Keyword OPTIMIZATION

This keyword controls the local geometry optimization and transition state search.
Options:
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. Default is $3 \cdot 10^{-4}$ 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.

Description:
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 ($\leq 100$ 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 $\leq 10^{-6}$ 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.

Table 11: 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 deMon.new.

GEOMETRY OPTIMIZATION option

option REDUNDANT INTERNAL CARTESIAN

$$\parbox{2cm}{Redundant Z-Matrix} \parbox{2cm}{Z-Matrix\break Z-Matrix} \parbox{2cm}{Cartesian Cartesian}$$ Z-MATRIX

$$\parbox{2cm}{Redundant Redundant} \parbox{2cm}{\textit{Impossible}} \parbox{2cm}{Cartesian Cartesian}$$ CARTESIAN

$$\parbox{2cm}{Redundant Redundant} \parbox{2cm}{Redundant Redundant} \parbox{2cm}{Cartesian Cartesian}$$ 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 $\leq 10^{-6}$ 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 [200] 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.