Methodology

The method depends on the following concepts and algorithms.

Unique Molecules

A simulation model may contain many small molecules (for example, a molecular liquid), several large molecules (for example, polymer blends), or a heterogeneous interface (for example, solid/liquid, liquid/liquid, liquid/solid, or liquid/vapor). Assuming that intermolecular interactions can be well described by nonbonded terms (Lennard-Jones for van der Waals interactions and Coulombic terms for electrostatics), we select unique molecules for force field development.

Molecule Type

Each unique molecule can be partitioned into a number of fragments. Using the standard fragmentation method, a molecule type is defined by its constituent fragments. Each fragment is represented by a SMILES string. Therefore, a combination of sorted SMILES strings (a cSMILES string) can be used to identify the molecule type.

A molecule type is independent of molecular size. For example, a polymer of 1000 repeat units and an oligomer of 5 repeat units are the same molecule type.

Molecule Type Force Field (MTFF)

An MTFF is a force field parameterized for a molecule type. It is derived by using its fragments as the training set and fitting their quantum mechanics data. The fragments are usually small molecules. QM data for parametrization are obtained using the QM sampling method. The data include energies, first and second derivatives of the energy, and atomic charges, computed on optimized and conformationally distorted structures. Using these data, the MTFF is derived by regression. The least-squares method is used in DFF.

Although some underlying fragments and QM data are shared among different molecule types, each MTFF is developed independently. Because the training set is small, developing an MTFF is much faster and more reliable than simultaneously regressing a dataset that is several orders of magnitude larger.

Using an MTFF is similar to using a traditional force field. For a simulation model, first identify its molecule types, then obtain the corresponding MTFFs, and then build an integrated force field by combining those MTFFs. The combination involves only intermolecular interactions. Lennard-Jones cross terms commonly use Lorentz–Berthelot combining rules; electrostatic interactions use Coulomb's law with the pre-assigned fixed atomic partial charges.

MFDFF Database

Fragments can appear in different molecule types, so the QM data of fragments are saved in a database for reuse. For any molecule types that have been parameterized, their MTFFs are also saved in the database. Because the database contains both fragment data and molecule-type force fields derived from those fragments, it is called the Molecule Fragment Derived Force Field database (MFDFF.db).

The database contents grow with applications. Using the MTFF database is fundamentally different from using the classic TEAMFF force field database. If a required MTFF is missing, a new one is made on the fly from its fragment data. If new fragment data are required, QM computations are launched and then used to derive the new MTFF. With an automated workflow and the MFDFF database, a self-learning cycle is closed.

The Result Force Field

The force field for the target simulation model is constructed by combining its MTFFs. The resulting force field contains all intramolecular energy terms. The intermolecular energy terms (Lennard-Jones and Coulombic) are calculated using combination rules, usually by the simulation engines.

Automated Workflow

The workflow has the following modules:

• Enquiry — identify molecule types and fragments
• Search — search and download MTFF and fragment QM data
• Compute — compute new fragment QM data
• Develop — fit and validate a new MTFF using the required fragment QM data
• Update — upload new MTFF and fragment QM data
• Combine — construct and test the resulting force field

For a set of simulation models, the workflow iterates over each model with the following logic:

1. Enquiry to find molecule types and fragments.
2. Search to download MTFFs. If successful: Combine to make the resulting force field, write output, and exit; otherwise go to the next step.
3. Use Search to download QM data for the required fragments. If successful: Develop a new MTFF, Update the new MTFF, and repeat step 2; otherwise go to the next step.
4. Compute new QM data, Update the QM data, and repeat step 3.

The entire process can be executed with minimal intervention.

Distributed Force Field Developments

In traditional force fields, missing parameters usually require central developers to repair the force field. The task is tedious and prone to error, mostly because of parameter correlation and the widespread use of atom types. The task becomes increasingly difficult as coverage increases.

The MTFF approach changes the landscape of force field development. Given basic infrastructure—the database and an automated parameterization workflow—new developments shift to the user's end. Demand is triggered by applications only. Each new development addresses specific missing parameters, independently of existing force field parameters and of other users' needs. This distributed approach is fundamentally different from centralized force field development.