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\subsection{Complete-Active-Space Self-Consistent-Field (CASSCF)} \label{casscf}
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CASSCF is a general method for obtaining a qualitatively correct
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wavefunction for highly strained molecules, diradicals, or bond
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breaking reactions. The \PSIdetcasman\ module performs
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Multi-configurational self-consistent-field (MCSCF)
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is a general method for obtaining qualitatively correct
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wavefunctions for highly strained molecules, diradicals, or bond
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breaking reactions. The most commonly used MCSCF procedure
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is the complete-active-space self-consistent-field (CASSCF)
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approach \cite{Roos:1980}, which includes all possible determinants
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(with the proper symmetry) that can be formed by distributing
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a set of active electrons among a set of active orbitals.
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The \PSIdetcasman\ module performs
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CASSCF optimization of molecular orbitals via a two-step
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procedure in which the CI wavefunction is computed using
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\PSIdetci\, and the orbital rotation step is computed using
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\PSIdetcas. The \PSIdetcas\ program is fairly simple
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and uses an approximate orbital Hessian and a Newton-Raphson update,
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accelerated by Pulay's DIIS procedure. Future versions of the
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program will allow RASSCF type wavefunctions.
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At present, CASSCF's work most efficiently if the inactive orbitals
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are treated as ``frozen'' in the {\tt FROZEN\_DOCC} and {\tt FROZEN\_UOCC}
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arrays. These orbitals are still optimized by the CASSCF. This
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procedure is being simplified for the next release of \PSIthree.
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See the {\tt casscf-sp} example in the \file{tests} directory for an
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example of the current input.
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and uses an approximate orbital Hessian \cite{Chaban:1997:88}
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and a Newton-Raphson update,
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accelerated by Pulay's DIIS procedure \cite{Pulay:1980}.
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We have also implemented a prototype version of the RASSCF method
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\cite{Malmqvist:1990:RASSCF}, which is another kind of MCSCF which
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is typically less complete (and less expensive) than CASSCF.
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However, orbital convergence for RASSCF can be difficult in our
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current implementation.
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Inactive orbitals in the MCSCF may be specified by the
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{\tt RESTRICTED\_DOCC} and {\tt RESTRICTED\_UOCC} keywords. These
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orbitals will remain doubly-occupied or doubly-unoccupied, respectively,
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in the MCSCF wavefunction. However, the form of these orbitals will
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be optimized in the MCSCF procedure. It is also possible to
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literally freeze inactive orbitals in their original (SCF) form
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using the {\tt FROZEN\_DOCC} and {\tt FROZEN\_UOCC} keywords.
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This is not normally what one wishes to do in an MCSCF computation
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(e.g., it complicates the computation of gradients),
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but it can make the computations faster and is helpful in some
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circumstances where unphysical mixing of inactive and active
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occupied orbitals might occur. Presently, it is not possible
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to mix the use of restricted and frozen orbitals in \PSIthree.
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The division of the molecular orbitals into various subspaces such as RAS
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spaces, or frozen vs active orbitals, etc, needs to be clear not only to
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the {\tt detci} program, but also at least to the transformation program
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(and in the case of MCSCF, to other programs as well). Thus,
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orbital subspace keywords such as {\tt RAS1}, {\tt RAS2}, {\tt RAS3}, {\tt
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frozen\_docc}, {\tt frozen\_uocc}, {\tt active}, etc., need to be
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in the {\tt psi:()} or {\tt default:()} sections of input so they may
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also be read by other modules.
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The ability to perform state-averaged
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\cite{Docken:1972:4928,Ruedenberg:1979:1069}
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CASSCF or RASSCF computations has been added. This is accomplished using the
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{\tt average\_states} keyword.
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See the {\tt casscf-sp} and {\tt casscf-sa-sp} examples in the
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\file{tests} directory and the example below.
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\subsubsection{Basic Keywords}
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\begin{description}
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\item[WFN = string]\mbox{}\\
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This should be {\tt detcas} for determinant-based CASSCF.
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This may be {\tt casscf} or {\tt rasscf}.
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\item[REFERENCE = string]\mbox{}\\
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Any of the references allowed by \PSIdetci\ should work (i.e., not
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{\tt uhf}), but there should be no reason not to use {\tt rhf}.
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\item[DERTYPE = string]\mbox{}\\
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Energies ({\tt none}) and gradients ({\tt first}) are supported.
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At present, only energies ({\tt none}) are supported; future
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releases will implement gradients ({\tt first}).
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\item[CONVERGENCE = integer]\mbox{}\\
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Convergence desired on the orbital gradient. Convergence is achieved when
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the RMS of the error in the orbital gradient is less than 10**(-n). The
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input, such as {\tt detcas: ( convergence = x )}.
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\item[ENERGY\_CONVERGENCE = integer]\mbox{}\\
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Convergence desired on the total MCSCF energy. The default is 7.
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\item[FROZEN\_DOCC = integer array]\mbox{}\\
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The number of lowest energy doubly occupied orbitals in each irreducible
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representation from which there will be no excitations.
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The Cotton ordering of the irredicible representations is used.
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The default is the zero vector.
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\item[FROZEN\_UOCC = integer array]\mbox{}\\
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The number of highest energy unoccupied orbitals in each irreducible
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representation into which there will be no excitations.
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\item[RESTRICTED\_DOCC = (integer array)]\mbox{}\\
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Should be in {\tt psi:()} or {\tt default:()} sections of input.
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The number of lowest energy doubly occupied orbitals in each irreducible
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representation from which there will be no excitations.
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These orbitals are optimized in the MCSCF.
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The Cotton ordering of the irredicible representations is used.
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The default is the zero vector.
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\item[RESTRICTED\_UOCC = (integer array)]\mbox{}\\
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Should be in {\tt psi:()} or {\tt default:()} sections of input.
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The number of highest energy unoccupied orbitals in each irreducible
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representation into which there will be no excitations.
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These orbitals are optimized in the MCSCF.
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The default is the zero vector.
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\item[FROZEN\_DOCC = (integer array)]\mbox{}\\
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Should be in {\tt psi:()} or {\tt default:()} sections of input.
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The number of lowest energy doubly occupied orbitals in each irreducible
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representation from which there will be no excitations.
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These orbitals are literally frozen and are not optimized in the MCSCF;
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usually one wishes to use {\tt RESTRICTED\_DOCC} instead.
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The current version of the program does not allow both
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{\tt RESTRICTED\_DOCC} and {\tt FROZEN\_DOCC}.
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Should be in {\tt psi:()} or {\tt default:()} sections of input.
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The Cotton ordering of the irredicible representations is used.
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The default is the zero vector.
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\item[FROZEN\_UOCC = (integer array)]\mbox{}\\
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Should be in {\tt psi:()} or {\tt default:()} sections of input.
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The number of highest energy unoccupied orbitals in each irreducible
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representation into which there will be no excitations.
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These orbitals are literally frozen and are not optimized in the MCSCF;
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usually one wishes to use {\tt RESTRICTED\_UOCC} instead.
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The current version of the program does not allow both
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{\tt RESTRICTED\_UOCC} and {\tt FROZEN\_UOCC}.
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Should be in {\tt psi:()} or {\tt default:()} sections of input.
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The default is the zero vector.
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\item[NCASITER = integer]\mbox{}\\
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Maximum number of iterations to optimize the orbitals. This option
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should be specified in the DEFAULT section of input, because
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it needs to be visible to the control program PSI. Defaults to 20.
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\item[AVERAGE\_STATES = (integer array)]\mbox{}\\
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This gives a list of what states to average for the orbital
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optimization. States are numbered starting from 1.
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\item[PRINT = integer]\mbox{}\\
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This option determines the verbosity of the output. A value of 1 or
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2 specifies minimal printing, a value of 3 specifies verbose printing.
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Values of 4 or 5 are used for debugging. Do not use level 5 unless
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the test case is very small (e.g. STO H2O CISD).
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the test case is very small (e.g. STO H$_2$O CISD).
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\subsubsection{Examples}
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% 6-31G** H2O Test CASSCF Energy Point
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label = "6-31G** CASSCF H2O"
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restricted_docc = (1 0 0 0)
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\caption{Example of a CASSCF single-point calculation for H$_2$O using
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a valence active space 3a$_1$ 1b$_1$ 2b$_2$.}
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\label{ex:casscf-sp-1}
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doc/userman/detcas.tex
