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# 9.3.8 Atomic Confining Potentials as Alternatives to Constrained Optimization

(December 20, 2021)

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 that 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) without collapsing the active-site model. 1031 Siegbahn P. E. M., Himo F.
Wiley Interdiscip. Rev.: Comput. Mol. Sci.
(2011), 1, pp. 323.
, 249 Dasgupta S., Herbert J. M.
J. Phys. Chem. B
(2020), 124, pp. 1137.

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. 1031 Siegbahn P. E. M., Himo F.
Wiley Interdiscip. Rev.: Comput. Mol. Sci.
(2011), 1, pp. 323.
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. 249 Dasgupta S., Herbert J. M.
J. Phys. Chem. B
(2020), 124, pp. 1137.

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 ($\mathbf{r}_{i}^{0}$) in the $coords section. HARM_OPT 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 HOATOMS Controls the number of confined atom TYPE: INTEGER DEFAULT: No default OPTIONS: User defined RECOMMENDATION: None HARM_FORCE HARM_FORCE Sets the force constant for harmonic confiner TYPE: INTEGER DEFAULT: No default OPTIONS: User defined RECOMMENDATION: None Example 9.9 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
METHOD        HF
BASIS         3-21G
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



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