9.4.7 Atomic Confining Potentials as Alternatives to Constrained Optimization‣ 9.4 Constrained Optimization ‣ Chapter 9 Exploring Potential Energy Surfaces: Searches for Critical Points and Molecular Dynamics ‣ Q-Chem 7.0 User’s Manual

In principle, the same effect of constrained optimization using fixed atoms can be achieved instead using a 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}\;.

(9.42)

This represents an external potential that confines the ith atom (having coodinates $\mathbf{r}_{i}$ ) around the position $\mathbf{r}_{i}^{0}$ . The above implementation will be referred to as the cartesian confiner, as it is based on the cartesian coordinates of each confined atom. An alternative way to implement harmonic confiners is to use a pairwise harmonic confining potential of the form

V_{\text{conf}}(\mathbf{r}_{1},\mathbf{r}_{2},\ldots,\mathbf{r}_{N})=\frac{1}{% 2}\sum^{N}_{i>j}k\|\mathbf{r}_{ij}-\mathbf{r}_{ij}^{0}\|^{2}\;.

(9.43)

This represents an external potential that confines the $i$ th and $j$ th atoms (having distance between them $\mathbf{r}_{ij}$ ) to the initial (or specified distance) of $\mathbf{r}_{ij}^{0}$ . 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. ¹²⁵³ Siegbahn P. E. M., Himo F.
Wiley Interdiscip. Rev.: Comput. Mol. Sci.
(2011), 1, pp. 323. Link ^, ³⁰² Dasgupta S., Herbert J. M.
J. Phys. Chem. B
(2020), 124, pp. 1137. Link ^, ¹⁴⁹ Bowling P. E., Dasgupta S., Herbert J. M.
J. Chem. Inf. Model
(2024), 64, pp. 3912. Link

Use of a pairwise confining potential between each unique pair of confined atoms allows optimizations to proceed in an unconstrained manner, using delocalized internal coordinates (rather than Cartesian coordinates) for efficiency, yet achieves a similar effect as the traditional fixed-atom approach that is widely used in cluster models of enzymatic reactions. The fixed atom constraint can be better mimicked by tethering an atom to a geometric position, but in doing so the ability to run optimization in internal coordinates is lost. ¹²⁵³ Siegbahn P. E. M., Himo F.
Wiley Interdiscip. Rev.: Comput. Mol. Sci.
(2011), 1, pp. 323. Link Moreover, the use of harmonic confining potentials results in fewer imaginary frequencies that plague fixed-atom optimizations, making it straightforward to compute zero-point vibrational corrections. ³⁰² Dasgupta S., Herbert J. M.
J. Phys. Chem. B
(2020), 124, pp. 1137. Link ^, ¹⁴⁹ Bowling P. E., Dasgupta S., Herbert J. M.
J. Chem. Inf. Model
(2024), 64, pp. 3912. Link

Harmonic confining potentials are activated by setting the $rem variable HARM_OPT to either 1 or 2, listing the indices of the confined atoms in the $harmonic_opt section. Only one type of confiner can be used for any specific jobs. For the cartesian confiners, the equilibrium positions ( $\mathbf{r}_{i}^{0}$ ) must be specified in the $coords section as shown in the example below.

Example 9.14 Geometry optimization and subsequent frequency calculation using cartesian 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
   point_group_symmetry false
   NO_REORIENT TRUE
   HARM_OPT 1 ! Turn on cartesian 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

$geom_opt
initial_hessian = simple
hessian_verify = recomputed !Recompute Exact Hessian for verification
final_vibrational_analysis = true !Perform Vibrational Analysis on optimized Hessian
$end

For pairwise confiners, pairwise distances between two constrained atoms ( $\mathbf{r}_{ij}^{0}$ ) may optionally be placed in these $coords section, and if no $\mathbf{r}_{ij}^{0}$ are specified, the starting atom distances given in the $molecule are used to calculate the equilibrium distances. An example of a pairwise confiner optimization followed by a frequency calculation is shown below.

Example 9.15 Geometry optimization and subsequent frequency calculation using pairwise confining potentials. Note the lack of a $coords in the frequency calculation. Compound jobs will carry the equilibrium coordinates from one job to the next. Separately run pairwise confiner jobs will need specified $coords to maintain the same potential energy surface.

$molecule

0 1
 H  -0.68168  -1.29335  0.69937
 C  -0.01515  -0.39524  0.63493
 N  1.06556  -0.59220  1.63009
 H  1.57017  -1.42548  1.41732
 H  1.68831  0.18821  1.62555
 C  -0.82092  0.86652  1.01181
 H  -1.07481  0.84874  2.09044
 H  -0.23531  1.78800  0.81958
 O  -1.99965  0.85940  0.24056
 H  -2.47074  1.65064  0.46275
 C  0.53081  -0.25778  -0.78386
 O  1.40105  0.49365  -1.18881
 O  -0.00029  -1.09878  -1.69507
 H  0.36786  -0.92650  -2.55634

$end

$rem
 JOBTYPE = OPT
 BASIS = MINIX
 METHOD = HF3c

 HARM_OPT = 2 ! Turn on pairwise harmonic confining potential
 HOATOMS = 2 ! No. of confined atoms
 HARM_FORCE = 50 ! force per spring (scaled by 1/1000)
$end

$harmonic_opt ! specifies which atoms to be confined
3 11
$end

$coords ! optional for pairwise - specifies distance between pairs of atoms
 3 11 50.0
$end

@@@

$molecule
 READ
$end

$rem
 JOBTYPE = FREQ
 BASIS = MINIX
 METHOD = HF3c

 HARM_OPT = 2
 HOATOMS = 2
 HARM_FORCE = 50
$end

$harmonic_opt
3 11
$end

After each geometry optimization using a pairwise harmonic confiner, the $coords section is printed in the output under "Harmonic Coords Print:". This allows users to be able to maintain the same potential energy surface between jobs. For example, a geometry optimization with pairwise confiners would generate a $coords section which could then used in a frequency job that needs to match the forces of the optimization job.

HARM_OPT

HARM_OPT
       Controls whether the job uses confining potentials
TYPE:
       INTEGER
DEFAULT:
       0
OPTIONS:
       0 Do not use the potentials 1 Use cartesian confining potential 2 Use pairwise confining 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, in units of N/m. For pairwise confiner the force is divided by 1000, so a set value of 5000 applies a force constant of 5 N/m to each spring.
TYPE:
       INTEGER
DEFAULT:
       No default
OPTIONS:
       User defined
RECOMMENDATION:
       None

Search Results

9.4.7 Atomic Confining Potentials as Alternatives to Constrained Optimization