Spectroscopic and theoretical optical properties of indoleninyl-substituted dibenzotetraaza[14]annulenes

Article abstract of DOI:10.1002/jhet.4074

Two new macrocyclic dibenzotetraaza[14]annulene (DBTAA) compounds with indolenine (5) and pyridoindolenine (6) moieties were synthesized and characterized by spectroscopy. Both DBTAAs exhibit strong UV-Vis absorption properties in the Soret band region. T

Full text of DOI:10.1002/jhet.4074

Spectroscopic and theoretical optical properties of indoleninyl-substituted
dibenzotetraaza[14]annulenes
a
b
c
d
Abdul Qaiyum Ramle *, Asli Karakas **, Abdul Kariem Mohd. Arof , Mustafa Karakaya ,
b
b
e
e
Mehmet Taser , Aysun Gozutok , Chee Chin Fei , Nurhidayatullaili Muhd. Julkapli , Wan
a
Jefrey Basirun ***
a
Department of Chemistry, University of Malaya, 50603 Kuala Lumpur, Malaysia.
b
Department of Physics, Faculty of Sciences, Selcuk University, 42049 Campus, Konya,
Turkey.
c
Department of Physics, University of Malaya, 50603 Kuala Lumpur, Malaysia.
d
Department of Energy Systems, Faculty of Engineering & Architecture, Sinop University,
5
7000 Sinop, Turkey.
e
Nanotechnology & Catalysis Research Centre (NanoCat), Institute of Postgraduate Studies,
0603, Kuala Lumpur, Malaysia.
5
Corresponding authors: qaiyum@um.edu.my. * (A. Q. Ramle),
akarakas@selcuk.edu.tr. ** (A. Karakas)
jeff@um.edu.my. *** (W. J. Basirun)
This article has been accepted for publication and undergone full peer review but has
not been through the copyediting, typesetting, pagination and proofreading process
which may lead to differences between this version and the Version of Record. Please
cite this article as doi: 10.1002/jhet.4074
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Abstract
Two new macrocyclic dibenzotetraaza[14]annulene (DBTAA) compounds with indolenine (5)
and pyridoindolenine (6) moieties were synthesized and characterized by spectroscopy. Both
DBTAAs exhibit strong UV-Vis absorption properties in the Soret band region. The theoretical
second-order non-linear optical (NLO) property, electric dipole moment (µ), dispersion–free
dipole polarizability (α) and first hyper-polarizability values were calculated by density
functional theory (DFT) and time dependent density functional theory (TDDFT). The ab-initio
quantum mechanical calculation by time-dependent Hartree–Fock (TDHF) method was utilized
to investigate the dynamic dipole polarizabilities, dynamic second-order, static and dynamic
third-order (γ) hyper-polarizabilities of the DBTAAs. The configuration interaction (CI)
technique of all doubly occupied molecular orbitals (MOs) possesses theoretically defined
single-photon absorption (OPA) specifications for the examined structures. The computed
maximum OPA wavelengths on both macrocyclic compounds coincide with the preceding
measurement outcomes.
Keywords: DBTAA; UV-Visible; Polarizability; Hyper-polarizability; DFT.
2
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1
. Introduction
Macrocyclic compounds based on porphyrin structures as optical materials have been
[
1,2]
widely explored and applied in important applications for the past few decades.
However a
similar analogue of porphyrin, the dibenzotetraaza[14]annulene (DBTAA) is seldom reported
and studied. Both structures consist of four nitrogen atoms in the inner ring which are easily
[3,4]
coordinated with a metal cation to form the metal complex.
DBTAA is classified as a Hückel
[
5,6]
anti-aromatic (4n) compound.
4n+2) with the π-electrons fully conjugated through the entire ring.
In contrast, the porphyrin molecule is a Hückel aromatic
[
7,8]
(
The geometry of
DBTAA is more flexible compared to the porphyrin, where the structure possesses a saddle-
shaped conformation with the introduction of a methyl group at the 1 and 3 positions of the
[
9,10]
propanediiminato moiety.
Besides, the DBTAA is easily synthesized by a simple [2+2]
Schiff base condensation reaction between a 1, 3-dicarbonyl and o-phenylene diamine
[
11]
reactants. However, changing the substituent at the meso-position of the DBTAA molecule is
quite challenging due to the limited synthetic possibilities.
The fundamental design of organic non-linear optical (NLO) structures is built on the π-
bond order in view of the overlapping effect of the π-orbital delocalization from the electronic
[
12-14]
charge dispersion.
The presence of electron-donor or acceptor substituents in the molecular
structure could promote the asymmetric electronic dispersion and consequently improve the
[
15-17]
NLO properties.
The quadratic NLO properties of organic compounds have been widely
3
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[18-20]
investigated due to their advantages in the synthesis of materials.
However, only few
delocalized π-electron systems with low optical transparencies could be utilized in useful
[
21]
applications such as optical wave guides and second-harmonic generators.
Furthermore,
efficient optical transmittance at the UV-Vis region is particularly preferable in a NLO crystal. In
addition to the linear optical and second-order NLO effects, the third-order optical nonlinearity
[
22,23]
gathers some interest.
third-harmonic generators (THG) and are optical limiting.
moments and the hyper-polarizability could be calculated by means of ab-initio computations
The third-order NLO systems have important applications such as
[
24,25]
The dipole and quadrupole
[
26,27]
using logically high correlation levels and suitable basis sets.
The DBTAA has promising NLO behavior and might possesses very interesting second
and third-order NLO properties. The NLO phenomena of the compounds could be preliminary
assessed via theoretical methodologies. The DFT and TDHF methodologies were performed on
the two DBTAA compounds to predict the second and third-order NLO responses of the
molecules. The theoretical computations of the linear optical, quadratic and cubic NLO
responses could provide accurate data for the synthesis of new and efficient DBTAA
compounds. Thus the objective of this work is to define the effects of microscopic second-order
and third-order optical nonlinearities of the DBTAA moieties. Apart from the NLO properties,
the HOMO-LUMO energies and energy band gaps of the first and second frontier MOs and the
electronic transition wavelengths belonging to the lowest lying electronic transitions were
attained by computational methods using the DFT/B3LYP and Cl processes, respectively. The
calculation results on the OPA wavelength were compared with the experimental results from
UV-Vis spectroscopy. The experimental details of the synthesis and characterization methods are
described in the electronic supporting information (ESI).
4
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2
. Computational studies
Computational studies include the assignment of electric dipole moments and tensor
components of static dipole polarizability and the first hyper-polarizability. Geometrical
optimizations were implemented on the DBTAA 5 and 6. The electric dipole moments,
dispersion-free dipole polarizabilities and the first hyper-polarizabilities were calculated after
generating the geometrical optimizations. The finite field (FF) method was used to calculate the
[
28]
µ, static α and β values.
The FF scheme introduces an apprehensible approach to the
[
29]
computation of the hyper-polarizability values. To achieve a certain polarizability and hyper-
polarizability level, the 6-31G(d) polarized basis set was used in this work and the results were
satisfactory. It is expected that this basis set could reveal the molecular structures in the near
[
30]
Hartree-Fock standard. The GAUSSIAN03W
program at the DFT/ B3LYP level with 6-
3
1G(d) polarized basis set were used to execute the geometrical optimizations, µ, static α and β
computations. The GaussView program was used as the interface program for the
GAUSSIAN03W in order to design the molecular models for both the macrocyclic DBTAA
compounds. The performance of the DFT techniques in the calculation of the electro-optical
[
31]
properties were investigated systematically in the literature.
The hyper-polarizability tensor
components of the organic and organometallic materials are extensively derived by means of the
[
32,33]
B3LYP function.
It is known that the subject functional generates the logical experimental
5
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[
34,35]
trends.
total first static hyper-polarizability) are as follows:
α> = (α + α + α ) / 3
The calculated averaged orientation (isotropic) dipole polarizability <α> and the βtot
[36]
(
<
(1)
(2)
xx
yy
zz
2
2
2 1/2
βtot = [(βxxx + βxyy + β ) + (β
+ βxzz + β ) + (β + βzxx + βzyy ) ]
yxx zzz
xzz
yyy
Computational methodologies are theoretical means for the calculation of hyper-polarizabilities.
The self-consistent field technique of the TDHF often generates the frequency-dependent hyper-
[
26]
polarizability values. The γ (0;0,0,0) at ω = 0 and α (-ω;ω), β (-2ω; ω, ω), γ (-3ω; ω, ω, ω)
computations at ω = 0.04282 atomic units (a.u.) (1064 nm) were achieved by the TDHF method
[
37]
with the 6-31G(d) basis set executed in the GAMESS program. The static third-order hyper-
polarizabilities are represented by γ (0;0,0,0) as stated above. The second-harmonic generation
(SHG) and THG groups in the TDHF method were utilized in the calculations of the β (-2ω; ω,
ω) and γ (-3ω; ω, ω, ω), respectively, at ω frequencies. The computations of dynamic quadratic
hyper-polarizabilities are frequently characterized by the style of β - V (β vector) which indicates
the vectorial portion of the second-order hyper-polarizability. The following equations were used
to calculate the β - V and averaged (isotropic) cubic hyper-polarizabilities

2
x
2
y
2 1 2
z

V  (     )
(3)
where  (i  x, y,z ) is designed by:
i
i  (1 3 )
(      )
(4)
(5)

ijj
jij
jji
jx, y,z



1 5


 xxxx  yyyy  zzzz  2

 xxyy  xxzz  yyzz


6
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The transition wavelength λmax with the lowest lying electronic transitions are indicated using the
CIDRT approach (configuration interaction including all doubly occupied MOs from the
Hartree-Fock reference determinant) of the TDHF procedure with 6-31G basis set executed in
the GAMESS program. Calculations of the dynamic dipole polarizabilities, hyper-polarizabilities
and maximum OPA wavelengths were accomplished on a PC with an Intel (R) core (TM) I7-
2
630QM operator, 5.8 GB RAM memory and 2 GHz frequency using Linux PC GAMESS
version running under Linux Fedora release 11 (Leonidas) environment. Besides, to perceive the
relevancy between the molecular structures and NLO behavior; the HOMOs, LUMOs and
HOMO-LUMO energy band gaps were derived from the GAUSSIAN03W program at the TD-
DFT/ B3LYP level utilizing the 6-31G(d) basis set. The energy band gap value of E for the first
g
and second frontier MOs is formulated as follows:
Eg = ELUMO – EHOMO
(6)
3
3
. Results and discussions
.1 Synthesis and characterizations
[38]
[39]
Scheme 1 shows that compounds 1 , 3 and 4 were synthesized according to the
literature. The reduction of 1 was catalyzed by SnCl .2H O in acidic media to produce diamine 2
2
2
in moderate yields. Subsequently, the crude diamine was used for the [2+2] condensation
reaction with diformyl 3 or 4, affording the desired macrocyclic DBTAA 5 or 6 in good yields.
The formation of macrocycle was achieved through the migration of double bonds from the
[
40]
pyrrole ring to the annulene ring. Additionally, the presence of linear octyloxyl group on the
dibenzo moiety enhances the solubility of the macrocycles in polar organic solvents of CH Cl,
3
7
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CH Cl , THF, acetic acid and pyridine. However, both compounds were insoluble in non-polar
2
2
hydrocarbons and alcoholic solvents.
<Scheme 1>
The structures of both macrocyclic compounds were confirmed by NMR spectroscopy,
where the two N-H ring protons of 5 and 6 appear as a triplet signal with similar J = 6.4 Hz at δ
1
4.96 and 15.10 ppm, respectively. Similarly, the four olefinic (N=CH) protons of 5 and 6
emerge as a doublet signal due to the coupling with the N-H ring protons, which is clearly
observed at δ values of 8.71 ppm (J = 6.0 Hz) and 8.92 ppm (J = 5.6 Hz), respectively. These
results confirm that the N-H ring exhibits the imine-enamine tautomerism conformation in the
[
41, 42]
solution, consistent with previous reports.
The FT-IR analysis of Fig. S11 and S12 (ESI),
-1
indicate that the N-H vibration signals of the inner ring are not clearly observed at ca. 3300 cm .
This is due to the N-H∙∙∙N intramolecular H-bonding interactions on the 1, 3-propanediiminato
-1
-1
fragments. Moreover, the presence of strong stretching bands at 1633 cm and 1632 cm are
assigned to the C=N annulene rings of 5 and 6, respectively. The two intense absorption bands at
-1
1
248-1249 and 1182-1184 cm ranges are correlated with the C-O-C stretching mode in the
dibenzo unit. Finally, the combination of the NMR and FT-IR spectroscopic results are in good
agreement with the proposed structures.
3
.2 UV-Vis absorption spectra
The UV-Vis absorption spectra for both macrocycles were recorded in CHCl solution
3
(5 µM concentration) between 300 nm to 650 nm and the electronic parameters are tabulated in
Table 1. As shown in Fig. 1, the most intense absorption Soret band for 5 is observed at 395 nm
8
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5
-1
-1
with a molar absorption coefficient, ε = 0.758 × 10 M cm . This spectrum displays a slight
bathochromic shift (ca. = 18 nm) in the presence of the electron donating octyloxyl group
[
43]
compared to the core indolenine-DBTAA structure. Furthermore, the spectrum of 6 exhibits a
bathochromic shift (ca. = 22 nm) compared to 5, due to extension of the π – conjugation system.
As a result, the HOMO-LUMO energy gap decreases by 0.063 eV. The most intense absorption
band of both macrocycles are assigned to the π-π* transition in the macrocylic DBTAA
[
44,45]
moiety,
whereas the weak absorption band at 339 nm of 6 is assigned to the π-π* transition
of the pyridoindolenine moiety. The calculated full-half width maximum (FWHM) of 6 is
broader than 5, indicating a strong absorption of light with a wide wavelength range.
<Figure 1>
<Table 1>
3
.3 Theoretical calculations
The geometrically optimized structures of 5 and 6 in Fig. S13 (ESI) were calculated by
the DFT/B3LYP method. The results show that both DBTAA structures are planar shaped and
[
46]
closely resembles the crystallographic data as tabulated in Table S1 (ESI). Moreover, to gain
some insight on the molecular orbital structures, the HOMO and LUMO energies for both
macrocycles have been examined and their electronic properties are presented in Table 2. As
shown in Fig. 2, the electron density of LUMOs of both DBTAAs are delocalized over the entire
annulene ring only, while the HOMOs are distributed around the indolenine and annulene ring.
Interestingly, the electron cloud of 6 at the LUMO+1 is clearly shifted to both sides of the
pyridoindolenine group as an extension of the π-conjugation in the structure. Unlike 5, the
9
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electron cloud did not change significantly compared to the LUMO. Moreover, the presence of
pyridoindolenine in the macrocyclic framework decreases the HOMO-LUMO gap of 6 by 0.05
eV compared to 5. This is due to the tuning of energy levels and the extension of the π –
conjugated system.
The electronic transitions of both macrocycles were calculated and the absorption
wavelength, oscillator strength and major contributions are presented in Table 3. Macrocycles 5
and 6 possess an intense simulated major absorption peak centered at λmax = 409.4 nm and 429.0
nm with a relatively high oscillator strength, f = 0.9150 and 0.8008, respectively. However, the
two calculated additional peaks of 5 at 486.8 nm and 620.5 nm, and 6 at 631.0 nm are absent in
the spectrum due to the extremely low f values. Furthermore, the simulated spectrum of 6 also
displays a bathochromic shift (ca. 20 nm) compared to 5, and is close to the experimental result
depicted in Fig. 1.
<Figure 2>
<Table 2>
<Table 3>
Table 4 shows the electric dipole moments of 5 and 6. As reported by Di Bella et al., the
computed ground level electric dipole moment of a tetraazamacrocyle ligand was 2.2 D by using
[47]
the INDO/S-SOS formalism. In comparison, we found that the μ value is roughly 1.3 and 2.7
times higher than the calculated data for 5 and 6, respectively. The differences in these values
could be due to the better π-electrons delocalization over the planar macrocycle. On the other
hand, the μ value of 6 is smaller than 5 which is attributed to the electron-donating effect of the
pyridoindolenine group.
1
0
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<Table 4>
The dispersion-free dipole polarizabilities, the second and third-order hyper-
polarizabilities data are tabulated in Table 5-7, respectively. As can be observed, the theoretical
results of static <α>, βtot and <γ> shows a decrease in 5 compared to 6. Compared to the
published literature, the calculated values of βtot for 5 and 6 are 9.6 and 15.5 times higher
-30
[47]
compared to the tetraazamacrocyle ligand (β = 4.3×10 esu), respectively.
This is because
both DBTAAs possess better charge transfer character due to the electron rich structures. Also,
the decrease of the HOMO-LUMO energy gap from the effect of the substituent groups might
[48,49]
contribute to a higher βtot value.
Interestingly, 6 has a larger βtot value compared to
-30
experimental values of various substituted metal free phthalocyanines (β = 25.1 – 44.9 ×10
[
50]
esu). Hence, 6 could be useful for NLO applications.
<Table 5>
<Table 6>
<Table 7>
Generally, the quadratic and cubic hyper-polarizability parameters strongly influence the
electro-optical coefficients. Both are dependent on the shape and size of the material and electron
delocalization around the charge transfer transmission. The NLO parameters are also affected by
the optical field frequencies. As shown in Table 8-10, the magnitudes of the frequency-
dependent dipole polarizabilities, second and third-order hyper-polarizabilities of 5 are lower
than 6. This indicates an identical decrease with the static ones. The involvement of the π –
1
1
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conjugated pyridoindolenine group enhances the static and dynamic <α>, β , β – V, and <γ>
tot
values of 6 compared to 5 (Table 5-10). Thus, an increase in the second and third-order NLO
properties of 6 is observed. The cubic hyper-polarizability, <γ> value of 6 is twice larger
compared to 5, which confirms that the introduction of a π – conjugated group in the DBTAA
structure increases the magnitude and molecular dipole moment parameter, which consequently
[
51]
improves the NLO properties.
<
Table 8>
Table 9>
<
<Table 10>
4
. Conclusions
In summary, two new DBTAAs were synthesized in good yields and successfully
characterized by NMR, IR and UV-Vis. The geometry of both DBTAAs were optimized by the
DFT method which suggests a planar structure. The simulated UV-Vis spectra and the calculated
HOMO-LUMO band gap for both DBTAAs matches well with the experimental results.
DBTAA 6 exhibits higher static and dynamic β , β – V, <γ> values and thereby possesses better
tot
second and third-order NLO properties compared to DBTAA 5. For future work, the
experimental and computational designs via structural modification of the DBTAA structures are
needed to improve NLO properties, as well as to discover the potential NLO applications.
5
. Acknowledgements
1
2
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This work is supported by Ministry of Higher Education, Malaysia (Grants: ST027-2019
and ST011-2019). The authors declare that there is not conflict of interest.
6
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Figure and table captions
Scheme 1: Synthetic routes of DBTAA 5 and 6. Reagents and conditions: (i) 1) EtOH, 37% HCl,
o
SnCl .2H O, 70 C, N , 16 h. 2) 4 M NaOH.; (ii) EtOH, AcOH, reflux, N , 6 h.
2
2
2
2
1
8
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Figure 1: Experimental UV-Vis absorption spectra of 5 and 6 measured in CHCl solution. The
3
solid and dashed lines indicate the main experimental and simulation absorption peaks,
respectively.
Figure 2: The frontier MOs of 5 and 6 calculated by DFT.
Table 1: Electronic paramerters of 5 and 6.
Table 2: Calculated first HOMO, LUMO and second HOMO-1, LUMO+1 frontier MO energies
and E for 5 and 6 using DFT method at B3LYP/6-31G(d) level.
g
Table 3: Calculated absorption wavelengths, oscillator strengths and major compositions in
terms of MO contributions for 5 and 6.
Table 4: Calculated electric dipole moments, μ (Debye) and dipole moment components for 5
and 6 using DFT method at B3LYP/6-31G(d) level.
-24
Table 5: Selected components of the static α(0;0) and <α>(0;0) (10 esu) values for 5 and 6
computed by DFT method at B3LYP/6-31G(d) level.
-30
Table 6: Selected components of the static β(0;0,0) and β (0;0,0) (10 esu) values for 5 and 6
tot
computed by DFT method at B3LYP/6-31G(d) level.
1
9
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-37
Table 7: All static γ(0;0,0,0) components and <γ>(0;0,0,0) (10 esu) values for 5 and 6
computed by TDHF method with 6-31G(d) basis set.
Table 8: Selected components of the frequency-dependent α(-ω;ω) and absolute values of <α>(-
-24
ω;ω) (10 esu) at ω = 0.04282 a.u for 5 and 6 computed by TDHF method with 6-31G(d) basis
set.
-30
Table 9: Selected components of the frequency-dependent β(-2 ω; ω, ω) and β – V (10 esu)
values at ω = 0.04282 a.u for 5 and 6 computed by TDHF method with 6-31G(d) basis set.
Table 10: Selected components of the frequency-dependent γ(-3ω; ω, ω, ω) and absolute values
-
37
of <γ>(-3ω; ω, ω, ω) (10 esu) at ω = 0.04282 a.u for 5 and 6 computed by TDHF method with
-31G(d) basis set.
6
2
0
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Table 1: Electronic paramerters of 5 and 6.
Compound
Absorption λmax (nm) /
λonset (nm)
Egap (eV)
FWHM
(nm)
5
-1
-1
ε (×10 M cm )
395 (0.758)
5
6
481
493
2.578
2.515
75.0
339 (0.348), 417 (0.766)
78.5
2
1
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Table 4: Calculated electric dipole moments, μ (Debye) and dipole moment components for 5
and 6 using DFT method at B3LYP/6-31G(d) level.
Compound
μx
μy
μz
μ
5
6
0.000
0.000
0.000
0.000
-1.726
-0.814
1.726
0.814
2
2
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-30
Table 9: Selected components of the frequency-dependent β(-2 ω; ω, ω) and β – V (10 esu)
values at ω = 0.04282 a.u for 5 and 6 computed by TDHF method with 6-31G(d) basis set.
Compound
βxxx
0.0
0.0
βyyy
0.0
0.0
βzzz
1.5
1.8
βx
βy
βz
β – V
52.6
85.9
5
6
0.0
0.0
0.0
0.0
52.6
85.9
-24
Table 5: Selected components of the static α(0;0) and <α>(0;0) (10 esu) values for 5 and 6
computed by DFT method at B3LYP/6-31G(d) level.
Compound
αxx
αyy
αzz
<α>
5
6
175.1
206.3
194.2
214.9
79.6
81.9
149.6
167.7
2
3
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-37
Table 7: All static γ(0;0,0,0) components and <γ>(0;0,0,0) (10 esu) values for 5 and 6
computed by TDHF method with 6-31G(d) basis set.
Compound
γxxxx
γyyyy
γzzzz
29.4
31.3
γxxyy
576.8
753.0
γxxzz
62.6
91.1
γyyzz
317.3
428.7
<γ>
5
6
1306.4
2007.3
3254.9
5586.5
1300.8
2034.1
2
4
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Table 10: Selected components of the frequency-dependent γ(-3ω; ω, ω, ω) and absolute values
-37
of < γ>(-3ω; ω, ω, ω) (10 esu) at ω = 0.04282 a.u for 5 and 6 computed by TDHF method with
-31G(d) basis set.
6
Compound
γxxxx
γyyyy
γzzzz
74.4
γxxyy
γxxzz
146.5
231.3
γyyzz
778.0
1502.6
<γ>
5
6
3025.0
4606.6
8268.0
19711.4
1273.9
2029.2
3126.8
6526.5
116.2
2
5
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Table 2: Calculated first HOMO, LUMO and second HOMO-1, LUMO+1 frontier MO energies and E for 5
g
and 6 using DFT method at B3LYP/6-31G(d) level.
Compound HOMO (eV) LUMO (eV) HOMO-1 (eV) LUMO+1 (eV)
Eg (eV)
2.65
5
6
-4.33
-4.27
-1.68
-1.67
-5.06
-4.95
-1.24
-1.39
2.60
2
6
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Table 3: Calculated absorption wavelengths, oscillator strengths and major compositions in
terms of MO contributions for 5 and 6.
Compound
State
Calculated absorption
Oscillator
strength (f)
0.0011
Major
λ (nm)
620.5
486.8
contribution
5
Excited state 1
Excited state 2
HOMO→LUMO
HOMO-1→LUMO
HOMO→LUMO+1
HOMO-1→LUMO
HOMO→LUMO+1
HOMO→LUMO+2
HOMO→LUMO
HOMO-1→LUMO
HOMO→LUMO+1
HOMO→LUMO+2
0.0800
Excited state 3
409.4
0.9150
6
Excited state 1
Excited state 2
631.0
429.0
0.0013
0.8008
Excited state 3
347.5
0.4104
2
7
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-30
Table 6: Selected components of the static β(0;0,0) and β (0;0,0) (10 esu) values for 5 and 6
tot
computed by DFT method at B3LYP/6-31G(d) level.
Compound
βx
βy
βz
βtot
5
6
0.0
0.0
0.0
0.0
41.3
66.5
41.3
66.5
2
8
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Table 8: Selected components of the frequency-dependent α(-ω;ω) and absolute values of <α>(-
-24
ω;ω) (10 esu) at ω = 0.04282 a.u for 5 and 6 computed by TDHF method with 6-31G(d) basis
set.
Compound
αxx
103.8
126.8
αyy
116.3
126.6
αzz
41.2
41.9
<α>
87.1
98.5
5
6
2
9
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Figure 1
3
1
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