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164
doc/user/tce.tex
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@ -1,5 +1,5 @@
%
% $Id: tce.tex,v 1.5 2004-04-22 04:50:29 edo Exp $
% $Id: tce.tex,v 1.6 2004-05-17 20:05:57 edo Exp $
%
\label{sec:tce}
@ -31,7 +31,16 @@ Hartree--Fock references,
\item Unrestricted coupled-cluster theory (LCCD, CCD, LCCSD, CCSD, QCISD, CCSDT, CCSDTQ),
\item Unrestricted iterative many-body perturbation theory [MBPT(2), MBPT(3), MBPT(4)] in its tensor formulation,
\end{itemize}
and the following optimizations have been used in the module:
New capabilities added in the version 4.6 are:
\begin{itemize}
\item Unrestricted coupled-cluster singles and doubles with perturbative connected triples \{CCSD(T), CCSD[T]\},
\item 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,
\item Unrestricted coupled-cluster theory (CCSD, CCSDT, CCSDTQ) for dipole moments.
\end{itemize}
Version 4.6 and onwards the distributed binary executables do not contain CCSDTQ and its
derivative methods, owing to their large volume. The source code includes them, so a user
can reinstate them by \verb+setenv CCSDTQ yes+ and recompile TCE module.
The following optimizations have been used in the module:
\begin{itemize}
\item Spin symmetry (spin integration is performed wherever possible within the
unrestricted framework, making the present unrestricted program
@ -67,6 +76,13 @@ referred to:
\item B. O. Roos (editor), Lecture Notes in Quantum Chemistry I and II.
\end{itemize}
For algorithms and applications of TCE, see:
\begin{itemize}
\item S. Hirata, J.\ Phys.\ Chem.\ A {\bf 107,} 9887 (2003).
\item S. Hirata, T. Yanai, W. A. de Jong, T. Nakajima, and K. Hirao, J.\ Chem.\ Phys. {\bf 120,} 3297 (2004).
\item S. Hirata, J.\ Chem. Phys. (in press) (2004).
\end{itemize}
\section{Algorithms of CI, MBPT, and CC methods}
\subsection{Spin, spatial, and index permutation symmetry}
@ -116,17 +132,25 @@ that details the calculations:
\begin{verbatim}
TCE
[(DFT||HF||SCF) default HF=SCF]
[FREEZE [[core] (atomic || <integer nfzc default 0>)] \
[virtual <integer nfzv default 0>]]
[(LCCD||CCD||CCSD||LCCSD||CCSDT||CCSDTQ|| \
QCISD||CISD||CISDT||CISDTQ|| \
CCSD(T)||CCSD[T]||QCISD||CISD||CISDT||CISDTQ|| \
MBPT2||MBPT3||MBPT4||MP2||MP3||MP4) default CCSD]
[THRESH <double thresh default 1e-6>]
[MAXITER <integer maxiter default 100>]
[IO (fortran||eaf||ga||sf||replicated) default ga]
[DIIS <integer diis default 5>]
[FREEZE [[core] (atomic || <integer nfzc default 0>)] \
[virtual <integer nfzv default 0>]]
[PRINT (none||low||medium||high||debug)
<string list_of_names ...>]
[IO (fortran||eaf||ga||sf||replicated||dra||ga_eaf) default ga]
[DIIS <integer diis default 5>]
[NROOTS <integer nroots default 0>]
[TARGET <integer target default 1>]
[TARGETSYM <character targetsym default 'none'>]
[SYMMETRY]
[DIPOLE]
[TILESIZE <no default (automatically adjusted)>]
[(NO)FOCK <logical recompf default .true.>]
[FRAGMENT <default -1 (off)>]
END
\end{verbatim}
Also supported are energy gradient calculation, geometry optimization,
@ -169,14 +193,22 @@ canonical MP2 implementation) already in place in NWChem.
\begin{verbatim}
(UCCSDT||UCC)
[(DFT||HF||SCF) default HF=SCF]
[THRESH <double thresh default 1e-6>]
[MAXITER <integer maxiter default 100>]
[IO (fortran||c||ga||sf||replicated) default ga]
[DIIS <integer diis default 5>]
[FREEZE [[core] (atomic || <integer nfzc default 0>)] \
[virtual <integer nfzv default 0>]]
[PRINT (none||low||medium||high||debug)
[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]
[DIIS <integer diis default 5>]
[NROOTS <integer nroots default 0>]
[TARGET <integer target default 1>]
[TARGETSYM <character targetsym default 'none'>]
[SYMMETRY]
[DIPOLE]
[TILESIZE <no default (automatically adjusted)>]
[(NO)FOCK <logical recompf default .true.>]
[FRAGMENT <default -1 (off)>]
END
\end{verbatim}
When a method (CCSDT in this example) is specified in the task directive,
@ -326,9 +358,11 @@ These keywords stand for the following models:
\item LCCD: linearized coupled-cluster doubles,
\item CCD: coupled-cluster doubles,
\item LCCSD: linearized coupled-cluster singles \& doubles,
\item CCSD: coupled-cluster singles \& doubles,
\item CCSDT: coupled-cluster singles, doubles, \& triples,
\item CCSDTQ: coupled-cluster singles, doubles, triples, \& quadruples,
\item CCSD: coupled-cluster singles \& doubles (also EOM-CCSD),
\item CCSDT: coupled-cluster singles, doubles, \& triples (also EOM-CCSDT),
\item CCSDTQ: coupled-cluster singles, doubles, triples, \& quadruples (also EOM-CCSDTQ),
\item CCSD(T): CCSD and perturbative connected triples,
\item CCSD[T]: CCSD and perturbative connected triples,
\item QCISD: quadratic configuration interaction singles \& doubles,
\item CISD: configuration interaction singles \& doubles,
\item CISDT: configuration interaction singles, doubles, \& triples,
@ -387,6 +421,9 @@ wisely chosen for a particular problem and computer architecture.
\item \verb+ga+ : Fully incore, Global Array virtual file,
\item \verb+sf+ : Shared File library,
\item \verb+replicated+ : Semi-replicated file on distributed file system with EAF library.
\item \verb+dra+ : Distributed file on distributed file system with DRA library.
\item \verb+ga_eaf+ : Semi-replicated file on distributed file system with EAF library. GA is used
to speedup the file reconciliation.
\end{itemize}
The GA algorithm, which is default, stores all input (integrals and
excitation amplitudes), output (residuals), and intermediate tensors in the shared memory area
@ -408,6 +445,13 @@ the global file system also share the same I/O buffer. For sequential execution
SF, EAF, and replicated schemes are interchangeable, while the Fortran77 scheme is appreciably
slower.
Two new I/O algorithms \verb+dra+ and \verb+ga_eaf+ combines GA and DRA or EAF based replicated
algorithm. In the former, arrays that are not active (e.g., prior $T$ 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.
\subsection{{\tt DIIS} --- the convergence acceleration}
It sets the number iterations in which a DIIS extrapolation is performed to accelerate
@ -443,6 +487,66 @@ keyword. For instance, to freeze the top 5 virtuals
FREEZE virtual 5
\end{verbatim}
\subsection{{\tt NROOTS} --- the number of excited states}
One can specify the number of excited state roots to be determined. The default
value is \verb+1+. 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.
\subsection{{\tt TARGET} and {\tt TARGETSYM} --- the target root and its symmetry}
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 \verb+TARGET 3+ and \verb+TARGETSYM a1g+ 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 \verb+a1g+ will be passed to the module which performs
the derivative calculations. The default values of these keywords are \verb+1+ and \verb+none+,
respectively.
The keyword \verb+TARGETSYM+ 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 \verb+TARGETSYM+,
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, \verb+TARGETSYM+ must be \verb+none+,
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.
\subsection{{\tt SYMMETRY} --- restricting the excited state symmetry}
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
\verb+TARGETSYM+. By default, this option is not set.
\verb+TARGETSYM+ must be specified when \verb+SYMMETRY+ is invoked.
\subsection{{\tt DIPOLE} --- the ground- and excited-state dipole moments}
When this is set, the ground-state CC calculation will enter another round
of iterative step for the so-called $\Lambda$ 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).
\subsection{{\tt (NO)FOCK} --- (not) recompute Fock matrix}
The default is \verb+FOCK+ 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,
\verb+NOFOCK+ must be set and orbital energies must be used for the Fock matrix.
\subsection{{\tt PRINT} --- the verbosity}
This keyword changes the level of output verbosity. One may also
@ -539,3 +643,33 @@ END
TASK UCCSD ENERGY
\end{verbatim}
EOM-CCSDT calculation for excitation energies, excited-state
dipole, and transition moments.
\begin{verbatim}
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
\end{verbatim}

83
doc/user/tddft.tex
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@ -1,5 +1,5 @@
%
% $Id: tddft.tex,v 1.4 2004-04-22 04:50:29 edo Exp $
% $Id: tddft.tex,v 1.5 2004-05-17 20:05:57 edo Exp $
%
\label{sec:tddft}
@ -34,6 +34,14 @@ by numerical differentiation,
\item Frozen core and virtual approximation.
\end{itemize}
New capability added in the latest version (4.6) is:
\begin{itemize}
\item Asymptotically correct exchange-correlation potential by van Leeuwen and Baerends,\footnote{R. van Leeuwen and E. J. Baerends, Phys.\ Rev.\ A {\bf 49,} 2421 (1994).}
\item Asymptotic correction by Casida and Salahub,\footnote{M. E. Casida, C. Jamorski, K. C. Casida, and D. R. Salahub, J.\ Chem.\ Phys. {\bf 108,} 4439 (1998).}
\item Asymptotic correction by Hirata, Zhan, Apr\`{a}, Windus, and Dixon.\footnote{S. Hirata, C.-G. Zhan, E. Apr\`{a}, T. L. Windus, and D. A. Dixon, J.\ Phys.\ Chem.\ A {\bf 107,} 10154 (2003).}
\end{itemize}
These are very effective way to rectify the shortcomings of TDDFT when applied to Rydberg excited states (see below).
\section{Performance of CIS, TDHF, and TDDFT methods}
The accuracy of CIS and TDHF for excitation energies of closed-shell systems
@ -70,6 +78,18 @@ as a simple one electron transition. The computational cost per state of TDDFT
scales as the same as the ground state DFT calculations, although the prefactor of the scaling
may be much greater in the former.
A very simple and effecive way to rectify the TDDFT's failure for Rydberg excited states
has been proposed by Tozer and Handy\footnote{D. J. Tozer and N. C. Handy, J.\ Chem.\ Phys. {\bf 109,} 10180 (1998).} and by Casida and Salahub (see previous reference). They proposed to splice a $-1/r$ asymptotic
tail to an exchange-correlation potential that does not have the correct asymptotic behavior.
Because the approximate exchange-correlation potentials are too shallow everywhere, a negative constant
must be added to them before they can be spliced to the $-1/r$ tail seamlessly in a region that is not
sensitive to chemical effects or to the long-range behavior. The negative constant or the shift is usually
taken to be the difference of the HOMO energy from the true ionization potential, which can be obtained
either from experiment or from a $\Delta$SCF calculation. Recently, we proposed a new, expedient, and
self-contained asymptotic correction that does not require an ionization potential (or shift) as an external parameter from a separate calculation.\footnote{S. Hirata, C.-G. Zhan, E. Apr\`{a}, T. L. Windus, and D. A. Dixon, J.\ Phys.\ Chem.\ A {\bf 107,} 10154 (2003).} In this scheme, the shift is computed by a semi-empirical
formula proposed by Zhan, Nichols, and Dixon.\footnote{C.-G. Zhan, J. A. Nichols, and D. A. Dixon, J.\ Phys.\ Chem. A {\bf 107,} 4184 (2003).} Both Casida-Salahub scheme and this new asymptotic correction scheme give considerably improved (Koopmans type) ionization potentials and Rydberg excitation energies.
The latter, however, supply the shift by itself unlike to former.
\section{Input syntax}
The module is called TDDFT as TDDFT employing a hybrid HF-DFT functional
@ -138,6 +158,11 @@ Since each keyword has a default value, a minimal input file will be
TASK TDDFT ENERGY
\end{verbatim}
Note that the keyword for the asymptotic correction must be given in the
DFT input block, since all the effects of the correction (and also changes in the
computer program) occur in the SCF calculation stage. See Chapter 11 (keyword \verb+CS00+ and
\verb+LB94+) for details.
\section{Keywords of {\tt TDDFT} input block}
\subsection{{\tt CIS} and {\tt RPA} --- the Tamm--Dancoff approximation}
@ -414,3 +439,59 @@ TASK TDDFT OPTIMIZE
TASK TDDFT FREQUENCIES
\end{verbatim}
TDDFT with an asymptotically corrected SVWN exchange-correlation potential.
Casida-Salahub scheme has been used with the shift value of 0.1837 a.u. supplied
as an input parameter.
\begin{verbatim}
START tddft_ac_co
GEOMETRY
O 0.0 0.0 0.0000
C 0.0 0.0 1.1283
END
BASIS SPHERICAL
C library aug-cc-pVDZ
O library aug-cc-pVDZ
END
DFT
XC Slater VWN_5
CS00 0.1837
END
TDDFT
NROOTS 12
END
TASK TDDFT ENERGY
\end{verbatim}
TDDFT with an asymptotically corrected B3LYP exchange-correlation potential.
Hirata-Zhan-Apra-Windus-Dixon scheme has been used (this is only meaningful
with B3LYP functional).
\begin{verbatim}
START tddft_ac_co
GEOMETRY
O 0.0 0.0 0.0000
C 0.0 0.0 1.1283
END
BASIS SPHERICAL
C library aug-cc-pVDZ
O library aug-cc-pVDZ
END
DFT
XC B3LYP
CS00
END
TDDFT
NROOTS 12
END
TASK TDDFT ENERGY
\end{verbatim}