# Theory

BespokeFit produces optimized classical molecular force field parameters for user-specified molecules. These “bespoke” parameters aim to be highly accurate, and support for efficiently computing parameters for multiple similar molecules, such as a lead series, is included. This page describes the theory behind the production of these parameters, as well as the assumptions and trade-offs BespokeFit makes.

The process by which bespoke parameters are generated generally follows five main stages:

1. Parameter selection - features of the molecule(s) that require bespoke parameters, such as rotatable bonds, are identified

2. Fragmentation - molecules are split into smaller fragments based on the identified features for faster quantum chemical calculations

3. QC generation - any required quantum chemical reference data is generated using the smaller chemical fragments

4. Parameter generation - bespoke SMIRKS patterns that match the identified chemical features are constructed and initial values sourced from a general force field

5. Parameter optimization - the bespoke parameters are trained to fit the reference QC data

## Parameter selection

The first stage in the bespoke fitting workflow is to identify the features of the molecule to optimize. BespokeFit targets features that benefit the most from molecule-specific parametrization. At present, this involves identifying all rotatable bonds in a molecule. Accurately reproducing the torsion profile around these bonds is critical to ensuring that the correct conformational preferences of a molecule are captured.

By default, we define a ‘rotatable bond’ as any bond that is not in a ring, and is between two ‘non-terminal’ atoms that each do not participate in a triple bond. Any atoms that are bonded to at least two other non-hydrogen atoms are considered to be non-terminal. See the bespoke workflow factory chapter and thetarget_torsion_smirks field for details on overriding this definition of a ‘rotatable bond’.

## Fragmentation

The second stage in the bespoke fitting workflow is to break the molecule of interest into smaller fragments.

Quantum chemical calculations are usually very computationally expensive, and their expense grows very quickly with the number of atoms — much more quickly than in molecular mechanics. A QC calculation with twice as many atoms generally takes much more than twice as long to complete. Like launching rockets in stages for fuel economy, the default fitting workflow breaks large molecules into fragments for computational economy.

These fragments are designed to be as small as possible without significantly changing the important features of the molecule identified in the first stage. To ensure the torsional profile of a rotatable bond is preserved, for example, fragments are generated in such a way as to preserve the electronic environment around that bond.

The default fitting workflow employs the Wiberg Bond Order[1] fragmentation engine made available by the openff-fragmenter package, though another fragmenter may be specified. At present only torsion drives take advantage of fragmentation, and one fragment will be generated for each rotatable bond identified by the previous step.

## QC Generation

The third stage in the bespoke fitting workflow is generating any reference quantum chemical data that the bespoke parameters will be trained to reproduce.

The default fitting workflow currently generates all reference data at the B3LYP-D3BJ/DZVP level of theory. This balances computational efficiency against accurately reproducing conformations generated using higher levels of theories. This is also the level of theory used in training the main OpenFF force fields, and so ensures that bespoke and general parameters can be mixed with minimal compatibility concerns.

Tip

See the quick start guide for details on how to swap out the default level of theory for a faster surrogate, such as ANI or XTB.

The types of quantum calculation that will be performed depend on the types of bespoke parameters to be generated. In particular if generating bespoke:

• torsion parameters: a one dimensional torsion scan around each identified bond will be performed

## Parameter generation

The fourth stage in the bespoke fitting workflow is to generate an initial set of ready-to-train parameters for each of the features identified in the first stage.

There are two aspects to this: we need to both select a sensible set of initial values for the parameter, and we need to generate a SMIRKS pattern that describes the chemical environment that the parameter will be applied to.

Note

SMIRKS[2] patterns are used extensively within OpenFF force fields as a more flexible and robust alternative to atom types.

### Selecting initial values

The initial values for the bespoke parameters are by default sourced from the “Rosemary” OpenFF 2.0.0 force field. This is done by applying the general force field to the molecule of interest, inspecting which parameters from the general force field were applied to the target features, and then copying the relevant values. For example, when selecting initial torsion parameters for biphenyl, BespokeFit would check which general torsion parameters were assigned to the central rotatable bond, and then copy the barrier height $$k_i$$, phase $$\psi_i$$ and periodicity $$N$$ of those parameters over to the bespoke parameter.

By default, extra degrees of freedom will also be added so that the specificity of the bespoke parameters is not limited by the starting force field. In the case of generating bespoke torsion parameters, the default fitting workflow will augment the initial values so that it contains periodicities $$n_i$$ from 1 to 4.

$U(\phi) = \sum_{i=1}^N k_i (1 + \cos(n_i \phi - \psi_i))$

This can be configured in the smirk_settings field of the workflow factory. This is a conservative approach that is often not needed; in these cases, added complexity is avoided because the barrier heights $$k_i$$ are kept close to zero by the optimizer, which prefers solutions with simpler parameters.

### Generating bespoke SMIRKS

Generating a SMIRKS pattern involves a trade-off between specificity and transferability. Ideally the pattern would be highly specific to the chemical environment in question while being transferable to other similar chemical environments, such as the same torsion of a pharmacophore across several molecule in a lead series. While general force fields favor generality, BespokeFit prefers specificity so that parameters can be highly optimized to the target. SMIRKS patterns generated by BespokeFit are constructed to include as much information about as many atoms as possible while being consistent across the parent molecule and any relevant fragments.

#### Torsion SMIRKS

Torsion SMIRKS generation begins by grouping symmetric torsions and treating them together. By symmetry, these torsions should have identical parameters, and this helps reduce the number of new parameters and simplify optimization. BespokeFit accomplishes this by identifying the symmetry classes of atoms in the parent molecule with RDKit or OpenEye and labeling torsions with the symmetry classes of their atoms. Two atoms will have the same symmetry class if and only if they are symmetry-equivalent, so symmetric torsions are those that share a (possibly reversed) label.

Once a minimal set of symmetry-equivalent torsions are collected, SMIRKS patterns are generated with ChemPer. We consider the fragments to be the minimum electronically decoupled substructure around each torsion which preserves the local chemical environment. Hence, SMIRKS patterns are constructed to include the maximum common substructure between the parent and fragment, making them as transferable as possible given complete specificity to their local chemical environment. In particular, they are guaranteed to be transferable between parent and fragment and to other molecules that share the computed fragment.

As a result, the common cores of congeneric series like the ligands of TYK2(pictured) can be parameterized once and cached. When a new molecule produces the same torsion SMIRKS, the parameter can be reused from the cache, saving the significant computational effort associated with a torsion drive.

## Optimization

The final stage in the bespoke fitting workflow is to optimize (“train”) the bespoke parameters against the QC reference data generating in the earlier stage.

The optimization first constructs a loss function to minimize. The loss function measures the deviations between a trained result and the reference value. In BespokeFit, we refer to the different contributions to the loss function as ‘fitting targets’. This terminology is consistent with the brilliantForceBalance force field optimization framework.

BespokeFit supports three main fitting targets, which measure the deviations of:

• torsion profile: the torsion profile computed by performing a torsion scan using the current force field parameters against the reference QC torsion profile.

• vibrational frequency: vibrational frequencies computed from MM hessian data against those computed from reference QC hessian calculations.

• optimized geometry: internal coordinates of a conformer of the molecule minimized using the current values of the force field against the same conformer minimized using QC methods.

These are the same fitting targets that are used to produce the mainline OpenFF force fields, ensuring that any bespoke parameters are compatible with those in the starting general force field. For more details, see the OpenFF 1.0.0 Parsley paper.[3]

Although in the future multiple optimization engines will be supported, by default the fitting workflow employs ForceBalance to train the parameters against the fitting targets outlined above. ForceBalance employs a Bayesian prior distribution to avoid over-fitting and to define the range of likely values the fitted parameter may take on. [4] Any complexity added to the force field must overcome a penalty imposed by the prior distribution. The Laplacian prior used by default is equivalent to an L1 regularizer, and is configured by setting a “prior width”, which sets the range over which the parameter can vary during optimization. BespokeFit defaults to quite large prior widths on the torsion barrier heights ($$k_i$$) so that the optimization is not hindered by a very general reference value.

## References

1

Chaya D Stern, Christopher I Bayly, Daniel G A Smith, Josh Fass, Lee-Ping Wang, David L Mobley, and John D Chodera. Capturing non-local through-bond effects in molecular mechanics force fields i: fragmenting molecules for quantum chemical torsion scans [article v1.1]. bioRxiv, 2022. URL: https://www.biorxiv.org/content/early/2022/01/30/2020.08.27.270934, doi:10.1101/2020.08.27.270934.

2

David L. Mobley, Caitlin C. Bannan, Andrea Rizzi, Christopher I. Bayly, John D. Chodera, Victoria T. Lim, Nathan M. Lim, Kyle A. Beauchamp, David R. Slochower, Michael R. Shirts, Michael K. Gilson, and Peter K. Eastman. Escaping atom types in force fields using direct chemical perception. Journal of Chemical Theory and Computation, 14(11):6076–6092, 2018. PMID: 30351006. URL: https://doi.org/10.1021/acs.jctc.8b00640, doi:10.1021/acs.jctc.8b00640.

3

Yudong Qiu, Daniel G. A. Smith, Simon Boothroyd, Hyesu Jang, David F. Hahn, Jeffrey Wagner, Caitlin C. Bannan, Trevor Gokey, Victoria T. Lim, Chaya D. Stern, Andrea Rizzi, Bryon Tjanaka, Gary Tresadern, Xavier Lucas, Michael R. Shirts, Michael K. Gilson, John D. Chodera, Christopher I. Bayly, David L. Mobley, and Lee-Ping Wang. Development and benchmarking of open force field v1.0.0—the parsley small-molecule force field. Journal of Chemical Theory and Computation, 17(10):6262–6280, 2021. PMID: 34551262. URL: https://doi.org/10.1021/acs.jctc.1c00571, doi:10.1021/acs.jctc.1c00571.

4

Lee-Ping Wang, Todd J. Martinez, and Vijay S. Pande. Building force fields: an automatic, systematic, and reproducible approach. The Journal of Physical Chemistry Letters, 5(11):1885–1891, 2014. PMID: 26273869. URL: https://doi.org/10.1021/jz500737m, doi:10.1021/jz500737m.