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Add state group

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q-posev 2022-04-13 16:37:10 +02:00
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@ -637,46 +637,71 @@ prim_factor =
* Slater determinants (determinant group)
The configuration interaction (CI) wave function $\Psi$
The configuration interaction (CI) wave function $\Psi$
can be expanded in the basis of Slater determinants $D_I$ as follows
\[
| \Psi> = \sum_I C_I | D_I>
| \Psi> = \sum_I C_I | D_I> |
\]
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
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
\[
| D_I > = | \alpha_1 \alpha_2 \ldots \alpha_{n\uparrow} \beta_1 \beta_2 \ldots \beta_{n\downarrow} >
| D_I > = | \alpha_1 \alpha_2 \ldots \alpha_{n\uparrow} \beta_1 \beta_2 \ldots \beta_{n\downarrow} > |
\]
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 special~ | ~(determinant.num, 2)~ | List of determinants as integer bit fields |
| ~coefficient~ | ~float special~ | ~(determinant.num)~ | Coefficients of the determinants from the CI expansion |
| Variable | Type | Dimensions | Description |
|---------------+-----------------+-------------------------------+--------------------------------------------------------|
| ~num~ | ~dim~ | | Number of determinants |
| ~list~ | ~int special~ | ~(determinant.num)~ | List of determinants as integer bit fields |
| ~coefficient~ | ~float special~ | ~(state.num,determinant.num)~ | Coefficients of the determinants from the CI expansion |
#+CALL: json(data=determinant, title="determinant")
#+RESULTS:
:results:
:RESULTS:
#+begin_src python :tangle trex.json
"determinant": {
"num" : [ "dim" , [] ]
, "list" : [ "int special" , [ "2", "determinant.num" ] ]
, "coefficient" : [ "float special", [ "determinant.num" ] ]
"num" : [ "dim" , [] ]
, "list" : [ "int special" , [ "determinant.num" ] ]
, "coefficient" : [ "float special", [ "determinant.num", "state.num" ] ]
} ,
#+end_src
:end:
:END:
* Excited states (state group)
By default, the ~determinant~ group corresponds to the ground state.
However, it should be also possible to store the coefficients that
correspond to excited state wave functions for the same set of
determinants. This is the goal of the present group
#+NAME: state
| Variable | Type | Dimensions | Description |
|----------+-------+---------------+------------------------------------------------|
| ~num~ | ~dim~ | | Number of states (including the ground state) |
| ~label~ | ~str~ | ~(state.num)~ | Label of a given state (e.g. 'S' for singlets) |
#+CALL: json(data=state, title="state")
#+RESULTS:
:RESULTS:
#+begin_src python :tangle trex.json
"state": {
"num" : [ "dim", [] ]
, "label" : [ "str", [ "state.num" ] ]
} ,
#+end_src
:END:
* Reduced density matrices (rdm group)