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108 lines
2.8 KiB
Groff
108 lines
2.8 KiB
Groff
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.\" Man page generated from reStructuredText.
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.TH "NATURAL_ORBITALS" "1" "Jan 17, 2019" "2.0" "Quantum Package"
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.SH NAME
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natural_orbitals \- | Quantum Package >
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.
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.nr rst2man-indent-level 0
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level \\n[rst2man-indent-level]
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level margin: \\n[rst2man-indent\\n[rst2man-indent-level]]
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-
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\\n[rst2man-indent0]
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\\n[rst2man-indent1]
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\\n[rst2man-indent2]
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..
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.de1 INDENT
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.\" .rstReportMargin pre:
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. RS \\$1
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. nr rst2man-indent\\n[rst2man-indent-level] \\n[an-margin]
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. nr rst2man-indent-level +1
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.\" .rstReportMargin post:
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..
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.de UNINDENT
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. RE
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.\" indent \\n[an-margin]
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.\" old: \\n[rst2man-indent\\n[rst2man-indent-level]]
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.nr rst2man-indent-level -1
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.\" new: \\n[rst2man-indent\\n[rst2man-indent-level]]
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.in \\n[rst2man-indent\\n[rst2man-indent-level]]u
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..
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.SH SUMMARY
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.sp
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To produce state\-average natural orbitals, run
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.INDENT 0.0
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.INDENT 3.5
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.sp
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.nf
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.ft C
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qp_run save_natorb file.ezfio
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.ft P
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.fi
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.UNINDENT
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.UNINDENT
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.sp
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The MOs will be replaced, so the two\-electron integrals and the wave function
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are invalidated as well.
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.SH EXTRACTING NATURAL ORBITALS
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.sp
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Once obtained the near FCI wave function, one can obtain many quantities related to it.
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One of these quantities are the natural orbitals which have the properties of diagonalizing the one\-body density matrix:
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.INDENT 0.0
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.INDENT 3.5
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.sp
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.ce
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\erho_{ij} = \edelta_{ij}
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.ce 0
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.UNINDENT
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.UNINDENT
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.sp
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where the element of the one\-body density matrix \erho_{ij} is define as:
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.INDENT 0.0
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.INDENT 3.5
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.sp
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.ce
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\erho_{ij} = \elangle \ePsi | \eleft( a^{\edagger}_{j,\ealpha} a_{i,\ealpha} + a^{\edagger}_{j,\ebeta} a_{i,\ebeta} \eright) |\ \ePsi\ \erangle
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.ce 0
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.UNINDENT
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.UNINDENT
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.sp
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These orbitals are in general known to be better than the usual HF MOs as they are obtained from a correlated wave function. To use these orbitals for future calculations, one has to replace the current MOs by the natural orbitals. To do so, just run:
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.INDENT 0.0
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.INDENT 3.5
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.sp
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.nf
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.ft C
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qp_run save_natorb file.ezfio
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.ft P
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.fi
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.UNINDENT
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.UNINDENT
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.SH HANDS ON
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.sp
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\fBIMPORTANT:\fP
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.INDENT 0.0
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.INDENT 3.5
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As the MOs are changed, for the sake of coherence of future calculations, the save_natorb program
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\fIautomatically removes the current wave function\fP stored in the \fI\%EZFIO\fP database and replace
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it by a single Slater determinant corresponding to a HF occupation of the new spin orbitals.
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Also, all the keywords to read the one\- and two\-electron integrals on the MO basis are set to “None”
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in order to be sure not to read integrals not corresponding to the current set of MOs\&.
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.UNINDENT
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.UNINDENT
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.sp
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\fBSEE ALSO:\fP
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.INDENT 0.0
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.INDENT 3.5
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The documentation of the \fBsave_natorb()\fP program.
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.UNINDENT
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.UNINDENT
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.SH AUTHOR
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A. Scemama, E. Giner
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.SH COPYRIGHT
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2018, A. Scemama, E. Giner
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.\" Generated by docutils manpage writer.
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