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9.2 Geometry Optimization Job Controls

9.2.3 Hessian-Free Characterization of Stationary Points

(July 14, 2022)

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. 1090 Sharada S. M., Bell A. T., Head-Gordon M.
J. Chem. Phys.
(2014), 140, pp. 164115.
Link
For a geometry optimization, it solves for the lowest eigenvalue of the Hessian (λ1) and checks if λ1>0 (a negative λ1 indicates a saddle point); for a TS search, it solves for the lowest two eigenvalues, and λ1<0 and λ2>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×Niter total energy + gradient calculations, where Niter 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.  1090 Sharada S. M., Bell A. T., Head-Gordon M.
J. Chem. Phys.
(2014), 140, pp. 164115.
Link
, 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

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

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.