Molecule Types Vibrational Structure Force Field Analysis | <Prev Next> |

The valence coordinates are closely based on
those described in L. Hedberg, I. M. Mills, *J. Molec.
Spectrosc. ***160**, 117 (1993), and this should be
referred to for precise definitions and units. Any differences are
noted below.

The units of the coordinates are Å for the stretches and radians for the others (all some form of angle), so the stretching force constants have different units to the others.

The units of the coordinates are Å for the stretches and radians for the others (all some form of angle), so the stretching force constants have different units to the others.

Bond length between atom *k* and *l*:

The angle *klm*:

For atoms in a line an additional constraint
is required, and four atoms must be specified rather than three.
(The name is still `bend` in the internal
coordinates object.) In contrast to the Hedberg and Mills paper
the coordinate is taken to be the angle *klm* in plane of
atom *n*, rather than specifying a separate vector. The
extra atom, *n*, will typically be a dummy atom. (If the
atoms are not in a line an additional atom can still be specified;
formally the displacements are then parallel to the plane
containing *k* *l* and *n*.)

and the side projection shows the motion:

This is type 1 out of plane bending in the
nomenclature of Hedberg and Mills. Given centre (or apex) atom *k*
and three other atoms in the same plane (*lmn*) the
coordinate is the scalar triple product of unit vectors along
bonds:

All the atoms are shown joined to the central atom:e_{kl}●e_{km}×e_{kn}.

and again a different projection is needed to show the motion

Given atoms *klmn* in a chain, the coordinate is the angle
between the planes *klm* and *lmn*. (The atoms *klm*
and *lmn* must not be collinear.) The chain is shown in the
plot window:

and a different projection shows the displacements:

In an extension to the torsion as defined by
Hedberg and Mills above, a generalised torsion can be given by
only specifying two (bonded) atoms, *kl* for a torsion. The
valence coordinate is then an average of all possible 4 atom
torsions defined as above, identifying the bonded atoms from all
the other valence coordinates. (All the bonds indicated above are
counted, apart from the 4^{th} atom in the linear bend.)
The plot window joins all the affected atoms:

and again a different projection shows the displacements: