Transfer integral is a crucial parameter that determines the charge mobility of organic semiconductors, and it is very sensitive to molecular packing motifs. The quantum chemical calculation of transfer integrals for all the molecular pairs in organic materials is usually an unaffordable task; fortunately, it can be accelerated by the data-driven machine learning method now. In this work, we develop machine learning models based on artificial neutral networks to predict transfer integrals accurately and efficiently for four typical organic semiconductor molecules: quadruple thiophene (QT), pentacene, rubrene, and dinaphtho[2,3-b:2′,3′-f]thieno[3,2-b]thiophene (DNTT). We test various forms of features and labels and evaluate the accuracy of different models. With the implementation of a data augmentation scheme, we have achieved a very high accuracy with the determination coefficient of 0.97 and mean absolute error of 4.5 meV for QT, and similar accuracy for the other three molecules. We apply these models to studying charge transport in organic crystals with dynamic disorders at 300 K and obtain the charge mobility and anisotropy in perfect agreement with the brutal force quantum chemical calculation. If more molecular packings representing the amorphous phase of organic solids are supplemented to the dataset, the current models can be refined to study charge transport in organic thin films with polymorphs and static disorders.
REFERENCES
1.
H.
Sirringhaus
, “Organic field-effect transistors: The path beyond amorphous silicon
,” Adv. Mater.
26
, 1319
–1335
(2014
).2.
Y.
Diao
, B. C.-K.
Tee
, G.
Giri
, J.
Xu
, D. H.
Kim
, H. A.
Becerril
, R. M.
Stoltenberg
, T. H.
Lee
, G.
Xue
, S. C. B.
Mannsfeld
, and Z.
Bao
, “Solution coating of large-area organic semiconductor thin films with aligned single-crystalline domains
,” Nat. Mater.
12
, 665
–671
(2013
).3.
J.
Rivnay
, L. H.
Jimison
, J. E.
Northrup
, M. F.
Toney
, R.
Noriega
, S.
Lu
, T. J.
Marks
, A.
Facchetti
, and A.
Salleo
, “Large modulation of carrier transport by grain-boundary molecular packing and microstructure in organic thin films
,” Nat. Mater.
8
, 952
–958
(2009
).4.
T.
Holstein
, “Studies of polaron motion: Part II. The ‘small’ polaron
,” Ann. Phys.
8
, 343
–389
(1959
).5.
N. W.
Ashcroft
and D.
Mermin
, Solid State Physics
(Holt, Reinhart and Winston
, New York
, 1976
).6.
T.
Holstein
, “Studies of polaron motion: Part I. The molecular-crystal model
,” Ann. Phys.
8
, 325
–342
(1959
).7.
K.
Marumoto
, S.-i.
Kuroda
, T.
Takenobu
, and Y.
Iwasa
, “Spatial extent of wave functions of gate-induced hole carriers in pentacene field-effect devices as investigated by electron spin resonance
,” Phys. Rev. Lett.
97
, 256603
(2006
).8.
R. A.
Marcus
, “On the theory of oxidation-reduction reactions involving electron transfer. I
,” J. Chem. Phys.
24
, 966
–978
(1956
).9.
M.
Bixon
and J.
Jortner
, “Non-Arrhenius temperature dependence of electron-transfer rates
,” J. Phys. Chem.
95
, 1941
–1944
(1991
).10.
G.
Nan
, X.
Yang
, L.
Wang
, Z.
Shuai
, and Y.
Zhao
, “Nuclear tunneling effects of charge transport in rubrene, tetracene, and pentacene
,” Phys. Rev. B
79
, 115203
(2009
).11.
E. F.
Valeev
, V.
Coropceanu
, D. A.
Da Silva Filho
, S.
Salman
, and J.-L.
Brédas
, “Effect of electronic polarization on charge-transport parameters in molecular organic semiconductors
,” J. Am. Chem. Soc.
128
, 9882
–9886
(2006
).12.
X.
Zheng
, H.
Geng
, Y.
Yi
, Q.
Li
, Y.
Jiang
, D.
Wang
, and Z.
Shuai
, “Understanding lattice strain-controlled charge transport in organic semiconductors: A computational study
,” Adv. Funct. Mater.
24
, 5531
–5540
(2014
).13.
K. T.
Schütt
, H. E.
Sauceda
, P.-J.
Kindermans
, A.
Tkatchenko
, and K.-R.
Müller
, “SchNet – A deep learning architecture for molecules and materials
,” J. Chem. Phys.
148
, 241722
(2018
).14.
J.
Behler
, “First principles neural network potentials for reactive simulations of large molecular and condensed systems
,” Angew. Chem., Int. Ed.
56
, 12828
–12840
(2017
).15.
P.
Reiser
, M.
Konrad
, A.
Fediai
, S.
Léon
, W.
Wenzel
, and P.
Friederich
, “Analyzing dynamical disorder for charge transport in organic semiconductors via machine learning
,” J. Chem. Theory Comput.
17
, 3750
–3759
(2021
).16.
H.
Wang
, L.
Zhang
, J.
Han
, and W.
E
, “DeePMD-kit: A deep learning package for many-body potential energy representation and molecular dynamics
,” Comput. Phys. Commun.
228
, 178
–184
(2018
).17.
J.
Li
, M. S.
Deng
, D. V.
Voronine
, S.
Mukamel
, and J.
Jiang
, “Two-dimensional near ultraviolet (2DNUV) spectroscopic probe of structural-dependent exciton dynamics in a protein
,” J. Phys. Chem. B
119
, 1314
–1322
(2015
).18.
F.
Brockherde
, L.
Vogt
, L.
Li
, M. E.
Tuckerman
, K.
Burke
, and K.-R.
Müller
, “By-passing the Kohn-Sham equations with machine learning
,” Nat. Commun.
8
, 872
(2017
).19.
M.
Rupp
, A.
Tkatchenko
, K.-R.
Müller
, and O. A.
von Lilienfeld
, “Fast and accurate modeling of molecular atomization energies with machine learning
,” Phys. Rev. Lett.
108
, 058301
(2012
).20.
S.
Atahan-Evrenk
and F. B.
Atalay
, “Prediction of intramolecular reorganization energy using machine learning
,” J. Phys. Chem. A
123
, 7855
–7863
(2019
).21.
O.
Çaylak
, A.
Yaman
, and B.
Baumeier
, “Evolutionary approach to constructing a deep feedforward neural network for prediction of electronic coupling elements in molecular materials
,” J. Chem. Theory Comput.
15
, 1777
–1784
(2019
).22.
J.
Lederer
, W.
Kaiser
, A.
Mattoni
, and A.
Gagliardi
, “Machine learning–based charge transport computation for pentacene
,” Adv. Theory Simul.
2
, 1800136
(2019
).23.
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
).24.
C.-I.
Wang
, M.
Braza
, E.
Braza
, G. C.
Claudio
, R. B.
Nellas
, and C. P.
Hsu
, “Machine learning for predicting electron transfer coupling
,” J. Phys. Chem. A
123
, 7792
–7802
(2019
).25.
C.-I.
Wang
, I.
Joanito
, C. F.
Lan
, and C. P.
Hsu
, “Artificial neural networks for predicting charge transfer coupling
,” J. Chem. Phys.
153
, 214113
(2020
).26.
X.
Bai
, X.
Guo
, and L. J.
Wang
, “Machine learning approach to calculate electronic couplings between quasi-diabatic molecular orbitals: The case of DNA
,” J. Phys. Chem. Lett.
12
, 10457
–10464
(2021
).27.
M. J.
Abraham
, T.
Murtola
, R.
Schulz
, S.
Pálla
, J. C.
Smith
, B.
Hess
, and E.
Lindahl
, “GROMACS: High performance molecular simulations through multi-level parallelism from laptops to supercomputers
,” SoftwareX
1–2
, 19
–25
(2015
).28.
M. J.
Frisch
, G. W.
Trucks
, H. B.
Schlegel
, G. E.
Scuseria
, M. A.
Robb
, J. R.
Cheeseman
, G.
Scalmani
, V.
Barone
, G. A.
Petersson
, H.
Nakatsuji
, X.
Li
, M.
Caricato
, A. V.
Marenich
, J.
Bloino
, B. G.
Janesko
, R.
Gomperts
, B.
Mennucci
, H. P.
Hratchian
, J. V.
Ortiz
, A. F.
Izmaylov
, J. L.
Sonnenberg
, D.
Williams-Young
, F.
Ding
, F.
Lipparini
, F.
Egidi
, J.
Goings
, B.
Peng
, A.
Petrone
, T.
Henderson
, D.
Ranasinghe
, V. G.
Zakrzewski
, J.
Gao
, N.
Rega
, G.
Zheng
, W.
Liang
, M.
Hada
, M.
Ehara
, K.
Toyota
, R.
Fukuda
, J.
Hasegawa
, M.
Ishida
, T.
Nakajima
, Y.
Honda
, O.
Kitao
, H.
Nakai
, T.
Vreven
, K.
Throssell
, J. A.
Montgomery
, Jr., J. E.
Peralta
, F.
Ogliaro
, M. J.
Bearpark
, J. J.
Heyd
, E. N.
Brothers
, K. N.
Kudin
, V. N.
Staroverov
, T. A.
Keith
, R.
Kobayashi
, J.
Normand
, K.
Raghavachari
, A. P.
Rendell
, J. C.
Burant
, S. S.
Iyengar
, J.
Tomasi
, M.
Cossi
, J. M.
Millam
, M.
Klene
, C.
Adamo
, R.
Cammi
, J. W.
Ochterski
, R. L.
Martin
, K.
Morokuma
, O.
Farkas
, J. B.
Foresman
, and D. J.
Fox
, Gaussian 16, Revision C. 01, Gaussian, Inc.
, Wallingford, CT
, 2016
.29.
B.
Baumeier
, J.
Kirkpatrick
, and D.
Andrienko
, “Density-functional based determination of intermolecular charge transfer properties for large-scale morphologies
,” Phys. Chem. Chem. Phys.
12
, 11103
–11113
(2010
).30.
N. E.
Jackson
, “Coarse-graining organic semiconductors: The path to multiscale design
,” J. Phys. Chem. B
125
, 485
–496
(2020
).31.
J. S.
Binkley
, J. A.
Pople
, and W. J.
Hehre
, “Self-consistent molecular orbital methods. 21. Small split-valence basis sets for first-row elements
,” J. Am. Chem. Soc.
102
, 939
–947
(1980
).32.
M. S.
Gordon
, J. S.
Binkley
, J. A.
Pople
, W.
Pietro
, and W.
Hehre
, “Self-consistent molecular-orbital methods. 22. Small split-valence basis sets for second-row elements
,” J. Am. Chem. Soc.
104
, 2797
–2803
(1982
).33.
J. H.
Friedman
, “Stochastic gradient boosting
,” Comput. Stat. Data Anal.
38
, 367
–378
(2002
).34.
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 É.
Duchesnay
, “Scikit-learn: Machine learning in Python
,” J. Mach. Learn Res.
12
, 2825
–2830
(2011
).35.
L.
Alzubaidi
, J. L.
Zhang
, A. J.
Humaidi
, A.
Al-Dujaili
, Y.
Duan
, O.
Al-Shamma
, J.
Santamaría
, M. A.
Fadhel
, M.
Al-Amidie
, and L.
Farhan
, “Review of deep learning: Concepts, CNN architectures, challenges, applications, future directions
,” J. Big Data
8
, 53
(2021
).36.
A.
Paszke
, S.
Gross
, F.
Massa
, A.
Lerer
, J.
Bradbury
, G.
Chanan
, T.
Killeen
, Z.
Lin
, N.
Gimelshein
, L.
Antiga
, A.
Desmaison
, A.
Kopf
, E.
Yang
, Z.
DeVito
, M.
Raison
, A.
Tejani
, S.
Chilamkurthy
, B.
Steiner
, L.
Fang
, J.
Bai
, and S.
Chintala
, “PyTorch: An imperative style, high-performance deep learning library
,” in Advances in Neural Information Processing Systems
, edited by H.
Wallach
, H.
Larochelle
, A.
Beygelzimer
, F.
dÁlché-Buc
, E.
Fox
, and R.
Garnett
(Curran Associates, Inc.
, 2019
), Vol. 32, pp. 8024
–8035
.37.
D. P.
Kingma
and J.
Ba
, “Adam: A method for stochastic optimization
,” arXiv:1412.6980 [cs.LG] (2014
).38.
J.
Westermayr
, M.
Gastegger
, M. F. S. J.
Menger
, S.
Mai
, L.
González
, and P.
Marquetand
, “Machine learning enables long time scale molecular photodynamics simulations
,” Chem. Sci.
10
, 8100
–8107
(2019
).© 2023 Author(s). Published under an exclusive license by AIP Publishing.
2023
Author(s)
You do not currently have access to this content.
