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Development:Geometry

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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>]]
   [ LOAD [format xyz||pdb]  [frame <int frame>] \
          [select [not] \
               [name <string atomname>] \
               [rname <string residue-name>]
               [id  <int atom-id>|<int range atom-id1:atom-id2> ... ]
               [resi <int residue-id>|<int range residue-id1:residue-id2> ... ]
         ]
   <string filename> ]
  
   <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:

  • keywords on the first line of the directive (to specify such optional input as the geometry name, input units, and print level for the output)
  • symmetry information
  • Cartesian coordinates or Z-matrix input to specify the locations of the atoms and centers
  • lattice parameters (needed only for periodic systems)

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.

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.

  • <name> - user-supplied name for the geometry; the default name is geometry, and all NWChem modules look for a geometry with this name. However, multiple geometries may be specified by using a different name for each. Subsequently, the user can direct a module to a named geometry by using the SET directive (see the example in Section 5.7) to associate the default name of geometry with the alternate name.
  • units - keyword specifying that a value will be entered by the user for the string variable <units>. The default units for the geometry input are Angstrøms (Note: atomic units or Bohr are used within the code, regardless of the option specified for the input units. The default conversion factor used in the code to convert from Angstrøms to Bohr is 1.8897265 which may be overidden with the angstrom_to_au keyword described below.). The code recognizes the following possible values for the string variable <units>:
    • angstroms or an -- Angstroms , the default (converts to A.U. using the Angstrom to A.U. conversion factor)
    • au or atomic or bohr -- Atomic units (A.U.)
    • nm or nanometers -- nanometers (converts to A.U. using a conversion factor computed as 10.0 times the Angstrom to A.U. conversion factor)
    • pm or picometers -- picometers (converts to A.U. using a conversion factor computed as 0.01 times the Angstrom to A.U. conversion factor)
  • angstrom_to_au - may also be specified as ang2au. This enables the user to modify the conversion factors used to convert between Angstrom and A.U.. The default value is 1.8897265.
  • bqbq - keyword to specify the treatment of interactions between dummy centers. The default in NWChem is to ignore such interactions when computing energies or energy derivatives. These interactions will be included if the keyword bqbq is specified.
  • print and noprint - complementary keyword pair to enable or disable printing of the geometry. The default is to print the output associated with the geometry. In addition, the keyword print may be qualified by the additional keyword xyz, which specifies that the coordinates should be printed in the XYZ format of molecular graphics program XMol
  • center and nocenter - complementary keyword pair to enable or disable translation of the center of nuclear charge to the origin. With the origin at this position, all three components of the nuclear dipole are zero. The default is to move the center of nuclear charge to the origin.
  • autosym - keyword to specify that the symmetry of the geometric system should be automatically determined. This option is on by default. Only groups up to and including Oh are recognized. Occasionally NWChem will be unable to determine the full symmetry of a molecular system, but will find a proper subgroup of the full symmetry. The default tolerance is set to work for most cases, but may need to be decreased to find the full symmetry of a geometry. Note that autosym will be turned off if the SYMMETRY group input is given (See Symmetry Group Input). Also note that if symmetry equivalent atoms have different tags in the geometry they will not be detected as symmetry equivalent by the autosym capability. The reason for this is that atoms with different tags might be assigned different basis sets, for example, after which they are no longer symmetry equivalent. Therefore autosym chooses to make the save choice.
  • noautoz - by default NWChem (release 3.3 and later) will generate redundant internal coordinates from user input Cartesian coordinates. The internal coordinates will be used in geometry optimizations. The noautoz keyword disables use of internal coordinates. The autoz keyword is provided only for backward compatibility. See Forcing internal coordinates for a more detailed description of redundant internal coordinates, including how to force the definition of specific internal variables in combination with automatically generated variables.
  • adjust - This indicates that an existing geometry is to be adjusted. Only new input for the redundant internal coordinates may be provided (Forcing internal coordinates). It is not possible to define new centers or to modify the point group using this keyword. See Forcing internal coordinates for an example of its usage.
  • nucleus - keyword to specify the default model for the nuclear charge distribution. The following values are recognized:
    • point or pt -- point nuclear charge distribution. This is the default.
    • finite or fi -- finite nuclear charge distribution with a Gaussian shape. The RMS radius of the Gaussian is determined from the nuclear mass number A by the expression rRMS = 0.836 * A1 / 3 + 0.57 fm.

NOTE: If you specify a finite nuclear size, you should ensure that the basis set you use is contracted for a finite nuclear size.

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 H2 (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


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 processed. 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:

  • c2v - for molecular symmetry C2v
  • d2h - for molecular symmetry D2h
  • Td - for molecular symmetry Td
  • d6h - for molecular symmetry D6h

The SYMMETRY directive is optional. The default is no symmetry (i.e., C1 point group). Automatic detection of point group symmetry is available through the use of autosym in the GEOMETRY directive main line (discussed in Keywords on the GEOMETRY directive). 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.

Names of 3-dimensional space groups

Web resources

- "A Hypertext Book of Crystallographic Space Group Diagrams and Tables" Birkbeck College, University of London [1]

- NRL Crystal Lattice Structures [2]

- Three-Dimensional Space Groups from Steven Dutch, Natural and Applied Sciences, University of Wisconsin - Green Bay [3]

- REPRES, Space Group Irreducible Representations [4]

Triclinic space groups (group numbers: 1-2)

P1          P-1

Monoclinic space groups (group numbers: 3-15)

                       P2          P2_1        C2          
Pm          Pc         Cm          Cc          P2/m        
P2_1/m      C2/m       P2/c        P2_1/c      C2/c

Orthorhombic space groups (group numbers: 16-74)

P222        P222_1      P2_12_12    P2_12_12_1  C222_1
C222        F222        I222        I2_12_12_1  Pmm2
Pmc2_1      Pcc2        Pma2        Pca2_1      Pnc2
Pmn2_1      Pba2        Pna2_1      Pnn2        Cmm2
Cmc2_1      Ccc2        Amm2        Abm2        Ama2
Aba2        Fmm2        Fdd2        Imm2        Iba2
Ima2        Pmmm        Pnnn        Pccm        Pban
Pmma        Pnna        Pmna        Pcca        Pbam
Pccn        Pbcm        Pnnm        Pmmn        Pbcn
Pbca        Pnma        Cmcm        Cmca        Cmmm
Cccm        Cmma        Ccca        Fmmm        Fddd
Immm        Ibam        Ibca        Imma

Tetragonal space groups (group numbers: 75-142)

                                                P4
P4_1        P4_2        P4_3        I4          I4_1
P-4         I-4         P4/m        P4_2/m      P4/n
P4_2/n      I4/m        I4_1/a      P422        P42_12
P4_122      P4_12_12    P4_222      P4_22_12    P4_322
P4_32_12    I422        I4_122      P4mm        P4bm
P4_2cm      P4_2nm      P4cc        P4nc        P4_2mc
P4_2bc      I4mm        I4cm        I4_1md      I4_1cd
P-42m       P-42c       P-42_1m     P-42_1c     P-4m2
P-4c2       P-4b2       P-4n2       I-4m2       I-4c2
I-42m       I-42d       P4/mmm      P4/mcc      P4/nbm
P4/nnc      P4/mbm      P4/mnc      P4/nmm      P4/ncc
P4_2/mmc    P4_2/mcm    P4_2/nbc    P4_2/nnm    P4_2/mbc
P4_2/mnm    P4_2/nmc    P4_2/ncm    I4/mmm      I4/mcm
I4_1/amd    I4_1/acd

Trigonal space groups (group numbers: 143-167)

                        P3          P3_1        P3_2
R3          P-3         R-3         P312        P321
P3_112      P3_121      P3_212      P3_221      R32
P3m1        P31m        P3c1        P31c        R3m
R3c         P-31m       P-31c       P-3m1       P-3c1
R-3m        R-3c

Hexagonal space groups (group numbers: 168-194)

                        P6          P6_1        P6_5
P6_2        P6_4        P6_3        P-6         P6/m
P6_3/m      P622        P6_122      P6_522      P6_222
P6_422      P6_322      P6mm        P6cc        P6_3cm
P6_3mc      P-6m2       P-6c2       P-62m       P-62c
P6/mmm      P6/mcc      P6_3/mcm    P6_3/mmc

Cubic space groups (group numbers: 195-230)

                                                P23
F23         I23         P2_13       I2_13       Pm-3
Pn-3        Fm-3        Fd-3        Im-3        Pa-3
Ia-3        P432        P4_232      F432        F4_132
I432        P4_332      P4_132      I4_132      P-43m
F-43m       I-43m       P-43n       F-43c       I-43d
Pm-3m       Pn-3n       Pm-3n       Pn-3m       Fm-3m
Fm-3c       Fd-3m       Fd-3c       Im-3m       Ia-3d


LOAD

   [ LOAD [format xyz||pdb]  [frame <int frame>] \
          [select [not] \
               [name <string atomname>] \
               [rname <string residue-name>]
               [id  <int atom-id>|<int range atom-id1:atom-id2> ... ]
               [resi <int residue-id>|<int range residue-id1:residue-id2> ... ]
         ]
  
   <string filename> ]

LOAD directive allows users to load Cartesian coordinates from external pdb or xyz files with the name <filename>. This directive works in addition to the explicit Cartesian coordinate declaration and can be repeated and mixed with the latter. This allows for complex coordinate assemblies where some coordinates are loaded from external files and some specified explicitly in the input file. The ordering of coordinates in the final geometry will follow the order in which LOAD statements and explicit coordinates are specified.

  • The actual file from which coordinates will be loaded is presumed to be located in the run directory (the same place where input file resides). Its name cannot coincide with any of the keywords in the LOAD statement. To keep things simple it is advised to specify it either at the beginning or the end of the LOAD directive.
  • format xyz || pdb - specifies format of the input file. The only formats that are supported at this point are pdb and xyz. Either one can contain multiple structures, which can be selected using the frame directive. Note that in case of PDB file multiple structures are expected to be separated by END keyword. If the format directive is not provided the format will be inferred from file extension - .xyz for xyz files and .pdb for pdb files
  • frame <int frame> - specifies which frame/structure to load from multiple structure xyz or pdb files. In the absence of this directive the 1st frame/structure will be loaded
  • select ... - this directive allows to selectively load parts of the geoemtry in the file within aspecified frame. Selections can be based on atom index (id), atom name (name), and for pdb files can also include residue index (resi) and residue name (rname). Atom and residue name selection are based on an exact single name match. Atom and residue index allow both multiple single number and multiple range selection. For example
 select id 2 4:6 9

will result in the selection of atom id's 2 4 5 6 9.

Multiple selection criteria are always combined as AND selections. For example

  select name O  id 2:4

will select atoms that are named O and whose id/index is between 2 and 4. Each selection criteria can be inverted by prepending not keyword. For example

  select not name O  id 2:4

will select all atoms that are not named O and whose id/index is between 2 and 4.

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, Water Molecule Input). 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:

  • If the entry for <tag> begins with either the symbol or name of an element (regardless of case), then the center is treated as an atom of that type. The default charge is the atomic number (adjusted for the presence of ECPs by the ECP NELEC directive ; see Section 8). Additional characters can be added to the string, to distinguish between atoms of the same element (For example, the tags oxygen, O, o34, olonepair, and Oxygen-ether, will all be interpreted as oxygen atoms.).
  • If the entry for <tag> begins with the characters bq or x (regardless of case), then the center is treated as a dummy center with a default zero charge (Note: a tag beginning with the characters xe will be interpreted as a xenon atom rather than as a dummy center.). Dummy centers may optionally have basis functions or non-zero charge.

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:

  • If the tag begins with characters that cannot be matched against an atom, and those characters are not BQ or X, then a fatal error is generated.
  • The tag of a center is used in the BASIS and ECP directives to associate functions with centers.
  • All centers with the same tag will have the same basis functions.
  • When using automatic symmetry detection, only centers with the same tag will be candidates for testing for symmetry equivalence.
  • The user-specified charges (of all centers, atomic and dummy) and any net total charge of the system are used to determine the number of electrons in the 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. 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 rRMS = 0.836 * A1 / 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 Z-matrix input.

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 (α) must be in the range 0 < α < 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 Cartesian coordinate input). Figures 1, 2 and 3 display the relationships between the input data and the definitions of centers and angles.

Zmat1.jpg
Figure 1: Relationships between the centers, bond angle and dihedral angle in Z-matrix input.


Zmat2.jpg
Figure 2: Relationships between the centers and two bond angles in Z-matrix input with optional parameter specified as +1.


Zmat3.jpg
Figure 3: Relationships between the centers and two bond angles in Z-matrix input with optional parameter specified as -1.


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 (RCi) 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 (RCi) 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 (RCi) relative to center i, the bond angle with centers i and j ( \alpha = \widehat{Cij}, and either the dihedral angle (β) between the current center and centers i, j, and k (Figure 1), or a second bond angle \beta = \widehat{Cik} and an orientation to the plane containing the other three centers (Figure 2 and 3).

By default, β is interpreted as a dihedral angle (see Figure 1), but if the optional final parameter (<orient>) is specified with the value ±1, then β 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 2); and if <orient> is -1, then C is below the plane (Figure 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 Applying constraints in geometry optimizations. 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 CH3CF3. 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 
  H 1 CH3 2 HCH3 3 -TOR2 
  F 2 CF1 1 CCF1 3  TOR3 
  F 2 CF2 1 CCF2 6  FCH1 
  F 2 CF3 1 CCF3 6  -FCH1
  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 
 end   
end

The input for any centers specified with Cartesian coordinates must be specified using the format of the <tag> lines described in Cartesian coordinate input 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:

  • The first center is placed at the origin.
  • The third center is placed in the z-x plane.

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:

  • cvr_scaling -- scaling factor applied to van der Waals radii.
  • bond -- a bond between the two centers.
  • angle -- a bond angle \widehat{ijk}.
  • torsion -- a torsion (or dihedral) angle. The angle between the planes i-j-k and j-k-l.

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. Each internal coordinate may also be named either for easy identification in the output, or for the application of constraints (Applying constraints in geometry optimizations).

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.

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 20).

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 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. The form of the UNSET directive is as follows:

 unset geometry:actlist

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

  • polymer -- system with 1-d translational symmetry (not currently available with NWPW module).
  • surface -- system with 2-d translational symmetry (not currently available with NWPW module).
  • crystal -- system with 3-d translational symmetry.
  • molecule -- no translational symmetry (this is the default)

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 H2O layer input (a 2-d periodic system), x and y coordinates are fractional, whereas z is expressed in Angstroms.

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