9.3 Constrained Optimization

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

Vconf⁢(𝐫1,𝐫2,…)=12⁢∑ik⁢∥𝐫i-𝐫i0∥2. (9.1)

This represents an external potential confines the ith atom (having coordinates 𝐫i) around the position 𝐫i0. 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.878, 203 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.878 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.203

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