A Theoretical Perspective on the Photovoltaic Performance of S,N

Article pubs.acs.org/JPCC

A Theoretical Perspective on the Photovoltaic Performance of S,NHeteroacenes: An Even−Odd Effect on the Charge Separation Dynamics Santu Biswas,† Anup Pramanik,† Sougata Pal,‡ and Pranab Sarkar*,† †

Department of Chemistry, Visva-Bharati University, Santiniketan 731235, India Department of Chemistry, University of Gour Banga, Malda 732103, India

‡

S Supporting Information *

ABSTRACT: The electronic structure and optical properties of fused S,N-heteroacenes (SNn, SN5−SN10) have been studied theoretically. The calculations reveal that, bond length alteration approaches zero with increasing number of heterocyclic rings in the conjugated molecules. As a general trend of optical property, the absorption maximum is red-shifted with increasing conjugation length, achieved through increasing the degree of polymerization or by incorporating strong electron withdrawing groups at the two ends of the molecules. However, an even−odd relationship is observed during electronic excitation followed by exciton dissociation. Thus, SN5 and SN9 experience better charge separation than SN6 and SN10, respectively. The theoretical results interpret the experimental finding where SN5 is reported to offer better photocurrent efficiency. To compare the photovoltaic performances of the materials, we compute the rate of charge recombination and charge transfer for the composites consisting of some SNn and a well reputed acceptor PC61BM.

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INTRODUCTION Global energy demands, which are predicted to be increased by 35% in the next 24 years, have driven scientists to develop new technologies that can efficiently fulfill renewable energy resources.1 Solar energy in that sense is the most promising, clean, and sustainable resource.2,3 After the novel work performed by Grätzel and O’regan in 1991, dye sensitized solar cells (DSSCs) have been received as one of the most potential and highly efficient photovoltaic technologies.4−9 At the beginning, transition metals, especially Ru-containing dyes, were being used as the sensitizer in DSSCs. However, the high cost, rarity of metal used in the dye, and other performance limitations restrict their future practical applications.10 In this connection, metal free organic dyes have drawn serious attention during the past few years primarily because of their lower cost, and most importantly, their energetic and structural tunability acquire a broad solar spectrum, thereby rendering them efficient solar energy harvesting materials.11−16 The organic dyes are in general blended with a suitable acceptor in a bulk heterojunction (BHJ) style, for having the optimum photovoltaic performances.17−19 A new milestone was reached in the field of organic photovoltaic (OPV) cells with the invention of C60 as a highly efficient acceptor.20 C60 and C70 and their analogues PC61BM and PC71BM are purposely used, and now they have become traditional acceptor parts in OPV cells.21,22 OPV cells containing small organic molecules show excellent photocurrent efficiency (PCE) in the range 8−11%.23−27 πConjugated small molecules consisting of electron rich donor (D) and electron deficient acceptor (A) moieties have shown good photovoltaic performances due to strong charge transfer, © XXXX American Chemical Society

lower optical gaps, strong absorption in the visible to near IR region, and excellent charge carrier mobilities.28,29 Among different π-conjugated systems, oligothiophenes comprised of the A−D−A type of architecture are well developed and have shown high performance in vacuum or solution-based organic solar cells.30,31 Moreover, in the case of a D−A system, the incorporation of rigid and coplanar heteroacene can suppress the conformation disorder and reduce the reorganization energy that finally enhances intrinsic charge mobility.32 Recently, a novel class of A−D−A type fused thiophenepyrrole-based heteroacenes and their acceptor capped derivatives have been reported to show good photovoltaic performance.33 However, N-alkylated S,N-heteropentacene (SN5) was developed a few years back as a new class of fused thiophene.34 Now, for the applications in organic solar cells, different acceptor-functionalized SN5 systems have also been studied experimentally. SN5 derivatives with a C60 acceptor achieved a PCE as much as 6.5% in vacuum-processed solar cells, up to 4.9% with a PC61BM acceptor in solution-processed solar cells, and up to 10.3% when applied as hole transporters in perovskite solar cells.35−37 Dicyanovinyl (−DCV) substituted SN5 showed PCE up to 5.64% which is higher than −DCV substituted SN6 (PCE = 3.02%) with C70 as an acceptor, as recently reported by Chung et al.38 The authors have also shown that a PCE of 5.52% could be achieved when cyanoacrylic acid substituted SN6 is used as the sensitizer for DSSCs.38,39 Upon combination of thermal annealing and Received: November 15, 2016 Revised: January 12, 2017 Published: January 18, 2017 A

DOI: 10.1021/acs.jpcc.6b11471 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C

composites were carried out by using density functional theory (DFT) methodologies where (6-31G**) basis sets were used to represent the elements. We used different hybrid functionals such as B3LYP,46 HSE06,47 etc., to calibrate the geometric parameters and the electronic properties. B3LYP is well tested for obtaining optimized ground state geometries even for composite systems,21,33,48−52 and thus, we adopted that HSE06, on the other hand, reproduces the electronic energy gap nicely.52 The minimum point of the optimization was confirmed by vibrational analysis which leads to all positive frequencies for normal modes. We performed time-dependent DFT (TDDFT) calculations on the optimized molecular geometries for obtaining the electronic excitations and the corresponding absorption spectra. The same sets of basis functions (6-31G**) and correlation functionals as in the DFT calculations were used for the TDDFT calculations. However, for computing the excitation energies of the composite systems, we used the long-range corrected functional CAM-B3LYP53 which treats the non-Coulomb interactions very well.21,54 To see the effect of solute−solvent interaction in the absorption spectra, we also performed TDDFT calculations in the solvent phase, dichloromethane (DCM), by applying the polarizable continuum model (PCM), using the integral equation formalism variant (IEFPCM)55 as implemented in G09.56 All of the excited state properties were analyzed with the help of “Multiwfn”, a multifunctional wave function based analyzer.57,58 We employed the generalized Mulliken−Hush (GMH) model59 to compute the charge transfer integral, i.e., the electronic coupling matrix at the donor−acceptor heterojunction. During this, the effect of finite field on the excitation energies of the composites was observed to evaluate the dipolar change during excitations.60 Now, TDDFT expresses the excited states, |Sn⟩, in terms of the configuration state function, Φli, by |Sn⟩ = ∑i→l cliΦli, where the summation runs over all occupied (i) and unoccupied (l) molecular orbitals (ϕ). However, we allowed only spin allowed singlet−singlet transitions for generating 20 excited states. Now, the density distribution of the electron (hole) is contributed from both the local and cross components of the density matrix and they can be expressed in terms of coefficients of configuration state function as58

subsequent solvent vapor annealing, the PCE of 6.64% with SN5 donor and PC71BM acceptor has been reported by Lee et al.40 A vacuum-processed planar heterojunction, based on −DCV substituted SN6, has very recently been developed by Wetzel et al.41 It has been demonstrated that proper functionalizaion to SN6 can lead to an excellent PCE up to 7.1% with C60 as an acceptor. Thus, to date, heterohexacene (SN6) is the longest heteroacene that has been used as a sensitizer in BHJ solar cells. In the meantime, Wetzel et al.42 have reported the systematic extension of the S,N-heteroacene series up to a stable S,N-heterodecane (SN10) which has potential application in organic electronic devices. As the longer heteroacenes have much pronounced optical absorption in the visible solar spectrum, we wish to investigate their applicability as sensitizers in BHJ solar cells. First of all, we here investigate the electronic structure and optical absorption properties of the heteroacenes. We also compute the exciton binding energy and the charge transfer length in different excited states which determine the carrier dynamics of the molecules. We put emphasis on the correlation between the optoelectronic properties and the structure of the heteroacenes, especially on the sequence of the thiophene−pyrrole fusion. Finally, in view of the photovoltaic measurements, we compute the photovoltaic properties of some donor−acceptor (D−A) composites consisting of the heteroacenes and some suitable acceptor like PC61BM. Quantum mechanical calculations on D−A types of complexes can provide important information about those properties and predict the quantitative performance of the materials. The predictability of such calculations is now well tested.21,43 Finally, on the basis of the Marcus theory of electron transfer,44,45 we provide the rates of charge transfer and charge recombination for the proposed complexes. The quantitative information on the basis of empirical relationships thus provides valuable insights on the charge separation and carrier transfer dynamics of the materials.

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MODEL AND COMPUTATION The S,N-heteroacenes were modeled as they have been synthesized recently.33,42 In Figure 1, we have shown the schematic representations of the molecules SN5−SN10. The geometry optimizations of the individual molecules and the

ρelec (r ) =

∑ (cil)2 ϕi(r)ϕi(r) + ∑ ∑ i→l

cilc jlϕi(r )ϕj(r )

i→l j≠i→l

(1)

ρ hole (r ) =

∑ (cil)2 ϕl(r)ϕl(r) + ∑ ∑ i→l

cilc jlϕl(r )ϕm(r )

i→l i→m≠l

(2) 61

The charge density difference (CDD) between any excited state and the corresponding ground state is then given by Δρ(r) = ρelec(r) − ρhole(r). Noteworthy, electron density is the enhancement of negative charge at a particular zone and hole density is the electron depletion at that particular point. Concerning the excited state charge densities in a molecule, there appears to be two more important parameters, the charge transfer length (lCT) and the overlap between the electron and hole (S). We define the charge transfer length as the distance between the barycenters of the electron and hole, while the extent of overlap can be expressed as62,63 Figure 1. Optimized geometries of the unsubstituted S,N-heteroacene molecules (SN5−10) showing the sequence of fusion of thiophene and pyrrole rings using the B3LYP/6-31G** level of theory.

S= B

∫ min(ρhole (r), ρelec (r)) dr

(3) DOI: 10.1021/acs.jpcc.6b11471 J. Phys. Chem. C XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry C We now define here the transition density and its real space representation. Applying the Slater−Condon rule, one may write the transition density matrix in terms of TDDFT excited state wave functions as T (r ; r′) =

∑ ∑ cilϕi(r)ϕl(r′) i

l

(4)

The transition density is defined by considering the diagonal terms only T (r ) =

∑ ∑ cilϕi(r)ϕl(r) i

l

(5)

Obviously, T(r) can be treated as a normal real space function that can be visualized in terms of a 3D isosurface plot. The transition density contains information about the spatial location of the electronic excitation and is directly related to the transition dipole moment.64 Therefore, visualization of the transition density related to a particular transition gives enormous information about that excited state. The transition dipole moment in a particular direction (say μtry) is related to the component of transition density by μtry = ∫ Ty(r) dr, where Ty(y) = −yT(r).

Figure 2. Variation of the HOMO−LUMO gap with increasing conjugation length of the unsubstituted and −DCV substituted S,Nheteroacene molecules. The energy values are computed in the gas phase using the HSE06/6-31G** level of theory.

unsubstituted SNn using the HSE06 (Figure 2) functional matches extremely well with the cyclic voltametric (CV) results performed by Wetzel et al.;42 however, the positions of the energy levels are slightly different. We wish to mention here that the HOMO−LUMO gaps obtained from the B3LYP functional are also in the same range. Figure 2 clearly indicates that, with increasing π conjugation length of the S,Nheteroacene, the HOMO−LUMO gap decreases. The similar trend is also followed by the substituted heteroacene with more and more electron withdrawing groups. The HOMO/LUMO energy levels for the −DCV substituted SN5 and SN6 are in excellent agreement with the CV derived HOMO/LUMO energies.33,38 The substitution driven significant lowering of the HOMO−LUMO gap as a result of prominent charge transfer interactions between the rigid backbone of the heteroacene and the electron withdrawing groups matches well with the experimental finding.33 However, the tunability of the optical gap with the conjugation length and nature of the substituting group could properly be utilized in controlling the solar energy harvesting process. We will show in the subsequent sections that the −DCV substituted heteroacenes show a broad absorption band and thus they have been successfully implemented in solar cell devices. Optical Absorption and Excited State Properties. As discussed in the methodology section, we employed TDDFT formulations for obtaining the electronically excited states and the corresponding absorption properties. Before further proceeding, let us now calibrate the theoretically calculated values with the available experimental data. Wetzel et al.33 have synthesized and investigated the optical properties of pristine and substituted S,N-hexacenes (SN6) in DCM solvent by using UV−vis and fluorescence spectroscopy. We computed the optical properties of the SN6 derivatives in the same solvent, and the corresponding absorption spectra are shown in Figure 3. The maximum absorption (λmax = 376 nm) for the pristine SN6 corresponds to the HOMO → LUMO transition, and a hump appears at 313 nm which is designated as the HOMO−1 → LUMO transition. Both of the transitions are characterized to be of ππ* type. However, with increasing electron withdrawing effect of the substituent, the absorption maximum is red-shifted. For −CHO and −DCV substituted heteroacenes, they are at 462 and 576 nm, respectively. The computed results using the B3LYP/6-31G** level of theory are in good

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RESULTS AND DISCUSSION Geometry and Electronic Structure of the Heteroacenes. In Figure 1, we have shown the optimized structures of the heteroacenes indicating the sequence of the fusion of the thiophene and pyrrole rings. A series of S,N-heteroacenes ranging from SN3 to SN10 with increasing number of conjugated double bonds has recently been characterized by Wetzel et al.42 by using NMR spectroscopy and mass spectrometric techniques. On the basis of the structural characteristics, S,N-heteroacenes can be classified into two main subgroups: odd heteroacenes, SN(2n+1) (n = 1−4), containing alternating thiophene and pyrrole rings having C2V symmetry and even heteroacenes, SN(2n) (n = 2−5), containing thienothiophene units, among which SN6, SN8, and SN10 have C2h symmetry. SN7′ is another heteroheptacene that has also been studied recently having the same chain length as that of SN7, but it has a different number and sequence of heterocyclic thiophene and pyrrole rings. All of the molecules exhibit a planar structure indicating a thorough delocalization around the heteroacene backbone, although a slight bondlength alteration (BLA) is noticed in the inner part of the heteroacenes. The pristine SN5 and SN6 show BLA in the order of 0.014 Å which is lower than that of the corresponding oligothiophenes,33,42,52 while it further reduces with increasing conjugation length. However, addition of an electron withdrawing group at the two edges of the heteroacenes increases the extent of delocalization, thereby further reducing the BLA. The computed BLA for −DCV substituted SN9 and SN10, which is in the order of 0.005 Å only, corroborates with the fact of “nearly complete equalization” in the inner part of the conjugated backbone.42 We now investigate the electronic properties of the heteroacenes. The computed energy gaps between the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) along with the frontier energy levels of the substituted and unsubstituted SNn molecules are displayed in Figure 2. Figure S1 in the Supporting Information shows the isosurface plots of some frontier molecular orbitals. Noteworthy, the computed HOMO−LUMO gap for the C


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simply mimic the alkyl side chains, we have studied the methyl substituted heteroacenes which in turn saves the computational expenses. As is obvious, the exchange correlation functionals have a great influence on the absorption maxima. However, as already stated, the hybrid functional B3LYP reproduces the experimental results of SN6 quite nicely (Figure 3). The computed gas-phase absorption spectra, in the same level of theory, for SN6 and other heteroacenes are given in Figure 4. As could be found, λmax is red-shifted with increasing conjugation length of the heteroacenes. Let us compare the excited state properties of −DCV substituted SN5 and SN6, as shown in Table 1 and Table 2, respectively (as hereafter we perform all computations on “− DCV substituted” heteroacenes, we omit that term in the table and figure captions). The first excitation energy, which is characterized to be the band gap (HOMO−LUMO gap) absorption, decreases by 0.07 eV on going from SN5 to SN6. The oscillator strengths ( f) for both transitions are very high, indicating a high light harvesting efficiency (LHE = 1−10−f) of the materials. The charge transfer amount (qCT) from the ground to the first excited state is also similar for both molecules (in the order of 0.3 e). However, the charge transfer length (lCT) shows a striking difference; for SN5 and SN6, they are 0.068 and 0.0001 Å, respectively. Although for both molecules, SN5 and SN6, all of the electronic excitations are characterized to be local excitations (LEs), lCT for the latter is extremely small in comparison to that of the former. Thus, excited state charge separation is much more difficult for SN6 which affects the charge transport and carrier dynamics seriously.

Figure 3. Absorption spectra of pristine (a), −CHO (b), and −DCV (c) substituted SN6 computed using the B3LYP/6-31G** level of theory in DCM solvent. With increasing the electron withdrawing effect of the substituent, the absorption maximum is shifted toward the red.

agreement with the experimental values reported by Wetzel et al.33 These authors, however, reported a multiple vibronic splitting in the absorption spectra of SN6 originating from the rigidity of the conjugated π system which is very difficult to reproduce theoretically. Note that the alkyl side chains attached to the N atoms of the pyrrole moiety hardly affect the optical and electronic gaps of the heteroacene backbone; rather, they have an influencing role on the thermal properties of the molecular aggregation which is beyond our scope.41 Thus, to

Figure 4. Absorption spectra of SN5, SN6, SN9, and SN10 (a−d, respectively) computed using the B3LYP/6-31G** level of theory in the gas phase. The positions of different excited states are marked by Sn. The maximum absorption peak of each molecule corresponds to the band gap absorption, and it is red-shifted with increasing conjugation length of the molecular backbone. D


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molecules, SN5 and SN6. In Figure 5, we have presented the isosurface of charge density difference (CDD) of both species for some transitions involving high absorption peaks. By comparing the isosurface of the HOMO, LUMO, and CDD of S1, one can easily say that the S1 originates from charge transfer from the HOMO to the LUMO. However, the CDD plots also resemble the lCT values, as shown in Table 1 and Table 2 for SN5 and SN6, respectively. All of these analyses clearly reveal that SN5 has superior intramolecular charge transfer and separation (at least for S1, S2, S5, S11, S12, etc.) in comparison to that of SN6 and this is responsible for its better PCE. In sharp contrast, comparing the oscillator strength of the major absorptions for SN5 and SN6, one may conclude that the latter offers better LHE. A similar thing is also reflected from the transition density (TD) plots (Figure 6) of the abovementioned states for SN5 and SN6. We find more intense TD for some low lying excited states of SN6 than that of SN5. Moreover, some subtransition dipoles are canceled out due to C2V symmetry of the SN5. Thus, the overall transition intensities are to some extent higher for SN6. However, the improper charge separation, in the case of SN6, leads to faster recombination and thus the PCE is expected to be lowered. Our theoretical analysis corroborates with the external quantum efficiency (EQE) results which also indicate that, in spite of absorption domination in the high photoflux regions, SN6 shows a lower PCE, indicating an obstacle for charge separation.38 In order to see the generality of the phenomena, we now compare the excited state properties of −DCV substituted SN9 and SN10. The absorption spectra of both species show an intense band at the visible region (604 and 613 nm, respectively) corresponding to the band gap absorption (please see Figure 4). Unlike the lower homologues (SN5 and SN6), the high energy absorption peak now enters into the visible/ near UV region with relatively higher intensity. Thus, these now cover a broad spectral region. The absorption characteristics and the nature of the excited state of both molecules are shown in Table 3 and Table 4, respectively. The maximum absorptions of SN9 correspond to two major transitions, S0 → S1 (604 nm) and S0 → S6 and S7 (406 and 397 nm), while, for SN10, the two major peaks correspond to S1 (613 nm) and S6 (423 nm) excited states, respectively. All of these transitions may, however, be referred to as local excitations (LE). It is clearly revealed that the intensities of major absorption of both species are comparable; the amount of charge transfer also varies only marginally. However, like the case of SN5 and SN6, the striking difference is in the charge transfer length. For SN9, the barycenters of net charge accumulation and charge depletion are separated by 1.69 Å in the S1 state, while that for the SN10 is only 0.003 Å. Similar is the situation for another high intensity transition from S0 to S6 excited state also. This means that, similar to SN6, SN10 also experiences a problem of charge separation in the excited states. The CDD and TD plots of both SN9 and SN10 are shown in Figure 7 and Figure 8, respectively. While comparing between SN5 and SN9, it is revealed that the lCT values are much better for the latter. Thus, we could expect easier charge separation and hence faster carrier mobility for SN9, even better than SN5. Exciton Binding Energy. The exciton binding (Eb) energy is one of the key parameters that determine the photovoltaic performance of a molecule. Eb is defined as the energy requirement for the dissociation of excitons to free polarons through an intermediate state of bound polaron.66 However, in

Table 1. Transition Energy, Oscillator Strength (f), and Other Excited-State Properties of SN5 Computed in the Gas Phase Using the B3LYP/6-31G** Level of Theory states S1 S2 S3 S4 S5 S6 S7 S8 S9 S10 S11 S12 S13 S14 S15

excitation energy (eV) 2.41 2.68 2.88 3.24 3.37 3.60 3.94 3.97 4.20 4.22 4.28 4.60 4.71 4.77 4.87

(515) (463) (430) (382) (367) (344) (314) (312) (295) (293) (290) (269) (263) (260) (255)

a

f

S

lCT (Å)

excited-state property

2.0240 0.0310 0.0040 0.0000 0.0114 0.1426 0.0840 0.0120 0.0840 0.0095 0.0000 0.0000 0.0259 0.0000 0.0090

0.487 0.297 0.555 0.278 0.352 0.609 0.644 0.293 0.683 0.357 0.197 0.196 0.649 0.241 0.484

0.068 0.126 0.017 0.135 0.218 0.003 0.087 0.170 0.154 0.182 1.290 1.198 0.206 1.229 0.218

LE LE LE LE LE LE LE LE LE LE LE LE LE LE LE

qCT (e) 0.326 0.612

0.258

a Values in parentheses indicate the corresponding wavelength (λ) in nm.

Table 2. Transition Energy, Oscillator Strength (f), and Other Excited-State Properties (Electron−Hole Overlap (S), Charge Transfer Length (lCT), etc.) of SN6 Computed in the Gas Phase Using the B3LYP/6-31G** Level of Theory states S1 S2 S3 S4 S5 S6 S7 S8 S9 S10 S11 S12 S13 S14 S15


(531) (451) (446) (393) (375) (363) (337) (334) (316) (310) (309) (283) (280) (278) (271)

a

f

S

lCT (Å)

excitedstate property

2.2749 0.0000 0.0385 0.0000 0.0000 0.0000 0.1947 0.0289 0.0456 0.0073 0.0000 0.0002 0.1722 0.0000 0.0000

0.479 0.541 0.327 0.343 0.0005 0.608 0.575 0.363 0.683 0.488 0.183 0.207 0.669 0.366 0.267

0.0001 0.0002 0.0022 0.0012 0.0021 0.0001 0.0002 0.0012 0.0005 0.0007 0.0076 0.0077 0.0003 0.0009 0.0101


qCT (e) 0.343 0.608

0.357

a

Values in parentheses indicate the corresponding wavelength (λ) in nm.

It is reported that polycyclic aromatic hydrocarbons show intense photoluminescence and high carrier mobilities because of their rigid coplanar backbone with high degree of π conjugation.38,65 The conjugation length further increases with incorporating them into donor−acceptor system. Moreover, it is believed that the stiffness and coplanar architecture of the molecules suppress the conformational disorder, which results in a decrease in reorganization energy, thereby increasing the intrinsic charge mobility.32 S,N-Heteroacenes are such type of molecules capable of showing a high PCE. The planar mixed active layer of −DCV substituted SN5 with C70 is reported to show an excellent PCE of 5.64%. Under similar conditions, SN6 derivative shows a PCE of 3.02%.38 To look into such phenomena, we perform charge transfer analysis on both of the E


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Figure 5. Charge density difference (CDD) for S1, S2, and S6 excited states (a−c) of SN5 and S1, S3, and S7 excited states (d−f) of SN6. The amount of charge transfer (qCT) and the charge transfer lengths (lCT) are shown in Table 1 and Table 2. Blue (red) stands for depletion (accumulation) of negative charges.

Figure 6. Transition densities for S1, S2, and S6 excited states (a−c) of SN5 and S1, S3, and S7 excited states (d−f) of SN6. The blue (red) color stands for the hole (electron).

Table 3. Transition Energy, Oscillator Strength (f), and Other Excited-State Properties of SN9 Computed in the Gas Phase Using the B3LYP/6-31G** Level of Theory states S1 S2 S3 S4 S5 S6 S7 S8 S9 S10 S11 S12 S13 S14 S15


(604)a (529) (455) (427) (414) (406) (397) (382) (362) (360) (337) (327) (320) (317) (312)

f

S

lCT (Å)


2.6405 0.0343 0.0293 0.0170 0.0285 0.2263 0.2928 0.0231 0.1827 0.0211 0.0062 0.0493 0.0180 0.0296 0.0003

0.378 0.427 0.293 0.332 0.515 0.426 0.509 0.308 0.641 0.399 0.318 0.345 0.538 0.539 0.372

1.694 1.364 1.892 0.860 2.075 0.502 0.849 2.355 0.624 1.453 1.540 1.836 2.941 3.662 1.575


Table 4. Transition Energy, Oscillator Strength (f), and Other Excited-State Properties of SN10 Computed in the Gas Phase Using the B3LYP/6-31G** Level of Theory

qCT (e) states

0.440 0.492 0.680

S1 S2 S3 S4 S5 S6 S7 S8 S9 S10 S11 S12 S13 S14 S15

0.527 0.445



(613) (544) (445) (439) (425) (423) (401) (391) (379) (366) (347) (340) (336) (334) (326)

a

f

S

2.7840 0.0000 0.0457 0.0000 0.0000 0.6785 0.0000 0.0714 0.1534 0.0108 0.0000 0.0000 0.1070 0.0000 0.0000

0.377 0.402 0.317 0.463 0.402 0.549 0.302 0.349 0.633 0.371 0.315 0.176 0.618 0.612 0.371

CT

l

(Å)

0.0032 0.0030 0.0021 0.0019 0.0003 0.0028 0.0022 0.0056 0.0011 0.0069 0.0066 0.0035 0.0020 0.0027 0.0101

excitedstate property LE LE LE LE LE LE LE LE LE LE LE LE LE LE LE

qCT (e) 0.458 0.520 0.665

0.378


organic solar cells, we correlate excitonic dissociation with charge separation, i.e., generation of free electron and hole. Thus, it can be viewed as the Coulomb interaction energy

between the positive (D+) and negative centers (A−) of a molecule. Thus, F


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Figure 7. Charge density difference (CDD) for S1, S2, and S6 excited states (a−c) of SN9 and S1, S3, and S6 excited states (d−f) of SN10. The amount of charge transfer (qCT) and the charge transfer lengths (lCT) are shown in Table 3 and Table 4. Blue (red) color stands for depletion (accumulation) of negative charges.

Figure 8. Transition densities for S1, S2, and S6 excited states (a−c) of SN9 and S1, S3, and S6 excited states (d−f) of SN10. The blue (red) color stands for the hole (electron).

Table 5. Comparing Charge Transfer/Recombination Rates and Associated Photovoltaic Properties of the SNn−PC61BM/PDI Composite Systems Computed in the Gas Phase (Eb = Exciton Binding Energy, Δμ = Dipole Moment Difference between Ground and Excited States, μtr = Transition Dipole between Ground and Excited States, VOC = Open-Circuit Voltage) system

Eb (eV)

Δμ (au)

μtr (au)

VDA (eV)

VOC (V)

SN5−PC61BM

0.35

3.06

0.0355

0.0357

1.88

SN6−PC61BM

0.31

6.92

0.0079

0.0036

1.81

SN9−PC61BM

0.26

4.17

0.4726

0.2745

1.29

SN10−PC61BM

0.23

7.98

0.1359

0.0451

1.28

SN5−PDI

0.35

5.47

0.1518

0.0686

1.29

SN9−PDI

ECoul =

0.26

∑ d ∈ D,a ∈ A

ε

6.60

0.0250

0.0089

qdqa lda

0.70

ΔGCR in eV (kCR in s−1) −2.18 (4.11 × −2.11 (4.60 × −1.59 (1.68 × −1.58 (7.56 × −1.59 (1.01 × −1.00 (1.40 ×

10−11) 10−11) 105) 103) 104) 1010)

ΔGCT in eV (kCT in s−1) −0.58 (2.67 × −0.53 (3.10 × −0.72 (6.97 × −0.67 (2.70 × −1.17 (1.85 × −1.31 (5.92 ×

1013) 1011) 1014) 1013) 1010) 106)

be obtained from TDDFT calculation. Therefore, the lower the exciton binding energy, the easier the separation of electron and hole. Our computed exciton binding energies (Eb) for different heteroacenes are given in Table 5 which are in the order of 0.25−0.30 eV. We wish to mention here that similar Eb values were reported for BT68 and PDDTT21 organic dyes. Note that, with increasing conjugation length of the heteroacene, the Eb value decreases. For the longest heteroacene studied here (SN10), the Eb value is 0.23 eV. It is worth mentioning here that the electronic and optical gaps are very sensitive to the

(6)

where qd and qa are the partial charges accumulated on D+ and A−, respectively, separated by a distance lda and ε is the dielectric constant of the medium. We estimate ECoul as the difference between the electronic and optical band gap energies,67 where the electronic band gap is the energy offset between the HOMO and LUMO and the optical gap is taken as the first excitation energy within the same spin state which can G


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The Journal of Physical Chemistry C functional used during DFT or TDDFT calculations. However, for the small organic molecules like S,N-heteroacenes, the HOMO−LUMO gap extremely matches well52 with the experimental value using the HSE06 functional as discussed earlier and thus we used these results for calculating the exciton binding energy. The first excitation energy value was computed by using CAM-B3LYP which employs long-range correction for the non-Coulomb part of the exchange functional. A similar strategy has recently been adopted for several species.21,68 Composite Systems and Charge Transfer Dynamics. It is well-known that the photovoltaic performance of a material is highly enhanced by the formation of a donor−acceptor (D−A) type of composite. In view of this, we have modeled a particular type of D−A adducts of different S,N-heteroacenes with the acceptor PC61BM. In the optimized structure (see Figure S2 in the Supporting Information), the PC61BM is placed vertically over the heteroacene molecular surface. The D−A adducts may be considered as a model for BHJ and thus we compute the photovoltaic properties of the complexes. Before doing this, let us have a glance at the optical properties and the nature of the excited states of the composites. Table 6 and Table 7 present

Table 7. Transition Energy, Oscillator Strength (f), and Other Excited-State Properties of the SN6−PC61BM Composite System Computed in the Gas Phase Using the CAM-B3LYP/6-31G** Level of Theory states S1 S2 S3 S4 S5 S6 S7 S8 S9 S10 S11 S12 S13 S14 S15 S16 S17 S18 S19 S20


excitation energy (eV) 2.42 2.44 2.52 2.55 2.65 2.66 2.71 2.78 2.83 2.86 2.94 2.96 2.99 3.07 3.10 3.12 3.14 3.18 3.24 3.35

(513)a (507) (491) (486) (468) (466) (458) (447) (439) (433) (421) (419) (415) (403) (399) (397) (395) (390) (383) (370)

f

S

lCT (Å)


0.0006 0.0000 0.0001 0.0000 1.8967 0.0002 0.0009 0.0000 0.0027 0.0007 0.0006 0.0016 0.0000 0.0002 0.0004 0.0017 0.0004 0.0165 0.0017 0.0357

0.435 0.581 0.549 0.419 0.489 0.363 0.646 0.628 0.578 0.636 0.534 0.550 0.624 0.010 0.554 0.614 0.027 0.558 0.010 0.374

0.551 0.463 0.197 0.231 0.052 0.315 0.388 0.451 0.271 0.247 0.416 0.922 0.561 6.557 0.455 0.529 7.116 0.236 6.105 0.082

LE LE LE LE LE LE LE LE LE LE LE LE LE ICT LE LE ICT LE ICT LE


(512)a (506) (491) (487) (474) (464) (456) (446) (439) (434) (421) (416) (414) (402) (396) (394) (392) (388) (371) (366)

f

S

lCT (Å)


0.0013 0.0000 0.0004 0.0001 2.2131 0.0001 0.0005 0.0000 0.0006 0.0019 0.0012 0.0007 0.0001 0.0010 0.0061 0.0001 0.0142 0.0014 0.0097 0.0317

0.438 0.591 0.547 0.412 0.495 0.372 0.649 0.653 0.587 0.612 0.519 0.565 0.618 0.509 0.432 0.376 0.546 0.083 0.081 0.464

0.456 0.454 0.027 0.134 0.193 0.277 0.284 0.323 0.184 0.035 0.366 0.825 0.479 0.976 2.392 3.175 0.410 6.304 5.619 0.469

LE LE LE LE LE LE LE LE LE LE LE LE LE LE LE LE LE ICT ICT LE

a


The nature of charge transfer in the excited states can easily be confirmed by the CDD plots of the composites for some selective states, as shown in Figure 9. Clearly, S14 for SN5 and S18 for SN6 involve an intermolecular charge transfer from the donor to the acceptor. Consequently, these states show a huge charge transfer length (lCT) of 6.557 and 6.304 Å, respectively. Noticeably, the lCT follows a similar sequence as that for the single heteroacene molecule. The generation of an electron−hole pair or exciton via the photoexcitonic movement of an electron from an occupied orbital to an unoccupied orbital can be understood by the twodimensional (2D) site representation of the transition density matrix.69,70 Each element of that matrix indicates the dynamics of an exciton projected on a pair of atomic orbitals, and this basically measures the probability of finding one charged particle on one site and the second one on the other site. Obviously, the number of charged particles reflects the strength of the coherence between the donor and acceptor sites. Figure 10 visualizes the electron−hole coherences, spatial span, and primary sites of electronic transitions for some excited states of the SN5−PC61BM composite. As shown in the figure, the excited states S1 and S5 involve the electron−hole coherences within the acceptor PC61BM and the donor SN5, respectively, thereby characterizing them as LE. On the other hand, S14 is an intermolecular charge transfer excited state as a result of the electron and hole coherence between SN5 and PC61BM. A deep analysis reveals that the electrons strongly cohere with holes involving the atoms of both the donor and the acceptor which are in close proximity to each other in the composite material. The nature of the excited states for the other composites is also similar. Reorganization Energy. Reorganization energy (λ) is another important parameter that determines the photovoltaic


the gas phase absorption characteristics and excited state properties of the composites formed by SN5 and SN6, respectively. Both for SN5- and SN6-composites, λ max corresponds to the corresponding S5 excited states with oscillator strengths of 1.8967 and 2.2131, respectively. However, all of the low-energy transitions are characterized as LE involving either the donor heteroacene or the acceptor PC61BM. The first intermolecular charge transfer (ICT) state for SN5 appears at 403 nm (S14), while that is S18 for SN6. The absorption intensities of those transitions are relatively low, but those states are mainly responsible for photovoltaic efficiencies. H


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Figure 9. Charge density difference (CDD) for S1, S5, and S14 excited states (a−c) of the SN5−PC61BM composite system and S1, S5, and S18 excited states (d−f) of the SN6−PC61BM composite system. Parts c and f are intermolecular charge transfer states, while the others are local excitations involving either donor (SN5/6) or acceptor (PC61BM). Blue (red) stands for depletion (accumulation) of negative charges.

Figure 10. 2D site representation of the transition density matrix (TDM) for S1, S5, and S14 excited states (from left to right) of the SN5−PC61BM composite system. S1 and S5 represent local excitations involving PC61BM acceptor and SN5 donor, respectively, whereas S14 represents the intermolecular charge transfer state. The color bars are shown at the right of each figure.

performance of a D−A composite. λ consists of two parts, inner reorganization energy (λi) and outer reorganization energy (λs).71 λi arises as a result of a change in equilibrium geometry of the D and A counterparts of the composite during the electron transfer process, and thus, it is the sum of two terms (λi = λe + λh), coming from the contribution of electron (e) and hole (h). On the other hand, λs appears due to electronic and nuclear polarization/relaxation of the surrounding medium. Now, λe and λh could be computed as λe = E(A−) − E(A) and λh = E(D) − E(D+), where E(A−) and E(A) are the energies of the neutral acceptor at the anionic geometry and optimal ground-state geometry, respectively, and E(D) and E(D+) are the energies of the radical cation donor at the neutral geometry and optimal cation geometry, respectively. We calculate the λi values of the dye−PC61BM composites which are in the range of 0.20 eV. The reported values are in line with those for other organic composites.21,72 It should be pointed out that λi can alternatively be determined by taking the average of λi1 and λi2, where the two terms come from the reorganization of the intramolecular excited state to the charge transfer state and vice versa, respectively.73,74 For the present case, the recomputed λi values are also in the same range (∼0.20 eV). However, for organic composites with fullerene or substituted fullerene, the overall λ, considering inner and outer counterparts, runs around

0.50 eV.21,43 Therefore, for the rate calculation in the next step, we consider an overall λ of 0.50 eV. Rates of Charge Transfer and Recombination Processes. The photovoltaic performance of a material is crucially determined by the carrier transfer dynamics within the system. We now determine the excitonic dissociation followed by the carrier transfer dynamics by means of the rate of charge transfer and charge recombination processes that can be calculated on the basis of Marcus theory45 as shown below k=

⎛ (ΔG + λ)2 ⎞ 4π 3 2 exp | V | ⎜− ⎟ DA 4λkBT ⎠ h2λkBT ⎝

(7)

where λ is the reorganization energy, VDA is the charge-transfer integral between the donor and acceptor states, and ΔG is the free energy change for the corresponding electron transfer processes at a particular temperature T. We define ΔGCT for charge transfer from the donor to acceptor moiety and ΔGCR for charge recombination, i.e., pairing of electron and hole. Now, the charge transfer integral (VDA) between the ground state (S0) and an excited state (Sn) can be expressed in terms of the generalized Mulliken−Hush (GMH) model59 I


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Figure 11. Charge density difference (CDD) for S1, S3, and S5 excited states (a−c) of the SN9−PC61BM composite system and S1, S3, and S6 excited states (d−f) of the SN10−PC61BM composite system. Blue (red) stands for depletion (accumulation) of negative charges.

VDA =

energy for PC61BM (= −3.48 eV) is overestimated by ∼0.50 eV while comparing that with the experimentally reported values.78,79 This LUMO energy deviation for PC61BM renders an overestimation of ΔGCR which is responsible for the very slow charge recombination rate. Some other functional like PBE080 improves the LUMO energy of the acceptor (= −3.62 eV), but it underestimates the HOMO−LUMO gap (=1.54 eV). The similar argument can also be cited for the ΔGCT values. Alternatively, ΔGCR and ΔGCT can directly be evaluated from the total energies of the isolated donor and acceptor species in their corresponding potential energy minima of the intramolecular excited state and the charge transfer state, respectively.71,73,74 The obtained ΔG values differ a bit from the previous ones, maybe due to improper consideration of correlation energy, and thus, the predicted electron transfer rates are also changed to some extent; however, the qualitative trend remains the same. Now, let us transmit the idea for the similar composites of SN9 and SN10 for which the first intermolecular charge transfer states are S5 and S6, respectively (please see Figure 11 for the CDD plots). The associated excited state properties of SN9 and SN10 are given in Table 8 and Table 9, respectively. Note that much lower excitons are now responsible for intermolecular charge separation. Our calculations reveal that the SN9 composite also shows a faster charge transfer rate than that of SN10. However, charge recombination rates for both composites are much larger while comparing those for SN5 and SN6 composites. Therefore, it can be rationalized that the odd heteroacenes (SN5/SN9) provide a much better photovoltaic efficiency than the even ones with very high charge transfer rates. Another interesting point is that SN9 produces a faster electron transfer rate (kCT = 6.97 × 1014 s−1) than that of SN5 (kCT = 2.67 × 1013 s−1), maybe due to the larger separation of electron and hole for the former. We now check how the charge transfer and recombination dynamics are affected by varying the acceptor material. Recently, considerable efforts have been devoted to exploring different kinds of nonfullerene acceptors used in BHJ organic solar cells and some of them show high power conversion efficiencies too.81−83 Among the various classes of nonfullerene acceptors, perylene diimide derivatives are the earliest and most common ones because of their high electron mobility, intense

μtr ΔE (Δμ)2 + 4(μtr )2

(8)

where μtr is the transition dipole moment along the major axis, Δμ is the difference between the dipole moments of the two states, S0 and Sn, and ΔE is the vertical excitation energy. Now, Δμ can be computed by using the finite field method on the excitation energy.70,75 The calculated Δμ, μtr, and hitherto obtained VDA values for some systems are shown in Table 5. It should be pointed out that the first intermolecular charge transfer states for SN5- and SN6-composites are S14 and S18, respectively. Thus, we choose those states for VDA calculations. The free energy change for charge recombination (ΔGCR) can be estimated as the difference in ionization potential of the donor (EIP(D)) and electron affinity of the acceptor (EEA(A)), i.e., ΔGCR = EIP(D) − EEA(A). As a general approximation, EIP(D) and EEA(A) are the HOMO and LUMO energies of the donor and acceptor counterparts, respectively.76 Now, with the help of ΔGCR, one can estimate the value of ΔGCT, the free energy change for charge recombination using the Rehm− Weller equation,77 ΔGCT = −ΔGCR − ΔE0−0 − Eb, where ΔE0−0 and Eb are the energy of the lowest excited state of the free-base donor and the exciton binding energy, respectively. In the case of the SN5−PC61BM composite, the estimated value of ΔGCR is −2.18 eV and hence ΔGCT = −0.58 eV. The negative value of ΔGCT indicates that the electron transfer is a thermodynamically favorable process. Finally, we calculate the rates of charge recombination (kCR) and charge transfer (kCT) for the SN5-composite which are 4.11 × 10−11 and 2.67 × 1013 s−1, respectively. For the SN6-composite, the kCR and kCT values are 4.60 × 10−11 and 3.10 × 1011 s−1, respectively. Therefore, we conclude that SN5 involves a slower charge recombination and faster charge transfer rate in comparison to that of SN6. The point should be discussed here that, the ΔGCR value is highly functional dependent, since it depends on the absolute HOMO and LUMO energies of the donor and acceptor species, respectively. We already mentioned that the computed HOMO/LUMO absolute energies (using the HSE06 functional) for the −DCV substituted heteroacenes are in excellent agreement with cyclic voltametric results and they give the best matching HOMO−LUMO gap.33,38 However, using the same functional, our computed LUMO J


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SN9. The calculated rate constants are summarized in Table 5 which reveals that here also the charge transfer rates are high enough, especially for SN5, however, the charge recombination rates are highly increased in comparison to the corresponding PC61BM-composites. We admit that PDI is not a good acceptor for SN9 for which the recombination rate is higher than charge transfer. It is worthwhile to mention here that, in organic photovoltaic cells, the charge separation and further transport occurs under the influence of an electric field generated via the difference of work-functions of the electrodes used. Thus, the electron transfer under the influence of an external field is an important issue.21,68,72 For doing this, one needs to study the properties of excited states and photoexcitations under the external electric field. Experimentally, this could be done by employing linear and nonlinear optical spectroscopic techniques; however, the theoretical basis of that is the variation of excitation energy (Eex) with static electric field (F) and is represented by



(513)a (510) (507) (506) (499) (492) (488) (465) (463) (457) (446) (438) (434) (422) (419) (416) (414) (401) (395) (390)

f

S

lCT (Å)


0.0086 0.0494 2.9551 0.0003 0.0237 0.0001 0.0000 0.0001 0.0013 0.0004 0.0001 0.0009 0.0008 0.0024 0.0241 0.0043 0.0006 0.0009 0.0020 0.0126

0.419 0.146 0.446 0.574 0.015 0.539 0.417 0.389 0.008 0.641 0.674 0.595 0.616 0.532 0.462 0.532 0.603 0.534 0.577 0.548

0.322 5.985 0.637 0.087 7.202 0.148 0.207 0.332 6.986 0.317 0.374 0.258 0.091 0.533 0.361 0.679 0.536 0.360 0.724 0.152

LE ICT LE LE ICT LE LE LE ICT LE LE LE LE LE LE LE LE LE LE LE

Eex (F ) = Eex (0) − ΔμF −


Table 9. Transition Energy, Oscillator Strength (f), and Other Excited-State Properties of the SN10−PC61BM Composite System Computed in the Gas Phase Using the CAM-B3LYP/6-31G** Level of Theory

S1 S2 S3 S4 S5 S6 S7 S8 S9 S10 S11 S12 S13 S14 S15 S16 S17 S18 S19 S20


(512)a (507) (507) (491) (486) (467) (465) (457) (456) (446) (438) (437) (433) (428) (422) (416) (414) (399) (396) (389)

f

S

lCT (Å)


0.0135 0.0963 3.2341 0.0004 0.0000 0.0016 0.0001 0.0008 0.0013 0.0000 0.0004 0.0021 0.0005 0.0178 0.0028 0.0017 0.0001 0.0004 0.0019 0.0109

0.438 0.583 0.461 0.547 0.414 0.049 0.367 0.319 0.509 0.650 0.458 0.366 0.617 0.441 0.543 0.549 0.623 0.540 0.598 0.560

0.477 0.471 0.135 0.042 0.125 6.589 0.029 4.697 2.5606 0.296 2.497 3.367 0.177 0.077 0.453 0.726 0.503 0.361 0.642 0.049

LE LE LE LE LE ICT LE ICT LE LE LE ICT LE LE LE LE LE LE LE LE

(9)

where Δμ is the dipole moment difference between the ground and excited states and Δα is the change in polarizability. The details of such computational results would be given in a future communication. However, the effect of the work-functions of the electrodes on the charge transport process can be understood in the absence of external bias by calculating the open-circuit voltage (VOC) of a BHJ solar cell. VOC can simply be estimated by50,84

a

states

1 ΔαF 2 2

D A VOC = 1/e(|E HOMO | − |E LUMO |) − 0.3V

(10)

assuming that an energy difference of 0.3 eV between the LUMO of the donor and the LUMO of the acceptor is sufficient for efficient charge separation. The computed VOC values of the composites are given in Table 5. The large value of VOC indicates the deep-lying HOMO states of the donors, and this ascertains the suitability of the materials for photovoltaic devices. Our results are in qualitative agreement with the previous experimental results where the S,N-heteroacene− fullerene composites are reported to show high VOC greater than or approximately equal to 1 V.36,38,41

■

CONCLUSION In summary, the present quantum chemical investigation provides quantitative information regarding the photovoltaic performance of the S,N-heteroacene dyes. We see that rigid architecture of the heteroacenes leads to a conjugated backbone which gets equalized C−C bond lengths for the longer chain molecules. The HOMO−LUMO gap of the molecules and hence energy of the first optical absorption gradually decreases with increasing conjugation length of the heteroacene backbone, irrespective of whether it is even or odd. A strong electron withdrawing group at the two ends of the heteroacene, however, imparts extended delocalization, thereby further redshifting the absorption value. An even−odd relationship is observed for the charge separation process of the heteroacenes; the odd ones provide better excited state charge separation, thereby undergoing faster charge transfer dynamics and thus photocurrent efficiencies of those molecules are better than the even ones. Our analysis strongly corroborates with the previous experimental observations. We also rationalize the idea for different pairs of such even/odd S,N-heteroacene molecules.

a


absorption, and high environmental and thermal stability.81 We chose helical perylene diimide dimer (PDI) as the nonfullerene acceptor (see Figure S3) and see the charge transfer rates for the composites of the two most efficient heteroacenes, SN5 and K


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Finally, we predict the charge transfer and recombination rates for the donor molecules embedded onto the PC61BM acceptor. We believe that the present work is complementary to the experimental works already performed and provides general information and predictability over the photovoltaic performance of the larger S,N-heteroacene dyes.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.6b11471. Isosurface plots of some frontier molecular orbitals of SN5 and SN6, optimized geometries of some composite systems, and Cartesian coordinates of the optimized geometries of some composite systems (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Pranab Sarkar: 0000-0003-0109-6748 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The financial supports from UGC [F. No. 43-174/2014 (SR)] and SERB-DST [Ref. No. CS-085/2014], New Delhi, Govt. of India, are gratefully acknowledged.

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