Keywords: user

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Subsections

- 7.1 Basis set library
- 7.2 Explicit basis set definition
- 7.3 Combinations of library and explicit basis set input

# 7. Basis sets

NWChem currently supports basis sets consisting of generally contracted7.1 Cartesian Gaussian functions up to a maximum angular momentum of six ( functions), and also (or L) functions7.2 . The `BASIS` directive is used to define these, and also to specify use of an effective core potential (ECP) that is associated with a basis set; see Section 8.

The basis functions to be used for a given calculation can be drawn from a standard set in the EMSL basis set library that is included in the release of NWChem (See Appendix A for a list of the standard basis sets currently supplied with the release of the code). Alternatively, the user can specify particular functions explicitly in the input, to define a particular basis set.

The general form of the `BASIS` directive is as follows:

      BASIS [<string name default "ao basis">] \
            [(spherical || cartesian) default cartesian] \
            [(segment || nosegment) default segment] \
            [(print || noprint) default print]
            [rel]

         <string tag> library [<string tag_in_lib>] \
                      <string standard_set> [file <filename>] \
                      [except <string tag list>] [rel]

            ...

         <string tag> <string shell_type> [rel]
            <real exponent> <real list_of_coefficients>
            ...

      END

Examining the keywords on the first line of the `BASIS` directive:

- `name`

  By default, the basis set is stored in the database with the name `"ao basis"`. Another name may be specified in the `BASIS` directive, thus, multiple basis sets may be stored simultaneously in the database. Also, the DFT (Section 11) and RI-MP2 (Section 16) modules and the Dyall-modified-Dirac relativistic method (Section 9.2) require multiple basis sets with specific names.

  The user can associate the `"ao basis"` with another named basis using the `SET` directive (see Section 5.7).

- `SPHERICAL` or `CARTESIAN`

  The keywords `spherical` and `cartesian` offer the option of using either spherical-harmonic (5 d, 7 f, 9 g, ...) or Cartesian (6 d, 10 f, 15 g, ...) angular functions. The default is Cartesian.

  Note that the correlation-consistent basis sets were designed using spherical harmonics and to use these, the `spherical` keyword should be present in the `BASIS` directive. The use of spherical functions also helps eliminate problems with linear dependence.

- `SEGMENT` or `NOSEGMENT`

  By default, NWChem forces all basis sets to be segmented, even if they are input with general contractions or or sp shells. This is because the current derivative integral program cannot handle general contractions. If a calculation is computing energies only, a performance gain can result from exploiting generally contracted basis sets, in which case `NOSEGMENT` should be specified.

- `PRINT` or `NOPRINT`

  The default is for the input module to print all basis sets encountered. Specifying the keyword `noprint` allows the user to suppress this output.

- `REL`

  This keyword marks the entire basis as a relativistic basis for the purposes of the Dyall-modified-Dirac relativistic integral code. The marking of the basis set is necessary for the code to make the proper association between the relativistic shells in the ao basis and the shells in the large and/or small component basis. This is only necessary for basis sets which are to be used as the ao basis. The user is referred to Section 9.2 for more details.

Basis sets are associated with centers by using the tag of a center in a geometry that has either been input by the user (Section 6) or is available elsewhere. Each atom or center with the same `tag` will have the same basis set. All atoms must have basis functions assigned to them -- only dummy centers (X or Bq) may have no basis functions. To facilitate the specification of the geometry and the basis set for any chemical system, the matching process of a basis set tag to a geometry tag first looks for an exact match. If no match is found, NWChem will attempt to match, ignoring case, the name or symbol of the element. E.g., all hydrogen atoms in a system could be labeled ``H1'', ``H2'', ..., in the geometry but only one basis set specification for ``H'' or ``hydrogen'' is necessary. If desired, a special basis may be added to one or more centers (e.g., ``H1'') by providing a basis for that tag. If the matching mechanism fails then NWChem stops with an appropriate error message.

A special set of tags, ``*'' and tags ending with a ``*'' (E.g. ``H*'') can be used in combination with the keyword `library` (see section below). These tags facilitate the definition of a certain type of basis set of all atoms, or a group of atoms, in a geometry using only a single or very few basis set entries. The ``*'' tag will not place basis sets on dummy atoms, Bq* can be used for that if necessary.

Examined next is how to reference standard basis sets in the basis set library, and finally, how to define a basis set using exponents and coefficients.

# 7.1 Basis set library

The keyword `library` associated with each specific `tag` entry specifies that the calculation will use the standard basis set in NWChem for that center. The variable `<standard_set>` is the name that identifies the functions in the library. The names of standard basis sets are not case sensitive. See Appendix A for a complete list of the basis sets in the NWChem library and their specifications.

The general form of the input line requesting basis sets from the NWChem basis set library is:

         <string tag> library [<string tag_in_lib>] \
                      <string standard set> [file < filename> \
                      [except <string tag list>] [rel]
            ...

For example, the NWChem basis set library contains the Dunning cc-pvdz basis set. These may be used as follows

      basis
        oxygen library cc-pvdz
        hydrogen library cc-pvdz
      end

A default path of the NWChem basis set libraries is provided on installation of the code, but a different path can be defined by specifying the keyword `file`, and one can explicitly name the file to be accessed for the basis functions. For example,

      basis
        o  library 3-21g file /usr/d3g681/nwchem/library
        si library 6-31g file /usr/d3g681/nwchem/libraries/
      end

This directive tells the code to use the basis set `3-21g` in the file `/usr/d3g681/nwchem/library` for atom `o` and to use the basis set `6-31g` in the directory `/usr/d3g681/nwchem/libraries/` for atom `si`, rather than look for them in the default libraries. When a directory is defined the code will search for the basis set in a file with the name `6-31g`.

The ``*'' tag can be used to efficiently define basis set input directives for large numbers of atoms. An example is:

      basis
        *  library 3-21g
      end

This directive tells the code to assign the basis sets `3-21g` to all the atom tags defined in the geometry. If one wants to place a different basis set on one of the atoms defined in the geometry, the following directive can be used:

      basis
        *  library 3-21g except H
      end

This directive tells the code to assign the basis sets `3-21g` to all the atoms in the geometry, except the hydrogen atoms. Remember that the user will have to explicitly define the hydrogen basis set in this directive! One may also define tags that end with a ``*'':

      basis
        oxy*  library 3-21g
      end

This directive tells the code to assign the basis sets `3-21g` to all atom tags in the geometry that start with ``oxy''.

If standard basis sets are to be placed upon a dummy center, the variable `<tag_in_lib>` must also be entered on this line, to identify the correct atom type to use from the basis function library (see the ghost atom example in Section 5.7 and below). For example: To specify the cc-pvdz basis for a calculation on the water monomer in the dimer basis, where the dummy oxygen and dummy hydrogen centers have been identified as `bqo` and `bqh` respectively, the `BASIS` directive is as follows:

      basis
        o   library cc-pvdz
        h   library cc-pvdz
        bqo library o cc-pvdz
        bqh library h cc-pvdz
      end

A special dummy center tag is `bq*`, which will assign the same basis set to all bq centers in the geometry. Just as with the ``*'' tag, the `except` list can be used to assign basis sets to unique dummy centers.

The library basis sets can also be marked as relativistic by adding the `rel` keyword to the tag line. See Section 9.2 for more details. The correlation consistent basis sets have been contracted for relativistic effects and are included in the standard library.

There are also contractions in the standard library for both a point nucleus and a finite nucleus of Gaussian shape. These are usually distinguished by the suffixex `_pt` and `_fi`. It is the user's responsibility to ensure that the contraction matches the nuclear type specified in the geometry object. The specification of a finite nucleus basis set does NOT automatically set the nuclear type for that atom to be finite. See Section 6 for information.

# 7.2 Explicit basis set definition

If the basis sets in the library or available in other external files are not suitable for a given calculation, the basis set may be explicitly defined. A generally contracted Gaussian basis function is associated with a center using an input line of the following form:

         <string tag> <string shell_type> [rel]
            <real exponent> <real list_of_coefficients>
            ...

The variable `<shell_type>` identifies the angular momentum of the shell, , , , .... NWChem is configured to handle up to shells. The keyword `rel` marks the shell as relativistic -- see Section 9.2 for more details. Subsequent lines define the primitive function exponents and contraction coefficients. General contractions are specified by including multiple columns of coefficients.

The following example defines basis sets for the water molecule:

      basis spherical nosegment
        oxygen s
          11720.0000    0.000710  -0.000160
           1759.0000    0.005470  -0.001263
            400.8000    0.027837  -0.006267
            113.7000    0.104800  -0.025716
             37.0300    0.283062  -0.070924
             13.2700    0.448719  -0.165411
              5.0250    0.270952  -0.116955
              1.0130    0.015458   0.557368
              0.3023   -0.002585   0.572759
        oxygen s
              0.3023    1.000000
        oxygen p
             17.7000    0.043018
              3.8540    0.228913
              1.0460    0.508728
              0.2753    0.460531
        oxygen p
              0.2753    1.000000
        oxygen d
              1.1850    1.000000
        hydrogen s
             13.0100    0.019685
              1.9620    0.137977
              0.4446    0.478148
              0.1220    0.501240
        hydrogen s
              0.1220    1.000000
        hydrogen p
              0.7270    1.000000
        oxygen s
              0.01      1.0
        hydrogen s
              0.02974   1.0
        hydrogen p
              0.141      1.0
      end

# 7.3 Combinations of library and explicit basis set input

The user can use a mixture of library basis and explicit basis set input to define the basis sets used on the various atoms.

For example, the following `BASIS` directive augments the Dunning cc-pvdz basis set for the water molecule with a diffuse s-shell on oxygen and adds the aug-cc-pVDZ diffuse functions onto the hydrogen.

      basis spherical nosegment
        oxygen library cc-pvdz
        hydrogen library cc-pvdz
        oxygen s
          0.01 1.0
        hydrogen library "aug-cc-pVDZ Diffuse"
      end

The resulting basis set defined is identical to the one defined above in the explicit basis set input.

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