## Similar protocols

## Protocol publication

[…] Atom-centered
point charges were first fitted to the baseline, unpolarized ESP using
the standard RESP, then atom-centered point dipoles, superimposed
on the point charges, were optimized separately for each polarized
QM ESP. This model reports on the maximal accuracy attainable by any
polarization model that uses the atom-centered point-dipole representation
of polarization along with RESP baseline point charges. However, like
the optimal-point-charge model above, it cannot be employed in simulations
because it requires a new quantum calculation for each molecular configuration.
The procedure for computing optimal point dipoles is described below.The ESP at rm due to the baseline RESP partial charges, qi, and the atom-centered point dipoles, μi, is
given by6where
well-known physical constants are omitted
for simplicity and rij is as given in and7For each external charge position rk, where index k refers
to the inducing charge, the error metric χk2 () may be written
as8where ϕmk′ contains all
quantities independent of the dipoles.Optimal dipoles are obtained
by setting for all μi. This yields the following
system of linear equations9Solving this matrix equation
yields the desired
atom-centered point dipoles optimized for the external charge position rk. The **NumPy** linalg.norm() function was used
to find the solution to the matrix equation. [...] All models require global
parameter optimization. For model 0 and models 3–6, the parameters
were optimized to minimize R2, the mean
of the squared potential deviations across all inducing charge sites k, for each molecule of interest (). For models 1 and 2, the parameters were
optimized to minimize Rk2, the mean-squared potential
deviations for each separate inducing charge position (). All optimizations were performed
with a **SciPy** implementation of L-BFGS-B,, a gradient-based constrained minimization method. Charges are left
unconstrained, whereas polarizabilities are restricted to positive
values. For the inducible dipole models with fixed RESP charges (models
3 and 5), only the atom-typed polarizabilities, αti, require adjustment;
for those with co-optimized point charges, the atom-typed charges, qti, are adjusted along with the polarizabilities.For each molecule,
multiple optimizations were run with initial parameter values drawn
from a uniform distribution using numpy.random.rand().() For model 0, five optimizations were
run using initial charges randomly drawn from the range −1.0e to 1.0e. For models 3–6, 50 optimizations
were run using initial polarizabilities randomly drawn from 0 to 10
bohr3 (0–1.482 Å3). The parameter
set with the lowest value of R2 was selected
as the optimum. When charges were co-optimized (models 4 and 6), the
baseline RESP charges were used as their starting values. Only 10
optimizations were run for tyrosine as the calculations became time-consuming
for this relatively large molecule. […]

## Pipeline specifications

Software tools | Numpy, SciPy |
---|---|

Applications | Miscellaneous, WGS analysis |