mirror of
https://github.com/TREX-CoE/trexio.git
synced 2024-12-23 12:56:53 +01:00
Add determinant group
This commit is contained in:
parent
54884358e5
commit
dab10cf466
44
trex.org
44
trex.org
@ -635,7 +635,49 @@ prim_factor =
|
|||||||
#+end_src
|
#+end_src
|
||||||
:end:
|
:end:
|
||||||
|
|
||||||
* TODO Slater determinants
|
* Slater determinants (determinant group)
|
||||||
|
|
||||||
|
The configuration interaction (CI) wave function $\Psi$
|
||||||
|
can be expanded in the basis of Slater determinants $D_I$ as follows
|
||||||
|
|
||||||
|
\[
|
||||||
|
|\Psi> = \sum_I C_I |D_I>
|
||||||
|
\]
|
||||||
|
|
||||||
|
For relatively small expansions, a given determinant can be represented as a list of ~mo.num~ occupation numbers.
|
||||||
|
However, this requires a lot of extra memory and would be technically impossible for larger expansions
|
||||||
|
(~millions of determinants). This is why the determinants are stored as bit fields in the TREXIO file
|
||||||
|
(see ~int bitfield~ type in the table below). By default, the chemist notation is used, namely
|
||||||
|
|
||||||
|
\[
|
||||||
|
| D_I > = | \alpha_1 \alpha_2 \ldots \alpha_{n\uparrow} \beta_1 \beta_2 \ldots \beta_{n\downarrow} >
|
||||||
|
\
|
||||||
|
|
||||||
|
where $\alpha$ and $\beta$ denote $\uparrow$-spin and $\downarrow$-spin electrons, respectively,
|
||||||
|
$n\uparrow$ and $n\downarrow$ correspond to ~electron.up_num~ and ~electron.dn_num~, respectively.
|
||||||
|
Internally, bit fields for $\alpha$ and $\beta$ electrons are stored separately,
|
||||||
|
which is why the ~determinant.list~ attribute has a second dimension.
|
||||||
|
|
||||||
|
#+NAME: determinant
|
||||||
|
| Variable | Type | Dimensions | Description |
|
||||||
|
|---------------+----------------+------------------------+--------------------------------------------------------|
|
||||||
|
| ~num~ | ~dim~ | | Number of determinants |
|
||||||
|
| ~list~ | ~int bitfield~ | ~(determinant.num, 2)~ | List of determinants as integer bit fields |
|
||||||
|
| ~coefficient~ | ~float~ | ~(determinant.num)~ | Coefficients of the determinants from the CI expansion |
|
||||||
|
|
||||||
|
#+CALL: json(data=determinant, title="determinant")
|
||||||
|
|
||||||
|
#+RESULTS:
|
||||||
|
:results:
|
||||||
|
#+begin_src python :tangle trex.json
|
||||||
|
"determinant": {
|
||||||
|
"num" : [ "dim" , [] ]
|
||||||
|
, "list" : [ "int binary", [ "2", "determinant.num" ] ]
|
||||||
|
, "coefficient" : [ "float" , [ "determinant.num" ] ]
|
||||||
|
} ,
|
||||||
|
#+end_src
|
||||||
|
:end:
|
||||||
|
|
||||||
* Reduced density matrices (rdm group)
|
* Reduced density matrices (rdm group)
|
||||||
|
|
||||||
The reduced density matrices are defined in the basis of molecular
|
The reduced density matrices are defined in the basis of molecular
|
||||||
|
Loading…
Reference in New Issue
Block a user