Added documentation and Makefile
This commit is contained in:
parent
20e3488df7
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sci.rc
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EZFIO
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irpf90
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WWW_SERVER = http://qmcchem.ups-tlse.fr/files/scemama
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IRPF90_TGZ = irpf90-latest-noarch-src.tar.gz
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EZFIO_TGZ = EZFIO.latest.tar.gz
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.PHONY: doc src
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default: src
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EZFIO:
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$(info ===== Fetching EZFIO from the web =====)
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@wget "$(WWW_SERVER)/$(EZFIO_TGZ)" || \
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(echo Unable to download EZFIO : $(WWW_SERVER)/$(EZFIO_TGZ) ; exit 1)
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@tar -zxf $(EZFIO_TGZ) && rm $(EZFIO_TGZ)
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irpf90:
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$(info ===== Fetching IRPF90 from the web =====)
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@wget "$(WWW_SERVER)/$(IRPF90_TGZ)" || \
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(echo Unable to download IRPF90 : $(WWW_SERVER)/$(IRPF90_TGZ) ; exit 1)
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@tar -zxf $(IRPF90_TGZ) && rm $(IRPF90_TGZ)
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$(MAKE) -C irpf90
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doc:
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$(MAKE) -C doc
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src: irpf90 EZFIO
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export SCI_ROOT=$$PWD ; \
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$(MAKE) -C src
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@ -3,4 +3,6 @@ Quantum package
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Set of quantum chemistry programs and libraries.
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For more information, you can visit the
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`wiki of the project <http://github.com/LCPQ/quantum_package/wiki>`_
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@ -0,0 +1 @@
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build
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# Makefile for Sphinx documentation
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#
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# You can set these variables from the command line.
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SPHINXOPTS =
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SPHINXBUILD = sphinx-build
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PAPER =
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BUILDDIR = build
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# Internal variables.
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PAPEROPT_a4 = -D latex_paper_size=a4
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PAPEROPT_letter = -D latex_paper_size=letter
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ALLSPHINXOPTS = -d $(BUILDDIR)/doctrees $(PAPEROPT_$(PAPER)) $(SPHINXOPTS) source
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# the i18n builder cannot share the environment and doctrees with the others
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I18NSPHINXOPTS = $(PAPEROPT_$(PAPER)) $(SPHINXOPTS) source
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.PHONY: help clean html dirhtml singlehtml pickle json htmlhelp qthelp devhelp epub latex latexpdf text man changes linkcheck doctest gettext default
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default: html
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help:
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@echo "Please use \`make <target>' where <target> is one of"
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@echo " html to make standalone HTML files"
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@echo " dirhtml to make HTML files named index.html in directories"
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@echo " singlehtml to make a single large HTML file"
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@echo " pickle to make pickle files"
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@echo " json to make JSON files"
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@echo " htmlhelp to make HTML files and a HTML help project"
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@echo " qthelp to make HTML files and a qthelp project"
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@echo " devhelp to make HTML files and a Devhelp project"
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@echo " epub to make an epub"
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@echo " latex to make LaTeX files, you can set PAPER=a4 or PAPER=letter"
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@echo " latexpdf to make LaTeX files and run them through pdflatex"
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@echo " text to make text files"
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@echo " man to make manual pages"
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@echo " texinfo to make Texinfo files"
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@echo " info to make Texinfo files and run them through makeinfo"
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@echo " gettext to make PO message catalogs"
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@echo " changes to make an overview of all changed/added/deprecated items"
|
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@echo " linkcheck to check all external links for integrity"
|
||||
@echo " doctest to run all doctests embedded in the documentation (if enabled)"
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clean:
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-rm -rf $(BUILDDIR)/*
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html:
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$(SPHINXBUILD) -b html $(ALLSPHINXOPTS) $(BUILDDIR)/html
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@echo
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@echo "Build finished. The HTML pages are in $(BUILDDIR)/html."
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dirhtml:
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$(SPHINXBUILD) -b dirhtml $(ALLSPHINXOPTS) $(BUILDDIR)/dirhtml
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@echo
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@echo "Build finished. The HTML pages are in $(BUILDDIR)/dirhtml."
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singlehtml:
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$(SPHINXBUILD) -b singlehtml $(ALLSPHINXOPTS) $(BUILDDIR)/singlehtml
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@echo
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@echo "Build finished. The HTML page is in $(BUILDDIR)/singlehtml."
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pickle:
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$(SPHINXBUILD) -b pickle $(ALLSPHINXOPTS) $(BUILDDIR)/pickle
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@echo
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@echo "Build finished; now you can process the pickle files."
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json:
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$(SPHINXBUILD) -b json $(ALLSPHINXOPTS) $(BUILDDIR)/json
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@echo
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@echo "Build finished; now you can process the JSON files."
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htmlhelp:
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$(SPHINXBUILD) -b htmlhelp $(ALLSPHINXOPTS) $(BUILDDIR)/htmlhelp
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@echo
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@echo "Build finished; now you can run HTML Help Workshop with the" \
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".hhp project file in $(BUILDDIR)/htmlhelp."
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qthelp:
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$(SPHINXBUILD) -b qthelp $(ALLSPHINXOPTS) $(BUILDDIR)/qthelp
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@echo
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@echo "Build finished; now you can run "qcollectiongenerator" with the" \
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".qhcp project file in $(BUILDDIR)/qthelp, like this:"
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@echo "# qcollectiongenerator $(BUILDDIR)/qthelp/SelectedCI.qhcp"
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@echo "To view the help file:"
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@echo "# assistant -collectionFile $(BUILDDIR)/qthelp/SelectedCI.qhc"
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devhelp:
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$(SPHINXBUILD) -b devhelp $(ALLSPHINXOPTS) $(BUILDDIR)/devhelp
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@echo
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@echo "Build finished."
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@echo "To view the help file:"
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@echo "# mkdir -p $$HOME/.local/share/devhelp/SelectedCI"
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@echo "# ln -s $(BUILDDIR)/devhelp $$HOME/.local/share/devhelp/SelectedCI"
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@echo "# devhelp"
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epub:
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$(SPHINXBUILD) -b epub $(ALLSPHINXOPTS) $(BUILDDIR)/epub
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@echo
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@echo "Build finished. The epub file is in $(BUILDDIR)/epub."
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latex:
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$(SPHINXBUILD) -b latex $(ALLSPHINXOPTS) $(BUILDDIR)/latex
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@echo
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@echo "Build finished; the LaTeX files are in $(BUILDDIR)/latex."
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@echo "Run \`make' in that directory to run these through (pdf)latex" \
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"(use \`make latexpdf' here to do that automatically)."
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latexpdf:
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$(SPHINXBUILD) -b latex $(ALLSPHINXOPTS) $(BUILDDIR)/latex
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@echo "Running LaTeX files through pdflatex..."
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$(MAKE) -C $(BUILDDIR)/latex all-pdf
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@echo "pdflatex finished; the PDF files are in $(BUILDDIR)/latex."
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text:
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$(SPHINXBUILD) -b text $(ALLSPHINXOPTS) $(BUILDDIR)/text
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@echo
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@echo "Build finished. The text files are in $(BUILDDIR)/text."
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man:
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$(SPHINXBUILD) -b man $(ALLSPHINXOPTS) $(BUILDDIR)/man
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@echo
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@echo "Build finished. The manual pages are in $(BUILDDIR)/man."
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texinfo:
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$(SPHINXBUILD) -b texinfo $(ALLSPHINXOPTS) $(BUILDDIR)/texinfo
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@echo
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@echo "Build finished. The Texinfo files are in $(BUILDDIR)/texinfo."
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@echo "Run \`make' in that directory to run these through makeinfo" \
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"(use \`make info' here to do that automatically)."
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info:
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$(SPHINXBUILD) -b texinfo $(ALLSPHINXOPTS) $(BUILDDIR)/texinfo
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@echo "Running Texinfo files through makeinfo..."
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make -C $(BUILDDIR)/texinfo info
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@echo "makeinfo finished; the Info files are in $(BUILDDIR)/texinfo."
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gettext:
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$(SPHINXBUILD) -b gettext $(I18NSPHINXOPTS) $(BUILDDIR)/locale
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@echo
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@echo "Build finished. The message catalogs are in $(BUILDDIR)/locale."
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changes:
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$(SPHINXBUILD) -b changes $(ALLSPHINXOPTS) $(BUILDDIR)/changes
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@echo
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@echo "The overview file is in $(BUILDDIR)/changes."
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linkcheck:
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$(SPHINXBUILD) -b linkcheck $(ALLSPHINXOPTS) $(BUILDDIR)/linkcheck
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@echo
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@echo "Link check complete; look for any errors in the above output " \
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"or in $(BUILDDIR)/linkcheck/output.txt."
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doctest:
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$(SPHINXBUILD) -b doctest $(ALLSPHINXOPTS) $(BUILDDIR)/doctest
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@echo "Testing of doctests in the sources finished, look at the " \
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"results in $(BUILDDIR)/doctest/output.txt."
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@ -0,0 +1,156 @@
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============================================================
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What is a selected CI caculation ? Some theoretical concepts
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============================================================
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Generalities
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============
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The selected CI algorithm can be seen as a way to compute the energies (and various properties) of a given number of eigenstates
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of a given :term:`target space` (ex : CISD, CAS-CI, DDCI etc ...),
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but by taking the freedom of splitting the wave function of the target space in term
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of :term:`internal determinants` treated variationally and :term:`perturbers` treated perturbatively.
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Why this freedom ? Because in a given :term:`target space` (except some really special cases) most of the information
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is concentrated within a tiny fraction of the :term:`target wave function`, and the remaining part can be reasonabely estimated by perturbtation.
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This splitting of the wave function is not done in one shot, it is done iteratively. The iterative procedure needs a :term:`stopping criterion` to end the calculation and to control the quality of the calculation.
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This :term:`stopping criterion` can be for example the number of determinants in the :term:`intern space`,
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or the value of the :term:`energetic perturbative correction` to estimate the importance of the perturbation, or the convergence of the :term:`estimated target energy`, or anything that can
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be defined in terms of available informations during the calculation.
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The heart of the selected CI algorithm is based on the CIPSI algorithm (ref Malrieu).
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Selected CI in a few words
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==========================
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First you define a :term:`target space`. Once the target space is defined, you define the :term:`stopping criterion`.
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After that, a starting wave function is chosen by the user (HF by default).
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This starting wave function is the first :term:`Internal determinants` wave function.
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After that, one would like to extend this :term:`Internal determinants` wave function by adding
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some :term:`perturbers` determinants.
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How do we select the good :term:`perturbers` ?
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do while (:term:`stopping criterion` is reached)
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1) Generates :term:`perturbers` determinants according to your chosen :term:`target space`.
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:math:`\Rightarrow` generates a set of :term:`perturbers` :math:`\{|D_P\rangle\}`
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2) The :term:`perturbers` importance are estimated by perturbation thanks to the current :term:`internal determinants`.
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3) The most important of the :math:`\{|D_P\rangle\}` are chosen to enter in the :term:`internal determinants`.
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4) You rediagonalize the H matrix with the previous set of :term:`internal determinants` and the chosen :term:`perturbers`.
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:math:`\Rightarrow` create a new wave function and a new set of the :term:`internal determinants`
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5) iterate
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Once the iterative procedure is stopped, the :term:`internal determinants` wave function have a :term:`variational energy`,
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and by adding the :term:`energetic perturbative correction` one have the :term:`estimated target energy`
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which is an approximation of the :term:`target energy`. One should notice that if one takes
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a :term:`stopping criterion` such as the all the determinants of the target space are in the :term:`intern space`,
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the :term:`estimated target energy` is the :term:`target energy`.
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If one is interested of how is built the selected CI wave function into more details, one can read the further section.
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What is a selected CI iteration in practice (and some details)
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==============================================================
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From the previous section we have roughly seen how the selected CI works. Now, getting a bit more into details,
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we will see what is done in practice during a selected CI iteration. To illustrate this, a simple CISD example wil be given.
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The general picture
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^^^^^^^^^^^^^^^^^^^
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The :term:`target space` defines entirely the method that is going to be approximated, and the stopping criterion will be the only approximation.
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This :term:`target space` can always be defined in terms of application of an :term:`H operator`
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(with some :term:`excitation restrictions`) on a given set of determinants that we shall call the :term:`generators` determinants.
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We call :term:`restricted H operator` this precise H operator.
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The target space intirely defines the :term:`restricted H operator`.
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The only flexibility is the perturbation theory to be used to estimate the coeficients of the :term:`perturbers`.
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If the target space is just defines in term of a CI matrix to diagonalize, the standard :term:`Diagonalization EN EG` perturbation will be used.
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If some other constraints are imposed in addition to the CI matrix
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(e.g. some physical conditions of size extensivity such as in the :term:`CISD+SC2` method),
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then the perturbation must be adapted to properly respect the :term:`target space`.
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CISD : the :term:`target space` is here defined intirely by all the single and double excitations acting on the HF determinant.
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So the :term:`generators` subset of determinants here is only the HF determinant and will not change along the iteration.
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If some occupied orbitals are chosen to be frozen (no excitations from those orbitals)
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or some virtuals are chosen to be deleted (no excitations going to these virtuals orbitals),
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this constraint imposes the :term:`excitation restrictions`. So here the :term:`restricted H operator` will be all the single and double excitations except those involving either a frozen core orbital or a deleted virtual orbital.
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Different choices of perturbation theory can be made for the CISD, but the standard :term:`Diagonalization EN EG` can be trustly used.
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Once the :term:`target space` have been defined, what does in practice a selected CI iteration.
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For the sake of simplicity, here we emphasize on the ground state :math:`| \psi_0 \rangle`. At a given iteration, one have a :term:`selected wave function` :math:`|\psi_0\rangle`, and the selected CI algorithm performs :
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do G = 1, N_Generators
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1) Apply the :term:`restricted H operator` on the :math:`|D_G \rangle` :term:`generators` determinant belonging to :math:`| \psi_0 \rangle`
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:math:`\Rightarrow` generates a set of :term:`perturbers` :math:`|D_P\rangle`
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2) Estimate the perturbative importance of each perturbers
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:math:`\Rightarrow` example for the :term:`EN EG` perturbation theory
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.. math::
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c_{D_P}^0= \frac{ \sum_{S=1,N_{\rm selectors}} c_S^0 \langle D_S|H|D_P\rangle}{ \langle \psi_0 |H|\psi_0 \rangle - \langle D_P |H|D_P\rangle } \\
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e_{D_P}^0= \frac{(\sum_{S=1,N_{\rm selectors}} c_S^0 \langle D_S|H|D_P\rangle) ^2}{\langle \psi_0 |H|\psi_0 \rangle - \langle D_P |H|D_P\rangle}
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3) Keep the most important :term:`perturbers` :math:`|D_P \rangle`
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:math:`\Rightarrow` they enter in the :term:`intern space`
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4) Rediagonalize H within this new subset of determinants
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:math:`\Rightarrow` better :term:`selected wave function`
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5) Iterate
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An important point here is that at a given iteration, the estimation of the perturbative coefficients of the :term:`perturbers`
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depends on the quality of the :term:`selected wave function` .
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As the iterations go on, the :term:`selected wave function` becomes closer
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and closer to the :term:`target wave function`, and so the perturbative estimation of the :term:`perturbers` coefficients or energetic contribution becomes more and more precise.
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CISD : At the first iteration, starting from the HF determinant :
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1) By applying H on the :term:`generators` (HF) one generates all singles and doubles
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2) For each :term:`perturbers` you estimate by perturbation its coefficient of energetic contribution.
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i) Here the :term:`selectors` is only the HF determinant.
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ii) If the :term:`Brillouin theorem` is respected, all the singles have zero coefficients since the :term:`selectors` here is only the HF determinant.
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iii) The most important double excitations entered
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iv) The :term:`energetic perturbative correction` is calculated
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v) The :term:`estimated target energy` is just the sum of the HF energy and the :term:`energetic perturbative correction`
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3) H is rediagonlaized in the new set of determinants : HF + the selected doubles
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:math:`\Rightarrow` better :term:`variational energy` and :term:`selected wave function`
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4) The :term:`generators` subset does not change.
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At the second iteration :
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1) By applying H on the :term:`generators` (still HF) one generates all singles and doubles
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2) For each :term:`perturbers` you estimate by perturbation its coefficient of energetic contribution.
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i) Here the :term:`selectors` is now HF + the previously selected doubles
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:math:`\Rightarrow` the :term:`perturbers` now interact with all the previously selected doubles
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:math:`\Rightarrow` better estimation of the coefficients of the :term:`perturbers`
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:math:`\Rightarrow` the singles have non zero coefficients
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ii) The most important :term:`perturbers` enter in the :term:`intern space`
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iv) The :term:`energetic perturbative correction` is re estimated
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v) The :term:`estimated target energy` is now the sum of the variational energy of the :term:`selected wave function` and the :term:`energetic perturbative correction`
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:math:`\Rightarrow` better estimation of the :term:`target energy`
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Iterate untill you reached the desired :term:`stopping criterion`
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@ -0,0 +1,228 @@
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=============================
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The Documentation of the code
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=============================
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The heart of the problem : how do we compute the perturbation ?
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===============================================================
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In this section we will present the basic ideas of how do we compute any kind of perturbative quantity.
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The main problem
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^^^^^^^^^^^^^^^^
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Consider a simple problem of perturbation theory in which you have a *general* multireference wave function :math:`| \psi \rangle`
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(no trivial way to know the kind of relations between those determinants) :
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.. math::
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| \psi \rangle = \sum_{I=1,N_{det}} c_I | D_I \rangle
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and you would like to compute its second order :term:`perturbative energetic correction`, which we can write like this for the sake of simplicity:
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.. math::
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E_{PT2} = \sum_{P \, \rm{that} \, \rm{are} \, \rm{not} \, \rm{in} \, | \psi \rangle } \frac{\langle \psi | H | D_P \rangle^2}{\Delta E_P}
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and the :math:`\Delta E_P` will determine what kind of PT you use. Note that you must not double count a determinant :math:`| D_P \rangle` and that you must not count those which are in :math:`| \psi \rangle`.
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What you have to do is to apply the :math:`H` operator on this :math:`| \psi \rangle` that would generate a lot of determinants :math:`|D \rangle`,
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and you must find a way to see if :
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#) the determinant :math:`|D \rangle` is in :math:`| \psi \rangle`
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#) the determinant :math:`|D \rangle` have already been counted
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How do we do in practice ? We apply :math:`H` succesively on each determinant of :math:`| \psi \rangle` and each :math:`H` application generates a lot of determinant :math:`|D \rangle`. For each determinants :math:`|D \rangle` we check with a very optimized subroutine if
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|
||||
#) :math:`|D\rangle` was a single or a double excitation respect to all the determinant on which we previously applyed :math:`H`
|
||||
|
||||
:math:`\Rightarrow` if it is the case then it have already been computed in the past and so we don't double count it.
|
||||
|
||||
#) :math:`|D\rangle` is already in the rest of the :math:`| \psi \rangle`
|
||||
|
||||
:math:`\Rightarrow` if it is the case you must not count it.
|
||||
|
||||
This subroutine (:samp:`connected_to_ref` ) is called a **HUGE** number of times and so it have been optimized in a proper way.
|
||||
Its basis is the :samp:`popcnt` hardware instruction that figures in the :samp:`SSE4.2` releases of processors.
|
||||
It allows to know how many bites are set to one in an integer within a few cycles of CPU.
|
||||
By manipulation of bits masks you can easily extract the excitation degree between two determinants.
|
||||
|
||||
One interesting feature of this approach is that it is easily and efficiently parallelizable (which of cours have been done),
|
||||
and you can easily reach an parallel efficiency of about :math:`95\%`.
|
||||
|
||||
|
||||
The link between the perturbation and the selection
|
||||
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
|
||||
|
||||
In the selected CI algorithm you have general :math:`| \psi \rangle` multi determinantal wave function and you want to make it better
|
||||
by proposing some new candidates to enter in this wave function.
|
||||
Those candidates must of course not be already in :math:`| \psi \rangle` and since their are selected thanks to their perturbative properties (on the energy or on the coefficient), their are generated through some application of the :math:`H` operator. So we see that we have exactly the same kind of feature than in the perturbation.
|
||||
|
||||
How do we select the determinant in practice ? Exactly like we do the perturbation !
|
||||
|
||||
do G = 1, :term:`N_{Generators}`
|
||||
|
||||
#) We apply :math:`H` on one :term:`generators`
|
||||
|
||||
:math:`\Rightarrow` :math:`H|D_G \rangle = \sum_D \langle D | H |D_G \rangle |D \rangle`
|
||||
|
||||
#) For each determinant :math:`|D \rangle` we check if it could have been generated from previous :term:`generators` :math:`| D_{G'} \rangle`
|
||||
|
||||
:math:`\Rightarrow` If it is not the case we check if it belongs to :math:`| \psi \rangle`
|
||||
|
||||
#) We compute its perturbative property
|
||||
|
||||
#) If it is important we put it in a buffer of the potential candidates to the new set of :term:`internal determinants`
|
||||
|
||||
#) go to 1
|
||||
|
||||
enddo
|
||||
|
||||
|
||||
So once you have applyed :math:`H` on all the :term:`generators`, you sort all the buffer of the candidates by their importance,
|
||||
and after you pick up the most important ones, which will enter in the wave function and be diagonalized.
|
||||
|
||||
|
||||
Just to be more precise, what we drescribe here is the standard CIPSI algorithm (which :term:`target space` is always the FCI). In practice, if you replace the :math:`H` operator by the :term:`restricted H operator` defined by the :term:`target` space you have exactly what is emplemented.
|
||||
|
||||
The typical feature of an iteration
|
||||
===================================
|
||||
|
||||
An iteration of the selected CI program is always built in the same way. This can be resumed in the following simple tasks.
|
||||
|
||||
Iteration :
|
||||
|
||||
#) :term:`restricted H operator` applyed on the :term:`generators`
|
||||
|
||||
:math:`\Rightarrow` :term:`perturbativ action` (*e.g* Selection of some :term:`perturbers`, calculation of the :math:`E_{PT2}^m`, etc ...)
|
||||
|
||||
#) Some update induced by the :term:`perturbative action` (*e.g* diagonalization of the new :math:`H` matrix, etc ...)
|
||||
#) Check the :term:`stopping criterion`
|
||||
#) Update the :term:`generators` subset
|
||||
#) Save restart data if needed
|
||||
#) Iterate
|
||||
|
||||
To go into details we list the various available options for each task.
|
||||
|
||||
The :samp:`restricted_H_apply` like subroutines
|
||||
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
|
||||
|
||||
Here we enter into details on the part of the subroutines that is responsible for the :term:`restricted H operator` part of the tasks.
|
||||
|
||||
The general ideas
|
||||
^^^^^^^^^^^^^^^^^
|
||||
|
||||
This subroutine takes in input a determinant (in term of an integer key) and some bits masks
|
||||
that are used to restrict the excitations (see the :term:`excitations bits masks` and :term:`excitations restrictions`).
|
||||
It generates the singles and doubles excitations from the input determinant and these :term:`excitations bits masks`.
|
||||
This subroutine will be applyed on the :term:`generators` determinants to generate the :term:`perturbers`.
|
||||
|
||||
This subroutine in itself does not exist, it is just a skeleton that generates all possible singles and doubles.
|
||||
As seen in the previsous section, once you apply :math:`H` on a given determinant, you will use the generated determinants
|
||||
to do a certain number of things that deal with in general a perturbative quantity, this is the :term:`perturbative action`.
|
||||
|
||||
A way to resume what is done in the subroutine and to make a mental representation can be explained like this :
|
||||
|
||||
|
||||
.. code-block:: fortran
|
||||
|
||||
subroutine restricted_H_apply(key_in)
|
||||
|
||||
do i = 1, available_holes(1)
|
||||
do j = 1, available_holes(2)
|
||||
do k = 1, available_particles(1)
|
||||
do l = 1, available_particles(2)
|
||||
! you generate some excitations on key_in that will generate some key_out
|
||||
call excitation(i,j,k,l,key_in,key_out)
|
||||
! you exploit key_out to do some perturbative work
|
||||
call perturbative_action(key_out)
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
|
||||
end
|
||||
|
||||
|
||||
So we see that here once we have made an excitation on :samp:`key_in` that generates :samp:`key_out`,
|
||||
we can do some work related to the :term:`perturbative action` on this :samp:`key_out`.
|
||||
|
||||
In this simple representation of the subroutine, there are some :samp:`available_holes` and :samp:`available_particle`.
|
||||
This is due to the :term:`excitation restrictions` that are implicitly defined by the :term:`target space`,
|
||||
and to the :term:`restricted orbitals` that are defined by the user.
|
||||
In practice those :term:`excitation restrictions` are just the excitations that are going to be allowed to a given :term:`generator determinant`.
|
||||
We do this by using some :term:`excitations bits masks`.
|
||||
The :term:`excitation restrictions` and the :term:`restricted orbitals` are built thanks to the use of :term:`excitations bits masks`.
|
||||
|
||||
Available :term:`excitation restrictions`
|
||||
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
|
||||
|
||||
The :term:`excitation restrictions` prohibits some kind of excitations because it is in the definition
|
||||
of the :term:`target space` to avoid a certain class of excitation.
|
||||
For instance, in the :term:`CAS+DDCI` method, you will apply all the single and double excitations on the top of the :term:`CAS wave function`.
|
||||
After those :term:`excitation restrictions` defined by the :term:`target space`, there can be some kind of excitations that the user wishes to avoid.
|
||||
For instance, within a :term:`CISD` or a :term:`CAS+DDCI` you can wish that all the excitations of the core electrons can be neglected,
|
||||
or that there are some virtuals that are not relevant for a certain kind of correlation effects.
|
||||
|
||||
This restrictions are done in the program by defining some classes of orbitals that depend both on the method you would like to use,
|
||||
and by the specific restrictions you would like to do on the top of that. So we see that there are classes of orbitals that depend on the method,
|
||||
and other classes that can be defined for any class of method.
|
||||
|
||||
This classes are the the :term:`frozen occupied orbitals` and the :term:`deleted virtual orbitals` .
|
||||
|
||||
Available :term:`perturbative action`
|
||||
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
|
||||
|
||||
From what we saw previously, when an excitation is performed on a given :term:`generator`,
|
||||
depending on the method defined by the user, different actions can be performed at that point of the calculation.
|
||||
|
||||
Nevertheless, all this actions here deal with the perturbation, that is why we called this step the :term:`perturbative action`.
|
||||
|
||||
The :term:`perturbative action` is very flexible. It consists in doing (or not) a certain kind of things.
|
||||
|
||||
When a given determinant :samp:`key_out` is generated, you can :
|
||||
|
||||
#) check if this determinants have to be taken into account (see :samp:`connected_to_ref` and :samp:`is_in_ref`)
|
||||
#) compute its :term:`perturbative energetic contribution` and its :term:`perturbative coefficient` (see :term:`perturbation theory`)
|
||||
#) use those perturbative quantities to do something that deals with it (see :term:`perturbative possibility` )
|
||||
|
||||
In principle, for each of those actions one would put a :samp:`if` statement and decline all the possible actions to do.
|
||||
However, because there can exist a *lot* of possible action and because this loop is really intern, putting a lot of :samp:`if` statement
|
||||
is not a good idea and will slow the code.
|
||||
|
||||
To avoid that we generate with a python script all possible subroutines corresponding to some actions, and the program will use the one
|
||||
that will be defined by the method desired by the user. In this way there is no unnecessary tests in the intern loop, it done in the input.
|
||||
|
||||
The :term:`perturbative possibility`
|
||||
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
|
||||
|
||||
Once you have compute the :term:`perturbative energetic contribution` and the :term:`perturbative coefficient` of a given :term:`perturber`,
|
||||
you must use those quantities. Here is listed what is available :
|
||||
|
||||
#) accumulate it :term:`perturbative energetic contribution` to compute the :term:`Energetic perturbative correction`
|
||||
#) accumulate it :term:`perturbative coefficient` to compute the :term:`first order perturbative norm`
|
||||
#) put or not the :samp:`key_out` determinant in a buffer to select some new :term:`intenal determinants` see :term:`selection`
|
||||
#) update the arrays of the :term:`correlation energy by holes and particles` (see :term:`CISD+SC2`)
|
||||
#) dress all the diagonal matrix elements of the :term:`internal determiants` (see :term:`Dressed MRCI`)
|
||||
|
||||
|
||||
|
||||
|
||||
Connected to ref / is in ref
|
||||
^^^^^^^^^^^^^^^^^^^^^^^^^^^^
|
||||
This subroutine takes in input a determinant (in term of an integer key), an array of determinants :samp:`keys` (containing :samp:`N_det` determinants)
|
||||
and an integer :samp:`i_past` which is smaller or equal to :samp:`N_det`.
|
||||
|
||||
It checks if the input determinant is connected by the :math:`H` matrix to all the determinants in :samp:`keys` that are before :samp:`i_past`.
|
||||
It also check if the input determinant is in the whole list of determinants :samp:`keys`.
|
||||
|
||||
In output you have an integer :samp:`c_ref` that have the following values :
|
||||
|
||||
#) 0 : the input determinant is not in :samp:`keys` and is not connected to any determinant
|
||||
in :samp:`keys` that is before :samp:`i_past`.
|
||||
|
||||
#) +m : the input determinant is connected by the :math:`H` matrix to the *m* th determinant :samp:`keys`.
|
||||
|
||||
#) -m : the input determinant is already in :samp:`keys` and it is the *m* th determinant in :samp:`keys`
|
||||
|
||||
|
||||
|
|
@ -0,0 +1,285 @@
|
|||
# -*- coding: utf-8 -*-
|
||||
#
|
||||
# Selected CI documentation build configuration file, created by
|
||||
# sphinx-quickstart on Mon Feb 10 15:53:11 2014.
|
||||
#
|
||||
# This file is execfile()d with the current directory set to its containing dir.
|
||||
#
|
||||
# Note that not all possible configuration values are present in this
|
||||
# autogenerated file.
|
||||
#
|
||||
# All configuration values have a default; values that are commented out
|
||||
# serve to show the default.
|
||||
|
||||
import sys, os
|
||||
|
||||
# If extensions (or modules to document with autodoc) are in another directory,
|
||||
# add these directories to sys.path here. If the directory is relative to the
|
||||
# documentation root, use os.path.abspath to make it absolute, like shown here.
|
||||
#sys.path.insert(0, os.path.abspath('.'))
|
||||
|
||||
# -- General configuration -----------------------------------------------------
|
||||
|
||||
# If your documentation needs a minimal Sphinx version, state it here.
|
||||
#needs_sphinx = '1.0'
|
||||
|
||||
# Add any Sphinx extension module names here, as strings. They can be extensions
|
||||
# coming with Sphinx (named 'sphinx.ext.*') or your custom ones.
|
||||
extensions = ['sphinx.ext.autodoc', 'sphinx.ext.doctest', 'sphinx.ext.todo', 'sphinx.ext.pngmath', 'sphinx.ext.mathjax', 'sphinx.ext.viewcode']
|
||||
|
||||
# Add any paths that contain templates here, relative to this directory.
|
||||
templates_path = ['_templates']
|
||||
|
||||
# The suffix of source filenames.
|
||||
source_suffix = '.rst'
|
||||
|
||||
# The encoding of source files.
|
||||
#source_encoding = 'utf-8-sig'
|
||||
|
||||
# The master toctree document.
|
||||
master_doc = 'index'
|
||||
|
||||
# General information about the project.
|
||||
project = u'Selected CI'
|
||||
copyright = u'2014, Giner Emmanuel , Scemama Anthony'
|
||||
|
||||
# The version info for the project you're documenting, acts as replacement for
|
||||
# |version| and |release|, also used in various other places throughout the
|
||||
# built documents.
|
||||
#
|
||||
# The short X.Y version.
|
||||
version = '1.0'
|
||||
# The full version, including alpha/beta/rc tags.
|
||||
release = version+'.1'
|
||||
|
||||
# The language for content autogenerated by Sphinx. Refer to documentation
|
||||
# for a list of supported languages.
|
||||
#language = None
|
||||
|
||||
# There are two options for replacing |today|: either, you set today to some
|
||||
# non-false value, then it is used:
|
||||
#today = ''
|
||||
# Else, today_fmt is used as the format for a strftime call.
|
||||
#today_fmt = '%B %d, %Y'
|
||||
|
||||
# List of patterns, relative to source directory, that match files and
|
||||
# directories to ignore when looking for source files.
|
||||
exclude_patterns = []
|
||||
|
||||
# The reST default role (used for this markup: `text`) to use for all documents.
|
||||
#default_role = None
|
||||
|
||||
# If true, '()' will be appended to :func: etc. cross-reference text.
|
||||
#add_function_parentheses = True
|
||||
|
||||
# If true, the current module name will be prepended to all description
|
||||
# unit titles (such as .. function::).
|
||||
#add_module_names = True
|
||||
|
||||
# If true, sectionauthor and moduleauthor directives will be shown in the
|
||||
# output. They are ignored by default.
|
||||
#show_authors = False
|
||||
|
||||
# The name of the Pygments (syntax highlighting) style to use.
|
||||
pygments_style = 'sphinx'
|
||||
|
||||
# A list of ignored prefixes for module index sorting.
|
||||
#modindex_common_prefix = []
|
||||
|
||||
|
||||
# -- Options for HTML output ---------------------------------------------------
|
||||
|
||||
# The theme to use for HTML and HTML Help pages. See the documentation for
|
||||
# a list of builtin themes.
|
||||
html_theme = 'default'
|
||||
|
||||
# Theme options are theme-specific and customize the look and feel of a theme
|
||||
# further. For a list of options available for each theme, see the
|
||||
# documentation.
|
||||
#html_theme_options = {}
|
||||
|
||||
# Add any paths that contain custom themes here, relative to this directory.
|
||||
#html_theme_path = []
|
||||
|
||||
# The name for this set of Sphinx documents. If None, it defaults to
|
||||
# "<project> v<release> documentation".
|
||||
#html_title = None
|
||||
|
||||
# A shorter title for the navigation bar. Default is the same as html_title.
|
||||
#html_short_title = None
|
||||
|
||||
# The name of an image file (relative to this directory) to place at the top
|
||||
# of the sidebar.
|
||||
#html_logo = None
|
||||
|
||||
# The name of an image file (within the static path) to use as favicon of the
|
||||
# docs. This file should be a Windows icon file (.ico) being 16x16 or 32x32
|
||||
# pixels large.
|
||||
#html_favicon = None
|
||||
|
||||
# Add any paths that contain custom static files (such as style sheets) here,
|
||||
# relative to this directory. They are copied after the builtin static files,
|
||||
# so a file named "default.css" will overwrite the builtin "default.css".
|
||||
html_static_path = ['_static']
|
||||
|
||||
# If not '', a 'Last updated on:' timestamp is inserted at every page bottom,
|
||||
# using the given strftime format.
|
||||
#html_last_updated_fmt = '%b %d, %Y'
|
||||
|
||||
# If true, SmartyPants will be used to convert quotes and dashes to
|
||||
# typographically correct entities.
|
||||
#html_use_smartypants = True
|
||||
|
||||
# Custom sidebar templates, maps document names to template names.
|
||||
#html_sidebars = {}
|
||||
|
||||
# Additional templates that should be rendered to pages, maps page names to
|
||||
# template names.
|
||||
#html_additional_pages = {}
|
||||
|
||||
# If false, no module index is generated.
|
||||
#html_domain_indices = True
|
||||
|
||||
# If false, no index is generated.
|
||||
#html_use_index = True
|
||||
|
||||
# If true, the index is split into individual pages for each letter.
|
||||
#html_split_index = False
|
||||
|
||||
# If true, links to the reST sources are added to the pages.
|
||||
#html_show_sourcelink = True
|
||||
|
||||
# If true, "Created using Sphinx" is shown in the HTML footer. Default is True.
|
||||
#html_show_sphinx = True
|
||||
|
||||
# If true, "(C) Copyright ..." is shown in the HTML footer. Default is True.
|
||||
#html_show_copyright = True
|
||||
|
||||
# If true, an OpenSearch description file will be output, and all pages will
|
||||
# contain a <link> tag referring to it. The value of this option must be the
|
||||
# base URL from which the finished HTML is served.
|
||||
#html_use_opensearch = ''
|
||||
|
||||
# This is the file name suffix for HTML files (e.g. ".xhtml").
|
||||
#html_file_suffix = None
|
||||
|
||||
# Output file base name for HTML help builder.
|
||||
htmlhelp_basename = 'SelectedCIdoc'
|
||||
|
||||
|
||||
# -- Options for LaTeX output --------------------------------------------------
|
||||
|
||||
latex_elements = {
|
||||
# The paper size ('letterpaper' or 'a4paper').
|
||||
#'papersize': 'letterpaper',
|
||||
|
||||
# The font size ('10pt', '11pt' or '12pt').
|
||||
#'pointsize': '10pt',
|
||||
|
||||
# Additional stuff for the LaTeX preamble.
|
||||
#'preamble': '',
|
||||
}
|
||||
|
||||
# Grouping the document tree into LaTeX files. List of tuples
|
||||
# (source start file, target name, title, author, documentclass [howto/manual]).
|
||||
latex_documents = [
|
||||
('index', 'SelectedCI.tex', u'Selected CI Documentation',
|
||||
u'Giner Emmanuel ', 'manual'),
|
||||
]
|
||||
|
||||
# The name of an image file (relative to this directory) to place at the top of
|
||||
# the title page.
|
||||
#latex_logo = None
|
||||
|
||||
# For "manual" documents, if this is true, then toplevel headings are parts,
|
||||
# not chapters.
|
||||
#latex_use_parts = False
|
||||
|
||||
# If true, show page references after internal links.
|
||||
#latex_show_pagerefs = False
|
||||
|
||||
# If true, show URL addresses after external links.
|
||||
#latex_show_urls = False
|
||||
|
||||
# Documents to append as an appendix to all manuals.
|
||||
#latex_appendices = []
|
||||
|
||||
# If false, no module index is generated.
|
||||
#latex_domain_indices = True
|
||||
|
||||
|
||||
# -- Options for manual page output --------------------------------------------
|
||||
|
||||
# One entry per manual page. List of tuples
|
||||
# (source start file, name, description, authors, manual section).
|
||||
man_pages = [
|
||||
('index', 'selectedci', u'Selected CI Documentation',
|
||||
[u'Giner Emmanuel '], 1)
|
||||
]
|
||||
|
||||
# If true, show URL addresses after external links.
|
||||
#man_show_urls = False
|
||||
|
||||
|
||||
# -- Options for Texinfo output ------------------------------------------------
|
||||
|
||||
# Grouping the document tree into Texinfo files. List of tuples
|
||||
# (source start file, target name, title, author,
|
||||
# dir menu entry, description, category)
|
||||
texinfo_documents = [
|
||||
('index', 'SelectedCI', u'Selected CI Documentation',
|
||||
u'Giner Emmanuel ', 'SelectedCI', 'One line description of project.',
|
||||
'Miscellaneous'),
|
||||
]
|
||||
|
||||
# Documents to append as an appendix to all manuals.
|
||||
#texinfo_appendices = []
|
||||
|
||||
# If false, no module index is generated.
|
||||
#texinfo_domain_indices = True
|
||||
|
||||
# How to display URL addresses: 'footnote', 'no', or 'inline'.
|
||||
#texinfo_show_urls = 'footnote'
|
||||
|
||||
|
||||
# -- Options for Epub output ---------------------------------------------------
|
||||
|
||||
# Bibliographic Dublin Core info.
|
||||
epub_title = u'Selected CI'
|
||||
epub_author = u'Giner Emmanuel '
|
||||
epub_publisher = u'Giner Emmanuel '
|
||||
epub_copyright = u'2014, Giner Emmanuel '
|
||||
|
||||
# The language of the text. It defaults to the language option
|
||||
# or en if the language is not set.
|
||||
#epub_language = ''
|
||||
|
||||
# The scheme of the identifier. Typical schemes are ISBN or URL.
|
||||
#epub_scheme = ''
|
||||
|
||||
# The unique identifier of the text. This can be a ISBN number
|
||||
# or the project homepage.
|
||||
#epub_identifier = ''
|
||||
|
||||
# A unique identification for the text.
|
||||
#epub_uid = ''
|
||||
|
||||
# A tuple containing the cover image and cover page html template filenames.
|
||||
#epub_cover = ()
|
||||
|
||||
# HTML files that should be inserted before the pages created by sphinx.
|
||||
# The format is a list of tuples containing the path and title.
|
||||
#epub_pre_files = []
|
||||
|
||||
# HTML files shat should be inserted after the pages created by sphinx.
|
||||
# The format is a list of tuples containing the path and title.
|
||||
#epub_post_files = []
|
||||
|
||||
# A list of files that should not be packed into the epub file.
|
||||
#epub_exclude_files = []
|
||||
|
||||
# The depth of the table of contents in toc.ncx.
|
||||
#epub_tocdepth = 3
|
||||
|
||||
# Allow duplicate toc entries.
|
||||
#epub_tocdup = True
|
||||
|
|
@ -0,0 +1,25 @@
|
|||
.. Selected CI documentation master file, created by
|
||||
sphinx-quickstart on Mon Feb 10 15:53:11 2014.
|
||||
You can adapt this file completely to your liking, but it should at least
|
||||
contain the root `toctree` directive.
|
||||
|
||||
Welcome to Selected CI's documentation!
|
||||
=======================================
|
||||
|
||||
Contents:
|
||||
|
||||
.. toctree::
|
||||
:maxdepth: 1
|
||||
|
||||
install
|
||||
Intro
|
||||
code_doc_intro
|
||||
wavefunction
|
||||
|
||||
Indices and tables
|
||||
==================
|
||||
|
||||
* :ref:`genindex`
|
||||
* :ref:`modindex`
|
||||
* :ref:`search`
|
||||
|
||||
|
|
@ -0,0 +1,40 @@
|
|||
============
|
||||
Installation
|
||||
============
|
||||
|
||||
Requirements
|
||||
------------
|
||||
|
||||
* `GNU make <http://www.gnu.org/software/make>`_
|
||||
* `The Intel Fortran Compiler with MKL <http://software.intel.com/en-us/fortran-compilers>`_
|
||||
* `IRPF90 <http://irpf90.ups-tlse.fr>`_
|
||||
* `EZFIO <http://ezfio.sourceforge.net>`_
|
||||
|
||||
Optional Requirements
|
||||
---------------------
|
||||
|
||||
* `Sphinx <http://sphinx-doc.org/>`_ is used to build the documentation
|
||||
|
||||
Setup
|
||||
-----
|
||||
|
||||
#) Run the :file:`setup_environment.sh` script. This will create the :file:`sci.rc` file
|
||||
that contains all the environment variables ::
|
||||
|
||||
$ ./setup_environment.sh
|
||||
|
||||
#) Source this file into your shell ::
|
||||
|
||||
$ source sci.rc
|
||||
|
||||
#) Go into the :file:`src` directory and create the :file:`Makefile.config` file using the
|
||||
:file:`Makefile.config.example` file as a template
|
||||
|
||||
#) Build the program ::
|
||||
|
||||
$ make
|
||||
|
||||
#) Build the documentation ::
|
||||
|
||||
$ make doc
|
||||
|
||||
|
|
@ -0,0 +1,169 @@
|
|||
=====================================
|
||||
Selection, perturbation ... keywords
|
||||
=====================================
|
||||
|
||||
.. |CISD| replace:: :abbr:`CISD (Configuration Interaction with Single and Double excitations)`
|
||||
.. |HF| replace:: :abbr:`HF (Hartree Fock)`
|
||||
.. |CAS-CI| replace:: :abbr:`CAS-CI (Complete Active Space Configuration Interaction)`
|
||||
.. |DDCI| replace:: :abbr:`DDCI (Difference Dedicated Configuration Interaction)`
|
||||
|
||||
.. glossary::
|
||||
:sorted:
|
||||
|
||||
Energetic perturbative correction
|
||||
Corresponds to the correction to the energy at the second order of a given perturbtation theory
|
||||
to a given state m.
|
||||
By convention it noted :math:`E_{PT2}^m`
|
||||
|
||||
Variational energy
|
||||
Corresponds to the variational energy of the :term:`selected wave function` for a given state .
|
||||
By convention it noted :math:`E_{Var}^m` for the mth eigenvector.
|
||||
|
||||
.. math::
|
||||
E_{Var}^m = \langle \psi_m |H|\psi_m \rangle
|
||||
|
||||
Estimated target energy
|
||||
Corresponds to the estimation of the target energy for a given :term:`selected wave function` and a given state.
|
||||
By convention it noted :math:`E_{Target}^m`.
|
||||
Its mathematical expression is :
|
||||
|
||||
.. math::
|
||||
E_{Target}^m = E_{Var}^m + E_{PT2}^m
|
||||
|
||||
Selected wave function
|
||||
Corresponds to the wave function that have been previously selected for a given state m at a current iteration.
|
||||
This wave function is defined by the set of the :term:`internal determinants` and by their coefficients
|
||||
on the state m.
|
||||
By convention it is noted :math:`|\psi_m\rangle`
|
||||
|
||||
.. math::
|
||||
| \psi_m \rangle = \sum_{I=1,N_{selected}} c_I^m | D_I \rangle
|
||||
|
||||
|
||||
|
||||
|
||||
EN EG
|
||||
Stands for Eipstein Nesbet with EigenValues zeroth order energy perturbation theory.
|
||||
It is a state specific 2nd order perturbation theory. Here m is the index of the eigenstate.
|
||||
The :math:`H_0` of this PT is defined as the diagonal part of the Hamiltonian such as
|
||||
the :math:`E_m` is equal to the average value of the Hamiltonian on the :term:`selected wave function`
|
||||
and the :math:`E_P` is equal to the average value of the Hamiltonian on the :term:`perturbers`
|
||||
|
||||
This perturbation have bad formal properties but some nice numerical features of convergence.
|
||||
|
||||
|
||||
From the definition, one get the first order coefficient and its related second order energetic contribution of a a perturber :
|
||||
|
||||
.. math::
|
||||
c_{D_P}^m= \sum_{S=1,N_{\rm selectors}} \frac{c_S^m \langle D_S|H|D_P\rangle}{ \langle \psi_m |H|\psi_m \rangle - \langle D_P|H| D_P \rangle } \\
|
||||
e_{D_P}^m= \frac{(\sum_{S=1,N_{\rm selectors}} c_S^m \langle D_S|H|D_P\rangle)^2}{\langle \psi_m |H|\psi_m \rangle - \langle D_P|H| D_P \rangle }
|
||||
|
||||
|
||||
Stopping criterion
|
||||
Condition decided by the user to stop the calculation.
|
||||
This criterion might be on the :term:`Energetic perturbative correction`, on the number of :term:`internal determinants` N_selected_max
|
||||
or on the stability of the :term:`estimated target energy`
|
||||
The user can also send a Ctrl+C to stop the calculation, and it will kill itself properly, saving the datas that need to be saved.
|
||||
|
||||
|
||||
Target wave function
|
||||
Wave function of the :term:`target space`
|
||||
|
||||
|
||||
|
||||
Target space
|
||||
Target of the CI calculation. Defining a method (CISD, CAS-CI and so on) is equivalent to define the :term:`target space`.
|
||||
|
||||
The target space defines the rules to define the :term:`Generators` ,
|
||||
the rules of the :term:`excitation restrictions`,
|
||||
and the perturbation theory to be used.
|
||||
|
||||
There are two type of methods/:term:`target space` proposed in the code :
|
||||
|
||||
#) the CAS-CI type methods where you do not restrict any kind of excitation degree within a given list of orbitals.
|
||||
#) the singles and doubles excitations on the top of a given reference wave function (:term:`CISD`, :term:`CISD+SC2`, :term:`CAS+SD`, :term:`CAS+DDCI`, :term:`CAS+MRPT2`)
|
||||
|
||||
Their is a great difference between those two types of method in the way it is implemented.
|
||||
|
||||
In the CAS-CI method, when you have chosen an :term:`active space` (so a list of orbitals and electrons to make a FCI within this active space),
|
||||
all the :term:`Internal determinants` that have been selected and that form the :term:`selected wave function`
|
||||
can potentially be part of the :term:`generators`, by mean that the :term:`restricted H operator`
|
||||
could be potentially applyed on all the :term:`internal determinants` to generate some other :term:`perturbers`.
|
||||
|
||||
In the singles and doubles excitation on the top of a given reference wave function, the subset of :term:`generators`
|
||||
and so the rules to recognize them, is fixed at the begining of the method. Those :term:`generators` are precisely
|
||||
all the determinants forming the :term:`reference wave function`.
|
||||
|
||||
|
||||
There are the different :term:`target space` that are available :
|
||||
|
||||
#) :term:`CISD`
|
||||
#) :term:`CISD+SC2`
|
||||
#) :term:`CASCI`
|
||||
#) :term:`CASCI+S`
|
||||
#) :term:`CASCI+SD`
|
||||
#) :term:`CASCI+DDCI`
|
||||
#) :term:`CASCI+DDCI+(2h-2p)PT2`
|
||||
#) :term:`CAS-CI+MRPT2`
|
||||
|
||||
|
||||
Target energy
|
||||
Energy of the target space.
|
||||
|
||||
H operator
|
||||
Hamiltonian operator defined in terms of creation and anihilation operators in the spin orbital space.
|
||||
|
||||
Excitation restrictions
|
||||
Restriction in the :term:`H operator` that the user imposes to define the target sapce.
|
||||
For example :
|
||||
|
||||
1) If one freeze some core orbitals or delete some virtuals, it is an :term:`excitation restrictions`
|
||||
2) If one prohibits the pure inactive double excitations in a CAS+SD one get a DDCI
|
||||
3) any kind of restriction in the full application of the :term:`H operator`
|
||||
|
||||
|
||||
Restricted H operator
|
||||
:term:`H operator` taking into account the :term:`Excitation restrictions`
|
||||
|
||||
|
||||
CISD+SC2
|
||||
Method developped by JP. Malrieu that can be seen as a cheap approximation of the CCSD.
|
||||
It makes a CISD size consistant and separable for closed shell systems.
|
||||
It is based on a CISD calculation
|
||||
where the diagonal part of the H matrix is dressed by the repeatable correlation energy previsously obtained.
|
||||
So it is a CISD dressed by the disconnected triples and quadruples.
|
||||
|
||||
Generators
|
||||
Set of generator determinants.
|
||||
By convention a generator is written as :math:`|D_G\rangle` .
|
||||
A generator determinant is a determinant on which
|
||||
the :term:`restricted H operator` is being applied for the selection and/or the perturbation.
|
||||
|
||||
Internal determinants
|
||||
Selected determinants in terms of integers keys.
|
||||
By convention an Internal determinant is written as :math:`|D_I\rangle` .
|
||||
By convention, the :term:`Generators` are at the begining of the array.
|
||||
|
||||
Intern space
|
||||
Set of all the :term:`internal determinants`.
|
||||
|
||||
Perturbers
|
||||
Determinants within the :term:`target space` but taht are not already included in the :term:`intern space`.
|
||||
They are created from the :term:`Generators` that belongs :term:`Intern space` for a given :term:`selected wave function`.
|
||||
By convention a perturber is written as :math:`|D_P\rangle`.
|
||||
|
||||
Selectors
|
||||
Determinants that are used to compute the perturbative properties of the :term:`perturbers`.
|
||||
By convention a selector is written as :math:`|D_S\rangle` .
|
||||
The selectors are a subset of determinant of the total wave function (that is the :term:`Internal determinants`).
|
||||
This subset contains at least the :term:`Generators` determinants.
|
||||
The perturbative properties (energy, coefficient or else) of the :term:`perturbers` are calculated on all the :term:`selectors` :math:`|D_S\rangle`
|
||||
|
||||
.. math::
|
||||
|
||||
c_{D_S}= \sum_{S=1,N_{\rm selectors}} \frac{c_S\langle D_S|H|D_P\rangle}{\Delta E_{P,S}} \\
|
||||
e_{D_S}= \frac{(\sum_{S=1,N_{\rm selectors}} c_S \langle D_S|H|D_P\rangle) ^2}{\Delta E_{P,S}}
|
||||
|
||||
|
||||
|
||||
|
||||
|
|
@ -0,0 +1,19 @@
|
|||
#!/bin/bash
|
||||
|
||||
SCI_ROOT=${PWD}
|
||||
|
||||
IRPF90=$(which irpf90)
|
||||
|
||||
if [[ -z ${IRPF90} ]] ;
|
||||
then
|
||||
make irpf90
|
||||
IRPF90=${SCI_ROOT}/irpf90/bin/irpf90
|
||||
fi
|
||||
make EZFIO
|
||||
|
||||
cat << EOF > sci.rc
|
||||
export IRPF90=${IRPF90}
|
||||
export SCI_ROOT=${SCI_ROOT}
|
||||
export PATH+=:${SCI_ROOT}/scripts
|
||||
export PATH+=:${SCI_ROOT}/bin
|
||||
EOF
|
||||
Loading…
Reference in New Issue