Second order hyperpolarizability of triphenylamine based organic sensitizers: a first principle theoretical study

Abstract

Designed metal-free dyes have been investigated by Density Functional Theory (DFT) and Time-Dependent DFT (TD-DFT) to evaluate the ground state and excited state geometries of triphenylamine-based organic sensitizers. The optoelectronic properties of five types triphenylamine (TPA)-based dyes, namely, C206, TPA, TPA-N(CH₃)₂, TPA-SCH₃, and TPA-OC₂H₅, were studied. Energy band modulation has been performed for these dyes with different electron donating groups and the same electron withdrawing group. The performance of the hybrid functionals B3LYP and wB97XD using a standard basis set, 6-311++G(d,p), has been analyzed. Solvent effects have been examined by Conductor-like Polarizable Continuum Model (C-PCM) formalisms. The C-PCM/TD-DFT results show that accurate absorption energies are obtained only when the solvent effect is included in the excited state geometries. Theoretical examination of the non-linear optical (NLO) properties was performed on the key parameters of static polarizability and first order and second order hyperpolarizability. Good photovoltaic performance based on the optimized geometry, the relative position of the frontier molecular orbital energy levels and the absorption maxima of the dye are expected for offering a remarkable response. The results provide a direction for optimizing dyes as efficient sensitizers in dye-sensitized solar cells (DSSCs) and NLO applications.

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1. Introduction

Dye-sensitized solar cells (DSSCs) are attracting considerable attention in recent years, as they offer photo to electrical energy conversion at low cost; thus, they are regarded as next generation photovoltaic cells.^1,2 Basically, two types of dyes exist: metal-based and metal-free dye sensitizers. Although ruthenium-metal based sensitizers^3–5 offer an overall light energy to electrical energy conversion efficiency of over 13.5%, limited resources and the environmental issues relating to ruthenium use make it necessary to identify alternative new dyes. In this regard, organic dyes have received much attention due to their environmental friendliness, low cost for device production and facile preparation processes.^6–12 Other major advantages of these metal-free dye sensitizers are their tunable absorption and photochemical properties through suitable molecular design.^13,14

Among DSSCs, the Bulk Hetero Junction model (BHJ)^15–17 is the most successful. A DSSC is composed of four components, namely, a transparent conducting oxide, counter-conducting electrodes, a wide band-gap semiconductor surface, a dye molecule as sensitizer and an electrolyte based on a redox couple.¹⁸ The working principle of DSSC involves photoexcitation of a dye molecule, thereby generating an electron–hole pair. In the subsequent step, upon absorption of light, the dye generates an exciton; the excited electron is injected into the conduction band of TiO₂; the dye regenerates the hole-transporting material (HTM), and the charge percolates to the electrodes. Two common back-reaction processes are observed in DSSCs: recombination of the electrons in TiO₂ with the holes in the HTM, and reduction of the oxidized dye. In this regard, TiO₂ is the mostly used semiconducting surface; its conductance band is located at 4.0 eV.^19–22

From the energetic point of view, the most crucial steps in a photovoltaic cell are the injection and regeneration processes. The following criteria facilitate these two processes: (i) the lowest unoccupied molecular orbital (LUMO) energy level of the dye molecules must lie above the conduction band of the semiconductor materials (E_CB). (ii) The highest occupied molecular orbital (HOMO) of the dye molecules must be at a lower energy than the chemical potential of the redox couple.^23,24 During the overall electronic dynamic process, the efficiency of electron injection to the CB of the semiconductor surface and the electron collection efficiency at the transparent conductive oxide electrode directly determine the short-circuit current density (J_SC) of the DSSC. The potential difference between the Fermi level of the electrons in the semiconductor substrate and the redox potential of the electrolyte gives the open circuit photovoltage (V_OC). These two parameters are important factors determining the efficiency of DSSCs, according to:²⁵

where FF is the fill factor at which the DSSC operates with the maximum power point, which is mainly related to the total series of the resistance in the DSSC, and P_IN is the input power of incident solar light. However, it should be pointed out the overall efficiency of a DSSC also depends on other parameters, such as recombination. Obviously, an embedded dye over a metal oxide plays a key role in the energy conversion efficiency of a DSSC. Generally, metal-free organic dye sensitizers consist of donor group (D), π-bridge (π), and acceptor (A) moieties, the so-called D–π–A structure. This push–pull structure can induce intramolecular charge transfer (ICT) from A to D through the π-conjugated molecules when the dye is irradiated with sunlight. This is important for harvesting solar energy.

In order to function efficiently in a BHJ cell, a dye sensitizer must have the following characteristics: (i) the dye must show a broad absorption spectrum, covering the whole UV and visible region to absorb maximum energy from sunlight, (ii) the dye should have a low band gap, (iii) the dye should be able to prevent electron–hole recombination effectively, (iv) the dye should have high oscillator strength, (v) the open circuit voltage of the dye must be very high, (vi) the HOMO of the dye must lie below the redox couple and the LUMO of the dye must lie above the conduction band (CB) of the semiconductor for the downhill movement of electrons and uphill movement of holes, and (vii) a good acceptor group must be added to the dye molecule to anchor it well on the semiconductor surface. As the electronic energy levels of an organic dye molecule are tunable by varying their donor–acceptor moieties, it is possible to design a dye with desired energy levels. An enormous effort has been undertaken for this purpose in recent years.^16,26,27

One of the interesting topics to emerge in organic photovoltaics in the past twenty-five years is the design and synthesis of low band-gap semiconducting materials, dye sensitizers and HTM for use in DSSCs.^28,29 Triphenylamine (TPA) is one such molecule; its excellent electron donating power and its huge steric hindrance give it the ability to prevent undesired dye aggregation at the semiconductor surface.^30–34 Dyes composed of TPA as a donor and cyanoacrylic acid/thiophene as an acceptor/linker have recently generated enormous interest.^35–38 In this work, functional groups such as N(CH₃)₂, SCH₃ and OC₂H₅ have been substituted in TPA molecules, and these substitutions have been compared with the C206 dye molecule. Fig. 1 shows the chemical structures of the TPA based dye sensitizers. These incorporate both electron-rich and electron-deficient moieties into the TPA unit. The aim is to tune the photovoltaic parameters by substitution, as well as to determine the optimum dye system within the selected dyes. Based on this molecular design, more efficient dyes, with higher V_OC and lower J_SC compared with the C206 dye, are identified.

Fig. 1 Chemical structures of the TPA-based dye sensitizers.

2. Model and computation details

All the calculations were performed using the Gaussian 09w³⁹ program. The geometries of the design dye molecules in the gas phase were optimized in the ground state via Density Functional Theory (DFT)⁴⁰ with the B3LYP⁴¹ hybrid functional and wB97XD⁴² with the 6-311++G(d,p) basis set. The greater deviation in estimating LUMO energy is properly addressed in DFT due to weak correlation effects. The designed molecules are optimized at minimum energy and no imaginary frequency.

Time-dependent DFT (TD-DFT) calculations were performed to determine the excited state geometries at 20 vertical excitations to the excited state of the molecules. Although it is more time consuming, the use of the range separated DFT functional is a good way to address this problem. Based on the optimized molecular structures of the dyes, we simulated their UV-visible spectra in the gas phase and solvent medium with the B3LYP hybrid function using a standard basis set. The DFT functional B3LYP contains no empirical parameters and is reported to reproduce good electronic properties in the gas phase as well as in solvent medium within reasonable computational resources.⁴³ In a solvent medium of chloroform, the computations were performed by applying C-PCM using the integral equation formalism variant to describe the electrostatic solute–solvent interactions by the creation of a solute cavity via a set of overlapping spheres.⁴⁴ The absorption spectra were spin-allowed in 20 singlet transitions.

3. Results and discussion

3.1 The electron-donating capacity of modified donor groups

Four main types of dyes which originated from C206 were chosen by modifying the donor portion of triphenylamine (TPA) with N(CH₃)₂, SCH₃ and OC₂H₅. By the addition of the various donors, three different dyes were substituted with TPA-N(CH₃)₂, TPA-SCH₃ and TPA-OC₂H₅. The optimized geometries of the dyes are shown in Fig. 2. To anchor the proposed dye molecules onto the semiconductor anatase surface, however, an anchoring group, namely cyanoacrylic acid, was attached to each of the dye molecules at the acceptor portion. Table 1 shows the geometric parameters with dihedral angles that were especially selected to design the dye molecules. It is expected that an efficient dye should maintain co-planarity between the anchoring group to the donor portion and the bridging unit to facilitate the electron transfer process from the donor portion to the semiconductor surface. It is revealed that the dyes TPA-N(CH₃)₂ and TPA are more coplanar than C206, indicating better electron delocalization and intramolecular charge transfer. Co-planarity facilitates the recombination process, which in turns decreases the efficiency of the dye molecules as a photovoltaic material. Therefore, a balance is required between the charge transfer and electron recombination processes.

Fig. 2 Optimized ground state geometries of the dyes in the gas phase obtained at the B3LYP/6-311++G(d,p) level of theory.

Table 1 Geometric parameters of some selected dihedral angles of the optimized dyes

Dye C206	Degree	TPA	Degree	TPA-N(CH3)2	Degree	TPA-SCH3	Degree	TPA-OC2H5	Degree
C50–C49–C42–H15	178.37	H41–C11–C10–H40	−179.60	H60–C49–C42–H15	−179.67	S59–C17–C16–H44	178.55	O51–C17–C16–H44	−179.64
C50–C49–C42–H16	−177.39	H41–C11–C12–H42	−179.72	H60–C17–C18–H48	−179.96	S59–C17–C16–H45	−179.70	O51–C17–C18–H45	−179.79
C71–C70–C11–H39	−177.94	H46–C17–C16–H45	−179.71	H51–C11–C12–H41	−179.99	S60–C11–C12–H41	−179.63	O59–C11–C12–H41	−179.76
C71–C70–C10–H38	178.92	H46–C17–C18–H47	−179.61	H51–C11–C12–H41	−179.56	S60–C11–C10–H40	178.46	O59–C11–C18–H40	−179.62

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To obtain further insight into the molecular structure and electronic distribution of these dye molecules, molecular orbital analysis (MOA) has been performed. In this method, occupied and unoccupied molecular orbitals are of particular interest because they may be involved in the electron charge transfer (CT) process. During photoexcitation, one electron of the HOMO of the dye is transferred to the LUMO, which thereafter participates in the subsequent energy injection processes. Fig. 3 indicates the electron density distributions of the frontier molecular orbitals of the dyes. It is clear that the HOMOs of the dye molecules are more concentrated over the donor portion of the TPA moiety. The adjacent π-spacer (thiophene) in the LUMOs is more concentrated over the entire acceptor portion. The situation becomes more pronounced when electron-withdrawing groups are attached to the donor moiety. A spatial separation between the electron densities within the dye molecule and facilitation of the charge transfer process from the dye to the semiconductor surface through photoexcitation result in an efficient dye that is useful for DSSC.

Fig. 3 Frontier molecular orbitals of the dyes: HOMO (left) and LUMO (right).

It is evident that the dyes N(CH₃)₂ and TPA, with spatial separation, are more promising and are consequently expected to give the best performance among the selected dyes. The energy gaps (Δ) of the dyes were optimized with the B3LYP and wB97XD methods, and the optical bands of the dyes are depicted in Table 2. It shows that the TPA-N(CH₃)₂ and TPA dyes have Δ values in the order of 2.10 eV, whereas that of TPA has a much higher value in the order of 0.15 eV. However, as also indicated by the energy positions of the HOMO and LUMO of the dyes, we expect type-II band alignment in most of the cases when attaching the dyes to the TiO₂ semiconductor surface, keeping in mind that, in the composite system, the quasi-particle energy levels are tunable depending upon the nature of the interaction of the dye molecules and the adsorbent.⁴⁵ It can be noted that the use of the TiO₂ semiconductor surface to link photoelectrons in a solar cell is currently a research topic of crucial interest; we use the TiO₂ surface value of E_CB = 4.0 eV as reported in ref. 20. Note that band bending, as is evident from recent studies,^45,46 may alter the conduction band edge of the TiO₂ surface, which has a direct influence on the performance of a DSSC, although a very recent experiment demonstrates the higher photocatalytic activity of the anatase surface of TiO₂ under flat-band conditions.⁴⁷

Table 2 Frontier molecular orbital energy levels (with respect to vacuum) and the corresponding optical gaps of the different dyes by the B3LYP and wB97XD methods

Dye/Method	B3LYP			wB97XD
	HOMO (in eV)	LUMO (in eV)	Band gap (in eV)	HOMO (in eV)	LUMO (in eV)	Band gap (in eV)
C206	−5.30	−2.88	2.42	−7.02	−1.28	5.74
TPA	−5.19	−2.94	2.25	−6.95	−1.35	5.6
TPA-N(CH3)2	−5.10	−3.20	2.10	−6.74	−1.16	5.58
TPA-SCH3	−5.44	−2.93	2.51	−7.20	−1.32	5.88
TPA-OC2H5	−5.91	−2.72	3.19	−6.25	−1.06	5.19

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3.2 Effects of chemical modifications

The electron injection process of dye molecules and, hence, the efficiency of dyes in DSSCs are governed by the energy levels of the dye with respect to the conduction band of the semiconductor surface. Interestingly, the most prominent feature of an organic dye is the tunability of these energy levels by introducing various functional groups, especially at the donor portion. For this purpose, we chose three different electron donating groups, namely, TPA-N(CH₃)₂, TPA-SCH₃, and TPA-OC₂H₅. The unsubstituted dyes are named C206 and TPA, respectively. It is worth mentioning here that all the groups are introduced at the donor part, firstly because the introduction of electron donating groups at the π-spacer increases steric repulsion, and secondly because electron-withdrawing groups at the π-spacer induce a negative effect on the efficiency of DSSCs.⁴⁸ In this regard, electron-withdrawing groups on the π-spacer suppress the electron injection from the LUMO level to the semiconductor of the conduction band. Table 2 depicts how the electronic energy levels of the dyes are changed by the substitution of the different functional groups. The HOMO and LUMO energy levels of the dyes C206, TPA-SCH₃ and TPA-N(CH₃)₂ (B3LYP method) are −5.30, −5.19, −5.10 eV and −2.88, −2.94, −3.20 eV, respectively. These values indicate that the HOMO energy in the TPA-N(CH₃)₂ dye is significantly lower due to the presence of the C206 group. In TPA-N(CH₃)₂, the LUMO level is greatly stabilized due to the highly electron withdrawing group, which is reflected by the low band gap of C206 (2.0 eV). Next, concerning the effects of substituents on the donor portion of the dyes, it was revealed that attaching –N(CH₃)₂ and SCH₃ groups on the triphenylamine group stabilizes both the HOMOs and LUMOs of TPA. The substituent –N(CH₃)₂ offers a very low band gap in TPA-N(CH₃)₂ (2.0 eV); however, the HOMO energy level is situated slightly higher than the reduction potential energy of the I₃⁻/I⁻ electrolyte (−4.80 eV). The –OC₂H₅ group destabilizes the HOMO energy and reduces the band gap to 3.19 in the dye C206. The HOMO and LUMO energy levels of all the TPA-N (CH₃)₂ dyes fulfill the requirements of a good sensitizer.

3.3 Electron transfer and photovoltaic process

As previously mentioned, a suitable energy band is necessary to design molecules with desired photovoltaic performance. Thermodynamically, the spontaneous electron charge transfer process from the excited state of the dye molecule to the conduction band of TiO₂ requires the LUMO energy of the dye to be at a more positive potential than the conduction band of TiO₂ (−4.0 eV), while the HOMO energy values of the dyes should be more negative than the reduction potential energy of the I₃⁻/I⁻ electrolyte (−4.80 eV). As displayed in Table 2, the chemical modification of substitution on the dye molecule changes the relative position of the frontier energy levels by a substantial amount, which affects the electron charge transfer process. As an example, TPA-N(CH₃)₂ increases the LUMO level of TPA-N(CH₃)₂ by 0.09 eV, thereby increasing the electron injection rate from the photo-excited dye to the TiO₂ surface. According to the Marcus theory of electron injection, the larger the value of ΔG, the faster the rate of electron injection. It is worth mentioning here that this assumption is valid as long as the injection is restricted to energy levels close to the conduction band edge, and that the density of the acceptor states in this energy range remains constant.⁴⁹ It is clearly indicated from Table 2 that the LUMOs of all the dye molecules lie above the ECB of TiO₂, and the HOMOs are situated below the redox potential of the I₃⁻/I⁻ electrolyte (−4.80 eV). Thus, it can be stated that all of these dyes possess a positive response to electron charge transfer and regeneration related to the photo-oxidation process. Fig. 4 displays the relative energy levels of the designed dyes with reference to the conduction band of the TiO₂ surface and triiodide/iodide as the redox couple. The figure depicts that TPA-N(CH₃)₂ is expected to show the fastest electron transfer among the dyes. Our prediction is also supported by the greater charge separation between the HOMO and LUMO of this specified dye, as can be found in Fig. 3.

Fig. 4 Schematic energy level diagrams of the dyes, the CB of TiO₂, and the electrolyte (I⁻/I₃⁻).

3.4 Non-linear optical properties

We have calculated the static dipole moment (μ), mean polarizability (α₀), polarizability anisotropy (Δα), static first hyperpolarizability (β) and second hyperpolarizability (γ) at the ground state for the designed dye molecules. These were calculated using the formulas described in:^50–54where α_xx, α_yy and α_zz are the polarizability tensor components and β_xxx, β_xyy, β_xzz, β_xxy, β_yyy, β_yzz, β_xxz, β_zyy, β_zzz and γ_xxxx, γ_yyyy, γ_zzzz are the first order and second order tensor components, respectively. The calculated values are summarized in Table 3. The –N(CH₃)₂ substituted TPA-N(CH₃)₂ molecule static polarizability is 3.73 × 10⁻²³ esu. The static polarizability of C206 is 4.98 × 10⁻²³ esu. The static polarizability is directly proportional to the dipole moment.⁵⁵ However, from Table 3 it can be seen that the value of the OC₂H₅ substituted TPA-OC₂H₅ molecule is 3.82 × 10⁻²³ esu.

Table 3 The dipole moment, static polarizability, and first and second order hyperpolarizability of dyes studied at the B3LYP/6-311+G(d,p) level of theory

Dye	Dipole debye	Polarizability × 10^−23 esu	First order hyperpolarizability × 10^−29 esu	Second order hyperpolarizability × 10^−28 esu
C206	4.79	4.98	1.25	7.089
TPA	14.75	3.14	1.43	3.080
TPA-N(CH3)2	16.57	3.73	2.01	4.188
TPA-SCH3	9.97	4.06	1.33	4.285
TPA-OC2H5	14.33	3.82	1.88	4.282

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The first hyperpolarizability is inversely proportional to the transition energy. Accordingly, the TPA-N(CH₃)₂ substituted molecule with the lowest transition energy (2.15 eV, obtained from TD-DFT calculations) exhibits the maximum value of 2.01 × 10⁻²⁸ esu. The second order hyperpolarizability was calculated using eqn (6), and Table 3 shows the second order hyperpolarizability results. Among the five dye molecules, the most efficient second order hyperpolarizability values were obtained in the C206 dye molecule. The above results were dependent on the donor, acceptor, π-bridge and functional group substitutions. Higher dipole moment values and high first and second-order hyperpolarizabilities are important for active NLO performance. The present results clearly include that the TPA-N(CH₃)₂ dye molecule is particularly promising for use in NLO applications.

3.5 Absorption properties

Based on the optimized molecular structures with the B3LYP/6-311++G(d,p) method, the UV-vis spectra of the dyes were calculated using TD-DFT calculations in chloroform with the B3LYP hybrid functional using the lowest 20 spin-allowed singlet–singlet transitions. Before computing the absorption spectra, the dipole moment values of the individual dye systems were analyzed and are tabulated in Table 3. The maximum dipole moment values indicate that all the dyes are polar molecules. Table 4 also provides the vertical excitation energy (E*), oscillator strength (f), and the light harvesting efficiency (LHE) of the parent and the substituted dyes. All the dyes show broad UV-vis spectra whose tails enter the chloroform IR region, indicating broad light harvesting power. Fig. 5 shows the computed UV-visible spectra of some representative dyes in chloroform solvent. It is clear from the figure that all the dyes show two absorption peaks, one in the visible region (at around 600 nm) and another in the far-infrared region; the corresponding values of maximum absorption wavelength (λ_max) for all the dyes are given in Table 4. For the dye TPA-N(CH₃)₂, λ_max = 576 nm is mainly attributed to the HOMO → LUMO transition, whereas the second broad absorption peak at 432 nm corresponds to the HOMO-3 → LUMO transition. On the other hand, for the TPA and TPA-SCH₃ dyes, the HOMO–LUMO transition becomes the highest intensity peak, which can be attributed to the more co-planar nature of TPA and TPA-SCH₃ compared to the C206 molecule. Table 4 indicates that there is a pronounced effect on the λ_max and oscillator strength, and, hence, on the LHE factors of the substituted dyes compared with the C206 dye.⁵⁶ For most of the substituted dye molecule systems, the oscillator strength is greater than that of the corresponding main dye system, C206. The LHE factor determines the efficiency of DSSC.

Table 4 Vertical excitation energies, oscillator strengths and photovoltaic parameters of the different dyes

Dye	E^a (eV)	λmax (nm)	Oscillator strength (f)	LHE	eVOC (eV)
a Ref. 56.
C206^a	2.44	508	0.6834	0.7926	1.12
TPA	2.65	468	1.3948	0.9597	1.06
TPA-N(CH3)2	2.15	576	0.8052	0.8433	0.80
TPA-SCH3	2.64	470	0.8095	0.8849	1.07
TPA-OC2H5	2.38	521	0.9716	0.8932	1.28

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Fig. 5 Computed UV-visible spectra of the representative dyes in chloroform solvent.

The highest oscillator strength and, hence, the highest LHE is found for TPA. λ_max is found to be the highest for the TPA-N(CH₃)₂ dye molecule, which gives an LHE of 0.8433. From the calculated data, it can also be inferred that in the case of the electron donating –N(CH₃)₂ substituent there is always a higher value of λ_max, oscillator strength, and LHE compared to the other substituted dyes. The overall efficiency (η) of the DSSC can be computed from the open circuit voltage (V_OC), the short-circuit current density (J_SC), the fill factor (FF) and the intensity of incident solar light (P_IN) as expressed in eqn (1). The values of J_SC, V_OC, and FF can be obtained from the current–voltage characteristics in the illuminated condition. The analytical relationship between the V_OC and E_LUMO of the dye may be expressed as:

eV_OC = E_LUMO − E_CB (7)

where E_CB is the conduction band energy of the semiconductor surface. This implies that the higher the value of E_LUMO, the larger the value of V_OC. The computed values of eV_OC for the dyes are given in Table 4, which depicts that the maximum V_OC is obtained for TPA-N(CH₃)₂.

4. Conclusions

In the present study, different structural modifications have been optimized for the photovoltaic and NLO properties of TPA-based dye molecules. Theoretical calculations to gain insights into the geometric and electronic structures of the dyes were discussed and compared with experimental data. All the dyes were found to fulfill the criteria for efficient sensitizers in DSSCs. Substitutions were found to have a huge effect on the optoelectronic properties of the dyes. Substitution of the TPA-N(CH₃)₂ group was found to be the most successful. Among all the dyes, the TPA-N(CH₃)₂ substitution resulted in a decrease in the open circuit voltage (eV_OC = 0.8 eV), accompanied by a significant decrease in band gap (2.15 eV) and a remarkably increased excitation wavelength (576 nm). Therefore, it can be concluded that substitution of the TPA-N(CH₃)₂ group is suitable to meet the needs of an efficient dye. C206 dye has the highest second order hyperpolarizability (7.089 × 10⁻²⁸ esu) compared to the other dyes. Meanwhile, the substitution of the TPA-OC₂H₅ group was not very successful. Substitution of TPA resulted in entirely positive results in the case of C206, leading to a decrease in band gap energy and an increase in oscillator strength; the latter led to an increase in the LHE value, along with a significant decrease in the open circuit voltage (eV_OC = 1.06 eV). Other substitutions, viz TPA-SCH₃ and TPA-OC₂H₅, gave mixed results. In both cases, the band gap energy decreased and the open circuit voltage increased; however, the oscillator strength decreased. The guidelines provided by these studies will be very effective for identifying NLO properties and for the fabrication of photovoltaic devices.

Acknowledgements

The authors are thankful to the learned referees for their useful and critical comments, which improved the quality of the manuscript. One of the authors, M. Prakasam, acknowledges Periyar University for financial support in the form of a University Research Fellowship (URF).

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c6ra11200e

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