The VCHAM programs are able to work with polyspherical parameterisations based on Jacobi, Radau and valence vectors.
The input syntax used to define these vectors is described in the following.
In both VCPNT and VCTRANS the desired set of Jacobi vectors for an N-atom system is specified using the syntax
jacobi_define
A1
A2
A3
.
.
.
AN
end-jacobi_define
Here, the first vector connects atoms A1
and A2
. The second vector connects the centre of
mass of the A1
, A2
subunit
and atom A3
, and so on.
In both VCPNT and VCTRANS the desired set of Radau vectors for an N-atom system is specified using the syntax
radau_define
A1
A2
A3
.
.
.
AN
end-radau_define
Here, atom A1
is the heliocentre. The first vector
connects atom A2
and the canonical point. The second
vector connects A3
and the canonical point, and so
on
In both VCPNT and VCTRANS the desired set of valence vectors for an N-atom system is specified using the syntax
valence_define
A1 A2
A3 A4
.
.
.
Am An
end-valence_define
Here, the first vector points from atom A2
to
atom A1
, the second vector points from
atom A4
to atom A3
, and so
on.
For an N-atom system there exists N-1 vectors Ri. The body-fixed (BF) frame used is defined such that the vector RN-1 lies along the z-axis of the BF frame, and the vector RN-2 lies in the x,z-plane of the BF frame. The 3N-6 internal coordinates used are then the N-1 vector lengths Ri, the N-2 planar angles θi, between the vectors RN-1 and Ri, and the N-3 dihedral angles φi, between the two vectors Ri and RN-2 and RN-1.
The coordinates are arranged such that:
The coordinates 1 to N-1 correspond to the vector lengths Ri;
The coordinates N to 2N-3 correspond to the planar angles θi
The coordinates 2N-2 to 3N-6 correspond to the dihedral angles φi.