Understanding and predicting the charge transport properties of π-conjugated materials is an important challenge for designing new organic electronic devices, such as solar cells, plastic transistors, light-emitting devices, and chemical sensors. A key component of the hopping mechanism of charge transfer in these materials is the Marcus reorganization energy which serves as an activation barrier to hole or electron transfer. While modern density functional methods have proven to accurately predict trends in intramolecular reorganization energy, such calculations are computationally expensive. In this work, we outline active machine learning methods to predict computed intramolecular reorganization energies of a wide range of polythiophenes and their use toward screening new compounds with low internal reorganization energies. Our models have an overall root mean square error (RMSE) of ±0.113 eV, but a much smaller RMSE of only ±0.036 eV on the new screening set. Since the larger error derives from high-reorganization energy compounds, the new method is highly effective to screen for compounds with potentially efficient charge transport parameters.

1.
Z.
Bao
and
A. J.
Lovinger
, “
Soluble regioregular polythiophene derivatives as semiconducting materials for field-effect transistors
,”
Chem. Mater.
11
,
2607
2612
(
1999
).
2.
R.
Porrazzo
,
S.
Bellani
,
A.
Luzio
,
C.
Bertarelli
,
G.
Lanzani
,
M.
Caironi
, and
M. R.
Antognazza
, “
Field-effect and capacitive properties of water-gated transistors based on polythiophene derivatives
,”
APL Mater.
3
,
014905
(
2015
).
3.
Y.
Kim
,
S. A.
Choulis
,
J.
Nelson
,
D. D. C.
Bradley
,
S.
Cook
, and
J. R.
Durrant
, “
Composition and annealing effects in polythiophene/fullerene solar cells
,”
J. Mater. Sci.
40
,
1371
1376
(
2005
).
4.
M.
Zhang
,
X.
Guo
,
W.
Ma
,
H.
Ade
, and
J.
Hou
, “
A polythiophene derivative with superior properties for practical application in polymer solar cells
,”
Adv. Mater.
26
,
5880
5885
(
2014
).
5.
Z. G.
Zhang
,
S.
Zhang
,
J.
Min
,
C.
Cui
,
H.
Geng
,
Z.
Shuai
, and
Y.
Li
, “
Side chain engineering of polythiophene derivatives with a thienylene-vinylene conjugated side chain for application in polymer solar cells
,”
Macromolecules
45
,
2312
2320
(
2012
).
6.
F.
Wang
,
H.
Gu
, and
T. M.
Swager
, “
Carbon nanotube/polythiophene chemiresistive sensors for chemical warfare agents
,”
J. Am. Chem. Soc.
130
,
5392
5393
(
2008
).
7.
P.
Schottland
,
M.
Bouguettaya
, and
C.
Chevrot
, “
Soluble polythiophene derivatives for NO2 sensing applications
,”
Synth. Met.
102
,
1325
(
1999
).
8.
L.
Wang
,
Q.
Feng
,
X.
Wang
,
M.
Pei
, and
G.
Zhang
, “
A novel polythiophene derivative as a sensitive colorimetric and fluorescent sensor for anionic surfactants in water
,”
New J. Chem.
36
,
1897
1901
(
2012
).
9.
B. H.
Barboza
,
O. P.
Gomes
, and
A.
Batagin-Neto
, “
Polythiophene derivatives as chemical sensors: A DFT study on the influence of side groups
,”
J. Mol. Model.
27
,
17
(
2021
).
10.
S. K.
Kang
,
J.-H.
Kim
,
J.
An
,
E. K.
Lee
,
J.
Cha
,
G.
Lim
,
Y. S.
Park
, and
D. J.
Chung
, “
Synthesis of polythiophene derivatives and their application for electrochemical DNA sensor
,”
Polym. J.
36
,
937
942
(
2004
).
11.
A.-L.
Ding
,
J.
Pei
,
Y.-H.
Lai
, and
W.
Huang
, “
Phenylene-functionalized polythiophene derivatives for light-emitting diodes: Their synthesis, characterization and properties
,”
J. Mater. Chem.
11
,
3082
3086
(
2001
).
12.
G. R.
Hutchison
,
M. A.
Ratner
, and
T. J.
Marks
, “
Hopping transport in conductive heterocyclic oligomers: Reorganization energies and substituent effects
,”
J. Am. Chem. Soc.
127
,
2339
2350
(
2005
).
13.
J.
Cornil
,
D.
Beljonne
,
J.-P.
Calbert
, and
J.-L.
Brédas
, “
Interchain interactions in organic π-conjugated materials: Impact on electronic structure, optical response, and charge transport
,”
Adv. Mater.
13
,
1053
(
2001
).
14.
S. S.
Zade
and
M.
Bendikov
, “
Study of hopping transport in long oligothiophenes and oligoselenophenes: Dependence of reorganization energy on chain length
,”
Chem.-Eur. J.
14
,
6734
6741
(
2008
).
15.
S.
Atahan-Evrenk
and
F. B.
Atalay
, “
Prediction of intramolecular reorganization energy using machine learning
,”
J. Phys. Chem. A
123
,
7855
7863
(
2019
).
16.
M.
Misra
,
D.
Andrienko
,
B.
Baumeier
,
J.-L.
Faulon
, and
O. A.
von Lilienfeld
, “
Toward quantitative structure–property relationships for charge transfer rates of polycyclic aromatic hydrocarbons
,”
J. Chem. Theory Comput.
7
,
2549
2555
(
2011
).
17.
C.
Bannwarth
,
S.
Ehlert
, and
S.
Grimme
, “
GFN2-xTB—An accurate and broadly parametrized self-consistent tight-binding quantum chemical method with multipole electrostatics and density-dependent dispersion contributions
,”
J. Chem. Theory Comput.
15
,
1652
1671
(
2019
).
18.
D.
Folmsbee
and
G.
Hutchison
, “
Assessing conformer energies using electronic structure and machine learning methods
,”
Int. J. Quantum Chem.
121
,
e26381
(
2020
).
19.
C.
Lee
,
W.
Yang
, and
R. G.
Parr
, “
Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density
,”
Phys. Rev. B
37
,
785
789
(
1988
).
20.
A. D.
Becke
, “
Density-functional thermochemistry. III. The role of exact exchange
,”
J. Chem. Phys.
98
,
5648
5652
(
1993
).
21.
H.
Sahu
and
H.
Ma
, “
Unraveling correlations between molecular properties and device parameters of organic solar cells using machine learning
,”
J. Phys. Chem. Lett.
10
,
7277
7284
(
2019
).
22.
M.
Rinderle
,
W.
Kaiser
,
A.
Mattoni
, and
A.
Gagliardi
, “
Machine-learned charge transfer integrals for multiscale simulations in organic thin films
,”
J. Phys. Chem. C
124
,
17733
17743
(
2020
).
23.
D.
Padula
,
J. D.
Simpson
, and
A.
Troisi
, “
Combining electronic and structural features in machine learning models to predict organic solar cells properties
,”
Mater. Horiz.
6
,
343
349
(
2019
).
24.
D.
Padula
and
A.
Troisi
, “
Concurrent optimization of organic donor–acceptor pairs through machine learning
,”
Adv. Energy Mater.
9
,
1902463
(
2019
).
25.
C.
Chen
,
Y.
Zuo
,
W.
Ye
,
X.
Li
,
Z.
Deng
, and
S. P.
Ong
, “
A critical review of machine learning of energy materials
,”
Adv. Energy Mater.
10
,
1903242
(
2020
).
26.
T.
Sato
,
T.
Honma
, and
S.
Yokoyama
, “
Combining machine learning and pharmacophore-based interaction fingerprint for in silico screening
,”
J. Chem. Inf. Model.
50
,
170
185
(
2010
).
27.
J.
Vamathevan
,
D.
Clark
,
P.
Czodrowski
,
I.
Dunham
,
E.
Ferran
,
G.
Lee
,
B.
Li
,
A.
Madabhushi
,
P.
Shah
,
M.
Spitzer
, and
S.
Zhao
, “
Applications of machine learning in drug discovery and development
,”
Nat. Rev. Drug Discovery
18
,
463
(
2019
).
28.
N. M.
O’Boyle
,
M.
Banck
,
C. A.
James
,
C.
Morley
,
T.
Vandermeersch
, and
G. R.
Hutchison
, “
Open Babel: An open chemical toolbox
,”
J. Cheminf.
3
,
33
(
2011
).
29.
N.
Yoshikawa
and
G. R.
Hutchison
, “
Fast, efficient fragment-based coordinate generation for open babel
,”
J. Cheminf.
11
,
49
(
2019
).
30.
V. A.
Rassolov
,
J. A.
Pople
,
M. A.
Ratner
, and
T. L.
Windus
, “
6-31G* basis set for atoms K through Zn
,”
J. Chem. Phys.
109
,
1223
1229
(
1998
).
31.
M. J.
Frisch
,
G. W.
Trucks
,
H. B.
Schlegel
,
G. E.
Scuseria
,
M. A.
Robb
,
J. R.
Cheeseman
,
G.
Scalmani
,
V.
Barone
,
B.
Mennucci
,
G. A.
Petersson
,
H.
Nakatsuji
,
M.
Caricato
,
X.
Li
,
H. P.
Hratchian
,
A. F.
Izmaylov
,
J.
Bloino
,
G.
Zheng
,
J. L.
Sonnenberg
,
M.
Hada
,
M.
Ehara
,
K.
Toyota
,
R.
Fukuda
,
J.
Hasegawa
,
M.
Ishida
,
T.
Nakajima
,
Y.
Honda
,
O.
Kitao
,
H.
Nakai
,
T.
Vreven
,
J. A.
Montgomery
,
J. E.
Peralta
,
F.
Ogliaro
,
M.
Bearpark
,
J. J.
Heyd
,
E.
Brothers
,
K. N.
Kudin
,
V. N.
Staroverov
,
R.
Kobayashi
,
J.
Normand
,
K.
Raghavachari
,
A.
Rendell
,
J. C.
Burant
,
S. S.
Iyengar
,
J.
Tomasi
,
M.
Cossi
,
N.
Rega
,
J. M.
Millam
,
M.
Klene
,
J. E.
Knox
,
J. B.
Cross
,
V.
Bakken
,
C.
Adamo
,
J.
Jaramillo
,
R.
Gomperts
,
R. E.
Stratmann
,
O.
Yazyev
,
A. J.
Austin
,
R.
Cammi
,
C.
Pomelli
,
J. W.
Ochterski
,
R. L.
Martin
,
K.
Morokuma
,
V. G.
Zakrzewski
,
G. A.
Voth
,
P.
Salvador
,
J. J.
Dannenberg
,
S.
Dapprich
,
A. D.
Daniels
,
Ö.
Farkas
,
J. B.
Foresman
,
J. V.
Ortiz
,
J.
Cioslowski
, and
D. J.
Fox
, Gaussian 09 Revision A 2,
2009
.
32.
F.
Pedregosa
,
G.
Varoquaux
,
A.
Gramfort
,
V.
Michel
,
B.
Thirion
,
O.
Grisel
,
M.
Blondel
,
P.
Prettenhofer
,
R.
Weiss
,
V.
Dubourg
,
J.
Vanderplas
,
A.
Passos
,
D.
Cournapeau
,
M.
Brucher
,
M.
Perrot
, and
E.
Duchesnay
, “
Scikit-learn: Machine learning in Python
,”
J. Mach. Learn. Res.
12
,
2825
2830
(
2011
).
33.
F.
Chollet
 et al., Keras, https://keras.io,
2015
.
34.
M.
Abadi
,
A.
Agarwal
,
P.
Barham
,
E.
Brevdo
,
Z.
Chen
,
C.
Citro
,
G. S.
Corrado
,
A.
Davis
,
J.
Dean
,
M.
Devin
,
S.
Ghemawat
,
I.
Goodfellow
,
A.
Harp
,
G.
Irving
,
M.
Isard
,
Y.
Jia
,
R.
Jozefowicz
,
L.
Kaiser
,
M.
Kudlur
,
J.
Levenberg
,
D.
Mané
,
R.
Monga
,
S.
Moore
,
D.
Murray
,
C.
Olah
,
M.
Schuster
,
J.
Shlens
,
B.
Steiner
,
I.
Sutskever
,
K.
Talwar
,
P.
Tucker
,
V.
Vanhoucke
,
V.
Vasudevan
,
F.
Viégas
,
O.
Vinyals
,
P.
Warden
,
M.
Wattenberg
,
M.
Wicke
,
Y.
Yu
, and
X.
Zheng
, TensorFlow: Large-scale machine learning on heterogeneous systems, software available from tensorflow.org,
2015
.
35.
D.
Rogers
and
M.
Hahn
, “
Extended-connectivity fingerprints
,”
J. Chem. Inf. Model.
50
,
742
754
(
2010
).
36.
RDKit
, RDKit: Open-source cheminformatics,
2020
, http://www.rdkit.org; accessed 1 March 2021.
37.
L.
Breiman
, “
Random forests
,”
Mach. Learn.
45
,
5
32
(
2001
).
38.
J.
Ye
,
J.-H.
Chow
,
J.
Chen
, and
Z.
Zheng
, “
Stochastic gradient boosted distributed decision trees
,” in
Proceedings of the 18th ACM Conference on Information and Knowledge Management, CIKM ’09
(
Association for Computing Machinery
,
New York, NY
,
2009
), pp.
2061
2064
.
39.
A. E.
Hoerl
and
R. W.
Kennard
, “
Ridge regression: Biased estimation for nonorthogonal problems
,”
Technometrics
42
,
80
816
(
2000
).
40.
V.
Vovk
, “
Kernel ridge regression
,” in
Empirical Inference
(
Springer
,
2013
), pp.
105
116
.
41.
W. S.
McCulloch
and
W.
Pitts
, “
A logical calculus of the ideas immanent in nervous activity
,”
Bull. Math. Biophys.
5
,
115
133
(
1943
).
42.
J.
Bergstra
,
D.
Yamins
, and
D. C.
Cox
, “
Making a science of model search: Hyperparameter optimization in hundreds of dimensions for vision architectures
,” in
Proceedings of the 30th International Conference on Machine Learning
,
2013
.
43.
M.
Pumperla
, Hyperas, https://github.com/maxpumperla/hyperas,
2020
.
44.
J. T.
Barron
, “
Continuously differentiable exponential linear units
,” arXiv:1704.07483 (
2017
).
45.
46.
D. P.
Kingma
and
J. L.
Ba
, “
Adam: A method for stochastic optimization
,” in
3rd International Conference on Learning Representations, ICLR 2015—Conference Track Proceedings
,
2015
; arXiv:1412.6980.
47.
X.
Ji
and
L.
Fang
, “
Quinoidal conjugated polymers with open-shell characters
,”
Polym. Chem.
12
,
1347
(
2021
).
48.
A. E.
London
,
H.
Chen
,
M. A.
Sabuj
,
J.
Tropp
,
M.
Saghayezhian
,
N.
Eedugurala
,
B. A.
Zhang
,
Y.
Liu
,
X.
Gu
,
B. M.
Wong
,
N.
Rai
,
M. K.
Bowman
, and
J. D.
Azoulay
, “
A high-spin ground-state donor-acceptor conjugated polymer
,”
Sci. Adv.
5
,
eaav2336
(
2019
).
49.
T. L.
Dexter Tam
,
C. K.
Ng
,
S. L.
Lim
,
E.
Yildirim
,
J.
Ko
,
W. L.
Leong
,
S.-W.
Yang
, and
J.
Xu
, “
Proquinoidal-conjugated polymer as an effective strategy for the enhancement of electrical conductivity and thermoelectric properties
,”
Chem. Mater.
31
,
8543
8550
(
2019
).
50.
T. L. D.
Tam
,
G.
Wu
,
S. W.
Chien
,
S. F. V.
Lim
,
S.-W.
Yang
, and
J.
Xu
, “
High spin pro-quinoid benzo[1,2-c;4,5-c′]bisthiadiazole conjugated polymers for high-performance solution-processable polymer thermoelectrics
,”
ACS Mater. Lett.
2
,
147
152
(
2020
).
51.
I. Y.
Kanal
,
S. G.
Owens
,
J. S.
Bechtel
, and
G. R.
Hutchison
, “
Efficient computational screening of organic polymer photovoltaics
,”
J. Phys. Chem. Lett.
4
,
1613
1623
(
2013
).
52.
L.
Chan
,
G. M.
Morris
, and
G. R.
Hutchison
, “
Understanding conformational entropy in small molecules
,”
J. Chem. Theory Comput.
17
,
2099
2106
(
2021
).
53.
J. T.
Blaskovits
,
K.-H.
Lin
,
R.
Fabregat
,
I.
Swiderska
,
H.
Wu
, and
C.
Corminboeuf
, “
Is a single conformer sufficient to describe the reorganization energy of amorphous organic transport materials?
,”
Theoret. Comput. Chem.
(published online) (2021).
54.
See https://github.com/hutchisonlab/ReorganizationEnergy for all data and scripts; accessed 11 March 2021.

Supplementary Material

You do not currently have access to this content.