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<TITLE>15. Tensor Contraction Engine Module: CI, MBPT, and CC</TITLE>
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<B> Next:</B> <A NAME="tex2html1273"
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HREF="node18.html">16. MP2</A>
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HREF="user.html">user</A>
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<B> Previous:</B> <A NAME="tex2html1263"
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HREF="node16.html">14. CIS, TDHF, and</A>
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  <B> <A NAME="tex2html1271"
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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="tex2html1274"
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HREF="node17.html#SECTION001710000000000000000">15.1 Overview</A>
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<LI><A NAME="tex2html1275"
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HREF="node17.html#SECTION001720000000000000000">15.2 Performance of CI, MBPT, and CC methods</A>
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<LI><A NAME="tex2html1276"
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HREF="node17.html#SECTION001730000000000000000">15.3 Algorithms of CI, MBPT, and CC methods</A>
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<UL>
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<LI><A NAME="tex2html1277"
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HREF="node17.html#SECTION001731000000000000000">15.3.1 Spin, spatial, and index permutation symmetry</A>
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<LI><A NAME="tex2html1278"
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HREF="node17.html#SECTION001732000000000000000">15.3.2 Runtime orbital range tiling</A>
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<LI><A NAME="tex2html1279"
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HREF="node17.html#SECTION001733000000000000000">15.3.3 Dynamic load balancing parallelism</A>
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<LI><A NAME="tex2html1280"
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HREF="node17.html#SECTION001734000000000000000">15.3.4 Parallel I/O schemes</A>
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</UL>
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<BR>
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<LI><A NAME="tex2html1281"
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HREF="node17.html#SECTION001740000000000000000">15.4 Input syntax</A>
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<LI><A NAME="tex2html1282"
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HREF="node17.html#SECTION001750000000000000000">15.5 Keywords of <TT>TCE</TT> input block</A>
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<UL>
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<LI><A NAME="tex2html1283"
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HREF="node17.html#SECTION001751000000000000000">15.5.1 <TT>HF</TT>, <TT>SCF</TT>, or <TT>DFT</TT> -- the reference wave function</A>
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<LI><A NAME="tex2html1284"
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HREF="node17.html#SECTION001752000000000000000">15.5.2 <TT>CCSD</TT>,<TT>CCSDT</TT>,<TT>CCSDTQ</TT>,<TT>CISD</TT>,<TT>CISDT</TT>,<TT>CISDTQ</TT>,
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<TT>MBPT2</TT>,<TT>MBPT3</TT>,<TT>MBPT4</TT>, etc.
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-- the correlation model</A>
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<LI><A NAME="tex2html1285"
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HREF="node17.html#SECTION001753000000000000000">15.5.3 <TT>THRESH</TT> -- the convergence threshold of iterative solutions of amplitude equations</A>
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<LI><A NAME="tex2html1286"
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HREF="node17.html#SECTION001754000000000000000">15.5.4 <TT>MAXITER</TT> -- the maximum number of iterations</A>
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<LI><A NAME="tex2html1287"
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HREF="node17.html#SECTION001755000000000000000">15.5.5 <TT>IO</TT> -- parallel I/O scheme</A>
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<LI><A NAME="tex2html1288"
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HREF="node17.html#SECTION001756000000000000000">15.5.6 <TT>DIIS</TT> -- the convergence acceleration</A>
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<LI><A NAME="tex2html1289"
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HREF="node17.html#SECTION001757000000000000000">15.5.7 <TT>FREEZE</TT> -- the frozen core/virtual approximation</A>
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<LI><A NAME="tex2html1290"
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HREF="node17.html#SECTION001758000000000000000">15.5.8 <TT>NROOTS</TT> -- the number of excited states</A>
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<LI><A NAME="tex2html1291"
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HREF="node17.html#SECTION001759000000000000000">15.5.9 <TT>TARGET</TT> and <TT>TARGETSYM</TT> -- the target root and its symmetry</A>
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<LI><A NAME="tex2html1292"
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HREF="node17.html#SECTION0017510000000000000000">15.5.10 <TT>SYMMETRY</TT> -- restricting the excited state symmetry</A>
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<LI><A NAME="tex2html1293"
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HREF="node17.html#SECTION0017511000000000000000">15.5.11 <TT>DIPOLE</TT> -- the ground- and excited-state dipole moments</A>
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<LI><A NAME="tex2html1294"
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HREF="node17.html#SECTION0017512000000000000000">15.5.12 <TT>(NO)FOCK</TT> -- (not) recompute Fock matrix</A>
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<LI><A NAME="tex2html1295"
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HREF="node17.html#SECTION0017513000000000000000">15.5.13 <TT>PRINT</TT> -- the verbosity</A>
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</UL>
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<BR>
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<LI><A NAME="tex2html1296"
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HREF="node17.html#SECTION001760000000000000000">15.6 Sample input</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="SECTION001700000000000000000">
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15. Tensor Contraction Engine Module: CI, MBPT, and CC</A>
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</H1>
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<A NAME="sec:tce"></A>
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<P>
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<H1><A NAME="SECTION001710000000000000000">
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15.1 Overview</A>
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</H1>
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<P>
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The Tensor Contraction Engine (TCE) Module of NWChem implements
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a variety of approximations that converge at the exact solutions
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of Schrödinger equation. They include configuration interaction theory
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through singles, doubles, triples, and quadruples substitutions,
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coupled-cluster theory through connected singles, doubles, triples, and quadruples substitutions,
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and many-body perturbation theory through fourth order in its
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tensor formulation. Not only optimized parallel programs of some
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of these high-end correlation theories are new, but also the way in
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which they have been developed is unique. The working equations
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of all of these methods have been derived completely automatically by
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a symbolic manipulation program called a Tensor Contraction Engine (TCE),
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and the optimized parallel programs have also been computer-generated by the same program,
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which were interfaced to NWChem. The development of the TCE
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program and this portion of the NWChem program has been financially
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supported by the United States Department of Energy, Office of Science,
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Office of Basic Energy Science, through the SciDAC program.
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<P>
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The capabilities of the module include:
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<UL>
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<LI>Restricted Hartree-Fock, unrestricted Hartree-Fock, and restricted open-shell
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Hartree-Fock references,
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</LI>
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<LI>Restricted KS DFT and unrestricted KS DFT references,
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</LI>
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<LI>Unrestricted configuration interaction theory (CISD, CISDT, and CISDTQ),
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</LI>
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<LI>Unrestricted coupled-cluster theory (LCCD, CCD, LCCSD, CCSD, QCISD, CCSDT, CCSDTQ),
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</LI>
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<LI>Unrestricted iterative many-body perturbation theory [MBPT(2), MBPT(3), MBPT(4)] in its tensor formulation,
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</LI>
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</UL>
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New capabilities added in the version 4.6 are:
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<UL>
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<LI>Unrestricted coupled-cluster singles and doubles with perturbative connected triples {CCSD(T), CCSD[T]},
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</LI>
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<LI>Unrestricted equation-of-motion coupled-cluster theory (EOM-CCSD, EOM-CCSDT, EOM-CCSDTQ) for excitation energies, transition moments and oscillator strengths, and excited-state dipole moments,
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</LI>
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<LI>Unrestricted coupled-cluster theory (CCSD, CCSDT, CCSDTQ) for dipole moments.
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</LI>
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</UL>
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Version 4.6 and onwards the distributed binary executables do not contain CCSDTQ and its
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derivative methods, owing to their large volume. The source code includes them, so a user
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can reinstate them by <code>setenv CCSDTQ yes</code> and recompile TCE module.
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The following optimizations have been used in the module:
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<UL>
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<LI>Spin symmetry (spin integration is performed wherever possible within the
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unrestricted framework, making the present unrestricted program
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optimal for an open-shell system. The spin adaption was not performed,
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although in a restricted calculation for a closed-shell system, certain spin blocks of
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integrals and amplitudes are further omitted by symmetry, and
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consequently, the present unrestricted CCSD requires only twice
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as many operations as a spin-adapted restricted CCSD for a closed-shell system),
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</LI>
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<LI>Point-group symmetry,
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</LI>
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<LI>Index permutation symmetry,
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</LI>
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<LI>Runtime orbital range tiling for memory management,
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</LI>
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<LI>Dynamic load balancing (local index sort and matrix multiplications) parallelism,
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</LI>
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<LI>Multiple parallel I/O schemes including fully incore algorithm using Global Arrays,
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</LI>
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<LI>Frozen core and virtual approximation.
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</LI>
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<LI>DIIS extrapolation and Jacobi update of excitation amplitudes
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</LI>
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</UL>
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<P>
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This extensible module is designed such that an existing or new model of many-electron
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theory can be added and further optimization can be incorporated with ease
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by virtue of the TCE.
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This module is still being
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actively enhanced by the TCE and we hope to include more models and optimizations
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in future releases!
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<P>
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|
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<H1><A NAME="SECTION001720000000000000000">
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15.2 Performance of CI, MBPT, and CC methods</A>
|
|
</H1>
|
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|
|
<P>
|
|
For reviews or tutorials of these highly-accurate correlation methods, the user is
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referred to:
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|
|
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<UL>
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|
<LI>A. Szabo and N. S. Ostlund, Modern Quantum Chemistry: Introduction to Advanced Electronic Structure Theory,
|
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</LI>
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|
<LI>R. J. Bartlett and J. F. Stanton, Applications of Post-Hartree-Fock Methods: A Tutorial, in Reviews in Computational Chemistry, Volume V,
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</LI>
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|
<LI>R. J. Bartlett, Coupled-Cluster Theory: An Overview of Recent Developments, in Modern Electronic Structure Theory, Part II,
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</LI>
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<LI>B. O. Roos (editor), Lecture Notes in Quantum Chemistry I and II.
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</LI>
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</UL>
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<P>
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For algorithms and applications of TCE, see:
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|
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<UL>
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<LI>S. Hirata, J. Phys. Chem. A <B>107,</B> 9887 (2003).
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</LI>
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|
<LI>S. Hirata, T. Yanai, W. A. de Jong, T. Nakajima, and K. Hirao, J. Chem. Phys. <B>120,</B> 3297 (2004).
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</LI>
|
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<LI>S. Hirata, J. Chem. Phys. (in press) (2004).
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</LI>
|
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</UL>
|
|
|
|
<P>
|
|
|
|
<H1><A NAME="SECTION001730000000000000000">
|
|
15.3 Algorithms of CI, MBPT, and CC methods</A>
|
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</H1>
|
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|
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<P>
|
|
|
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<H2><A NAME="SECTION001731000000000000000">
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15.3.1 Spin, spatial, and index permutation symmetry</A>
|
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</H2>
|
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|
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<P>
|
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The TCE thoroughly analyzes the working equation of many-electron theory models and
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automatically generates a program that takes full advantage of these symmetries at the same time.
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To do so, the TCE first recognizes the index permutation symmetries among the working equations,
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and perform strength reduction and factorization by carefully monitoring the index permutation
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symmetries of intermediate tensors. Accordingly, every input and output tensor (such as
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integrals, excitation amplitudes, residuals) has just two independent but strictly ordered index strings,
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and each intermediate tensor has just four independent but strictly ordered index strings.
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The operation cost and storage size of tensor contraction is minimized by using the index range
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restriction arising from these
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index permutation symmetries and also spin and spatial symmetry integration.
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|
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<P>
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<H2><A NAME="SECTION001732000000000000000">
|
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15.3.2 Runtime orbital range tiling</A>
|
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</H2>
|
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|
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<P>
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To maintain the peak local memory usage at a manageable level, in the beginning of the calculation,
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the orbitals are rearranged into tiles (blocks) that contains orbitals with the same spin and spatial
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symmetries. So the tensor contractions in these methods are carried out at the tile level; the spin,
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spatial, and index permutation symmetry is employed to reduce the operation and storage cost at the tile
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level also.
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<P>
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<H2><A NAME="SECTION001733000000000000000">
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15.3.3 Dynamic load balancing parallelism</A>
|
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</H2>
|
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|
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<P>
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In a parallel execution, dynamic load balancing of tile-level local tensor index sorting and local
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tensor contraction (matrix multiplication) will be invoked.
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<P>
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<H2><A NAME="SECTION001734000000000000000">
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15.3.4 Parallel I/O schemes</A>
|
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</H2>
|
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|
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<P>
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Each process is assigned a local tensor index sorting and tensor contraction dynamically. It must first
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retrieve the tiles of input tensors, and perform these local operations, and accumulate the output
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tensors to the storage. We have developed a uniform interface for these I/O operations to either
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(1) a global file on a global file system, (2) a global memory on a global or distributed memory system,
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and (3) semi-replicated files on a distributed file systems. Some of these operations depend on
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the ParSoft library.
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<P>
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<H1><A NAME="SECTION001740000000000000000"></A>
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<A NAME="sec:inputsyntax"></A>
|
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<BR>
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15.4 Input syntax
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</H1>
|
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<P>
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The keyword to invoke the many-electron theories in the module is
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<code>TCE</code>. To perform a single-point energy calculation, include
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<PRE>
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TASK TCE ENERGY
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</PRE>
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in the input file, which may be preceeded by the TCE input block
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that details the calculations:
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<PRE>
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TCE
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[(DFT||HF||SCF) default HF=SCF]
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[FREEZE [[core] (atomic || <integer nfzc default 0>)] \
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[virtual <integer nfzv default 0>]]
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[(LCCD||CCD||CCSD||LCCSD||CCSDT||CCSDTQ|| \
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CCSD(T)||CCSD[T]||QCISD||CISD||CISDT||CISDTQ|| \
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MBPT2||MBPT3||MBPT4||MP2||MP3||MP4) default CCSD]
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[THRESH <double thresh default 1e-6>]
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[MAXITER <integer maxiter default 100>]
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[PRINT (none||low||medium||high||debug)
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<string list_of_names ...>]
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[IO (fortran||eaf||ga||sf||replicated||dra||ga_eaf) default ga]
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[DIIS <integer diis default 5>]
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[NROOTS <integer nroots default 0>]
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[TARGET <integer target default 1>]
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[TARGETSYM <character targetsym default 'none'>]
|
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[SYMMETRY]
|
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[DIPOLE]
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[TILESIZE <no default (automatically adjusted)>]
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[(NO)FOCK <logical recompf default .true.>]
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[FRAGMENT <default -1 (off)>]
|
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END
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</PRE>
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Also supported are energy gradient calculation, geometry optimization,
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and vibrational frequency (or hessian) calculation, on the basis of
|
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numerical differentiation. To perform these calculations, use
|
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<PRE>
|
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TASK TCE GRADIENT
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</PRE>
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or
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<PRE>
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TASK TCE OPTIMIZE
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</PRE>
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or
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<PRE>
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TASK TCE FREQUENCIES
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</PRE>
|
|
|
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<P>
|
|
Alternatively, more descriptive keywords for each individual method can be used.
|
|
For instance, to perform a CCSDT energy, gradient, etc. calculation, use
|
|
<PRE>
|
|
TASK UCCSDT ENERGY
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</PRE>
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or
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<PRE>
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TASK UCCSDT GRADIENT
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</PRE>
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or
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<PRE>
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TASK UCCSDT OPTIMIZE
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</PRE>
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or
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|
<PRE>
|
|
TASK UCCSDT FREQUENCIES
|
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</PRE>
|
|
with an (optional) input block enclosed either by <code>UCCSDT</code> and <code>END</code> or
|
|
by <code>UCC</code> and <code>END</code>. The keywords for individual methods of TCE module
|
|
always start with letter <code>U</code> which stands for ``unrestricted'' to avoid
|
|
confusion with other related methods (such as spin-restricted CCSD and various
|
|
canonical MP2 implementation) already in place in NWChem.
|
|
<PRE>
|
|
(UCCSDT||UCC)
|
|
[(DFT||HF||SCF) default HF=SCF]
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[FREEZE [[core] (atomic || <integer nfzc default 0>)] \
|
|
[virtual <integer nfzv default 0>]]
|
|
[THRESH <double thresh default 1e-6>]
|
|
[MAXITER <integer maxiter default 100>]
|
|
[PRINT (none||low||medium||high||debug)]
|
|
<string list_of_names ...>]
|
|
[IO (fortran||eaf||ga||sf||replicated||dra||ga_eaf) default ga]
|
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[DIIS <integer diis default 5>]
|
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[NROOTS <integer nroots default 0>]
|
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[TARGET <integer target default 1>]
|
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[TARGETSYM <character targetsym default 'none'>]
|
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[SYMMETRY]
|
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[DIPOLE]
|
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[TILESIZE <no default (automatically adjusted)>]
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[(NO)FOCK <logical recompf default .true.>]
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[FRAGMENT <default -1 (off)>]
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END
|
|
</PRE>
|
|
When a method (CCSDT in this example) is specified in the task directive,
|
|
a duplicate method specification
|
|
is not necessary (indeed not allowed) in the corresponding (<code>UCCSDT</code> or <code>UCC</code> in this case)
|
|
input block. The keywords of the other methods for task directive are:
|
|
<PRE>
|
|
TASK (UCCD||ULCCD||UCCSD||ULCCSD||UQCISD||UCCSDT||UCCSDTQ) ENERGY
|
|
</PRE>
|
|
or
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|
<PRE>
|
|
TASK (UCISD||UCISDT||UCISDTQ) ENERGY
|
|
</PRE>
|
|
or
|
|
<PRE>
|
|
TASK (UMP2||UMP3||UMP4||UMBPT2||UMBPT3||UMBPT4) ENERGY
|
|
</PRE>
|
|
etc. The input block can be specified by the same name (<code>UCISDT</code> and <code>END</code>
|
|
block for <code>TASK UCISDT ENERGY</code>) or <code>UCC</code> for the CC family, <code>UCI</code> for
|
|
the CI family, and <code>UMP</code> or <code>UMBPT</code> for the MP family of methods.
|
|
|
|
<P>
|
|
The user may also specify the parameters of reference wave function calculation
|
|
in a separate block for either HF (SCF) or DFT, depending on the first keyword
|
|
in the above syntax.
|
|
|
|
<P>
|
|
Since each keyword has a default value, a minimal input file will be
|
|
<PRE>
|
|
GEOMETRY
|
|
Be 0.0 0.0 0.0
|
|
END
|
|
|
|
BASIS
|
|
Be library cc-pVDZ
|
|
END
|
|
|
|
TASK TCE ENERGY
|
|
</PRE>
|
|
which performs a CCSD/cc-pVDZ calculation of the Be atom in its
|
|
singlet ground state with a spin-restricted HF reference.
|
|
|
|
<P>
|
|
|
|
<H1><A NAME="SECTION001750000000000000000">
|
|
15.5 Keywords of <TT>TCE</TT> input block</A>
|
|
</H1>
|
|
|
|
<P>
|
|
|
|
<H2><A NAME="SECTION001751000000000000000">
|
|
15.5.1 <TT>HF</TT>, <TT>SCF</TT>, or <TT>DFT</TT> -- the reference wave function</A>
|
|
</H2>
|
|
|
|
<P>
|
|
This keyword tells the module
|
|
which of the HF (SCF) or DFT module is going to be used for the calculation
|
|
of a reference wave function. The keyword <code>HF</code> and <code>SCF</code> are
|
|
one and the same keyword internally, and are default. When these are used,
|
|
the details of the HF (SCF) calculation can be specified in the SCF input
|
|
block, whereas if <code>DFT</code> is chosen, DFT input block may be provided.
|
|
|
|
<P>
|
|
For instance, RHF-RCCSDT calculation (R standing for spin-restricted)
|
|
can be performed with the following input blocks:
|
|
<PRE>
|
|
SCF
|
|
SINGLET
|
|
RHF
|
|
END
|
|
|
|
TCE
|
|
SCF
|
|
CCSDT
|
|
END
|
|
|
|
TASK TCE ENERGY
|
|
</PRE>
|
|
or
|
|
<PRE>
|
|
SCF
|
|
SINGLET
|
|
RHF
|
|
END
|
|
|
|
UCCSDT
|
|
SCF
|
|
END
|
|
|
|
TASK UCCSDT ENERGY
|
|
</PRE>
|
|
or
|
|
<PRE>
|
|
SCF
|
|
SINGLET
|
|
RHF
|
|
END
|
|
|
|
UCC
|
|
SCF
|
|
END
|
|
|
|
TASK UCCSDT ENERGY
|
|
</PRE>
|
|
This calculation (and any correlation calculation in the TCE module using a RHF or RDFT
|
|
reference for a closed-shell system) skips the storage and computation of all <IMG
|
|
WIDTH="14" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
|
|
SRC="img49.gif"
|
|
ALT="$\beta$"> spin
|
|
blocks of integrals and excitation amplitudes. ROHF-UCCSDT (U standing for spin-unrestricted)
|
|
for an open-shell doublet system can be requested by
|
|
<PRE>
|
|
SCF
|
|
DOUBLET
|
|
ROHF
|
|
END
|
|
|
|
TCE
|
|
SCF
|
|
CCSDT
|
|
END
|
|
|
|
TASK TCE ENERGY
|
|
</PRE>
|
|
and likewise, UHF-UCCSDT for an open-shell doublet system can be specified with
|
|
<PRE>
|
|
SCF
|
|
DOUBLET
|
|
UHF
|
|
END
|
|
|
|
TCE
|
|
SCF
|
|
CCSDT
|
|
END
|
|
|
|
TASK TCE ENERGY
|
|
</PRE>
|
|
The operation and storage costs of the last two calculations are identical. To use the
|
|
KS DFT reference wave function for a UCCSD calculation of an open-shell doublet system,
|
|
<PRE>
|
|
DFT
|
|
ODFT
|
|
MULT 2
|
|
END
|
|
|
|
TCE
|
|
DFT
|
|
CCSD
|
|
END
|
|
|
|
TASK TCE ENERGY
|
|
</PRE>
|
|
Note that the default model of the DFT module is LDA.
|
|
|
|
<P>
|
|
|
|
<H2><A NAME="SECTION001752000000000000000">
|
|
15.5.2 <TT>CCSD</TT>,<TT>CCSDT</TT>,<TT>CCSDTQ</TT>,<TT>CISD</TT>,<TT>CISDT</TT>,<TT>CISDTQ</TT>,
|
|
<TT>MBPT2</TT>,<TT>MBPT3</TT>,<TT>MBPT4</TT>, etc.
|
|
-- the correlation model</A>
|
|
</H2>
|
|
|
|
<P>
|
|
These keywords stand for the following models:
|
|
|
|
<UL>
|
|
<LI>LCCD: linearized coupled-cluster doubles,
|
|
</LI>
|
|
<LI>CCD: coupled-cluster doubles,
|
|
</LI>
|
|
<LI>LCCSD: linearized coupled-cluster singles & doubles,
|
|
</LI>
|
|
<LI>CCSD: coupled-cluster singles & doubles (also EOM-CCSD),
|
|
</LI>
|
|
<LI>CCSDT: coupled-cluster singles, doubles, & triples (also EOM-CCSDT),
|
|
</LI>
|
|
<LI>CCSDTQ: coupled-cluster singles, doubles, triples, & quadruples (also EOM-CCSDTQ),
|
|
</LI>
|
|
<LI>CCSD(T): CCSD and perturbative connected triples,
|
|
</LI>
|
|
<LI>CCSD[T]: CCSD and perturbative connected triples,
|
|
</LI>
|
|
<LI>QCISD: quadratic configuration interaction singles & doubles,
|
|
</LI>
|
|
<LI>CISD: configuration interaction singles & doubles,
|
|
</LI>
|
|
<LI>CISDT: configuration interaction singles, doubles, & triples,
|
|
</LI>
|
|
<LI>CISDTQ: configuration interaction singles, doubles, triples, & quadruples,
|
|
</LI>
|
|
<LI>MBPT2=MP2: iterative tensor second-order many-body or Møller-Plesset perturbation theory,
|
|
</LI>
|
|
<LI>MBPT3=MP3: iterative tensor third-order many-body or Møller-Plesset perturbation theory,
|
|
</LI>
|
|
<LI>MBPT4=MP4: iterative tensor fourth-order many-body or Møller-Plesset perturbation theory,
|
|
</LI>
|
|
</UL>
|
|
|
|
<P>
|
|
All of these models are based on spin-orbital expressions of the amplitude and energy equations,
|
|
and designed primarily for spin-unrestricted reference wave functions. However, for a restricted
|
|
reference wave function of a closed-shell system, some further reduction of operation and storage
|
|
cost will be made. Within the unrestricted framework, all these methods take full advantage
|
|
of spin, spatial, and index permutation symmetries to save operation and storage costs at every
|
|
stage of the calculation. Consequently, these computer-generated programs will perform significantly
|
|
faster than, for instance, a hand-written spin-adapted CCSD program in NWChem, although the nominal
|
|
operation cost for a spin-adapted CCSD is just one half of that for spin-unrestricted CCSD (in spin-unrestricted
|
|
CCSD there are three independent sets of excitation amplitudes, whereas in spin-adapted CCSD there
|
|
is only one set, so the nominal operation cost for the latter is one third of that of the former. For
|
|
a restricted reference wave function of a closed-shell system, all <IMG
|
|
WIDTH="14" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
|
|
SRC="img49.gif"
|
|
ALT="$\beta$"> spin block of the excitation
|
|
amplitudes and integrals can be trivially mapped to the all <IMG
|
|
WIDTH="14" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
|
|
SRC="img42.gif"
|
|
ALT="$\alpha$"> spin block, reducing the ratio
|
|
to one half).
|
|
|
|
<P>
|
|
While the MBPT (MP) models implemented in the TCE module give identical correlation energies as
|
|
conventional implementation for a canonical HF reference of a closed-shell system, the former are intrinsically
|
|
more general and theoretically robust for other less standard reference wave functions and open-shell systems.
|
|
This is because the zeroth order of Hamiltonian is chosen to be the full Fock operatior (not just the diagonal
|
|
part), and no further approximation was invoked. So unlike the conventional implementation where the Fock
|
|
matrix is assumed to be diagonal and a correlation energy is evaluated in a single analytical formula that involves
|
|
orbital energies (or diagonal Fock matrix elements), the present tensor MBPT requires the iterative solution
|
|
of amplitude equations and subsequent energy evaluation and is generally more expensive than the former.
|
|
For example, the operation cost of many conventional implementation of MBPT(2) scales as the fourth power
|
|
of the system size, but the cost of the present tensor MBPT(2) scales as the fifth power of the system size,
|
|
as the latter permits non-canonical HF reference and the former does not (to reinstate the non-canonical HF
|
|
reference in the former makes it also scale as the fifth power of the system size).
|
|
|
|
<H2><A NAME="SECTION001753000000000000000">
|
|
15.5.3 <TT>THRESH</TT> -- the convergence threshold of iterative solutions of amplitude equations</A>
|
|
</H2>
|
|
|
|
<P>
|
|
This keyword specifies the convergence threshold of iterative solutions of amplitude equations,
|
|
and applies to all of the CI, CC, and MBPT models.
|
|
The threshold refers to the norm of residual,
|
|
namely, the deviation from the amplitude equations.
|
|
The default value is <code>1e-6</code>.
|
|
|
|
<P>
|
|
|
|
<H2><A NAME="SECTION001754000000000000000">
|
|
15.5.4 <TT>MAXITER</TT> -- the maximum number of iterations</A>
|
|
</H2>
|
|
|
|
<P>
|
|
It sets the maximum allowed number iterations for the iterative solutions of amplitude equations.
|
|
The default value is <code>100</code>.
|
|
|
|
<P>
|
|
|
|
<H2><A NAME="SECTION001755000000000000000">
|
|
15.5.5 <TT>IO</TT> -- parallel I/O scheme</A>
|
|
</H2>
|
|
|
|
<P>
|
|
There are five parallel I/O schemes implemented for all the models, which need to be
|
|
wisely chosen for a particular problem and computer architecture.
|
|
|
|
<UL>
|
|
<LI><code>fortran</code> : Fortran77 direct access,
|
|
</LI>
|
|
<LI><code>eaf</code> : Exclusive Access File library,
|
|
</LI>
|
|
<LI><code>ga</code> : Fully incore, Global Array virtual file,
|
|
</LI>
|
|
<LI><code>sf</code> : Shared File library,
|
|
</LI>
|
|
<LI><code>replicated</code> : Semi-replicated file on distributed file system with EAF library.
|
|
</LI>
|
|
<LI><code>dra</code> : Distributed file on distributed file system with DRA library.
|
|
</LI>
|
|
<LI><code>ga_eaf</code> : Semi-replicated file on distributed file system with EAF library. GA is used
|
|
to speedup the file reconciliation.
|
|
</LI>
|
|
</UL>
|
|
The GA algorithm, which is default, stores all input (integrals and
|
|
excitation amplitudes), output (residuals), and intermediate tensors in the shared memory area
|
|
across all nodes by virtue of GA library. This fully incore algorithm replaces disk I/O by
|
|
inter-process communications. This is a recommended algorithm whenever feasible. Note that
|
|
the memory management through runtime orbital range tiling described above applies to local
|
|
(unshared) memory of each node, which may be separately allocated from the shared memory space
|
|
for GA. So when there is not enough shared memory space (either physically or due to software
|
|
limitations, in particular, shmmax setting), the GA algorithm can crash due to an out-of-memory error.
|
|
The replicated scheme is the currently the only disk-based algorithm for a genuinely distributed
|
|
file system. This means that each node keeps an identical copy of input tensors and
|
|
it holds non-identical overlapping segments of intermediate and output tensors in its local disk.
|
|
Whenever data coherency is required, a file reconcilation process will take place to make the intermediate
|
|
and output data identical throughout the nodes. This algorithm, while requiring redundant data space on
|
|
local disk, performs reasonably efficiently in parallel. For sequential execution, this reduces
|
|
to the EAF scheme. For a global file system, the SF scheme is recommended. This together with
|
|
the Fortran77 direct access scheme does not usually exhibit scalability unless shared files on
|
|
the global file system also share the same I/O buffer. For sequential executions, the
|
|
SF, EAF, and replicated schemes are interchangeable, while the Fortran77 scheme is appreciably
|
|
slower.
|
|
|
|
<P>
|
|
Two new I/O algorithms <code>dra</code> and <code>ga_eaf</code> combines GA and DRA or EAF based replicated
|
|
algorithm. In the former, arrays that are not active (e.g., prior <IMG
|
|
WIDTH="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
|
|
SRC="img127.gif"
|
|
ALT="$T$"> amplitudes used in DIIS
|
|
or EOM-CC trial vectors) in GA algorithm will be moved to DRA. In the latter, the intermediates
|
|
that are formed by tensor contractions are initially stored in GA, thereby avoiding the need to
|
|
accumulate the fragments of the intermediate scattered in EAFs in the original EAF algorithm.
|
|
Once the intermediate is formed completely, then it will be replicated as EAFs.
|
|
|
|
<P>
|
|
|
|
<H2><A NAME="SECTION001756000000000000000">
|
|
15.5.6 <TT>DIIS</TT> -- the convergence acceleration</A>
|
|
</H2>
|
|
|
|
<P>
|
|
It sets the number iterations in which a DIIS extrapolation is performed to accelerate
|
|
the convergence of excitation amplitudes. The default value is 5, which means in every
|
|
five iteration, one DIIS extrapolation is performed (and in the rest of the iterations,
|
|
Jacobi rotation is used). When zero or negative value is specified, the DIIS is turned
|
|
off. It is not recommended to perform DIIS every iteration, whereas setting a large
|
|
value for this parameter necessitates a large memory (disk) space to keep the excitation
|
|
amplitudes of previous iterations.
|
|
|
|
<P>
|
|
|
|
<H2><A NAME="SECTION001757000000000000000">
|
|
15.5.7 <TT>FREEZE</TT> -- the frozen core/virtual approximation</A>
|
|
</H2>
|
|
|
|
<P>
|
|
Some of the lowest-lying core orbitals and/or some of the highest-lying
|
|
virtual orbitals may be excluded in the calculations
|
|
by this keyword (this does not affect the ground state HF or DFT calculation).
|
|
No orbitals are frozen by default. To exclude the atom-like
|
|
core regions altogether, one may request
|
|
<PRE>
|
|
FREEZE atomic
|
|
</PRE>
|
|
To specify the number of lowest-lying occupied orbitals be excluded, one may use
|
|
<PRE>
|
|
FREEZE 10
|
|
</PRE>
|
|
which causes 10 lowest-lying occupied orbitals excluded.
|
|
This is equivalent to writing
|
|
<PRE>
|
|
FREEZE core 10
|
|
</PRE>
|
|
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>
|
|
|
|
<P>
|
|
|
|
<H2><A NAME="SECTION001758000000000000000">
|
|
15.5.8 <TT>NROOTS</TT> -- the number of excited states</A>
|
|
</H2>
|
|
|
|
<P>
|
|
One can specify the number of excited state roots to be determined. The default
|
|
value is <code>1</code>. It is advised that the users request several more roots than actually
|
|
needed, since owing to the nature of the trial vector algorithm, some low-lying
|
|
roots can be missed when they do not have sufficient overlap with the initial guess
|
|
vectors.
|
|
|
|
<P>
|
|
|
|
<H2><A NAME="SECTION001759000000000000000">
|
|
15.5.9 <TT>TARGET</TT> and <TT>TARGETSYM</TT> -- the target root and its symmetry</A>
|
|
</H2>
|
|
|
|
<P>
|
|
At the moment, the first and second geometrical derivatives of excitation
|
|
energies that are needed in force, geometry, and frequency calculations are
|
|
obtained by numerical differentiation. These keywords may be used to specify
|
|
which excited state root is being used for the geometrical derivative calculation.
|
|
For instance, when <code>TARGET 3</code> and <code>TARGETSYM a1g</code> are included in the
|
|
input block, the total energy (ground state energy plus excitation energy)
|
|
of the third lowest excited state root (excluding the ground state) transforming as
|
|
the irreducible representation <code>a1g</code> will be passed to the module which performs
|
|
the derivative calculations. The default values of these keywords are <code>1</code> and <code>none</code>,
|
|
respectively.
|
|
|
|
<P>
|
|
The keyword <code>TARGETSYM</code> is essential in excited state geometry
|
|
optimization, since it is very common that the order of excited states changes due to
|
|
the geometry changes in the course of optimization. Without specifying the <code>TARGETSYM</code>,
|
|
the optimizer could (and would likely) be optimizing the geometry of an excited state that
|
|
is different from the one the user had intended to optimize at the starting geometry.
|
|
On the other hand, in the frequency calculations, <code>TARGETSYM</code> must be <code>none</code>,
|
|
since the finite displacements given in the course of frequency calculations will lift
|
|
the spatial symmetry of the equilibrium geometry. When these finite displacements can
|
|
alter the order of excited states including the target state, the frequency calculation
|
|
is not be feasible.
|
|
|
|
<P>
|
|
|
|
<H2><A NAME="SECTION0017510000000000000000">
|
|
15.5.10 <TT>SYMMETRY</TT> -- restricting the excited state symmetry</A>
|
|
</H2>
|
|
|
|
<P>
|
|
By adding this keyword to the input block, the user can request the module to
|
|
seek just the roots of the specified irreducible representation as
|
|
<code>TARGETSYM</code>. By default, this option is not set.
|
|
<code>TARGETSYM</code> must be specified when <code>SYMMETRY</code> is invoked.
|
|
|
|
<P>
|
|
|
|
<H2><A NAME="SECTION0017511000000000000000">
|
|
15.5.11 <TT>DIPOLE</TT> -- the ground- and excited-state dipole moments</A>
|
|
</H2>
|
|
|
|
<P>
|
|
When this is set, the ground-state CC calculation will enter another round
|
|
of iterative step for the so-called <IMG
|
|
WIDTH="15" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
|
|
SRC="img128.gif"
|
|
ALT="$\Lambda$"> equation to obtain the one-particle
|
|
density matrix and dipole moments. Likewise, for excited-states (EOM-CC), the
|
|
transition moments and dipole moments will be computed when (and only when) this
|
|
option is set. In the latter case, EOM-CC left hand side solutions will be sought
|
|
incurring approximately three times the computational cost of excitation energies
|
|
alone (note that the EOM-CC effective Hamiltonian is not Hermitian and has distinct
|
|
left and right eigenvectors).
|
|
|
|
<P>
|
|
|
|
<H2><A NAME="SECTION0017512000000000000000">
|
|
15.5.12 <TT>(NO)FOCK</TT> -- (not) recompute Fock matrix</A>
|
|
</H2>
|
|
|
|
<P>
|
|
The default is <code>FOCK</code> meaning that the Fock matrix will
|
|
be reconstructed (as opposed to using the orbital energies as the diagonal part of
|
|
Fock). This is essential in getting correct correlation energies with ROHF or DFT
|
|
reference wave functions. However, currently, this module cannot reconstruct the
|
|
Fock matrix when one-component relativistic effects are operative. So when a user
|
|
wishes to run TCE's correlation methods with DK or other relativistic reference,
|
|
<code>NOFOCK</code> must be set and orbital energies must be used for the Fock matrix.
|
|
|
|
<P>
|
|
|
|
<H2><A NAME="SECTION0017513000000000000000">
|
|
15.5.13 <TT>PRINT</TT> -- the verbosity</A>
|
|
</H2>
|
|
|
|
<P>
|
|
This keyword changes the level of output verbosity. One may also
|
|
request some particular items in Table <A HREF="node17.html#tbl:tce-printable">15.1</A> printed.
|
|
|
|
<P>
|
|
<BR>
|
|
<DIV ALIGN="CENTER">
|
|
<A NAME="tbl:tce-printable"></A><A NAME="4802"></A>
|
|
<TABLE CELLPADDING=3 BORDER="1" ALIGN="CENTER">
|
|
<CAPTION><STRONG>Table 15.1:</STRONG>
|
|
Printable items in the TCE 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">``time''</TD>
|
|
<TD ALIGN="LEFT">vary</TD>
|
|
<TD ALIGN="LEFT">CPU and wall times</TD>
|
|
</TR>
|
|
<TR><TD ALIGN="LEFT">``tile''</TD>
|
|
<TD ALIGN="LEFT">vary</TD>
|
|
<TD ALIGN="LEFT">Orbital range tiling information</TD>
|
|
</TR>
|
|
<TR><TD ALIGN="LEFT">``t1''</TD>
|
|
<TD ALIGN="LEFT">debug</TD>
|
|
<TD ALIGN="LEFT"><IMG
|
|
WIDTH="21" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
|
|
SRC="img129.gif"
|
|
ALT="$T_1$"> excitation amplitude dumping</TD>
|
|
</TR>
|
|
<TR><TD ALIGN="LEFT">``t2''</TD>
|
|
<TD ALIGN="LEFT">debug</TD>
|
|
<TD ALIGN="LEFT"><IMG
|
|
WIDTH="21" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
|
|
SRC="img130.gif"
|
|
ALT="$T_2$"> excitation amplitude dumping</TD>
|
|
</TR>
|
|
<TR><TD ALIGN="LEFT">``t3''</TD>
|
|
<TD ALIGN="LEFT">debug</TD>
|
|
<TD ALIGN="LEFT"><IMG
|
|
WIDTH="21" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
|
|
SRC="img131.gif"
|
|
ALT="$T_3$"> excitation amplitude dumping</TD>
|
|
</TR>
|
|
<TR><TD ALIGN="LEFT">``t4''</TD>
|
|
<TD ALIGN="LEFT">debug</TD>
|
|
<TD ALIGN="LEFT"><IMG
|
|
WIDTH="21" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
|
|
SRC="img132.gif"
|
|
ALT="$T_4$"> excitation amplitude dumping</TD>
|
|
</TR>
|
|
<TR><TD ALIGN="LEFT">``general information''</TD>
|
|
<TD ALIGN="LEFT">default</TD>
|
|
<TD ALIGN="LEFT">General information</TD>
|
|
</TR>
|
|
<TR><TD ALIGN="LEFT">``correlation information''</TD>
|
|
<TD ALIGN="LEFT">default</TD>
|
|
<TD ALIGN="LEFT">TCE information</TD>
|
|
</TR>
|
|
<TR><TD ALIGN="LEFT">``mbpt2''</TD>
|
|
<TD ALIGN="LEFT">debug</TD>
|
|
<TD ALIGN="LEFT">Caonical HF MBPT2 test</TD>
|
|
</TR>
|
|
<TR><TD ALIGN="LEFT">``get_block''</TD>
|
|
<TD ALIGN="LEFT">debug</TD>
|
|
<TD ALIGN="LEFT">I/O information</TD>
|
|
</TR>
|
|
<TR><TD ALIGN="LEFT">``put_block''</TD>
|
|
<TD ALIGN="LEFT">debug</TD>
|
|
<TD ALIGN="LEFT">I/O information</TD>
|
|
</TR>
|
|
<TR><TD ALIGN="LEFT">``add_block''</TD>
|
|
<TD ALIGN="LEFT">debug</TD>
|
|
<TD ALIGN="LEFT">I/O information</TD>
|
|
</TR>
|
|
<TR><TD ALIGN="LEFT">``files''</TD>
|
|
<TD ALIGN="LEFT">debug</TD>
|
|
<TD ALIGN="LEFT">File information</TD>
|
|
</TR>
|
|
<TR><TD ALIGN="LEFT">``offset''</TD>
|
|
<TD ALIGN="LEFT">debug</TD>
|
|
<TD ALIGN="LEFT">File offset information</TD>
|
|
</TR>
|
|
<TR><TD ALIGN="LEFT">``ao1e''</TD>
|
|
<TD ALIGN="LEFT">debug</TD>
|
|
<TD ALIGN="LEFT">AO one-electron integral evaluation</TD>
|
|
</TR>
|
|
<TR><TD ALIGN="LEFT">``ao2e''</TD>
|
|
<TD ALIGN="LEFT">debug</TD>
|
|
<TD ALIGN="LEFT">AO two-electron integral evaluation</TD>
|
|
</TR>
|
|
<TR><TD ALIGN="LEFT">``mo1e''</TD>
|
|
<TD ALIGN="LEFT">debug</TD>
|
|
<TD ALIGN="LEFT">One-electron integral transformation</TD>
|
|
</TR>
|
|
<TR><TD ALIGN="LEFT">``mo2e''</TD>
|
|
<TD ALIGN="LEFT">debug</TD>
|
|
<TD ALIGN="LEFT">Two-electron integral transformation</TD>
|
|
</TR>
|
|
</TABLE>
|
|
</DIV>
|
|
<BR>
|
|
|
|
<P>
|
|
|
|
<H1><A NAME="SECTION001760000000000000000">
|
|
15.6 Sample input</A>
|
|
</H1>
|
|
|
|
<P>
|
|
The following is a sample input for a ROHF-UCCSD energy calculation of a water radical cation.
|
|
<PRE>
|
|
START h2o
|
|
|
|
TITLE "ROHF-UCCSD/cc-pVTZ H2O"
|
|
|
|
CHARGE 1
|
|
|
|
GEOMETRY
|
|
O 0.00000000 0.00000000 0.12982363
|
|
H 0.75933475 0.00000000 -0.46621158
|
|
H -0.75933475 0.00000000 -0.46621158
|
|
END
|
|
|
|
BASIS
|
|
* library cc-pVTZ
|
|
END
|
|
|
|
SCF
|
|
ROHF
|
|
DOUBLET
|
|
THRESH 1.0e-10
|
|
TOL2E 1.0e-10
|
|
END
|
|
|
|
TCE
|
|
CCSD
|
|
END
|
|
|
|
TASK TCE ENERGY
|
|
</PRE>
|
|
The same result can be obtained by the following input:
|
|
<PRE>
|
|
START h2o
|
|
|
|
TITLE "ROHF-UCCSD/cc-pVTZ H2O"
|
|
|
|
CHARGE 1
|
|
|
|
GEOMETRY
|
|
O 0.00000000 0.00000000 0.12982363
|
|
H 0.75933475 0.00000000 -0.46621158
|
|
H -0.75933475 0.00000000 -0.46621158
|
|
END
|
|
|
|
BASIS
|
|
* library cc-pVTZ
|
|
END
|
|
|
|
SCF
|
|
ROHF
|
|
DOUBLET
|
|
THRESH 1.0e-10
|
|
TOL2E 1.0e-10
|
|
END
|
|
|
|
TASK UCCSD ENERGY
|
|
</PRE>
|
|
|
|
<P>
|
|
EOM-CCSDT calculation for excitation energies, excited-state
|
|
dipole, and transition moments.
|
|
<PRE>
|
|
START tce_h2o_eomcc
|
|
|
|
GEOMETRY UNITS BOHR
|
|
H 1.474611052297904 0.000000000000000 0.863401706825835
|
|
O 0.000000000000000 0.000000000000000 -0.215850436155089
|
|
H -1.474611052297904 0.000000000000000 0.863401706825835
|
|
END
|
|
|
|
BASIS
|
|
* library sto-3g
|
|
END
|
|
|
|
SCF
|
|
SINGLET
|
|
RHF
|
|
END
|
|
|
|
TCE
|
|
CCSDT
|
|
DIPOLE
|
|
FREEZE CORE ATOMIC
|
|
NROOTS 1
|
|
END
|
|
|
|
TASK TCE ENERGY
|
|
</PRE>
|
|
|
|
<P>
|
|
<HR>
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<ADDRESS>
|
|
Edoardo Apra
|
|
2004-05-25
|
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</ADDRESS>
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</BODY>
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</HTML>
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