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4.8 Symmetry
MOLPRO can use Abelian point group symmetry only. For molecules with
degenerate symmetry, an Abelian subgroup must be used  e.g., or
for linear molecules. The symmetry group which is used is defined in
the integral input by combinations of the symmetry elements , , and ,
which specify which coordinate axes change sign under the corresponding
generating symmetry operation. It is usually wise to choose to be the
unique axis where appropriate (essential for and ). The
possibilities in this case are shown in Table 1.
Normally, MOLPRO determines the symmetry automatically, and rotates
and translates the molecule accordingly. However, explicit symmetry
specification is sometimes useful to fix the orientation of the molecule
or to use lower symmetries.
Table 1:
The symmetry generators for the point groups
Generators 
Point group 




(null card) 
(i.e. no point group symmetry) 
X (or Y or Z) 

XY 

XYZ 

X,Y 

XY,Z 

XZ,YZ 

X,Y,Z 



The irreducible representations of each group are numbered 1 to 8. Their
ordering is important and given in Tables 2  4. Also shown
in the tables are the transformation properties of products of , , and
. stands for an isotropic function, e.g., orbital, and for these
groups, this gives also the transformation properties of , ,
and . Orbitals or basis functions are generally referred to in the format number.irrep, i.e. 3.2 means the third orbital in the second irreducible representation
of the point group used.
Table 2:
Numbering of the irreducible representations in


No. 
Name 
Function 



1 


2 


3 


4 


5 


6 


7 


8 





Table 3:
Numbering of the irreducible representations in the fourdimensional groups




No. 
Name 
Function 
Name 
Function 
Name 
Function 







1 






2 






3 






4 













Table 4:
Numbering of the irreducible representations in the twodimensional groups




No. 
Name 
Function 
Name 
Function 
Name 
Function 







1 






2 













Next: 4.9 Defining the wavefunction
Up: 4 GENERAL PROGRAM STRUCTURE
Previous: 4.7 Multiple passes through
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