Integrated amplitudes

trex.org

@@ -943,6 +943,79 @@ power = [
    #+end_src
    :end:
 
+** Amplitudes (amplitude group)
+
+   The wave function may be expressed in terms of action of the cluster
+   operator $\hat{T}$:
+
+   \[
+   \hat{T} = \hat{T}_1 + \hat{T}_2 + \hat{T}_3 + \dots
+   \]
+
+   on a reference wave function $\Psi$, where $\hat{T}_1$ is the single excitation operator,
+
+   \[
+   \hat{T}_1 = \sum_{ia} t_{i}^{a}\, \hat{a}^\dagger_a \hat{a}_i 
+   \],
+
+   $\hat{T}_2$ is the double excitation operator,
+
+   \[
+   \hat{T}_2 = \frac{1}{4} \sum_{ijab} t_{ij}^{ab}\, \hat{a}^\dagger_a \hat{a}^\dagger_b \hat{a}_j \hat{a}_i 
+   \],
+
+ /etc/. Indices $i,j,a,b$ denote molecular orbital indices.
+
+   Wave functions obtained with perturbation theory of configuration
+   interaction are of the form
+
+   \[ |\Phi\rangle = \hat{T}|\Psi\rangle  \]
+
+   and coupled-cluster wave functions are of the form
+
+   \[ |\Phi\rangle = e^{\hat{T}}| \Psi \rangle \]
+
+   The reference wave function is stored using the ~determinant~ and/or 
+ ~csf~ groups, and the amplitudes are stored using the current group.
+   The attributes with the ~exp~ suffix correspond to exponentialized operators.
+
+   The order of the indices is chosen such that
+   - ~t(i,a)~ = $t_{i}^{a}$.
+   - ~t(i,j,a,b)~ = $t_{ij}^{ab}$,
+   - ~t(i,j,k,a,b,c)~ = $t_{ijk}^{abc}$,
+   - ~t(i,j,k,l,a,b,c,d)~ = $t_{ijkl}^{abcd}$,
+   - $\dots$
+
+   #+NAME: amplitude
+   | Variable        | Type           | Dimensions                                                  | Description                                     |
+   |-----------------+----------------+-------------------------------------------------------------+-------------------------------------------------|
+   | ~single~        | ~float sparse~ | ~(mo.num,mo.num)~                                           | Single excitation amplitudes                    |
+   | ~single_exp~    | ~float sparse~ | ~(mo.num,mo.num)~                                           | Exponentialized single excitation amplitudes    |
+   | ~double~        | ~float sparse~ | ~(mo.num,mo.num,mo.num,mo.num)~                             | Double excitation amplitudes                    |
+   | ~double_exp~    | ~float sparse~ | ~(mo.num,mo.num,mo.num,mo.num)~                             | Exponentialized double excitation amplitudes    |
+   | ~triple~        | ~float sparse~ | ~(mo.num,mo.num,mo.num,mo.num,mo.num,mo.num)~               | Triple excitation amplitudes                    |
+   | ~triple_exp~    | ~float sparse~ | ~(mo.num,mo.num,mo.num,mo.num,mo.num,mo.num)~               | Exponentialized triple excitation amplitudes    |
+   | ~quadruple~     | ~float sparse~ | ~(mo.num,mo.num,mo.num,mo.num,mo.num,mo.num,mo.num,mo.num)~ | Quadruple excitation amplitudes                 |
+   | ~quadruple_exp~ | ~float sparse~ | ~(mo.num,mo.num,mo.num,mo.num,mo.num,mo.num,mo.num,mo.num)~ | Exponentialized quadruple excitation amplitudes |
+
+   #+CALL: json(data=amplitude, title="amplitude")
+
+   #+RESULTS:
+   :results:
+   #+begin_src python :tangle trex.json
+       "amplitude": {
+                  "single" : [ "float sparse", [ "mo.num", "mo.num" ]                                                             ]
+         ,    "single_exp" : [ "float sparse", [ "mo.num", "mo.num" ]                                                             ]
+         ,        "double" : [ "float sparse", [ "mo.num", "mo.num", "mo.num", "mo.num" ]                                         ]
+         ,    "double_exp" : [ "float sparse", [ "mo.num", "mo.num", "mo.num", "mo.num" ]                                         ]
+         ,        "triple" : [ "float sparse", [ "mo.num", "mo.num", "mo.num", "mo.num", "mo.num", "mo.num" ]                     ]
+         ,    "triple_exp" : [ "float sparse", [ "mo.num", "mo.num", "mo.num", "mo.num", "mo.num", "mo.num" ]                     ]
+         ,     "quadruple" : [ "float sparse", [ "mo.num", "mo.num", "mo.num", "mo.num", "mo.num", "mo.num", "mo.num", "mo.num" ] ]
+         , "quadruple_exp" : [ "float sparse", [ "mo.num", "mo.num", "mo.num", "mo.num", "mo.num", "mo.num", "mo.num", "mo.num" ] ]
+       } ,
+   #+end_src
+   :end:
+
 ** Reduced density matrices (rdm group)
 
    The reduced density matrices are defined in the basis of molecular