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328 lines
13 KiB
TeX
328 lines
13 KiB
TeX
%
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% $Id$
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%
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\label{sec:basis}
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NWChem currently supports basis sets consisting of generally
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contracted\footnote{Generally contracted meaning that the same
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primitive, Gaussian functions are contracted into multiple
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contracted functions using different contraction coefficients.
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Reuse of the radial functions increases the efficiency of integral
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generation.} Cartesian Gaussian functions up to a maximum angular
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momentum of six ($h$ functions), and also $sp$ (or L)
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functions\footnote{An $sp$ shell is two-component general contraction.
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However, the first component specifies an $s$ shell and the second a
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$p$ shell. Again, reuse of the radial functions increases the efficiency
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of integral generation.} . The {\tt BASIS} directive is used to
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define these, and also to specify use of an effective core potential
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(ECP) that is associated with a basis set; see Section \ref{sec:ecp}.
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The basis functions to be used for a given calculation can be drawn
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from a standard set in the EMSL basis set library that is included in
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the release of NWChem (See Appendix \ref{sec:knownbasis} for a list
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of the standard basis sets currently supplied with the release of the
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code). Alternatively, the user can specify particular functions
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explicitly in the input, to define a particular basis set.
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The general form of the \verb+BASIS+ directive is as follows:
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\begin{verbatim}
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BASIS [<string name default "ao basis">] \
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[(spherical || cartesian) default cartesian] \
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[(segment || nosegment) default segment] \
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[(print || noprint) default print]
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[rel]
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<string tag> library [<string tag_in_lib>] \
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<string standard_set> [file <filename>] \
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[except <string tag list>] [rel]
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...
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<string tag> <string shell_type> [rel]
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<real exponent> <real list_of_coefficients>
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...
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END
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\end{verbatim}
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Examining the keywords on the first line of the \verb+BASIS+ directive:
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\begin{itemize}
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\item {\tt name}
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By default, the basis set is stored in the database with the name
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\verb+"ao basis"+. Another name may be specified in the \verb+BASIS+
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directive, thus, multiple basis sets may be stored simultaneously in the
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database. Also, the DFT (Section \ref{sec:dft})
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and RI-MP2 (Section \ref{sec:rimp2}) modules and the
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Dyall-modified-Dirac relativistic method (Section \ref{sec:dyall-mod-dir})
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require multiple basis sets with specific names.
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The user can associate the \verb+"ao basis"+ with another named basis
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using the \verb+SET+ directive (see Section \ref{sec:set}).
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\item {{\tt SPHERICAL} or {\tt CARTESIAN}}
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The keywords \verb+spherical+ and \verb+cartesian+ offer the option of
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using either spherical-harmonic (5 d, 7 f, 9 g, \ldots) or Cartesian
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(6 d, 10 f, 15 g, \ldots) angular functions. The default is
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Cartesian.
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Note that the correlation-consistent basis sets were designed using
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spherical harmonics and to use these, the \verb+spherical+ keyword
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should be present in the \verb+BASIS+ directive. The use of spherical
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functions also helps eliminate problems with linear dependence.
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\item {{\tt SEGMENT} or {\tt NOSEGMENT}}
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By default, NWChem forces all basis sets to be segmented,
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even if they are input with general contractions or $L$ or sp
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shells. This is because the current derivative integral program cannot
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handle general contractions. If a calculation is
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computing energies only, a
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performance gain can result from exploiting generally contracted basis
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sets, in which case {\tt NOSEGMENT} should be specified.
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\item {{\tt PRINT} or {\tt NOPRINT}}
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The default is for the input module to print all basis sets encountered.
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Specifying the keyword \verb+noprint+ allows the user to suppress this output.
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\item {{\tt REL}}
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This keyword marks the entire basis as a relativistic basis for the purposes
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of the Dyall-modified-Dirac relativistic integral code. The marking of the
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basis set is necessary for the code to make the proper association between
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the relativistic shells in the ao basis and the shells in the large and/or
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small component basis. This is only necessary for basis sets which are to be
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used as the ao basis. The user is referred to Section \ref{sec:dyall-mod-dir}
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for more details.
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\end{itemize}
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Basis sets are associated with centers by using the tag of a center in
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a geometry that has either been input by the user (Section
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\ref{sec:geom}) or is available elsewhere. Each atom or center with
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the same \verb+tag+ will have the same basis set. All atoms must have
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basis functions assigned to them --- only dummy centers (X or Bq) may have no
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basis functions. To facilitate the specification of the geometry and
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the basis set for any chemical system, the matching process of a basis
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set tag to a geometry tag first looks for an exact match. If no match
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is found, NWChem will attempt to match, ignoring case, the name or
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symbol of the element. E.g., all hydrogen atoms in a system could be
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labeled ``H1'', ``H2'', \ldots, in the geometry but only
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one basis set specification for ``H'' or ``hydrogen'' is necessary.
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If desired, a special basis may be added to one or more centers (e.g.,
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``H1'') by providing a basis for that tag.
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If the matching mechanism fails then NWChem stops with an appropriate
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error message.
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A special set of tags, ``*'' and tags ending with a ``*'' (E.g. ``H*'')
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can be used in combination with the keyword \verb+library+ (see section
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below). These tags facilitate the definition of a certain type of basis
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set of all atoms, or a group of atoms, in a geometry using only a single
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%<<<<<<< basis.tex
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or very few basis set entries. The ``*'' tag will not place basis sets
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on dummy atoms, Bq* can be used for that if necessary.
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%=======
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%or very few basis set entries. The ``*'' tag will not place basis sets
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%on dummy atoms, Bq* can be used for that if necessary.
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%>>>>>>> 1.25
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Examined next is how to reference standard basis sets in the basis set
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library, and finally, how to define a basis set using exponents and
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coefficients.
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\section{Basis set library}
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The keyword \verb+library+ associated with each specific \verb+tag+
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entry specifies that the calculation will use the standard basis set
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in NWChem for that center. The variable \verb+<standard_set>+ is the
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name that identifies the functions in the library. The names of
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standard basis sets are not case sensitive. See Appendix
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\ref{sec:knownbasis} for a complete list of the basis sets in the
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NWChem library and their specifications.
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The general form of the input line requesting basis sets from the NWChem
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basis set library is:
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\begin{verbatim}
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<string tag> library [<string tag_in_lib>] \
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<string standard set> [file < filename> \
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[except <string tag list>] [rel]
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...
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\end{verbatim}
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For example, the NWChem basis set library contains the Dunning cc-pvdz
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basis set. These may be used as follows
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\begin{verbatim}
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basis
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oxygen library cc-pvdz
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hydrogen library cc-pvdz
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end
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\end{verbatim}
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A default path of the NWChem basis set libraries is provided on installation
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of the code, but a different path can be defined by specifying the keyword
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\verb+file+, and one can explicitly name the file to be accessed
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for the basis functions. For example,
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\begin{verbatim}
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basis
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o library 3-21g file /usr/d3g681/nwchem/library
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si library 6-31g file /usr/d3g681/nwchem/libraries/
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end
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\end{verbatim}
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This directive tells the code to use the basis set \verb+3-21g+ in
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the file {\tt /usr/\-d3g681/\-nwchem/\-library} for atom \verb+o+ and
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to use the basis set \verb+6-31g+ in the directory
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{\tt /usr/\-d3g681/\-nwchem/\-libraries/} for atom \verb+si+, rather
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than look for them in the default libraries. When a directory is defined
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the code will search for the basis set in a file with the name {\tt 6-31g}.
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The ``*'' tag can be used to efficiently define basis set input directives
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for large numbers of atoms. An example is:
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\begin{verbatim}
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basis
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* library 3-21g
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end
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\end{verbatim}
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This directive tells the code to assign the basis sets \verb+3-21g+ to
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all the atom tags defined in the geometry. If one wants to place a
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different basis set on one of the atoms defined in the geometry, the
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following directive can be used:
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\begin{verbatim}
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basis
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* library 3-21g except H
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end
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\end{verbatim}
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This directive tells the code to assign the basis sets \verb+3-21g+ to
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all the atoms in the geometry, except the hydrogen atoms. Remember that
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the user will have to explicitly define the hydrogen basis set in this
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directive! One may also define tags that end with a ``*'':
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\begin{verbatim}
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basis
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oxy* library 3-21g
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end
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\end{verbatim}
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This directive tells the code to assign the basis sets \verb+3-21g+ to
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all atom tags in the geometry that start with ``oxy''.
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If standard basis sets are to be placed upon a dummy center, the
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variable \verb+<tag_in_lib>+ must also be entered on this line, to
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identify the correct atom type to use from the basis function library
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(see the ghost atom example in Section \ref{sec:set} and below). For
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example: To specify the cc-pvdz basis for a calculation on the water
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monomer in the dimer basis, where the dummy oxygen and dummy hydrogen
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centers have been identified as \verb+bqo+ and \verb+bqh+
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respectively, the \verb+BASIS+ directive is as follows:
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\begin{verbatim}
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basis
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o library cc-pvdz
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h library cc-pvdz
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bqo library o cc-pvdz
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bqh library h cc-pvdz
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end
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\end{verbatim}
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A special dummy center tag is \verb+bq*+, which will assign the same basis
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set to all bq centers in the geometry. Just as with the ``*'' tag, the
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\verb+except+ list can be used to assign basis sets to unique dummy centers.
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The library basis sets can also be marked as relativistic by adding the
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\verb+rel+ keyword to the tag line. See Section \ref{sec:dyall-mod-dir} for
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more details. The correlation consistent basis sets have been contracted for
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relativistic effects and are included in the standard library.
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There are also contractions in the standard library for both a point nucleus
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and a finite nucleus of Gaussian shape. These are usually distinguished by
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the suffixex {\tt \_pt} and {\tt \_fi}. It is the user's responsibility to
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ensure that the contraction matches the nuclear type specified in the
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geometry object. The specification of a finite nucleus basis set does NOT
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automatically set the nuclear type for that atom to be finite. See
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Section \ref{sec:geom} for information.
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\section{Explicit basis set definition}
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If the basis sets in the library or available in other external files
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are not suitable for a given calculation,
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the basis set may be explicitly defined.
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A generally contracted Gaussian basis function is associated with a
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center using an input line of the following form:
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\begin{verbatim}
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<string tag> <string shell_type> [rel]
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<real exponent> <real list_of_coefficients>
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...
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\end{verbatim}
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The variable \verb+<shell_type>+ identifies the angular momentum of the
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shell, $s$, $p$, $d$, \ldots. NWChem is configured to handle up to $h$
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shells. The keyword \verb+rel+ marks the shell as relativistic --- see
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Section \ref{sec:dyall-mod-dir} for more details. Subsequent lines define
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the primitive function exponents and contraction coefficients. General
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contractions are specified by including multiple columns of coefficients.
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The following example defines basis sets for the water molecule:
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\begin{verbatim}
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basis spherical nosegment
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oxygen s
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11720.0000 0.000710 -0.000160
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1759.0000 0.005470 -0.001263
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400.8000 0.027837 -0.006267
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113.7000 0.104800 -0.025716
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37.0300 0.283062 -0.070924
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13.2700 0.448719 -0.165411
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5.0250 0.270952 -0.116955
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1.0130 0.015458 0.557368
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0.3023 -0.002585 0.572759
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oxygen s
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0.3023 1.000000
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oxygen p
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17.7000 0.043018
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3.8540 0.228913
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1.0460 0.508728
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0.2753 0.460531
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oxygen p
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0.2753 1.000000
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oxygen d
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1.1850 1.000000
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hydrogen s
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13.0100 0.019685
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1.9620 0.137977
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0.4446 0.478148
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0.1220 0.501240
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hydrogen s
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0.1220 1.000000
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hydrogen p
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0.7270 1.000000
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oxygen s
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0.01 1.0
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hydrogen s
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0.02974 1.0
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hydrogen p
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0.141 1.0
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end
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\end{verbatim}
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\section{Combinations of library and explicit basis set input}
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The user can use a mixture of library basis and explicit basis set
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input to define the basis sets used on the various atoms.
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For example, the following \verb+BASIS+ directive augments the Dunning
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cc-pvdz basis set for the water molecule with a diffuse s-shell on
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oxygen and adds the aug-cc-pVDZ diffuse functions onto the hydrogen.
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\begin{verbatim}
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basis spherical nosegment
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oxygen library cc-pvdz
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hydrogen library cc-pvdz
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oxygen s
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0.01 1.0
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hydrogen library "aug-cc-pVDZ Diffuse"
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end
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\end{verbatim}
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The resulting basis set defined is identical to the one defined above
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in the explicit basis set input.
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