Re: CCL:force constants of diatomics in GAUSSIAN-03

On Wed, Jul 21, 2004 at 03:15:48PM +0400, Dmitry Rozmanov wrote:
 Dmitry Rozmanov wrote
 > If this is the case, then I guess this is just a wrong way of doing things
 > and the force constants got by Gaussian are not correct at all. There is a
 > definition of the thing and there is no two way of calculation.
 >
 > ---Dmitry.
 >
 This is nonsense.  The details are in a white paper on our web site,
 but the key point is that the force constant is the second derivative
 with respect to a normal mode displacement and the units for the
 normal mode, or equivalently the convention for what consititues a
 unit step, are arbitrary.
 For polyatomic molecules, one typically diagonalizes the force
 constant matrix in mass-weighted coordinates, so the natural unit step
 is a normalized displacement in these coordinates.  This approach is
 general and applicable to any polyatomic molecule.  In the particular
 case of H2 with the molecule along the x-axis, this normalized step
 would be (1/sqrt(2),0,0,1/sqrt(2),0,0) in the 6 cartesian coordinates.
 This unit step changes the H-H distance by sqrt(2).  For the particular
 case of diatomic molecules when people calculate by hand, they use the
 distance between atoms as the coordinate, which simpler for diatomics
 but doesn't apply to polyatomics.  In that coordinate system, a unit
 displacement changes the distance by 1 rather than sqrt(2), so the force
 constants (second derivatives of the energy) differ by a factor of 2.
 The corresponding reduced masses for the mode also differ by a factor
 of two and the frequency is the same.
 For the diatomic, the "by hand" coordinates give a reduced mass for
 the mode which is the same as the overall reduced mass for the
 molecule.  For a general polyatomic molecule, the reduced mass
 corresponding to a particular mode is not an observable quantity and
 is not defined until one adopts a convention for the (arbitrary) size
 of a unit normal mode displacement.
 Mike Frisch