MOLPRO

10 MOLECULAR GEOMETRY 63
α
Internuclear angle α(p 0 , p 1 , p 2 ). This angle is given in degrees
and must be in the range 0 < α < 180 0 .
p 3 A third atom needed to define the dihedral angle β(p 0 , p 1 , p 2 , p 3 ).
Only applies if J = 0, see below.
β
J
x,y,z
Dihedral angle β(p 0 , p 1 , p 2 , p 3 ) in degree. This angle is defined
as the angle between the planes defined by (p 0 , p 1 , p 2 )
and (p 1 , p 2 , p 3 ) (−180 0 ≤ β ≤ 180 o ). Only applies if J = 0,
see below.
If this is specified and nonzero, the new position is specified by
two bond angles rather than a bond angle and a dihedral angle.
If J = ±1, β is the angle β(p 0 , p 1 , p 3 ). If J = 1, the triple vector
product (p 1 −p 0 )·[(p 1 −p 2 )×(p 1 −p 3 )] is positive, while this
quantity is negative if J = −1.
Cartesian coordinates of the new atom. This form is assumed
if p 1 ≤ 0; if p 1 < 0, the coordinates are frozen in geometry
optimizations.
All atoms, including those related by symmetry transformations, should be specified in the Z-
matrix. Note that for the first atom, no coordinates need be given, for the second atom only
p 1 ,r are needed, whilst for the third atom p 3 ,β,J may be omitted. The 6 missing coordinates
are obtained automatically by the program, which translates and re-orients the molecule such
that the origin is at the centre of mass, and the axes correspond to the eigenvectors of the inertia
tensor (see also CHARGE option above).
Variable names, and in general expressions that are linear in all dependent variables, may be
used as well as fixed numerical values for the parameters r, α and β. These expressions are
evaluated as late as possible, so that it is possible, for example, to set up loops in which these
parameters are changed; the geometry optimizer also understands this construction, and will
optimize the energy with respect to the value of the variables. Non-linear expressions should
not be used, because the geometry optimization module is unable to differentiate them.
Once the reorientation has been done, the program then looks for symmetry (D 2h and subgroups),
unless the NOSYM option has been given. It is possible to request that reduced symmetry
be used by using appropriate combinations of the options X,Y,Z,XY,XZ,YZ,XYZ. These
specify symmetry operations, the symbol defining which coordinate axes change sign under the
operation. The point group is constructed by taking all combinations of specified elements. If
symmetry is explicitly specified in this way, the program checks to see that the group requested
can be used, swapping the coordinate axes if necessary. This provides a mechanism for ensuring
that the same point group is used, for example, at all points in the complete generation of
a potential energy surface, allowing the safe re-utilization of neighbouring geometry molecular
orbitals as starting guesses, etc..
Note that symmetry is not implemented in density fitting methods, and in these cases the
NOSYM option is implied automatically.
Also note that by default the automatic orientation of the molecule only takes place if the geometry
is defined by internal (Z-matrix) coordinates. In case of XYZ Input the orientation is
unchanged, unless the MASS option is specified in the geomnetry block.
10.1.2 XYZ input
Simple cartesian coordinates in Ångstrom units can be read as an alternative to a Z matrix. This
facility is triggered by setting the MOLPRO variable GEOMTYP to the value XYZ before the