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* Note: This post contains 'preliminary valence parameter fitting results’, which was carried out with currently available QM data from 2nd generation training data sets.

Description

This post contains benchmark of preliminary valence parameter fitting (v1.2.0-preliminary).

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Fitting Data and Results

• Fitting targets: 581 1-D torsion profiles; 2,974 optimized geometries; 278 vibrational frequencies

• Input force field : same initial force field used in v1.1.0 fitting

• The objective function decreased from 1.02809e+04 to 3.21676e+03 in 28 steps.

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The benchmarks are performed with the first generation test sets: primary(neighboring (primary) set and full(diverse (full) set. Second generation test set generation is a WIP.

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The final objective function value(X2) from FB single point calculation gives a brief overview of the agreement between QM and MM. The lower X2 is, the better the force field reproduces QM structures and energetics.

To provide more intuitive insights on the benchmark results, we aggregated the resulting data and made the following plots.

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Optgeo

To investigate the improved performance in reproducing QM optimized geometries, the weighted root-mean-square error (WRMSE) of each molecule, which is weighted root-mean-square deviation of internal coordinates of MM optimized geometry from QM optimized geometry was calculated and compared.

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( Metrics for bond, angle, improper torsion are set to be 0.05 Angstrom, 8 degree and 20 degree respectively and torsion contributions were intentionally excluded.)

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y values in the plots(Δ WRMSE) are the difference in the WRMSE between different v1.2.0-pre and v1.1.0; Negative y value indicates better reproduction in v1.2.0-pre compared to v1.1.0. The average change in WRMSE is -1.248, indicating that overall the v1.2.0-pre better performs in reproducing QM optimized geometry than v1.1.0.

The major contribution of significant improvement in reproducing QM optimized geometry seems to be the inclusion of eMolecules discrepancy set( a set having geometries that are substantially different in smirnoff99Frosst relative to the other force fields) in QM training set generation.

All geometries shown significant improvement with v1.2.0-pre( delta WRMSE < -0.25, blue-circled) are deprotonated phosphonates, RP(=O)(OH)(O^-). The input molecule sets(Roche set, Coverage set) used to generate the first generation optimization dataset for valence parameter fitting didn't have the phosphono group. And by using eMolecules discrepancy set during the second generation optimization dataset generation process, C=C(C(=O)O)OP(=O)(O)O has been added to the new dataset, which enabled to properly fit the parameter related to phosphono group.

Here’s one example of the improved performance on phsphonates.

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QM optimized geometry of ([P@@](=O)(O)[O-])[P@](=O)(O)[O-]. ( transparent red: MM optimized geometry with v1.1.0 force field, transparent green: v1.2.0-pre force field)

In the optimized geometry from the v1.1.0 force field, the hydroxyl hydrogen is much closer to the negatively charged oxygen (1.10 Å) than in the QM optimized geometry (2.32 Å). This can be interpreted as forming an overly strong intramolecular hydrogen bond. The v1.2.0pre force field corrects this error.

2. Abinitio Targets

To investigate the improved performance of the new parameter set in reproducing QM relative energies between conformers, QM vs MM relative energies between conformers “at QM optimized geometries” were calculated.

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The distribution from v1.2.0-pre is more centered to zero and mean absolute deviation(MAD) is smaller than v1.1.0 and v1.0.0, indicating that overall the v1.2.0-pre better performs in reproducing QM energetics than the old versions.

v1.2.0-pre force field file: