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Added Integrals and renamed functions

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Anthony Scemama 2022-12-01 17:27:36 +01:00
parent 71604e1d16
commit 98bb2d6b4f
2 changed files with 74 additions and 30 deletions
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@ -17,6 +17,8 @@ CHANGES
- Added OCaml binding - Added OCaml binding
- Added spin and energy in MOs - Added spin and energy in MOs
- Added CSF group - Added CSF group
- Added Cholesky-decomposed two-electron integrals
- Added Cholesky-decomposed RDMs for Gammcor
- Added `trexio_flush` functionality - Added `trexio_flush` functionality
- Optional compilation `--without-fortran` - Optional compilation `--without-fortran`

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@ -651,15 +651,25 @@ prim_factor =
** Two-electron integrals (~mo_2e_int~ group) ** Two-electron integrals (~mo_2e_int~ group)
The operators as the same as those defined in the The operators are the same as those defined in the
[[#ao_two_e][AO two-electron integrals section]]. Here, the integrals are given in [[#ao_two_e][AO two-electron integrals section]]. Here, the integrals are given in
the basis of molecular orbitals. the basis of molecular orbitals.
The Cholesky decomposition of the integrals can also be stored:
\[
\A_{ijkl} = \sum_{\alpha} G_{il\alpha} G_{jl\alpha}
\]
#+NAME: mo_2e_int #+NAME: mo_2e_int
| Variable | Type | Dimensions | Description | | Variable | Type | Dimensions | Description |
|----------+----------------+------------------------------------+-----------------------------------------| |-----------------------+----------------+-----------------------------------------+-----------------------------------------------|
| ~eri~ | ~float sparse~ | ~(mo.num, mo.num, mo.num, mo.num)~ | Electron repulsion integrals | | ~eri~ | ~float sparse~ | ~(mo.num, mo.num, mo.num, mo.num)~ | Electron repulsion integrals |
| ~eri_lr~ | ~float sparse~ | ~(mo.num, mo.num, mo.num, mo.num)~ | Long-range Electron repulsion integrals | | ~eri_lr~ | ~float sparse~ | ~(mo.num, mo.num, mo.num, mo.num)~ | Long-range Electron repulsion integrals |
| ~eri_cholesky_num~ | ~dim~ | | Number of Cholesky vectors for ERI |
| ~eri_cholesky~ | ~float sparse~ | ~(mo.num, mo.num, rdm.2e_cholesky_num)~ | Cholesky decomposition of the ERI |
| ~eri_lr_cholesky_num~ | ~dim~ | | Number of Cholesky vectors for long range ERI |
| ~eri_lr_cholesky~ | ~float sparse~ | ~(mo.num, mo.num, rdm.2e_cholesky_num)~ | Cholesky decomposition of the long range ERI |
#+CALL: json(data=mo_2e_int, title="mo_2e_int") #+CALL: json(data=mo_2e_int, title="mo_2e_int")
@ -667,8 +677,12 @@ prim_factor =
:results: :results:
#+begin_src python :tangle trex.json #+begin_src python :tangle trex.json
"mo_2e_int": { "mo_2e_int": {
"eri" : [ "float sparse", [ "mo.num", "mo.num", "mo.num", "mo.num" ] ] "eri" : [ "float sparse", [ "mo.num", "mo.num", "mo.num", "mo.num" ] ]
, "eri_lr" : [ "float sparse", [ "mo.num", "mo.num", "mo.num", "mo.num" ] ] , "eri_lr" : [ "float sparse", [ "mo.num", "mo.num", "mo.num", "mo.num" ] ]
, "eri_cholesky_num" : [ "dim" , [] ]
, "eri_cholesky" : [ "float sparse", [ "rdm.2e_cholesky_num", "mo.num", "mo.num" ] ]
, "eri_lr_cholesky_num" : [ "dim" , [] ]
, "eri_lr_cholesky" : [ "float sparse", [ "rdm.2e_cholesky_num", "mo.num", "mo.num" ] ]
} , } ,
#+end_src #+end_src
:end: :end:
@ -835,21 +849,41 @@ prim_factor =
To compress the storage, the Cholesky decomposition of the RDMs can To compress the storage, the Cholesky decomposition of the RDMs can
also be stored. be stored:
\[
\Gamma_{ijkl} = \sum_{\alpha} G_{ij\alpha} G_{kl\alpha}
\]
Warning: as opposed to electron repulsion integrals, the
decomposition is made such that the Cholesky vectors are expanded
in a two-electron basis
$f_{ij}(\mathbf{r}_1,\mathbf{r}_2) = \phi_i(\mathbf{r}_1) \phi_j(\mathbf{r}_2)$,
whereas in electron repulsion integrals each Cholesky vector is
expressed in a basis of a one-electron function
$g_{ik}(\mathbf{r}_1) = \phi_i(\mathbf{r}_1) \phi_k(\mathbf{r}_1)$.
#+NAME: rdm #+NAME: rdm
| Variable | Type | Dimensions | Description | | Variable | Type | Dimensions | Description |
|---------------+----------------+------------------------------------+-----------------------------------------------------------------------| |------------------------+----------------+----------------------------------------------+-----------------------------------------------------------------------|
| ~1e~ | ~float~ | ~(mo.num, mo.num)~ | One body density matrix | | ~1e~ | ~float~ | ~(mo.num, mo.num)~ | One body density matrix |
| ~1e_up~ | ~float~ | ~(mo.num, mo.num)~ | \uparrow-spin component of the one body density matrix | | ~1e_up~ | ~float~ | ~(mo.num, mo.num)~ | \uparrow-spin component of the one body density matrix |
| ~1e_dn~ | ~float~ | ~(mo.num, mo.num)~ | \downarrow-spin component of the one body density matrix | | ~1e_dn~ | ~float~ | ~(mo.num, mo.num)~ | \downarrow-spin component of the one body density matrix |
| ~2e~ | ~float sparse~ | ~(mo.num, mo.num, mo.num, mo.num)~ | Two-body reduced density matrix (spin trace) | | ~2e~ | ~float sparse~ | ~(mo.num, mo.num, mo.num, mo.num)~ | Two-body reduced density matrix (spin trace) |
| ~2e_upup~ | ~float sparse~ | ~(mo.num, mo.num, mo.num, mo.num)~ | \uparrow\uparrow component of the two-body reduced density matrix | | ~2e_upup~ | ~float sparse~ | ~(mo.num, mo.num, mo.num, mo.num)~ | \uparrow\uparrow component of the two-body reduced density matrix |
| ~2e_dndn~ | ~float sparse~ | ~(mo.num, mo.num, mo.num, mo.num)~ | \downarrow\downarrow component of the two-body reduced density matrix | | ~2e_dndn~ | ~float sparse~ | ~(mo.num, mo.num, mo.num, mo.num)~ | \downarrow\downarrow component of the two-body reduced density matrix |
| ~2e_updn~ | ~float sparse~ | ~(mo.num, mo.num, mo.num, mo.num)~ | \uparrow\downarrow component of the two-body reduced density matrix | | ~2e_updn~ | ~float sparse~ | ~(mo.num, mo.num, mo.num, mo.num)~ | \uparrow\downarrow component of the two-body reduced density matrix |
| ~2e_dnup~ | ~float sparse~ | ~(mo.num, mo.num, mo.num, mo.num)~ | \downarrow\uparrow component of the two-body reduced density matrix | | ~2e_dnup~ | ~float sparse~ | ~(mo.num, mo.num, mo.num, mo.num)~ | \downarrow\uparrow component of the two-body reduced density matrix |
| ~chol_num~ | ~dim~ | | Number of cholesky vector | | ~2e_cholesky_num~ | ~dim~ | | Number of Cholesky vectors |
| ~2e_cholesky~ | ~float sparse~ | ~(mo.num, mo.num, rdm.chol_num)~ | Two-body RDM (spin trace) in the basis of Cholesky vectors | | ~2e_cholesky~ | ~float sparse~ | ~(mo.num, mo.num, rdm.2e_cholesky_num)~ | Cholesky decomposition of the Two-body RDM (spin trace) |
| ~2e_upup_cholesky_num~ | ~dim~ | | Number of Cholesky vectors |
| ~2e_upup_cholesky~ | ~float sparse~ | ~(mo.num, mo.num, rdm.2e_upup_cholesky_num)~ | Cholesky decomposition of the Two-body RDM (\uparrow\uparrow) |
| ~2e_dndn_cholesky_num~ | ~dim~ | | Number of Cholesky vectors |
| ~2e_dndn_cholesky~ | ~float sparse~ | ~(mo.num, mo.num, rdm.2e_dndn_cholesky_num)~ | Cholesky decomposition of the Two-body RDM (\downarrow\downarrow) |
| ~2e_updn_cholesky_num~ | ~dim~ | | Number of Cholesky vectors |
| ~2e_updn_cholesky~ | ~float sparse~ | ~(mo.num, mo.num, rdm.2e_updn_cholesky_num)~ | Cholesky decomposition of the Two-body RDM (\uparrow\downarrow) |
| ~2e_dnup_cholesky_num~ | ~dim~ | | Number of Cholesky vectors |
| ~2e_dnup_cholesky~ | ~float sparse~ | ~(mo.num, mo.num, rdm.2e_dnup_cholesky_num)~ | Cholesky decomposition of the Two-body RDM (\downarrow\uparrow) |
#+CALL: json(data=rdm, title="rdm") #+CALL: json(data=rdm, title="rdm")
@ -857,16 +891,24 @@ prim_factor =
:results: :results:
#+begin_src python :tangle trex.json #+begin_src python :tangle trex.json
"rdm": { "rdm": {
"1e" : [ "float" , [ "mo.num", "mo.num" ] ] "1e" : [ "float" , [ "mo.num", "mo.num" ] ]
, "1e_up" : [ "float" , [ "mo.num", "mo.num" ] ] , "1e_up" : [ "float" , [ "mo.num", "mo.num" ] ]
, "1e_dn" : [ "float" , [ "mo.num", "mo.num" ] ] , "1e_dn" : [ "float" , [ "mo.num", "mo.num" ] ]
, "2e" : [ "float sparse", [ "mo.num", "mo.num", "mo.num", "mo.num" ] ] , "2e" : [ "float sparse", [ "mo.num", "mo.num", "mo.num", "mo.num" ] ]
, "2e_upup" : [ "float sparse", [ "mo.num", "mo.num", "mo.num", "mo.num" ] ] , "2e_upup" : [ "float sparse", [ "mo.num", "mo.num", "mo.num", "mo.num" ] ]
, "2e_dndn" : [ "float sparse", [ "mo.num", "mo.num", "mo.num", "mo.num" ] ] , "2e_dndn" : [ "float sparse", [ "mo.num", "mo.num", "mo.num", "mo.num" ] ]
, "2e_updn" : [ "float sparse", [ "mo.num", "mo.num", "mo.num", "mo.num" ] ] , "2e_updn" : [ "float sparse", [ "mo.num", "mo.num", "mo.num", "mo.num" ] ]
, "2e_dnup" : [ "float sparse", [ "mo.num", "mo.num", "mo.num", "mo.num" ] ] , "2e_dnup" : [ "float sparse", [ "mo.num", "mo.num", "mo.num", "mo.num" ] ]
, "chol_num" : [ "dim" , [] ] , "2e_cholesky_num" : [ "dim" , [] ]
, "2e_cholesky" : [ "float sparse", [ "rdm.chol_num", "mo.num", "mo.num" ] ] , "2e_cholesky" : [ "float sparse", [ "rdm.2e_cholesky_num", "mo.num", "mo.num" ] ]
, "2e_upup_cholesky_num" : [ "dim" , [] ]
, "2e_upup_cholesky" : [ "float sparse", [ "rdm.2e_upup_cholesky_num", "mo.num", "mo.num" ] ]
, "2e_dndn_cholesky_num" : [ "dim" , [] ]
, "2e_dndn_cholesky" : [ "float sparse", [ "rdm.2e_dndn_cholesky_num", "mo.num", "mo.num" ] ]
, "2e_updn_cholesky_num" : [ "dim" , [] ]
, "2e_updn_cholesky" : [ "float sparse", [ "rdm.2e_updn_cholesky_num", "mo.num", "mo.num" ] ]
, "2e_dnup_cholesky_num" : [ "dim" , [] ]
, "2e_dnup_cholesky" : [ "float sparse", [ "rdm.2e_dnup_cholesky_num", "mo.num", "mo.num" ] ]
} , } ,
#+end_src #+end_src
:end: :end: