Quantitative Structure-Property Relationship Modelling for the Prediction of Singlet Oxygen Generation by Heavy-Atom-Free BODIPY Photosensitizers**

Article abstract of DOI:10.1002/chem.202100922

Heavy-atom-free sensitizers forming long-living triplet excited states via the spin-orbit charge transfer intersystem crossing (SOCT-ISC) process have recently attracted attention due to their potential to replace costly transition metal complexes in photonic applications. The efficiency of SOCT-ISC in BODIPY donor-acceptor dyads, so far the most thoroughly investigated class of such sensitizers, can be finely tuned by structural modification. However, predicting the triplet state yields and reactive oxygen species (ROS) generation quantum yields for such compounds in a particular solvent is still very challenging due to a lack of established quantitative structure-property relationship (QSPR) models. In this work, the available data on singlet oxygen generation quantum yields (Φ_Δ) for a dataset containing >70 heavy-atom-free BODIPY in three different solvents (toluene, acetonitrile, and tetrahydrofuran) were analyzed. In order to build reliable QSPR model, a series of new BODIPYs were synthesized that bear different electron donating aryl groups in the meso position, their optical and structural properties were studied along with the solvent dependence of singlet oxygen generation, which confirmed the formation of triplet states via the SOCT-ISC mechanism. For the combined dataset of BODIPY structures, a total of more than 5000 quantum-chemical descriptors was calculated including quantum-chemical descriptors using density functional theory (DFT), namely M06-2X functional. QSPR models predicting ΦΔ values were developed using multiple linear regression (MLR), which perform significantly better than other machine learning methods and show sufficient statistical parameters (R=0.88–0.91 and q²=0.62–0.69) for all three solvents. A small root mean squared error of 8.2 % was obtained for Φ_Δ values predicted using MLR model in toluene. As a result, we proved that QSPR and machine learning techniques can be useful for predicting ΦΔ values in different media and virtual screening of new heavy-atom-free BODIPYs with improved photosensitizing ability.

Full text of DOI:10.1002/chem.202100922

Accepted Article
Accepted Article
Title: Quantitative Structure–Property Relationship Modelling for the
Prediction of Singlet Oxygen Generation by Heavy-atom-free
BODIPY Photosensitizers
Authors: Andrey A. Buglak, Asterios Charisiadis, Aimee Sheehan,
Christopher J. Kingsbury, Mathias O. Senge, and Mikhail A.
Filatov
This manuscript has been accepted after peer review and appears as an
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of the final Version of Record (VoR). This work is currently citable by
using the Digital Object Identifier (DOI) given below. The VoR will be
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to this Accepted Article as a result of editing. Readers should obtain
the VoR from the journal website shown below when it is published
to ensure accuracy of information. The authors are responsible for the
content of this Accepted Article.
To be cited as: Chem. Eur. J. 10.1002/chem.202100922
Link to VoR: https://doi.org/10.1002/chem.202100922
01/2020

10.1002/chem.202100922
Chemistry - A European Journal
FULL PAPER
Quantitative Structure–Property Relationship Modelling for the
Prediction of Singlet Oxygen Generation by Heavy-atom-free
BODIPY Photosensitizers**
Andrey A. Buglak,[a] Asterios Charisiadis,[b] Aimee Sheehan,[c] Christopher J. Kingsbury,[b] Mathias O.
Senge*[d] and Mikhail A. Filatov*[c]
[a]
Dr. Andrey A. Buglak
Faculty of Physics, Saint-Petersburg State University, Universiteteskaya Emb. 7-9, 199034 St. Petersburg, Russia
Dr. Asterios Charisiadis, Dr. Christopher J. Kingsbury
[b]
Chair of Organic Chemistry, School of Chemistry, Trinity Biomedical Sciences Institute, Trinity College Dublin, The University of Dublin, 152-160 Pearse
Street, Dublin 2, Ireland
[c]
[d]
Aimee Sheehan, Dr. Mikhail A. Filatov
School of Chemical and Pharmaceutical Sciences, Technological University Dublin, City Campus, Kevin Street, Dublin 8, Ireland
E-mail: mikhail.filatov@tudublin.ie
Prof. Dr. Mathias O. Senge
Institute for Advanced Study (TUM-IAS), Technical University of Munich, Lichtenberg-Str. 2a, 85748 Garching, Germany
E-mail: sengem@tcd.ie; twitter: @mathiassenge
[**]
A previous version of this manuscript has been deposited on a preprint server (DOI: https://doi.org/10.26434/chemrxiv.14199335.v1)
Supporting information for this article is given via a link at the end of the document.
Abstract: Heavy-atom-free sensitizers forming long-living triplet
excited states via the spin-orbit charge transfer intersystem crossing
(SOCT-ISC) process have recently attracted attention due to their
potential to replace costly transition metal complexes in photonic
applications. The efficiency of SOCT-ISC in BODIPY donor-acceptor
dyads, so far the most thoroughly investigated class of such
sensitizers, can be finely tuned by structural modification. However,
predicting the triplet state yields and reactive oxygen species (ROS)
generation quantum yields for such compounds in a particular
Introduction
Photosensitizers (PSs) which efficiently form long-lived triplet
excited states are crucially important in such fields as
photoredox catalysis,[1] photodynamic therapy (PDT)[2] and
triplet-triplet annihilation upconversion.[3] Common approach for
enhancing the triplet state yield (T) in organic chromophores
relies on the introduction of heavy atoms, such as halogens (Br
or I) or transition metals (e.g., Ru, Pd or Pt) in the structure
(Figure 1A), which promote the intersystem crossing process via
spin-orbit coupling interactions.[4] However, introduction of heavy
atoms often requires tedious synthesis and thus leads to high
cost of such photosensitizers.[5] Moreover, the presence of
heavy atoms can also result in shortening the triplet state
lifetimes.[6] The replacement of costly transition metal complexes
in industrial-scale photocatalytic processes with organic PSs has
drawn considerable attention,[7] and has stimulated a search for
alternative methods to promote ISC, not relying on the heavy
atom effect, e.g., using a spin converter,[8] exciton coupling,[9]
doubly-substituted excited states,[10] twisting of the aromatic
systems[11] and radical-induced ISC have been very actively
studied in recent years.[12]
solvent is still very challenging due to
a lack of established
quantitative structure-property relationship (QSPR) models. Herein,
we analyzed the available data on singlet oxygen generation
quantum yields (ΦΔ) for a dataset containing > 70 heavy-atom-free
BODIPY in three different solvents (toluene, acetonitrile, and
tetrahydrofuran). In order to build reliable QSPR model, we
synthesized a series of new BODIPYs bearing different electron
donating aryl groups in the meso position, studied their optical and
structural properties along with the solvent dependence of singlet
oxygen generation, which confirmed the formation of triplet states via
the SOCT-ISC mechanism. For the combined dataset of BODIPY
structures, a total of more than 5000 quantum-chemical descriptors
was calculated including quantum-chemical descriptors using
Density Functional Theory (DFT), namely M06-2X functional. QSPR
models predicting ΦΔ values were developed using multiple linear
regression (MLR), which perform significantly better than other
machine learning methods and show sufficient statistical parameters
(R = 0.88 ̶ ̶ 0.69) for all three solvents. A small
0.91 and q2 = 0.62
root mean squared error of 8.2% was obtained for ΦΔ values
predicted using MLR model in toluene. As a result, we proved that
QSPR and machine learning techniques can be useful for predicting
ΦΔ values in different media and virtual screening of new heavy-
atom-free BODIPYs with improved photosensitizing ability.
Figure 1. (a) Examples of heavy-atom-containing dyes.  – singlet oxygen
quantum yield (solvent and excitation wavelength are given). (b) Jablonski
diagram illustrating the formation of triplet excited state via the SOCT-ISC
mechanism.
1
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The formation of triplet excited states in electron donor-acceptor
dyads via the process of spin-orbit charge transfer intersystem
crossing (SOCT-ISC) does not require introduction of transition
metals or other heavy atoms into the molecule. So far, it has
been observed in donor-acceptor dyads based on BODIPYs[13]
and other difluoroboron complexes,[14] metal dipyrrins,[15]
phenoxazines,[16] biphenyls,[17] naphthalene and perylene
imides.[18] In these molecules, photoinduced electron transfer
between the donor (D) and acceptor (A) subunits leads to
the rates of charge recombination into the ground state and into
the lowest triplet excited state (kCRS and kCRT, respectively).
Orthogonal geometry between the electron donor and the
acceptor, which is beneficial for efficient SOCT-ISC, can be
secured by introduction of substituents in positions 1 and 7 of
the BODIPY core. On the other hand, the rates of charge
transfer and recombination steps can be modulated by varying
the number of alkyl substituents, which affect the reduction
potentials of the BODIPY core.[37] Since the energy of the CT
state, and consequently GCT and GCR values, is strongly
affected by polarity of the media, triplet state formation and
generation of singlet oxygen by SOCT-ISC sensitizers is
solvent-dependent. Generally, most of BODIPY dyads studied
so far showed higher T and Δ values in polar solvents, where
the CT state is stabilized, and the charge transfer process is
energetically favorable. However, strong stabilization of the CT
state in polar media leads to a reduced CT-S0 energy gap that
causes enhancement of the ground state recombination rate.
For this reason, many dyads show reduced T and Δ values in
highly polar solvents, such as acetonitrile or water.[38] In
particular, for dyads bearing electron accepting groups in the
BODIPY core, which stabilize the CT states, photosensitization
process is more efficient in non-polar solvents (hexane,
toluene).[39] BODIPY dimers showed highest Δ values in
solvents of intermediate polarity (chloroform, THF).[40] Overall,
predicting T and Δ in a specific solvent is difficult and relies on
test-and-trial approach. This largely limits the potential of SOCT-
ISC sensitizers, for instance in advanced PDT utilizing controlled
generation of cytotoxic singlet oxygen in target cells.[41]
formation of
a charge-transfer state (CT), which further
undergoes a non-radiative charge recombination into the ground
state (CRs) or into the lowest triplet excited state (CRT) via
SOCT-ISC (Figure 1B).[19] The latter process is commonly
observed for dyads with orthogonal mutual arrangement of
donor and acceptor subunits, which induces a large variation of
the orbital magnetic momentum during the recombination
process and thus compensates the change of spin magnetic
momentum.[20] High yields of triplet state formation are observed
for molecules in which the CT state lies close in energy to the
lowest singlet excited state (S1). In this case, the CRs process
falls within the Marcus inverted region[21] and is relatively slow
due to a large negative value of the free energy change (GCRS).
Under such circumstances, the CRT process is considerably
faster due to a smaller energy gap between the CT state and the
lowest triplet excited state (T1).[22]
Many reported molecular systems undergoing SOCT-ISC
exhibit triplet state yields and singlet oxygen generation
quantum yields () values that are comparable or even higher
than those of transition metal complexes and halogenated dyes.
Such dyes have other important advantages, e.g., synthetic
accessibility, high phototoxicity in cells (nM-M range) with
negligible dark toxicity,[23] long triplet excited state lifetimes
(hundreds of s),[24] and intense absorption in the 400-600 nm
region (extinction coefficients up to 105).[25]
Computational methods for predicting the SOCT-ISC efficiency
in media of a given polarity could be valuable for pre-synthetic
screening of potential sensitizer structures. However, accurate
computations of charge transfer excited states and triplets
formation by charge recombination using first-principle
techniques are rather challenging and time-demanding.[42] In
recent years, quantitative structure-activity relationship (QSAR)
and quantitative structure-property relationship (QSPR)
modelling have emerged as a useful tool for the design of
fluorophores and photoactive materials.[43] QSAR/QSPR
analysis has been applied in the studies of photophysics[44] and
photodynamic activity of BODIPYs,[45] proving that “big data”
approach can provide a powerful platform for the design of new
photosensitizers. Yet, QSAR modelling for predicting 1O2
generation quantum yields is rare.[46] However, earlier we
showed that QSPR may be used for the analysis of 1O2
production by pterins and flavins,[47] psoralens and angelicins,[48]
BODIPY dyes have been actively employed in the design of
SOCT-ISC photosensitizers due to their excellent photophysical
properties, ease of derivatization and predictable structural
parameters (1464 crystal structures reported in the CCDC CSD
in 2020).[26] In particular, a series of BODIPY dyads containing
different electron donors, such as anthracene,[27] pyrene,[28]
]
perylene,[29 phenothiazine,[30] carbazole,[31] and phenoxazine[32]
has been systematically investigated. Recently, we reported
biocompatible derivatives of such dyads, bearing polar
solubilizing groups for enhancing cell penetration and studied
their toxicity as well as fluorogenic response to singlet oxygen in
cancer cells.[33] A library of BODIPYs having high  values (up
to 70%) has been screened by us as candidates for PDT with
potential clinical relevance.[34] Concurrently, we explored
application of these sensitizers in the process of triplet-triplet
annihilation upconversion (TTA-UC) and showed their
unprecedented dual performance, namely the ability to play a
role of either a sensitizer or an emitter component, depending on
the media polarity.[35] We also found another unique feature of
BODIPY dyads – a relatively strong fluorescence from the CT
state and, using this property, developed a method for precise
determination of TTA-UC quantum efficiency.[36]
]
porphyrins and metalloporphyrins.[49 In this regard, applying
QSPR for the prediction of Δ values for heavy-atom-free
BODIPYs in solvents of different polarity offers a means to
estimate SOCT-ISC efficiency in these systems. Hence, we
started to search BODIPY structures which undergo SOCT-ISC
to correlate molecular features to singlet oxygen quantum yields
with the aid of machine learning methods. To develop a reliable
model we analyzed a dataset which includes several classes of
compounds (Figure 2): 1) parent BODIPY compounds with
different substitution patterns; 2) BODIPY dyads with different
nature, position, or number of donor/acceptor subunits; 3)
symmetrical and asymmetrical BODIPY dimers; 4) a validation
set comprised of a newly synthesized library of BODIPYs with
various meso-methoxyphenyl groups as electron donors.
Previously reported and experimentally obtained data on Δ for
As has been shown in previous works, the key factors which
affect the efficiency of SOCT-ISC in BODIPY dyads are: 1)
mutual orientation of the donor and acceptor subunits; 2) values
of the driving force for the charge separation and recombination
processes (GCT and GCR, respectively); 3) the ratio between
2
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these molecules in solvents of different polarity – toluene (non-
polar), tetrahydrofuran (moderately polar) and acetonitrile
(strongly polar) were used for analysis. We performed QSPR
analysis and optimized models for each solvent to ensure
sufficient statistical parameters for photosensitizing ability
prediction. To our knowledge, this is the first report of a QSPR
model for predicting the activity of polarity-sensitive
photosensitizers. The simplicity and versatility of this approach
allows for virtual screening of structures with singlet oxygen
quantum yields optimized for a desired range of polarities.
SOCT-ISC photosensitizers can be activated by recognition of
the appropriate environment, e.g., cell membranes[50] and certain
proteins.[51] We believe that the results obtained in this work will
unlock a more target-oriented exploration of this class of
photosensitizers in biomedical applications relying on
controlled ROS generation.
a
4-64
BODIPY dimers and donor-acceptor dyads
Reference BODIPYs 1-3
A
D
D/A
EDG
Ar
Ar
R3
R3
R3
R3
R2
R2
EDG
N
N
F
(CO2H)n
B
D
D
D
R2
R2
R2
F
N
N
N
N
N
N
1
B
B
B
EDG
R1
R1
N
R
R1
R1
R1
R1
F
F
F
F
F
F
N
R1-3 = H, Me, Et, styryl
N
N
F
N
N
B
Ar
B
F
R3
R3
2
D/A
R1
R2
R2
R2
R1
F
R1
R2
R1
R1
Ph
R2
N
N
N
B
N
X
CO2H
F
F
N
F
N
N
F
F
F
R1
R3
B
N
B
R1
D
B
F
F
F
N
N
N
N
R3
N
R
N
N
B
R2
R1
B
R2
R1
R2
R2
R1
R1
F
F
R1
F
NO2
F
R2
Ar
X = O, S R = Alk, Ar
EDG = OMe, NR2
3
Validation set: methoxyphenyl BODIPYs
OMe
MeO
OMe
OMe
(OMe)n
D
A
OMe
MeO
OMe
OMe
MeO
OMe
OMe
MeO
OMe
N
N
F
B
BDP-1
BDP-7
BDP-2
BDP-3
BDP-4
BDP-5
BDP-6
F
Figure 2. General structures of BODIPY dimers, donor-acceptor (D-A) dyads and reference compounds investigated in this work.
polar and non-polar solvents. Such dyads are potentially
interesting for application in PDT as alternative to cyclic
tetrapyrroles (porphyrins, chlorins, and bacteriochlorins), which
often require tedious synthesis. Moreover, these common PDT
agents are rather large molecules which must be injected and as
Results and Discussion
Compound dataset
a
result retain in the bloodstream for long, leading to
photodermatosis among other side-effects.[55] Thus there is a
growing interest to non-porphyrin sensitizers, based on small
photoactive molecules with higher absorption and excretion
rates. With this in mind, we prepared compounds BDP 1-7
(Figure 2) bearing different methoxyphenyl groups in the meso-
position of the BODIPY core.
The general dataset used here to build QSPR models includes
compounds reported in experimental studies on triplets’
formation in heavy-atom-free BODIPYs via SOCT-ISC. We
examined all related works published before September 2020
and combined experimental values of Δ measured in various
solvents using chemical trapping method and phosphorescence
of singlet oxygen (Table S1).[52] Several reference compounds
(structures 1-3, Figure 2) were included into the dataset to
guarantee the reliability of models in cases when Δ values are
very low. Other compounds in the dataset (4-64) include donor-
acceptor dyads and dimers, with various substitution patterns of
the BODIPY core and nature of electron donating or electron
accepting subunits. Values of ΦΔ measured in toluene (r = 2.4),
tetrahydrofuran (r = 7.6), acetonitrile (r = 37.5) were used for
analysis since these solvents have been employed to study
charge transfer and 1O2 generation for the highest number of
compounds in the dataset.
These seven BODIPY compounds (BDP 1-7) were synthesized
in the stepwise manner as shown in Scheme S1. In the first step,
a standard dipyrromethane synthesis was performed of each
aldehyde and pyrrole in the presence of trifluoroacetic acid.[56]
Dipyrromethanes (DPM 1-7) were prepared and purified by
following earlier reports.[57] The second step involved the well-
known one-pot two-step oxidation-deprotonation-complexation
reaction for the synthesis of the desired BODIPY compounds.[58]
More specifically, DPM 1-7 derivatives were oxidized to
dipyrromethenes using DDQ, which were subsequently treated
.
with triethylamine (TEA) and BF3 OEt2. All BODIPY products
were isolated by silica gel column chromatography and final
To ensure the reliability of the QSPR models developed in this
work for the development of practical sensitizers, several new
BODIPYs derivatives were also synthesized and investigated by
us. BODIPY dyads bearing electron-donating aryl groups such
as aminophenyl[53] or methoxyphenyl[54] groups were previously
shown to undergo charge transfer and generate 1O2 both in
purification was performed through recrystallization in
a
MeOH/H2O mixture in good to high yields. Mono-methoxy
substituted BODIPY derivatives (BDP-1, BDP-2 and BDP-3)
were prepared as reference compounds following previously
published procedures.[59]
3
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All BODIPY compounds (BDP 1-7) were fully characterized
through 1H, 13C, 19F, 11B NMR spectroscopy and HRMS (see
Supporting Information). The spectroscopic data of the three
reference derivatives (BDP 1-3) were identical with those
reported previously.[60] The successful formation of the final
BODIPY products was confirmed by the appearance of the
corresponding molecular ion peaks in their HRMS spectra. All 1H
and 13C NMR spectroscopic data are in agreement with the
proposed structures of the four newly reported compounds (BDP
X-ray crystallography. Compounds BDP-4, BDP-5 and BDP-7
were crystallized from dichloromethane at 4 °C, while BDP-6
was crystallized from acetonitrile by slow evaporation; details of
crystallographic refinement for these representative species are
provided in the Supporting Information (Table S2). The crystal
structures for BDP 1-3 have been previously reported.[58]
Two crystallographically inequivalent molecules of BDP-4
(Figure 3a), co-crystallize with a dichloromethane solvate; nearly
perpendicular aryl components (81.54(5)° and 82.129(5)° for the
4-7). Regarding the 19F NMR spectra of these four final products, two inequivalent molecules) are as expected for the steric bulk
the typical doublet of doublets signal[61] was observed for both
BDP-4 and BDP-7 at approximately -145 ppm (Figures S3 and
S18). On the other hand, the remaining two BODIPY
compounds (BDP-5 and BDP-6) presented two multiplets at ~-
144 and -146 ppm (Figures S8 and S13), which can be
attributed to the single ortho-methoxy substituent forming an
inequivalent environment for the F-atoms.[58,62] Finally, all
compounds showed a typical triplet peak (~0.3 ppm) in their 11B
NMR spectra, as expected.[60]
of the bis(o-methoxy) units. This dihedral angle has been shown
to be critically important for efficient SOCT-ISC process.[28] In
BDP-5 (Figure 3b), the aryl ring is inclined at 50.163(13)° to the
plane of the BODIPY core. Molecules were found to adopt a
dimeric arrangement in the solid state, mediated by weak aryl C-
H⋯F of 3.292 Å (C20-F13) shown in Figure 4; the formation of
dimers can modulate fluorescence behaviour.[38] The related
compound BDP-6 (Figure 3c) shows an aryl-BODIPY angle of
66.14(6)°; although crystallizing in the chiral space-group
P212121, this compound exhibits no permanent chirality due to
equivalency of the two rotamers. Close contact C-H⋯O
interactions (3.28 Å C⋯O) form one-dimensional chains, shown
in Figure S56. The aryl group in compound BDP-7 (Figure 3d) is
rotated 72.04(3)° to the BODIPY component. Molecules of BDP-
7 exhibit close π-π stacks of pyrrole moieties, with a plane
separation of 3.23 Å; directional C-H⋯F interactions are
observed, at 3.316 Å C3⋯F14. Unit cell packing diagrams are
shown in Figures S52-S55.
Increasing the number of methoxy substituents leads to reduced
oxidation potentials[63] of the aryl subunit in these dyads and, as
a consequence, promotes intramolecular charge transfer. The
absorption and fluorescence emission parameters of the
prepared dyads in different solvents are given in Table 1.
Changing the solvent polarity significantly impacts the emission
properties. For instance, dyad BDP-7 in toluene exhibits
fluorescence emission with quantum yield of 0.661, associated
with S0→S1 transition. On the other hand, in polar acetonitrile,
the fluorescence is strongly quenched leading to quantum yield
of < 0.001. This behavior is observed for other dyads and is the
signature of intramolecular charge transfer.
Figure 3. The individual molecular units of compound (a) BDP-4ꞏ½DCM
(solvate omitted), (b) BDP-5, (c) BDP-6 and (d) BDP-7; thermal ellipsoids are
shown at the 50% probability level, H-atoms are represented as spheres of
fixed radius.
Table 1. Spectroscopic data and singlet oxygen quantum yield for compounds
BDP 1-7.
[b]
[c]
Compound
Solvent
abs (nm)

em (nm) [a]
em

BDP-1
toluene
THF
ACN
toluene
THF
ACN
toluene
THF
ACN
toluene
THF
ACN
toluene
THF
ACN
toluene
THF
ACN
toluene
THF
ACN
506
503
500
504
501
497
501
498
494
507
504
500
506
502
499
507
503
499
507
504
500
523
519
516
522
518
515
518
513
512
524
521
516
525
513
505
521
517
505
522
519
518
0.381
0.238
0.104
0.057
0.029
0.014
0.093
0.044
0.017
0.988
0.904
0.062
0.028
0.001
0.001
0.002
0.0006
0.0013
0.661
0.316
0.0003
0.009
0.011
0.041
0.005
0.009
0.004
0.005
0.021
0.007
0.022
0.036
0.059
0.251
0.061
0.003
0.158
0.011
0.004
0.110
0.363
0.193
BDP-2
BDP-3
BDP-4
BDP-5
BDP-6
BDP-7
Figure 4. The dimeric C-H⋯F of 3.292 Å (C20-F13) interaction observed
within the crystal structure of BDP-5; the symmetry-equivalent red and blue
molecules are related by an inversion center. Thermal ellipsoids are shown at
the 50% probability level, H-atoms not involved in this interaction have been
omitted.
Furthermore, the structures of all four newly synthesized donor-
acceptor dyads (BDP 4-7) were analyzed through single crystal
4
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The QSPR approach employed here is based on the assumption
that the efficiency of triplet state formation and singlet oxygen
generation by the photosensitizer molecule depends on its
structure and attempts to formulate mathematical relationship
between calculated features of the structure (known as
molecular descriptors) and its singlet oxygen quantum yield
value.
[a] The fluorescence was excited at the vibrational shoulder of the BODIPY
absorption. Excitation wavelengths: 470
Fluorescence quantum yields were measured using Rhodamine 6G (Φem
0.95 in ethanol). [c] Quantum yields were measured using 1,9-
dimethylanthracene as
1O2 trap and 2,6-diiodo-8-phenylBODIPY as
reference photosensitizer (Φ= 0.85 in toluene).
- 490 nm for BDP 1-7. [b]
=
a
a
Singlet oxygen sensitization by BDP 1-7 was evaluated using
chemical trapping method with 1,9-dimethylanthracene (DMA) in
toluene, THF and acetonitrile to ensure the consistency of the
resulting dataset. Upon irradiation of air-saturated solutions
containing each BODIPY compound at 514 nm, DMA selectively
reacts with singlet oxygen forming corresponding endoperoxide.
The BODIPY absorption shows no change during irradiation,
while the DMA absorption decreases. The change of DMA
absorbance with time is linear (Figure 5, inset), allowing to
obtain ΦΔ value from comparison with reference sensitizers (2,6-
diiodo-8-phenylBODIPY). As shown in Table 1, the resulting ΦΔ
values vary depending on the solvent and the structure of
electron-donating aryl group. The most efficient 1O2 sensitization
was observed for BDP-7 in THF (Δ = 0.363) that correlates with
efficient charge transfer process in this solvent. This correlates
with efficient charge transfer process in this solvent. Dyads
BDP-5 and BDP-6 showed Δ values of 0.25 and 0.16,
respectively, in toluene and low 1O2 sensitization ability in the
remaining two solvents. Dyads BDP 1-4 showed very modest ΦΔ
values in all solvents.
The contribution of each descriptor to the model was estimated
using equation (1):
ꢁ
ꢄ
ꢆ ꢂꢃ
ꢁ
ꢄ
ꢅ
ꢀ ꢂꢃ
ꢉ 100
ꢁ1ꢄ
ꢁ
ꢄ
ꢁ
ꢄ
ꢆ ꢂꢃ ꢇ ⋯ ꢇ ꢆ ꢂꢈ
where α(x1) is the relative contribution of the descriptor x1 to the
ꢁ
ꢄ
model with several descriptors, ꢆ ꢂꢈ is the correlation
coefficient of the nth descriptor towards Log Δ.
Three different machine learning methods were used for models
search: support vector regression (SVR), multiple linear
regression (MLR), and random forest regression (RFR). QSPR
models were selected on the basis of statistical parameters,
such as R2 (determination coefficient of the training set) and
Rꢍꢊꢋꢌꢊ (predictive R2 for the test set of compounds). Predicting
ability of the obtained models was evaluated for a test set of
compounds, Rꢍꢊꢋꢌꢊ parameter was used for model validation and
comparison. A QSPR model is considered to be predictive if the
following conditions are met: R2 > 0.6, q2 > 0.6, and Rꢍꢊꢋꢌꢊ
>
0.5.[64] Among the different machine learning methods applied,
only MLR models showed satisfactory statistical parameters and
thus was used in further analysis. Statistical parameters for
toluene, acetonitrile, and tetrahydrofuran (THF) models are
summarized in Table 2 and a detailed description of the
statistical parameter calculation is given in the Experimental
Section.
Table 2. Statistical parameters for multiple linear regression (MLR) models
predicting the quantum yield of singlet oxygen generation by BODIPYs in
toluene, acetonitrile, and tetrahydrofuran (THF).
Parameter
Toluene
Acetonitrile
THF
R
0.882
0.778
0.739
0.890
0.792
0.744
0.906
0.820
0.773
R2
Figure 5. Photosensitized oxidation of 1,9-dimethylanthracene in the presence
of BDP-7 in air saturated acetonitrile solution irradiated with 514 nm laser (12
mW cm-2). Inset: change of absorbance at 376 nm with time.
Rꢍꢎꢏꢐꢑꢌꢊꢋꢏ
SEE
0.282
0.240
0.686
0.306
0.800
0.635
8.2
0.319
0.283
0.693
0.344
0.823
0.722
18.3
0.325
0.285
0.620
0.414
0.879
0.584
12.0
RMSE
q2
SDEP
Rꢍꢊꢋꢌꢊ
The resulting general dataset combining previously studied
compounds and dyads BDP 1-7 was divided into the training set
(80% of the compounds) and the test set (20%) using random
number generation. The activity of compounds, expressed as
Log ΦΔ, was used as a dependent variable during QSPR. Four
newly synthesized compounds were put into the so-called
external set. The toluene dataset was divided into the training
set (35 compounds), the test set (9 compounds), and the
external set (4 compounds). The acetonitrile dataset consisted
of 33 compounds in the training set, 8 compounds in the test set,
and 4 compounds in the external set. The tetrahydrofuran
dataset was divided into the training set (30 compounds), the
test set (7 compounds), and the external set (4 compounds).
Rꢍꢋꢒꢊꢋꢓꢔꢎꢕ
RMS
error
(ΦΔ in %)
ΦΔ
[a] R2, Rꢍꢎꢏꢐꢑꢌꢊꢋꢏ, SEE, and RMSE relate to the training set. SDEP and q2 relate
to leave-one-out cross validation of the training set. Rꢍꢊꢋꢌꢊ relates to the test set
whereas Rꢍꢋꢒꢊꢋꢓꢔꢎꢕ describes the external set of compounds. Root-mean-
square (RMS) ΦΔ error relates to the whole dataset, which combines the
training set, the test set and the external set.
Comparison of the root-mean-square (RMS) error for Models 1-3
and those previously reported for other types of phosensitizers
demonstrates good predictive ability of models developed in this
work. For instance,
models reported for pteridines,
furicoumarins and porphyrins showed RMS Δ errors of 5.7-
24.8%.[47-49] It should be noted that in these studies the values of
singlet oxygen quantum yields were measured in identical
Molecular descriptors and model search
5
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10.1002/chem.202100922
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conditions for all compounds in the dataset. In the current study
we used larger datasets (>40 BODIPYs for each model) with Δ
values measured using different 1O2 traps and reference
photosensitizers. As one can see, the resulting RMS error
shows comparable values: 8.2-18.3%. Therefore, we conclude
that possible inconsistencies in ΦΔ values which might be due to
the difference in experimental conditions did not significantly
influence predictive ability of the developed models.
Model 1 (toluene)
The model for predicting activity of photosensitizers in toluene
was developed using data for the highest number of compounds
– 48 BODIPYs from the general dataset. The MLR equation for
the model includes seven descriptors:
The resulting MLR equations have the following form:
Log ΦΔ = 1.5424(+/-0.2559) - 1.4403(+/-0.3471) DLS_04 -
0.4718(+/-0.1024) Mor24m + 0.536(+/-0.0995) ATSC6e -
0.1479(+/-0.0529) F09[N-N] - 4.1433(+/-0.9008) R6s+ +
0.8055(+/-0.1948) S1_fosc + 0.012(+/-0.0031) TPSA(Tot)
(Model 1)
y = c+a1*x1+ … +an*xn
(2)
where y is the dependent variable Log Δ, c is a regression
constant, a1 and an are regression coefficients, x1 and xn are
independent variables. The equation obtained for toluene model
includes seven descriptors, whereas in the case of acetonitrile
and THF the MLR models include six descriptors.
Among the seven descriptors involved in Model 1, the two most
influential are R6s+ (relative contribution α is equal to -29.9%
and ATSC6e (α = 25.8%). R6s+ is a GETAWAY (GEometry,
Topology, and Atom-Weights AssemblY) descriptor, an
R
maximum autocorrelation of lag 6 (a path length, or topological
distance between atoms) weighted by intrinsic state (I-state).[65]
The I-state of the i-th atom is calculated by the formula:
ꢜ
ꢚ
ꢁ ⁄
ꢄ
ꢍ ꢘ ꢛ ꢝꢃ
ꢙ
ꢙ
ꢖꢗ ꢅ
(3)
ꢛ
ꢙ
where ꢞꢗ is the principal quantum number (2 for C, N, O, F, 3 for
S), ꢟꢗꢠ is the number of valence electrons, and ꢟꢗ is the number
of sigma electrons of the i-th atom.
The I-state of an atom can be considered as the ratio of n and
lone pair electrons to the count of the σ bonds. Thus, the I-state
evaluates the possible partitioning of non-sigma electrons
influence along the paths starting from the regarded atom; with
less partitioning of the electron influence, the more available are
the valence electrons for intermolecular interactions.[66] I-state is
higher for electron withdrawing groups: for example, for –CH2–,
–NH–, and –O– groups I-state is equal to 1.5 and 2.5, and 3.5,
respectively. Hence, the descriptor captures the through-bond
effects of the rest of the molecule on the electron density of
atoms that can be involved in the charge transfer process.
ATSC6e descriptor is defined as the centered Broto-Moreau
autocorrelation
–
lag
6
/
weighted by the Sanderson
electronegativities.[67] In general, the presence of electron
withdrawing groups, such as F, Cl, and -COOH decrease
ATSC6e values, whereas electron-donating alkyl and alkoxy
groups increase the value of ATSC6e. In the obtained model,
the descriptor is inversely correlated with Log ФΔ. Symmetrical
BODIPY dimer 57 has the highest value of ATSC6e equal to
2.15, whereas BODIPY-perylene dyad 32 possesses the lowest
value equal to 0.112.
TPSA(Tot) (α = 13.3%) is a total topological polar surface area,
corresponding to the polar surface area derived from polar
contributions of N, O and S atoms and is related to the hydrogen
bonding ability of the compound.[68] TPSA(Tot) is directly
proportional to Log ΦΔ of studied BODIPYs. Polar substituents
increase the value of this descriptor whereas non-polar
substituents decrease the value of TPSA(Tot). Compound 53,
containing two phenothiazine groups, has the highest value of
the descriptor equal to 75.4 whereas for BODIPY-anthracene
dyad 30 TPSA(Tot) is equal to 6.48.
Figure 6. Experimental vs predicted Log ФΔ values for BODIPYs in toluene (a),
acetonitrile (b), and THF (c). Three sample molecules from the general dataset
are highlighted for each model.
6
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Table 3. Values of the descriptors used in Model 1 (toluene).
Compound
2
3
21
DLS_04
0.8
0.8
0.8
0.4
0.6
0.6
0.4
0.4
0.6
0.5
0.4
0.5
0.6
0.6
0.8
0.5
0.7
0.4
0.5
0.5
0.7
0.6
0.8
0.7
0.6
0.8
0.4
0.4
0.4
0.4
0.4
0.6
0.6
0.7
0.6
0.6
0.8
0.7
0.7
0.7
0.7
0.6
0.6
0.6
0.6
0.6
0.6
0.6
Mor24m
0.362
0.466
0.429
0.424
0.507
0.678
0.737
0.568
-0.00895
-0.12
0.171
0.158
-0.761
0.0461
-0.581
0.531
-0.6
ATSC6e
0.509
0.489
0.493
0.48
F09[N-N]
R6s+
0.254
0.187
0.131
0.184
0.142
S1_fosc
0.5982
0.5741
0.3868
0.0147
0.1667
0.3985
0.3966
0.8794
0.0265
0.3872
0.3404
0.7044
0.1024
0.0313
0.2843
0.117
0.4448
0.0787
0.0095
0.4147
0.6649
0.0835
0.0011
0.0843
0.2915
0.4534
0.701
0.8677
0.2483
0.2885
0.0589
0.9164
0.8045
0.3811
0.3454
0.4058
0.4318
0.698
0.1135
0.0819
0.0011
0.3557
0.276
TPSA(Tot)
8.81
8.81
8.81
46.1
46.1
8.81
8.81
8.81
6.48
8.81
8.81
8.81
35
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
1
2
2
2
2
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
25
26test [a]
27
0.788
0.486
0.505
0.552
0.909
0.505
0.112
0.516
0.827
0.566
0.661
0.297
0.995
0.828
0.807
0.56
0.0646
0.057
0.0996
0.0869
0.101
0.0967
0.0729
0.065
0.0532
0.0635
0.186
0.0625
0.0702
0.0695
0.103
0.132
0.109
28
29 test [a]
30
31
32
33
34
35
42
19
26.9
19
36 test [a]
37
38
39
40
41
0.633
0.665
0.482
0.473
0.707
0.546
1.06
26.9
74.5
26.9
26.9
18.7
18.7
27.5
13.7
13.7
13.7
13.7
18.7
15.3
75.2
18.7
36.7
17.6
17.6
17.6
17.6
17.6
63.4
43.6
17.6
18
42
0.709
0.251
0.597
1.15
43 test [a]
44
0.0815
0.0756
0.0881
0.0653
0.112
46
47
48
49
50
51
0.89
0.118
0.518
0.597
0.608
0.752
0.782
0.752
0.644
0.847
2.15
2.14
2.14
2.03
1.47
1.64
1.27
1.08
0.878
0.868
0.734
0.784
0.35
0.267
1.56
1.69
0.739
0.728
0.768
0.91
0.976
0.972
0.89
0.709
0.346
0.576
0.55
0.609
0.362
0.483
0.665
0.122
0.0695
0.0641
0.0845
0.0836
0.0342
0.0826
0.0603
0.0609
0.0644
0.0796
0.09
0.0911
0.0699
0.199
0.244
0.245
52 test [a]
53
55
56
57
58 test [a]
59
60 test [a]
61
62 test [a]
63
64 test [a]
BDP-1 ext [b]
BDP-2 ext [b]
BDP-3
BDP-4
BDP-5 ext [b]
BDP-6
BDP-7 ext [b]
0.356
0.308
0.253
0.666
0.51
18
18
27.3
27.3
36.5
36.5
0.2689
0.3084
0.3352
0.3005
0.0017
0.093
0.113
0.0884
0.093
0.727
0.987
[a] test designates compounds belonging to the test set. [b] ext relates to the molecules of the external set
DLS_04 (α = -12.2%) descriptor is related to drug-like score
indices, similar to drug-like filters (7 rules) described by Chen et
al.[69] This descriptor considers several characteristics: partition
coefficient, the amount of hydrogen bond donors, number of
hydrogen bond acceptors, molecular weight, ratio of the number
of C(sp3) atoms over the total number of non-halogen heavy
atoms, the ratio of H atoms to non-halogen heavy atoms, and
the ratio of the molecular unsaturation over the total number of
non-halogen heavy atoms. In the studied dataset the values of
DLS_04 fall within the range of 0.4-0.8. Lower values of the
DLS_04 index indicates that the compound is not good for drug-
like purposes and is in accordance with the aim of our study,
since efficient photosensitization of 1O2 leads to high cytotoxicity.
Mor24m (α = -10.3%) is a 3D-MoRSE-signal 24 / weighted by
atomic masses,[70] which was found to be useful in predicting the
toxicity of drugs.[71] 3D-MoRSE descriptors (Molecular
Representation of Structures based on Electronic diffraction) are
often regarded as “black box”, although the mathematical
formula for the MoRSE descriptors is rather simple:
ꢦꢗꢈꢦꢧ
ꢙꢨ
ꢡꢢꢣ ꢅ ꢗꢪꢍ ꢗꢥꢩꢪꢃꢃ ꢤꢗꢤꢥ
ꢁ4ꢄ
ꢫ
∑
∑
ꢦꢧ
ꢙꢨ
where s is the scattering parameter, ꢣ is the euclidean distance
ꢗꢥ
between i-th and j-th atoms, N is the total number of atoms, ꢤꢗ
and ꢤꢥ are different atomic properties used as weights,[70] in the
case of Mor03s and Mor18s – I-state.
The presence of Mor24m in the Model 1 reveals a significant
dependence of ФΔ on the size of a molecule. The descriptor is
inversely correlated with Log ΦΔ. Compound 56 has the highest
molecular weight among the studied compounds and its Mor24m
value is the highest in the dataset. BODIPY-phenothiazine 34,
on the contrary, has the lowest value of Mor24m descriptor.
Two descriptors have minor contributions to Model 1 (α < 10%).
F09[N-N] (α = -5.3%) is a frequency of topological distance N-N
7
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10.1002/chem.202100922
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equal to 9. The descriptor is inversely correlated with Log ΦΔ.
Phenylene-separated BODIPY dimer 64 possesses the highest
value of F09[N-N] equal to 4, while for most compounds in the
analyzed dataset it is equal to 0.
S1_fosc (α = 3.3%) is an oscillator strength of the S0S1
transition. This parameter correlates with quantum yield of the
fluorescence from the lowest singlet excited state (fl). As was
shown in previous works, fluorescence from the S1 state
competes with the charge transfer process in BODIPY dyads
and molecules with high fl values show inefficient SOCT-
ISC.[38]
The predicted versus experimental values of Log ΦΔ are
presented in Figure 6b and in Table S4 (Supporting Information).
MATS6s (α = -28.9) is a 2D Moran autocorrelation of lag 6 /
weighted by the I-state as described by Todeschini and
Consonni.[72] The correlation coefficient between MATS6s and
Log ΦΔ is high and equal to 0.569. The negative regression
coefficient before MATS6s in Model 2 equation indicates that
increased autocorrelation of six-membered structural graphs is
unfavorable for high quantum yield ΦΔ values. The importance of
topological distance 6 is apparently due to the presence of aryl
fragments (electron donors/acceptors) in most of the BODIPYs
structures included in the dataset. The Moran coefficients
usually fall within the [-1,+1] interval, whereas in the analyzed
dataset most compounds possess MATS6s in the [-0.2,-0.1]
interval. BODIPY 16 bearing dimethylaminophenyl group in the
meso position has the highest value of MATS6s equal to 0.0676
whereas 1,3,5,7-tetramethylBODIPY 2 has the minimal MATS6s
value in the acetonitrile dataset (-0.214) (Table 4). The reason
for such diverse values of the descriptor for these two
compounds is the I-state values of certain atom types: for
example, 16 contains tertiary amine N atom having rather low I-
state value of 1.0882, whereas 2 is a relatively small molecule
and contains four methyl groups: I-state equals to 2.0 which is
high compared to other types of compounds.[73]
Model 2 (acetonitrile)
A total of 45 compounds from the general dataset are involved in
this model. The MLR equation includes six descriptors:
Log ΦΔ = 3.2341(+/-0.4672) + 0.0872(+/-0.0456) Mor18s +
0.0342(+/-0.0079) Mor03s + 0.1974(+/-0.0648) F06[C-B] -
0.0304(+/-0.0138) RDF065m - 5.6375(+/-0.9105) MATS6s -
76.4904(+/-12.1236) R8u+
(Model 2)
Table 2 demonstrates that Model 2 performed as the most
internally stable one (q2 = 0.693) and the best in predicting the
properties for the external set of compounds (Rꢍꢋꢒꢊꢋꢓꢔꢎꢕ = 0.722).
Table 4. Values of the descriptors used in Model 2 (acetonitrile).
Compound
R8u+
MATS6s
-0.214
-0.142
-0.124
-0.121
-0.0955
0.0526
-0.126
-0.142
-0.127
-0.147
-0.109
-0.13
F06[C-B]
Mor03s
-19.5
-22.7
-22.6
-35.9
-28.4
-29.9
-20.9
-22
-21.7
-21.9
-24.1
-29.7
-24.8
-18.3
-15.8
-29.1
-25.2
-30.8
-27.7
-23.9
-25.3
-26.5
-23.2
-28.1
-26.2
-27.1
-27.8
-32.1
-63
-24.5
-27.2
-52.7
-33.3
-28.2
-28.5
-51.1
-49.4
-43.9
-26.5
-27.1
-25.2
-28.3
-28.4
-32.2
-29.8
RDF065m
1.16
7.86
10.2
11.8
13.3
15.7
6.67
7.88
10.5
14.5
11.9
14.1
16.2
11.3
10.1
9.85
9.11
9.35
8.6
11.6
14.5
12.8
11.9
9.81
10.8
11.1
22.3
21.8
23.5
18.8
27.6
25.9
9.88
13.5
21.5
13.3
22.8
29.4
9.32
7.78
7.5
Mor18s
-2.72
-5.08
-3.28
-5.11
-5.45
-3.34
-2.85
-4.24
-4.32
-5.36
-4.74
-4.55
-4.91
-5.03
-5.2
2 test [a]
0.0349
0.0351
0.0328
0.0331
0.0311
0.0304
0.0392
0.0362
0.0243
0.017
0
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
3
3
2
2
3
3
4
4
6
4
3
3
4
2
2
2
5
7
4
2
2
2
2
2
2
2
3
4 test [a]
5
6 test [a]
7 test [a]
8
9 test [a]
10
11 test [a]
12 test [a]
0.0211
0.0236
0.0215
0.019
13
14
15
16
17
18
19
20
21
22
23
24
-0.197
-0.117
0.0676
-0.109
0.0515
-0.111
0.0555
-0.134
-0.126
-0.141
0.0262
-0.051
-0.143
-0.133
-0.126
-0.115
-0.0437
-0.131
-0.124
0.0582
0.0351
-0.108
-0.121
-0.159
-0.127
-0.128
0.0179
0.0549
0.0562
-0.0496
0.0429
2.30E-04
-0.132
0.0185
0.0179
0.0161
0.0182
0.0163
0.0239
0.0177
0.0283
0.0195
0.0235
0.0249
0.0158
0.0146
0.0166
0.0163
0.0183
0.0131
0.013
0.0159
0.0131
0.0145
0.0173
0.0157
0.0156
0.0252
0.0292
0.0294
0.019
-5.67
-5.14
-5.72
-5.23
-5.89
-5.3
-5.84
-5.25
-3.89
-5.87
-8.06
-8.42
-7.21
-5.81
-3.55
-8.05
-3.94
-3.16
-5.63
-8.79
-4.43
-7.31
-5.22
-1.7
25
26 test [a]
27
28
29
30
31
33
45
47
48
54
61
63
64
BDP-1 ext [b]
BDP-2 ext [b]
BDP-3
BDP-4
BDP-5 ext [b]
BDP-6
BDP-7 ext [b]
-1.88
-1.76
-2.36
-2.29
-2.04
-1.99
12.1
10.5
12.9
13.5
0.0237
0.0258
0.0236
8
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[a] test designates compounds belonging to the test set. [b] ext relates to the molecules of the external set
R8u+ (α = -22.2) is an R maximal autocorrelation of lag 8 /
unweighted. The descriptor is inversely correlated with Log ΦΔ.
meso-Pyridyl-substituted BODIPY 8 has the highest value of
R8u+ equal to 0.0392, whereas dihydrophenazine-separated
BODIPY dimer 45 has the lowest value of the descriptor (0.013).
Here, the importance of GETAWAY descriptors is demonstrated
once again: Model 1 included R6s+ descriptor with high relative
contribution. Apparently, as in the case of R6s+, the maximum
leverage influences the activity and R8u+ value decreases with
increasing the number of atoms.
Model 2 involves two 3D-MoRSE descriptors weighted by I-
state: Mor18s (α = 20.3) and Mor03s (α = 10.3). Both descriptors
are directly proportional to Log ΦΔ. Dyad 54, containing N-
phenylcarbazol as an electron donating subunit, has the lowest
value of Mor18s (-8.79) whereas BPD-1 possesses the highest
value (-1.7) in the analyzed dataset. All compounds in the
validation set (BDP 1–7) possess high values of Mor18s, which
is apparently caused by the presence of methoxy groups in their
structures (-O- atom has a high I-state equal to 3.5). In
comparison, dyad 54 is characterized by the presence of
multiple aromatic rings with carbon atoms having I-state values
of 1.5-2.0.
anthracene dyad 30, which is a relatively small molecule and
contains four six-membered rings with carbon atoms having low
I-state values. Although the structure of 16 is rather compact, it
contains nitrogen atom and four methyl groups, each having
high I-state of 2.
F06[C-B] (α = 12.2%) is a frequency of topological distance C-B
equal to 6. The descriptor is directly correlated with Log ΦΔ.
BODIPY dimer 63 possesses the highest value (7) of F06[C-B],
whereas compound 2 shows the lowest value equal to 0. It can
be concluded that the descriptor allows to distinguish some
cases when a more complicated molecular topology is favorable
for efficient ISC.
RDF065m is a descriptor with minor relative contribution to
Model 2 (α = -6.3%). It is a radial distribution function at 6.5 Å /
weighted by atomic masses. In simple terms, RDF065m can be
regarded as a contribution of the atomic masses within the 6.5 Å
radius of the molecule center. The lowest value is equal to 1.16
for compound 2, having the lowest molecular weight in the
dataset, whereas 64 is one of the largest molecules in the
analyzed dataset and possesses the highest value of RDF065m
equal to 29.4.
Regarding Mor03s, dyad 16 showed the highest value of -15.8,
whereas the lowest value (-63) was obtained for BODIPY-
Table 5. Values of the descriptors used in Model 3 (THF).
Compound
ATSC7i
0.0498
0.443
1.7
LLS_01
1
N-071
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
F03[C-N]
CATS3D_07_PL
S2_nm
277.52
237.18
293.08
340.14
336.33
334.9
369.32
321.06
299.85
335.9
1
4
6
8
11
10
10
13
11
9
8
8
8
8
8
10
8
11
9
10
8
8
8
8
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
1
0
0
1
1
0
0
0
0
3
0
0
0
0
0
0
0
2 test [a]
1
3
4
5
6
0.667
0.5
0.5
2
1.86
1.76
2.05
1.55
1.66
1.99
2.35
2.16
2.32
2.53
1.84
1.42
2.05
1.63
1.97
1.55
2.24
2.4
2.01
1.57
1.63
2.46
2.89
2.48
2.79
1.72
2.51
3.08
4.65
4.1
0.5
7
0.333
0.833
0.833
0.667
0.667
0.667
0.5
8 test [a]
9
10
11
12
13
14
15
16
345
325.8
320.85
368.96
294.79
301.55
293.3
304.64
295.06
301.8
0.5
0.667
0.833
0.667
0.667
0.667
0.667
0.667
0.667
0.667
0.667
0.667
0.5
0.667
0.667
0.667
0.667
0.5
17
18 test [a]
19
20
21
335.93
335.77
337.59
339.04
337.27
365.96
357.51
339.7
364.79
368.72
368.04
366.31
367.39
369.51
320.26
324.36
321.65
326.55
319.95
324.17
314.59
22 test [a]
23 test [a]
24
25
6
8
8
8
26 test [a]
27
31
33
43
44
8
14
16
20
24
17
6
6
6
6
6
45 test [a]
46
0.667
0.5
0.5
61
BDP-1 ext [b]
BDP-2 ext [b]
BDP-3
BDP-4
BDP-5 ext [b]
BDP-6
BDP-7 ext [b]
1.21
1.07
0.973
1.55
1.37
1.53
1.72
1
1
1
0.667
0.667
0.5
6
6
0.5
9
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[a] test designates compounds belonging to the test set. [b] ext relates to the molecules of the external set
Model 3 (THF)
and halogen atoms have high ATSC7i values due to higher
ionization potential of such atoms.
The total number of compounds involved in this model is 41. The
MLR equation includes six descriptors:
Conclusion
Log ΦΔ = 4.201(+/-1.4119) + 0.6225(+/-0.1328) ATSC7i -
0.1358(+/-0.0243) F03[C-N] - 0.0099(+/-0.0039) S2_nm +
0.8736(+/-0.2111) N-071 - 0.4099(+/-0.5512) LLS_01 +
0.3846(+/-0.098) CATS3D_07_PL
Herein we present for the first time a QSPR approach for
predicting the efficiency of singlet oxygen generation by heavy-
atom-free BODIPY in solvents of different polarity. Models
developed using multiple linear regression (MLR) are
quantitatively accurate and show good statistical parameters (R
(Model 3)
= 0.88 ̶ ̶ 0.69) for ΦΔ prediction in all solvents,
0.91 and q2 = 0.62
This model possessed the best statistical parameters in terms of
correlation coefficient of the training set (R = 0.906) and
predicting ability towards the test set ( Rꢍꢊꢋꢌꢊ = 0.879). The
predicted versus experimental values of Log ΦΔ are presented
on Figure 6c and in Table S5 (Supporting Information).
outperforming other machine learning methods, such as support
vector regression (SVR) and random forest regression (RFR).
The models were built using a combination of alvaDesc and
quantum-chemical descriptors which can be obtained via simple
calculations in a highly efficient manner.
For acetontrile and toluene models topological descriptors, such
as GETAWAY which tries to match 3D-molecular geometry
provided by the molecular influence matrix and atom relatedness
N-071 (α = 29.3) has a major contribution to the model. The
descriptor counts the number of tertiary nitrogen atoms attached
to aromatic carbons. Only nine such compounds (15-20 and 44-
46) are present in the dataset. The lone pair of nitrogen
contributes to the electron π-system and causes charge transfer
process in these dyads, ultimately leading to SOCT-ISC.[53]
CATS3D_07_PL (α = 24.0) is a Chemically Advanced Template
Search (CATS) 3D descriptor, namely the frequency of polar
and non-polar groups separated by 7-8 Å. The descriptor is
directly proportional to Log ΦΔ. For most of the compounds in
the dataset CATS3D_07_PL is equal to 0. Dimer 64 has the
highest value of the descriptor equal to 3 (Table 5). Seemingly,
in the case of 64 the descriptor evaluates the frequency of pairs
between nitrogen atoms and methyl groups.
F03[C-N] (α = -20.2) is a frequency of C and N atoms at a
topological distance of 3. The higher the value of the descriptor,
the lower the quantum yield of 1O2 generation. Parent BODIPY 1
has the lowest value of F03[C-N] equal to 4, whereas dimer 46
possesses the highest value of 24.
S2_nm (α = -19.7) is the energy of the second lowest singlet
excited state in nanometers. The descriptor is inversely
correlated with the quantum yield logarithm. Therefore, high S2
state energy (in eV) is favorable for high quantum yield.
Compound 61 has the highest value of the descriptor equal to
370 nm, whereas 2 possesses the lowest value equal to 237 nm.
BODIPYs are known to emit from the S2 state;[74] apparently this
process can compete with intersystem crossing and triplet state
formation which leads to lower ΦΔ values.
Two descriptors have a minor contribution to Model 3: LLS_01
(α = -4.3) and ATSC7i (α = 2.1). LLS_01 is a lead-like score
derived from the rules proposed by Congreve et al.[75] It takes
into account the number of H-bond donors, number of H-bond
acceptors, molecular weight, lipophilicity (logP), rotatable bond
number, and polar surface area. Compounds with high LLS_01
(BDP-1, BDP-2, and BDP-3) show low photosensitization
efficiency, in contrast to compounds with the low descriptor
value like dyad 12, which have ΦΔ value of 0.46 in this solvent.
ATSC7i is a centered Broto-Moreau autocorrelation of lag 7 /
weighted by ionization potential. Dimer 46 has the highest
ATSC7i equal to 4.65 whereas the ATSC7i of 1 is equal to
0.0498. The descriptor is directly proportional to Log ΦΔ.
Apparently, structures with high numbers of nitrogen, oxygen,
by
molecular
topology,
Broto-Moreau,
and
Moran
autocorrelations were the most influential (see Results section
for details). Model 3 (THF) is dominated by N-071 (constitutional
descriptor) and CATS3D_07_PL (frequency of polar and non-
polar groups separated by 7-8 Å). Therefore, Models 1 and 2 are
slightly different from Model 3. In terms of atomic properties,
intrinsic state of the atoms played a significant role for the used
descriptors and strongly correlates with the photosensitizing
ability of BODIPYs. Interestingly, quantum-chemical descriptors
such as frontier molecular orbital energies, HOMO-LUMO gap,
energies of the lowest singlet and triplet excited states, as well
as the singlet-triplet energy gap (EST) were found to have a low
relative contribution to the models. BODIPY structures involved
in our study possess rather large substituents, which strongly
influence mutual orientation between the donor and acceptor
subunits (one of the key factors determining SOCT-ISC
efficiency) and probably due to this reason topological and 3D
descriptors play more significant role than QC descriptors.
However, when smaller subsets of BODIPY structures are
considered, strong correlations between quantum-chemical
descriptors and Log ΦΔ can be observed. For compounds 10-14
(BODIPYs containing methoxy-substituted phenyl group in the
meso position) from the THF dataset, there is
a strong
correlation (R2 = 0.694) between the HOMO energy and Log ΦΔ.
For BODIPYs 15-20 (containing amino-substituted phenyl group
in the meso position), we found a determination coefficient
between HOMO-LUMO gap and Log ΦΔ equal to 0.683.
However, when the whole THF dataset is regarded
determination coefficients are very low: 0.214 and 0.094 for
HOMO energy and HOMO-LUMO gap, respectively. A possible
explanation is the structural diversity of molecules involved in
the dataset. Previously, for
a
dataset containing 26
furocoumarins we have shown that Log ΦΔ strongly correlates
with the triplet state energy.[48] For pteridines, Log ΦΔ correlated
with ionization potential (R2 = 0.806) and electronegativity (R2 =
0.840).[47] However, in both cases datasets were smaller and
more homogenous (having less structural diversity).
10
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10.1002/chem.202100922
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FULL PAPER
default. In the case of MLR, Genetic Algorithm v. 4.1[79] was used for the
model search. Data pre-treatment included variance cut-off equal to
0.001 and inter-correlation cut-off equal to 0.9. Default values of all the
parameters in Genetic Algorithm were used, except the equation length:
the number of iterations/generations was equal to 100, the mutation
probability was equal to 0.3, and the number of equations selected in
each generation was equal to 30.
These results show that challenging first-principle computations
of triplets formation by charge recombination for predicting
SOCT-ISC efficiency can to a certain extend be replaced by
QSPR involving AlvaDesc molecular descriptors which are
computationally much faster to calculate and can be determined
“on click” even for rather large molecules. The generated
predictive models can serve as a simple and effective tool for
guiding the design of SOCT-ISC photosensitizers with singlet
oxygen quantum yield values optimized for desired range of
polarity. Instead of randomly synthesizing donor-acceptor
structures, QSPR models can be employed for in silico
screening of large virtual libraries. Based on these predictions, a
focused series of photosensitizers with tailored properties may
be specifically selected and synthesized. As a proof of concept,
in this work we succeeded to accurately predict 1O2 yields for
several newly synthesized BODIPYs. Such approach is well-
established in medicinal chemistry, where QSPR allow to
achieve much higher success rate and speed up the search of
lead compounds. However, in the field of photochemistry and
photosensitizers design, QSPR methods are still largely
unexplored. The results reported here, in conjunction with our
previous studies, demonstrate that QSPR prediction of 1O2
generation is applicable to various types of organic dyes and
that this methodology requires minimal resources and time for
accurate prediction of the photosensitizers’ activity.
Statistical parameters. Rꢍꢎꢏꢐꢑꢌꢊꢋꢏ is an adjusted coefficient of
determination:
ꢚ
ꢁ
ꢄ
ꢴ ꢈꢩꢃ
ꢆꢬꢍꢭꢥꢮꢦꢯꢰꢭ ꢅ 1 ꢱ ꢲꢃꢩꢳ
(5)
ꢈꢩꢵꢩꢃ
where n is the total number of compounds in the training set; p is the
number of predictors used by the model. Standard error of estimate
(SEE) was calculated using the following formula:
ꢚ
ꢄ
ꢙ
ꢶꢷꢷ ꢅ ꢸ∑ꢁ
(6)
ꢹ ꢩŷ
ꢙ
ꢈꢩꢵꢩꢃ
where yi and ŷi are the actual and predicted Log ФΔ value of the i-th
molecule in the training set. To calculate root mean square error (RMSE)
similar equation was used:
ꢚ
ꢄ
ꢸ∑ꢁ
ꢹ ꢩŷ
ꢙ
ꢙ
ꢆꢡꢶꢷ ꢅ
(7)
ꢈ
To calculate q2 (leave-one-out (LOO) cross-validation parameter) each
molecule in the training set was excluded once and Log ΦΔ of the
excluded molecule was predicted by using the model developed for the
remaining compounds. q2 describes the internal stability of a model and
was calculated using the following formula:
ꢚ
∑
ꢁꢹ ꢩŷ
ꢄ
ꢙ,ꢻꢙ
ꢙ
ꢺꢍ ꢅ 1 ꢱ ∑
(8)
Experimental Section
ꢚ
ꢄ
ꢁꢹ ꢩꢹ
ꢼꢽꢾꢿ
ꢙ
where yi and ŷi,-i are the actual and predicted Log ФΔ values of the ith
molecule in the training set, respectively; ymean is the average Log ФΔ of
all compounds in the training set. To calculate standard deviation error of
Synthesis of BODIPY
Compounds BDP 1-3 were prepared according to published
procedures.[57,59] The four newly reported BODIPY compounds (BDP 4-7)
were prepared according to a previously described general procedure.[58]
All synthetic details and analytical data for new compounds are
presented in the supplementary information.
prediction (SDEP) during LOO cross-validation equation (9) was used:
ꢚ
ꢸ∑
ꢲꢹ ꢩŷ
ꢙ
ꢴ
ꢙ,ꢻꢙ
ꢶꣀꢷꣁ ꢅ
(9)
ꢈ
where yi and ŷi,-i are the actual and predicted Log ФΔ values of the i-th
molecule, respectively.
The activity of each compound in the test set was predicted using the
model developed with the training set. Rꢍꢊꢋꢌꢊ reflects the predictive ability
of the model and was calculated using the following equation:
Computations
Conformational analysis of BODIPY molecules was performed using
Spartan v. 16 modeling software from Wavefunction, Inc.
(www.wavefun.com). Generation of low-energy conformers was
performed using the MMFF force filed.[76] Geometry optimization was
done using Density Functional Theory. M06-2X functional[77] and 6-
31G(d,p) basis set in Spartan v. 16 were used.
A total of 5305 molecular descriptors were calculated using alvaDesc
v.1.0.22 program and online chemical modeling environment OCHEM.[78]
The number of alvaDesc descriptors was reduced to 87 in the case of
toluene, to 101 for acetonitrile, and to 107 for THF using Generic
Algorithm v. 4.1 developed by the DTC lab and Kunal Roy.[79] Twenty
three quantum-chemical descriptors, such as dipole moment, frontier
molecular orbital energies, HOMO-LUMO gap, electronegativity,
polarizability, and partial atomic charges were obtained at M06-2X/6-
31G(d,p) level of theory for the gas phase. Energies of the two lowest
singlet excited states (S1 and S2), energies of the two lowest triplet states
(T1 and T2), as well as the singlet-triplet energy gap (EST) and oscillator
strengths were calculated using Time-Dependent Density Functional
Theory (TD-DFT).
ꢚ
∑
ꢁꢹ
ꢩꢹ
ꢄ
꣄ꣅꢽ꣆
ꢾꣂꣃ
ꢆꢯꢍꢰꢦꢯ ꢅ 1 ꢱ ∑
(10)
ꢚ
ꢄ
ꢁꢹ
ꢩꢹ
ꢼꢽꢾꢿ
ꢾꣂꣃ
where yact and ypred are the actual and predicted activity of the i-th
compound in the test set, respectively; ymean is the average value of Log
ФΔ in the training set. Both summations are over all compounds in the
test set. Rꢍꢋꢒꢊꢋꢓꢔꢎꢕ was calculated in a similar way as Rꢍꢊꢋꢌꢊ , but for
compounds included in the external set.
Singlet oxygen quantum yield determination
The singlet oxygen quantum yield measurements were performed
according to the literature.[80] Solutions of the 1O2 trap, 1,9-
dimethylanthracene (DMA), with an optical density of around 1.4 in air-
saturated solvent (acetonitrile, toluene, and tetrahydrofuran respectively)
were employed. Corresponding BODIPY was added to the cuvette, and
its absorbance was adjusted to around 0.29 at the wavelength of
irradiation. The solutions in the cuvette were irradiated with 514 nm laser
light at a constant power density of 12 mW cm-2. The absorption spectra
of the solutions were measured every 30 - 90 s. The slope of plots of
absorbance of DMA at 376 nm vs. irradiation time for each
photosensitizer was calculated.
Machine learning (ML) was performed using scikit-learn library of Python
programming language. SVR and RFR models search was performed in
scikit-learn using grid-search method and 5-fold cross validation. During
SVR model search three parameters were varied: C, epsilon, and kernel
(linear, polynominal, sigmoid or radial basis function). RFR search was
performed by changing the values of two parameters: number of
estimators (trees) and maximal depth. Other parameters were used by
Singlet oxygen quantum yields were calculated based on the equation:
ꣅꢽ꣋
ꢾ꣍꣎
꣌
꣌
꣊
꣇꣈ ꢅ ꣇ꢧꢰ꣉
(11)
꣈
꣊
ꣅꢽ꣋
ꢾ꣍꣎
11
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10.1002/chem.202100922
Chemistry - A European Journal
FULL PAPER
where ΦΔ is the singlet oxygen quantum yield; the superscript ref stands
for 2,6-diiodoBODIPY (0.85 in toluene)[81]; k is the slope of the curves of
DMA absorption (376 nm) change vs. irradiation time; Iabs represents the
absorption correction factor which is given by I = 1–10-OD (OD is the
optical density at 514 nm).
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Acknowledgements
This work was prepared with the support of funding from the
European Union’s Horizon 2020 research and innovation
programme under the FET-OPEN grant agreement No.828779
and the Technical University of Munich – Institute for Advanced
Study through a Hans Fischer Senior Fellowship. M.A.F. and
A.S. acknowledge the TU Dublin Research Scholarship
programme for support of this work.
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Keywords: BODIPY • photosensitization • singlet oxygen •
quantitative structure-property relationship • machine learning.
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Entry for the Table of Contents
Data on singlet oxygen generation for a library of heavy-atom-free BODIPYs undergoing spin-orbit charge transfer intersystem
crossing (SOCT-ISC) were used to build quantitative structure– property relationship (QSPR) predictive models. These models
estimate quantum yields of singlet oxygen (1O2) generation for a given photosensitizer structure in non-polar, moderately polar and
highly polar solvent. This allows for virtual screening of environment-activatable BODIPY photosensitizers and hence speeding up the
development of new lead compounds for photomedicine.
Running title: Photosensitizer Design
Institute and/or researcher Twitter usernames: @mathiassenge @TUDub_ChemPharm @TCD_Chemistry @TU_Munchen
14
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