Accuracy

Accuracy is a crucial aspect in the computation of frequencies, in particular for modes with low frequencies: the gradients at the geometries displaced along that mode will hardly change - analytically - from their equilibrium values, so numerical integration noise may easily affect the reliability of the computed differences in gradients. It is worthwhile to consider carefully the size of the displacements. At one hand they should be small in order to suppress the effect of higher order (anharmonic) terms in the energy surface around the minimum, at the other hand they should be large enough to get significant differences in gradients so that these are computed reliably.

High precision calculations where low frequency modes are involved may require high integration settings [14]. The default (i.e. automatic) value in a FREQUENCIES run is 6.0 (!). This may not be necessary in all cases, but it turns out to be required quite often in order to get accurate results. The calculation of frequencies by evaluating a series of displaced geometries, as it is implemented in ADF, is very time-consuming. This is even more so in view of the high (default) integration precision. This means that you should be prepared for long calculations.

Using 2-point differentiation rather than 1-point differentiation implies two-sided displacements of the atoms. This doubles the computational effort but in the so-computed force constants all anharmonic terms of odd order are eliminated. Since in general the lowest anharmonicity is third order this eliminates the first anharmonicity. Again, this is a feature directed primarily at obtaining highly accurate and reliable results.

The 3- and 4-point methods are intended to assist in special cases and as an extra check when the results obtained with the 2-point formula are not satisfactory. The 3-point formula should be used when residual forces after geometry optimization are between 0.01 and 0.0001 a.u./angstrom. In this case frequencies obtained with the 3-point formula are much closer to those that would be computed at the exact optimum geometry.

If a Frequencies calculation is carried out only to construct a good start-up Hessian for a TS search (see the restart key), accurate results are not crucial. The most important thing in such a situation is to get a fair guess for the negative eigenvalue and its associated mode, and to avoid spurious additional negative eigenvalues. We recommend to avoid the rather time-consuming standard Hessian-computing preparation run for a TS search and to lower the precision of the Frequencies run. A reasonable value should be 4.0.