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Added Integrals and renamed functions
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@ -17,6 +17,8 @@ CHANGES
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- Added OCaml binding
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- Added spin and energy in MOs
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- Added CSF group
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- Added Cholesky-decomposed two-electron integrals
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- Added Cholesky-decomposed RDMs for Gammcor
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- Added `trexio_flush` functionality
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- Optional compilation `--without-fortran`
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102
trex.org
102
trex.org
@ -651,15 +651,25 @@ prim_factor =
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** Two-electron integrals (~mo_2e_int~ group)
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The operators as the same as those defined in the
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The operators are the same as those defined in the
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[[#ao_two_e][AO two-electron integrals section]]. Here, the integrals are given in
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the basis of molecular orbitals.
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The Cholesky decomposition of the integrals can also be stored:
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\[
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\A_{ijkl} = \sum_{\alpha} G_{il\alpha} G_{jl\alpha}
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\]
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#+NAME: mo_2e_int
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| Variable | Type | Dimensions | Description |
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|----------+----------------+------------------------------------+-----------------------------------------|
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| ~eri~ | ~float sparse~ | ~(mo.num, mo.num, mo.num, mo.num)~ | Electron repulsion integrals |
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| ~eri_lr~ | ~float sparse~ | ~(mo.num, mo.num, mo.num, mo.num)~ | Long-range Electron repulsion integrals |
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| Variable | Type | Dimensions | Description |
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|-----------------------+----------------+-----------------------------------------+-----------------------------------------------|
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| ~eri~ | ~float sparse~ | ~(mo.num, mo.num, mo.num, mo.num)~ | Electron repulsion integrals |
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| ~eri_lr~ | ~float sparse~ | ~(mo.num, mo.num, mo.num, mo.num)~ | Long-range Electron repulsion integrals |
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| ~eri_cholesky_num~ | ~dim~ | | Number of Cholesky vectors for ERI |
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| ~eri_cholesky~ | ~float sparse~ | ~(mo.num, mo.num, rdm.2e_cholesky_num)~ | Cholesky decomposition of the ERI |
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| ~eri_lr_cholesky_num~ | ~dim~ | | Number of Cholesky vectors for long range ERI |
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| ~eri_lr_cholesky~ | ~float sparse~ | ~(mo.num, mo.num, rdm.2e_cholesky_num)~ | Cholesky decomposition of the long range ERI |
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#+CALL: json(data=mo_2e_int, title="mo_2e_int")
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@ -667,8 +677,12 @@ prim_factor =
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:results:
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#+begin_src python :tangle trex.json
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"mo_2e_int": {
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"eri" : [ "float sparse", [ "mo.num", "mo.num", "mo.num", "mo.num" ] ]
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, "eri_lr" : [ "float sparse", [ "mo.num", "mo.num", "mo.num", "mo.num" ] ]
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"eri" : [ "float sparse", [ "mo.num", "mo.num", "mo.num", "mo.num" ] ]
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, "eri_lr" : [ "float sparse", [ "mo.num", "mo.num", "mo.num", "mo.num" ] ]
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, "eri_cholesky_num" : [ "dim" , [] ]
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, "eri_cholesky" : [ "float sparse", [ "rdm.2e_cholesky_num", "mo.num", "mo.num" ] ]
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, "eri_lr_cholesky_num" : [ "dim" , [] ]
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, "eri_lr_cholesky" : [ "float sparse", [ "rdm.2e_cholesky_num", "mo.num", "mo.num" ] ]
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} ,
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#+end_src
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:end:
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@ -835,21 +849,41 @@ prim_factor =
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To compress the storage, the Cholesky decomposition of the RDMs can
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also be stored.
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be stored:
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\[
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\Gamma_{ijkl} = \sum_{\alpha} G_{ij\alpha} G_{kl\alpha}
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\]
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Warning: as opposed to electron repulsion integrals, the
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decomposition is made such that the Cholesky vectors are expanded
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in a two-electron basis
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$f_{ij}(\mathbf{r}_1,\mathbf{r}_2) = \phi_i(\mathbf{r}_1) \phi_j(\mathbf{r}_2)$,
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whereas in electron repulsion integrals each Cholesky vector is
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expressed in a basis of a one-electron function
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$g_{ik}(\mathbf{r}_1) = \phi_i(\mathbf{r}_1) \phi_k(\mathbf{r}_1)$.
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#+NAME: rdm
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| Variable | Type | Dimensions | Description |
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|---------------+----------------+------------------------------------+-----------------------------------------------------------------------|
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| ~1e~ | ~float~ | ~(mo.num, mo.num)~ | One body density matrix |
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| ~1e_up~ | ~float~ | ~(mo.num, mo.num)~ | \uparrow-spin component of the one body density matrix |
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| ~1e_dn~ | ~float~ | ~(mo.num, mo.num)~ | \downarrow-spin component of the one body density matrix |
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| ~2e~ | ~float sparse~ | ~(mo.num, mo.num, mo.num, mo.num)~ | Two-body reduced density matrix (spin trace) |
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| ~2e_upup~ | ~float sparse~ | ~(mo.num, mo.num, mo.num, mo.num)~ | \uparrow\uparrow component of the two-body reduced density matrix |
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| ~2e_dndn~ | ~float sparse~ | ~(mo.num, mo.num, mo.num, mo.num)~ | \downarrow\downarrow component of the two-body reduced density matrix |
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| ~2e_updn~ | ~float sparse~ | ~(mo.num, mo.num, mo.num, mo.num)~ | \uparrow\downarrow component of the two-body reduced density matrix |
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| ~2e_dnup~ | ~float sparse~ | ~(mo.num, mo.num, mo.num, mo.num)~ | \downarrow\uparrow component of the two-body reduced density matrix |
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| ~chol_num~ | ~dim~ | | Number of cholesky vector |
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| ~2e_cholesky~ | ~float sparse~ | ~(mo.num, mo.num, rdm.chol_num)~ | Two-body RDM (spin trace) in the basis of Cholesky vectors |
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| Variable | Type | Dimensions | Description |
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|------------------------+----------------+----------------------------------------------+-----------------------------------------------------------------------|
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| ~1e~ | ~float~ | ~(mo.num, mo.num)~ | One body density matrix |
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| ~1e_up~ | ~float~ | ~(mo.num, mo.num)~ | \uparrow-spin component of the one body density matrix |
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| ~1e_dn~ | ~float~ | ~(mo.num, mo.num)~ | \downarrow-spin component of the one body density matrix |
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| ~2e~ | ~float sparse~ | ~(mo.num, mo.num, mo.num, mo.num)~ | Two-body reduced density matrix (spin trace) |
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| ~2e_upup~ | ~float sparse~ | ~(mo.num, mo.num, mo.num, mo.num)~ | \uparrow\uparrow component of the two-body reduced density matrix |
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| ~2e_dndn~ | ~float sparse~ | ~(mo.num, mo.num, mo.num, mo.num)~ | \downarrow\downarrow component of the two-body reduced density matrix |
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| ~2e_updn~ | ~float sparse~ | ~(mo.num, mo.num, mo.num, mo.num)~ | \uparrow\downarrow component of the two-body reduced density matrix |
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| ~2e_dnup~ | ~float sparse~ | ~(mo.num, mo.num, mo.num, mo.num)~ | \downarrow\uparrow component of the two-body reduced density matrix |
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| ~2e_cholesky_num~ | ~dim~ | | Number of Cholesky vectors |
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| ~2e_cholesky~ | ~float sparse~ | ~(mo.num, mo.num, rdm.2e_cholesky_num)~ | Cholesky decomposition of the Two-body RDM (spin trace) |
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| ~2e_upup_cholesky_num~ | ~dim~ | | Number of Cholesky vectors |
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| ~2e_upup_cholesky~ | ~float sparse~ | ~(mo.num, mo.num, rdm.2e_upup_cholesky_num)~ | Cholesky decomposition of the Two-body RDM (\uparrow\uparrow) |
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| ~2e_dndn_cholesky_num~ | ~dim~ | | Number of Cholesky vectors |
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| ~2e_dndn_cholesky~ | ~float sparse~ | ~(mo.num, mo.num, rdm.2e_dndn_cholesky_num)~ | Cholesky decomposition of the Two-body RDM (\downarrow\downarrow) |
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| ~2e_updn_cholesky_num~ | ~dim~ | | Number of Cholesky vectors |
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| ~2e_updn_cholesky~ | ~float sparse~ | ~(mo.num, mo.num, rdm.2e_updn_cholesky_num)~ | Cholesky decomposition of the Two-body RDM (\uparrow\downarrow) |
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| ~2e_dnup_cholesky_num~ | ~dim~ | | Number of Cholesky vectors |
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| ~2e_dnup_cholesky~ | ~float sparse~ | ~(mo.num, mo.num, rdm.2e_dnup_cholesky_num)~ | Cholesky decomposition of the Two-body RDM (\downarrow\uparrow) |
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#+CALL: json(data=rdm, title="rdm")
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@ -857,16 +891,24 @@ prim_factor =
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:results:
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#+begin_src python :tangle trex.json
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"rdm": {
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"1e" : [ "float" , [ "mo.num", "mo.num" ] ]
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, "1e_up" : [ "float" , [ "mo.num", "mo.num" ] ]
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, "1e_dn" : [ "float" , [ "mo.num", "mo.num" ] ]
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, "2e" : [ "float sparse", [ "mo.num", "mo.num", "mo.num", "mo.num" ] ]
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, "2e_upup" : [ "float sparse", [ "mo.num", "mo.num", "mo.num", "mo.num" ] ]
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, "2e_dndn" : [ "float sparse", [ "mo.num", "mo.num", "mo.num", "mo.num" ] ]
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, "2e_updn" : [ "float sparse", [ "mo.num", "mo.num", "mo.num", "mo.num" ] ]
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, "2e_dnup" : [ "float sparse", [ "mo.num", "mo.num", "mo.num", "mo.num" ] ]
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, "chol_num" : [ "dim" , [] ]
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, "2e_cholesky" : [ "float sparse", [ "rdm.chol_num", "mo.num", "mo.num" ] ]
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"1e" : [ "float" , [ "mo.num", "mo.num" ] ]
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, "1e_up" : [ "float" , [ "mo.num", "mo.num" ] ]
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, "1e_dn" : [ "float" , [ "mo.num", "mo.num" ] ]
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, "2e" : [ "float sparse", [ "mo.num", "mo.num", "mo.num", "mo.num" ] ]
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, "2e_upup" : [ "float sparse", [ "mo.num", "mo.num", "mo.num", "mo.num" ] ]
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, "2e_dndn" : [ "float sparse", [ "mo.num", "mo.num", "mo.num", "mo.num" ] ]
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, "2e_updn" : [ "float sparse", [ "mo.num", "mo.num", "mo.num", "mo.num" ] ]
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, "2e_dnup" : [ "float sparse", [ "mo.num", "mo.num", "mo.num", "mo.num" ] ]
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, "2e_cholesky_num" : [ "dim" , [] ]
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, "2e_cholesky" : [ "float sparse", [ "rdm.2e_cholesky_num", "mo.num", "mo.num" ] ]
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, "2e_upup_cholesky_num" : [ "dim" , [] ]
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, "2e_upup_cholesky" : [ "float sparse", [ "rdm.2e_upup_cholesky_num", "mo.num", "mo.num" ] ]
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, "2e_dndn_cholesky_num" : [ "dim" , [] ]
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, "2e_dndn_cholesky" : [ "float sparse", [ "rdm.2e_dndn_cholesky_num", "mo.num", "mo.num" ] ]
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, "2e_updn_cholesky_num" : [ "dim" , [] ]
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, "2e_updn_cholesky" : [ "float sparse", [ "rdm.2e_updn_cholesky_num", "mo.num", "mo.num" ] ]
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, "2e_dnup_cholesky_num" : [ "dim" , [] ]
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, "2e_dnup_cholesky" : [ "float sparse", [ "rdm.2e_dnup_cholesky_num", "mo.num", "mo.num" ] ]
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} ,
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#+end_src
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:end:
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