Density Functional Theory Study of the Secondorder Nonlinear Optical Properties of Novel Fluorenone Derivatives

Abstract

Based on the molecular structure of novel fluorenone derivative named FO52, a series of new molecules have been designed by extending its π-conjugated bridge and introducing electron donor or acceptor substituents. The electronic transition and second-order non-linear optical response properties of these fluorenone derivatives were theoretically studied in detail by using the density functional theory computational methods. The results showed that the non-linear optical response of the molecule FO52 can be improved by introducing five-membered heterocycles into its skeleton structure. In addition, the introduction of strong substituents results in significant enhancement of the first hyperpolarizability of molecular nonlinear optical properties. These fluorenone derivatives could be treated as excellent candidates for nonlinear optical materials due to the narrow energy gap of its frontier molecular orbitals, distinct intramolecular charge transfer character and large first hyperpolarizabilities

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Japan J Res. (2023) Vol 4, Issue 3 Page 1 of 10
Original Article
Japan Journal of Research
Citation: Jia Y, Peng D. Density Functional Theory Study of the Second-order Nonlinear Optical Properties of Novel
Fluorenone Derivatives. Japan J Res. 2023;4(3):1-8.
Density Functional Theory Study of the Second-
order Nonlinear Optical Properties of Novel
Fluorenone Derivatives
Yuanyuan Jia1, Daoling Peng2
1School of Chemistry, South China Normal University, Guangzhou 510006, China
2Key Laboratory of Theoretical Chemistry of Environment, Ministry of Education; School of Environment, South China Normal
University, Guangzhou 510006, China
Introduction
Nonlinear optics (NLO) has been a hot area
of modern optoelectronics since the second
harmonic was observed by Franken et al. [1,2].
Nonlinear optical materials have attracted
signicant interest among researchers due
to their broad application prospects such as
optoelectronics, photonic devices, frequency
doubling second harmonic generation, ber-
optic telecom communication, etc [3-7].
During the last few decades, some experimental
and theoretical scientists have been invested
a great deal of eort in designing and
synthesizing new nonlinear optical materials
at the molecular level [8-10]. Among these
NLO materials, organic materials are popular
over the conventional inorganic crystalline
materials due to its larger NLO response,
higher laser damage threshold and easier
synthesis [11-14]. In the design and synthesis
of organic molecules, donor/conjugated-
bridge/acceptor (D-π-A) structure molecules
are favored by researchers [15-17]. is special
D-π-A structure promotes intramolecular
charge transfer (ICT), resulting in large dipole
moments and hyperpolarizabilities[18-20].
e hyperpolarizability is one of the vital
parameters to evaluate the NLO properties
for materials. It is necessary to explore new
molecules with larger NLO response to develop
novel NLO materials.
However, unimolecule with high
hyperpolarizability does not always result in
materials with outstanding macroscopic NLO
response, because many molecules always
assemble in centrosymmetric way [21,22].
Fluorenone, as an aromatic organic building
block, has been usually employed as an electron
acceptor in ICT molecules due to its good electron
delocalization characteristics and planarity
[23,24]. e uorenone-based compounds
generally seem to have a very high damage
threshold. Furthermore, the centrosymmetry
of uorenone derivatives is broken owing to
the introduction of the carbonyl group, and it
is also gives them a permanent dipole moment
that is always towards the carbonyl group.
e uorenone derivatives not only have high
unimolecular hyperpolarizability, but also are
easy to assemble in non-centrosymmetric ways
[25,26]. ese make uorenone derivatives
display great potential for application in the eld
of nonlinear optics.
Although multiphoton absorption in
uorenone compounds has been reported many
times [27,28], little attention has been paid to their
second order nonlinear optics. However, most of
the study focus on the experiments of synthesis,
related theoretical researches are scarce. Recently,
a novel NLO molecule abbreviated as FO52 was
Correspondence
Daoling Peng
Key Laboratory of Theoretical Chemistry of
Environment, Ministry of Education; School of
Environment, South China Normal University,
Guangzhou 510006, China
• Received Date: 25 Feb 2023
• Accepted Date: 02 Mar 2023
• Publication Date: 05 Mar 2023
Copyright
© 2023 Authors. This is an open- access article
distributed under the terms of the Creative
Commons Attribution 4.0 International license.
Abstract
Based on the molecular structure of novel uorenone derivative named FO52, a series of new molecules
have been designed by extending its π-conjugated bridge and introducing electron donor or acceptor
substituents. The electronic transition and second-order non-linear optical response properties of
these uorenone derivatives were theoretically studied in detail by using the density functional theory
computational methods. The results showed that the non-linear optical response of the molecule FO52
can be improved by introducing ve-membered heterocycles into its skeleton structure. In addition, the
introduction of strong substituents results in signicant enhancement of the rst hyperpolarizability
of molecular nonlinear optical properties. These uorenone derivatives could be treated as excellent
candidates for nonlinear optical materials due to the narrow energy gap of its frontier molecular
orbitals, distinct intramolecular charge transfer character and large rst hyperpolarizabilities.

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Yuanyuan Jia & Daoling Peng. Japan Journal of Research. 2023;4(3):1-8
Japan J Res. (2023) Vol 4 Issue 3
negligible. But other basis set are larger than 6-31+G(d) and
leading to longer computational time. In order to shorten the
calculation time, the basis set 6-31+G(d) was then employed in
this work.
e static rst hyperpolarizability are calculated according to
the following equation
( )
1/2
222
0xyz
β βββ
= ++
(1)
where
,,
i ikk
k xyz
ββ
=
=∑
(2)
e Hyper-Rayleigh-Scattering (HRS) method established by
Champagne and his co-workers[41] is dened as
( )
( )
1/2
22
-2 , ,
HRS ZZZ ZXX
β ωωω β β
= +
(3)
Where βzzz
2 and βzxx
2 represent the orientational averages of β
tensor components, and they also can be considered as contributed
by dipolar (βJ=1) and octupolar (βJ=3) tensor components, namely
2 22
13
10 10
( ) ( | | | |)
45 105
HRS HRS J J
ββ β β
= =
= = +
(4)
In addition, the nonlinear anisotropy parameter ρ (eq 5) is
utilized to evaluate the ratio of the dipolar (eq 6) and octupolar
(eq 7) contributions to the hyperpolarizability tensor.
3
1
J
J
β
ρβ
=
=
=
(5)
1
1
1
J
ρ
=
Φ=
+
(6)
31
J
ρ
ρ
=
Φ=
+
(7)
synthesized [29]. As illustrated in Figure 1, this molecule consists
of a uorenone core and triphenylamine donor on both sides. In
order to prolong the conjugated chain length, three dierent ve-
membered heterocycles were introduced between the uorenone
core and triphenylamines of molecule FO52. en the eects of
dierent push-pull electron substituents on NLO properties were
investigated. It is expected that this theoretical work could provide
eective guidance for the synthesis of novel NLO materials.
Computational details
We rst performed the basis set and functional tests. the results
show that several electronic properties such as the highest occupied
molecular orbital (HOMO) energies, the lowest unoccupied
molecular orbital (LUMO) energies and the HOMO–LUMO
energy gaps (Egap) of molecule FO52 in optimized geometry at the
B3LYP/6-31G(d) level are fairly closed to experimental work [29].
erefore, it is reasonable to optimize FO52 and its derivatives
at the B3LYP/6-31G(d) level. e detailed calculation results
can be found in the Table S1 and S2 of supporting materials. e
vibrational frequencies of all molecules are real values, which
indicates that the optimized geometrical structures of these
components are reliable.
It is vital to select a suitable calculation method and basis set
to obtain accurate rst hyperpolarizability. e conventional
exchange correlation functional of DFT may overestimate the
rst hyperpolarizability due to its wrong asymptotic exchange
potentials [30]. However, the hybrid exchange correlation
functional CAM-B3LYP can solve this problem because it includes
a long-range correction. To perform the functional and basis set
tests, several molecules are selected as testing set. At the same basis
set 6-31+G(d) level, we selected the traditional functional B3LYP
[31] and four functionals with dierent Hartree-Fock exchange
components, including CAM-B3LYP [32,33], BHandHLYP
[34], M06-2X [35] and ωB97XD [36]. As shown in Figure 2, the
rst hyperpolarizabilities calculated by ve dierent exchange-
correlation functionals have the same variation trend. However,
the functional CAM-B3LYP has been successfully applied to
evaluate the NLO properties of charge transfer systems [37-40].
CAM-B3LYP was selected to evaluate the NLO properties of the
present system. Besides functional tests, we also perform the basis
set tests by using the CAM-B3LYP functional in combination
with dierent basis sets including 6-31+G(d), 6-31+G(d,p),
6-31++G(d,p) and 6-311++G(d,p). As shown in Table S3, the
relative errors comparing to 6-31+G(d) are about 1% which is
Figure 1. Structure of the FO52 molecule, a) Front view, b) Top view.
Figure 2. The static rst hyperpolarizability values of molecule A, D,
I, I7, I8 obtained by employing 6-31+G(d) basis set with varies DFT
funtionals.

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Japan J Res. (2023) Vol 4 Issue 3
All the above calculations were carried out using the Gaussian
16 program package [42]. Furthermore, the distributions of
electron and hole were done with the Multiwfn suite of programs
(revision 3.7) [43]. All orbital visualization was obtained with the
Multiwfn in combination with the VMD program [44].
Results and discussions
Geometric structures
As illustrated in Figure 3, the molecule FO52 synthesized in
the experiment is named FO(A) in this work. In order to explore
the eect of extended π-conjugated bridge on the second-order
NLO properties, a ve-membered heterocycle (thiophene,
thiazole, oxazole) was inserted between the uorenone core and
triphenylamine on both sides, and corresponding molecules
FTP(B),FTZ(C) and FOZ(D) were obtained. en, on the basis
of FOZ(D) molecule, dierent electron-donating groups (-CH3,
-OCH3, -NH2, -NH (CH3), -N(CH3)2) were simultaneously
introduced at the positions of R1, R2, R3 and R4 to obtain the
corresponding molecules FOZ-Me (E), FOZ-OMe (F), FOZ-N
(G). FOZ-NMe (H) and FOZ-NMe2 (I) were used to investigate
FOZ(D): R
1
=R
2
=R
3
=R
4
=R
5
=R
6
=H
FOZ-Me(E): R1=R2=R3=R4=CH3, R5=R6=H
FOZ-OMe(F): R1=R2=R3=R4=OCH3, R5=R6=H
FOZ-N(G): R1=R2=R3=R4=NH2, R5=R6=H
FOZ-NMe(H): R1=R2=R3=R4=NH(CH3), R5=R6=H
FOZ-NMe2(I): R1=R2=R3=R4=N(CH3)2, R5=R6=H
FOZ-NMe2-Cl(I1): R1=R2=R3=R4=N(CH3)2, R5=Cl, R6=H
FOZ-NMe2-2Cl(I2): R1=R2=R3=R4=N(CH3)2, R5=R6=Cl
FOZ-NMe2-F(I3): R1=R2=R3=R4=N(CH3)2, R5=F, R6=H
FOZ-NMe2-2F(I4): R1=R2=R3=R4=N(CH3)2, R5=R6=F
FOZ-NMe2-CN(I5): R1=R2=R3=R4=N(CH3)2, R5=CN, R6=H
FOZ-NMe2-2CN(I6): R1=R2=R3=R4=N(CH3)2, R5=R6=CN
FOZ-NMe2-NO2(I7): R1=R2=R3=R4=N(CH3)2, R5=NO2, R6=H
FOZ-NMe2-2NO2(I8): R1=R2=R3=R4=N(CH3)2, R5=R6=NO2
Figure 3. Structures and notations of designed uorenone derivatives.
the eect of enhanced electron donor capacity on the molecular
second-order NLO response. Finally, based on the molecule FOZ-
NMe2(I), one or two identical electron- accepting groups (-Cl,
-F, -CN, -NO2) were introduced at the positions of R5 and R6 to
obtain the molecules FOZ-NMe2-Cl(I1), FOZ-NMe2-2Cl(I2),
FOZ-NMe2-F(I3), FOZ-NMe2-F(I3), FOZ-NMe2-Cl(I1), FOZ-
NMe2-2Cl (I2), FOZ-NMe2-F(I3). FOZ-NMe2-2F(I4), FOZ-
NMe2-CN(I5), FOZ-NMe2-2CN(I6), FOZ-NMe2-NO2(I7), FOZ-
NMe2-2NO2(I8). For the sake of discussion, the corresponding
abbreviations in parentheses will be mainly used for discussion
below.
Frontier molecular orbital and state density
It is well known that the frontier molecular orbitals can be used
to reveal the relationship between photophysical properties and
geometric structures [45]. In addition, the HOMO–LUMO energy
gap (Egap) is one of the important parameters regulating optical
properties. Compounds with smaller energy gap might contribute
to more signicant second-order NLO response. As depicted in
Figure 4, the HOMO and LUMO energies are in the range of –4.95

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Japan J Res. (2023) Vol 4 Issue 3
to –4.24 eV and −2.76 to –2.18 eV, respectively. ese energies
supply the energy gap between 1.53 and 2.72 eV. e Egap variation
trend of molecule A-D is as follows: D(2.47eV) < C(2.50eV) <
B(2.51eV) < A(2.72eV). Also the energy gap decreased due to
the progressive increase in the electron-donating ability of the
substituent by the following order: I(2.06eV) < H(2.11eV) <
G(2.18eV) < F(2.31eV) < E(2.39eV). e Egap value of unilateral
substitution molecules I1, I3, I5 and I7 is 1.98, 1.97, 1.79 and
1.77eV respectively, which is smaller than molecule I(2.06eV).
Similarly, the Egap value of bilateral substitution molecules I2,
I4, I6 and I8 is 1.90, 1.88, 1.57 and 1.53eV, respectively. Hence,
incorporation of acceptor substitution is an eective way to
tune the Egap values. And the Egap values for molecules I8 have
obvious decrease, which can be attributed to the enhancement of
electron-accepting ability of acceptor. In addition, it can be seen
from Figure 4 that the frontier molecular orbital distributions of
these molecules are similar. For molecule A-I, the HOMOs are
delocalized on the entire molecular skeleton, whereas the LUMOs
are mainly located on the uorenone core, indicating that these
molecules are locally excited. With regard to molecules I1-I8, their
LUMO distributions are similar to those of molecule A-I, while the
HOMO are more distributed on the donors’ side of the uorenone
core than molecule A-I, indicating large amount of charge transfer
in these molecules. In conclusion, Egap can be eectively regulated
by extension of conjugated bridge and enhancement of donor
and acceptor intensity. In addition, these molecules have obvious
intramolecular charge transfer, which might contribute to large
second-order nonlinear optical response.
Figure 4. Frontier molecular orbital diagrams, energy levels (eV) and
HOMO–LUMO energy gaps (eV): (a) Molecules A-I, (b) Molecules
I1-I8.
Figure 5. Total and partial density of states of molecule A, D, I and I8.

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Japan J Res. (2023) Vol 4 Issue 3
A more detailed study of the relationship between the
geometric structures and electronic properties could be obtained
by analysis of density of states. erefore, the total density of
states (TDOS) and partial density of states (PDOS) calculations
of molecules A, D, I and I8 have been carried out. As described
in Figure 5, molecule A is divided into uorenone core and
triphenylamines (TPA), molecule D is divided into uorenone
core, triphenylamines (TPA) and oxazole-π bridge (OZ), and
molecule I is divided into uorenone core, triphenylamines
(TPA) and -NMe2 groups, oxazole-π bridge (OZ). e molecule
I8 is divided into three parts: uorenone core and -NO2 groups,
triphenylamines and- NMe2 group, oxazole π-bridge (OZ). e
results show that triphenylamines play a signicant role in the
formation of HOMO. However, for the LUMO, the uorenone
core is the main contribution. is phenomenon indicates that
these molecules might still have obvious charge transfer aer the
accumulation of crystals, and the electron density is transferred to
the uorenone core, which is in good agreement with the results
shown in the frontier molecular orbital diagram.
Static rst hyperpolarizability
e rst static hyperpolarizabilities of the studied molecules
A-I8 were calculated at CAM-B3LYP/6-31+G(d) level, and the
results are shown in Table 1. the total rst hyperpolarizability (βtot)
values of molecules A-D increase as the order of βtot(A)< βtot(B)<
βtot(C)< βtot(D). e βtot value of molecule D, which introduced
oxazole as the conjugated bridge, is about 6 times that of its parent
molecule A, indicating that using ve-membered heterocycles to
prolong the conjugated bridge is an eective method to enhance
the NLO response. For molecules D-I, the order of βtot values
is βtot(D) <βtot(E) <βtot(F) <βtot(G) <βtot(H) <βtot(I). is indicates
that the stronger the electron-donating ability, the higher the βtot
value of the molecules, and the strong electron-donating group
-NMe2 can signicantly increase the βtot value. For molecules
I1, I3, I5, I7 and I2, I4, I6, I8 their βtot values enhance with the
increased capacity of electron-withdrawing group. For the
unilateral substitution, the order of βtot values is βtot(I1)< βtot(I3)<
βtot(I5)< βtot(I7). For the bilateral substitution, the βtot values show
as βtot(I2)< βtot(I4)< βtot(I6)< βtot(I8). Moreover, the βtot values of
molecules I2, I4, I6, I8 are larger than that of molecules I1, I3,
I5, I7, showing that bilateral substitution might produces more
remarkable NLO response than unilateral substitution. Besides,
the βtot value of molecules I8 are about three times relative to
alkalide compounds Li+(calix[4]pyrrole)M− (M = Li and Na)
where β0 values of 10969 and 14772 a.u. [46]. is indicates that
molecule I8 is a good potential candidate for NLO materials.
In addition, the relationship between βtot and Egap is analyzed.
As shown in Figure 6, the variation trend of Egap is opposite to
that of βtot, which means that extending the conjugated bridge,
introducing the electron donors and acceptors can eectively
reduce the Egap and obtain a larger βtot value.
In order to understand the reason for the large second-order
NLO response of the studied molecules, we use two-level and
three-level models [47,48] for qualitative analysis. ese models
are derived from sum-of-state (SOS) [43,49], which is specically
expressed in the following formulas (8) and (9).
( ) ( )
0
3
00
00
22
=6 +12 6
sos
ZZ Z Z
ZZ Z
ii j j
i j ij
sos
f
E
i ij j
µ
β
µµ µ µ
µµ µ
β
∆⋅
∝∆
∆∆
+
∆ ∆∆ ∆
(8)
Molecule βx/a.u. βy/a.u. βz/a.u. βtot/a.u.
A -0.5 1610.7 -0.2 1610.7
B 381.9 7307.9 552.4 7338.7
C -205.1 7523.4 -460.2 7537.2
D -256.7 9095.2 -224.5 9180.9
E 199.6 11492.2 872.9 11527.1
F -51.3 14158.8 -676.5 14175.1
G 91.5 16396.2 1054.4 16430.3
H 566.9 18302.8 34.5 18311.6
I -2.8 19598.2 930.6 19620.3
I1 323.0 20185.3 -136.4 20188.4
I2 -116.2 20146.6 2910.6 20356.1
I3 730.3 21521.9 49.5 21533.9
I4 -1246.7 23381.6 2665.9 23566.1
I5 3190.4 25263.6 5.8 25464.2
I6 -2449.4 31149.5 -5491.2 31724.5
I7 -1894.8 25844.9 1291.6 25946.4
I8 -628.4 33738.5 233.3 33745.2
Table 1. Static total rst hyperpolarizability (βtot) and components of
frst hyperpolarizability (βi) for all studied molecules.
Figure 6. The relationship between the static rst hyperpolarizability (βtot) and the HOMO-LUMO energy gap (Egap)
(9)

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Japan J Res. (2023) Vol 4 Issue 3
It can be clearly seen from Equation (8)) that βsos value is related
to the electronic excitation energy (ΔE), oscillator strength (f0) and
the dierence of transition dipole moment between the ground
state and the crucial excited state (Δμ). e most important factor
is the excitation energy as βsos is proportional to the inversion of its
cubic. If two excited states are critical, they need to be discussed
using the three-level formula (9). e rst and third terms are the
separate contributions of the two excited states, and the second
term is the coupling term of the two excited states. e molecules
A,B,C,D,E,F,G,H,I,I7 and I8 was used as examples to perform
time-dependent density functional theory (TDDFT) calculations
at the same level as the rst static hyperpolarizability. First, the
convergence behavior between βsos and the number of excited
states was tested (Figure S1). e results show that molecule A
Molecule State ΔE/eV
B 4 3.50
C 4 3.48
D 4 3.51
E 2 3.45
F 2 3.41
G 2 3.32
H 2 3.27
I 2 3.22
I7 2 2.97
6 3.46
I8 2 2.70
5 3.25
Figure 7. Relationship between the βtot value (green circle) and the corresponding βsos values (red triangle).
Table 2. The crucial excited states and corresponding excitation energies.
does not have one or two crucial excited states, so it does not
meet the conditions of two-level or three-level model, while other
molecules have converged before 50 excited states. In addition,
the variation trend of βsos value (a.u.) shows the same trend as βtot
value (Figure 6), that is B(4037) < C(4132) < D(12369) < E(14161)
< F(14970) < G(15220) < H(16568) < I(17621) < I7(25189) <
I8(27625). In addition, two-level or three-level model analysis
revealed the crucial excited states and corresponding electronic
transition energy (ΔE) of these molecules (Table 2). Molecules I7
and I8 have two main excited states. Compared with the excited
states S6, S2 of molecule I7 has a lower transition energy, and
excited state S2 of Molecule I8 has a lower transition energy than
S5. erefore, excited states S2 with low transition energy are
mainly discussed below.
Molecule B C D E F G H I I7 I8
Dindex 1.274 1.368 2.341 2.623 2.894 3.367 3.656 3.965 4.338 4.540
tindex -1.034 -0.832 -0.395 -0.120 0.176 0.678 0.936 1.183 1.786 2.097
Table 3. The distance (Dindex in Å) and the separation degree (tindex in Å) between hole and electron of corresponding excited state.

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Japan J Res. (2023) Vol 4 Issue 3
Distribution of electron and hole
In the case of NLO materials, the degree of charge transfer (CT)
also aects the NLO response. e process of electron excitation
can be graphically described as electrons and holes. Remarkably,
these holes are formed where the electrons leave. To measure CT
length, the distance between electron centroid and hole (Dindex) is
dened by Equation 10. e larger Dindex is, the more obvious CT
is. In addition, tindex is used to describe the degree of separation
between electrons and holes in the direction of CT (Equation
11). e large tindex value usually corresponds to molecule with
signicant CT.
( )
/
index x y z
index index CT
CT CT
D DDD
tDH
HH
µ
= ++
= −
= ⋅
12
222
(10)
e Dindex and tindex values of molecules B,C,D,E,F,G,H,I,I7 and
I8 are shown in Table 3. e results show that Dindex and tindex values
show the same trend as βtot values. In addition, combined with the
distribution of electrons and holes (Figure 8), it can be shown
that there is a good separation of electrons and holes in these
molecules, resulting in an obvious intramolecular charge transfer
(ICT), which is conducive to enhancing the second-order NLO
response.
Conclusions
In this work, a series of novel D-π-A type uorenone derivatives
were investigated by DFT and TDDFT computational methods.
Results including their geometric structures, frontier molecular
orbitals, charge transfer directions and second-order NLO
properties were obtained. e calculated results show that the
HOMO-LUMO energy gap of the compounds can be eectively
reduced, the intramolecular charge transfer is remarkable,
and the second-order NLO response of the compounds can be
enhanced by extending the conjugated bridge and enhancing
the strength of the electron-donating or electron-withdrawing
substituents. In addition, all designed molecules have large βtot
values, and the molecule FOZ-NMe2-2NO2 (I8) has the largest
rst hyperpolarizability (βtot=33745a.u.), indicating that these
molecules are potential candidates for excellent NLO materials. It
is hoped that this work could provide benecial guidance for the
development of excellent NLO materials.
Figure 8. Distribution of electron and hole (plotted with isovalue 0.0005)
Acknowledgement
e authors would like to thank the National Key Research and
Development Program of China (2017YFB0203403) for nancial
support.
References
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Supplemental Information
Basis Sets HOMO/eV Error/% LUMO/eV Error/% Egap
Exp. - -4.91 - -2.19 - 2.72
Cal.
6-31G -4.92 -0.2 -2.31 -5.5 2.61
6-31+G -5.19 -5.7 -2.65 -21.0 2.54
6-31G(d) -4.90 0.2 -2.18 0.5 2.72
6-31+G(d) -5.19 -5.7 -2.55 -16.4 2.64
6-31+G(d,p) -5.20 -5.9 -2.56 -16.9 2.64
6-31++G(d,p) -5.20 -5.9 -2.55 -16.4 2.65
6-311++G(d,p) -5.25 -6.9 -2.58 -17.8 2.67
Table S1. Calculated HOMO (eV), LUMO (eV) energies and Egap(eV) of molecule FO52 with the same functional B3LYP combined with dierent
basis sets.
Functionals HOMO/eV Error/% LUMO/eV Error/% Egap
Exp. - -4.91 - -2.19 - 2.72
Cal.
B3LYP -4.90 0.2 -2.18 0.5 2.72
BhandHLYP -5.95 -21.2 -1.35 38.4 4.60
ωB97XD -6.72 -36.9 -0.44 79.9 6.28
M06-2X -6.09 -24.3 -1.32 39.7 4.77
CAM-B3LYP -6.15 -25.3 -0.96 56.2 5.19
Table S2. Calculated HOMO (eV), LUMO (eV) energies and Egap(ev) of molecule FO52 with the same basis set 6-31G(d) combined with dierent
functionals.same functional B3LYP combined with dierent basis sets.
Molecule Basis sets βtot/a.u. error(%)
A
6-31+G(d) 1610.7 -
6-31+G(d,p) 1607.2 0.2
6-31++G(d,p) 1599.1 0.7
6-311++G(d,p) 1593.2 1.0
D
6-31+G(d) 9180.9 -
6-31+G(d,p) 9131.7 0.5
6-31++G(d,p) 9094.3 0.9
6-311++G(d,p) 9270.3 1.0
I
6-31+G(d) 19620.3 -
6-31+G(d,p) 19653.7 0.2
6-31++G(d,p) 19401.9 1.0
6-311++G(d,p) 19512.2 0.6
I7
6-31+G(d) 25946.4 -
6-31+G(d,p) 25985.7 0.2
6-31++G(d,p) 25733.2 0.8
6-311++G(d,p) 26018.3 0.3
I8
6-31+G(d) 33745.2 -
6-31+G(d,p) 33795.1 0.2
6-31++G(d,p) 33541.9 0.6
6-311++G(d,p) 34054.3 0.9
Table S3. The static rst hyperpolarizability values of molecules A,D,I,I7,I8 obtained by employing CAM-B3LYP functional with varies basis
sets.
Supplemental Information

Supplemental Information
Figure S1. Convergent behavior of molecules A-I and molecules I7, I8 on the rst 50 excited states of the TDDFT calculation