{ECP}} =
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V_{A \ell_{\max}+1} +
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@ -127,6 +127,9 @@ arrays are 0-based. Hence, we introduce the ~index~ type which is an
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V_{A \ell} - V_{A \ell_{\max}+1} \right] \langle Y_{\ell m} |
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\]
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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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\[
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V_{A \ell}(\mathbf{r}) =
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@ -135,13 +138,13 @@ arrays are 0-based. Hence, we introduce the ~index~ type which is an
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e^{-\alpha_{A q \ell} |\mathbf{r}-\mathbf{R}_{A}|^2 }
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\]
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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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| ~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~ | ~float~ | ~(nucleus.num)~ | Charges to remove |
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| ~z_core~ | ~float~ | ~(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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@ -150,10 +153,17 @@ arrays are 0-based. Hence, we introduce the ~index~ type which is an
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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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in the H5LT module. For example, in the ECP group we use ~max_ang_mom~ and
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~ang_mom_max~ due to this.
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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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@ -202,19 +212,19 @@ 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, same for the second H atom
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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 l=1 of the first H atom, then 1 ECP for l=0; same for the second H atom
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# 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
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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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# flat arrays with ECP quantities that can be parsed based on the aforementioned ecp_ang_mom and ecp_nucleus
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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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