This keyword controls the local geometry optimization and transition
REDUNDANT / INTERNAL / CARTESIAN
REDUNDANT || The optimization is performed in delocalized redundant
internal coordinates. This is the default. |
INTERNAL || The optimization is performed in the defined internal
coordinates (Z-matrix input). |
CARTESIAN || The optimization is performed in Cartesian coordinates. |
MAX=Integer || Maximum number of optimization steps. Default is 50. |
TOL=Real || Optimization convergence criterion for RMS gradient.
atomic units. |
STEP=Real || Maximum step size in optimization. Default is
0.3 atomic units. |
TS || Activate local transition state search. |
MOD=Integer || Hessian eigenmode to be followed in the transition
state search. Default is 1, the mode with the lowest
(most negative) frequency. |
By default, deMon2k uses delocalized internal redundant coordinates for the
geometry optimization or transition state search [194,195]. For full
geometry optimizations, this is also the recommended method. Because of the
possible linear dependencies of the internal coordinates defined in the
Z-matrix, optimization in these coordinates with OPTIMIZATION INTERNAL may become
problematic even for small systems ( atoms). With the REDUNDANT option
and a Cartesian input, deMon2k constructs a Z-matrix from the Cartesian input and
a set of linear combinations of internal coordinates (delocalized coordinates)
which avoids linear dependencies. This option should be used if an optimization
gets stuck and has to be restarted. With the REDUNDANT option and an internal
Z-matrix input, the optimization is also performed in delocalized internal
redundant coordinates. However, now the user-defined internal coordinates of the
Z-matrix are included in the delocalized internal redundant coordinates. At each
optimization step these delocalized internal redundant coordinates are transformed
back to the coordinates of the Z-matrix input. Therefore the combination of a
Z-matrix input and the option REDUNDANT can lead to different results than the
combination of a Z-matrix input and the option INTERNAL. In particular, equivalent
internal coordinates could be broken during a redundant optimization. To enforce
coordinate equivalences the option INTERNAL must be used for the optimization.
Even though the default optimization in redundant coordinates is usually most
efficient some exceptions exist. For very tight optimizations (TOL
a.u.) the iterative back transformation may hamper convergence of the optimization.
Another problem can arise from the automatic Z-matrix construction for redundant
coordinates. This construction is prone to linear dependencies in systems that
consist of many individual molecules, e.g. solvent clusters. In such cases it
is advisable to optimize in Cartesian coordinates by using OPTIMIZATION CARTESIAN.
Table 11 shows the relationships between the types of input and
types of optimization options. Each cell in that Table contains two values. The
upper value shows the coordinate system used for an optimization step, while the
lower value shows the coordinate system in the deMon.new file which contains
the optimized geometry.
Relationship between different options for the keywords
GEOMETRY and OPTIMIZATION. Upper values denote the coordinate system for
the optimization and lower values the geometry definition in the file
|GEOMETRY || OPTIMIZATION option|
option || REDUNDANT || INTERNAL || CARTESIAN |
Z-MATRIX || ||
CARTESIAN || ||
MIXED || ||
With the MAX and TOL options, the maximum number of optimization steps
and the optimization convergence criterion can be specified. Convergence of
the optimization is based on the remaining maximum and root mean square (RMS)
forces. The TOL option specifies the RMS force convergence criterion. The other
convergence criteria are calculated from this value. Note that the SCF convergence
criteria are also tightened according to Table 9. For very tight
optimizations (TOL a.u.) it might also be necessary to use finer
grids for the numerical integration of the exchange-correlation contributions
(see 4.3.6). The maximum step length (in atomic units) used in the
optimization can be specified with the STEP option.
The option TS activates a local transition state search based on the
eigenvector-following of the Hessian matrix. The success of this approach depends
crucially upon the starting structure and quality of the starting Hessian.
Therefore, use of a calculated start Hessian (see 4.6.5) is recommended
for the transition state search. By default, deMon2k employs an uphill trust
region method [196,197] for the local transition state search. As an
alternative (P)-RFO steps [198,199] can be chosen by selecting the
RFO STEPTYPE (see 4.6.7). Both methods guarantee that the
(right) Hessian structure (one negative eigenvalue) is preserved. To avoid
reversion to a positive-definite Hessian, the Powell update  is
used by default for the transition state search.
If a mode other than the lowest Hessian eigenmode is to be followed, the
option MOD is used to select the desired eigenvector (use the PRINT
keyword 4.12.2 with the DE2 option to print the Hessian eigenvectors).
On subsequent steps, this mode is selected by the largest overlap with the
eigenvector followed in the previous cycle.