Development of a Computer-Guided Workflow for Catalyst Optimization. Descriptor Validation, Subset Selection, and Training Set Analysis

Article abstract of DOI:10.1021/jacs.0c04715

Modern, enantioselective catalyst development is driven largely by empiricism. Although this approach has fostered the introduction of most of the existing synthetic methods, it is inherently limited by the skill, creativity, and chemical intuition of the practitioner. Herein, we present a complementary approach to catalyst optimization in which statistical methods are used at each stage to streamline development. To construct the optimization informatics workflow, a number of critical components had to be subjected to rigorous validation. First, the critically important molecular descriptors were validated in two case studies to establish the importance of conformation-dependent molecular representations. Next, with a large data set available, it was possible to investigate the amount of data necessary to make predictive models with different modeling methods. Given the commercial availability of many catalyst structures, it was possible to compare models generated with algorithmically selected training sets and commercially available training sets. Finally, the augmentation of limited data sets is demonstrated in a method informed by unsupervised learning to restore the accuracy of the generated models.

Full text of DOI:10.1021/jacs.0c04715

pubs.acs.org/JACS
Article
Development of a Computer-Guided Workflow for Catalyst
Optimization. Descriptor Validation, Subset Selection, and Training
Set Analysis
Jeremy J. Henle,† Andrew F. Zahrt,† Brennan T. Rose, William T. Darrow, Yang Wang,
and Scott E. Denmark*
Cite This: https://dx.doi.org/10.1021/jacs.0c04715
Read Online
sı
*
Metrics & More
Article Recommendations
Supporting Information
ACCESS
ABSTRACT: Modern, enantioselective catalyst development is
driven largely by empiricism. Although this approach has fostered
the introduction of most of the existing synthetic methods, it is
inherently limited by the skill, creativity, and chemical intuition of
the practitioner. Herein, we present a complementary approach to
catalyst optimization in which statistical methods are used at each
stage to streamline development. To construct the optimization
informatics workflow, a number of critical components had to be
subjected to rigorous validation. First, the critically important
molecular descriptors were validated in two case studies to
establish the importance of conformation-dependent molecular
representations. Next, with a large data set available, it was possible
to investigate the amount of data necessary to make predictive
models with different modeling methods. Given the commercial availability of many catalyst structures, it was possible to compare
models generated with algorithmically selected training sets and commercially available training sets. Finally, the augmentation of
limited data sets is demonstrated in a method informed by unsupervised learning to restore the accuracy of the generated models.
The complexity of this problem has inspired the develop-
ment of many approaches to aid in catalyst design. Among
them, computational methods are particularly appealing owing
to the increasing power of computational resources, the
decreased demand for materials, and the ability of modern
statistical learning methods to recognize patterns in high
dimensional data.3−26 In particular, the capability to evaluate
catalysts in silico without preparing and testing them
experimentally makes these approaches particularly desirable.
The most established method for computational catalyst
design is in the application of quantum chemistry to
understand the relative energy differentials leading to
enantiomers which then enables more informed catalyst
design.4,7,8,10,12−14 Alternatively, surveying catalysts computa-
tionally by computing the relative energies of competing
transition structures is a viable approach. One such example is
Q2MM, in which a transition-state force field is derived for a
INTRODUCTION
■
Enantioselective catalysis is an enabling technology for the
synthesis of chiral, enantiomerically pure organic compounds
using substoichiometric quantities of a chiral catalyst.1,2
Traditionally, catalyst design is guided by empiricism, wherein
experimentalists attempt to identify qualitative trends in
catalyst structure that dictate catalyst performance. Informed
by these trends, new structures are proposed with modifica-
tions that are anticipated to afford higher selectivity catalysts.
The proposed catalysts must then be synthesized and
evaluated, a process which is repeated iteratively until a
satisfactory level of performance is achieved. Although
frequently successful, this approach is inherently limited
because it depends on the ability of the chemist to correctly
identify those catalyst features responsible for enantioinduction
and for the proposed modifications of the next generation of
catalyst structure to improve performance. Even the most
experienced practitioner cannot quantitatively discern the
many subtle influences each component of the catalyst
structure has on dictating the relative energy of competing
diastereomeric transition structures. In many cases, the factors
influencing selectivity in complex systems are high dimen-
sional; thus, the unaided human mind is incapable of grasping
all of the relative contributors related to catalyst performance.
Received: April 29, 2020
https://dx.doi.org/10.1021/jacs.0c04715
J. Am. Chem. Soc. XXXX, XXX, XXX−XXX
© XXXX American Chemical Society
A

Journal of the American Chemical Society
pubs.acs.org/JACS
Article
Figure 1. Chemoinformatics-guided process for catalyst discovery and optimization. Adapted with permission from ref 49. Copyright 2019
American Association for the Advancement of Science.
catalytic system, enabling rapid evaluation of many catalyst
candidates computationally.27−29 Similarly, workflows have
enabled screening campaigns using quantum chemical
methods that are reliable, proceed in a reasonable time
frame, and are accessible to the general community.30 These
approaches are attractive in that they do not require any
experimental data for evaluation of catalyst candidates.
However, they rely on mechanistic knowledge of the
enantiodetermining transition structures which is not always
available.
combination of critical design features including (1) a
systematic method for training set selection that is applicable
to any reaction and agnostic to mechanism, (2) a conformer-
dependent representation of catalyst properties, (3) accurate
predictions for catalyst structures and substrate structures that
are novel to the model, and (4) accurate predictions for
catalyst structures and substrate structures outside the
selectivity range of the training set points. The outline of the
general workflow is as follows: (1) a large, in silico library of
synthetically accessible catalyst candidates is constructed
(Figure 1A); (2) for each member of this library, descriptors
are calculated which define the chemical space of the library
(Figure 1A); (3) from this library, a representative subset is
algorithmically selected, termed the Universal Training Set
(UTS) because it is selected only considering catalyst
properties and is thus agnostic to reaction and mechanism
(Figure 1B); (4) this UTS is synthesized and evaluated in the
reaction of interest (Figure 1C); (5) mathematical models are
constructed relating the calculated descriptors to experimental
outcome (Figure 1E); and (6) the in silico library is virtually
screened with the model, and the best catalyst candidates for
the particular transformation can be identified for synthesis
(Figure 1F,G). This process can be performed interactively,
with each subsequent iteration added to the training data, until
an ideal catalyst is identified.
An alternative to calculating the relative energies of
competing structures is the use of quantitative structure−
selectivity relationships (QSSR).31 In this method, catalyst
structures are correlated with experimental data, generating a
mathematical model which can be used to evaluate new
catalyst structures in silico. Further, QSSR does not require
mechanistic information and, in some cases, can be used to
extract important mechanistic insights. The seminal example of
QSSR in enantioselective catalysis was reported by Norrby and
co-workers in which ratios of isomeric products from various
nucleophilic substitution reactions on palladium η3-allyl
complexes was predicted.32 Other early examples of QSSR
include the use of molecular interaction fields (MIFs) by
Kozlowski,33−37 Lipkowitz,38 and Hirst,39,40 the use of chirality
codes by Gasteiger and Aires-de-Sousa,41−43 and other
parameter-based approaches by You44 and Damen and
Hoogenraad.45,46 More recently, Sigman and co-workers have
pioneered a new era of QSSR using linear free energy
relationships (LFERs) to identify key structural features of
catalysts as well as to predict more selective catalysts.47
In our own laboratories, MIF-based approaches have been
used in an attempt to elucidate important structural character-
istics of phase transfer catalysts.48,49 More recently, we have
used more statistical learning protocols with MIF-type
descriptors to evaluate chiral catalysts, culminating in a
computer-driven workflow for the optimization of enantiose-
lective catalysts.50 This workflow is unique in that it contains a
BACKGROUND
■
In our previous study, the enantioselective formation of N,S-
acetals developed by Antilla and co-workers was selected to
demonstrate the workflow (Scheme 1).51
This system was selected for a number of reasons including
short reaction time, clean product profiles, experimental
robustness, reproducible reaction outcomes, and sensitivity to
perturbations in catalyst structure. In addition to these
experimental considerations, other aspects of this reaction
made it ideal for benchmarking the viability of the chemo-
informatic workflow. Foremost, the reaction had already been
B
https://dx.doi.org/10.1021/jacs.0c04715
J. Am. Chem. Soc. XXXX, XXX, XXX−XXX

Journal of the American Chemical Society
pubs.acs.org/JACS
Article
represent the possible chemical diversity in the parent in silico
library. Similarly, owing to the relative rigidity of the catalyst
scaffold, it is reasonable to hypothesize that for this system the
difference between conformer-dependent and single-conformer
molecular representations would be negligible. It follows from
these points that (1) if the algorithmically selected subset provides
more accurate models than the commercially available subset, one
would expect this divergence to increase as the protocol is extended
to more complicated systems, and (2) if conformer-dependent
descriptors are superior in this case, their superiority will only
increase as more flexible catalyst scaffolds are investigated.
Scheme 1. Enantioselective Formation of N,S-Acetals
To represent the steric properties of molecules, Average
Steric Occupancy (ASO) descriptors were calculated as
described previously.50 This work is in essence an application
of the 4D-QSAR formalism introduced by Hopfinger and co-
workers and first applied to enantioselective catalysis by Hirst
and co-workers.40,52 The reader is referred to the original
report for the specific parametrization used for this library, but
a general overview is provided here.50 Descriptors are
calculated by first generating a conformer distribution for
every member of the in silico library of catalyst candidates. The
optimized; thus, if an optimal catalyst could not be identified
using our method, it would clearly be the fault of the
computational workflow. Further, two other aspects of this
system make it an interesting case study for benchmarking: (1)
commercially available catalysts give a wide range of selectivity
and (2) the catalyst structures are relatively inflexible
compared to many other catalyst scaffolds. Because commer-
cially available catalysts cover a wide range of selectivity space,
one might expect that readily available catalysts adequately
Figure 2. (a) Calculation of ASO descriptors and (b) graphical representation of ASO descriptors for different molecules. Adapted with permission
from ref 49. Copyright 2019 American Association for the Advancement of Science.
C
https://dx.doi.org/10.1021/jacs.0c04715
J. Am. Chem. Soc. XXXX, XXX, XXX−XXX

Journal of the American Chemical Society
pubs.acs.org/JACS
Article
in silico library of BINOL-phosphoric acids used in this study
contains 806 members.53 Every conformer for every catalyst is
then superimposed with respect to a common core scaffold and
placed in a common grid containing ca. 600 grid points. The
ASO descriptors are then generated from the collection of
conformers for a given molecule. For each conformer, every
grid point is queried if it falls within the van der Waals radius
of an atom in the molecule and assigned a binary value: yes =
1, no = 0. This process is repeated for every conformer for a
given molecule. Thus, if an individual catalyst candidate has n
conformers, possible values at each grid point range from 0 to
n for that molecule. The occupancy values at each grid point
are then normalized to the number of conformers, so that
every grid point contains a value between 0 and 1. These
numbers are the ASO descriptors (Figure 2).54,55
To capture the electronic character of the 3,3′-substituents
on the phosphoric acid catalysts, a new descriptor was
developed to emulate Hammett parameters. Hammett
parameters represent the through-bond electronic perturbation
a substituent has on a system, whereas other electrostatic
potential mapping methods represent through-space effects.56
However, the 3,3′-substituents in the in silico library are too
diverse to be represented with experimentally derived
Hammett parameters, owing to the presence of multiple
substituents at various positions and other groups that are not
simple substituted benzenes. Thus, a new calculable parameter
had to be developed that reflects the perturbation of the
substituent on a charged particle. First, a tetramethylammo-
nium ion probe is constructed. Then, one of hydrogen atoms
of a methyl group is replaced with the 3-substituent of the
catalyst. The most positive point on the electrostatic potential
map (ESPMAX) still resides around the ammonium residue
(specifically, the other methyl groups). Thus, the substituent
simply modulates the extent of positive charge around this
group. The most positive point on the electrostatic potential
energy surface is the ESPMAX descriptor (Figure 3).
Figure 4. Evaluation of ESPMAX descriptor by correlating relative
ESPMAX with Hammett parameters.
tional flexibility in descriptor calculation is investigated
through rigorous comparison with other descriptor classes.
Second, a common criticism of more advanced statistical
learning methods is that the amount of data necessary to
generate accurate models is prohibitively large. In Case Studies
3 and 4, this criticism is investigated by examining the number
of data points needed to generate accurate models with
different modeling methods. Finally, in our prior work we
posed the hypothesis that models generated from a data set
containing an algorithmically selected set of molecules will be
superior to models generated from a data set containing
molecules selected on the basis of their availability. In Case
Studies 5 and 6, we more thoroughly investigate this
hypothesis by comparing models generated from data sets
using algorithmically selected catalysts and commercially
available molecules. Then, to extend the utility of our workflow
to existing data sets more similar to the latter set, we propose
using unsupervised learning as a tool by which to augment
such data sets, restoring the accuracy of the models to levels
similar to the algorithmically selected set.
Figure 3. Calculation of the ESPMAX descriptor.
This metric has excellent correlation with Hammett
parameters (R2 = 0.98) and can be rapidly calculated for any
desired substituent (Figure 4). Thus, this parameter was
selected to represent the electronic character of the 3,3′-
substituents. This parameter can be extended to any
substituent in any context as an easily calculable electronic
descriptor. It is worth noting that this is a substituent-based
descriptor, much like Sterimol parameters or Hammett values.
Thus, the numerical value for each catalyst structure with the
same substituent will be the same.
RESULTS AND DISCUSSION
■
2.1. Case Study 1: Increased Accuracy of Conformer-
Dependent Descriptors. The suitability of this descriptor set
(ASO + ESPMAX) was compared with two different single-
conformer representations. The first is a simple steric indicator
field (SIF). In this case, the calculation protocol is identical to
the ASO, except only one conformer of each catalyst is used in
the calculation rather than an ensemble of conformers. Thus,
all descriptors are either 1 or 0 in the indicator field. These
descriptors were also augmented with the ESPMAX descriptor
to represent electronic contributions. The second is the use of
electronic and steric molecular interaction fields (MIFs), as
employed in comparative molecular field analysis (CoMFA).57
In this case, a steric MIF was calculated using Lennard-Jones
potentials with an sp3-hybridized carbon atom as a probe atom
RESEARCH PLAN
■
Although our previous report represented the first disclosure of
this workflow, the rigorous validation of every step of the
workflow was not provided. Accordingly, we present herein the
necessary validation underpinning the success of this approach.
First, in Case Studies 1 and 2, the importance of conforma-
D
https://dx.doi.org/10.1021/jacs.0c04715
J. Am. Chem. Soc. XXXX, XXX, XXX−XXX

Journal of the American Chemical Society
pubs.acs.org/JACS
Article
Figure 5. Matrix of 25 different possible substrate combinations derived from imines 1−5 and thiols A−E. Adapted with permission from ref 49.
Copyright 2019 American Association for the Advancement of Science.
at each grid point, and an electronic MIF was calculated using
the electrostatic potential energy at each grid point using a
positron as a probe. For each single-conformer representation,
a C2-symmetric conformer of the molecule was selected for
minimization such that each catalyst structure used occupied
similar relative conformations. These structures were then
minimized at the PM6 level of theory. In this way, differences
in descriptor profiles will be attributed to structural differences
rather than a difference in the relative conformations of the
structures.
As a first experiment, the 1075-reaction data set (generated
from 43 catalysts and 25 substrate combinations) published
previously was used to compare these different descriptor
classes. This data set comprises every substrate/catalyst
combination of the 25 substrate combinations in Figure 5,
the 24 training set catalysts in Figure 6, and the 19 external set
of catalysts in Figure 7. The parametrization of substrates was
identical to those found in the original report and was used
with all three different catalyst representations to discern only
the influence of catalyst representation on accuracy.50
In this study, certain catalysts and substrate combinations
are intentionally withheld from the training data to ensure
some reaction components would be novel to the model.
Namely, the 24 UTS catalysts in reactions generating products
1A−4D were used in model training and cross-validation, and
reactions with imine 5, thiol E, or any of the external test
catalysts in Figure 7 were used as an external test set. Thus, the
set used for training and cross-validation was 384 reactions (24
catalysts × 16 substrate combinations = 384 reactions), and
the external test set was composed of the remaining 691
reactions. Models were made using support vector machines
(with linear, radial basis function, or second-order polynomial
kernels, abbreviated herein as SVR_kernel), random forests
(RF), gradient boosting regression (GBR), Lasso, Ridge,
ElasticNet, Lars, LassoLars, kernel Ridge (with linear, RBF,
and second order polynomial kernels), and projection to latent
structure (PLS). In each case, the descriptors were first
preprocessed with either principle component analysis, mutual
information regression, or f-regression to reduce the
dimensionality of the input space. Hyperparameter optimiza-
tion was performed with a Bayesian optimization process when
applicable.58 Models were generated with Sci-Kit learn,59 and
the modeling and evaluation process were automated with in-
house Python2 scripts that are available on our GitLab site.54
The best models were selected of the basis of q2 from 5-fold
cross-validation. A summary of all models generated and their
E
https://dx.doi.org/10.1021/jacs.0c04715
J. Am. Chem. Soc. XXXX, XXX, XXX−XXX

Journal of the American Chemical Society
pubs.acs.org/JACS
Article
Figure 6. Twenty-four-member UTS of chiral phosphoric acids.
q2 values are available in the Supporting Information. These
best models were then further compared by evaluating their
accuracy on the 691 test reactions. As different models were
the best performing model for each respective descriptor class,
three different models have been evaluated for each descriptor
class. Thus, a 3 × 3 matrix was constructed, with the best
model for each descriptor class generated with each descriptor
class. In this way, bias is avoided by selecting a modeling
method suited better for modeling with one of the descriptor
type compared to the others (i.e., selecting the best model for
one descriptor class to compare all descriptor classes could bias
the results in favor of that descriptor class). A summary of best
models identified in this study is given in Table 1.
The ASO + ESPMAX descriptors produce models with the
lowest MAD for each model type. It is noteworthy that the
indicator field-type descriptors dramatically outperformed the
interaction field type descriptors, with comparable MADs to
conformer-dependent descriptors. To examine the means in
more detail, a more rigorous statistical analysis was performed
to verify whether the errors are statistically significantly
F
https://dx.doi.org/10.1021/jacs.0c04715
J. Am. Chem. Soc. XXXX, XXX, XXX−XXX

Journal of the American Chemical Society
pubs.acs.org/JACS
Article
Figure 7. Nineteen-member external catalyst test set of chiral phosphoric acids.
Table 1. Comparison of Descriptor Classes
descriptor class
a
preprocessing and model
ASO + ESPMAX (kcal/mol MADTest
)
SIF + ESPMAX (kcal/mol MADTest
)
steric and electronic MIFs (kcal/mol MADTest)
FREG500_Kernel_Ridge_poly2
FREG500_SVR_poly2
FREG100_GBR
0.24
0.21
0.35
0.27
0.26
0.36
0.46
0.44
0.36
a
Preprocessing and model type. FREG500_Kernel_Ridge_poly2 is selection of the top 500 features with f-regression, then modeling with Kernel
Ridge using a second order polynomial kernel. FREG500_SVR_poly2 is using f-regression to select the best 500 descriptors, then modeling with a
support vector regressor with a second order polynomial kernel. FREG100_GBR is first selecting of the best 100 descriptors with f-regression, then
modeling with gradient boosting regression.
different. Because Levene’s test for homogeneity indicated
variances between groups were statistically significantly
different and both the Kolmogorov−Smirnov and Shapiro-
Wilk tests for normality indicated the data was not normally
distributed, a Kruskal−Wallis analysis of variance was
performed with pairwise comparisons between groups and
significance values adjusted with the Bonferroni correction for
multiple tests. This analysis revealed that indeed the support
vector machine trained with ASO descriptors produced
statistically significantly lower errors in the test set than
every other model except the kernel ridge model trained with
ASO descriptors. The kernel ridge models trained with ASO
descriptors was not, however, statistically significantly different
than the support vector machine or the kernel ridge model
G
https://dx.doi.org/10.1021/jacs.0c04715
J. Am. Chem. Soc. XXXX, XXX, XXX−XXX

Journal of the American Chemical Society
pubs.acs.org/JACS
Article
trained with steric indicator field descriptors. In general, the
molecular interaction field descriptors performed poorly,
although the best model for this descriptor class, gradient
boosting regression, was not statistically significantly worse
than the gradient boosting regression models for ASO and SIF
descriptor classes. One plausible explanation for the low
performance of this descriptor set is that there are many
relatively high-variance data points and extracting relevant
stereochemical information from a noisy data set is
challenging. However, this hypothesis has not been rigorously
evaluated.
Scheme 2. Model Reaction System for Enantioselective
Alkylation
In general, the conformer-dependent descriptors outperform a
single conformer descriptors in this case study. However, it is
noteworthy that the SIF + ESPMAX descriptors still performed
well, generating accurate models. Conceivably, the ASO and
SIF descriptors give similar accuracies in this case because the
scaffold is very rigid; we suspect the difference between conformer
dependent and single-conformer methods will increase as more
flexible conformer scaffolds are investigated. To probe this
hypothesis, a literature data set was selected as an additional
case study which uses a catalyst scaffold significantly more
flexible than BINOL-phosphoric acids. These descriptors have
been compared with fingerprints and 1-hot encoding elsewhere
in the literature using this data set.50,60
2.2. Case Study 2: APTC Alkylation of a Glycine Imine.
In the selected study, Lygo, Hirst, and co-workers analyzed 88
different enantioselective alkylation reactions performed with
different cinchona alkaloid-derived asymmetric phase transfer
catalysts (APTC) (Scheme 2).39 For this study, catalyst
structures were represented with both ASO descriptors and
our newly implemented, average electronic indicator field
(AEIF) descriptors. The AEIF descriptors are conceptually
similar to the ASO descriptors, but instead of a binary indicator
of occupancy, the atomic charge of the overlapping atom at
each point is assigned to that grid point. The sum of these
values is then normalized to the number of conformers,
furnishing the AEIF value at each grid point. We have
developed a Python2 package for calculating AEIF descriptors,
which is available on our GitLab page.54 Notably, these
descriptors will change depending on the method of atomic
charge calculation used. This conformer dependent represen-
tation was compared with a single conformer representation in
which a steric indicator field and an electronic indicator field
were used. Ten different 70/18 partitions were used to select
the 18-member external test set. The 70-member set was then
used in training and cross-validation of PLS models, after
which the best models were selected to predict the test set
(complete modeling details can be found in the Supporting
Information). PLS models were chosen because of the large
number of descriptors with respect to data points and because
of colinearity between descriptor values. The overlaid plots of
the external test sets (180 points in total) are depicted in
Figure 8.
As is clearly illustrated by the graphs in Figure 8, the
conformer dependent representation is much more accurate
than the single conformer representation (0.22 kcal/mol
MADTest vs 0.30 kcal/mol MADTest and q2 = 0.71 vs 0.53,
respectively). Further, the conformer dependent models have a
higher R2 (0.77 vs 0.37), a slope closer to unity (0.68 vs 0.43),
and a y-intercept closer to zero (0.23 vs 0.40) than the single
conformer models. When testing the difference between the
test set errors, the models trained with conformer-dependent
descriptors are statistically significantly more accurate than the
Figure 8. Overlaid test sets for models made with SIF and EIF
descriptors (top, MAD = 0.30 kcal/mol) and models made with ASO
and AEIF descriptors (bottom, MAD = 0.22 kcal/mol).
single conformer model (p = 0.0019, full description of test is
available in the SI). This observation supports the hypothesis that
the difference in accuracy between conformer dependent and
conformer independent models increases as catalyst flexibility
increases.
H
https://dx.doi.org/10.1021/jacs.0c04715
J. Am. Chem. Soc. XXXX, XXX, XXX−XXX

Journal of the American Chemical Society
pubs.acs.org/JACS
Article
Figure 9. Truncated UTS of chiral phosphoric acids.
Figure 10. Predicted vs observed for the 1003-member external test sets with PLS models (left, MAD = 0.25 kcal/mol), SVR (middle, MAD = 0.24
kcal/mol), and random forest models (right, MAD = 0.23 kcal/mol).
2.3. Case Study 3: Modeling with Limited Data. As
previously mentioned, an often-cited limitation of machine
learning methods in enantioselective catalysis is the large
number of data points necessary to produce accurate models.
Although this assertion is true if broad generality is the goal, we
posit that if the goal of the endeavor is the optimization of a more
limited system then accurate predictive models can be made using
significantly less experimental overhead. To illustrate this
simplified approach, the modeling of the enantioselective
formations of N,S-acetals was revisited using a limited number
of data points. As a preliminary exploration of data-limited
modeling in this system, only the first 12 catalysts (50%)
I
https://dx.doi.org/10.1021/jacs.0c04715
J. Am. Chem. Soc. XXXX, XXX, XXX−XXX

Journal of the American Chemical Society
pubs.acs.org/JACS
Article
selected from the in silico library of phosphoric acids with the
Kennard-Stone algorithm were used in the training set (Figure
9). Further, only reactions containing imines 1 and 2 and thiols
A−C (Figure 5) used in training and cross-validation. Thus, 12
catalysts with 6 substrate combinations gave 72 reactions for
model training and validation. Although not an insignificant
number of reactions, performing this number of reactions is
well within the capability of most synthetic organic chemistry
laboratories. The remaining 1003 reactions were used as an
external test set.
Three different model types were investigated: PLS, SVR,
and random forest (RF). PLS was selected because it is a
simple linear model with well precedented use in chemo-
informatics using molecular field-type descriptors with
relatively limited data sets. SVR and RF were selected because
they are popular machine learning methods capable of
modeling nonlinear relationships. For the PLS model, the
optimal number of latent variables was determined using 3-fold
cross-validation. Similarly, hyperparameter optimization for the
SVR and RF models were selected by a grid search of
hyperparameters, with the best performers identified by q2.
The complete protocol for model optimization and selection is
given in the Supporting Information.
When comparing the cross-validation results, the SVR model
is the highest performer (q2 = 0.803), followed by the PLS
model (q2 = 0.785) and finally the RF model (q2 = 0.693).
Using this metric, the more complex model is actually a higher
performer in this data-limited case study. When the perform-
ance of each model is compared by predicting the external test
set, a similar result is observed (Figure 10). In this analysis, the
Figure 11. Learning curve, depicting MADtest and q2(5-fold) plotted
against the number of training reactions.
performance. In practice, if one desired to run only 24
reactions, it is likely that a single substrate combination would
be used with the Universal Training Set (UTS). To illustrate
this, we have constructed a PLS model examining only one
reaction, the enantioselective addition of thiol B to imine 1.
The 24 UTS catalysts have been used to train the model and
the 19 test set catalyst have been used to evaluate the model.
This model is indeed very accurate (q2 = 0.70, MADTest
=
0.156 kcal/mol), and the most selective catalyst for this
reaction, which was not included in the training data, is indeed
predicted as the most selective catalyst (Figure 12).
RF most accurately predicts the external test set (MADtest
=
0.23 kcal/mol), followed by the SVR model (MADtest = 0.24
kcal/mol), and third the PLS model (MADtest = 0.25 kcal/
mol).61 Thus, even in data limited cases, more complicated
machine learning models can be as good or better than simpler
modeling techniques. This illustration indicates that researchers
should consider using more complex models even in data-limited
scenarios. It is noteworthy that this phenomenon is likely
dependent on the specific system and molecular representation
used in any study.
2.4. Case Study 4: Learning Curve Generation. To
further examine the amount of data necessary to create
accurate models, a learning curve was constructed. To be
consistent in analysis of the results, the 384 training +
validation/691 test reaction partitioning used in the original
study was used at the outset of this experiment. From the 384
possible training reactions, some number of reactions n were
randomly selected to use in model training and cross-
validation, and those models were further evaluated by the
MAD in the 691-member external test set. For each value of n,
five training sets were randomly selected. These training sets
were used in an ensemble of linear models, and the average
MAD of the test set for each value of n was used to evaluate
the ensemble. The results are depicted in Figure 11.
As the number of training reactions increases from 24 to
336, a notable increase in q2 occurs until 96 training reactions
is reached. From 144 to 336 training reactions, only
incremental improvements in q2 are observed. However, the
MADtest continues to improve with an increasing number of
training reactions, reaching 0.21 kcal/mol at 336 reactions. It is
worth noting that this model is relating both catalyst and
substrate features to enantioselectivity; thus, it is unsurprising
that extremely data limited sets (n = 24) have poor
Figure 12. Model for the enantioselective addition of thiol B to imine
1.
2.5. Case Study 5: Improved Predictive Performance
with Algorithmic Training Set Selection. In our first
publication of this computer-guided workflow,49 an algorithmi-
cally selected set of compounds from the in silico library was
identified, termed the UTS. The logic behind this subset
selection using the Kennard−Stone algorithm62 is as follows:
(1) the in silico library contains every catalyst candidate that is
of interest to be evaluated experimentally on the basis of its
synthetic accessibility, (2) the Kennard−Stone algorithm will
select boundary cases and sample uniformly over the chemical
space of interest, and (3) consequently, all future predictions
should be within the convex hull of the training data.
Consequently, future predictions will be interpolative; we
hypothesize this process will lead to greater confidence in future
predictions. Alternatively, many researchers might be interested
J
https://dx.doi.org/10.1021/jacs.0c04715
J. Am. Chem. Soc. XXXX, XXX, XXX−XXX

Journal of the American Chemical Society
pubs.acs.org/JACS
Article
in using readily accessible training sets such as sets of
commercially available compounds to use in our workflow
rather than synthesizing a training set for the particular catalyst
scaffold of interest. To examine the importance of using an
algorithmically selected set, two ensembles of linear models
were constructed (see the Supporting Information for
computational details). The first ensemble was trained and
validated using every reaction in our data set which contains
one of the first 12 catalysts selected using the Kennard−Stone
algorithm (Figure 9). The second ensemble was trained and
validated using every reaction in our data set which contains
one of the 12 commercially available compounds in the in
silico library (Figure 13).63 Thus, each set for model training
and cross-validation was comprised of 300 reactions (12
catalysts × 25 substrate combinations). Reactions which were
not included in either set were used as an external test set, and
the models generated from training on the truncated UTS and
the commercially available set were compared by the
performance in predicting the test set (Figure 14).
Figure 14. Predicted vs observed plots for models trained with data
from 12 UTS catalysts (top, MAD = 0.21 kcal/mol) and 12
commercial catalysts (bottom, MAD = 0.28 kcal/mol). Only the test
set is shown.
2.6. Case Study 6: Augmentation of Existing Data
Sets Informed by Unsupervised Learning. As demon-
strated in Case Study 5, models trained using data sets which
are comprised of readily accessible compounds underperform
with respect to algorithmically selected sets. However, in many
instances, experimentalists may have an existing data set which
was not systematically selected and therefore does not span the
breadth of chemical space. Rather than collect data for the entire
UTS to use this workflow, it would be desirable to augment the
existing data set such that the models generated with that data set
are of similar performance to models trained with the UTS. Here,
we introduce a tool to achieve this goal by using unsupervised
learning to identify underrepresented regions of catalyst space.
Once identified, these catalysts can be introduced to the
existing data set by selecting a resident of the unrepresented
regions. To illustrate this concept, the commercially available
catalyst set in Figure 13 has been augmented with additional
structures, informed by performing the K-means clustering
algorithm on the entire in silico library of 806 BINOL
phosphoric acid catalysts (which contains all of the
commercially available catalysts in Figure 14).65
Figure 13. Set of 12 commercially available phosphoric acid catalysts.
As depicted in Figure 14, the models trained using the truncated
UTS perform significantly better than those trained with
commercially available catalysts (MADTest = 0.21 and 0.28
kcal/mol, respectively). Further, it is worth considering that the
structural diversity in our in silico library of phosphoric acids is
relatively limited when compared with other privileged ligand
scaffolds in that only the 3,3′-positions of the catalyst structure
is varied.64 Owing to the limited structural variability afforded
by the BINOL-phosphoric acid library, the resulting chemical
space is quite limited. It follows that the overlap of chemical
space coverage between random and systematic subset
selection would be highest in this case as compared to more
diverse chemical libraries. Thus, in cases with more diversifiable
scaffolds and larger in silico libraries, one would expect that the
difference between the readily available set and the algorithmically
selected set will be larger, with less accurate models from the
readily available set when compared with the algorithmically
selected set.
Conceptually, the task of augmenting existing data sets was
divided into two parts: (1) dividing the space of interest into
K
https://dx.doi.org/10.1021/jacs.0c04715
J. Am. Chem. Soc. XXXX, XXX, XXX−XXX

Journal of the American Chemical Society
pubs.acs.org/JACS
Article
clusters and (2) selecting representatives from unoccupied
clusters. First, the optimal number of clusters, k, is identified
using the elbow method (see the Supporting Information for a
full description of the elbow method).66 In this method, some
cost function is plotted against the k (Figure 15). In this case,
the average distortion (the average distance between catalyst
and corresponding cluster centroid) was plotted against k. The
location of an elbow, the point at which the change in
distortion decreases sharply, is taken at the optimal number of
clusters. Loosely, this elbow corresponds to the point at which
subdividing the data into additional clusters is unnecessary. In
this case, because at least one catalyst must be present per
cluster, we equate this with diminishing returns per catalyst
synthesized.
Figure 15. Elbow plot suggesting that the appropriate number of
clusters is k = 6.
Figure 16. Predicted vs observed plot for models trained on the
Kennard Stone selected training set (top, MAD = 0.20 kcal/mol) and
the augmented commercial data set (bottom, MAD = 0.21 kcal/mol).
With an optimal number of k = 6 identified for the 806-
member in silico library, the clusters were inspected for
members of the commercially available training set. Five of the
six clusters contained members of the commercially available
training set, whereas one cluster did not contain any of the
commercially available catalysts. Thus, it was postulated that
adding a catalyst from this cluster would substantially increase
the overall performance of the model. Of the possible catalysts
in this cluster, catalyst 18 was selected because it is a
representative of this cluster for which experimental data was
already available.67 This 13-member set was then used to
create models using the ensemble of linear methods previously
employed, and the models were evaluated by examining the
predictive performance for the 450-member external test set
(identical to the above 475-member external test set minus the
25 reactions of catalyst 18 have been removed). Remarkably,
these new models have similar performance to the models with the
truncated UTS (MADTest = 0.21 kcal/mol for augmented set, 0.20
kcal/mol for Kennard Stone set), supporting the hypothesis that
using unsupervised learning to inform augmentation of existing
data sets can enable statistically guided optimization endeavors
(Figure 16). This protocol can be used to explore new regions
of chemical space and augment data sets for machine learning
guided optimization.
CONCLUSIONS
■
In summary, validation of every step of our recently disclosed
computational workflow, from the conformer-dependent
representation of catalyst structures to algorithmically guided
subset selection, has been provided. The conformer-dependent
catalyst representations outperform their single-conformer
analogues even in structurally inflexible systems, with the
difference between single-conformer descriptors and con-
former-dependent descriptors increasing as the catalyst system
becomes more flexible. The superiority of algorithmically
selected training sets compared to commercially available
training sets has been demonstrated. Finally, the ability to use
unsupervised learning to augment existing data sets to achieve
predictive performance similar to the algorithmically selected
data set has been illustrated. We anticipate that these tools will
help experimentalists engaged in challenging optimization
problems to leverage a statistically guided solution without
prohibitive experimental investment.
ASSOCIATED CONTENT
* Supporting Information
The Supporting Information is available free of charge at
https://pubs.acs.org/doi/10.1021/jacs.0c04715.
■
sı
L
https://dx.doi.org/10.1021/jacs.0c04715
J. Am. Chem. Soc. XXXX, XXX, XXX−XXX

Journal of the American Chemical Society
pubs.acs.org/JACS
Article
(5) Burello, E.; Rothenberg, G. In Silico Design in Homogeneous
Catalysis Using Descriptor Modelling. Int. J. Mol. Sci. 2006, 7, 375−
404.
General experimental summary of enantioselective
reactions computational methods (PDF)
(6) Reid, J. P.; Sigman, M. S. Comparing Quantitative Prediction
Methods for the Discovery of Small-Molecule Chiral Catalysts. Nat.
Rev. Chem. 2018, 2, 290−305.
AUTHOR INFORMATION
■
Corresponding Author
̈
(7) Cheong, P. H.-Y.; Legault, C. Y.; Um, J. M.; Çelebi-Olcu̧ m, N.;
̈
Scott E. Denmark − Roger Adams Laboratory, Department of
Chemistry, University of Illinois, Urbana, Illinois 61801, United
States; orcid.org/0000-0002-1099-9765;
Email: sdenmark@illinois.edu
Houk, K. N. Quantum Mechanical Investigations of Organocatalysis:
Mechanisms, Reactivities, and Selectivities. Chem. Rev. 2011, 111,
5042−5137.
(8) Lam, Y.-H.; Grayson, M. N.; Holland, M. C.; Simon, A.; Houk,
K. N. Theory and Modeling of Asymmetric Catalytic Reactions. Acc.
Chem. Res. 2016, 49, 750−762.
Authors
Jeremy J. Henle − Roger Adams Laboratory, Department of
Chemistry, University of Illinois, Urbana, Illinois 61801, United
States; orcid.org/0000-0001-9045-1726
Andrew F. Zahrt − Roger Adams Laboratory, Department of
Chemistry, University of Illinois, Urbana, Illinois 61801, United
States; orcid.org/0000-0002-1835-5163
Brennan T. Rose − Roger Adams Laboratory, Department of
Chemistry, University of Illinois, Urbana, Illinois 61801, United
States; orcid.org/0000-0002-7225-3600
William T. Darrow − Roger Adams Laboratory, Department of
Chemistry, University of Illinois, Urbana, Illinois 61801, United
States; orcid.org/0000-0002-4784-0133
(9) Peng, Q.; Paton, R. S. Catalytic Control in Cyclizations: From
Computational Mechanistic Understanding to Selectivity Prediction.
Acc. Chem. Res. 2016, 49, 1042−1051.
(10) Poree, C.; Schoenebeck, F. A. Holy Grail in Chemistry:
Computational Catalyst Design: Feasible or Fiction. Acc. Chem. Res.
2017, 50, 605−608.
(11) Peng, Q.; Duarte, F.; Paton, R. S. Computing Organic
Stereoselectivity - from Concepts to Quantitative Calculations and
Predictions. Chem. Soc. Rev. 2016, 45, 6093−6107.
(12) Wheeler, S. E.; Seguin, T. J.; Guan, Y.; Doney, A. C.
Noncovalent Interactions in Organocatalysis and the Prospect of
Computational Catalyst Design. Acc. Chem. Res. 2016, 49, 1061−
1069.
Yang Wang − Roger Adams Laboratory, Department of
Chemistry, University of Illinois, Urbana, Illinois 61801, United
States; orcid.org/0000-0002-7584-6188
(13) Tantillo, D. J. Faster, Catalyst! React! React! Exploiting
Computational Chemistry for Catalyst Development and Design. Acc.
Chem. Res. 2016, 49, 1079.
(14) Balcells, D.; Maseras, F. Computational Approaches to
Asymmetric Synthesis. New J. Chem. 2007, 31, 333−343.
(15) Houk, K. N.; Cheong, P. H-Y. Computational Prediction of
Small-Molecule Catalysts. Nature 2008, 455, 309−313.
(16) Fey, N.; Orpen, A. G.; Harvey, J. N. Building Ligand
Knowledge Bases for Organometallic Chemistry: Computational
Description of Phosphorus(III)-Donor Ligands and the Metal-
Phosphorus Bond. Coord. Chem. Rev. 2009, 253, 704−722.
(17) Corbeil, C. R.; Moitessier, N. Theory and Application of
Medium to High Throughput Prediction Method Techniques for
Asymmetric Catalyst Design. J. Mol. Catal. A: Chem. 2010, 324, 146−
155.
(18) Fey, N. The Contribution of Computational Studies to
Organometallic catalysis: Descriptors, Mechanisms and Models.
Dalton Trans. 2010, 39, 296−310.
(19) Maldonado, A. G.; Rothenberg, G. Predictive Modeling in
Homogeneous Catalysis: a Tutorial. Chem. Soc. Rev. 2010, 39, 1891−
1902.
Complete contact information is available at:
https://pubs.acs.org/10.1021/jacs.0c04715
Author Contributions
†J.J.H. and A.F.Z. contributed equally.
Notes
The authors declare no competing financial interest.
ACKNOWLEDGMENTS
■
We are grateful to the W. M. Keck Foundation and the
National Science Foundation for generous financial support
(NSF CHE1900617). A.F.Z. is grateful to the University of
Illinois for Graduate Fellowships. B.T.R. thanks the National
Science Foundation for Graduate Fellowships. Y.W. thanks
Janssen Research Development LLC, San Diego for a
́
postdoctoral fellowship. We thank Dr. Raquel Mendizabal
(20) Neel, A. J.; Hilton, M. J.; Sigman, M. S.; Toste, F. D. Exploiting
Non-Covalent π-Interactions for Catalyst Design. Nature 2017, 543,
637−646.
(21) Baskin, I. I.; Madzhidov, T. I.; Antipin, I. S.; Varnek, A.
Artificial Intelligence in Synthetic Chemistry: Achievements and
Prospects. Russ. Chem. Rev. 2017, 86, 1127−1156.
Martell for assistance with statistical analysis. We are also
grateful for the support services of the NMR, mass
spectrometry X-ray crystallographic, and microanalytical
laboratories of the University of Illinois at Urbana−
Champaign.
(22) Engkvist, O.; Norrby, P.-O.; Selmi, N.; Lam, Y.-H.; Peng, Z.;
Sherer, E. C.; Amberg, W.; Erhard, T.; Smyth, L. A. Computational
Prediction of Chemical Reactions: Current Status and Outlook. Drug
Discovery Today 2018, 23, 1203−1218.
REFERENCES
■
(1) (a) Comprehensive Asymmetric Catalysis; Jacobsen, E. N., Pfaltz,
A., Yamamoto, H., Eds.; Springer-Verlag: Heidelberg, 1999; Vols. I−
III. (b) Comprehensive Chirality; Carreira, E. M., Yamamoto, H., Eds.;
Elsevier: Amsterdam, 2012.
(2) Walsh, P. J.; Kozlowski, M. C. Fundamentals of Asymmetric
Catalysis; University Science Books: Sausalito, 2009.
(3) Lipkowitz, K.; Kozlowski, M. Understanding Stereoinduction in
Catalysis via Computer: New Tools for Asymmetric Synthesis. Synlett
2003, 10, 1547−1565.
(4) Ahn, S.; Hong, M.; Sundararajan, M.; Ess, D. H.; Baik, M.-H.
Design and Optimization of Catalysts Based on Mechanistic Insights
Derived from Quantum Chemical Reaction Modeling. Chem. Rev.
2019, 119, 6509−6560.
(23) Santiago, C. B.; Guo, J.-Y.; Sigman, M. S. Predictive and
Mechanistic Multivariate Linear Regression Models for Reaction
Development. Chem. Sci. 2018, 9, 2398−2412.
(24) Durand, D. J.; Fey, N. Computational Ligand Descriptors for
Catalyst Design. Chem. Rev. 2019, 119, 6561−6594.
(25) Eksterowicz, J. E.; Houk, K. N. Transition-State Modeling with
Empirical Force Fields. Chem. Rev. 1993, 93, 2439−2461.
(26) Friederich, P.; dos Passos Gomes, G.; De Bin, R.; Aspuru-
Guzik, A.; Balcells, D. Machine Learning Dihydrogen Activation in
the Chemical Space Surrounding Vaska’s Complex. Chem. Sci. 2020,
11, 4584−4601.
M
https://dx.doi.org/10.1021/jacs.0c04715
J. Am. Chem. Soc. XXXX, XXX, XXX−XXX

Journal of the American Chemical Society
pubs.acs.org/JACS
Article
(27) Hansen, E.; Rosales, A. R.; Tutkowiski, B.; Norrby, P.-O.;
Wiest, O. Prediction of Stereochemistry using Q2MM. Acc. Chem. Res.
2016, 49, 996−1005.
(46) van der Linden, J. B.; Ras, I.-J.; Hooijschuur, S. M.; Klaus, G.
M.; Luchters, N. T.; Dani, P.; Verspui, G.; Smith, A. A.; Damen, E. W.
P.; McKay, B.; Hoogenraad, M. Asymmetric Catalytic Ketone
Hydrogenation: Relating Substrate Structure and Product Enantio-
metic Excess Using QSPR. QSAR Comb. Sci. 2005, 24, 94−98.
(47) Sigman, M. S.; Harper, K. C.; Bess, E. N.; Milo, A. The
Development of Multidimensional Analysis Tools for Asymmetric
Catalysis and Beyond. Acc. Chem. Res. 2016, 49, 1292−1301.
(48) Denmark, S. E.; Gould, N. D.; Wolf, L. M. A Systematic
Investigation of Quaternary Ammonium Ions as Asymmetric Phase-
Transfer Catalysts. Synthesis of Catalyst Libraries and Evaluation of
Catalyst Activity. J. Org. Chem. 2011, 76, 4260−4336.
(49) Denmark, S. E.; Gould, N. D.; Wolf, L. M. A Systematic
Investigation of Quaternary Ammonium Ions as Asymmetric Phase-
Transfer Catalysts. Application of Quantitative Structure Activity/
Selectivity Relationships. J. Org. Chem. 2011, 76, 4337−4357.
(50) Zahrt, A. F.; Henle, J. J.; Rose, B. T.; Wang, Y.; Darrow, W. T.;
Denmark, S. E. Prediction of Higher-Selectivity Catalysts by
Computer-Driven Workflow and Machine Learning. Science 2019,
363, No. eaau5631.
(28) Rosales, A. R.; Quinn, T. R.; Wahlers, J.; Tomberg, A.; Zhang,
X.; Helquist, P.; Wiest, O.; Norrby, P.-O. Application of Q2MM to
Predictions in Stereoselective Synthesis. Chem. Commun. 2018, 54,
8294−8311.
́
(29) Rosales, A. R.; Wahlers, J.; Lime, E.; Meadows, R. E.; Leslie, K.
W.; Savin, R.; Bell, F.; Hansen, E.; Helquist, P.; Munday, R. H.; Wiest,
O.; Norrby, P.-O. Rapid Virtual Screening of Enantioselective
Catalysts Using CatVS. Nature Catalysis. 2019, 2, 41−45.
(30) Guan, Y.; Ingman, V. M.; Rooks, B. J.; Wheeler, S. E. AARON:
An Automated Reaction Optimizer for New Catalysts. J. Chem. Theory
Comput. 2018, 14, 5249−5261.
(31) Zahrt, A. F.; Athavale, S. V.; Denmark, S. E. Quantitative
Structure-Selectivity Relationships in Enantioselective Catalysis: Past,
Present, and Future. Chem. Rev. 2020, 120, 1620−1689.
(32) Oslob, J. D.; Åkermark, B.; Helquist, P.; Norrby, P.-O. Steric
Influences on the Selectivity in Palladium-Catalyzed Allylation.
Organometallics 1997, 16, 3015−3021.
(33) Kozlowski, M. C.; Dixon, S. L.; Panda, M.; Lauri, G. Quantum
Mechanical Models Correlating Structure with Selectivity: Predicting
the Enantioselectivity of β-Amino Alcohol Catalysts in Aldehyde
Alkylation. J. Am. Chem. Soc. 2003, 125, 6614−6615.
(34) Phuan, P.-W.; Ianni, J. C.; Kozlowski, M. C. Is the A-Ring of
Sparteine Essential for High Enantioselectivity in the Asymmetric
Lithiation-Substitution of N-Boc-pyrrolidine? J. Am. Chem. Soc. 2004,
126, 15473−15479.
(35) Ianni, J. C.; Annamalai, V.; Phuan, P.-W.; Panda, M.;
Kozlowski, M. C. A Priori Theoretical Prediction of Selectivity in
Asymmetric Catalysis: Design of Chiral Catalysts by Using Quantum
Molecular Interaction Fields. Angew. Chem. 2006, 118, 5628−5631.
(36) Huang, J.; Ianni, J. C.; Antoline, J. E.; Hsung, R. P.; Kozlowski,
M. C. De Novo Chiral Amino Alcohols in Catalyzing Asymmetric
Additions to Aryl Aldehydes. Org. Lett. 2006, 8, 1565−1568.
(37) Kozlowski, M. C.; Ianni, J. Quantum Molecular Interaction
Field Models of Substrate Enantioselection in Asymmetric Processes.
J. Mol. Catal. A: Chem. 2010, 324, 141−145.
(38) Lipkowitz, K.; Pradhan, M. Computational Studies of Chiral
Catalysts: A Comparative Molecular Field Analysis of an Asymmetric
Diels-Alder Reaction with Catalysts Containing Bisoxazoline or
Phosphinooxazoline Ligands. J. Org. Chem. 2003, 68, 4648−4656.
(39) Melville, J. L.; Andrews, B. I.; Lygo, B.; Hirst, J. D.
Computational Screening of Combinatorial Catalyst Libraries.
Chem. Commun. 2004, 0, 1410−1411.
(40) Melville, J. L.; Lovelock, K. R. J.; Wilson, C.; Allbutt, B.; Burke,
E. K.; Lygo, B.; Hirst, J. D. Exploring Phase-Transfer Catalysis with
Molecular Dynamics and 3D/4D Quantitative Structure-Selectivity
Relationships. J. Chem. Inf. Model. 2005, 45, 971−981.
(41) Aires-de-Sousa, J.; Gasteiger, J. New Description of Molecular
Chirality and Its Application to the Prediction of the Preferred
Enantiomer in Stereoselective Reactions. J. Chem. Inf. Comput. Sci.
2001, 41, 369−375.
(42) Aires-de-Sousa, J.; Gasteiger, J. Prediction of Enantiomeric
Selectivity in Chromatography: Application of Conformation-
Dependent and Conformation-Independed Descriptors of Molecular
Chirality. J. Mol. Graphics Modell. 2002, 20, 373−388.
(43) Aires-de-Sousa, J.; Gasteiger, J. Prediction of Enantiomeric
Excess in a Combinatorial Library of Catalytic Enantioselective
Reactions. J. Comb. Chem. 2005, 7, 298−301.
(51) Ingle, G. K.; Mormino, M. G.; Wojtas, L.; Antilla, J. C. Chiral
Phosphoric Acid-Catalyzed Addition of Thiols to N-Acyl Imines:
Access to Chiral N, S-Acetals. Org. Lett. 2011, 13, 4822−4825.
(52) Hopfinger, A. J.; Wang, S.; Tokarski, J. S.; Jin, B.; Albuquerque,
M.; Madhav, P. J.; Duraiswami, C. Construction of 3D-QSAR Models
Using the 4D-QSAR Analysis Formalism. J. Am. Chem. Soc. 1997, 119,
10509−10524.
(53) For other notable works investigating structural features of
BINOL-phosphoric acids responsible for stereoinduction, see:
(a) Reid, J. P.; Ermanis, K.; Goodman, J. M. BINOPtimal: a Web
Tool for Optimal Chiral Phosphoric Acid Catalyst Selection. Chem.
Commun. 2019, 55, 1778−1781. (b) Reid, J. P.; Sigman, M. S.
Holistic Prediction of Enantioselectivity in Asymmetric Catalysis.
Nature 2019, 571, 343−348.
(54) The code to calculate both representations is available on our
Gitlab page: https://gitlab.com/SEDenmarkLab/ccheminfolib/.
(55) Owing to the unreliable accuracy of the molecular mechanics
energies, Boltzmann weighting was not reliable. To accurately weight
the contribution of each conformer to the ASO, accurate energies
computed at a higher level of theory would be required for each
conformer. The computational resources required to perform accurate
energy calculations on all structures (∼80000) are inaccessible. Thus,
given the empirical accuracy of the models generated, no weighting is
performed.
(56) Wheeler, S. E.; Houk, K. N. Through-Space Effects of
Substituents Dominate Molecular Electrostatic Potentials of Sub-
stituted Arenes. J. Chem. Theory Comput. 2009, 5, 2301−2312.
(57) Kubinyi, H. Comparative Molecular Field Analysis (CoMFA).
In Handbook of Chemoinformatics; Gasteiger, J., Ed.; Wiley, 2008.
(58) More information regarding the relevant hyperparameter
optimization and preprocessing is available in the Supporting
Information.
(59) Pedregosa, F.; Varoquaux, G.; Gramfort, V.; Michel, B.;
Thirion, O.; Grisel, M.; Blondel, P.; Prettenhofer, R.; Weiss, V.;
Dubourg, V.; Vanderplas, J.; Passos, A.; Cournapeau, D.; Brucher, M.;
Perrot, M.; Duchesnay, E. Scikit-learn: Machine Learning in Python. J.
Mach. Learn. Res. 2011, 12, 2825−2830.
̈
(60) Sandfort, F.; Strieth-Kalthoff, F.; Kuhnemund, M.; Beecks, C.;
Glorius, F. A Structure-Based Platform for Predicting Chemical
Reactivity. Chem. 2020, 6, 1379−1390.
(44) Chen, J.; Jiwu, W.; Mingzong, L.; You, T. Calculation on
Enantiomeric Excess of a Catalytic Asymmetric Reactions of
Diethylzinc Addition to Aldehydes with Topological Indices and
Artificial Network. J. Mol. Catal. A: Chem. 2006, 258, 191−197.
(45) Hoogenraad, M.; Klaus, G. M.; Elders, N.; Hooijschuur, S. M.;
McKay, B.; Smith, A. A.; Damen, E. W. P. Oxazaborolidine Mediated
Asymmetric Ketone Reduction: Prediction of Enantiomeric Excess
Based on Catalyst Structure. Tetrahedron: Asymmetry 2004, 15, 519−
523.
(61) It is worth noting that the test sets, models, and preprocessing
used in these studies are different than in case study 1. Because of this,
comparisons between different case studies are convoluted and not
recommended.
(62) Kennard, R. W.; Stone, L. A. Computer Aided Design of
Experiments. Technometrics 1969, 11, 137−148.
(63) Each catalyst in this set is available from Strem.
(64) It is worth noting that other permutations of this catalyst
scaffold are feasible, but the Gen1-in silico library was a limited, proof-
N
https://dx.doi.org/10.1021/jacs.0c04715
J. Am. Chem. Soc. XXXX, XXX, XXX−XXX

Journal of the American Chemical Society
pubs.acs.org/JACS
Article
of-concept study. Efforts are underway to expand the chemical space
of this in silico library.
(65) For more information regarding the K-means clustering
algorithm and its specific implementation, we refer the reader to
Sci-kit Learn’s documentation: https://scikit-learn.org/stable/
modules/clustering.html#k-means.
(66) Thorndike, R. L. Who Belongs in the Family? Psychometrika
1953, 18, 267−276.
(67) Catalyst 18 was chosen because it was present in the cluster
with no commercially available representatives and experimental data
for that catalyst was already available. We hypothesize that any
catalyst from that cluster would improve the model, such that catalysts
on the border of the unrepresented cluster would result in a smaller
increase in model accuracy.
O
https://dx.doi.org/10.1021/jacs.0c04715
J. Am. Chem. Soc. XXXX, XXX, XXX−XXX