Triphenylamine-based fluorescent NLO phores with ICT characteristics: Solvatochromic and theoretical study

Article abstract of DOI:10.1016/j.molstruc.2017.08.084

The static first and second hyperpolarizability and their related properties were calculated for triphenylamine-based “push-pull” dyes using the B3LYP, CAM-B3LYP and BHHLYP functionals in conjunction with the 6-311+G(d,p) basis set. The electronic coupling for the electron transfer reaction of the dyes were calculated with the generalized Mulliken-Hush method. The results obtained were correlated with the polarizability parameter α_CT, first hyperpolarizability parameter β_CT, and the solvatochromic descriptor of ?γ? _SD obtained by the solvatochromic method. The dyes studied show a high total first order hyperpolarizability (70–238 times) and second order hyperpolarizability (412–778 times) compared to urea. Among the three functionals, the CAM-B3LYP and BHHLYP functionals show hyperpolarizability values closer to experimental values. Experimental absorption and emission wavelengths measured for all the synthesized dyes are in good agreement with those predicted using the time-dependent density functional theory. The theoretical examination on non-linear optical properties was performed on the key parameters of polarizability and hyperpolarizability. A remarkable increase in non-linear optical response is observed on insertion of benzothiazole unit compared to benzimidazole unit.

Full text of DOI:10.1016/j.molstruc.2017.08.084

Accepted Manuscript
Triphenylamine-based fluorescent NLO phores with ICT characteristics:
Solvatochromic and theoretical study
Santosh B. Katariya, Dinesh Patil, Lydia Rhyman, Ibrahim A. Alswaidan, Ponnadurai
Ramasami, Nagaiyan Sekar
PII:
S0022-2860(17)31151-1
10.1016/j.molstruc.2017.08.084
MOLSTR 24222
DOI:
Reference:
To appear in: Journal of Molecular Structure
Received Date: 7 January 2017
Revised Date: 1 August 2017
Accepted Date: 23 August 2017
Please cite this article as: S.B. Katariya, D. Patil, L. Rhyman, I.A. Alswaidan, P. Ramasami, N. Sekar,
Triphenylamine-based fluorescent NLO phores with ICT characteristics: Solvatochromic and theoretical
study, Journal of Molecular Structure (2017), doi: 10.1016/j.molstruc.2017.08.084.
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Triphenylamine-based fluorescent NLO phores with ICT
characteristics: Solvatochromic and Theoretical study
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Santosh B Katariya , Dinesh Patil , Lydia Rhyman , Ibrahim A. Alswaidan,
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Ponnadurai Ramasami , Nagaiyan Sekar
Graphical Abstract:

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Triphenylamine-based fluorescent NLO phores with ICT characteristics:
Solvatochromic and Theoretical study
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Santosh B Katariya , Dinesh Patil , Lydia Rhyman
, Ibrahim A. Alswaidan , Ponnadurai
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Ramasami , Nagaiyan Sekar
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Department of Dyestuff Technology, Institute of Chemical Technology, N. P. Marg, Matunga,
Mumbai (MH) India-400019
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Computational Chemistry Group, Department of Chemistry, Faculty of Science University of
Mauritius, Réduit 80837, Mauritius.
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Department of Applied Chemistry, University of Johannesburg, Doornfontein Campus,
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Johannesburg 2028, South Africa
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Department of Chemistry, University of Johannesburg, PO Box 524, Auckland Park,
Johannesburg, 2006, South Africa
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Department of Pharmaceutical Chemistry, College of Pharmacy, King Saud University, Riyadh
11451, Saudi Arabia
Email: n.sekar@ictmumbai.edu.in, nethi.sekar@gmail.com, ramchemi@intnet.mu
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Tel.: +91 22 3361 1111/ 2707; Fax.: +91 22 3361 1020
Tel.: +230 403 7507; Fax.: +230 465 6928
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Abstract:
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The static first and second hyperpolarizability and their related properties were calculated for
triphenylamine-based “push-pull” dyes using the B3LYP, CAM-B3LYP and BHHLYP
functionals in conjunction with the 6-311+G(d,p) basis set. The electronic coupling for the
electron transfer reaction of the dyes were calculated with the generalized Mulliken-Hush
method. The results obtained were correlated with the polarizability parameter ꢀꢁꢂꢃ , first
hyperpolarizability parameter βCT, and the solvatochromic descriptor of 〈ꢄ〉SD obtained by the
solvatochromic method. The dyes studied show a high total first order hyperpolarizability (70 to
238 times) and second order hyperpolarizability (412 to 778 times) compared to urea. Among the
three functionals, the CAM-B3LYP and BHHLYP functionals show hyperpolarizability values
closer to experimental values. Experimental absorption and emission wavelengths measured for
all the synthesized dyes are in good agreement with those predicted using the time-dependent
density functional theory. The theoretical examination on non-linear optical properties was

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performed on the key parameters of polarizability and hyperpolarizability. A remarkable increase
in non-linear optical response is observed on insertion of benzothiazole unit compared to
benzimidazole unit.
Introduction
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Non-linear optic (NLO) deals with the interactions of applied electromagnetic fields with
materials to yield new optical properties such as electromagnetic fields, altered frequency, phase,
and amplitude [1,2]. The search for efficient organic non-linear optical (NLO) materials has been
of interest in both academia and industry because of their potential applications in the design of
photon-based materials for optical switching, information processing, and data manipulation
[3,4]. The molecular structure of organic NLO materials is based on the π bond system. The
overlap of π orbital and delocalization of electronic charge distribution lead to a high mobility of
the electron density. Functionalization of both ends of the π system with appropriate electron
donor and acceptor groups can enhance the asymmetric electronic distribution in either or both
ground and excited states leading to an increased optical non-linearity [5,6]. NLO materials have
good non-linear susceptibilities but low laser damage threshold than inorganic counter parts [7].
Conjugated organic molecules have some advantages over inorganic molecules as they possess
low dielectric constant, small refractive indices, faster response time and they crystalize in non–
centrosymmetric system [8]. Large second-order non-linearities can be obtained from the NLO
materials containing a push-pull type chromophore which possesses large dipole moments and
polarizabilities and consisting of strong electron-donating and-withdrawing groups linked by a π-
ꢅ×ꢆ
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delocalized moiety [9]. Such types of molecules have a distinctive figure of merit given as ꢇꢈ
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where ꢀ is the dipole moment, β is the first hyperpolarizability and MW the molecular weight of
the chromophore [10]. On the basis of experimental and theoretical studies, the design of second-
order NLO materials to create large hyperpolarizability has primarily focused on the following:
(a) the planar D–π–A model [11], (b) auxiliary donors and acceptors model of heterocycle
[12,13] and (c) twisted π-electron systems [14–16].
There are experimental and theoretical methods reported to evaluate β. A common experimental
method used to obtain β is to polarize the sample dissolved in a non-polar solvent with a strong
electric field in order to induce molecular alignment. A laser beam is sent through the solution
and the intensity of second harmonic generation (SHG) is measured. This method for evaluating
the second-order molecular polarizability is the electric field induced second harmonic

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generation (EFISH) [17]. Another technique is the hyper-Rayleigh scattering (HRS) [18]. These
two methods are expensive and they require sophisticated experimental set up and trained
manpower to handle the instruments. The solvatochromic method is not only a simple practice
but it is also cost-effective. This method used for the determination of the first order
hyperpolarizability (βijk or βxxx or β ) was successfully applied first by Paley et al. [19]. The
CT
solvent dependent absorption and emission properties throw light on the nature of the excited
state and hence the solvatochromic method is used to understand the NLO properties which
mainly are the manifestations of the excited state nature of an organic molecule [20,21]. In this
work, we have used the solvatochromic method in which only the absorption/emission data is
required for the two level microscopic model of β based on the Oudar formulae [22]. The
solvatochromic method gives only the dominant tensor component of hyperpolarizability, i.e. βijk
assuming that the charge-transfer in a donor-acceptor molecule takes place along the axis of the
permanent ground state dipole moment [19] and thus the two level microscopic model of β will
give the βxxx or βCT. Besides the solvatochromic method, in the past few decades theoretical
computations have become a priori tool to compute the NLO properties of organic materials
[23,24]. Computational methods are useful in having prior understanding of the structure in
relation to the properties and the factors governing the efficiency of NLO properties, such as the
contribution of the donor-acceptor and solvent effects. The hyperpolarizability of the molecule is
largely influenced by the contribution from the higher excited states particularly the first excited
state in addition to the ground state [25,26].
In an attempt to understand the organic NLO materials, we were interested in triphenylamine
derivatives since triphenylamine is unique and widely accepted donating group due to its very
good electron donating ability and its charge-transfer characteristic has been known to exhibit
rigid plane, long conjugation length and good hole transporting properties [27]. Thus
triphenylamine and its derivatives display promising properties in the development of light
emitting [28], organic field-effect transistors (OFET) [29], photovoltaic devices [30] and dye-
sensitized solar cells [27]. In addition, electron transfer or electron separation between the
triphenylamine and the accepting group provides this class of compounds highly anisotropic
structures and interesting photo physical properties [31]. Gao et al. reported a range of
triphenylamine-based derivatives with various substituent groups [32]. It was reported that the
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the electron-donating ability, which improves the hyperpolarizability [33,34]. In the current
decade several research groups have achieved the large second-order NLO response by
extending the conjugated bridge through π-spacer [9,35–37]. The modulation of non-linear
optical properties by attaching various strong electron-withdrawing groups to a triphenylamine
backbone are reported in literature [38,39]. Recently, Zhou et al showed that the introduction of
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benzimidazole derivatives in the phenyl ring of the triphenylamine core increases the molar
extinction coefficients together with absorption maxima (due to the increased ꢀ-conjugation)
when compared to the un-substituted counterpart [40].
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In view of the above, in this work, we synthesized two triphenylamine-based dyes namely, TPA
BIZ and TPA BTZ [41] as they have intramolecular charge transfer (ICT) characteristics. We
also shed light into the effect of benzothiazole and benzimidazole group of the π-conjugated
system in terms of the photo-physical characterization and non-linear optical (NLO) properties of
triphenylamine-based dyes. We used the solvatochromic two level microscopic model to obtain
the polarizability parameterꢁ , first hyperpolarizability parameter (
β
CT), and solvatochromic
) and its related properties (ꢀ,
) (ꢀ measured in Debye and other quantities in esu) were determined using density
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descriptor of 〈 ꢄ 〉SD. The static first hyperpolarizability (
β
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functional theory (DFT) and time-dependent DFT (TD-DFT) methods .
< Please insert Fig.1 Synthesis of TPA BIZ and TPA BTZ
>
Methodology
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All the chemicals were purchased from Sigma Aldrich and S. D. Fine Chemicals Ltd, Mumbai,
India. The solid reagents were characterized by melting points and used without further
purification. The liquid reagents were distilled at their boiling points and used without any
further purification. Solvents were used after distillation at their boiling point and drying
according to standard processes. All the reactions were monitored on pre-coated silica gel
aluminium based plates kisel gel 60 F254 Merck, India. Purification of all the dyes was achieved
by recrystallization. Melting points were recorded on instrument from Sunder Industrial Product
Mumbai by using open capillary and are uncorrected. The absorption spectra of the dyes were
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recorded on a Lambda 25 UV-Visible spectrophotometer. H NMR spectra were recorded on a
Varian Cary Eclipse Australia. The chemical shift values are expressed in δ ppm using CDCl as
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a solvent and chemical shifts are reported relative to tetramethylsilane (Me
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Si) (δ=0.0) as an
internal standard.
Synthesis of compound TPA BIZ
To a stirring solution of o-phenylenediamine (108 mg, 1.0 mmol) in 20 ml methanol, solution of
4-(diphenylamino) benzaldehyde (273 mg, 1.0 mmol) was added drop wise through a dropping
funnel. After that the mixture was heated to reflux for 4 hour. On completion of the reaction the
mixture was cooled and poured into water. The resulting precipitate was filtered, washed with
water and dried. The residue was chromatographed on silica gel (petroleum ether: CH Cl = 10:1
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V/V) to give the compound TPA BIZ as a milk white powder in 60% yield. Melting point 279°C
(lit. 280°C)
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H NMR (500 MHz, DMSO) δ 8.03 (d, J = 7.9 Hz, 1H), 7.94 (d, J = 8.1 Hz, 1H), 7.90 (d, J = 8.7
Hz, 2H), 7.46 (t, J = 7.6 Hz, 1H), 7.39 – 7.31 (m, 5H), 7.11 (dd, J = 15.9, 7.7 Hz, 6H), 6.95 (d, J
= 8.7 Hz, 2H).
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C NMR (126 MHz, DMSO) δ 167.36, 154.16, 150.54, 146.63, 134.58, 130.28, 128.91, 126.90,
125.90, 125.83, 125.42, 124.94, 122.80, 122.57, 121.06.
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HRMS (ESI): m/z calcd for (M + H) C25
H
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N
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362.1579; found 362.1566.
Synthesis of compound TPA BTZ
To a solution of 2-aminobenzenethiol (125 mg, 1.0 mmol) in 20 mL DMSO and 4-
(diphenylamino) benzaldehyde (273 mg, 1.0 mmol) was added and the mixture was heated at
120 °C for 2 h. When the reaction was complete, the reaction mixture was cooled, poured into
2 2 4
water and extracted with CH Cl (90 ml). The organic layer was dried with MgSO and the
solvents were evaporated under vacuum. The residue was chromatographed on silica gel
(petroleum ether: CH Cl = 5:1 V/V) to give the compound TPA BTZ as a white powder in 75%
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yield. Melting Point 271°C (lit. 272°C).
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H NMR (500 MHz, CDCl ) δ 8.03 (d, J = 8.1 Hz, 1H), 7.93 (dd, J = 8.8, 2.3 Hz, 2H), 7.87 (d, J
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= 7.9 Hz, 1H), 7.49 – 7.45 (m, 1H), 7.37 – 7.29 (m, 5H), 7.18 (d, J = 7.4 Hz, 4H), 7.14 – 7.09
(m, 4H).
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C NMR (126 MHz, CDCl ) δ 167.81, 154.30, 150.42, 146.91, 134.82, 129.50, 128.53, 126.57,
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126.16, 125.40, 124.70, 124.03, 122.77, 121.73, 121.47).
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HRMS (ESI): m/z calcd for (M + H) C H N S 379.1109; found 379.1183.
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Computational method

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To get further insight into the effect of molecular structure and electron distribution on the
spectroscopic properties of the TPA BIZ and TPA BTZ, their geometries and energies were
optimized by DFT calculations using B3LYP/6-311+G(d,p) method [42]. TD-DFT was
employed for the excited state optimization. The functionals used were B3LYP [43,44],
BHHLYP [45,46] and CAM-B3LYP [47]. The hybrid functionals B3LYP and BHHLYP are
based on the LYP functional for the correlation part whereas they differ by the amount of HF
exchange, 20% in B3LYP and 50% in BHHLYP. The CAM-B3LYP functional comprises of
0.19 Hartree–Fock (HF) plus 0.81 Becke 1988 (B88) exchange interaction at short-range and
0.65 HF plus 0.35 B88 at long-range. The basis sets used for all atoms were the popular Pople’s
split-valence basis sets [48,49]. The triple zeta basis set is employed for all the three functionals
with both diffuse and polarization functions, 6−311+G(d,p). The choice of the functionals is
based on the fact that the charge-transfer states are better modeled with increasing amount of HF
in the hybrid (B3LYP and BHHLYP) as well as range separation (CAM-B3LYP) [50]
The vibrational frequencies of the optimized structures were computed using the same method to
verify that the optimized structures correspond to local minima on the energy surface. All the
computations in solvents of different polarities were carried out using the self-consistent reaction
field incorporated in the IEFPCM model as implemented in Gaussian 09 [51,52]. The excitation
energies, oscillator strengths and orbital contribution for the lowest 10 singlet-singlet transitions
at the optimized geometry in the ground state were obtained by TD-DFT calculations using the
same basis set as for the geometry minimization. The static second-order polarizability or first
hyperpolarizability (β) and its related properties for TPA BIZ and TPA BTZ dyes were
calculated on the basis of the finite-field approach [53]. The values of Onsager cavity radii were
obtained using the DFT-optimized geometries in the respective solvents by performing volume
computations. All computations were performed using the Gaussian 09 software [54] operating
on GridChem [55–57]. The BHHLYP and the CAM-B3LYP functionals are found to yield
values of hyperpolarizabilities closer to experimental values than the B3LYP functional [58].
Electronic vertical excitation spectra (TD-DFT)
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For the calculation of vertical excitations, the ground state optimized geometries were subjected
to TD-DFT computations for the first 10 states using the B3LYP/6-311+G(d,p) method and the
results are listed in Table 1. The results from the DFT and TD-DFT calculations support the

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experimental results suggesting that there was no influence of the variation in the solvent polarity
on the absorption of the TPA BIZ and TPA BTZ dyes (Table 1). The absorption spectra for the
TPA BIZ and TPA BTZ dyes are shown in Fig. 2. The computed absorption wavelength for the
TPA BIZ dye ranges from 380 to 381 nm while the experimental values ranges from 350 to 355
nm. For TPA BTZ dye, the computed absorption wavelength ranges from 370 to 376 nm while
the experimental value is 407 nm. For TPA BIZ and TPA BTZ, the observed lowest energy
absorption bands are associated to the predicted S0ꢁS1 transitions (HOMOꢁLUMO); with
major contribution > 97% and strong oscillator strengths ranging from 0.987 to 1.048. Both the
experimental absorption and the computed vertical excitation of the compounds were correlated
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with each other and are independent of the solvent polarity.
< Please insert Fig 2 Absorption and Emission spectra of TPA BIZ and TPA BTZ >
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< Please insert Table 1 Observed absorption and computed vertical excitation for TPA BIZ and TPA BTZ >
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Emission Spectra
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The experimental and computed emission spectra for the TPA BIZ and TPA BTZ dyes are
shown in Fig. 2. The minimum energy S1, B3LYP-optimized structures were used for the
emission computations, and the results are listed in Table 2. From the calculated emissions, it can
be observed that there is little influence of solvent polarity on the emission of the TPA BIZ and
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TPA BTZ dyes. In case of TPA BIZ, the emission wavelength is red shifted by 1364 cm (20
nm) from toluene to ethanol. A similar trend is observed in TPA BTZ but it is red shifted by
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2309 cm (50 nm).
The TD-DFT emission maxima calculated for all the dyes in various solvents are associated with
the LUMO→HOMO transition with major contribution (>98%). The experimental emissions
values range from 412 to 484 nm and the computed emissions range from 442 to 506 nm with an
oscillator strength in the order of 0.274 to 0.808 (Table 2).
For the TPA BIZ and TPA BTZ dyes, the observed large Stokes shift values are found at 3696
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and 3897 cm in toluene solution and 6006 and 5261 cm in ethanol respectively (SI Tables 1
and 2) and these points out to the occurrence of an ICT process [59–61] between the donor
(triphenylamine) unit and the electron-acceptor benzimidazole or benzothiazole moiety. The
experimental values are higher in ethanol than in toluene which is the sign of solvatochromism
and charge-transfer. The computational values are showing opposite trend [62] (SI tables 1and

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2). This is in agreement to the reported observation for triphenylamine-substituted benzimidazole
derivatives where the longer wavelength absorption band around 340 nm was attributed to the
charge-transfer (CT) ꢀꢂꢀ* transition from the electron-donating triphenylamine moiety to the
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electron-accepting benzimidazole moiety [63,64]. These are further confirmed by experimental
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(solvatochromic) calculations (SI tables 1 and 2).
< Please insert Table 2 Observed emission and computed emission for TPA BIZ and TPA BTZ .dyes in
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various solvents>
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HOMO–LUMO energy gap
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In order to explain the process of the charge-transfer, we obtained the isodensity plots showing
the distributions of electron clouds of HOMO - LUMO of TPA BIZ and TPA BTZ dyes (Fig 3).
Spatial distribution of molecular orbital, especially those of highest occupied molecular orbital
(HOMO) and lowest unoccupied molecular orbital (LUMO) are excellent indicators of electron
transport in molecular systems. The conjugated chromophores are characterized by a small
HOMO–LUMO separation, which is the result of a significant degree of ICT from the end-
capping electron donor groups to the efficient electron-acceptor groups through conjugated path
[65]. The charge-transfer from HOMO to LUMO is determined by electron donor and electron
acceptor group, which is responsible for the second order hyperpolarizability [66]. The electron
density of the HOMO orbital is mainly located on the triphenylamine moiety or spreads over the
entire molecule. The electron density of the LUMO shows a decrease in the electron density on
the triphenylamine moiety (donor) and an increase in the electron-acceptor benzimidazole or
benzothiazole unit. This behavior is in agreement with previous theoretical studies on similar
electron donorꢂacceptor molecules where the lowest energy absorption band is associated with a
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charge-transfer (CT) type, ꢀꢂꢀ* transition from the HOMO to the LUMO orbitals [40,58,62].
The absorption and emission spectra of these compounds were also obtained in the nonpolar
solvent toluene (see tables 1, 2) to further investigate the CT character of the lowest energy
transition. Comparison between the spectroscopic features in ethanol and toluene reveals a
solvent independent absorption spectra while the fluorescence emission spectra displays a clear
solvent dependence with a significant bathochromic shift in the emission wavelength maxima
with increasing solvent polarity. The higher solvatochromic shifts observed in the fluorescence
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emission spectra compared to those in the absorption spectra suggests an excited state with
stronger CT character and thus, supporting the behavior found in the electron density distribution
of the LUMO for the TPA BIZ and TPA BTZ dyes [63,64].
In general, if the energy gap between the HOMO and LUMO decreases, it is easier for the
electrons of the HOMO to be excited. In TPA BIZ and TPA BTZ dyes, the HOMO–LUMO
energy gaps are 3.79 eV and 3.56 eV respectively in gas phase and 3.75 eV and 3.49 eV
respectively in acetone (Table 3). From these values, it is clear that TPA BTZ is chemically more
reactive than TPA BIZ [70]. The lowering of the HOMO–LUMO band gap is essentially a
consequence of the large stabilization of the LUMO due to the strong electron-accepting ability
of the electron-acceptor group.
The chemical hardness and softness of a molecule are good indicators of the chemical stability.
In order to compare the stability of conformers energy was calculated. Molecules having large
energy gap are known as hard and molecules having a small energy gap are known as soft
molecules. Hard molecules are considered to be more stable than soft molecules .The soft
molecules are more polarizable and more reactive than those which are hard because they need
small energy for excitation. The hardness value of a molecule can be calculated using the
formula [71],
(
−Eꢉꢊꢋꢊ + Eꢌꢍꢋꢊ)
ƞ =
2
2
2
2
2
2
2
2
2
2
2
65
66
67
68
69
70
71
72
73
74
where EHOMO and ELUMO are the energies of the HOMO and LUMO orbitals obtained by DFT
computations.
Frontier molecular orbitals, i.e. HOMO and LUMO significantly affect the UV-Visible spectra
and reactions between molecules. Variations in the energy gap change the kinetic stability,
chemical hardness–softness and chemical reactivity. Thus, the HOMO–LUMO energy gap can
be used for qualitative estimation of the NLO behavior of a molecule. A small energy gap leads
L H
to a high NLO optical response. The HOMO–LUMO energy gap (E -E ) of the TPA BIZ and
TPA BTZ dyes were calculated and are given in Table 3. These dyes would be outstanding for
NLO properties as indicated by their small HOMO–LUMO energy gaps. The energy of the
frontier molecular orbital of TPA BIZ and TPA BTZ dyes obtained using the B3LYP/6-
2
2
75
76
311+G(d,p) method in various medium are presented in Fig S1 and S2 (SI).
< Please insert Fig 3 Frontier molecular orbitals of TPA BIZ and TPA BTZ dyes in the ground state>

ACCEPTED MANUSCRIPT
2
2
77
78
< Please insert Table 3 Energy of HOMO, LUMO and HOMO-LUMO gap of the TPA BIZ and TPA BTZ
dyes in gas phase and solvents using TD-DFT [B3LYP/6-311+G(d,p)] method>
2
79
Optimized Geometry
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
3
3
3
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
00
01
02
To understand the structures and origin of broad absorption of TPA BIZ and TPA BIZ dyes, the
geometry of the dyes were optimized in the ground state in solvents of various polarities. The
optimized structure of TPA BIZ and TPA BIZ dyes in the ground state and excited state are
shown in Figs. 4 and 5. A major bond lengthening is observed between the bonds C –C , C –
2
7
31
29
C , C –N , C –N by 0.033, 0.033, 0.022 and 0.034 Å and bond length shortened for the
31
40
45
40
46
bonds C
the case of TPA BIZ. While in the case of TPA BTZ and a major bond lengthening is observed
between the bonds N12–C24, 40–S46, C40–N45 by 0.025, 0.028, 0.028, 0.023 and
0.039Å and bond length shortened for the bonds C –N , N –C , C –C , N –C with 0.025,
3
–N12, N12–C13, C31–C40, N45–C35 with -0.020, -0.021,-0.048 and-0.019 Å respectively in
C
22–C31, C29–C31, C
3
12
12
13
31
40
45
35
0.025, 0.043 and 0.023 Å respectively (Figs. 4and 5). The bond lengths alteration are due to the
effect of the donor and the acceptor groups present in the TPA BIZ and TPA BIZ dyes This is
due to the partial double-bond character on the bridge bond between triphenyl moiety and the
acceptor unit caused by π-bonding interaction, thereby strengthening and shortening the bridge
bond. This change in the bond length indicates that there is charge-transfer observed from
triphenylamine core to benzimidazole and benzothiazole groups.
In agreement with previous studies [40], it is observed that the three benzene rings in the
triphenylamine core are non-planar (with the phenyl rings of the triphenylamine chromophore
displaying dihedral angles in the (145.9° to 146.1°), (148.7° to 149.0°) and (-33.9° to 34.0°), (-
31.0° to -31.3°) range with respect to the plane formed by the phenyl ring connected to the
benzimidazole moiety) and that the benzimidazole moiety presents a slightly distorted
conformation with the phenyl linkage of the triphenylamine moiety displaying a dihedral angle
in the (11.4° to 11.6°), (4.6° to 5.0°) range with respect to the plane formed by the phenyl group
for the TPA BIZ and TPA BIZ dyes respectively.
3
3
3
3
03
04
05
06
< Please insert Fig. 4 Optimized geometry parameters of TPA BIZ dye in acetone solvent in the ground state
and excited state (bond length are in Å, dihedral angles are in degree)>
< Please insert Fig. 5 Optimized geometry parameters of TPA BTZ dye in acetone solvent in the ground state
and excited state (bond length are in Å, dihedral angles are in degree)>
3
3
3
3
07
08
09
10
Mulliken charge distributionThe Mulliken charge distribution in the ground and the excited
states (in acetone) of the compounds are summarized in Table S2. In the excited state of TPA
BIZ, the net positive charge on the atom N increases and the net positive charge on the atom
1
2

ACCEPTED MANUSCRIPT
3
3
11
12
C
2
, C15, C31 decreases while the net negative charge on C24 increases and the net negative charge
on C C C C decreases.
1
,
3, 5, 13
3
3
3
3
3
13
14
15
16
17
In the excited state of TPA BTZ the net positive charge on the atom N12, C increases and the
40
net positive charge on the atom C
2 24
, C15, C34 decreases while the net negative charge on C6.C
increases and the net negative charge on C C C C C decreases which is suggestive of the
1
,
3, 5, 13, 26
charge delocalization in the molecule from the donor core to the acceptor core Fig. 6 and Table
S3 (SI).
3
3
3
3
18
19
20
21
< Please insert Fig 6 The ground state (GS) and excited state (ES) Mulliken charge (e) distribution of the
compound TPA BIZ and TPA BTZ in acetone
>
Charge transfer Characteristics
3
3
3
3
3
22
23
24
25
26
An efficient charge-transfer (between donor and acceptor) leading to a characteristic charge-
transfer excited state in a donor-π-acceptor chromophore is responsible for the manifestation of
NLO properties [72]. Within a two-level approximation the strength of electronic coupling HDA
between the ground and charge-transfer excited states is related to the vertical excitation energy
(∆ꢎ ), the difference between the adiabatic dipole moments of the ground and excited states
ꢏꢐ
ꢒ
3
3
27
28
(∆μ ), ∆ꢑ is the difference in diabatic state dipole moments, and the transition dipole moment
ꢏꢐ
ꢏꢐ
µ by the generalized Mulliken-Hush (GMH) equation [73–75]:
1
2
ꢅꢕꢖꢀ∆ꢗꢖꢕ
ꢘ
ꢅꢕꢖꢀ∆ꢗꢖꢕ
3
29
ꢓꢒꢔ =ꢀ
= ꢙ∆ꢅꢚ
(1)
ꢞ/ꢚ
∆
ꢅ
ꢚ
ꢖꢕ
ꢛꢜꢅ
ꢝ
ꢕꢖ
ꢀ
ꢖꢕ
3
3
3
3
3
3
3
30
31
32
33
34
35
36
The adiabatic states are assumed to be composed of these three adiabatic states - a donor ground
state (GS), a donor locally excited state (LE), and a charge-transfer state (CT) with the
“transferring electron” localized on the acceptor. This approach has been carefully used in a few
charge-transfer systems [76–78]. For weak donor-acceptor interactions, the adiabatic states are
nearly equivalent to the adiabatic states, and thus it is possible to use the parameters like
difference in dipole moments, transition dipole moments and the frequency of absorption
obtained from the steady state absorption measurements.

ACCEPTED MANUSCRIPT
ꢃꢄꢅꢆꢇ
ꢈ
ꢅꢆꢇ∆ꢄꢉꢊ
3
37
ꢓꢒꢔ = 2.06 ꢀ 10ꢁꢂ
(2)
ꢋꢌꢍ
−
1
−1
3
3
3
38
39
40
where εmax is the molar extinction coefficient at maximum absorption, in the units of M cm ,
and ∆ꢎꢏꢂ is the full width at half-maximum (FWHM) of charge-transfer band. In the above
ꢂ
1
equation, H , ν , and ∆ꢎ are in units of cm . Equation (2) provides a simple method to
DA
max
ꢏꢂ
3
3
3
41
42
43
calculate charge-transfer coupling from the characteristic values of the charge-transfer band in
absorption spectra, and it is an experimental coupling value.
3
3
44
45
(2a)
(2b)
3
3
3
46
47
48
3
3
3
3
3
3
3
3
3
3
3
49
50
51
52
53
54
55
56
57
58
59
The degree of delocalization or fractional degree of localization of the excess
ꢂ
charge (ꢐꢑ ) and electronic coupling matrix (H ) for the diabatic states are expressed by
ꢒ
DA
ꢂ
equations (2) and (2a, 2b). The values ofꢐꢑ , HDA and RDA were estimated from equations (2) and
ꢒ
ꢂ
(2a, 2b) respectively, and summarized in Table 4. When ꢐꢑ is zero, there is total delocalization
ꢒ
and when it is unity there is called total localization of the charge [53]. TPA BIZ possesses good
values of degree of delocalization in different microenvironments and thus, the effective ICT
characteristics at ground state rather than excited state. This observation is also supported by the
ratio of dipole moment. Its values are less than unity. This indicates that in the ground state
compounds are more polar than in the excited state. Out of two molecules TPA BTZ is more
polar than TPA BIZ.

ACCEPTED MANUSCRIPT
3
3
3
60
61
62
< Please insert Table 4 Coupling strength (HDA), coupling distance (RDA), degree of delocalization
ꢕ
ꢓ ꢐꢐꢐand ratio of dipole moment for the TPA BIZ and TPA BTZ dyes in various solvents >
ꢔ
3
3
3
3
3
3
3
3
63
64
65
66
67
68
69
70
Table 4 summarises the coupling strength of donor-acceptor fluorophores TPA BIZ and TPA
-1
BTZ. The large distribution of the CT coupling values ranging from 10453 to 12808 cm for the
TPA BIZ and TPA BTZ dyes only few such D−A pairs will likely have the strongest coupling
values. The charge-transfer coupling is higher for the TPA BIZ dye in chloroform and EtOAc.
However the lowest coupling is observed for the TPA BTZ dye. In case of TPA BIZ dye the
lowest coupling distance is observed in EtOAc while the highest is in ethanol. Hence the above
observation indicates that the coupling strength and coupling distance are important parameters
for the donor charge-transfer molecules.
3
3
71
72
Solvatochromic method for determination of non-linear optical properties (NLO)
Calculation of ꢖꢓꢗ from the solvatochromic data
3
3
3
3
3
3
3
73
74
75
76
77
78
79
Here we report the experimentally derived value of the linear polarizability ꢘ ꢐꢐof TPA BIZ and
ꢙꢚ
TPA BTZ dyes as obtained in the framework of the two-level model using UV-Visible
absorption/emission spectroscopy was used to determine these values. The solvatochromic
method was utilized for determination of dipole moment of the lowest lying charge-transfer
excited state. Considering that in the TPA BIZ and TPA BIZ dyes charge-transfer direction is
essentially coincident with the molecular long axis (here taken as X-axis),ꢐꢘꢙꢚ can be indicated
asꢐꢘ whose explicit expression is [79,80]:
ꢛꢛ
ꢚ
ꢚ
ꢅ
ꢟꢅ ꢠꢖꢕ
ꢖꢕ
ꢕꢖ
3
80
ꢘꢙꢚ = ꢘꢛꢛ = 2
=
(3)
ꢗꢕꢖ
ꢡꢢ
3
3
3
3
81
82
83
84
x = direction of charge-transfer,
ℎ = Planck’s constant, (in erg s)
-1
c = velocity of light in vacuum (in cm s )
ꢣꢏꢐ =ꢀThe wavelength of transition from the ground state to excited state,
3
3
85
86
ꢑꢐꢏ = The transition dipole moment which is related to the oscillator strength f by the following
equation:

ACCEPTED MANUSCRIPT
ꢂ
3
ꢟ ℎ
ꢣ
ꢂ
ꢜ
=
ꢀ
ꢐꢐꢐꢐꢐꢐꢐꢐꢐꢐꢐꢐꢐꢐꢐꢐꢐꢐꢐꢐ(4)
ꢝꢞ
ꢂ
8
ꢠ ꢡꢢ
ꢎ̅
ꢝꢞ
3
3
3
3
87
88
89
90
Where,
m = mass of electron,
f = oscillator strength,
ꢎ
̅
= Absorption frequency,
ꢝꢞ
3
3
3
3
3
3
91
92
93
94
95
96
e = charge on electron,
The oscillator strength can be obtained by integrated absorption coefficient of the absorption
band:
ꢤꢥ
ꢣ = 4.32ꢀ × 10 ꢦ ꢧ(ꢨ
̅
) ꢩꢨ
̅
(5)
−
1
−1
-1
Where ε is the extinction coefficient (L mol cm ) and ꢨ
̅
ꢀ= absorption wave number in cm
The transition dipole moment ꢑ ꢀandꢀthe oscillator strength (f) were calculated using equations
ꢐꢏ
3
3
3
4
4
4
4
4
4
4
4
4
4
4
97
98
99
00
01
02
03
04
05
06
07
08
09
10
(4) and (5). (The transition dipole moment obtained using Equation (4) is in esu, if all the
constants are used in c.g.s units.). The values for ꢁꢂꢃ were calculated and the results obtained
were compared with theoretically obtained ꢁꢂꢃ or ꢁ . These are collected in Table 5.
xx
The computational values of ꢁꢂꢃ obtained by BHHLYP functional are closer to experimental
values than B3LYP and CAM-B3LYP functionals. The computational values of ꢁꢂꢃ are almost
1.5 to 2.0 times higher than the experimental values. This can be attributed to the approximations
exercised in the computational model, as well the inherent simplifications associated with the
solvatochromic methods in obtaining the ground and excited state dipole moments [81].
Furthermore the solvation model used here is also evolved with several assumptions [82].
Nonetheless the trends in the solvent system coincide with experimental values. The linear
polarizability is sensitive to solvents and is evident in both the experimental and computational
studies. Both dyes show higher ꢁꢂꢃ values in polar solvents. There is substantial increase in of
−24
−24
15-21 × 10 esu to 16-25 × 10 esu experimentally but computationally no major change was
observed from TPA BIZ to TPA BTZ.
4
4
11
12
< Please insert Table 5 Linear polarizability ꢪꢫꢬcalculated by solvatochromic and computed methodꢀfor
TPA BIZ and TPA BTZ>
4
13
Calculation of βCT from the solvatochromic data
4
4
4
14
15
16
The two-level microscopic model to determine solvent dependent hyperpolarizability is based on
the Oudar equation [23,24] which in modified form can be presented as

ACCEPTED MANUSCRIPT
ꢟ
ꢟ
3
ꢮ
̅
μ
Δꢑꢂꢃ
ꢏꢐ ꢏꢐ
ꢟ
ꢤꢙꢚ = ꢤꢛꢛꢛ
=
×
… … … . (6)
ꢟ
ꢟ
ꢟ
ꢟ
ꢟ
2
ℎ ꢭ
ꢙꢮ −ꢀꢮ ꢝꢙꢮ − 4ꢮ
̅
ꢝ
ꢏꢐ
ꢯ
ꢏꢐ
ꢯ
4
4
4
17
18
19
Where,
x = direction of charge-transfer,
ꢀ = Planck’s constant (in erg s)
−
1
4
4
4
4
4
4
20
21
22
23
24
25
c = speed of light in vacuum (in cm s )
ꢀeg = transition dipole moment,
νeg = transition frequency,
L
ν = frequency of the reference incident radiation to which the β value would be referred,
ꢁꢑꢂꢃ =ꢀdifference between the charge-transfer excited state and ground state dipole moment
4
4
4
4
4
26
27
28
29
30
The hyperpolarizability calculated by this equation is the dominant component of the
hyperpolarizability tensor i.e. ꢰꢱꢱꢱ and as the formula refers to charge-transfer transition [19], the
hyperpolarizability obtained is often indicated as βCT (charge-transfer). When there is no laser
excitation (ν = 0), we get the static hyperpolarizability and Equation (6) reduces to the
L
following equation:
ꢟ
3
2
μ
Δꢑꢂꢃ
2
ꢏꢐ
ꢰꢂꢃ = ꢰꢱꢱꢱ
=
×
… … … . (6ꢴ)
ꢎ
ꢲꢳ
4
31
The Δꢑꢂꢃis obtained by using Equation (2’ derived on the basis of McRaeꢀs theory [83,84]
ꢟ
ℇ − 1 ꢼꢟ − 1
2
Δꢑ
ꢂꢃ
νꢵꢶꢷ − ꢮꢏꢸ = (ꢹꢵꢶꢷ − ꢹꢏꢸ) +
ꢻ
− ꢽ … … … . (7)
ℎꢭꢴꢺ ℇ + 2 ꢼꢟ + 2
4
4
4
4
4
4
4
4
32
33
34
35
36
37
38
39
Where,
νꢵꢶꢷ − ꢮꢏꢸ= Stokes shift in cm ,
abs - δem = differences in the vibrational energy (in cm ) of the molecule in the excited and
-1
-1
δ
ground state for absorption and emission,
a = cavity radius within Onsager’s model (in cm),
-1
-1
ε = dielectric constant (L mol cm )
n = refractive index of the solvent
a was calculated by integration of the solvent accessible surface using density functional theory
4
40
optimized geometry.

ACCEPTED MANUSCRIPT
4
4
41
42
Treating Equation (7’ as
ꢥ = ꢡꢦ + ꢢ
(8’
4
43
Where
ꢥ
= νꢧꢨꢩ − ꢎꢟꢡ
ꢟ
ℇ − 1 ꢼꢟ − 1
− ꢽ
2
Δꢑ
ꢂꢃ
ꢪ =
ꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢾ =
ꢻ
ℎꢭꢴꢺ
ℇ + 2 ꢼꢟ + 2
ꢴꢼꢩꢀꢭ = (ꢹꢵꢶꢷ − ꢹꢏꢸ)
4
4
44
45
Using the value of slope m, ꢁꢀCT was then derived, finally substituting the values of ꢁꢀCT and
ꢑꢐꢏ in Equation (7), βCT or βxxx is obtained. The values for first hyperpolarizability obtained
4
4
4
4
4
46
47
48
49
50
using the solvatochromic method (Table 6) are based on several assumptions and thus allow only
approximate estimate of dominant tensor of total hyperpolarizability along the direction of
charge-transfer which is the major contributor to the total hyperpolarizability. Although the
values are approximate, it has advantages over the other well-known expensive methods to
understand the facts. The calculated βCT values are given in Table 6.
4
4
51
52
< Please insert Table 6 Total first order hyperpolarizability βCT calculated by solvatochromic and
computed method for TPA BIZ and TPA BTZ>
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
The difference in the experimental and computed values of βxxx for TPA BIZ and TPA BTZ are
-30
in order of (x 10 ) esu. The trends across the non-polar to polar solvents is well described by the
computational methods. Polar solvents show higher βxxx values and these are reflected both in
-30
computational methods. The compound TPA BIZ has calculated values of 26 (× 10 ) esu to 41 (×
-
30
-30
-30
10 ) esu and experimental values from 20 (× 10 ) esu to 24 (× 10 ) esu across the solvents. The
-30
-30
compound TPA BTZ has calculated values of 59 (× 10 ) esu to 88 (× 10 ) esu and experimental
-30
-30
values from 32 (× 10 ) esu to 41 (× 10 ) esu across the solvents. The value of ꢰ or total first
ꢿ
order hyperpolarizability of the molecule gives an estimate of the NLO properties of the organic
molecules. This value considers all the directional tensor components of hyperpolarizability. The
computed values were compared with the values obtained for urea. As urea is one of the
exemplary molecules used in the study of the NLO properties of molecular systems, it is used
often as a threshold value for virtual purpose of comparison. The total hyperpolarizability
−30
calculated is 70-110 times and 159-238 times greater than that of urea (0.37 × 10 esu) in case

ACCEPTED MANUSCRIPT
4
4
4
68
69
70
of TPA BIZ and TPA BTZ. The effect of the substitution of benzothiazole ring system as against
benzimidazole is clear and shows a higher first order hyperpolarizability. The solvent effect is
consistently shows higher value in polar solvents by computational method.
4
71
Calculation of solvatochromic descriptor of γSD from the solvatochromic data
4
4
4
4
72
73
74
75
The second-order (or cubic) hyperpolarizability at molecular level originating from the electronic
polarization in the non-resonant region can be treated by a three-level model [21,22,85–87]. The
quasi-two level model in place of the three level model using the density matrix formalism to a
simpler expression [88–90].
1
ꢟ
ꢙ∆ꢑ − ∆ꢑ ꢏꢟ ꢐꢝ … … … . (9)
ꢟ
<
ꢫ >∝
ꢑ
ꢏꢐ
ꢺ
ꢎ
ꢏꢐ
4
4
76
77
The value
ꣀ
ꢟ
ꢙ∆ꢑ − ∆ꢑꢟ
ꢟ
ꢑ
ꢝ (10’
ꣁ
ꢏꢐ
ꢏꢐ
ꢗ
ꢖꢕ
4
4
4
78
79
80
4
4
81
82
< Please insert Table 7 Second order static hyperpolarizability obtained by solvatochromic and
computational method >
4
83
The second order hyperpolarizability can be expressed as the ‘‘solvatochromic descriptor” and
4
84
the values calculated are given in Table 7. The solvatochromic descriptor ( γ ) of second order
4
4
4
4
4
4
4
4
4
4
85
86
87
88
89
90
91
92
93
94
hyperpolarizability of compounds show higher values in case of a benzothiazole ring containing
molecules than benzimidazole containing molecules. This can be understood on the basis of
higher electron pulling effect of benzothiazole ring as compared to benzimidazole ring system,
which helps in creating a stronger dipole and contribute to the hyperpolarizabilities. Like βxxx and
ꢰꢿꢀthe solvatochromic descriptor is also affected by the polarity of solvent. The solvent effect is
also observed on this parameter, higher the polarity of the solvent, higher the second order
-36
hyperpolarizability. The compound TPA BIZ has calculated values of 280 (× 10 ) esu to 426 (×
-30
-36
-36
10 ) esu and experimental values from 9 (× 10 ) esu to 10 (× 10 ) esu. The compound TPA
-36
-36
BTZ has calculated values of 446 (× 10 ) esu to 540 (× 10 ) esu and experimental values from
-36
-36
27 (× 10 ) esu to 31 (× 10 ) esu. The second order hyperpolarizability calculated is 412-626
−36
4
95
times and 493-778 times greater than that of urea (γurea = 0.68 ×10 esu) in case of TPA BIZ and

ACCEPTED MANUSCRIPT
4
4
4
96
97
98
TPA BTZ
.
The individual components of the second order static hyperpolarizability γ were
obtained computationally. The values are considered to be proportional to the solvatochromic
descriptor of the second order hyperpolarizability. The values show a trend where higher
γ
4
5
99
00
polarity solvents show higher values of
solvatochromically obtained values.
γ and a similar trend is followed by the
5
5
01
02
Non-linear optical properties TPA BIZ and TPA BTZ dyes using DFT and TD-DFT
method
5
5
03
04
The static first hyperpolarizability (βο’ and its related properties (ꢀ, α0, ∆α, β, γ) for TPA BIZ
and TPA BTZ dyes were calculated using the B3LYP, CAM-B3LYP and BHHLYP functionals
5
5
5
05
06
07
with 6-311+G(d,p) basis set on the basis of the finite-field approach [91]. In the presence of an
applied field, the energy of the system is a function of the electric field, and the
hyperpolarizability is a rank three tensor that can be described by a 3 × 3 × 3 matrix. The 27
components of three-dimensional matrix can be reduced to 10 components due to Kleinman
symmetry [92]. The matrix can be given in the lower tetrahedral format. It is obvious that the
5
5
5
08
09
10
lower part of the 3 × 3 × 3 matrices is tetrahedral. The components of
β are defined as the
5
5
11
12
coefficient in the Taylor series expansion of the energy in the external electric field. When the
external electric field is weak and homogeneous, this expansion becomes
ꢏ
ꢏ
ꢬ
5
5
13
14
E = E − μ ꢣ −
− ꢣ ꢲꢳ
…… (11)
ꢱ ꢱ ꢱ
ꢴ
ꢭ ꢮ
ꢂꢮꢯꢰꢱꢯꢱꢰ
ꢯꢰꢴ
ꢯ
ꢰ
5
5
15
16
Where E° is the energy of the unperturbed molecules,
Fα is the field at the origin,ℎℎ
5
5
5
17
18
19
ꢀ
α
,
α
αβ and β
α
β
γ
are the components of dipole moment ,polarizability and the first
hyperpolarizabilities respectively. The complete equations for calculating the magnitude of total
static dipole moment (ꢀ), the mean polarizability α0’, the anisotropy of the polarizability ∆α’,
(
(
5
5
20
21
the mean first hyperpolarizability
(β’ and static second hyperpolarizability (γ) using the x, y, z
components from Gaussian 09W output are defined as follows [53]:
2
2
2 1/2
5
5
22
23
µ = (µ +µ +µ
)
(12)
x
y
z

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5
5
5
5
5
5
5
5
24
25
26
27
28
29
30
31
α = (1/3) α + α + α
(13)
(14)
(15)
0
xx
yy
zz
−
1/2
2
2
2
2
1/2
∆α =
2
[(α − α ) + ( αyy
−
αzz) + ( αzz
−
αxx) + 6α xx]
xx
yy
2
2
2
βtotal = [(β + β + β ) + (β + β + β ) + (β + β + β ) ]
xxx
xyy
xzz
yyy
xxy
yzz
zzz
xxz
yyz
 γ = (1/5) [(γ + γ + γ + 2γ +
2
γ +
yyzz
2
γzzxx)]
(16)
α0’, the
xxxx
yyyy
zzzz
xxyy
The values calculated for total static dipole moment (ꢀ), the mean polarizability
anisotropy of the polarizability ∆α’, the mean first hyperpolarizability
hyperpolarizability (γ) of the TPA BIZ and TPA BTZ dyes in different solvent environments
(
5
5
32
33
(
(β’ and static second
,
5
5
34
35
using Equations (12ꢃ16), respectively, are enlisted in Tables 5ꢃ7and Supporting Information
533 (SI) tables S6ꢃS11. A comparison of the B3LYP, CAM-B3LYP and BHHLYP
hyperpolarizabilities suggests that the results obtained using the B3LYP functional might be
overestimating the hyperpolarizability values. This conclusion is based on benchmark studies
[93–95] in which CAM-B3LYP was found to perform much better than B3LYP for nonlinear
optical properties based on comparison with highly accurate coupled-cluster models pointed out
by Hammond and Kowalski [96].
5
5
5
5
5
5
36
37
38
39
40
41
Vibrational contribution to the linear and NLO response:
5
5
5
5
5
5
5
5
42
43
44
45
46
47
48
49
In push-pull chromophores, vibrations are generally strongly coupled with conjugated electrons
in the system. Hence along with the electronic transitions the vibrational transitions play vital
role in determining the NLO properties. The coupling between the electronic polarization and
vibration leads to a considerable vibrational contribution to the overall NLO response [97] .In
this context, DFT is a good computational tool to study the vibrational contribution to
polarizability and hyperpolarizabilities of NLO chromophores [98,99]. We have obtained the
vibrational contributions to static electronic polarizability and hyperpolarizabilities using B3LYP
functional with 6-311+G(d,p) basis set in two solvents. Table-8 presents the DFT results of the

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5
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51
diagonal electronic and vibrational contributions to the linear polarizability (α) and first
hyperpolarizability (β).
5
52
5
5
5
53
54
55
< Please insert Table 8 Diagonal electronic and vibrational contributions to dipole polarizabilities and first
hyperpolarizabilities of TPA BIZ and TPA BTZ obtained from of B3LYP/6-311+G(d,p) calculations in
various solvent. (All values are in a.u.)>
5
5
5
5
5
5
56
57
58
59
60
61
Table-8 shows that along with electronic part there is substantial contribution of vibrational part
to the polarizability and hyperpolarizability. For TPA BIZ and TPA BTZ the ratios of vibrational
v
e)
to electronic contribution in polarizability (α /α are 0.451 to 0.557 and 0.313 to 0.401 in toluene
(nonpolar) and ethanol (polar with hydrogen bonding effect) respectively. In case of first
v
e)
hyperpolarizability the ratios of vibrational to electronic contribution (β /β are -1.239 to -1.061
and -0.040 to 0.003 in toluene and ethanol respectively. This confirms that the vibrational
motions play crucial role in determining the NLO properties of these dyes particularly in solvent
5
62
5
5
63
64
environments wherein solvation is likely to affect the vibrations.
Fundamental limits for the first and second order hyperpolarizability values
5
5
5
5
5
5
5
65
66
67
68
69
70
71
The fundamental limits of NLO response for the TPA BIZ and TPA BTZ Push-pull
chromophores can be obtained by the limiting theory proposed by Kuzyk [100,101]. It is the
sum-rule-restricted (SR) three-level model which produce a two-level-limit (2L) for β (ꢤ ꢂ∗ ꢵꢶ ꢋ or
βmax) depends exclusively on the conjugated π electrons N from double or triple bond and the
transition energy E between the ground and first excited state, obtained from λmax absorption.
1
0
The limit for β* is obtained from eq.17 in different solvents using their respective refractive
indexes (n) of respective solvent.
ꢹꢂ + 2 ꢺ ꢳћ ꣅꢺ/ꢟ
ꢺ
ꢷ
∗
ꢶꢋ
ꢤ
≤ √3 ꢸ
ꢽ ꣂ
꣄
ꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀ(17)ꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀꢀ
/ꢟ
ꢂꢵ
꣆
3
ꣃ
√
ꢎꣀ
ꢿ
5
72
e and m are the charge and mass of electron. ћ = ℎ/2꣇.
5
5
5
73
74
75
Similarly limit for the second order hyperpolarizability (γ) can be estimated by eq. 18[102,103].
The γ values have two possible fundamental limits for i.e. negative limit which is for a
centrosymmetric molecule and positive limit for an asymmetric molecule.

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ꢷ
ꢷ
ꢼꢊ
ꢷ
ꢷ
ꢼꢊ
ꢝ ћ
ꢝ ћ
5
76
− ꢺ
ꢻ
ꣀ ≤ ꢫꢐ ≤ 4
ꢻ
ꣀꢐꢐꢐꢐꢐꢐꢐꢐꢐꢐꢐꢐꢐꢐꢐꢐꢐꢐꢐꢐ(18)ꢀꢀꢀꢀꢀꢀꢀ
ꢊ
ꢿ
ꢺꢊ
ꢿ
ꢽ
ꢽ
ꢉꢾ
ꢉꢾ
5
5
5
77
78
79
The limiting values for β and γ obtained from eq. 17 and 18 are compared with the corresponding
values obtained by solvatochromic and computational methods for TPA BIZ and TPA BTZ in
table 9.
5
5
80
81
< Please insert Table 9 Comparison of solvatochromic and theoretical values with the limiting values of
hyperpolarizability for TPA BIZ and TPA BTZ>
5
82
5
5
83
84
Table 9 shows that for TPA BIZ and TPA BTZ in all solvents the β values below the βmax limit
and γ values are within the estimated limiting values.
5
5
85
86
Conclusions
5
5
5
5
5
5
5
5
5
5
87
88
89
90
91
92
93
94
95
96
In summary, NLO properties of triphenylamine-based dyes TPA BIZ and TPA BTZ were studied
using the solvatochromic method and the solvent dependent shift in the emission wavelength is
observed. Furthermore DFT and TD-DFT computations were performed to estimate the NLO
properties of triphenylamine-based dyes TPA BIZ and TPA BTZ using the B3LYP functional (in
the ground- and excited-state geometries) and the CAM-B3LYP and BHHLYP functionals (in
the ground-state geometry only). The theoretical examination on non-linear optical properties
was performed on the key parameters of polarizability and hyperpolarizability. A remarkable
increase in non-linear optical response is observed on insertion of benzothiazole unit compared
to benzimidazole unit. Triphenylamine-based dyes TPA BIZ and TPA BTZ can act as a
promising organic NLO material for optoelectronic devices.
5
5
97
98
Acknowledgments SK is thankful to UGC for giving study leave (FIP) and SIES College for
sanctioning the study leave. PR and LR acknowledge facilities from the University of Mauritius.
IAA and PR extend their appreciation to the International Scientific Partnership Program ISPP at
King Saud University for funding this research work through ISPP# 0070.
5
6
6
99
00
01
6
6
02
03

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