From bbd2f6a70af2f20028dfbeaf62c9b01d9daabd11 Mon Sep 17 00:00:00 2001 From: kossoski Date: Fri, 4 Mar 2022 22:40:52 +0100 Subject: [PATCH] saving work --- HF_cc-pvqz/pes_CIo3.dat | 6 +++--- Manuscript/seniority.tex | 28 ++++++++++++++-------------- 2 files changed, 17 insertions(+), 17 deletions(-) diff --git a/HF_cc-pvqz/pes_CIo3.dat b/HF_cc-pvqz/pes_CIo3.dat index c025f0e..ff0dfa4 100644 --- a/HF_cc-pvqz/pes_CIo3.dat +++ b/HF_cc-pvqz/pes_CIo3.dat @@ -13,10 +13,10 @@ 1.1 -100.34082054 1.2 -100.31681221 1.3 -100.29161378 -1.4 -100.26726006 +1.4 -100.26725190 1.5 -100.24478990 1.6 -100.22471020 -1.7 -100.20686180 +1.7 -100.20726028 1.8 -100.19248605 1.9 -100.18030559 2.0 -100.17053512 @@ -24,7 +24,7 @@ 2.2 -100.15710956 2.3 -100.15279779 2.4 -100.14965242 -2.5 -100.14738942 +2.5 -100.14739270 3.0 -100.14295682 3.5 -100.14220595 4.0 -100.14209414 diff --git a/Manuscript/seniority.tex b/Manuscript/seniority.tex index ac05082..963c7ca 100644 --- a/Manuscript/seniority.tex +++ b/Manuscript/seniority.tex @@ -55,7 +55,7 @@ \newcommand{\LCPQ}{Laboratoire de Chimie et Physique Quantiques (UMR 5626), Universit\'e de Toulouse, CNRS, UPS, France} -\title{Configuration interaction with seniority number and excitation degree} +\title{Configuration Interaction with Seniority Number and Excitation Degree} \author{F\'abris Kossoski} \email{fkossoski@irsamc.ups-tlse.fr} @@ -69,20 +69,20 @@ % Abstract \begin{abstract} %aimed at recovering both static and dynamic correlation, -Here we propose a novel partitioning of the Hilbert space, hierarchy configuration interaction (hCI), +We propose a novel partitioning of the Hilbert space, hierarchy configuration interaction (hCI), where the degree of excitation (with respect to a given reference) and the seniority number (number of unpaired electrons) are combined in a single hierarchy parameter. -The key appealing feature of hCI is that it includes all classes of determinants that share the same scaling with the number of electrons and basis functions. -In this way, it accounts for low-seniority high-excitation determinants lacking in excitation-based CI, while keeping the same computational scaling with system size. -By surveying the dissociation of multiple molecular systems, we examined how fast hCI and their excitation-based and seniority-based parents converge as -we step up towards the exact full CI limit. -We found that the overall performance of hCI usually exceeds or at least parallels that of excitation-based CI. -For small systems and basis sets, doubly-occupied CI (the first level of seniority-based CI) often remains the best option. -However, for larger systems or basis sets, and for higher accuracy, seniority-based CI becomes impractical. -However, some of its interesting features, particularly the small non-parallelity errors, are partially recovered with hCI, at only a polynomical cost. -We have futher explored the role of optimizing the orbitals at several levels of CI. +The key appealing feature of hCI is that each level of the hierarchy accounts for all classes of determinants that share the same scaling with the system size. +%number of electrons and basis functions. +%In this way, it accounts for low-seniority high-excitation determinants lacking in excitation-based CI, while keeping the same computational scaling with system size. +By surveying the dissociation of multiple molecular systems, we found that the overall performance of hCI usually exceeds or at least parallels that of excitation-based CI. +%By surveying the dissociation of multiple molecular systems, we examined how fast hCI and their excitation-based and seniority-based parents converge as we step up towards the exact full CI limit. +%The overall performance of hCI usually exceeds or at least parallels that of excitation-based CI. +%For small systems and basis sets, doubly-occupied CI (the first level of seniority-based CI) often remains the best option, but becomes impractical for larger systems or basis sets, and for higher accuracy. +%However, for larger systems or basis sets, and for higher accuracy, seniority-based CI becomes impractical. +%However, some of its interesting features, particularly the small non-parallelity errors, are partially recovered with hCI, at only a polynomial cost. +%We have further explored the role of optimizing the orbitals at several levels of CI. For higher orders of hCI and excitation-based CI, -the additional computational burden and other known issues related to orbital optimization usually do not compensate the marginal improvements often observed, -when compared with results obtained with canonical Hartree-Fock orbitals. +the additional computational burden related to orbital optimization usually do not compensate the marginal improvements compared with results obtained with Hartree-Fock orbitals. The exception is orbital-optimized CI with single excitations, a minimally correlated model displaying the qualitatively correct description of single bond breaking, at a very modest computational cost. %\bigskip @@ -191,7 +191,7 @@ at the same time as static correlation, by moving down (increasing the seniority The second justification is computational. %Fig.~\ref{fig:scaling} also illustrates how the number of determinants within each block scales with the number of occupied orbitals $O$ and the number of virtual orbitals $V$. -In the hCI class of methods, each next level of theory accomodates additional determinants from different excitation-seniority sectors (each block of Fig.~\ref{fig:allCI}). +In the hCI class of methods, each level of theory accomodates additional determinants from different excitation-seniority sectors (each block of Fig.~\ref{fig:allCI}). The key realization behind hCI is that the number of additional determinants presents the same scaling with respect to $N$, for all excitation-seniority sectors entering at a given hierarchy $h$. %to $O$ and $V$, for all excitation-seniority sectors of a given hierarchy $h$. %This computational realization represents the second justification for the introduction of the hCI method.