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Subsections

6. Geometries

The GEOMETRY directive is a compound directive that allows the user to define the geometry to be used for a given calculation. The directive allows the user to specify the geometry with a relatively small amount of input, but there are a large number of optional keywords and additional subordinate directives that the user can specify, if needed. The directive therefore appears to be rather long and complicated when presented in its general form, as follows: 

  GEOMETRY [<string name default geometry>] \
           [units <string units default angstroms>] \
           [(angstrom_to_au || ang2au) \
                  <real angstrom_to_au default 1.8897265>] \
           [print [xyz] || noprint] \
           [center || nocenter] \
           [bqbq] \
           [autosym [real tol default 1d-2]] \
           [autoz || noautoz] \
           [adjust] \
           [(nuc || nucl || nucleus) <string nucmodel>]
           
    
    [SYMMETRY [group] <string group_name> [print] \
           [tol <real tol default 1d-2>]]



    <string tag> <real x y z> [vx vy vz] [charge <real charge>] \
           [mass <real mass>] \
           [(nuc || nucl || nucleus) <string nucmodel>]
    ... ]

    [ZMATRIX || ZMT || ZMAT
         <string tagn> <list_of_zmatrix_variables>
         ... 

         [VARIABLES
              <string symbol> <real value>
              ... ]
 
         [CONSTANTS
              <string symbol> <real value>
              ... ]

     (END || ZEND)]

         [ZCOORD
              CVR_SCALING <real value>
              BOND    <integer i> <integer j> \
                      [<real value>] [<string name>] [constant]
              ANGLE   <integer i> <integer j> \
                      [<real value>] [<string name>] [constant]
              TORSION <integer i> <integer j> <integer k> <integer l> \
                      [<real value>] [<string name>] [constant]
          END]
          
          [SYSTEM surface  <molecule polymer surface crystal default molecule>
               lat_a <real lat_a> lat_b <real lat_b> lat_c <real lat_c>
               alpha <real alpha> beta <real beta> gamma <real gamma>
          END]
 
   END

The three main parts of the GEOMETRY directive are:

The following sections present the input for this compound directive in detail, describing the options available and the usages of the various keywords in each of the three main parts.


6.1 Keywords on the GEOMETRY directive

This section presents the options that can be specified using the keywords and optional input on the main line of the GEOMETRY directive. As described above, the first line of the directive has the general form, 

  GEOMETRY [<string name default geometry>] \
           [units <string units default angstroms>] \
           [bqbq] \
           [print [xyz] || noprint] \
           [center || nocenter] \
           [autosym [real tol default 1d-2]] \
           [autoz || noautoz] \
           [adjust] \
           [(nuc || nucl || nucleus) <string nucmodel>]

All of the keywords and input on this line are optional. The following list describes all options and their defaults.

The following examples illustrate some of the various options that the user can specify on the first input line of the GEOMETRY directive, using the keywords and input options described above.

The following directives all specify the same geometry for $H_2$ (a bond length of 0.732556 Å): 

  geometry                           geometry units nm    
    h 0 0 0                            h 0 0 0            
    h 0 0 0.732556                     h 0 0 0.0732556    
  end                                end                  

  geometry units pm                  geometry units atomic 
    h 0 0 0                            h 0 0 0             
    h 0 0 73.2556                      h 0 0 1.3843305     
  end                                end


6.2 SYMMETRY -- Symmetry Group Input

The SYMMETRY directive is used (optionally) within the compound GEOMETRY directive to specify the point group for the molecular geometry. The general form of the directive, as described above within the general form of the GEOMETRY directive, is as follows: 

    [SYMMETRY [group] <string group_name> [print] \
           [tol <real tol default 1d-2>]]
The keyword group is optional, and can be omitted without affecting how the input for this directive is processed6.1. However, if the SYMMETRY directive is used, a group name must be specified by supplying an entry for the string variable <group_name>. The group name should be specified as the standard Schöflies symbol. Examples of expected input for the variable group_name include such entries as:

The SYMMETRY directive is optional. The default is no symmetry (i.e., $C_1$ point group). Automatic detection of point group symmetry is available through the use of autosym in the GEOMETRY directive main line (discussed in Section 6.1). Note: if the SYMMETRY directive is present the autosym keyword is ignored.

If only symmetry-unique atoms are specified, the others will be generated through the action of the point group operators, but the user if free to specify all atoms. The user must know the symmetry of the molecule being modeled, and be able to specify the coordinates of the atoms in a suitable orientation relative to the rotation axes and planes of symmetry. Appendix C lists a number of examples of the GEOMETRY directive input for specific molecules having symmetry patterns recognized by NWChem. The exact point group symmetry will be forced upon the molecule, and atoms within $10^{-3}$ A.U. of a symmetry element (e.g., a mirror plane or rotation axis) will be forced onto that element. Thus, it is not necessary to specify to a high precision those coordinates that are determined solely by symmetry.

The keyword print gives information concerning the point group generation, including the group generators, a character table, the mapping of centers, and the group operations.

The keyword tol relates to the accuracy with which the symmetry-unique atoms should be specified. When the atoms are generated, those that are within the tolerance, tol, are considered the same.


6.3 Cartesian coordinate input

The default in NWChem is to specify the geometry information entirely in Cartesian coordinates, and examples of this format have appeared above (e.g, Section 2.3). Each center (usually an atom) is identified on a line of the following form: 

    <string tag> <real x y z> [vx vy vz] \
        [charge <real charge>] [mass <real mass>] \
        [(nuc || nucl || nucleus) <string nucmodel>]

The string <tag> is the name of the atom or center, and its case (upper or lower) is important. The tag is limited to 16 characters and is interpreted as follows:

It is important to be aware of the following points regarding the definitions and usage of the values specified for the variable <tag> to describe the centers in a system:

The Cartesian coordinates of the atom in the molecule are specified as real numbers supplied for the variables x, y, and z following the characters entered for the tag. The values supplied for the coordinates must be in the units specified by the value of the variable <units> on the first line of the GEOMETRY directive input.

After the Cartesian coordinate input, optional velocities may be entered as real numbers for the variables vx, vy, and vz. The velocities should be given in atomic units and are used in QMD and PSPW calculations.

The Cartesian coordinate input line also contains the optional keywords charge, mass and nucleus, which allow the user to specify the charge of the atom (or center) and its mass (in atomic mass units), and the nuclear model. The default charge for an atom is its atomic number, adjusted for the presence of ECPs (see Section 8). In order to specify a different value for the charge on a particular atom, the user must enter the keyword charge, followed by the desired value for the variable <charge>.

The default mass for an atom is taken to be the mass of its most abundant naturally occurring isotope or of the isotope with the longest half-life. To model some other isotope of the element, its mass must be defined explicitly by specifying the keyword mass, followed by the value (in atomic mass units) for the variable <mass>.

The default nuclear model is a point nucleus. The keyword nucleus (or nucl or nuc) followed by the model name <nucmodel> overrides this default. Allowed values of <nucmodel> are point or pt and finite or fi. The finite option is a nuclear model with a Gaussian shape. The RMS radius of the Gaussian is determined by the atomic mass number via the formula $r_{\rm RMS} = 0.836*A^{1/3}+0.57$ fm. The mass number $A$ is derived from the variable <mass>.

The geometry of the system can be specified entirely in Cartesian coordinates by supplying a <tag> line of the type described above for each atom or center. The user has the option, however, of supplying the geometry of some or all of the atoms or centers using a Z-matrix description. In such a case, the user supplies the input tag line described above for any centers to be described by Cartesian coordinates, and then specifies the remainder of the system using the optional ZMATRIX directive described below in Section 6.4.


6.4 ZMATRIX -- Z-matrix input

The ZMATRIX directive is an optional directive that can be used within the compound GEOMETRY directive to specify the structure of the system with a Z-matrix, which can include both internal and Cartesian coordinates. The ZMATRIX directive is itself a compound directive that can include the VARIABLES and CONSTANTS directives, depending on the options selected. The general form of the compound ZMATRIX directive is as follows: 

    [ZMATRIX || ZMT || ZMAT
         <string tagn> <list_of_zmatrix_variables> 
         ... 

         [VARIABLES
              <string symbol> <real value>
              ... ]
 
         [CONSTANTS
              <string symbol> <real value>
              ... ]

    (END || ZEND)]

The input module recognizes three possible spellings of this directive name. It can be invoked with ZMATRIX, ZMT, or ZMAT. The user can specify the molecular structure using either Cartesian coordinates or internal coordinates (bond lengths, bond angles and dihedral angles. The Z-matrix input for a center defines connectivity, bond length, and bond or torsion angles. Cartesian coordinate input for a center consists of three real numbers defining the x,y,z coordinates of the atom.

Within the Z-matrix input, bond lengths and Cartesian coordinates must be input in the user-specified units, as defined by the value specified for the variable <units> on the first line of the GEOMETRY directive. All angles are specified in degrees.

The individual centers (denoted as i, j, and k below) used to specify Z-matrix connectivity may be designated either as integers (identifying each center by number) or as tags (If tags are used, the tag must be unique for each center.) The use of ``dummy'' atoms is possible, by using X or BQ at the start of the tag.

Bond lengths, bond angles and dihedral angles (denoted below as R, alpha, and beta, respectively) may be specified either as numerical values or as symbolic strings that must be subsequently defined using the VARIABLES or CONSTANTS directives. The numerical values of the symbolic strings labeled VARIABLES may be subject to changes during a geometry optimization say, while the numerical values of the symbolic strings labeled CONSTANTS will stay frozen to the value given in the input. The same symbolic string can be used more than once, and any mixture of numeric data and symbols is acceptable. Bond angles ($\alpha$) must be in the range $0 < \alpha < 180$.

The Z-matrix input is specified sequentially as follows: 

   tag1
   tag2 i R
   tag3 i R j alpha
   tag4 i R j alpha k beta [orient]
   ...

The structure of this input is described in more detail below. In the following discussion, the tag or number of the center being currently defined is labeled as C (``C'' for current). The values entered for these tags for centers defined in the Z-matrix input are interpreted in the same way as the <tag> entries for Cartesian coordinates described above (see Section 6.3). Figures 6.1, 6.2 and 6.3 display the relationships between the input data and the definitions of centers and angles.

Figure 6.1: Relationships between the centers, bond angle and dihedral angle in Z-matrix input.
\begin{figure}\centering\psfig{figure=zmat1.eps,angle=270,width=6in}\end{figure}

Figure 6.2: Relationships between the centers and two bond angles in Z-matrix input with optional parameter specified as $+1$.
\begin{figure}\centering\psfig{figure=zmat2.eps,angle=270,width=6in}\end{figure}

Figure 6.3: Relationships between the centers and two bond angles in Z-matrix input with optional parameter specified as $-1$.
\begin{figure}\centering\psfig{figure=zmat3.eps,angle=270,width=6in}\end{figure}

The Z-matrix input shown above is interpreted as follows:

  1. tag1

    Only a tag is required for the first center.

  2. tag2 i R

    The second center requires specification of its tag and the bond length ($R_{Ci}$) distance to a previous atom, which is identified by i.

  3. tag3 i R j alpha

    The third center requires specification of its tag, its bond length distance ($R_{Ci}$) to one of the two previous centers (identified by the value of i), and the bond angle $\alpha = \widehat{Cij}$.

  4. tag i R j alpha k beta [<integer orient default 0>]

    The fourth, and all subsequent centers, require the tag, a bond length ($R_{Ci}$) relative to center i, the bond angle with centers i and j ( $\alpha = \widehat{Cij}$), and either

    1. the dihedral angle ($\beta$) between the current center and centers i, j, and k (Figure 6.1), or
    2. a second bond angle $\beta = \widehat{Cik}$ and an orientation to the plane containing the other three centers (Figure 6.2 and 6.3).

    By default, $\beta$ is interpreted as a dihedral angle (see Figure 6.1), but if the optional final parameter (<orient>) is specified with the value $\pm 1$, then $\beta$ is interpreted as the angle $\widehat{Cik}$. The sign of <orient> specifies the direction of the bond angle relative to the plane containing the three reference atoms. If <orient> is $+1$, then the new center (C) is above the plane (Figure 6.2); and if <orient> is $-1$, then C is below the plane (Figure 6.3).

Following the Z-matrix center definitions described above, the user can specify initial values for any symbolic variables used to define the Z-matrix tags. This is done using the optional VARIABLES directive, which has the general form: 

  VARIABLES
    <string symbol>  <real value>
    ...
Each line contains the name of a variable followed by its value. Optionally, an equals sign (=) can be included between the symbol and its value, for clarity in reading the input file.

Following the VARIABLES directive, the CONSTANTS directive may be used to define any Z-matrix symbolic variables that remain unchanged during geometry optimizations. To freeze the Cartesian coordinates of an atom, refer to Section 6.6. The general form of this directive is as follows: 

  CONSTANTS
    <string symbol>  <real value>
    ...
Each line contains the name of a variable followed by its value. As with the VARIABLES directive, an equals sign (=) can be included between the symbol and its value.

The end of the Z-matrix input using the compound ZMATRIX directive is signaled by a line containing either END or ZEND, following all input for the directive itself and its associated optional directives.

A simple example is presented for water. All Z-matrix parameters are specified numerically, and symbolic tags are used to specify connectivity information. This requires that all tags be unique, and therefore different tags are used for the two hydrogen atoms, which may or may not be identical. 

  geometry
    zmatrix 
      O
      H1 O 0.95
      H2 O 0.95 H1 108.0
    end
  end

The following example illustrates the Z-matrix input for the molecule $CH_3CF_3$. This input uses the numbers of centers to specify the connectivity information (i, j, and k), and uses symbolic variables for the Z-matrix parameters R, alpha, and beta, which are defined in the inputs for the VARIABLES and CONSTANTS directives. 

geometry 
 zmatrix
   C 
   C 1 CC 
   H 1 CH1 2 HCH1 
   H 1 CH2 2 HCH2 3  TOR1  0 
   H 1 CH3 2 HCH3 3 -TOR2  0 
   F 2 CF1 1 CCF1 3  TOR3  0 
   F 2 CF2 1 CCF2 6  FCH1  1 
   F 2 CF3 1 CCF3 6  FCH2 -1
   variables
     CC    1.4888 
     CH1   1.0790 
     CH2   1.0789  
     CH3   1.0789  
     CF1   1.3667 
     CF2   1.3669 
     CF3   1.3669
   constants
     HCH1  104.28 
     HCH2  104.74 
     HCH3  104.7 
     CCF1  112.0713 
     CCF2  112.0341 
     CCF3  112.0340 
     TOR1  109.3996 
     TOR2  109.3997 
     TOR3  180.0000 
     FCH1  106.7846 
     FCH2  106.7842
 end   
end

The input for any centers specified with Cartesian coordinates must be specified using the format of the <tag> lines described in Section 6.3 above. However, in order to correctly specify these Cartesian coordinates within the Z-matrix, the user must understand the orientation of centers specified using internal coordinates. These are arranged as follows:


6.5 ZCOORD -- Forcing internal coordinates

By default redundant internal coordinates are generated for use in geometry optimizations. Connectivity is inferred by comparing inter-atomic distances with the sum of the van der Waals radii of the two atoms involved in a possible bond, times a scaling factor. The scaling factor is an input parameter of ZCOORD which maybe changed from its default value of 1.3. Under some circumstances (unusual bonding, bond dissociation, ...) it will be necessary to augment the automatically generated list of internal coordinates to force some specific internal coordinates to be included in among the internal coordinates. This is accomplished by including the optional directive ZCOORD within the geometry directive. The general form of the ZCOORD directive is as follows: 

  ZCOORD
     CVR_SCALING <real value>
     BOND    <integer i> <integer j> \
             [<real value>] [<string name>] [constant]
     ANGLE   <integer i> <integer j> <integer k> \
             [<real value>] [<string name>] [constant]
     TORSION <integer i> <integer j> <integer k> <integer l> \
             [<real value>] [<string name>] [constant]
  END

The centers i, j, k and l must be specified using the numbers of the centers, as supplied in the input for the Cartesian coordinates. The ZCOORD input parameters are defined as follows:

A value may be specified for a user-defined internal coordinate, in which case it is forced upon the input Cartesian coordinates while attempting to make only small changes in the other internal coordinates. If no value is provided the value implicit in the input coordinates is kept. If the keyword constant is specified, then that internal variable is not modified during a geometry optimization with DRIVER (Section 21). Each internal coordinate may also be named either for easy identification in the output, or for the application of constraints (Section 6.6).

If the keyword adjust is specified on the main GEOMETRY directive, only ZCOORD data may be specified and it can be used to change the user-defined internal coordinates, including adding/removing constraints and changing their values.


6.6 Applying constraints in geometry optimizations

Internal coordinates specified as constant in a ZCOORD directive or in the constants section of a ZMATRIX directive, will be frozen at their initial values if a geometry optimization is performed with DRIVER (Section 21).

If internal coordinates have the same name (give or take an optional sign for torsions) then they are forced to have the same value. This may be used to force bonds or angles to be equal even if they are not related by symmetry.

When atoms have been specified by their Cartesian coordinates, and internal coordinates are not being used, it is possible to freeze the cartesian position of selected atoms. This is useful for such purposes as optimizing a molecule absorbed on the surface of a cluster with fixed geometry. Only the gradients associated with the active atoms are computed. This can result in a big computational saving, since gradients associated with frozen atoms are forced to zero (Note, however, that this destroys the translational and rotational invariance of the gradient. This is not yet fully accommodated by the STEPPER geometry optimization software, and can sometimes result in slower convergence of the optimization. The DRIVER optimization package does not suffer from this problem).

The SET directive (Section 5.7) is used to freeze atoms, by specifying a directive of the form: 

  set geometry:actlist <integer list_of_center_numbers>
This defines only the centers in the list as active. All other centers will have zero force assigned to them, and will remain frozen at their starting coordinates during a geometry optimization.

For example, the following directive specifies that atoms numbered 1, 5, 6, 7, 8, and 15 are active and all other atoms are frozen: 

  set geometry:actlist 1 5:8 15
or equivalently, 
  set geometry:actlist 1 5 6 7 8 15

If this option is not specified by entering a SET directive, the default behavior in the code is to treat all atoms as active. To revert to this default behavior after the option to define frozen atoms has been invoked, the UNSET directive must be used (since the database is persistent, see Section 3.2). The form of the UNSET directive is as follows: 

  unset geometry:actlist


6.7 SYSTEM -- Lattice parameters for periodic systems

This keyword is needed only for for 1-, 2-, and 3-dimensional periodic systems.

The system keyword can assume the following values

When the system possess translational symmetry, fractional coordinates are used in the directions where translational symmetry exists. This means that for crystals $x$, $y$ and $z$ are fractional, for surfaces $x$ and $y$ are fractional, whereas for polymers only $z$ is fractional. For example, in the following H$_2$O layer input (a 2-d periodic system), $x$ and $y$ coordinates are fractional, whereas $z$ is expressed in Å. 

geometry units angstrom
  O     0.353553    0.353553         2.100000000
  H     0.263094    0.353553         2.663590000
  H     0.444007    0.353553         2.663590000

Since no space group symmetry is available yet other than $P1$, input of cell parameters is relative to the primitive cell. For example, this is the input required for the cubic face-centered type structure of bulk MgO. 

  system crystal
   lat_a 2.97692 lat_b 2.97692 lat_c 2.97692 
   alpha 60.00 beta 60.00 gamma 60.00
  end

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2003-10-08