TD-DFT benchmark for UV-Vis spectra of coumarin derivatives
Cite this paper: Vietnam J. Chem., 2021, 59(2), 203-210
DOI: 10.1002/vjch.202000200
Article
TD-DFT benchmark for UV-Vis spectra of coumarin derivatives
Mai Van Bay1,2, Nguyen Khoa Hien3, Phan Thi Diem Tran3, Nguyen Tran Kim Tuyen4,
Doan Thi Yen Oanh5, Pham Cam Nam6*, Duong Tuan Quang1*
1University of Education, Hue University, 34 Le Loi, Hue City, Thua Thien Hue 49000, Viet Nam
2The University of Danang- University of Science and Education, 41 Le Duan, Hai Chau, Da Nang City
50000, Viet Nam
3Mientrung Institute for Scientific Research, Vietnam Academy of Science and Technology, 312 Huynh Thuc
Khang, Phu Hoa, Hue City, Thua Thien Hue 49000, Viet Nam
4Kontum Community College, 704 Phan Dinh Phung, Kon Tum City, Kon Tum 60000, Viet Nam
5Publishing House for Science and Technology, Vietnam Academy of Science and Technology, 18 Hoang
Quoc Viet, Cau Giay, Hanoi 10000, Viet Nam
6The University of Danang - University of Science and Technology, 41 Le Duan, Hai Chau, Da Nang City
50000, Viet Nam
Submitted December 9, 2020; Accepted December 30, 2020
Abstract
The predictive performances for maximum absorption wavelength of the PBE, BP86, PBE0, B3LYP, M06, M06-
2X, CAM-B3LYP, LC-wPBE, APDF, wB97XD, and PW6B9D3 functionals have been benchmarked through
comparison of maximum absorption wavelength values between calculation and experiment of 21 coumarin derivatives.
For the results obtained from direct calculation by these functionals, the predictive performance decreases gradually in
the following order: B3LYP > APDF > M06 > PW6B9D3 > PBE0 > BP86 > PBE > M06-2X > CAM-B3LYP >
wB97XD > LC-wPBE. B3LYP functional gives the best predictive performance, with the smallest value of the mean
absolute error (MAE = 15 nm) and the root mean square deviation (RMSD=19 nm). When using the results obtained
through correction based on the linear correlation, the predictive performance decreases gradually in the following
order: M06-2X > PBE0, M06, PW6B9D3 > B3LYP, APDF > CAM-B3LYP, LC-wPBE, wB97XD > PBE and BP86.
M06-2X functional gives the best predictive performance, with the smallest values of MAEfix (7 nm) and RMSDfix
(9nm). The correction is very necessary because the values of the corrected maximum absorption wavelengths are
closer to the experimental maximum absorption wavelengths. The values of MAEfix and RMSDfix are much smaller than
those of MAE and RMSD.
Keywords. DFT, TD-DFT, UV-Vis, coumarin, benchmark.
1. INTRODUCTION
and fluorescence spectra is necessary in order to
provide a scientific basis for the design and
Coumarins are from the benzoryrone family, an development
important class of phytochemicals. Over 1300 thesederivatives.[3,7,8]
different coumarin derivatives have been identified, Based on methods of electronic structure theory
of
new
materials
from
including natural and synthetic derivatives.[1] for studying the electron excited states, theoretical
Coumarin derivatives are widely used in medicine, calculations allow predicting quite accurately optical
food, and industry.[2] In particular, many properties of molecules. Some recent publications
applications are based on the outstanding optical show that the UV-Vis spectra of some large organic
properties of coumarin derivatives such as dyes, molecules are predictable with high accuracy and
color indicators, sunscreens, organic light-emitting reasonable computing costs by using the time-
diodes, fluorescent markers, and fluorescence dependent density functional theory (TD-DFT)
sensors[3-6] Therefore, the prediction of the optical method. Therefore, TD-DFT is the current popular
properties of coumarin derivatives such as UV-Vis method for calculation of the electron excited states
203 Wiley Online Library © 2021 Vietnam Academy of Science and Technology, Hanoi & Wiley-VCH GmbH
Vietnam Journal of Chemistry
Duong Tuan Quang et al.
of large molecules[9-13] So far, many DFT methods for calculation of the UV-Vis spectra of 20
(pure, hybrid, long-range-corrected, dispersion conjugated organic compounds in solvent.[18] The
corrected, etc.) have been developed.[14] However, results show that B3LYP functional gives the
accurate prediction of UV-Vis spectra using DFT smallest mean signed error (MSE) and mean
methods depends on the structure of molecules. unsigned error (MUE) for the position of absorption
Therefore, it is necessary to choose suitable DFT peaks, but is not the most efficient in terms of root
functional for each group of compounds to get the mean square deviation (RMSD) or largest standard
accurate calculation results.[15,16] Denis Jacquemin et deviation (SD). Meanwhile, M06-2X functional
al. used 29 DFT functionals to predict the UV-Vis provides the most appropriate results with the
spectra of about 500 compounds including bio- experiment for the band shapes corresponding to the
organic molecules and dyes. The obtained results absorption spectra of conjugated compounds.[18] So
were compared with the previous theoretical far, some studies, but not many, have been
calculations or experimental measurements. The successful in using TD-DFT method to calculate the
results show that the predictive performance of the UV-Vis spectra of coumarin derivatives.[19,20]
DFT functionals strongly depends on the molecular
In this work, the predictive performances of the
structure of organic compounds. For example, PBE0 PBE, BP86, PBE0, B3LYP, M06, M06-2X, CAM-
and LC-ωPBE(20) give very good results in B3LYP, LC-wPBE; APDF, wB97XD, and
predicting the UV-Vis spectra of many neutral PW6B9D3 functionals for maximum absorption
organic dyes but are completely inconsistent with wavelength of 21 coumarin derivatives (figure 1) are
cyanine-like derivatives.[17] Azzam Charaf-Eddin et benchmarked through comparison of maximum
al used the six hybrid functionals, including B3LYP, absorption wavelength values between calculation
PBE0, M06, M06-2X, CAM-B3LYP and LC-PBE and experiment.
Figure 1: Coumarin derivatives for this investigation
Vietnam Journal of Chemistry
TD-DFT benchmark for UV-Vis spectra of…
2. COMPUTATIONAL METHODS
root mean square error, RMSE) are frequently used
to evaluate the performance of these models.[24] The
In this study, the optimized geometry of all mean signed error (MSE) (or average signed
difference, MSD) is also used for the purpose of
examining the direction of the errors.[14,25] In
addition, the linear correlation relationship between
the experimental and the calculated values of the
maximum absorption wavelength is also used to
evaluate the method's predicted performance.[26]
molecules in the ground state is carried out by using
density functional theory (DFT) at the PBE0/6-
311++G(d,p) level of theory.[15] Here, it should be
emphasized that the PBE0 density functional has
been evaluated to accurately predict the geometrical
structure of most of the organic molecules in the
ground states.[21] The UV-Vis spectra of coumarin
derivatives are carried out by using time-dependent
density functional theory (TD-DFT)[9,10] at the X/6-
311++G(d,p) level of theory, where X: PBE, BP86,
PBE0, B3LYP, M06, M06-2X, CAM-B3LYP, LC-
wPBE; APDF, wB97XD and PW6B9D3. The
polarizable continuum model (PCM) is applied for
all DFT and TD-DFT calculations, with the solvent
used in the calculations being the same as that used
in the experiment.[22] All calculations are performed
using Gaussian 16 Revision A.03 program.[23]
Then, the corrected calculated maximum absorption
wavelength
is also determined based on the
linear correlation equations between
and
.
The predictive performance of DFT
functionals is once again evaluated through
[14,25]
comparison between values of
and
.
3. RESULTS AND DISCUSSION
3.1. TD-DFT benchmark based on comparison
between the
and
The predictive performance of DFT functionals
for maximum absorption wavelength of coumarin
derivatives is benchmarked through comparison
The results of calculation of maximum absorption
wavelength of 21 coumarin derivatives using 11
DFT functionals, difference between the calculated
maximum absorption wavelength and the
experimental maximum absorption wavelength
(Δλmax), and statistical analysis data of MAE,
RMSM, and MSE are presented in table 1 and
figure 2.
between the calculated maximum absorption
wavelength (
) and experimental maximum
absorption wavelength (
). In this case, both the
mean absolute error (MAE) (or mean unsigned error,
MUE), and root mean square deviation (RMSD) (or
70
50
62
49
45
43
30
29
29
29
30
10
23
22
20
21
15
-10
-30
-50
-70
-12
-19
-21
-20
-22
-42
-45
-49
MSE MAE
-62
Figure 2: Graph of MSE and MAE values by DFT functionals based on comparison between the
and
of coumarin derivatives
Vietnam Journal of Chemistry
Table 1: Results of comparison between the
Duong Tuan Quang et al.
of coumarin derivatives
and
Δλmax =
-
(nm)
CAM-
B3LYP wPBE
Compound
LC-
PW6B9
D3
PBE
BP86 PBE0 B3LYP M06 M06-2X
APDF wB97XD
[Ref]
M1
M2
M3
M4
M5
M6
M7
M8
M9
M10
M11
M12
M13
M14
M15
M16
M17
M18
M19
M20
M21
MSE
MAE
RMSD
6
6
-26 -19 -20 -39 -36 -48 -24 -38 -25
-11 -9 -19 -10
326
[27]
[27]
[27]
[27]
[27]
[27]
[27]
[27]
[27]
[27]
[27]
[27]
[27]
[27]
[27]
[27]
[27]
[27]
[27]
[27]
[27]
30 30
1
7
6
3
2
280
351
384
360
324
355
370
376
400
373
459
436
436
408
420
376
278
340
445
436
22 21 -24 -15 -21 -41 -41 -56 -21 -43 -22
25 25 -28 -17 -25 -52 -50 -70 -24 -54 -27
46 46
23 22 -15
17 16 -20 -13 -16 -35 -33 -45 -18 -35 -19
50 49 -13
50 49 -15
46 45 -16
39 38 -22 -11 -22 -46 -47 -64 -18 -50 -21
16 17 -38 -27 -37 -63 -66 -88 -35 -70 -38
25 25 -37 -25 -37 -59 -61 -79 -33 -65 -36
36 37 -23 -11 -21 -50 -52 -75 -19 -57 -23
32 32 -28 -17 -26 -52 -55 -75 -25 -59 -28
-8
3
-4 -28 -26 -42
-5 -29
-7
-8 -11 -31 -29 -42 -13 -31 -14
-2 -13 -39 -39 -59
-9 -43 -13
-4 -16 -42 -43 -63 -11 -47 -15
-5 -16 -42 -43 -64 -14 -47 -16
4
4
-46 -36 -45 -64 -66 -81 -43 -69 -44
63 63 -11
34 34
53 52
-5
0
3
10
6
-11 -43 -44 -65
-7 -49 -11
3
-3
11
0
3
-57 -67
5
0
-59
-26
3
-3
-27 -25 -41
-6 -50 -41 -48 -66 -68 -83 -47 -71 -48
-46 -37 -44 -62 -64 -81 -43 -68 -44
0
29 29 -22 -12 -20 -42 -45 -62 -19 -49 -21
30 29
34 34
23
27
15
19
21
25
43
46
45
48
62
65
20
24
49
51
22
26
The calculation results show that the DFT functional for other derivatives.[14,25] This indicates
functionals used to predict the maximum absorption that it is necessary to choose right functionals for
wavelength of coumarin derivatives can be divided each compound. The studied results also show that
into three groups with different performance. The there is no difference between MAE and RMSD
best performing group includes 5 functionals, sorted when using them for these model evaluation studies.
in descending order B3LYP (MAE = 15, RMSD =
19) > APDF (MAE = 20, RMSD = 24) > M06
(MAE = 21, RMSD = 25) > PW6B9D3 (MAE = 22,
RMSD = 26) > PBE0 (MAE = 23, RMSD = 27).
When considering the direction of the errors,
PBE and BP86 functionals give values of
systematically higher than the values of
.
Meanwhile, the remaining functionals give values of
The average performing group includes
2
systematically smaller than the values of
. The results indicate that the values of λmax
functionals, sorted in descending order BP86 (MAE
= 29, RSMSD = 34) > PBE (MAE = 30, RMSD =
34). The worst performing group includes 4
functionals, sorted in descending order M06-2X
(MAE = 43, RMSD = 46) > CAM-B3LYP (MAE =
45, RMSD = 48) > wB97XD (MAE = 49, RMSD =
51) > LC-wPBE (MAE = 62, RMSD = 65).
In this study, B3LYP and PBE0 belong to the
group of functionals that give the best predictive
performance of the maximum absorption
systematically obey the order of PBE > BP86 >
B3LYP > APDF > M06 > PW6B9D3 > PBE0 >
M06-2X > CAM-B3LYP > wB97XD > LC-wPBE.
3.2. TD-DFT benchmark based on comparison
between the (
) and (
)
The results of the linear correlation analysis between
experimental maximum absorption wavelength and
calculated maximum absorption wavelength are
shown in figure 3. The results show that all the DFT
functionals used above yield a very good linear
wavelength,
consistent
with
previous
publications.[14,25] B3LYP functional gives better
performance than PBE0 functional for coumarin
derivatives, whereas in some previous studies, PBE0
functional gave better performance than B3LYP
correlation between
and
. The evidence is
Vietnam Journal of Chemistry
TD-DFT benchmark for UV-Vis spectra of…
that the linear correlation coefficient (R) ranges from equation y = x. Meanwhile, the remaining
0.932 to 0.982, sorted in descending order functionals result in all the points on the graph as
corresponding to the functionals as follows: M06-2X being above a line with the equation y = x. This
(R = 0.982) > PW6B9D3 (R = 0.979) > M06 (R = shows that whole recommended DFT functionals
0.977) > PBE0 (R = 0.976) > APDF (R = 0.975) > give the calculated maximum absorption wavelength
B3LYP (R = 0.971) > CAM-B3LYP (R = 0.967) > systematically larger, or smaller than the
LC-wPBE (R = 0.9654) > wB97XD (R = 0.9649) > experimental maximum absorption wavelength.
BP86 (R = 0.933) > PBE (R = 0.932). Thus, if it is
On the basis of the linear relationship between
based on MAE and RMSE (obtained from experimental maximum absorption wavelengths and
calculated maximum absorption wavelengths (figure
3), the calculated maximum absorption wavelengths
can be determined according to the equations in
table 2. The calculated differences between the
comparison between
and
), M06-2X
belongs to the group of functionals with the worst
predictive performance (with the largest error), but
from linear correlation analysis, M06-2X belongs to
the group of functionals with the best predictive
performance (with the largest linear correlation
coefficient). When considering the direction of the
errors, the PBE and BP86 functionals result in all the
points on the graph as being below a line with the
corrected
calculated
maximum
absorption
wavelengths and experimental maximum absorption
wavelengths ∆
and statistical analysis data of
MAE, RMSM, and MSE are presented in table 3 and
figure 4.
Figure 3: Diagrams of linear correlation between the
and
The calculation results show that the MAEfix the RMSDfix values decrease from 37.1 % (B3LYP)
values decrease from 33.8 % (B3LYP) to 84.6 % to 79.8 % (M06-2X) compared to those without
(LC-wPBE) compared to those without correction, correction. The values of MAEfix and RMSDfix obey
Vietnam Journal of Chemistry
Duong Tuan Quang et al.
a M06-2X (MAEfix = 7, RMSDfix = 9) < PBE0, M06, maximum absorption wavelength of coumarin
PW6B9D3 (MAEfix = 9, RMSDfix = 11) < B3LYP, derivatives. These results show the importance of
APDF (MAEfix = 10, RMSDfix = 12) < CAM- correcting the calculated results for the maximum
B3LYP, LC-wPBE, wB97XD (MAEfix = 10, absorption wavelength of coumarin derivatives by
RMSDfix = 13) < PBE, BP86 (MAEfix = 15, RMSDfix TD-DFT, in order to obtain the values of corrected
= 19) order. These results indicate that M06-2X maximum absorption wavelength that are closer to
functional gives the best predictive performance for experimental maximum absorption wavelengths.
Table 2: Equations for calculation of
according to
of DFT functionals
Functionals
Equations
PBE
- 17.802
BP86
- 16.424
- 66.822
- 59.939
- 89.388
- 93.783
- 24.851
PBE0
B3LYP
M06
M06-2X
CAM-B3LYP
LC-wPBE
APDF
- 31.871
- 65.196
- 28.301
wB97XD
PW6B9D3
- 69.671
70
60
50
40
30
20
10
0
62
MAE without fixing
MAE with linear fixing
49
45
43
30
15
29
23
15
22
21
20
15
10
10
9
10
9
10
9
9
7
Figure 4: Graph of MAE values with/without linear fixing
4. CONCLUSION
between
and
. For the results obtained
from direct calculation by functionals, B3LYP
functional gives the best predictive performance of
the maximum absorption wavelengths, with the
smallest values of MAE and RMSD. However,
when using the results obtained through correction
based on the linear correlation between the
experimental maximum absorption wavelengths and
the calculated maximum absorption wavelengths,
the M06-2X functional gives the best predictive
performance, with the smallest values of MAEfix and
The predictive performances of the PBE, BP86,
PBE0, B3LYP, M06, M06-2X, CAM-B3LYP, LC-
wPBE; APDF, wB97XD, and PW6B9D3
functionals for maximum absorption wavelength
have been benchmarked through comparison of
maximum absorption wavelength values between
calculation and experiment of 21 coumarin
derivatives. The results show that all the DFT
functionals yield a very good linear correlation
Vietnam Journal of Chemistry
TD-DFT benchmark for UV-Vis spectra of…
RMSDfix. This correction is very necessary because maximum absorption wavelengths. The values of
the values of the corrected maximum absorption MAEfix and RMSDfix are much smaller than MAE
wavelengths are closer to the experimental and RMSD.
Table 3: Results of comparison between the
and
of coumarin derivatives
=
-
(nm)
Compounds
M1
M2
M3
M4
M5
M6
M7
M8
M9
-21
4
-6
-4
17
-4
-11
20
20
16
10
-15
-6
-21
4
-7
-4
17
-5
-12
20
20
15
9
-14
-5
6
-18
4
-18
4
-8
-4
15
-5
-16
4
-16
4
-9
-11
13
-6
1
2
0
0
23
0
-4
20
9
10
6
3
3
27
0
-8
21
10
16
2
-2
4
-4
-9
-4
1
-8
-12
-4
-36
16
-7
-7
0
-18
4
-9
-5
13
-5
1
25
1
-5
20
9
11
5
2
-18
4
-9
-6
13
-5
-3
9
-10
-5
15
-5
-2
7
-8
-5
14
-4
-3
9
-5
-4
11
10
13
1
-1
-4
13
0
-20
18
7
14
-21
-18
0
10
12
11
10
12
0
-1
-3
14
0
-20
15
6
15
-19
-16
0
10
12
9
4
8
M10
M11
M12
M13
M14
M15
M16
M17
M18
M19
M20
M21
MSEfix
MAEfix
RMSDfix
13
-1
1
-4
14
0
-19
14
6
14
-18
-15
0
12
-4
2
-5
16
1
-20
11
10
14
-16
-14
0
9
-7
4
8
7
12
-1
0
-3
13
-1
-18
13
5
13
-16
-14
0
-3
-8
-7
4
-5
-16
1
-35
17
-13
-10
0
-3
-7
-7
3
-6
-15
-1
-36
19
-12
-10
0
0
5
2
13
-1
-13
-2
23
6
-6
-4
0
2
-26
33
7
24
-35
-30
0
-25
33
8
24
-36
-30
0
15
19
15
19
9
11
9
11
7
9
10
13
10
13
10
13
9
11
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Acknowledgment. This research was funded by the
Vietnam National Foundation for Science and
Technology Development (NAFOSTED) under grant
number 104.06-2017.51 (Duong Tuan Quang).
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Corresponding authors: Duong Tuan Quang
University of Education, Hue University
34 Le Loi, Hue City, Thua Thien Hue 49000, Viet Nam
E-mail: duongtuanquang@gmail.com.
Pham Cam Nam
The University of Danang - University of Science and Education
41 Le Duan, Hai Chau, Da Nang City 50000, Viet Nam
E-mail: pcnam@dut.udn.vn.
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