# Grid Optimization

Grid optimizations perform geometry optimizations on a grid of chosen coordinates, or in other words give relaxed scans of the potential energy surface. They can be useful for:

• Exploring a relevant region of a potential energy surface (PES)
• Helping to find a particular transition state
• Developing force field parameters, e.g. dihedral force constants

A grid optimization is specified via the GridOptimizationInput object, which requires an initial_molecule, an optimization_method for the energy method used in the optimizations, and a scans field that specifies both the set of coordinates for the scan, as well as the initial and final values.

There are two optional fields: energy_method and constraints.

The energy_method field can be specified to evaluate the final energy at the optimized geometries at each grid point. If it is not specified, the optimization_method is used for final energy evaluation.

The constraints field can be specified to add geometrical constraints to the remaining coordinates (e.g. for freezing the rotation of the -CH3 groups while performing relaxed scan on a C-C bond).

The results of a grid optimization are stored in the GridOptimizationResult object.

## Example

The following example demonstrates how to perform grid optimizations:

import sierra
from sierra.inputs import *

import numpy as np

# Geometry of an HOOH molecule
# note the coordinates are in Angstrom
HOOH = Molecule(
data="""
H 0 -0.3 1
O 0 0 0
O 0 1.2 0
H 0 1.5 1
"""
)

# Perform a grid optimization along the dihedral angle
# at GFN1-xTB level of theory
# Note: the angles are in degrees
inp = GridOptimizationInput(
molecule=HOOH,
scans=[
{
"indices": [0, 1, 2, 3],
"span": {"start": -20, "stop": 20, "nsteps": 3},
}
],
optimization_method=XTBMethod(model="GFN1"),
)

result = sierra.run(inp)

final_relative_energies = {
k: v - min(result.energies.values()) for k, v in result.energies.items()
}

print("Final relative energies (in Hartree) at each grid point:")
#> Final relative energies (in Hartree) at each grid point:
print(final_relative_energies)
"""
{
(1,): 0.0008328854665666796,
(0,): 8.881784197001252e-15,
(2,): 0.0,
}
"""


## GridOptimizationInput

#### Fields

constraints

Constraints to place on the geometry optimizations.

energy_method

The method for final energy evaluation. If None the final energies are computed using the level of theory specified by optimization_method.

initial_molecule

The initial molecule for the grid optimization.

optimization_method

The method with which to optimize the molecule at each grid point.

scans

Specifies the coordinates and grid density to scan over.

## GridOptimizationResult

#### Fields

All of the fields in GridOptimizationInput and the following:

energies

The energies of the optimized molecules at each grid point.

• Type: Mapping[int, float]
• Default: {}
optimizations

A record of each optimization evaluation that the GridOptimization workflow completed.

optimized_molecules

The optimized molecules at each grid point.