MCHammer 0.0.1

Contains MC algorithm for optimising molecules.

MCHammer

:author: Andrew Tarzia

A Monte Carlo-based molecular optimizer for optimizing the length of specified bonds in a molecule toward a target using cheap and unphysical potentials.

Please contact me with any questions ([e-mail]) or submit an issue!

Installation

Install using pip:

pip install XXXXX

Algorithm

MCHammer implements a simple Metropolis Monte-Carlo algorithm to optimize the desired bonds toward a target bond length. We define a graph of the molecule at the atomic level, which is further coarse-grained into subunits that are separated by the bonds to be optimized. All atom positions/bond lengths within a subunit are kept rigid and do not contribute to the potential energy, other than through nonbonded interactions. The algorithm uses a simple Lennard-Jones nonbonded potential and parabolic bond potential to define the potential energy surface such that the target bond length is the energy mininum and steric clashes are avoided.

The MC algorithm is as follows:

For step in N steps: 1. Choose a bond B at random: Using random.choice(). 2. Choose a subunit s on either side of B at random: Using random.choice(). 3. Define two possible translations of s, a and b and choose at random: a is defined by a random [-1, 1) step along the s to molecule centre of mass (com). b is defined by a random [-1, 1) step along the vector B. Step size is defined by user input. 4. Compute system potential U = U_b + U_nb: U_b is the bonded potential, defined by the sum of all parabolic bond stretches about the target bond length for all B: U_b = sum_i (epsilon_b * (r_i - R_t)^2 ), where R_t is the target bond length, epsilon_b defines the strength of the potential and r_i is the ith bond length. U_nb is the nonbonded potential, defined by the repulsive part of the Lennard-Jones potential: U_nb = sum_i,j (epsilon_nb * (sigma / r_ij)^mu), where epsilon_nb defines the strength of the potential, sigma defines the position where the potential becomes repulsive, mu defines the steepness of the potential and r_ij is the pairwise distance between atoms i and j. 5. Accept or reject move: Accept if U_i < U_(i-1) or exp(-beta(U_i - U_(i-1)) > R, where R is a random number [0, 1) and beta is the inverse Boltzmann temperature. Reject otherwise.

The workflow for a porous organic cage built using stk (https://stk.readthedocs.io/) is shown schematically below (this example is shown in examples/stk_example.py):

.. image:: https://raw.githubusercontent.com/andrewtarzia/MCHammer/main/docs/workflow.png?sanitize=true

Examples

This code was originally written for use with stk (https://stk.readthedocs.io/), which assembles structures with long bonds that we wanted to optimize quickly. Now it has been generalized to take any molecule (defined by atoms and bonds) and a set of bonds to optimize to some target bond length. The algorithm is unphysical in that the bonded and nonbonded potential we apply is meaningless, other than to give a reasonable structure for futher optimisation or use in a workflow!

In this example, we use stk for I/O only with the input file available in examples/minimum_example.py:

.. code-block:: python

# Load in molecule with stk.
benzene = stk.BuildingBlock.init_from_file('benzene.mol')
# Define atoms and bonds.
benzene_atoms = [
    (atom.get_id(), atom.__class__.__name__)
    for atom in benzene.get_atoms()
]
benzene_bonds = []
for i, bond in enumerate(benzene.get_bonds()):
    # Must ensure that bond atom ids are ordered by atom id.
    b_ids = (
        (bond.get_atom1().get_id(), bond.get_atom2().get_id())
        if bond.get_atom1().get_id() < bond.get_atom2().get_id()
        else (bond.get_atom2().get_id(), bond.get_atom1().get_id())
    )
    benzene_bonds.append((i, b_ids))

# Define MCHammer molecule.
mch_mol = mch.Molecule(
    atoms=(
        mch.Atom(id=i[0], element_string=i[1]) for i in benzene_atoms
    ),
    bonds=(
        mch.Bond(id=i[0], atom1_id=i[1][0], atom2_id=i[1][1])
        for i in benzene_bonds
    ),
    position_matrix=benzene.get_position_matrix(),
)

# Define optimizer.
optimizer = mch.Optimizer(
    output_dir='benzene_mch',
    step_size=0.25,
    target_bond_length=1.2,
    num_steps=100,
)
mch_mol = optimizer.optimize(
    mol=mch_mol,
    bond_pair_ids=((2, 3), (1, 5)),
)

# Update stk molecule and write to file.
benzene = benzene.with_position_matrix(mch_mol.get_position_matrix())
benzene.write('benzene_opt.mol')

Contributors and Acknowledgements

I developed this code as a post doc in the Jelfs research group at Imperial College London (http://www.jelfs-group.org/, https://github.com/JelfsMaterialsGroup).

This code was reviewed and edited by: Lukas Turcani (https://github.com/lukasturcani), Steven Bennett (https://github.com/stevenbennett96)

License

This project is licensed under the MIT license.