1. Synthetic Metals 195 (2014) 54–60
Contents lists available at ScienceDirect
Synthetic Metals
journal homepage: www.elsevier.com/locate/synmet
Evaluation of various density functionals for predicting the
electrophosphorescent host HOMO, LUMO and triplet energies
Bee Kian Onga,c
, Kai Lin Woonb,∗
, Azhar Ariffina
a
Department of Chemistry, University of Malaya, 50603 Kuala Lumpur, Malaysia
b
Low Dimensional Materials Research Center, Department of Physics, University of Malaya, 50603 Kuala Lumpur, Malaysia
c
ItraMAS Corporation. Sdn. Bhd., 542A-B Mukim 1, Lorong Perusahaan Baru 2, Kawasan Perindustrian Perai 13600, Penang, Malaysia
a r t i c l e i n f o
Article history:
Received 11 March 2014
Received in revised form 12 May 2014
Accepted 13 May 2014
Available online 2 June 2014
Keywords:
Density functional theory
Triplet
HOMO
LUMO
Phosphorescence
Organic light emitting diode
a b s t r a c t
Design of phosphorescent hosts for deep blue emitter with suitable electronic states for high efficiency
electrophosphorescent light emitting diodes is often carried out by using wet-lab techniques and trial
and error. Although, quantum computation has been carried out to study the influence of certain sub-
stituents on the materials, an accurate prediction of the highest occupied molecular orbital (HOMO), the
lowest unoccupied molecular orbital (LUMO) and the triplet energies (ET) of electrophosphorescent hosts
remains challenging. Here, we evaluate different density functionals on a set of electrophosphorescent
hosts of different sizes using time-dependent density functional theory. M062X is found to be the best
predictor for ET. Other methods such as B3LYP and O3LYP are potentially good estimators for HOMO
and LUMO levels. By using empirical relationships between the predicted HOMO, LUMO and ET energies
with respect to the experimental values, more accurate estimations can be obtained. The empirical rela-
tionships mean absolute error for ET, LUMO and HOMO energy levels are 0.11 eV, 0.21 eV and 0.17 eV,
respectively. These techniques are used to predict a new electron transporting electrophosphorescent
host. These empirical relationships would greatly assist in the accurate prediction of electronic states of
solution processable electrophophorescent hosts.
© 2014 Elsevier B.V. All rights reserved.
1. Introduction
Organic light-emitting diodes (OLEDs), especially the phos-
phorescent ones (PhOLEDs), have been widely studied due to its
potential to reach 100% internal quantum efficiency [1]. This makes
PhOLEDs a promising alternative as energy efficient displays and
solid state lighting. Among the three different colors, red and
green PhOLEDs fabricated by solution processing have been devel-
oped with success, while the high efficiency deep-blue PhOLEDs
remain scarce [2]. High triplet OLED materials that can be solu-
tion processed are highly desirable due to the lower manufacturing
cost. Other than color display, deep-blue PhOLEDs can be used to
produce white light in solid-state lighting. However, the need of
wide triplet bandgap hosts and dopants makes synthesizing high
quantum efficiency deep blue hosts challenging [3]. Furthermore,
screening all potential novel deep blue hosts solely with wet-lab
techniques and by trial and error is time-consuming and very
expensive.
∗ Corresponding author. Tel.: +60 3 79674287.
E-mail address: ph7klw76@um.edu.my (K.L. Woon).
Reliable and accurate methods for predicting the electronic
states of such molecules would offer a solution for screening a
wide range of potential deep blue hosts. However, solution pro-
cessable hosts are usually large. Accurate predictions of triplet
energy levels (ET) and frontier orbitals of such molecules constitute
a significant computational challenge. Time-dependent density
functional theory (TD-DFT) is an extension of density functional
theory and has become one of the most prominent methods for
calculating excited states. It is used in the presence of time-
dependent potentials, such as electric or magnetic fields. External
time-dependent potentials such as electromagnetic waves can be
considered a weak perturbation. Hence, the dynamic process such
as transition between two eigenstates can be described. TD-DFT
can be used to extract information such as excitation energies,
frequency-dependent response properties and photoabsorption
spectra of a given molecule. TD-DFT is chosen for its compromise
between accuracy and computational performance for typical chro-
mophores of about 100 atoms [4,5]. TD-DFT is an exact theory but
the implementation of it requires selection of an exchange corre-
lation function which approximates the model. Hence the results
are profoundly functional-dependent. Computational studies on
OLED materials generally focus on the effect of certain substituents,
http://dx.doi.org/10.1016/j.synthmet.2014.05.015
0379-6779/© 2014 Elsevier B.V. All rights reserved.

2. B.K. Ong et al. / Synthetic Metals 195 (2014) 54–60 55
Table 1
HOMO, LUMO, band gap and triplet energies of selected electrophosphorescent hosts.
Molecular structure Experimental data References
HOMO (eV) LUMO (eV) Triplet energy (eV) Bandgap (eV)
BCP
−6.4 −3.0 2.6 3.4 [17]
TAPC
−5.1 −2.0 2.87 3.1 [22]
PO14
−7.45 −2.50 3.14 4.95 [23]
HM-A1
−5.59 −2.56 2.84 3.03 [18,21]
CBP
−6.2 −2.17 2.56 4.03 [15]
PO1
−7.2 −2.9 2.72 4.3 [14]
mCP
−5.8 −2.4 2.9 3.4 [19]
DHM-A2
−5.37 −2.46 2.7 2.91 [21]
NPD
−5.4 −2.4 2.26 3.0 [20]

3. 56 B.K. Ong et al. / Synthetic Metals 195 (2014) 54–60
Table 1 (Continued)
Molecular structure Experimental data References
HOMO (eV) LUMO (eV) Triplet energy (eV) Bandgap (eV)
TCTA
−5.2 −2.2 2.85 3.0 [16]
Table 2
HOMO, LUMO, band gap and triplet energies of TCTA calculated from various functionals using TD-DFT.
Method HOMO (eV) LUMO (eV) Band gap (eV) Triplet energy (eV)
B3LYP −5.40 −1.43 3.97 2.51
CAM-B3LYP −6.64 −0.32 6.32 2.31
BHandHLYP −6.32 −0.42 5.90 1.85
O3LYP −5.13 −1.50 3.63 2.62
X3LYP −5.40 −1.33 4.07 2.49
␻B97a
−7.58 0.53 8.11 1.97
␻B97XD −7.15 0.26 7.41 2.45
M062X −6.47 −0.66 5.81 2.83
M062X//O3LYP −6.72 −0.61 6.11 2.88
Experimental −5.20 −2.20 3.00 2.85
a
Job not terminated normally.
such as the carbazoles, fluorene, phosphine oxides, and anthracenes
rather than searching for the most suitable computational method
to predict electronic properties of OLED materials [6–10]. Further-
more, the assessment of TD-DFT is restricted to small compounds or
the subunits but not the whole OLED material [11]. A more exten-
sive research, where TD-DFT was compared with Hartree–Fock (HF)
simulations to predict optical excitations of organic oligomers, was
done by A. Pogantsch et al. [12]. Again, the study is confined to
thiophene subunits. Recently, a semi-empirical method, PM6, was
reported but only analysis of ground-state properties is discussed
[13]. Appropriate selection of the exchange correlation is often
crucial to grasp the chemical sound conclusions. Furthermore, the
estimation of ET of the electrophosphorescent hosts against differ-
ent density functionals remains scarce. High ET energy levels are
important for the deep blue emitter as the host must be higher
than that of the guest to favor exothermic energy transfer from the
host to the guest. Estimation of the ET energy level with chemical
accuracy (0.1 eV) may be highly desirable.
TD-DFT was selected in order to calculate frontier orbitals ener-
gies and ET in vacuum. The goal was to determine exchange
correlation functions that give the closest theoretical frontier
orbital energies and ET to the experimental results. However, exper-
imental results are often done in solid state or in a dilute solvent.
The calculated results might differ from the experimental results.
Bulk solvent effects can be incorporated in the calculation but it will
result in unnecessary computational cost. Hence, we also develop
empirical relationships between the predicted HOMO, LUMO and
ET energies with respect to the experimental values. This will allow
us to predict more accurately the calculated electronic states of
electrophosphorescent hosts. Determination of such a relationship
requires TD-DFT calculations on a set of representative electrophos-
phorescent hosts. In this investigation, we use a set of 10 molecules
since their respective electronic states are well characterized.
2. Computational methodology
The chemical structures of the electrophosphorescent hosts
including their HOMO, LUMO and ET are investigated theoretically
in this work and are depicted in Table 1 [14–23]. The HOMO and
LUMO levels in Table 1 are obtained by cyclic voltammetry. The
ET in Table 1 are usually obtained as the first vibronic mode of
the corresponding phosphorescence spectra at a temperature less
than 77 K. The aromatic cores consist mainly of carbazole, phos-
phine oxide, biphenyl and triphenylamine. Calculations are done
with the Gaussian09 [24] program installed in the Symmetric Multi
Processing (SGiAltix4700, 64x Dual Core Intel Itanium 2 64 bits
Processors) at University of Malaya High Performance Computing
and Academic GRID (2× Quad Core Intel(R) Xeon(R) CPU E5450 @
3.00 GHz). All structures were optimized at the ground state (So)
using spin restricted DFT 6-311G(d,p). Then spin restricted TD-
DFT 6-311G(d,p) is used to obtain the first excited triplet state
(T1), the HOMO and LUMO energies. Generally, the computational
cost for chromophores that are less than 50 atoms is around 1–2
days (16 processors, 1 GB memory) and a week for larger chro-
mophores. Due to time restriction and the need to identify suitable
Fig. 1. MSE and MAE of ET, LUMO and HOMO for M062X//B3LYP, M062X//O3LYP,
O3LYP and B3LYP.

4. B.K. Ong et al. / Synthetic Metals 195 (2014) 54–60 57
Fig. 2. Plots of computed LUMO, HOMO and ET for M062X//B3LYP, M062X//O3LYP, O3LYP and B3LYP against experimental values. The linear regression equations and their
corresponding R2
are shown on the top left corner.
functionals, only 8 DFT functionals are selected. These include
hybrid functionals (B3LYP [25], BHandHLY [26], O3LYP [27], X3LYP
[28], M062X [29]) and range-separated functionals (CAM-B3LYP
[30], ␻B97 [31], ␻B97XD [32]). These functionals were applied
to tris(4-carbazoyl-9-ylphenyl)amine (TCTA) as training sets. Four
promising functionals are selected and applied to the OLED hosts
in Table 1. The band gap was determined here to be the differ-
ence between the HOMO and LUMO energies. The calculated results
were compared with literature.
3. Results and discussion
3.1. Training sets
The training set data are obtained and 4 potential function-
als are identified for further investigation. These functionals are
B3LYP, O3LYP, M062X//B3LYP, and M062X//O3LYP. Results showed
that B3LYP and O3LYP are both good functionals to estimate fron-
tier orbital energies. M062X is among the best in estimating ET
as shown in Table 2. The O3LYP functionals are similar to the
B3LYP functionals, but the O3LYP uses better optimized exchange
functionals developed by Handy and Cohen [33]. In contrast with
B3LYP, O3LYP has a reduced HF-exchange contribution, a larger
coefficient multiplying OPTX functional in place of the standard
XB88 exchange and a new Vosko, Wilks, and Nusair’s local cor-
relation [34]. The M062X functional is a non locality functional
with twice the amount of nonlocal exchange, parametrized only
for nonmetals. It treats opposite-spin and parallel-spin correla-
tion differently [35]. This functional has terms that depend on
spin-up and spin-down electron densities, spin density gradients
and spin kinetic energy densities. In phosphorescence, electrons
change their spin direction creating triplet states. Hence, M062X is

5. 58 B.K. Ong et al. / Synthetic Metals 195 (2014) 54–60
a good estimator of electronic process that involves spin-flipping.
B3LYP and O3LYP use electron density and its first derivatives
while M062X includes the second derivatives of the electron den-
sity in their exchange-correlation functionals. Although M062X
is potentially more accurate, further terms in the expansion of
M062X functional increase the computational time. To shorten
the amount of time used to calculate the ET, the TCTA structure
that is optimized with O3LYP was submitted for direct calculation
using M062X functionals (M062X//O3LYP). The same method was
repeated with B3LYP to generate M062X//B3LYP. It was noted that
calculations that were done with B3LYP and O3LYP on other elec-
trophosphorescent hosts have the tendency to underestimate the
ET. M062X//B3LYP and M062X//O3LYP have a better estimation of
the electrophosphorescent hosts triplet energies.
3.2. Benchmark data
In terms of HOMO and LUMO levels, the B3LYP, O3LYP and
X3LYP functionals produce closer experimental values than other
functionalstestedhere.Therelativelygoodperformanceof thepop-
ular B3LYP/6-31G* model chemistry has been used for calculating
the HOMO and LUMO levels for various organic semiconduct-
ing materials. However, these three functionals over-estimate the
bandgaps with O3LYP showing the most promising estimate. This
is consistent with the recent results obtained by L. Ling et al. on
triphenylamine-fluorene copolymers [36]. While for the ET, M062X
produces the closest value while the HOMO and LUMO levels were
rather far from experimental values. This is consistent with the
work of D. Jacquemin et al., where a set of small molecules with
the largest being naphthalene, is benchmarked with mean abso-
lute error (MAE) of 0.07 eV [37]. TCTA is about 5 times larger than
naphthalene and the accuracy of the result is remarkable. Indeed
large HF exchange contributions such as M062X (54% HF exchange)
are required for an accurate prediction of the triplet energy [38].
The next closest is O3LYP followed by B3LYP. It is important to
note that the ET of electrophosphorescent hosts are often obtained
using B3LYP functionals [39]. Although M062X offers excellent
accuracy, it demands high computational cost for large molecules
such as TCTA without pre-optimized molecular structure at high
accuracy. Hence, we pre-optimized the ground state of the TCTA
using O3LYP before submitting a direct calculation using M062X
(referred as M062X//O3LYP). As expected, a high accuracy ET can
be obtained using M062X//O3LYP. In order to obtain a meaningful
evaluation of the accuracy of different functionals, a comparison
set of electrophosphorescent materials are required. It would be
interesting to compare values calculated with experimental data
for the molecules listed in Table 1.
Four different methods (B3LYP, O3LYP, M062X//O3LYP and
M062X//B3LYP) are used to evaluate the accuracy of electronic
states of different electrophosphorescent hosts as listed in Table 1.
The MAE and mean signed error (MSE) is given in Fig. 1. These meth-
ods tend to underestimate the triplet energy. M062X/O3LYP and
M062X/B3LYP are the best triplet energy predictors with MAEs of
0.18 eV and 0.21 eV respectively. MSEs of −0.12 eV and −0.18 eV are
obtained for M062X/O3LYP and M062X/B3LYP respectively. How-
ever, both methods are the worst predictors for LUMO levels with
MAEs of more than 1 eV. B3LYP is the best predictor for HOMO
levels with an MAE of 0.28 eV. However, the error is considerably
large for the LUMO with an MAE of 0.64 eV. Linear regressions
were performed on the data sets from each methodology and these
are plotted in Fig. 2. These regressions are used to correct empiri-
cally the electronic states. By adding the regression slope and the
regression intercept, all methods have significantly smaller errors
as shown in Fig. 3 as the “corrected MAE”. Although the “corrected
MAE” has lower error, it is important to note that the correlation
coefficient for an estimation of the LUMO level is poor (R2 ∼ 0.4).
Fig. 3. “Corrected MAE” of ET, LUMO and HOMO for M062X//B3LYP, M062X//O3LYP,
O3LYP and B3LYP.
However, the correlation coefficient for the HOMO is rather good
(R2 ∼ 0.7). ET shows the highest correlation with O3LYP having an
R2 of 0.76. The “corrected MAE” for ET falls between 0.11 and 0.16 eV
making the regression method a promising method for estimating
the triplet energy.
3.3. Application on novel OLED materials
Some of the more interesting OLED materials are TCTA
derivatives with diphenylphosphine oxide. Tris[4-(3,6-
diphenylphosphinoyl-9H-carbazoyl-9-yl)phenyl]amine (T6POCA)
is a new TCTA derivative with six diphenylphosphine oxides.
TD-B3LYP 6-311G(d,p) calculation is carried out on T6POCA.
The HOMO, LUMO and ET energy levels are −5.61 eV, −1.84 eV
and 2.44 eV respectively. Using the empirical relationship,
the calculated results for HOMO, LUMO, and ET energy lev-
els are corrected to be (−5.90 ± 0.19) eV, (−2.61 ± 0.21) eV, and
(2.92 ± 0.14) eV. The ET and bandgap are expected to be very similar
to TCTA and (9-(4-(bis(4-(9H-carbazol-9-yl)phenyl)amino)-
phenyl)-9H-carbazol-3-yl) diphenylphosphine oxide (TCTAPO)
(EHOMO = −5.30 eV, ELUMO = −1.83 eV, ET = 2.83 eV) synthesized by
X. Yang et al. [40]. This observation supports that the electron-
withdrawing diphenylphosphine oxide group only lowers the
HOMO and LUMO energy levels, but give little changes to the ET
and the bandgap. Compared to TCTAPO, the presence of five extra
diphenylphosphine oxide units in T6POCA leads to deeper HOMO
and LUMO levels. This would give better hole-blocking properties
and enhanced electron injection. This material will be suitable
for an electron transporting layer for solution processable blue
PHOLEDs.
Unlike TCTA where the electron delocalization at the HOMO is
more evenly distributed, the electron delocalization for T6POCA is
concentrated at the core as shown in Fig. 4. The LUMO levels for both
molecules, however, are concentrated at the triphenylamine core.
From the electrostatic potential map, the carbazole chromophores
of TCTA are very electronegative while the triphenylamine core is
highly electropositive reducing the net dipole moment (0.03 D). In
T6POCA, the six electron withdrawing diphenylphosphine oxides
pull all the electrons toward the oxygen atoms (red) as depicted
in Fig. 5. The triphenylamine core becomes less electropositively
charged (cyan) while the carbazole chromophores are neutral
(green). This accounts for the high net dipole moment (3.76 D) and
indicates that T6POCA is very polar.
A novel dispirofluorene (2,1-b)-indenofluorene has been syn-
thesized and computed at B3LYP//6-311G(d,p) [9]. Using our
derived empirical equation, the HOMO and LUMO levels are

6. B.K. Ong et al. / Synthetic Metals 195 (2014) 54–60 59
Fig. 4. Chemical structures, HOMO and LUMO of TCTA and T6POCA. The frontier orbitals plots are calculated with B3LYP, 6-311G(d,p) at ground state.
Fig. 5. Electrostatic potential map of TCTA and T6POCA.
predicted to be (−5.9 ± 0.19) eV and (−2.1 ± 0.21) eV respectively
while the values obtained by cyclic voltammetry are −5.73 eV and
−2.1 eV. These values are within the predicted range.
4. Conclusion
M062X is found to be the best predictor for ET while other meth-
ods such as B3LYP and O3LYP are potentially good estimators for
HOMO and LUMO levels. Using linear regression, a more accurate
estimation is obtained. The “corrected” results of B3LYP, O3LYP,
M062X//B3LYP, and M062X//O3LYP show great promise in the esti-
mation of the ET energy level with an MAE of less than 0.16 eV.
We applied these techniques to predict a new electron trans-
porting electrophosphorescent host. Using these simple empirical
relationships, the electronic properties of a wide range of phos-
phorescent hosts, especially the large solution processable hosts
can be estimated with sufficient accuracy. This is very useful for
screening a large set of potential hosts and reducing the amount of
time wasted in synthesizing non-optimized materials in the wet-
lab.
Acknowledgements
This research is funded by ItraMAS Sdn. Bhd. (PV002-2013),
Chancellery High Impact Research Grant (UM.C/625/1/HIR/195)
and (UM.C/625/1/HIR/208) Malaysia Long Term Research Grant
Scheme (LR003-2011A), and Postgraduate Research Fund (PPP)
(PG021-2013A) by University of Malaya. We would like to thank
Pusat Teknologi Maklumat Universiti Malaya and Academic GRID
for high performance computer access. Special thanks to Mr.
Safwan (UM PTM) and Mr. Farhan (Academic GRID) for providing
technical support.
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