From 38d1b9e0620fb34356a32e06289d7f78e78507a4 Mon Sep 17 00:00:00 2001 From: vijay Date: Wed, 16 Dec 2020 11:21:53 +0100 Subject: [PATCH] Some clarifications and minor phrasing changes --- docs/source/intro/selected_ci.rst | 26 +++++++++++++------------- 1 file changed, 13 insertions(+), 13 deletions(-) diff --git a/docs/source/intro/selected_ci.rst b/docs/source/intro/selected_ci.rst index 21062e62..de99cba2 100644 --- a/docs/source/intro/selected_ci.rst +++ b/docs/source/intro/selected_ci.rst @@ -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 on-the-fly 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 on-the-fly. 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 3-class |CIPSI| approximation to accelerate the selection, +This is nothing but the three-class |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 |CAS-SD|. 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 +|CAS|-|CI|. If the rules allow for single and double-excitations in the |FCI| space, we obtain +a selected |CAS-SD|. 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|. -----------------------------------