The Graphical Analysis Program

Revision: 1.3 Date: 1997/08/14 14:14:00


Table of Contents

 
                                  PREFACE
                                  _______
 
    This   manual  describes  the  ATMOL  Graphical  Analysis  program,  as
implemented on the Cyber-205 at UMRCC. This document is one in a series  of
twelve, supporting the ATMOL packages on the Cyber-205.
 
 
                               ATMOL MANUALS
                               _____________
 
 
                          1.   Introduction.
                          2.   Allocator.
                          3.   Gaussian Integrals.
                          4.   Gaussian Library.
                          5.   SCF.
                          6.   APSG.
                          7.   Transformation.
                          8.   Direct CI.
                          9.   Mulliken Analysis.
                         10.   Graphical Analysis.
                         11.   Properties.
                         12.   Service.
 
 
                             TABLE OF CONTENTS
                             _________________
 
 
    1.   Introduction.                                               1
    2.   Plotting Techniques.                                        1
    3.   The Mode Structure of the Program.                          2
    4.   Data Input Structure.                                       4
    5.   BASIC MODE Data Input.                                      4
    6.   GRID MODE Data Input.                                       5
      6.1   The GRIDMODE Directive.                                  5
      6.2   The TITLE Directive.                                     5
      6.3   The OCCDEF Directive.                                    5
      6.4   The CONFIG Directive.                                    6
      6.5   The GRID Directive.                                      8
      6.6   The PLANE Directive.                                     9
      6.7   The IPRINT Directive.                                   10
      6.8   The GTYPE Directive.                                    11
      6.9   The RESTART Directive.                                  12
      6.10  The DIFFERENCE Directive.                               14
   7.    PLOT MODE Data Input.                                      17
      7.1   The PLOTMODE Directive.                                 17
      7.2   The CVALUES Directive.                                  17
      7.3   The VIEW Directive.                                     18
      7.4   The SCALE Diretive.                                     19
      7.5   The LABEL Directive.                                    20
      7.6   The NOKEY Directive.                                    20
      7.7   The ROTATION Directive.                                 20
      7.8   The TITLE Directive.                                    21
      7.9   The WINDOW Directive.                                   21
      7.10  The MULTPLOT Directive.                                 21
      7.11  The NEXTFRAME Directive.                                22
      7.12  The ENDFRAME Directive.                                 22
      7.13  The PTYPE Directive.                                    22
    8.   TERMINATION MODE Data Input : The STOP Directive.          23
    9.   Electron Density and Electrostatic Potential Functions.    24
      9.1   Electron Density Function.                              24
      9.2   Density Difference Function.                            24
      9.3   Electrostatic Potential Function.                       25
   10.   Printed and Graphical Output.                              25
   11.   Error Monitoring.                                          27
   12.   Specimen Jobs.                                             30
   13.   References.                                                35
 
 

Introduction


 
    The   PLOT   program   provides   graphical   analysis   of   molecular
wavefunctions. To invoke the Graphical Analysis program on the Cyber-205 at
UMRCC use the following JCL:
 
              PATTACH,ATMOL.
              PLOT.
 
    The  program  is  capable  of  generating contour and perspective plots
which depict :
 
(a) the electron density associated with one or more molecular orbitals
 
(b) the amplitude of a molecular orbital
 
(c) the rearrangement of electron density upon molecular formation
 
(d) a comparison of the density  distribution  in  two  or  more  molecular
systems
 
(e) the   interaction   energy  between  a  molecular  distribution  and  a
hypothetical point charge, generating the so-called electrostatic potential
plot.
 
    In  default the program will request 3 large pages of main memory, this
can be varied by means of the  pre-directives  LPAGE  or  MEMORY  [1].  All
pre-directives  [1]  are applicable and should be presented before the main
program directives.
 
    Data  input  and  printed  output  are  on  FORTRAN  streams  5  and  6
respectively. These streams need not normally be mentioned in the JCL.
 
    The  following  data  sets  will  be used by the program, and should be
mentioned in the JCL, in REQUEST, ATTACH, MFLINK or GETFEP commands:
 
    DUMP FILE: The data set used by the Gaussian integrals program  [2]  to
store the geometry and basis of the system under investigation. Recovery of
the eigen vectors from a specified section is used to generate the required
graphical  output.  This  data set may be used by the program to store grid
data used in the generation of contour and perspective plots.
 
    SCRATCH FILE: A data set used as a scratch area for the program, should
be assigned to AFN ED7.
 
    PLOT  FILE:  The  user  is  directed  to  reference  [3]  to obtain the
mechanism by which  the  graphical  output  is  produced  on  UMRCC  Benson
plotters, by a GINO file.
 

Plotting Techinques


 
    Two  types  of  plot  may  be  generated  by  the  program to provide a
pictorial representation of a given density  or  potential  function  in  a
specified molecular plane:
 
(a)  A contour plot, with contours representing  lines  of  constant  value
depicting the spatial characteristics of the given function.
 
(b) A  perspective  plot,  with the values of the function in a given plane
displayed as a 3-D perspective picture.
 
    Both types of plot  are  generated  from  a  grid  of  function  values
produced by the program.
 

The Mode Structure of the Program


 
    The generation of graphical output involves four stages of computation,
which can be summarised as follows:
 
(a) Details of the molecular geometry and basis set specifications are read
from  the  dump  control area (section 191) of the DUMP FILE, as created by
the Gaussian integrals program [2], while the set of eigen  vectors  to  be
analysed  are  read from a nominated section of the DUMP FILE, such vectors
having been placed on the DUMP FILE by a module of  the  SCF  program  [4],
APSG  program  [5]  or  Direct  CI  program  [6]. This mode of the plotting
program shall be known as the BASIC MODE.
 
(b) The construction of a grid of values of a specific density or potential
function spanning a certain area of the molecular plane to be studied. This
phase of the computation, the constrution of the grid, is known as the GRID
MODE. Note that the grid values may be output to a nominated section of the
DUMP FILE.
 
(c) The generation of a single perspective or contour plot based on a  grid
of  values constructed in (b). This is referred to the program as operating
in PLOT MODE, during the generation of the graphical output.
 
(d) Job termination, when all ATMOL and graphical data sets are closed, and
execution   ended.  This  is  referred  to  the  program  as  operating  in
TERMINATION MODE.
 
    Each of the stages outlined has certain data input  associated  to  it.
While  the  program  operates in BASIS MODE at the commencement of the job,
and in TERMINATION MODE upon completion  of  the  graphical  analysis,  the
intermediate  processing is determined by the user, who specifies, via data
input, the sequence of GRID MODE and PLOT MODE  to  be  undertaken  by  the
program.  The  following notes give an indication of typical mode sequences
which may be specified:
 
(a) If the user wants to generate two plots in the same run of the program,
each  plot  being  based  on a different grid of values. Then the following
sequence:
 
      BASIC MODE
      GRID MODE
      PLOT MODE   ------ Plot 1
      GRID MODE
      PLOT MODE   ------ Plot 2
      TERMINATION MODE
 
should be specified, so that the generation of each plot requires that  the
program should run in GRID MODE and PLOT MODE.
 
(b) If the user wants two different plots based on the same grid of values.
This may be accomplished by the following sequence:
 
      BASIS MODE
      GRID MODE
      PLOT MODE   ------ Plot 1
      PLOT MODE   ------ Plot 2
      TERMINATION MODE
 
    Since the program can only produce a single plot when operating in PLOT
MODE,   it  is  necessary  to  specify  two  successive  PLOT  MODES,  each
responsible for generating a plot. Note that the grid  of  values  used  in
generating  a  plot  is  that constructed when the program was last in GRID
MODE. Thus the following sequence:
 
      BASIC MODE
      PLOT MODE
      TERMINATION MODE
 
is not valid, since no mechanism is  present  to  make  a  grid  of  values
accessible for plotting.
 
(c) The facility exists to route a grid of values generated in GRID MODE to
a specific section on the DUMP FILE prior to constructing a plot  based  on
the grid. This will allow additional plots to be generated from the grid in
later jobs in which, for example, contours representing lines  of  constant
values  are  varied,  or different output medium is specified for graphical
output, without the expense of having to regenerate the entire  grid.  This
technique  of  restoring  one, or more, grids from the DUMP FILE and, after
suitable  manipulation,  plotting  the  resultant  grid  is  used  in   the
generation  of  Molecular  Difference plots. Note that grid restoration is,
like grid construction, performed by the program  when  operating  in  GRID
MODE. The following sequence:
 
      BASIS MODE
      GRID MODE
      GRID MODE
      GRID MODE
      TERMINATION MODE
 
may  be  specified, in which case the program will be concerned solely with
the construction of grids,  and  not  with  plotting.  In  such  cases  all
references  to  the  data sets assigned for graphical output may be omitted
from the JCL. When operating in this manner it  is  clearly  imperative  to
route  each  grid  to the DUMP FILE, failure to do so for a given grid will
result in that grid being inaccessible to a subsequent job  concerned  with
generation of graphical output. The following sequence:
 
      BASIS MODE
      GRID MODE
      PLOT MODE   ------ Plot 1
      GRID MODE
      PLOT MODE   ------ Plot 2
      GRID MODE
      PLOT MODE   ------ Plot 3
      TERMINATION MODE
 
must  be  specified  in the subsequent job, where each grid in turn will be
restored from the DUMP FILE and the graphical output generated.
 

Data Input Structure


 
    As detailed previously, a typical run of the analysis program  involves
four  distinct  modes of operation, namely BASIS MODE, GRID MODE, PLOT MODE
and TERMINATION MODE, each of which requires certain data input. While  the
program  operates  in BASIC MODE only once, at the commencement of the job,
subsequent processing undertaken by the program is determined by the  user,
who  controls,  via  data  input, the sequence of modes required. The input
associated with both GRID MODE and PLOT MODE  consists  of  a  sequence  of
directives,  introduced by a mode definition line. Upon detection of such a
data line the program switches control to the  specific  mode,  and  having
input  the data associated with the nominated mode, carries out the process
requested, either the construction of a grid of function values (GRID MODE)
or  the  generation  of  graphical output based on such a grid (PLOT MODE).
When all the necessary computation has been completed, the  program  should
be  placed into TERMINATION MODE by means of the STOP directive, which must
be presented last in the data input. The data input applicable to each mode
will now be discribed.
 

BASIC MODE Data Input


 
    Details  of  the  molecular and basis set specifications, together with
the wavefunction under analysis, are retreived exclusively  from  the  DUMP
FILE  at  commencement of the job, when the program operates in BASIC MODE.
The first  two  data  lines  in  the  input  stream  provide  the  relavent
information to effect this retrieval, and must be presented as follows:
 
    The  first  data  line  is  read to variables NBASIS,IBKLD,DDDUMP using
format (2I,A).
 
    NBASIS  specifies the number of basis functions as defined  during  the
Gaussian integral evaluation.
 
    IBKLD   specifies the starting block of the DUMP FILE.
 
    DDDUMP  specifies  the  AFN  used  to  assign the DUMP FILE. Valid AFNs
being ED0-ED6 and MT0-MT7. If the DDDUMP parameter  is  omitted,  the  DUMP
FILE will be assumed to reside on AFN ED3.
 
    The  second  line  is  read  to variables TEXT,ISECT,TEXTA using format
(A,I,A).
 
    TEXT    should be set to the character string VECTORS.
 
    ISECT   should be used to identify the section on the DUMP  FILE  where
the  set  of  eigen  vectors  that  are  to be analysed, may be found. Such
vectors will normally have been placed on the DUMP FILE  by  the  SCF  [3],
APSG [4] and Direct CI [5] program.
 
    TEXTA   should be set to the character string PRINT if a listing of the
restored  eigen  vectors  is  required.  If  this  parameter is omitted, no
listing will be generated.
 

GRID MODE Data Input


 
    Data input consists a sequence of directives, which should be presented
as outlined below. Not all directives may be required.
 
The GRIDMODE Directive
 
    This directive consists of a single data line with the character string
GRIDMODE in the first data field, and acts as the mode definition line.  It
causes  control  to  be  passed to those routines responsible for the input
data specifying details of the grid of  function  values  to  be  computed,
while operating in GRID MODE.
 
The TITLE Directive
 
    This  directive allows the user to define an 80 character title for use
in labelling the grid and any graphical output subsequently generated  from
the  grid.  The  first data line contains the character string TITLE in the
first data field, the second data line contains the required  80  character
title.
 
   example :
 
       TITLE
       H2O --- GRAPHICAL ANALYSIS
 
The OCCDEF Directive
 
    The purpose of this directive is  to  allow  the  user  to  define  the
occupation  numbers  for  the  molecular  orbitals  to  be analysed. In the
absence of the OCCDEF directive, the occupation numbers will be taken  from
the section of the DUMP FILE specified in the BASIC MODE data input.
 
    The  first  data line contains the character string OCCDEF in the first
data field. Following the directive initiator are the occupation definition
lines.  The first data field of such a line is read in F-format, and should
contain a specified occupation number. Subsequent data fields are  read  in
I-format.  Let the value of an integer specified in such a field be j. Then
the j'th molecular orbital will be assigned the occupation number specified
in the first data field of the line. The following:
 
      2.0 1 2 3 4 5 7
 
comprises  a valid occupation definition line. Such a line may be shortened
if a sequence of consecutive integers appear  by  means  of  the  character
string TO. Thus the abbreviated form of the above line is:
 
      2.0 1 TO 5 7
 
    The occupation definition lines are presented until all the orbitals to
be  assigned  a finite occupancy have been declared. A data line containing
the text END in the first data field must be  presented  to  terminate  the
OCCDEF directive.
 
    The following points must be noted:
 
(a) Any   orbital  omitted  from  the  list  specified  on  the  occupation
definition lines will be assigned zero occupancy, and  thus  will  make  no
contribution to the grid of function values to be constructed.
 
(b) It  is  envisaged  that  the OCCDEF directive will not be required when
generating grids of total electron density, atomic density  difference  and
interaction  potentials. In these three cases the occupation numbers should
reflect the overall orbital occupancy in the molecule, and should  be  just
the values calculated during the construction of the molecular orbitals and
output to the DUMP FILE.
 
(c) When generating a grid of values to be used in constructing the plot of
amplitude  of  a  specified  orbital,  the OCCDEF directive must be used to
specify that orbital, with its occupation number typically set to unity.
 
    example 1:
 
    The appropriate OCCDEF directive when generating a grid of  values  for
use in construction of the amplitude of the 13th molecular orbital is:
 
      OCCDEF
      1.0 13
      END
 
(d) The  OCCDEF  directive  should  be  used  when analysis of the electron
density associated with a certain subset of orbitals is required.
 
    example 2:
 
      OCCDEF
      2.0 1 TO 5 7
      END
 
    The grid of values will be generated assuming the first five  molecular
orbitals,  together  with orbital 7 are doubly occupied. All other orbitals
will be assigned zero occupancy.
 
The CONFIG Directive
 
    The CONFIG directive is only  applicable  when  generating  a  grid  of
atomic density difference, and may be used to specify the configurations to
be used in computing the atomic density distribution corresponding  to  the
ground  state  of  the  atoms. In the absence of this directive spherically
symmetric atoms are chosen, with equal occupation of  the  degenerate  open
shell orbitals.
 
    example :
 
    The atomic configuration chosen in default for the  carbon  atom  would
be:
 
        2    2      .666667     .666667     .666667
     (1s) (2s)  (2px)       (2py)       (2pz)
 
for the iron atom (d6s2 high spin):
 
        2     2      2      2      2     2      2      2      2     2
     (1s)  (2s)  (2px)  (2py)  (2pz)  (3s)  (3px)  (3py)  (3pz)  (4s)
          1.2      1.2      1.2       1.2      1.2
     (3dxy)   (3dxz)   (3dyz)   (3dx-y)   (3dz2)
 
    The  CONFIG  directive  consists of three types of data line. The first
line, the directive initiator, consists of the character string  CONFIG  in
the  first data field, the last line, the directive terminator, consists of
the character string END in the first data field. Lines  presented  between
the  directive  initiator and terminator are the 'configuration definition'
lines. If there are NAT atoms whose configuration are to be specified, then
NAT 'configuration' lines are required. Each line consists of (NORB+1) data
fields, where NORB is the total number of  doubly  and  partially  occupied
orbitals  in  the  atom. The first data field is read to the variable ALAB,
using format A, while the remainder of the data line  should  contain  real
numbers  read in F-format to a vector (OCC(I),I=1,NORB). ALAB should be set
to the label parameter of the nucleus, as specified  by  the  corresponding
'nucleus  definition'  lines  in  the GEOMETRY or GEOMGEN directives of the
Gaussian integrals program [2]. OCC(I) should  be  set  to  the  occupation
number  of  the  i'th  atomic orbital. The latter must be input in order of
symmetry - s,p,d etc - with the partially occupied orbitals preceded by the
doubly occupied orbitals, within each symmetry class.
 
    example 1:
 
    Suppose  the user wishes the following configuration for a carbon atom,
which has been labelled as nucleus C1:
 
             2    2     1     1
      C : (1s) (2s) (2px) (2py)
 
then the following configuration definition line should be presented:
 
      C1 2.0 2.0 1.0 1.0 0.0
 
    example 2:
 
    To specify the configuration :
 
         2    2    6    2     1
      (1s) (2s) (2p) (3s) (3pz)
 
for an aluminium atom, labelled AL by the GEOMETRY directive, the user must
present the following configuration definition line:
 
      AL 2.0 2.0 2.0 2.0 2.0 2.0 0.0 0.0 1.0
 
where the first three 2.0 give the occupation of the s orbitals, while  the
remainder details the occupation of the p orbitals.
 
    example 3:
 
    To specify the configuration
 
         2    2    6    2    6
      (1s) (2s) (2p) (3s) (3p)
           2      2      2       0      0
      (3dxy) (3dxz) (3dyz) (3dx-y) (3dz2)
 
for an iron atom, which has been labelled 1, the user  should  present  the
following line :
 
      1 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 0.0 0.0
        < s orbitals  > <     p orbitals      > <    d orbitals   >
 
    Note that the occupation numbers of the  three  p  orbitals  should  be
input  in  the  order  x,y,z  and those of the five d orbitals in the order
dxy,dxz,dyz,dx-y,dz2.
 
The GRID Directive
 
    The GRID directive consists of a single data  line  read  to  variables
TEXT,NGRID using format (A,I).
 
    TEXT    should be set to the character string GRID.
 
    NGRID   is an integer used to control the appearance of the final plot.
The area to be studied (see PLANE directive) is  divided  into  a  mesh  of
(NGRID*NGRID) points, and the appropriate function evaluated at each point.
The plotting routine will subsequently interpolate  the  computed  grid  to
produce  as  smooth contours as possible. Obviously the finer the mesh (the
larger NGRID), the smoother the resultant contours,  but  the  greater  the
computer time and memory allocation required to generate the grid. The size
of line printer contour plot is also affected by the grid  size  parameter,
and is (NGRID*NGRID) characters in area.
 
    Some points to note on the GRID directive:
 
(a) The  GRID directive may be omitted, when NGRID will be set to the value
51.
 
(b) Experience suggests that little benefit results from using a  value  of
NGRID  > 97, since no visible inprovement in the smoothness of the contours
is evident beyond this point. It is not recommended that the value of NGRID
< 25.
 
(c) Use  of  the  default  GRID  directive,  in  general,  prove  very time
consuming for the generation of potential plots. It is recommended  that  a
(25*25) mesh be adequate in generating potential plots.
 
 
The PLANE Directive
 
    The PLANE directive is  used  to  define  the  molecular  plane  to  be
studied.  The  first  data line is read to variables TEXT,SIZE using format
(A,F).
 
    TEXT    should be set to the character string PLANE.
 
    SIZE    is the area covered  by  the  plot,  in  the  molecular  plane,
defined  as (SIZE*SIZE) Bohr. This variable may be omitted, when an area of
(10*10) Bohr will be covered.
 
    The remainder of the PLANE directive consists of three data  lines,  in
which the molecular plane is defined.
 
    Line  1  is read to varaibles X1,Y1,Z1 using format (3F). These are the
co-ordinates of a point P1 in the molecular  co-ordinate  system,  defining
the centre of the the plane to be studied.
 
    Line  2  is read to variables X2,Y2,Z2 using format (3F). These are the
molecular co-ordinates of a second point, P2, which in conjunction with P1,
define the y (vertical) axis of the plot (see Figure 1).
 
    Line  3  is read to variables X3,Y3,Z3 using format (3F). These are the
molecular co-ordinates of a third point, P3, which should not be  co-linear
with  P1  and  P2.  P3,  in conjuction with P1 and P2, define the molecular
plane being studied. The x (horizontal) axis is given in figure 6.1, and is
generated by Schmidt orthogonalising the vector P1-P3 to the vector P1-P2.
 
 
                                 Figure 1
                                 ________
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
    Definition of the points P1,P2 and P3 specified by the PLANE directive
 
    example 1:
 
    The  following  example is based on the HCO radical. To generate a grid
covering and area of (5*5)  Bohr  in  the  plane  containing  the  molecule
(xy-plane),  with the C atom at the centre of the plane (see Figure 2), the
user should present the following data lines for the PLANE directive:
 
      PLANE 5.0
      0.0 0.0 0.0
      0.0 0.0 1.0
      0.0 1.0 0.0
 
                                     Figure 2
                                     ________
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
    example 2:
 
    Based  on the planar structure of the H2O molecule, the generation of a
grid covering an area of (7*7) Bohr, in the plane containing the O  H1  and
H2  atoms  (Figure 3), with the O atom at the centre of the plane. The user
should  present  the  GRID  data  (geometry  is  assumed  to  be  that   of
experimental) as :
 
      PLANE 7.0
      0.0 0.0 0.0
      0.0 1.0 0.0
      0.0 0.0 1.0
 
The IPRINT Directive
 
    The IPRINT directive may be used to increase the  quantity  of  printed
output produced by the program, while operating in GRID MODE. The directive
consists of one data line, the first  data  field  contains  the  character
string  IPRINT.  Subsequent  data  fields are read in A-format, and specify
that printing as in Table 1 is to occur.
 
 
                                        Figure 3
                                        ________
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
                          Table 1
                          _______
 
              Parameters of the IPRINT directive
              __________________________________
 
              Data Field        Causes printing
 
              ATOMSCF           Various intermediate results from
                                the atomic SCF calculations performed
                                in generating a grid of atomic density
                                differences. Includes matrices of
                                integrals over basis functions and
                                final closed and open shell Fock
                                matrices.
              GVAL              The (NGRID*NGRID) matrix of grid
                                values.
 
The GTYPE Directive
 
    This  directive  is  used  to  specify  the function to be used in grid
construction (the type of grid to be generated), and consists of  a  single
data line read to variables TEXT,TEST,ISECT using format (2A,I).
 
    TEXT    should be set to the character string GTYPE.
 
    TEST    should  be  set  to  one  of the character strings specified in
Table 2.
 
    ISECT   specifies the section number on the DUMP FILE where the grid of
values  is  to  be  placed. ISECT may be omitted, in which case the grid of
values will not be routed to the DUMP FILE.
 
 
                          Table 2
                          _______
 
              Parameters of the GTYPE Directive
              _________________________________
 
              TEST           Grid Function
              DENSITY        Electron density
              NOSQUARE       Orbital amplitude
              ATOM           Atomic difference density
              POTENTIAL      Molecular electrostatic potential
 
    The following points when using the GTYPE directive, should be noted:
 
(a) When generating a grid of electrostatic potentials (TEST=POTENTIAL), it
is  recommended that the grid of values should always be routed to the DUMP
FILE. Note also  that  the  generation  of  the  Molecule-difference  plots
requires  all  the  component  grids  to be located on the appropriate DUMP
FILE.
 
(b) The nominated section of the DUMP FILE used to hold the grid of  values
is of TYPE=50. While a detailed account of the structure of this section is
not given, the following may be used to deduce the  space  requirements  of
the section.
 
    Let :
 
      L = ((NGRID+2) * (NGRID+2) + 1) / 2
 
where  NGRID  is the integer parameter of the GRID directive. The number of
blocks in the grid section is given by :
 
      N = ((L-1) / 511) + 2
 
where division is accomplished by rounding down  to  the  nearest  integer.
Thus  the  output  of a grid of (97*97) points would require 11 blocks, the
output of a grid of (51*51) points would require 4 blocks and the output of
a grid of (25*25) points 2 blocks.
 
(c) The GTYPE directive instructs the program to commence generation of the
specified grid, and should be the last of the  current  set  of  GRID  MODE
directives to be presented.
 
    example :
 
    To  generate a grid of atomic difference density, and to route the grid
to section 30 of the DUMP FILE, the user should present the following  data
line :
 
      GTYPE ATOM 30
 
The RESTART Directive
 
    The  considerable increase in computer time required to generate a grid
of electrostatic potentials relative to that used in the  generation  of  a
density function grid, has required the introduction of restart facilities.
The graphical analysis program will monitor SBU time remaining for  a  run,
and when insufficient time remains to usefully continue, a standard dump is
invoked.  Dump control information, together with the current status of the
grid of potentials, is sent to the nominated section of the  DUMP  FILE  as
specified  by  the  GTYPE  directive.  Line  printer  output  is generated,
informing the user of the current status of the calculation. The message :
 
       GRID GENERATION INCOMPLETE--RESTART
 
will be sent to the output file, indicating the need for a restart job. The
RESTART  directive  may  be used to restart the PLOT job, and consists of a
single data line read to variables TEXT,ISECT using format (A,I).
 
    TEXT    should specify the character string RESTART.
 
    ISECT   should be used to identify the section on  the  DUMP  FILE,  as
specified  by  the  GTYPE  directive  of the startup run, where the grid of
potentials may be found.
 
    The following points on the RESTART directive should be noted:
 
(a) The only GRID MODE directive which may precede a RESTART  directive  is
the  GRIDMODE  directive.  All  other  directives will either be ignored or
cause an error condition.
 
(b) The RESTART directive causes retrieval of dump control information from
the nominated section of the DUMP FILE, together with the current status of
the grid potentials. It will be immediately followed by the GTYPE directive
to initiate commencement of grid evaluation from the appropriate point. Any
directive presented between the RESTART and GTYPE directive will  cause  an
error condition.
 
(c) A  restart  job may run out of time and initate a dump. If this occurs,
resubmit the restart job until the message :
 
      RESTORED GRID IS COMPLETED
 
is seen on the printed output.
 
(d) Restart facilities are only available when generating potential grids.
 
    example :
 
    Suppose that the following GRID MODE data was used in the startup job:
 
      GRIDMODE
      TITLE
      WATER POTENTIAL PLOT
      GRID 25
      0.0 0.0 0.0
      0.0 1.0 0.0
      0.0 0.0 1.0
      GTYPE POTE 20
 
with the grid of potentials routed to section 20 of the DUMP FILE. The GRID
MODE data for the restart would be :
 
      GRIDMODE
      RESTART 20
      GTYPE POTE 20
 
The DIFFERENCE Directive
 
    This directive may be used to  construct  a  grid  resulting  from  the
addition  and/or  subtraction of up to a maximum of 15 component grids, and
provides a mechanism for generating a grid of Molecular Density difference.
All  component  grids must have been previously written to the current DUMP
FILE or to a foreign DUMP FILE (a DUMP FILE different from that  associated
with the present job). The first data line contains the directive initiator
in the first data field, read to the variable TEXT using A-format.  If  the
resultant grid to be constructed is generated from a total of N grids, then
successive data fields are read to the vectors (SIGN(I),LABEL(I),I=1,N)  in
A-format.
 
    TEXT    should be set to the character string DIFF.
 
    SIGN(I) contains  the character string '+' or '-', depending on whether
the I'th grid is to be added to, or subtracted from, the resultant grid.
 
    LABEL(I) is used to give the I'th grid a label  by  which  it  will  be
subsequently  known.  LABEL  may be up to eight characters long, and should
not include a space character.
 
    N subsequent 'grid definition' lines are input,  the  format  of  which
depends  on  the  location  of the component grid. In those cases where the
grid resides on the current DUMP FILE,  the  definition  line  is  read  to
variables TEXT,ISECT using variables (A,I).
 
    TEXT    should  be  set  to  the  LABEL  of  the  grid  in question, as
specified on the first data line.
 
    ISECT   is an integer used to specify the section wherein the  required
grid  is  to  be  found on the DUMP FILE. This integer was specified on the
GTYPE directive of the job which created the grid.
 
    In the case of a grid to be restored from a 'foreign'  DUMP  FILE,  the
grid  definition lines are read to variables TEXT,DDFORN,IBLKF,ISECTF using
format (2A,2I).
 
    TEXT    should be set to the LABEL of the grid in question.
 
    DDFORN,IBLKF the location of the 'foreign' DUMP FILE resides on the AFN
specified  by  DDFORN  which  commences  at  block  specified by IBLKF. The
'foreign' DUMP FILE may reside on the AFNs ED0-ED6 or MT0-MT7.
 
    ISECTF  is an integer used to specify the section wherein the  required
grid  is to be found on the 'foreign' DUMP FILE. This integer was specified
on the GTYPE directive of the run which created the grid.
 
    The  following  points  should  be  noted  when  using  the   DIFFERNCE
directive.
 
(a) The only GRID MODE directives which may precede a DIFFERENCE  directive
are GRIDMODE, TITLE and IPRINT. All other directives will either be ignored
or cause an error conition.
 
(b) The  DIFFERENCE  directive   initiates   the   commencement   of   grid
construction  from the specified component grids, and when used must be the
last of the present GRID MODE directives presented.
 
(c) Since the facility to output the resultant grid generated under control
of  the DIFFERENCE directive to a section of the DUMP FILE is not provided,
                                                              ___
it is envisaged  that  control  will  be  immediately  transferred  to  the
plotting routines by the PLOT MODE directives, to construct the appropriate
plot based on this grid.
 
(d) Note  that  all  the  component  grids  referenced  by  the  DIFFERENCE
directive must:
 
(1) have been created with the same dimensions.
 
(2) contain  values  of  the  same  function,  as  specified  by  the GTYPE
directive, on creation of the grid values.
 
(3) relate to the same molecular plane.
 
    Any  attempt  to  combine  grids  which  do  not  satisfy  these  three
conditions will be treated as an invalid operation, and results in an error
condition.
 
    example 1:
 
    Suppose the user wishes to construct a grid, and a  subsequent  contour
plot, to illustrate the changes in electron density resulting from addition
of polarisation functions to a double zeta (DZ) basis  set  calculation  on
water.  Having constructed the wavefunction from each basis set, assume the
following:
 
    Basis Set           DZ        DZPOL
                    (4s2p/2s) (4s2p1d/2s1p)
 
    NBASIS              14        25
 
    Starting block      1         50
    of DUMP FILE
 
    SCF vectors routed  2         4
    to section
 
where the DUMP FILE from each calculation resides on the same data set. The
construction of the required grid is achieved by  using  two  runs  of  the
graphical analysis program.
 
    Run  1,  generates  the  grid  of total electron density from the DZPOL
basis. Assuming the grid is to be output to section  5  of  the  DUMP  FILE
which  is  assigned  using the AFN ED2, the following BASIS MODE, GRID MODE
and TERMINATION MODE data should be presented:
 
      25 50 ED2
      VECTORS 4
      GRIDMODE
      TITLE
      H2O - DZPOL BASIS
      GRID 97
      PLANE 5.0
      0.0 0.0 0.0
      0.0 1.0 0.0
      0.0 0.0 1.0
      GTYPE DENS 5
      STOP
 
Note that the molecular plane definition is based on the co-ordinate system
of the water geometry. The absence of the PLOT MODE directives  means  that
no graphical output will be generated from this job.
 
    Run  2, contains two sets of GRID MODE directives, the first generating
the grid of total electron density for the DZ basis set and routing  it  to
section 6 of the DZ-DUMP FILE. The second generates the required (DZPOL-DZ)
molecular difference grid, with the DZPOL-DUMP  FILE  being  treated  as  a
'foreign'  DUMP  FILE in the DIFFERNCE directive. The following data should
be presented :
 
      14 1 ED2
      VECTORS 1
      GRIDMODE
      TITLE
      H2O - DZ BASIS                   Grid Mode 1
      GRID 97
      PLANE 5.0
      0.0 0.0 0.0
      0.0 1.0 0.0
      0.0 0.0 1.0
      GTYPE DENS 6
      GRIDMODE
      TITLE
      H2O DZPOL - DZ                   Grid Mode 2
      IPRINT GVAL
      DIFF + DZPOL - DZ
      DZPOL ED2 50 5
      DZ 6
      PLOTMODE
      PTYPE CONTOUR LINE
      STOP
 
Note that the definition of the molecular plane under study  and  the  grid
size  are identical in both cases. The resultant grid of difference density
will be output to the line printer. Details of  the  PLOT  MODE  directives
used in generating the required contour plot are given in section 7.
 
    example 2:
 
    Suppose  that  having generated the difference plot from example 1, the
user subsequently requires a plot of the DZPOL density  alone.  Remembering
that the DZPOL grid was output to section 5 of  the  DZPOL-DUMP  FILE,  the
user  may  use  the DIFFERENCE directive to restore the grid for subsequent
processing by the PLOT MODE directives. The following sequence of data  may
be presented to accomplish this task:
 
      25 50 ED2
      VECTORS 4
      GRIDMODE
      TITLE
      H2O DZPOL BASIS
      DIFF + DZPOL
      DZPOL 5
 
which will restore the appropriate grid prior to plotting.
 

PLOT MODE Data Input


 
    Data  input  consists  of  a  sequence  of  directives  which should be
presented in the following order. Not all directives may be required  in  a
single run.
 
The PLOTMODE Directive
 
    This directive consists of a single data line with the character string
PLOTMODE in the  first  data  field.  This  data  line  acts  as  the  mode
definition  line  and  causes  control  to  be  passed  to  those  routines
reponsible for the input of data to be used in generating graphical output.
 
The CVALUES Directive
 
    This directive may be used to define a set of function values for which
contours are required. The first data line consists of the character string
CVALUES in the first data field. If contours at NOCON values are  required,
subsequent  data  lines should contain NOCON real numbers, read in F format
to a vector (CVAL(I),I=1,NOCON). The last data  field  should  contain  the
character string END. Thus the sequences :
 
      CVALUES
      .7 .5 .3 .1 .03 END
 
and
 
      CVALUES
      .7 .5 .1
      .03
      END
 
are  equivalent.  CVAL(I) should be set to the values to be associated with
the I'th contour.
 
    The CVALUES directive may be omitted, when the default set  of  contour
values given in Table 3 will be used. The following points should be noted.
 
(a) Following  the  conventions  commonly  adopted  in  the literature, the
iso-energy curves of the potential plot are in units of kcal/mol, while the
iso-density curves of various electron density plots are in  atomic  units.
This  convention  should also be adopted when overriding the default values
of Table 3 using the CVALUES directive.
 
(b) The CVALUES directive is  not  applicable  and  will  be  ignored  when
generating perspective plots.
 
                                 Table 3
                                 _______
 
                   Default contour values used for potential
                   and density contour plots as a function
                   of the grid type.
 
                   iso-energy               iso-density curves
                   (kcal/mol)                 (atomic units)
 
 GTYPE setting       POTE         DENS      NOSQUARE   ATOM or DIFF
 
                     210.0        64.7837   1.0        0.8691
                     180.0        16.1959   0.5        0.43455
                     150.0         4.0490   0.25       0.21727
                     120.0         1.0122   0.125      0.10864
                      90.0         0.5061   0.0625     0.05432
                      75.0         0.2531   0.03125    0.02716
                      60.0         0.1265   0.01562    0.01358
                      40.0         0.0633   0.00781    0.00697
                      20.0         0.0316   0.00391    0.00339
                      10.0         0.0158   0.00195    0.00170
                       5.0         0.0079   0.00098    0.00085
                       2.0         0.0040   0.00049    0.00042
                       0.0         0.0020   0.0        0.0
                                   0.0010
 
    Contour  values  for  POTE,  NOSQUARE, ATOM and DIFF settings have also
corresponding negative values.
 
The VIEW Directive
 
    The VIEW directive is only relevant when generating perspective  plots,
and  when plotting via the J06HEF routine (not the default), and is used to
specify the angle of view and viewing distance  (Figure  4).  The  grid  of
electron  densities  or  potentials define the z-values of the surface on a
two-dimensional (x,y) grid of points covering the  specified  area  of  the
molecular plane under investigation.
 
    The  directive  consists  of a single data line read to variables TEXT,
THETAV,THETAH,DIST using format (A,3F).
 
    TEXT    should be set to the character string VIEW.
 
    THETAV  specifies the elevation of the view axis above  the  horizontal
base-plane in degrees (see Figure 4)
 
    THETAH  specifies  the rotation of the vertical axis through the centre
of the grid in a clockwise direction, in degrees (see Figure 4). For 0.0  <
THETAH < 180.0, the surface appears to rotate in a clockwise  direction  as
THETAH increases.
 
    DIST    specifies the viewing distance (R in Figure 4) in Bohr.
 
    The  VIEW  directive  may be omitted, when THETAV and THETAH will given
the value 30, and DIST will be set to the value of SIZE  specified  by  the
PLANE directive.
 
                                       Figure 4
                                       ________
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
    example :
 
    To  view  the  surface  edge-on along the y-axis, from a distance of 10
Bohr, the following data line should be presented :
 
      VIEW 0.0 0.0 10.0
 
The SCALE Directive
 
    This directive is only relevant when generating perspective plots,  and
may be used to normalise the stereo-graphic projection to certain values of
electron density or potential function. The directive consists of a  single
data line read to variables TEXT,SCAMAX,SCAMIN,FACTOR using format (A,4F).
 
    TEXT    should be set to the character string SCALE.
 
    SCAMAX,FACTOR the grid of values to be plotted is scanned to detect all
local maxima, which will appear as peaks on the project plot, and  thus  to
determine  VMAX,  the  value of the greatest maximum < SCAMAX. In the event
that no such maximum is detected, VMAX will be set to  SCAMAX.  All  maxima
with  a  greater  value than (VMAX*FACTOR) will appear as beheaded peaks on
the final plot.
 
    SCAMIN,FACTOR the grid of values is scaned to detect all local  minima,
which  will  appear as troughs on the projected plot, and thus to determine
VMIN, the value of the lowest minimum > SCAMIN. In the event that  no  such
minimum  is  detected,  VMIN will be set to SCAMIN. All minima with a value
less than (VMIN*FACTOR) will appear as  'beheaded'  troughs  on  the  final
plot.
 
    The projected plot will be normalised to (VMAX*FACTOR-VMIN*FACTOR). The
SCALE directive may be omitted, when SCAMAX is set to 0.7, SCAMIN  to  -0.7
and FACTOR to 1.2.
 
The LABEL Directive
 
    The  LABEL  directive  allows  the user to specify the frequency of the
contour heights that are labelled. The directive consists of a single  data
line read to variables TEXT, NLABEL using format (A,I).
 
    TEXT    should be set to the character string LABEL.
 
    NLABEL  is  an  integer used to control the frequency of the labelling.
NLABEL contour heights will be labelled.
 
    This directive is only valid when a CONTOUR NAG plot  is  produced.  By
default  every  second contour is labelled. If a user does not wish to have
any contours labelled, it is suggested  to  set  NLABEL  to  a  very  large
integer.
 
    example :
 
     LABEL 4
 
Invoking  this  directive,  every fourth contour height will be labelled in
the subsequent contour plot.
 
The NOKEY Directive
 
    The NOKEY directive surpresses the contour key. The directive  consists
of a single data line containing the character string NOKEY. This directive
is valid only when a CONTOUR NAG plot is produced.
 
The ROTATION Directive
 
    This diretive allows the user to specify the view generated by PERSPECT
in default mode (J06HBF). The directive consists of a single data line read
to variables TEXT, IROT using format (A,I).
 
    TEXT    should be set to the character string ROTATION.
 
    IROT    should be set to a integer in the range 0 to 3.
 
    By default, IROT is set to  0.  Each  increment  of  IROT  rotates  the
perspective  view by 90 degrees through the centre of the vertical axis, in
a clockwise direction.  This  directive  is  valid  for  only  the  default
PERSPECT mode (J06HBF).
 
    example :
 
     ROTATION 2
 
This will rotate the perspective view through 180 degrees, from the default
setting.
 
The TITLE Directive
 
    This directive should not be confused with the TITLE directive in  GRID
MODE.  The  purpose  of  this  directive  is to allow the user to specify a
title, that will be printed on  the  hardcopy  graphical  plot.  The  TITLE
directive  consists  of  two  data  lines, the first data line contains the
character string TITLE in the first data field. Second data  line  contains
the  required  title  to be printed on the hardcopy graphics output, upto a
maximium 80 character title is permitted.
 
The WINDOW Directive
 
    This directive allows the user to specify the position of the  hardcopy
plot  within  the  graphic frame. The WINDOW directive consists of a single
data line  read  to  variables  TEXT,SMINX,SMAXX,SMINY,SMAXY  using  format
(A,4F)
 
    TEXT    should be set to the character string WINDOW.
 
    SMINX,SMAXX,SMINY,SMAXY specifies  the  position of the plot within the
graphic frame. SMINX and SMAXX give  minimum  and  maximum  values  in  the
x-direction,  while  SMINY and SMAXY give minimum and maximum vaules in the
y-direction for a given plot. The parameters must be within 0.0 to 1.0.
 
    For a contour plot, the WINDOW directive can  be  used  to  enlarge  or
reduce  the  size  of the plot, the contour key box will also vary in size.
The WINDOW directive is only valid for contour hardcopy plots.
 
    Default values for the WINDOW paramters are:
 
         SMIN = 0.0     SMAXX = 0.6    SMINY = 0.0    SMAXY = 0.8
 
    example :
 
     WINDOW 0.1 0.65 0.1 0.85
 
The MULTPLOT Directive
 
    This directive consists of a single data line  read  to  the  variables
TEXT,NPLOT using format (A,I).
 
    TEXT    should specify the character string MULTPLOT.
 
    NPLOT   is an integer specifying the number of the plot within a single
frame. This should be set to 1.
 
    This directive should be used in the first PLOTMODE  of  a  multi-frame
plot  run, this tells the job that subsequent plots are to be processed and
this is the first plot. This directive is not required  in  a  single  plot
job.
 
The NEXTFRAME Directive
 
    The  purpose of this directive is to allow the user to have multi-frame
plots produced in a single job. The directive consists  of  a  single  data
line read to the character string NEXTFRAME.
 
    This  directive  must  be  presented  when ever a new plot is produced,
except on the first plot. This directive is not required in a  single  plot
job.
 
The ENDFRAME Directive
 
    The  ENDFRAME directive terminates a multi-frame plot job and should be
presented in the last PLOTMODE of the job.  The  directive  consists  of  a
single  data  line  read  to  the  character string ENDFRAME. The NEXTFRAME
directive should also appear in the last PLOTMODE.
 
The PTYPE Directive
 
    This directive is used to specify the type of plot to be generated  and
to  define  the  output  medium  for  the  graphical  output. The directive
consists of a single data line, the first two data fields of which are read
to the variables TEXT,PLOT using format (2A).
 
    TEXT    should be set to the character string PTYPE.
 
    PLOT    should be set to the character string CONTOUR if a contour plot
of the function is required, or to  the  character  string  PERSPECT  if  a
perspective plot of the function is required.
 
    Subsequent  data  fields  are  read in A-format, and specify the output
media as detailed in Table 4, for the graphical output.
 
 
                             Table 4
                             _______
 
                  Parameters for the PTYPE directive.
 
      Data Field             Media Output
 
      LINE                   lineprinter. Note that it is only possible
                             to generate a contour plot, and not a
                             perspective plot.
      NAG                    if specified, a contour plot will be
                             generated via the NAG-GINO package. The hard
                             copy graphical output is generated on the
                             Benson plotter-B1130 (narrow drum). Valid
                             only with the CONTOUR sub-directive.
                             NAG routine used J06GBF.
      J06HEF                 if specified, a perspective plot will be
                             generated via the NAG-GINO package. The
                             hard copy graphical output is generated on
                             the Benson plotter-B1130 (narrow drum).
                             Valid only with the PERSPECT sub-directive.
                             This directive will override the default
                             perspective plot.
                             NAG routine used J06HEF.
 
    A perspective plot may be generated by just specifying PERSPECT in  the
PTYPE  data  line.  The  graphical  plot  will be generated by the NAG-GINO
package. The hard copy  plot  is  generated  on  the  Benson  plotter-B1130
(narrow drum). NAG routine used J06HBF.
 
    Users  are  referred to the reference [7] for more detailed information
on the NAG routines used in the Graphical Anaylsis program  and  the  error
codes that may be generated.
 
    The PTYPE directive instructs the program to commence generation of the
specified plot, and should be presented last in the PLOT MODE  sequence  of
directives.
 
    example 1:
 
    To generate a version of a contour plot on the Benson plotter, the user
should present the following data line :
 
      PTYPE CONTOUR NAG
 
    example 2:
 
    To generate a perspective plot on the Benson plotter using the  default
option (J06HBF), the user should present the following data line :
 
      PTYPE PERSPECT
 

TERMINATION MODE Data Input : The STOP Directive


 
    The  STOP  directive consists of a single data line, with either of the
character strings STOP or EXIT in the first data field, and indicates  that
no more GRID MODE or PLOT MODE data is to be processed. The STOP  directive
must  be  the  last presented in the data input stream, the effect being to
cause the program to terminate execution: any  directives  presented  after
STOP will be ignored.
 

Electron Density and Electrostatic Potential Functions


 
    A  pictorial  representation of the electronic charge distribution of a
molecular system is provided by the construction of plots  associated  with
the following functions.
 
Electron Density Functions
 
    In depicting the spatial characteristics of the density associated with
one, or more molecular orbitals, the program computes  densities  according
to the formula:
 
            equation
 
where  O  denotes the i'th molecular orbital and OCC its occupation number.
Plots of the amplitude of a single orbital, i,
 
        equation
 
may also be generated.
 
Density Difference Function
 
    The atomic density difference function is defined as:
 
        equation
 
the first term is the total electron density associated  with  a  molecule.
The  second  term  represents the sum of the electron denities of the atoms
which constitute the molecule, these being placed at the same positions  as
they  occupy in the molecule, but assumed to have undergone no interactions
with each other and have remained undistorted as in  the  free  state.  The
atomic  density  difference  function provides an indication of the overall
rearrangement of density which occurs when the  atoms  come  together  upon
molecular formation. The program incorporates an atomic SCF module, so that
calculations on the ground states of the component atoms are  performed  in
line,  with  the basis set of each atom the same as that used in the parent
molecule. These plots are known as 'atom-differnce' plots, the  program  is
capable  of generating such plots of molecular systems with component atoms
up to, and including zinc.
 
    A more general form of the density difference function,  the  molecular
density difference:
 
      equation
 
is  used  in  construction  of molecular-difference plots, which allows the
user to display the density resulting from the addition or  subtraction  of
up  to  15  component  density functions. Two examples of the value of such
plots are:
 
(a) in illustrating the effect on a molecular charge distribution resulting
from  an  extension  of  the  basis  set,  so  that a typical plot would be
constructed using the function:
 
    equation
 
 
(b) in  depicting  the  rearrangement of electron density which occurs when
the component ligands and metal atom of a  transition  metal  complex  come
together  to  form  the  molecular  system,  so  that for a complex MX, the
following difference function:
 
      equation
 
would  be  constructed,  the  molecular  analogue  of  the  atomic  density
difference function.
 
Electrostatic Potential Function
 
    The  value  of  the  electrostatic  potential created by the electronic
distribution and nuclear charge of a molecule, in the different regions  of
space surrounding it, provides information about possible sites involved in
protonation or in reactions  with  electrophilic  agents.  The  interaction
energy  between  a  molecular distribution and an external unitary positive
charge at a given point i, is given by:
 
      equation
 
where Z is the nuclear charge of nucleus a and n(1) the first order density
function.  The  program  permits the construction of plots of electrostatic
interaction  energies  based  on  the  density  distribution  arising  from
wavefunctions constructed in Gaussian orbital basis sets.
 

Printed and Graphic Output


 
    The  output generated by each MODE of the Graphical Analysis program is
as follows.
 
    BASIS MODE: output commences with an ordered list  of  basis  functions
and  details  of  the  molecular  geometry,  as  read from the dump control
section of the DUMP FILE. If the PRINT parameter on the second program data
line  is  used  a  listing  of  the  matrix  eigen vectors as read from the
nominated section of the DUMP FILE is printed, with each column  containing
the coefficients of the LCBF in a given molecular orbital.
 
    GRID  MODE:  output commences with a summary of the options selected by
the user. When generating a grid of atomic density differnce,  the  program
will  output  details of the atomic SCF calculations performed. This output
includes details of the basis set used, together with the final SCF results
including  total  energy,  kinetic  energy,  virial  test, eigen values and
vectors. Various intermediary results from the  SCF  calculations  will  be
output if the ATOMSCF parameter of the IPRINT is used.
 
    The co-ordinates of the points P1, P2 and P3, as specified by the PLANE
directive are output as in the following example:
 
                    INPUT PLANE DEFINITION
 
                    X         Y         Z
 
         P1        0.0       0.0       0.0
 
         P2        0.0       1.0       0.0
 
         P3        0.0       0.0      -1.0
 
Upon completion of grid construction, the program scans the grid to  detect
all  local  maxima  and minima, which will be output to the printer. If the
GVAL parameter of the IPRINT directive is used, the complete grid of values
is  output  in  a  matrix labelled 'MATRIX OF GRID VALUES'. The columns and
rows of this matrix are labelled by an index running from -NGRID/2  through
zero  to  +NGRID/2,  where  NGRID  is  the  integer  parameter  of the GRID
directive.
 
    PLOT MODE: output commences with a summary of the options  selected  by
the  user.  If  the  LINE  parameter  of  the  PTYPE directive is used when
generating a contour plot, there follows a plane definition  normalized  to
one character displacements on the line printer plot, as follows:
 
         NORMALISED PLANE DEFINITION (FOR 1 CHARACTER ON LINE PRINTER PLOT)
 
                   X         Y         Z
 
         P1       0.0       0.0       0.0
 
         P2       0.0       0.2       0.0
 
         P3       0.0       0.0      -0.2
 
The  co-ordinates  of P1 denote the molecular co-ordinates corresponding to
the  centre  of  the  line  printer  output.  P2  denotes   the   molecular
co-ordinates  (relative to the molecular co-ordinates of the point P1) of a
point displaced 1 character vertically from the centre of the line  printer
plot.  P3  denotes  the  molecular  co-ordinates (relative to the molecular
co-ordinates of the point P1) of a point displaced 1 character to the right
of the centre of the line printer plot. Thus if a point on the line printer
plot is displaced vertically by 'a'  characters  and  horizontally  by  'b'
characters from the centre, the corresponding co-ordinates in the molecular
frame are:
 
         equation
 
The line printer contour plot  is  framed  in  a  grid  of  NGRID  *  NGRID
characters.  The  axes of this plot are labelled in the same way as 'MATRIX
OF GRID VALUES'. Each of the distinct function values  for  which  contours
are  required  is  associated  with a given plotting character. Contours of
positive value will be labelled alphabetically, whilst  numeric  (0-9)  and
certain  other characters are used to label contours of negative value. The
characters, together with their associated values,  are  listed  under  the
plot.
 
 

Error Monitoring


 
    The possible ATMOL error codes with a brief explanation  are  given  in
the following table:
 
  Error Code   Explanation
  __________   ___________
 
          16   Directive unknown.
          50   Invalid parameter in WIDTH pre-directive.
          61   Index block of DUMP FILE is not in correct
               format.
          62   ATMOL block with invalid checksum has been read,
               or input/output error on ATMOL file. If the latter,
               a finite VSOS error code will be given whose
               explanation will be found in [8].
          63   An attempt has been made to use a section number on a
               DUMP FILE outside the allowed range.
          64   Section number specified on input has not been
               defined on the DUMP FILE.
          65   Section specified on the DUMP FILE is of the wrong
               TYPE.
          66   ATMOL data set not assigned.
          67   Illegal search of an ATMOL data set.
          68   A data field was read in F-free format, and an illegal
               character was found.
          69   A data field was read in I-free format, and an illegal
               character was found.
          71   The program has attemped to expand the DUMP FILE
               beyond its maximum size.
          72   An attempt has been made to overwrite a section
               on the DUMP FILE with a section of greater length.
         666   End of file condition detected on FORTRAN stream 5.
               The program expects more data.
         700   Mode not known. This error may occur when attempting
               to interpret a MODE directive, and may be caused by
               a faulty ordering of directives.
         701   Illegal value for NBASIS (1 10**(-3) and
               < 10**(4).
         722   Invalid number of contours specified in the CVALUES
               directive (should be 2< and <51).
         724   An error has been detected in contour plotting routines.
               This may be caused by the plotting algorithm 'breaking
               down' for a specific contour : in such case details of the
               'rogue' contour will be printed, allowing the user to
               regenerate the plot, deleting the function value involved
               by means of the CVALUES directive.
         725   An error has been detected in the perspective plotting
               routines, which are unable to generate a plot from the
               grid of dunction values supplied.
         728   The generation of a grid of electrostatic potentials has
               been requested, when using a wavefunction constructed
               from non-Gaussian orbitals.
         730   An invalid parameter has been detected in the first data
               line of a DIFFERENCE directive.
         731   Invalid number of component grids specified on the DIFF
               line (valid 1-15).
         732   Invalid LABEL presented in the first data field of a grid
               definition line of a DIFFERENCE directive.
         734   The component grids specified in a DIFFERENCE directive are
               not compatible. Note that all grids combined under control
               of this directive must contain values of the same density
               or potential function, and should have been created with
               the same dimensions and PLANE specifications.
         737   A grid retrieved by the DIFFERENCE directive is not complete.
               This error should only arise when retrieving a grid of
               potentials, and indicates that further restart jobs are
               necessary to construct the grid.
         740   Invalid number of parameters specified in VIEW directive.
         741   Invalid number of parameters specified in SCALE directive.
         742   An illegal parameter has been detected in a PTYPE directive.
         743   Invalid number of parameters specified in WINDOW directive.
         744   Invalid integer in ROTATION directive.
               Valid integers are 0,1,2 or 3.
         745   Values specified in the WINDOW directive are invalid.
               SMINX must be less than SMAXX, SMINY must be less than SMAXY.
         999   Insufficient main memory for the program to continue.
        3333   AFN not recognized in the FILE pre-directive.
 
    Error codes 718-721 (*) may only result when generating atom-difference
grids, and are necessitated by the requirements of the Atomic SCF program.
 
 

Specimen Jobs


 
    The following examples do not illustrate all the features of  Graphical
Analysis program, only a guide is intended.
 
    Specimen Job 1
 
    This  example is based on the H2O molecule, the eigen vectors are taken
from the closed shell SCF calculation [4]. The plane to be analysed is  the
yz  plane,  the  same plane as specified by the H2O molecular geometry [2].
The mode of the graphic program is to calculate an  atom  difference  plot.
Grid values have been routed to section 10 of the DUMP FILE. A contour plot
will be generated on line printer output.
 
     /*JOB JOBNAME,ACCOUNT,ST=(C20,LP=1,WS=300),PW=PASSWWORD,TI=20,C=B
     REQUEST,ED7V,RT=U.
     ATTACH,ED3V,ACC=RW.
     PATTACH,ATMOL.
     PLOT.
     ####S
     LPAGE 1
     CHANGE ED3 ED3V ED7 ED7V
     25 1 ED3
     VECT 1
     GRIDMODE
     TITLE
     H2O  CONTOUR LINE PRINTER
     PLANE
     0 0 0
     0 1 0
     0 0 1
     GTYP ATOM 10
     PLOTMODE
     PTYPE CONTOUR LINE
     STOP
     ####S
 
 
    Specimen Job 2
 
    As  with  the  previous  example,  an  atom  difference  plot  is to be
generated. This time a line printer and  hardcopy  NAG-GINO  plot  will  be
produced.  The  user  will  notice  extra  data lines in the JCL, this will
invoke the transfer of the NAG-GINO plot grid to the UMRCC Benson  plotters
[3].
 
    A  title, as shown in PLOT MODE phase, will be printed on the hard copy
plot. The LABEL directive has been used, to label every 4th contour.
 
     /*JOB JOBNAME,ACCOUNT,ST=(C20,LP=1,WS=300),PW=PASSWWORD,TI=20,C=B
     REQUEST,ED7V,RT=U.
     ATTACH,ED3V,ACC=RW.
     PATTACH,ATMOL.
     PLOT.
     PATTACH,PROCLIB.
     BEGIN,,PLOTPEN,F=TAPE7.
     ####S
     LPAGE 1
     CHANGE ED3 ED3V ED7 ED7V
     25 1 ED3
     VECT 1
     GRIDMODE
     TITLE
     H2O  CONTOUR  NAG-GINO
     PLANE
     0 0 0
     0 1 0
     0 0 1
     GTYP ATOM 10
     PLOTMODE
     TITLE
     ATOM DIFFERENCE PLOT  CONTOUR
     LABEL 4
     PTYPE CONTOUR LINE NAG
     STOP
     ####S
 
 
    Specimen Job 3
 
    Again  an  atom  difference  plot  is produced. The graphic analysis is
based on a perspective plot. The VIEW directive has been used to  view  the
graphic  analysis,  45  degrees  from the horizontal and vertical axis at a
distance of 10 Bohrs, from the centre of the plane. A hard copy  plot  will
be produced.
 
     /*JOB JOBNAME,ACCOUNT,ST=(C20,LP=1,WS=300),PW=PASSWWORD,TI=20,C=B
     REQUEST,ED7V,RT=U.
     ATTACH,ED3V,ACC=RW.
     PATTACH,ATMOL.
     PLOT.
     PATTACH,PROCLIB.
     BEGIN,,PLOTPEN,F=TAPE7.
     ####S
     LPAGE 1
     CHANGE ED3 ED3V ED7 ED7V
     25 1 ED3
     VECT 1
     GRIDMODE
     TITLE
     H2O  PERSPECT NAG-GINO
     PLANE
     0 0 0
     0 1 0
     0 0 1
     OCCDEF
     2.0 1 TO 5
     END
     GTYP ATOM 10
     PLOTMODE
     TITLE
     ATOM DIFFERENCE PLOT : PERSPECTIVE PLOT
     VIEW 45 45 10
     PTYPE PERSPECT J06HEF
     STOP
     ####S
 
 
    Specimen Job 4
 
    The  following  example  illustrates  a multi-plot job. Three plots are
produced, ATOM DIFFERENCE, ELECTRON  DENSITY  and  ELECTROSTATIC  POTENTIAL
plots, of the H2O molecule.
 
     /*JOB JOBNAME,ACCOUNT,ST=(C20,LP=1,WS=300),PW=PASSWORD,TI=99,C=B,
     ATTACH,ED3V,ACC=RW.
     REQUEST,ED7V,RT=U.
     PATTACH,ATMOL.
     PLOT.
     PATTACH,PROCLIB.
     BEGIN,,PLOTPEN,F=TAPE7.
     ####S
     LPAGE 1
     CHANGE ED3 ED3V ED7 ED7V
     25 1 ED3
     VECT 1
     GRIDMODE
     TITLE
     H2O  ATOM DIFFERENCE
     PLANE
     0 0 0
     0 0 1
     0 1 0
     GTYP ATOM 10
     PLOTMODE
     TITLE
     MULTI-PLOT ATOM DIFFERENCE CONTOUR PLOT
     LABEL 4
     MULTPLOT 1
     PTYPE CONTOUR NAG
     GRIDMODE
     TITLE
     H2O  ELECTRON DENSITY
     PLANE
     0 0 0
     0 0 1
     0 1 0
     GTYP DENS 11
     PLOTMODE
     TITLE
     MULTI-PLOT ELECTRON DENSITY CONTOUR PLOT
     LABEL 4
     NEWFRAME
     PTYPE CONTOUR NAG
     GRIDMODE
     TITLE
     H2O  ELECTROSTATIC POTENTIAL
     PLANE
     0 0 0
     0 0 1
     0 1 0
     GTYP POTE 12
     PLOTMODE
     TITLE
     MULTI-PLOT ELECTROSTATIC POTENTIAL CONTOUR PLOT
     LABEL 4
     NEWFRAME
     ENDFRAME
     PTYPE CONTOUR NAG
     STOP
     ####S
 
 

References


 
  [1] D.Moncrieff and V.R. Saunders, ATMOL-Introductory Notes.
  [2] D.Moncrieff and V.R. Saunders, ATMOL-Gaussian Integrals Program.
  [3] GINO Manual (FORTRAN 77 Version), NWD 35 (second edition),
      November, 1985.
  [4] D.Moncrieff and V.R. Saunders, ATMOL-SCF Program.
  [5] D.Moncrieff and V.R. Saunders, ATMOL-APSG Program.
  [6] D.Moncrieff and V.R. Saunders, ATMOL-Direct CI Program.
  [7] The NAG Graphical Supplement Manual - Mark 2, 1st Edition, 1985;
      Cyber-205 Note, Number 34, UMRCC, March 1986.
  [8] CDC VSOS Manual, Form 60459410, Control Data Corporation;
      VSOS Reference Manual, NAT 208, UMRCC, 1985.