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Some clarifications and minor phrasing changes
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@ 77,7 +77,7 @@ The determinants in SetDI will be characterized as **internal**.


e_\alpha = \frac{ \langle \Psi^{(n)} {\hat H}  \alpha \rangle^2 }{E^{(n)}  \langle \alpha  {\hat H}  \alpha \rangle }.




`E^{(n)}` is the variational energy of the wave function at the current


iteration. Note that another perturbation theory could be used to estimate


iteration. Note that other perturbation theory baesd methods could be used to estimate


ealpha.




#. An estimate of the total missing correlation energy can be computed



@ 96,22 +96,22 @@ The determinants in SetDI will be characterized as **internal**.


\{ D_I \rangle \}^{(n+1)} = \{D_I\rangle\}^{(n)} \cup \{ \alpha\rangle \}_\star^{(n)}






#. Go to iteration n+1, or exit on some criterion (number of determinants in


#. Go to iteration n+1, or exit based upon some criteria (number of determinants in


the wave function, low EPT, ...).






Of course, such a procedure can be applied on any state and therefore can allow to treat both ground and excited states.


Of course, such a procedure can be applied on any state and therefore can allow the treatment of both ground and excited states.






Stochastic approximations for the selection and the computation of EPT







The simple algorithm would be too slow to make calculations possible. Instead,


the QP uses a stochastic algorithm :cite:`Garniron_2017.2` in order to compute


efficiently the EPT and to select onthefly the best Slater determinants.


The simple algorithm described above would be too slow to make calculations practical. Instead,


QP uses a stochastic algorithm :cite:`Garniron_2017.2` in order to compute


EPT efficiently and to select the best Slater determinants onthefly.




In such a way, the selection step introduces no extra cost with respect to the EPT calculation and the EPT


itself is unbiased but associated with a statistical error bar rapidly converging.


itself is unbiased but associated with a rapidly converging statistical error bar.






Deterministic approximations for the selection



@ 134,7 +134,7 @@ The default is to use :option:`determinants threshold_generators` = 0.99 for


the generators, and :option:`determinants threshold_selectors` = 0.999 for the


selectors.




This is nothing but the 3class CIPSI approximation to accelerate the selection,


This is nothing but the threeclass CIPSI approximation to accelerate the selection,


:cite:`Evangelisti_1983` where instead of generating all possible kalpha,


we only generate a subset which are likely to be selected.





@ 156,13 +156,13 @@ one will produce a selected CISD. If one also changes the rules for the genera


to generate only the double excitations, one will have a selected CID.




The generators can also be chosen as determinants belonging to a CAS. If the


rules allow only for excitations inside the CAS, we obtain a selected


CAS CI. If the rules allow for excitations in the FCI space, we obtain


a selected CASSD. And if one add the rule to prevent for doing double


excitations with two holes and two particles outside of the active space, one


rules allow for excitations only inside the CAS, we obtain a selected


CASCI. If the rules allow for single and doubleexcitations in the FCI space, we obtain


a selected CASSD. And if one adds the rule to exclude those double


excitations which contain two holes and two particles outside of the active space, one


obtains a selected DDCI method.




All such things can be done very easily when programming the qp.


All such things can be done very easily when programming within the qp.











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