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<TITLE>16. MP2</TITLE>
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<BR>
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<B> Next:</B> <A NAME="tex2html1308"
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HREF="node19.html">17. Multiconfiguration SCF</A>
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HREF="user.html">user</A>
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<B> Previous:</B> <A NAME="tex2html1298"
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HREF="node17.html">15. Tensor Contraction Engine</A>
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  <B> <A NAME="tex2html1306"
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HREF="node2.html">Contents</A></B>
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<BR>
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<BR>
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<!--End of Navigation Panel-->
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<!--Table of Child-Links-->
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<A NAME="CHILD_LINKS"><STRONG>Subsections</STRONG></A>
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<UL>
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<LI><A NAME="tex2html1309"
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HREF="node18.html#SECTION001810000000000000000">16.1 <TT>FREEZE</TT> -- Freezing orbitals</A>
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<LI><A NAME="tex2html1310"
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HREF="node18.html#SECTION001820000000000000000">16.2 <TT>TIGHT</TT> -- Increased precision</A>
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<LI><A NAME="tex2html1311"
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HREF="node18.html#SECTION001830000000000000000">16.3 <TT>SCRATCHDISK</TT> -- Limiting I/O usage</A>
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<LI><A NAME="tex2html1312"
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HREF="node18.html#SECTION001840000000000000000">16.4 <TT>PRINT</TT> and <TT>NOPRINT</TT></A>
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<LI><A NAME="tex2html1313"
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HREF="node18.html#SECTION001850000000000000000">16.5 <TT>VECTORS</TT> -- MO vectors</A>
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<LI><A NAME="tex2html1314"
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HREF="node18.html#SECTION001860000000000000000">16.6 RI-MP2 fitting basis</A>
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<LI><A NAME="tex2html1315"
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HREF="node18.html#SECTION001870000000000000000">16.7 <TT>FILE3C</TT> -- RI-MP2 3-center integral filename</A>
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<LI><A NAME="tex2html1316"
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HREF="node18.html#SECTION001880000000000000000">16.8 <TT>RIAPPROX</TT> -- RI-MP2 Approximation</A>
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<LI><A NAME="tex2html1317"
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HREF="node18.html#SECTION001890000000000000000">16.9 Advanced options for RI-MP2</A>
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<UL>
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<LI><A NAME="tex2html1318"
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HREF="node18.html#SECTION001891000000000000000">16.9.1 Control of linear dependence</A>
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<LI><A NAME="tex2html1319"
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HREF="node18.html#SECTION001892000000000000000">16.9.2 Reference Spin Mapping for RI-MP2 Calculations</A>
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<LI><A NAME="tex2html1320"
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HREF="node18.html#SECTION001893000000000000000">16.9.3 Batch Sizes for the RI-MP2 Calculation</A>
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<LI><A NAME="tex2html1321"
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HREF="node18.html#SECTION001894000000000000000">16.9.4 Energy Memory Allocation Mode: RI-MP2 Calculation</A>
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<LI><A NAME="tex2html1322"
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HREF="node18.html#SECTION001895000000000000000">16.9.5 Local Memory Usage in Three-Center Transformation</A>
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</UL>
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<BR>
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<LI><A NAME="tex2html1323"
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HREF="node18.html#SECTION0018100000000000000000">16.10 One-electron properties and natural orbitals</A>
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</UL>
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<!--End of Table of Child-Links-->
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<HR>
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<H1><A NAME="SECTION001800000000000000000">
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16. MP2</A>
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</H1>
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<A NAME="sec:mp2"></A><A NAME="sec:rimp2"></A>
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<P>
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There are (at least) three algorithms within NWChem that compute the
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Møller-Plesset (or many-body) perturbation theory second-order
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correction to the Hartree-Fock energy (MP2). They vary in capability,
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the size of system that can be treated and use of other approximations
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<UL>
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<LI>Semi-direct -- this is recommended for most large applications
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(up to about 2800 basis functions), especially on the IBM SP and
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other machines with significant disk I/O capability. Partially
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transformed integrals are stored on disk, multi-passing as necessary.
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RHF and UHF references may be treated including computation of
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analytic derivatives. This is selected by specifying <code>mp2</code> on
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the task directive, e.g.
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<PRE>
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TASK MP2
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</PRE>
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</LI>
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<LI>Fully-direct -- this is of utility if only limited I/O
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resources are available (up to about 2800 functions). Only RHF
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references and energies are available. This is selected by
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specifying <code>direct_mp2</code> on the task directive, e.g.
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<PRE>
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TASK DIRECT_MP2
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</PRE>
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</LI>
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<LI>Resolution of the identity (RI) approximation MP2 (RI-MP2) --
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this uses the RI approximation and is therefore only exact in the
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limit of a complete fitting basis. However, with some care, high
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accuracy may be obtained with relatively modest fitting basis sets.
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An RI-MP2 calculation can cost over 40 times less than the
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corresponding exact MP2 calculation. RHF and UHF references with
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only energies are available. This is selected by specifying
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<code>rimp2</code> on the task directive, e.g.,
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<PRE>
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TASK RIMP2
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</PRE>
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</LI>
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</UL>
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<P>
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All three MP2 tasks share the same input block.
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<P>
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<PRE>
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MP2
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[FREEZE [[core] (atomic || <integer nfzc default 0>)] \
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[virtual <integer nfzv default 0>]]
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[TIGHT]
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[PRINT]
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[NOPRINT]
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[VECTORS <string filename default scf-output-vectors> \
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[swap [(alpha||beta)] <integer pair-list>] ]
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[RIAPPROX <string riapprox default V>]
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[FILE3C <string filename default $file_prefix$.mo3cint">]
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[SCRATCHDISK <integer>]
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END
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</PRE>
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<P>
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<H1><A NAME="SECTION001810000000000000000"></A>
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<A NAME="mp2:core"></A>
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<BR>
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16.1 <TT>FREEZE</TT> -- Freezing orbitals
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</H1>
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<P>
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All MP2 modules support frozen core orbitals, however, only the direct
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MP2 and RI-MP2 modules support frozen virtual orbitals.
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<P>
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By default, no orbitals are frozen. The <code>atomic</code> keyword causes
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orbitals to be frozen according to the rules in Table
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<A HREF="node18.html#tbl:freeze-by-atoms">16.1</A>. Note that <EM>no</EM> orbitals are frozen on
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atoms on which the nuclear charge has been modified either by the user
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or due to the presence of an ECP. The actual input would be
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<PRE>
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freeze atomic
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</PRE>
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For example, in a calculation on <IMG
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WIDTH="67" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
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SRC="img133.gif"
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ALT="$Si(OH)_2$">, by default the lowest
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seven orbitals would be frozen (the oxygen 1<IMG
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WIDTH="12" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
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SRC="img61.gif"
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ALT="$s$">, and the silicon 1<IMG
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WIDTH="12" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
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SRC="img61.gif"
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ALT="$s$">,
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2<IMG
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WIDTH="12" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
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SRC="img61.gif"
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ALT="$s$"> and 2<IMG
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WIDTH="12" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
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SRC="img62.gif"
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ALT="$p$">).
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<P>
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<BR><P></P>
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<DIV ALIGN="CENTER"><A NAME="5043"></A>
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<TABLE>
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<CAPTION><STRONG>Table 16.1:</STRONG>
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Number of orbitals considered ``core'' in the ``freeze by
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atoms'' algorithm.</CAPTION>
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<TR><TD><A NAME="tbl:freeze-by-atoms"></A>
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<P>
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<P>
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<TABLE CELLPADDING=3 BORDER="1">
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<TR><TD ALIGN="CENTER">Period</TD>
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<TD ALIGN="CENTER">Elements</TD>
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<TD ALIGN="LEFT">Core Orbitals</TD>
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<TD ALIGN="RIGHT">Number of Core</TD>
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</TR>
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<TR><TD ALIGN="CENTER">0</TD>
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<TD ALIGN="CENTER">H - He</TD>
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<TD ALIGN="LEFT">--</TD>
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<TD ALIGN="RIGHT">0</TD>
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</TR>
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<TR><TD ALIGN="CENTER">1</TD>
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<TD ALIGN="CENTER">Li - Ne</TD>
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<TD ALIGN="LEFT">1<IMG
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WIDTH="12" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
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SRC="img61.gif"
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ALT="$s$"></TD>
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<TD ALIGN="RIGHT">1</TD>
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</TR>
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<TR><TD ALIGN="CENTER">2</TD>
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<TD ALIGN="CENTER">Na - Ar</TD>
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<TD ALIGN="LEFT">1<IMG
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WIDTH="12" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
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SRC="img61.gif"
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ALT="$s$">2<IMG
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WIDTH="12" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
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SRC="img61.gif"
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ALT="$s$">2<IMG
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WIDTH="12" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
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SRC="img62.gif"
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ALT="$p$"></TD>
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<TD ALIGN="RIGHT">5</TD>
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</TR>
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<TR><TD ALIGN="CENTER">3</TD>
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<TD ALIGN="CENTER">K - Kr</TD>
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<TD ALIGN="LEFT">1<IMG
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WIDTH="12" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
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SRC="img61.gif"
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ALT="$s$">2<IMG
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WIDTH="12" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
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SRC="img61.gif"
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ALT="$s$">2<IMG
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WIDTH="12" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
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SRC="img62.gif"
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ALT="$p$">3<IMG
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WIDTH="12" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
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SRC="img61.gif"
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ALT="$s$">3<IMG
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WIDTH="12" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
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SRC="img62.gif"
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ALT="$p$"></TD>
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<TD ALIGN="RIGHT">9</TD>
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</TR>
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<TR><TD ALIGN="CENTER">4</TD>
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<TD ALIGN="CENTER">Rb - Xe</TD>
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<TD ALIGN="LEFT">1<IMG
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WIDTH="12" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
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SRC="img61.gif"
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ALT="$s$">2<IMG
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WIDTH="12" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
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SRC="img61.gif"
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ALT="$s$">2<IMG
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WIDTH="12" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
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SRC="img62.gif"
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ALT="$p$">3<IMG
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WIDTH="12" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
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SRC="img61.gif"
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ALT="$s$">3<IMG
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WIDTH="12" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
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SRC="img62.gif"
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ALT="$p$">4<IMG
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WIDTH="12" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
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SRC="img61.gif"
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ALT="$s$">3<IMG
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WIDTH="12" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
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SRC="img64.gif"
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ALT="$d$">4<IMG
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WIDTH="12" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
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SRC="img62.gif"
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ALT="$p$"></TD>
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<TD ALIGN="RIGHT">18</TD>
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</TR>
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<TR><TD ALIGN="CENTER">5</TD>
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<TD ALIGN="CENTER">Cs - Rn</TD>
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<TD ALIGN="LEFT">1<IMG
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WIDTH="12" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
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SRC="img61.gif"
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|
ALT="$s$">2<IMG
|
|
WIDTH="12" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
|
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SRC="img61.gif"
|
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ALT="$s$">2<IMG
|
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WIDTH="12" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
|
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SRC="img62.gif"
|
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ALT="$p$">3<IMG
|
|
WIDTH="12" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
|
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SRC="img61.gif"
|
|
ALT="$s$">3<IMG
|
|
WIDTH="12" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
|
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SRC="img62.gif"
|
|
ALT="$p$">4<IMG
|
|
WIDTH="12" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
|
|
SRC="img61.gif"
|
|
ALT="$s$">3<IMG
|
|
WIDTH="12" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
|
|
SRC="img64.gif"
|
|
ALT="$d$">4<IMG
|
|
WIDTH="12" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
|
|
SRC="img62.gif"
|
|
ALT="$p$">5<IMG
|
|
WIDTH="12" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
|
|
SRC="img61.gif"
|
|
ALT="$s$">4<IMG
|
|
WIDTH="12" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
|
|
SRC="img64.gif"
|
|
ALT="$d$">5<IMG
|
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WIDTH="12" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
|
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SRC="img62.gif"
|
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ALT="$p$"></TD>
|
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<TD ALIGN="RIGHT">27</TD>
|
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</TR>
|
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<TR><TD ALIGN="CENTER">6</TD>
|
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<TD ALIGN="CENTER">Fr - Lr</TD>
|
|
<TD ALIGN="LEFT">1<IMG
|
|
WIDTH="12" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
|
|
SRC="img61.gif"
|
|
ALT="$s$">2<IMG
|
|
WIDTH="12" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
|
|
SRC="img61.gif"
|
|
ALT="$s$">2<IMG
|
|
WIDTH="12" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
|
|
SRC="img62.gif"
|
|
ALT="$p$">3<IMG
|
|
WIDTH="12" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
|
|
SRC="img61.gif"
|
|
ALT="$s$">3<IMG
|
|
WIDTH="12" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
|
|
SRC="img62.gif"
|
|
ALT="$p$">4<IMG
|
|
WIDTH="12" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
|
|
SRC="img61.gif"
|
|
ALT="$s$">3<IMG
|
|
WIDTH="12" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
|
|
SRC="img64.gif"
|
|
ALT="$d$">4<IMG
|
|
WIDTH="12" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
|
|
SRC="img62.gif"
|
|
ALT="$p$">5<IMG
|
|
WIDTH="12" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
|
|
SRC="img61.gif"
|
|
ALT="$s$">4<IMG
|
|
WIDTH="12" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
|
|
SRC="img64.gif"
|
|
ALT="$d$">5<IMG
|
|
WIDTH="12" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
|
|
SRC="img62.gif"
|
|
ALT="$p$">6<IMG
|
|
WIDTH="12" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
|
|
SRC="img61.gif"
|
|
ALT="$s$">4<IMG
|
|
WIDTH="14" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
|
|
SRC="img134.gif"
|
|
ALT="$f$">5<IMG
|
|
WIDTH="12" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
|
|
SRC="img64.gif"
|
|
ALT="$d$">6<IMG
|
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WIDTH="12" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
|
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SRC="img62.gif"
|
|
ALT="$p$"></TD>
|
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<TD ALIGN="RIGHT">43</TD>
|
|
</TR>
|
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</TABLE>
|
|
|
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<P>
|
|
|
|
<P>
|
|
</TD></TR>
|
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</TABLE>
|
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</DIV><P></P>
|
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<BR>
|
|
|
|
<P>
|
|
<EM>Caution:</EM> The rule for freezing orbitals ``by atoms'' are
|
|
rather unsophisticated: the number of orbitals to be frozen is
|
|
computed from the Table <A HREF="node18.html#tbl:freeze-by-atoms">16.1</A> by summing the number
|
|
of core orbitals in each atom present. The corresponding number of
|
|
lowest-energy orbitals are frozen -- if for some reason the actual
|
|
core orbitals are not the lowest lying, then correct results will not
|
|
be obtained. From limited experience, it seems that special attention
|
|
should be paid to systems including third- and higher- period atoms.
|
|
|
|
<P>
|
|
The user may also specify the number of orbitals to be frozen by atom.
|
|
Following the <IMG
|
|
WIDTH="67" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
|
|
SRC="img133.gif"
|
|
ALT="$Si(OH)_2$"> example, the user could specify
|
|
<PRE>
|
|
freeze atomic O 1 Si 3
|
|
</PRE>
|
|
In this case only the lowest four orbitals would be frozen. If the user does
|
|
not specify the orbitals by atom, the rules default to Table <A HREF="node18.html#tbl:freeze-by-atoms">16.1</A>.
|
|
|
|
<P>
|
|
<EM>Caution:</EM> The system does not check for a valid number of orbitals per
|
|
atom. If the user specifies to freeze more orbitals then are available for
|
|
the atom, the system will not catch the error. The user must specify a logical
|
|
number of orbitals to be frozen for the atom.
|
|
|
|
<P>
|
|
The <code>FREEZE</code> directive may also be used to specify the number of
|
|
core orbitals to freeze. For instance, to freeze the first 10 orbitals
|
|
<PRE>
|
|
freeze 10
|
|
</PRE>
|
|
or equivalently, using the optional keyword <code>core</code>
|
|
<PRE>
|
|
freeze core 10
|
|
</PRE>
|
|
Again, note that if the 10 orbitals to be frozen do not correspond to
|
|
the first 10 orbitals, then the <code>swap</code> keyword of the
|
|
<code>VECTORS</code> directive must be used to order the input orbitals
|
|
correctly (Section <A HREF="node18.html#sec:mp2vectors">16.5</A>).
|
|
|
|
<P>
|
|
To freeze the highest virtual orbitals, use the <code>virtual</code>
|
|
keyword. For instance, to freeze the top 5 virtuals
|
|
<PRE>
|
|
freeze virtual 5
|
|
</PRE>
|
|
Again, note that this only works for the direct-MP2 and RI-MP2 energy
|
|
codes.
|
|
|
|
<P>
|
|
|
|
<H1><A NAME="SECTION001820000000000000000">
|
|
16.2 <TT>TIGHT</TT> -- Increased precision</A>
|
|
</H1>
|
|
|
|
<P>
|
|
The <code>TIGHT</code> directive can be used to increase the precision
|
|
in the MP2 energy and gradients.
|
|
|
|
<P>
|
|
By default the MP2 gradient package should compute energies accurate
|
|
to better than a micro-Hartree, and gradients accurate to about five
|
|
decimal places (atomic units). However, if there is significant
|
|
linear dependence in the basis set the precision might not be this
|
|
good. Also, for computing very accurate geometries or numerical
|
|
frequencies, greater precision may be desirable.
|
|
|
|
<P>
|
|
This option increases the precision to which both the SCF (from
|
|
<IMG
|
|
WIDTH="37" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
|
|
SRC="img98.gif"
|
|
ALT="$10^{-6}$"> to <IMG
|
|
WIDTH="37" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
|
|
SRC="img99.gif"
|
|
ALT="$10^{-8}$">) and CPHF (from <IMG
|
|
WIDTH="37" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
|
|
SRC="img97.gif"
|
|
ALT="$10^{-4}$"> to <IMG
|
|
WIDTH="37" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
|
|
SRC="img98.gif"
|
|
ALT="$10^{-6}$">) are
|
|
solved, and also tightens thresholds for computation of the AO and MO
|
|
integrals (from <IMG
|
|
WIDTH="37" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
|
|
SRC="img135.gif"
|
|
ALT="$10^{-9}$"> to <IMG
|
|
WIDTH="44" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
|
|
SRC="img136.gif"
|
|
ALT="$10^{-11}$">) within the MP2 code.
|
|
|
|
<P>
|
|
|
|
<H1><A NAME="SECTION001830000000000000000">
|
|
16.3 <TT>SCRATCHDISK</TT> -- Limiting I/O usage</A>
|
|
</H1>
|
|
|
|
<P>
|
|
This directive - used only in the semi-direct algorithm - allows to
|
|
limit the per process disk usage. Mandatory argument for this keyword
|
|
is the maximum number of MBytes.
|
|
For example, the following input line
|
|
<PRE>
|
|
scratchdisk 512
|
|
</PRE>
|
|
puts an upper limit of 512 MBytes to the semi-direct MP2 usage of disk
|
|
(again, on a per process base).
|
|
|
|
<P>
|
|
|
|
<H1><A NAME="SECTION001840000000000000000">
|
|
16.4 <TT>PRINT</TT> and <TT>NOPRINT</TT></A>
|
|
</H1>
|
|
|
|
<P>
|
|
The standard print control options are recognized. The list of
|
|
recognized names are given in Table <A HREF="node18.html#tbl:mp2-printable">16.2</A>.
|
|
|
|
<P>
|
|
<BR><P></P>
|
|
<DIV ALIGN="CENTER">
|
|
|
|
<A NAME="tbl:mp2-printable"></A><A NAME="5072"></A>
|
|
<TABLE CELLPADDING=3 BORDER="1">
|
|
<CAPTION><STRONG>Table 16.2:</STRONG>
|
|
Printable items in the MP2 modules and their default print levels.</CAPTION>
|
|
<TR><TD ALIGN="LEFT">Item</TD>
|
|
<TD ALIGN="LEFT">Print Level</TD>
|
|
<TD ALIGN="LEFT">Description</TD>
|
|
</TR>
|
|
<TR><TD ALIGN="LEFT"> </TD>
|
|
<TD ALIGN="LEFT"> </TD>
|
|
<TD ALIGN="LEFT"> </TD>
|
|
</TR>
|
|
<TR><TD ALIGN="LEFT"><B>RI-MP2</B></TD>
|
|
<TD ALIGN="LEFT"> </TD>
|
|
<TD ALIGN="LEFT"> </TD>
|
|
</TR>
|
|
<TR><TD ALIGN="LEFT"> </TD>
|
|
<TD ALIGN="LEFT"> </TD>
|
|
<TD ALIGN="LEFT"> </TD>
|
|
</TR>
|
|
<TR><TD ALIGN="LEFT">``2/3 ints''</TD>
|
|
<TD ALIGN="LEFT">debug</TD>
|
|
<TD ALIGN="LEFT">Partial 3-center integrals</TD>
|
|
</TR>
|
|
<TR><TD ALIGN="LEFT">``3c ints''</TD>
|
|
<TD ALIGN="LEFT">debug</TD>
|
|
<TD ALIGN="LEFT">MO 3-center integrals</TD>
|
|
</TR>
|
|
<TR><TD ALIGN="LEFT">``4c ints b''</TD>
|
|
<TD ALIGN="LEFT">debug</TD>
|
|
<TD ALIGN="LEFT">``B'' matrix with approx. 4c integrals</TD>
|
|
</TR>
|
|
<TR><TD ALIGN="LEFT">``4c ints''</TD>
|
|
<TD ALIGN="LEFT">debug</TD>
|
|
<TD ALIGN="LEFT">Approximate 4-center integrals</TD>
|
|
</TR>
|
|
<TR><TD ALIGN="LEFT">``amplitudes''</TD>
|
|
<TD ALIGN="LEFT">debug</TD>
|
|
<TD ALIGN="LEFT">``B'' matrix with denominators</TD>
|
|
</TR>
|
|
<TR><TD ALIGN="LEFT">``basis''</TD>
|
|
<TD ALIGN="LEFT">high</TD>
|
|
<TD ALIGN="LEFT"> </TD>
|
|
</TR>
|
|
<TR><TD ALIGN="LEFT">``fit xf''</TD>
|
|
<TD ALIGN="LEFT">debug</TD>
|
|
<TD ALIGN="LEFT">Transformation for fitting basis</TD>
|
|
</TR>
|
|
<TR><TD ALIGN="LEFT">``geombas''</TD>
|
|
<TD ALIGN="LEFT">debug</TD>
|
|
<TD ALIGN="LEFT">Detailed basis map info</TD>
|
|
</TR>
|
|
<TR><TD ALIGN="LEFT">``geometry''</TD>
|
|
<TD ALIGN="LEFT">high</TD>
|
|
<TD ALIGN="LEFT"> </TD>
|
|
</TR>
|
|
<TR><TD ALIGN="LEFT">``information''</TD>
|
|
<TD ALIGN="LEFT">low</TD>
|
|
<TD ALIGN="LEFT">General information about calc.</TD>
|
|
</TR>
|
|
<TR><TD ALIGN="LEFT">``integral i/o''</TD>
|
|
<TD ALIGN="LEFT">high</TD>
|
|
<TD ALIGN="LEFT">File size information</TD>
|
|
</TR>
|
|
<TR><TD ALIGN="LEFT">``mo ints''</TD>
|
|
<TD ALIGN="LEFT">debug</TD>
|
|
<TD ALIGN="LEFT"> </TD>
|
|
</TR>
|
|
<TR><TD ALIGN="LEFT">``pair energies''</TD>
|
|
<TD ALIGN="LEFT">debug</TD>
|
|
<TD ALIGN="LEFT">(working only in direct_mp2)</TD>
|
|
</TR>
|
|
<TR><TD ALIGN="LEFT">``partial pair energies''</TD>
|
|
<TD ALIGN="LEFT">debug</TD>
|
|
<TD ALIGN="LEFT">Pair energy matrix each time it is updated</TD>
|
|
</TR>
|
|
<TR><TD ALIGN="LEFT">``progress reports''</TD>
|
|
<TD ALIGN="LEFT">default</TD>
|
|
<TD ALIGN="LEFT">Report completion of time-consuming steps</TD>
|
|
</TR>
|
|
<TR><TD ALIGN="LEFT">``reference''</TD>
|
|
<TD ALIGN="LEFT">high</TD>
|
|
<TD ALIGN="LEFT">Details about reference wavefunction</TD>
|
|
</TR>
|
|
<TR><TD ALIGN="LEFT">``warnings''</TD>
|
|
<TD ALIGN="LEFT">low</TD>
|
|
<TD ALIGN="LEFT">Non-fatal warnings</TD>
|
|
</TR>
|
|
</TABLE>
|
|
</DIV>
|
|
<BR>
|
|
|
|
<P>
|
|
|
|
<H1><A NAME="SECTION001850000000000000000"></A>
|
|
<A NAME="sec:mp2vectors"></A>
|
|
<BR>
|
|
16.5 <TT>VECTORS</TT> -- MO vectors
|
|
</H1>
|
|
|
|
<P>
|
|
All of the (supported) MP2 modules require use of converged canonical
|
|
SCF (RHF or UHF) orbitals for correct results. The vectors are by
|
|
default obtained from the preceding SCF calculation, but it is
|
|
possible to specify a different source using the <code>VECTORS</code>
|
|
directive. For instance, to obtain vectors from the file
|
|
<code>/tmp/h2o.movecs</code>, use the directive
|
|
<PRE>
|
|
vectors /tmp/h2o.movecs
|
|
</PRE>
|
|
|
|
<P>
|
|
As noted above (Section <A HREF="node18.html#mp2:core">16.1</A>) if the SCF orbitals are not in
|
|
the correct order, it is necessary to permute the input orbitals using
|
|
the <code>swap</code> keyword of the <code>VECTORS</code> directive. For
|
|
instance, if it is desired to freeze a total six orbitals
|
|
corresponding to the SCF orbitals 1-5, and 7, it is necessary to swap
|
|
orbital 7 into the 6th position. This is accomplished by
|
|
<PRE>
|
|
vectors swap 6 7
|
|
</PRE>
|
|
The swap capability is examined in more detail in Section
|
|
<A HREF="node12.html#sec:vectors">10.5</A>.
|
|
|
|
<P>
|
|
|
|
<H1><A NAME="SECTION001860000000000000000">
|
|
16.6 RI-MP2 fitting basis</A>
|
|
</H1>
|
|
|
|
<P>
|
|
|
|
<P>
|
|
The RI-MP2 method requires a fitting basis, which must be specified
|
|
with the name <code>"ri-mp2 basis"</code> (see Section <A HREF="node9.html#sec:basis">7</A>).
|
|
For instance,
|
|
<PRE>
|
|
basis "ri-mp2 basis"
|
|
O s; 10000.0 1
|
|
O s; 1000.0 1
|
|
O s; 100.0 1
|
|
...
|
|
end
|
|
</PRE>
|
|
|
|
<P>
|
|
Alternatively, using a standard capability of basis sets (Section
|
|
<A HREF="node9.html#sec:basis">7</A>) another named basis may be associated with the
|
|
fitting basis. For instance, the following input specifies a basis
|
|
with the name <code>"small fitting basis"</code> and then defines this to be
|
|
the <code>"ri-mp2 basis"</code>.
|
|
<PRE>
|
|
basis "small fitting basis"
|
|
H s; 10 1
|
|
H s; 3 1
|
|
H s; 1 1
|
|
H s; 0.1 1
|
|
H s; 0.01 1
|
|
end
|
|
|
|
set "ri-mp2 basis" "small fitting basis"
|
|
</PRE>
|
|
|
|
<P>
|
|
|
|
<P>
|
|
|
|
<H1><A NAME="SECTION001870000000000000000">
|
|
16.7 <TT>FILE3C</TT> -- RI-MP2 3-center integral filename</A>
|
|
</H1>
|
|
|
|
<P>
|
|
|
|
<P>
|
|
The default name for the file used to store the transformed 3-center
|
|
integrals is <code>"$file_prefix$.mo3cint"</code> in the scratch directory.
|
|
This may be overridden using the FILE3C directive. For instance, to
|
|
specify the file <code>/scratch/h2o.3c</code>, use this directive
|
|
<PRE>
|
|
file3c /scratch/h2o.3c
|
|
</PRE>
|
|
|
|
<P>
|
|
|
|
<P>
|
|
|
|
<H1><A NAME="SECTION001880000000000000000">
|
|
16.8 <TT>RIAPPROX</TT> -- RI-MP2 Approximation</A>
|
|
</H1>
|
|
|
|
<P>
|
|
The type of RI approximation used in the RI-MP2 calculation is controlled
|
|
by means of the RIAPPROX directive. The two possible values are
|
|
<code>V</code> and <code>SVS</code> (case sensitive), which correspond to the
|
|
approximations with the same names described in O. Vahtras, J Almlöf,
|
|
and M. W. Feyereisen, <EM>Chem. Phys. Lett.</EM> <B>213</B>, 514-518
|
|
(1993). The default is <code>V</code>.
|
|
|
|
<P>
|
|
|
|
<H1><A NAME="SECTION001890000000000000000">
|
|
16.9 Advanced options for RI-MP2</A>
|
|
</H1>
|
|
|
|
<P>
|
|
These options, which functioned at the time of writing, are not
|
|
currently supported.
|
|
|
|
<P>
|
|
|
|
<H2><A NAME="SECTION001891000000000000000">
|
|
16.9.1 Control of linear dependence</A>
|
|
</H2>
|
|
|
|
<P>
|
|
Construction of the RI fit requires the inversion of a matrix of
|
|
fitting basis integrals which is carried out via diagonalization. If
|
|
the fitting basis includes near linear dependencies, there will be
|
|
small eigenvalues which can ultimately lead to non-physical RI-MP2
|
|
correlation energies. Eigenvectors of the fitting matrix
|
|
are discarded if the corresponding eigenvalue is less than
|
|
<code>$mineval$</code> which defaults to <IMG
|
|
WIDTH="37" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
|
|
SRC="img99.gif"
|
|
ALT="$10^{-8}$">. This
|
|
parameter may be changed by setting the a parameter in the database.
|
|
For instance, to set it to <IMG
|
|
WIDTH="44" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
|
|
SRC="img100.gif"
|
|
ALT="$10^{-10}$">
|
|
|
|
<P>
|
|
<PRE>
|
|
set "mp2:fit min eval" 1e-10
|
|
</PRE>
|
|
|
|
<P>
|
|
|
|
<H2><A NAME="SECTION001892000000000000000">
|
|
16.9.2 Reference Spin Mapping for RI-MP2 Calculations</A>
|
|
</H2>
|
|
|
|
<P>
|
|
The user has the option of specifying that the RI-MP2 calculations are
|
|
to be done with variations of the SCF reference wavefunction. This is
|
|
accomplished with a <code>SET</code> directive of the form,
|
|
|
|
<P>
|
|
<PRE>
|
|
set "mp2:reference spin mapping" <integer array default 0>
|
|
</PRE>
|
|
|
|
<P>
|
|
Each element specified for <code>array</code> is the SCF spin case to be
|
|
used for the corresponding spin case of the correlated calculation.
|
|
The number of elements set determines the overall type of correlated
|
|
calculation to be performed. The default is to use the unadulterated
|
|
SCF reference wavefunction.
|
|
|
|
<P>
|
|
For example, to perform a spin-unrestricted calculation (two elements)
|
|
using the alpha spin orbitals (spin case 1) from the reference for
|
|
both of the correlated reference spin cases, the <code>SET</code> directive
|
|
would be as follows,
|
|
<PRE>
|
|
set "mp2:reference spin mapping" 1 1
|
|
</PRE>
|
|
The SCF calculation to produce the reference wavefunction could be either
|
|
RHF or UHF in this case.
|
|
|
|
<P>
|
|
The <code>SET</code> directive for a similar case, but this time using the
|
|
beta-spin SCF orbitals for both correlated spin cases, is as follows,
|
|
<PRE>
|
|
set "mp2:reference spin mapping" 2 2
|
|
</PRE>
|
|
The SCF reference calculation must be UHF in this case.
|
|
|
|
<P>
|
|
The <code>SET</code> directive for a spin-restricted calculation (one
|
|
element) from the beta-spin SCF orbitals using this option is as
|
|
follows,
|
|
<PRE>
|
|
set "mp2:reference spin mapping" 2
|
|
</PRE>
|
|
|
|
<P>
|
|
The <code>SET</code> directive for a spin-unrestricted calculation with the
|
|
spins flipped from the original SCF reference wavefunction is as
|
|
follows,
|
|
<PRE>
|
|
set "mp2:reference spin mapping" 2 1
|
|
</PRE>
|
|
|
|
<P>
|
|
|
|
<H2><A NAME="SECTION001893000000000000000">
|
|
16.9.3 Batch Sizes for the RI-MP2 Calculation</A>
|
|
</H2>
|
|
|
|
<P>
|
|
The user can control the size of each batch in the transformation and
|
|
energy evaluation in the MP2 calculation, and consequently the memory
|
|
requirements and number of passes required. This is done using two
|
|
<code>SET</code> directives of the following form,
|
|
|
|
<P>
|
|
<PRE>
|
|
set "mp2:transformation batch size" <integer size default -1>
|
|
set "mp2:energy batch size" <integer isize jsize default -1 -1>
|
|
</PRE>
|
|
|
|
<P>
|
|
The default is for the code to determine the batch size based on the
|
|
available memory. Should there be problems with the
|
|
program-determined batch sizes, these variables allow the user to
|
|
override them. The program will always use the smaller of the user's
|
|
value of these entries and the internally computed batch size.
|
|
|
|
<P>
|
|
The transformation batch size computed in the code is the number of
|
|
occupied orbitals in the <!-- MATH
|
|
$({occ}\ {vir} | {fit})$
|
|
-->
|
|
<IMG
|
|
WIDTH="90" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
|
|
SRC="img137.gif"
|
|
ALT="$({occ}\ {vir} \vert {fit})$"> three-center
|
|
integrals to be produced at a time. If this entry is less than the
|
|
number of occupied orbitals in the system, the transformation will
|
|
require multiple passes through the two-electron integrals. The
|
|
memory requirements of this stage are <EM>two</EM> global arrays of
|
|
dimension <!-- MATH
|
|
${<batch size>}\times {vir} \times {fit}$
|
|
-->
|
|
<IMG
|
|
WIDTH="184" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
|
|
SRC="img138.gif"
|
|
ALT="${<batch size>}\times {vir} \times {fit}$"> with the ``fit''
|
|
dimension distributed across all processors (on shell-block
|
|
boundaries). The compromise here is memory space versus multiple
|
|
integral evaluations.
|
|
|
|
<P>
|
|
The energy evaluation batch sizes are computed in the code from the
|
|
number of occupied orbitals in the two sets of three-center
|
|
integrals to be multiplied together to produce a matrix of approximate
|
|
four-center integrals. Two blocks of integrals of dimension <!-- MATH
|
|
$({<batch
|
|
isize>}\times {vir})$
|
|
-->
|
|
<IMG
|
|
WIDTH="162" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
|
|
SRC="img139.gif"
|
|
ALT="$({<batch
|
|
isize>}\times {vir})$"> and <!-- MATH
|
|
$({<batch jsize>}\times {vir})$
|
|
-->
|
|
<IMG
|
|
WIDTH="164" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
|
|
SRC="img140.gif"
|
|
ALT="$({<batch jsize>}\times {vir})$"> by fit are
|
|
read in from disk and multiplied together to produce <!-- MATH
|
|
$<batch isize>
|
|
<batch jsize> {vir}^2$
|
|
-->
|
|
<IMG
|
|
WIDTH="248" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
|
|
SRC="img141.gif"
|
|
ALT="$<batch isize>
|
|
<batch jsize> {vir}^2$"> approximate integrals. The compromise here is
|
|
performance of the distributed matrix multiplication (which requires
|
|
large matrices) versus memory space.
|
|
|
|
<P>
|
|
|
|
<H2><A NAME="SECTION001894000000000000000">
|
|
16.9.4 Energy Memory Allocation Mode: RI-MP2 Calculation</A>
|
|
</H2>
|
|
|
|
<P>
|
|
The user must choose a strategy for the memory allocation in the energy
|
|
evaluation phase of the RI-MP2 calculation, either by minimizing the amount
|
|
of I/O, or minimizing the amount of computation. This can be accomplished
|
|
using a <code>SET</code> directive of the form,
|
|
|
|
<P>
|
|
<PRE>
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|
set "mp2:energy mem minimize" <string mem_opt default I>
|
|
</PRE>
|
|
|
|
<P>
|
|
A value of <code>I</code> entered for the string <code>mem_opt</code> means that a
|
|
strategy to minimize I/O will be employed. A value of <code>C</code> tells
|
|
the code to use a strategy that minimizes computation.
|
|
|
|
<P>
|
|
When the option to minimize I/O is selected, the block sizes are made
|
|
as large as possible so that the total number of passes through the
|
|
integral files is as small as possible. When the option to minimize
|
|
computation is selected, the blocks are chosen as close to square as
|
|
possible so that permutational symmetry in the energy evaluation can
|
|
be used most effectively.
|
|
|
|
<P>
|
|
|
|
<H2><A NAME="SECTION001895000000000000000">
|
|
16.9.5 Local Memory Usage in Three-Center Transformation</A>
|
|
</H2>
|
|
|
|
<P>
|
|
For most applications, the code will be able to size the blocks
|
|
without help from the user. Therefore, it is unlikely that users will
|
|
have any reason to specify values for these entries except when doing
|
|
very particular performance measurements.
|
|
|
|
<P>
|
|
The size of <code>xf3ci:AO 1 batch size</code> is the most important of the
|
|
three, in terms of the effect on performance.
|
|
|
|
<P>
|
|
Local memory usage in the first two steps of the transformation is
|
|
controlled in the RI-MP2 calculation using the following <code>SET</code>
|
|
directives,
|
|
|
|
<P>
|
|
<PRE>
|
|
set "xf3ci:AO 1 batch size" <integer max>
|
|
set "xf3ci:AO 2 batch size" <integer max>
|
|
set "xf3ci:fit batch size" <integer max>
|
|
</PRE>
|
|
|
|
<P>
|
|
The size of the local arrays determines the sizes of the two matrix
|
|
multiplications. These entries set limits on the size of blocks to be
|
|
used in each index. The listing above is in order of importance of
|
|
the parameters to performance, with <code>xf3ci:AO 1 batch size</code> being
|
|
most important.
|
|
|
|
<P>
|
|
Note that these entries are only upper bounds and that the program
|
|
will size the blocks according to what it determines as the best usage of
|
|
the available local memory. The absolute maximum for a block size is
|
|
the number of functions in the AO basis, or the number of fitting basis
|
|
functions on a node. The absolute minimum value for block size is the
|
|
size of the largest shell in the appropriate basis. Batch size entries
|
|
specified for <code>max</code> that are larger than these limits are
|
|
automatically reset to an appropriate value.
|
|
|
|
<P>
|
|
|
|
<H1><A NAME="SECTION0018100000000000000000">
|
|
16.10 One-electron properties and natural orbitals</A>
|
|
</H1>
|
|
|
|
<P>
|
|
If an MP2 energy gradient is computed, all contributions are available
|
|
to form the MP2 linear-response density. This is the density that
|
|
when contracted with any spin-free, one-electron operator yields the
|
|
associated property defined as the derivative of the energy. Thus,
|
|
the reported MP2 dipole moment is the derivative of the energy
|
|
w.r.t. an external magnetic field and is <EM>not</EM> the expectation
|
|
value of the operator over the wavefunction. Only dipole moments are
|
|
printed by the MP2 gradient code, but natural orbitals are produced
|
|
and stored in the permanent directory with a file extension of
|
|
<code>".mp2nos"</code>. These may be fed into the property package (see
|
|
Section <A HREF="node30.html#sec:property">28</A>) to compute more general properties. Note
|
|
that the MP2 linear response density matrix is not necessarily
|
|
positive definite so it is not unusual to see a few small negative
|
|
natural orbital occupation numbers.
|
|
|
|
<P>
|
|
|
|
<P>
|
|
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<ADDRESS>
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Edoardo Apra
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2004-05-25
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