# 9.3.6 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

 $V_{\text{conf}}(\mathbf{r}_{1},\mathbf{r}_{2},\ldots)=\frac{1}{2}\sum_{i}k\|% \mathbf{r}_{i}-\mathbf{r}_{i}^{0}\|^{2}\;.$ (9.1)

This represents an external potential confines the $i$th atom (having coordinates $\mathbf{r}_{i}$) around the position $\mathbf{r}_{i}^{0}$. 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, say) without collapsing the active-site model.Siegbahn:2011, Dasgupta:2020 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 “coordinate-lock” (i.e., fixed-atom) approach that is widely used in cluster models of enzymatic reactions.Siegbahn:2011 Moreover, the harmonic-confiner approach is also free of imaginary frequencies that can plague fixed-atom optimizations, and makes it possible to compute zero-point vibrational corrections in a straightforward manner.Dasgupta:2020

HARM_OPT
Controls whether the job uses confining potentials
TYPE:
LOGICAL
DEFAULT:
False
OPTIONS:
False Do not use the potential True Use the potential
RECOMMENDATION:
False

HOATOMS
Controls the number of confined atom
TYPE:
INTEGER
DEFAULT:
No default
OPTIONS:
User defined
RECOMMENDATION:
None

HARM_FORCE
Sets the force constant for harmonic confiner
TYPE:
INTEGER
DEFAULT:
No default
OPTIONS:
User defined
RECOMMENDATION:
None

Example 9.8  Optimization using soft harmonic confining potentials

$molecule 0 1 C 2.2847229688 -0.3069830925 -0.2968221397 C 0.9156471557 0.1503924513 0.1693932675 N -0.0576877706 -0.7876400788 0.0645249649 H 2.9837678662 0.5043669375 -0.1693203557 H 2.2497378474 -0.5929607607 -1.3422589452 H 2.6126794028 -1.1626691284 0.2825927880 O 0.6966207559 1.2669942030 0.6077661092 C -1.4350712383 -0.4874947903 0.4670886412 H 0.1463602169 -1.6783001309 -0.3307859180 C -2.1768099264 0.3412632672 -0.5936684676 H -1.3995705380 0.0636682083 1.3955334557 H -1.9421824240 -1.4270154508 0.6422037013 H -1.6624625664 1.2829541077 -0.7297597438 H -3.1943263155 0.5415731987 -0.2762358302 H -2.2051967614 -0.1880845317 -1.5391034623$end

$rem JOBTYPE OPT BASIS 3-21G METHOD HF SYM_IGNORE TRUE NO_REORIENT TRUE HARM_OPT 1 !Turn on harmonic confining potential HOATOMS 2 ! No. of confined atoms HARM_FORCE 450 ! Force constant of the potential$end

$harmonic_opt 1 10 ! indices of the confined atoms$end

$coords !coordinates of confined atoms C1 2.2847229688 -0.3069830925 -0.2968221397 C10 -2.1768099264 0.3412632672 -0.5936684676$end