Q-Chem allows the user to characterize the stationary point found by a
geometry optimization or transition state search without performing a full
analytical Hessian calculation, which is sometimes unavailable or
computationally unaffordable. This is achieved via a finite difference Davidson
procedure developed by Sharada *et al.*^{832} For a geometry
optimization, it solves for the lowest eigenvalue of the Hessian (${\lambda}_{1}$)
and checks if ${\lambda}_{1}>0$ (a negative ${\lambda}_{1}$ indicates a saddle
point); for a TS search, it solves for the lowest two eigenvalues, and
$$ and ${\lambda}_{2}>0$ indicate a transition state. The lowest
eigenvectors of the updated P-RFO (approximate) Hessian at convergence are used
as the initial guess for the Davidson solver.

The cost of this Hessian-free characterization method depends on the rate of convergence of the Davidson solver. For example, to characterize an energy minimum, it requires $2\times {N}_{\mathrm{iter}}$ total energy + gradient calculations, where ${N}_{\mathrm{iter}}$ is the number of iterations that the Davidson algorithm needs to converge, and “2" is for forward and backward displacements on each iteration. According to Ref. 832, this method can be much more efficient than exact Hessian calculation for substantially large systems.

Note: At the moment, this method does not support QM/MM or systems with fixed atoms.

GEOM_OPT_CHARAC

Use the finite difference Davidson method to characterize the resulting energy
minimum/transition state.

TYPE:

BOOLEAN

DEFAULT:

FALSE

OPTIONS:

FALSE
do not characterize the resulting stationary point.
TRUE
perform a characterization of the stationary point.

RECOMMENDATION:

Set it to TRUE when the character of a stationary point needs to be
verified, especially for a transition structure.

GEOM_OPT_CHARAC_CONV

Overide the built-in convergence criterion for the Davidson solver.

TYPE:

INTEGER

DEFAULT:

0 (use the built-in default value 10${}^{-5}$)

OPTIONS:

$n$
Set the convergence criterion to 10${}^{-n}$.

RECOMMENDATION:

Use the default. If it fails to converge, consider loosening the criterion with caution.

$molecule -1 1 C 0.00000 -0.00078 0.98436 F -1.09414 -0.63166 1.47859 S 0.00000 0.00008 -0.94745 O 1.25831 -0.72597 -1.28972 O -1.25831 -0.72597 -1.28972 O 0.00000 1.45286 -1.28958 F 1.09414 -0.63166 1.47859 F 0.00000 1.26313 1.47663 $end $rem JOBTYPE opt METHOD BP86 GEOM_OPT_DMAX 50 BASIS 6-311+G* SCF_CONVERGENCE 8 THRESH 14 SYMMETRY FALSE SYM_IGNORE TRUE GEOM_OPT_TOL_DISPLACEMENT 10 GEOM_OPT_TOL_ENERGY 10 GEOM_OPT_TOL_GRADIENT 10 GEOM_OPT_CHARAC TRUE $end

$molecule 0 1 C 3.21659 -1.41022 -0.26053 C 2.16708 -0.35258 -0.59607 N 1.21359 -0.16703 0.41640 C 0.11616 0.82394 0.50964 C -1.19613 0.03585 0.74226 N -2.18193 -0.02502 -0.18081 C -3.43891 -0.74663 0.01614 O 2.19596 0.25708 -1.63440 C 0.11486 1.96253 -0.53088 O -1.29658 -0.59392 1.85462 H 3.25195 -2.14283 -1.08721 H 3.06369 -1.95423 0.67666 H 4.20892 -0.93714 -0.22851 H 1.24786 -0.78278 1.21013 H 0.25990 1.31404 1.47973 H -2.02230 0.38818 -1.10143 H -3.60706 -1.48647 -0.76756 H -4.29549 -0.06423 0.04327 H -3.36801 -1.25875 0.98106 H -0.68664 2.66864 -0.27269 H 0.01029 1.65112 -1.56461 H 1.06461 2.50818 -0.45885 $end $rem JOBTYPE freq EXCHANGE B3LYP BASIS 6-31G SCF_MAX_CYCLES 250 SYMMETRY false SYM_IGNORE true $end @@@ $molecule read $end $rem JOBTYPE ts SCF_GUESS read GEOM_OPT_DMAX 100 GEOM_OPT_MAX_CYCLES 1500 EXCHANGE B3LYP BASIS 6-31G MAX_SCF_CYCLES 250 GEOM_OPT_HESSIAN read SYMMETRY false SYM_IGNORE true GEOM_OPT_CHARAC true $end