MOLPRO

29 LOCAL CORRELATION TREATMENTS 222
geometries and harmonic vibrational frequencies the default values are normally appropriate,
larger distance criteria are sometimes needed when computing energy differences, in particular
barrier heights. In cases of doubt, RWEAK should first be increased until convergence is reached,
and then RCLOSE can be varied as well. Such tests can be performed with small basis sets like
cc-pVDZ, and the optimized values then be used in the final calculations with large basis sets.
29.9.7 Gradients and frequency calculations
Geometry optimizations [15-17] and numerical frequency calculations [18-20] can be performed
using analytical energy gradients [15-17] for local MP2. LMP2 geometry optimizations are particularly
attractive for weakly bound systems, since virtually BSSE free structures are obtained
(see section 29.9.8 and Refs. [21-23]). For reasons of efficiency it is strongly advisable to use the
DF-LMP2 Gradient [17] for all geometry optimizations. Setting SCSGRD=1 on the DF-LMP2
command or DFIT directive activates the gradient with respect to Grimmes SCS scaled MP2
energy functional (see also section DFIT). Analytical energy gradients are not yet available for
the multipole approximation of distant pairs, and therefore MULTP cannot be used in geometry
optimizations or frequency calculations.
In geometry optimizations, the domains are allowed to vary in the initial optimization steps.
When the stepsize drops below a certain threshold (default 0.01) the domains are automatically
frozen. In numerical Hessian or frequency calculations the domains are also frozen. It is therefore
not necessary to include SAVE and START options.
Particular care must be taken in optimizations of highly symmetric aromatic systems, like, e.g.,
benzene. In D 6h symmetry, the localization of the π-orbitals is not unique, i.e., the localized
orbitals can be rotated around the C 6 axis without changing the localization criterion. This
redundancy is lost if the symmetry is slightly distorted, which can lead to sudden changes of
the localized orbitals. If now the domains are kept fixed using the SAVE and START options,
a large error in the energy might result. On the other hand, if the domains are not kept fixed,
their size and quality might change during the optimization, again leading to spurious energy
changes and divergence of the optimization.
The best way to avoid this problem is to use the MERGEDOM=1 option (see section 29.6). If this
option is given, the domains for the π orbitals will comprise the basis functions of all six carbon
atoms, and the energy will be invariant with respect to unitary transformations among the three
π orbitals. Note that this problem does not occur if the symmetry of the aromatic system is
lowered by a substituent.
Redundant orbital rotations can also lead to convergence difficulties of the Pipek-Mezey
localization. This can be overcome by using
PIPEK,METHOD=2
or
PIPEK,METHOD=3
With METHOD=2, the second derivatives of the localization criterion with respect to the orbital
rotations is computed and diagonalized, and rotations corresponding to zero eigenvalues are
eliminated. This method converges quadratically. With METHOD=3 first a few iterations with
the standard Pipek-Mezey method are performed, then the second-order method is invoked. This
appears to be the most robust and accurate localization method.
Finally, we note that the LMP2 gradients are quite sensitive to the accuracy of the SCF convergence
(as is also the case for MP2). If very accurate structures are required, or if numerical
frequencies are computed from the gradients, the default SCF accuracy might be insufficient.