9.3 Constrained Optimization 9.3.7 Additional Atom Connectivity 9.4 Application of Pressure

9.3.8 Atomic Confining Potentials as Alternatives to Constrained Optimization

(February 4, 2022)

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, 249}

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 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

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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9.3.8 Atomic Confining Potentials as Alternatives to Constrained Optimization