Calculation of the numerical frequencies is specified using the FREQUENCIES keyword in the GEOMETRY block. Most of the subkeys in the geometry block are meaningless for the calculation of frequencies. Indeed, a Frequencies calculation is not a variation on optimization, but rather a sequence of Single Point runs for the equilibrium geometry and a series of slightly different geometries. By comparison of the computed gradients the force constants and hence the frequencies are computed (in the harmonic approximation of the energy surface).
GEOMETRY
Frequencies {Symm} {Allowed} {Numdif=Numdif} {Disrad=drad} {Disang=dang} {SCANALL} {NOSCAN}
iterations Niter
end
Symm
This switch requests that frequencies are calculated in symmetric displacements. During such a calculation first symmetric atomic displacements are constructed. The number of such displacements in each irreducible representation corresponds to the number of frequencies with the corresponding symmetry. All displaced geometries within one representation have the same symmetry, which enables us to use it to speed up the computation significantly. Another advantage of having the same symmetry is that the numerical integration data can be reused efficiently (see SMOOTH option) thus reducing the level of numerical noise in gradients and force constant matrix. This is a new option and for now it only works with geometries specified in Cartesian coordinates. This option does not work correctly with a restart file. This option does not work correctly when symmetry is explicitly specified in the input file.
Allowed
Another advantage of the symmetric displacements is that only a subset of frequencies can be calculated. The ALLOWED option requests computation of only IR-visible frequencies. This option is only useful for symmetric molecules where it can be a big time-saver.
Numdif
Must have the value between 1 and 4 and specifies the type of numerical
differentiation that is applied to compute the force constants from
gradients in slightly displaced geometries: 1-, 2-, 3-, or 4-point
numerical differentiation. In the case of 1-point differentiation the gradients of the
displaced geometry are compared with the gradients at the input
(equilibrium) geometry. In 2-point case both a negative and a positive
displacement are applied, yielding much more accurate results but at the
expense of more computations. This option is the default.
In certain cases the 3-point differentiation method gives better result than 2-point
because it also takes gradients in the middle point into account. This is the case
when geometry has not completely converged and the residual gradients are not
quite close to zero. In this method, a formula is used that interpolates the
second derivative (i.e. force constant) at the zero-force point.
This way, the error due to a small
deviation from the minimum geometry is decreased. The requirement is
that the residual forces are small enough, more precisely, less that
forces at displaced geometries
(that is, using numdif=3 for arbitrary geometries is a bad idea).
When Numdif=4 is specified, force constants matrix will be computed by
making two displacements in each direction, the standard (see drad, dang below) and twice
as short. The force constant is then computed using the Romberg formula that reduces
the higher-order and noise components: H(tot)=(4*H(dx/2)-H(dx))/3.
Although this method requires twice as many single-point evaluations, one can
probably get reliable results using lower integration accuracy, which might be faster
than the default.
dang and drad
The displacements of the coordinates that will be varied. Dang applies to angles (bond and dihedral) in degrees and drad applies to Cartesian (x, y, z) coordinates and to bond lengths, in angstrom. Defaults: 1 degree and 0.01 angstrom.
Niter
In a calculation of frequencies it is the total number of (displaced) geometries for which gradients are computed. By default this is internally determined such that the calculation of frequencies can be completed. If you reduce it, the run will only partially build the matrix of force constants and a restart is required to complete the computation.
WARNING: you cannot combine a Frequencies calculation with the QM/MM feature.
SCANALL and NOSCAN
ADF can scan some or all normal modes after a frequency calculation to verify the corresponding frequencies. By default, the normal modes corresponding all found imaginary frequencies are scanned. This can be switched off by specifying NOSCAN. Specifying SCANALL will tell ADF to scan along all normal modes. These options apply only to calculations in atomic displacements, that is when SYMM is not specified. These two options are mutually exclusive, the one specified last taking precedence.
