9.4.7 Atomic Confining Potentials as Alternatives to Constrained Optimization

In principle, the same effect of constrained optimization using fixed atoms can be achieved instead using soft harmonic confining potentials of the form

This represents an external potential that confines the $i$th atom (having coordinates ${𝐫}_i$) around the position ${𝐫}_i^0$. In applications to cluster models of enzymes (as a low-cost alternative to QM/MM simulations), it is necessary to lock certain atoms at their crystallographic positions in order to relax the geometry (in the gas phase or in continuum solvent) without collapsing the active-site model. ¹¹⁶⁷ Siegbahn P. E. M., Himo F.
Wiley Interdiscip. Rev.: Comput. Mol. Sci.
(2011), 1, pp. 323. Link ^{, 284} Dasgupta S., Herbert J. M.
J. Phys. Chem. B
(2020), 124, pp. 1137. Link

Use of a confining potential allows this optimization to proceed in an unconstrained manner, using delocalized internal coordinates (rather than Cartesian coordinates) for efficiency, yet achieves the same effect as the traditional fixed-atom approach that is widely used in cluster models of enzymatic reactions. ¹¹⁶⁷ Siegbahn P. E. M., Himo F.
Wiley Interdiscip. Rev.: Comput. Mol. Sci.
(2011), 1, pp. 323. Link Moreover, the use of harmonic confining potentials does not result in imaginary frequencies that can plague fixed-atom optimizations, making it straightforward to compute zero-point vibrational corrections. ²⁸⁴ Dasgupta S., Herbert J. M.
J. Phys. Chem. B
(2020), 124, pp. 1137. Link

Harmonic confining potentials are activated by setting the $rem variable HARM_OPT to true, listing the indices of the confined atoms in the $harmonic_opt section and their corresponding equilibrium positions (${𝐫}_i^0$) in the $coords section.