Theoretical studies on charge transport and optical properties of tris(N-saclicylideneanilines)

Abstract

The structural, charge transport and optical properties of the discotic liquid crystalline molecule tris(N-saclicylideneanilines) (TSANs) have been studied using quantum chemical methods. The TSANs have enol-imine and keto-enamine tautomeric forms, and the relative energy calculations show that the keto form is more stable than the enol form. The effective charge transfer integral and site energy corresponding to the hole and electron transport in TSAN molecules were calculated directly from the matrix elements of Kohn–Sham Hamiltonian. The calculated charge carrier mobility using the Monte Carlo simulation of the polaron hopping transport method shows that the TSAN molecules are n-type organic semiconductors and the charge transport strongly depends on the substituted functional groups and the orientation of the π-stacked molecules. The absorption and emission spectra of TSANs have been analyzed using a time-dependent density functional theory (TDDFT) method. The results obtained from this study will reveal the relationships between the molecular structure and charge transport as well as the optical properties of the TSAN molecules.

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1. Introduction

Over the past two decades, there has been active and interesting research on organic semiconducting materials due to their extensive applications in molecular electronics.^1–3 Among the organic semiconductors, discotic liquid crystalline materials are the best candidates for molecular electronic applications because of their unique properties such as long-range self assembly and ease of processing and high solubility.^4–8 A typical discotic molecule contains a central aromatic core functionalized with electron withdrawing and electron donating groups and flexible side chains. In the liquid crystalline phase, the self assembled disk-like molecules are stacked one over the other to form columnar molecular stacks. The existence of overlap between the π-orbitals of nearby molecules leads to a one dimensional pathway for charge transport between the adjacent molecules. Charge transport studies on the different types of discotic liquid crystalline molecules, such as triphenylenes, polycyclic aromatic hydrocarbons, and perylene diimide, show that these molecules exhibit high charge carrier mobility and their values range between 0.002–1.3 cm² V⁻¹ s⁻¹.^7–9 Although a number of experimental and theoretical investigations have been performed on liquid crystalline materials^4,6,10–13 and organic semiconductors,^14–16 it is necessary to investigate the charge transport and optical properties of newly synthesized molecules to improve the performance of the organic semiconducting materials by modifying the structure through the substitution of functional groups and side chains.

Among the organic molecules, N-saclicylideneaniline based molecules are unusual due to the reversible proton transfer mechanism between their enol-imine (OH) and keto-enamine (NH) forms.¹⁷ Yelamaggad et al.^18–23 synthesized and analyzed the thermal and photophysical properties of tris(N-saclicylideneanilines) (TSANs) with different side chains attached at different positions on the end phenyl rings. These molecules exhibit a discotic liquid crystalline phase in enol and keto tautomeric forms. TSANs exhibit multiple proton transfer process, and this property makes them a promising material for molecular electronics applications such as switches.^24,25 In general, most of the reported discotic liquid crystalline molecules, such as triphenylene and hexabenzocoronene, are p-type materials, and only a few studies on n-type materials are reported in the literature.⁶ A few discotic molecules, such as hexaazatriphenylene and perylene diimide,^6,7,26 were reported to be n-type materials. The studied TSAN molecules have an electron-accepting flat core with multiple intramolecular hydrogen bonds, which provide an n-type semiconducting property.¹⁹ It has been reported in previous studies^18,27 that the presence of hydrogen bonds in discotic liquid crystalline molecules will enhance the interaction between the adjacent molecules and result in a small core separation (π-stacking distance). The presence of hydrogen bonds in TSAN molecules leads to a small intermolecular distance of 3.29 Å in the columnar phase, which decreases to 3.26 Å upon freezing.¹⁸ Therefore, there will be an enhanced π orbital overlap between adjacent molecules, facilitating increased charge carrier mobility. Earlier studies have reported that the studied TSAN molecules exhibit a columnar phase at room temperature.

In the present investigation, the structural, charge transport and optical properties of six TSAN molecules synthesized by Yelamaggad et al.^18,19 have been studied using quantum chemical methods (see Fig. 1). In these molecules, 2,4,6-tris[(E)-(dimethoxy phenylimino)methyl] benzene-1,3,5-triol (named TSAN1) is in the enol-imine (OH) form, while 2,4,6-tris[(E)-(dimethoxy phenylimino)methyl] cyclohexane-1,3,5-trione (TSAN2, TSAN3, TSAN4) and 2,4,6-tris[(E)-(trimethoxy phenylimino)methyl] cyclohexane-1,3,5-trione (TSAN5, TSAN6) are in the keto-enamine (NH) form. TSAN1, TSAN2, TSAN4 and TSAN5 exhibit C_3h symmetry, and TSAN3 and TSAN6 exhibit C_s symmetry.^18,19 Among the studied molecules, TSAN1, TSAN2, TSAN3 and TSAN4 are tautomers, and TSAN5 and TSAN6 are tautomers. As mentioned earlier, TSAN1 is in the enol form while TSAN2 is in the keto form. The rotation of the C30=C55 bond (for atom numbers see Fig. 2) in TSAN2 leads to the TSAN3 isomer. The TSAN4 isomer is similar to TSAN2 except for the position of the substituted OCH₃ group at the end phenyl rings. TSAN5 and TSAN6 exhibit the same tautomerism as TSAN2 and TSAN3 but with three OCH₃ groups at the end phenyl rings. Although many experimental studies^{18,19,21–23,25} have been performed on TSANs, only a few theoretical studies have been reported.^24,28 Previous experimental studies on TSANs have shown that these molecules have fluorescent properties due to the extended π-conjugation.¹⁸ To design new molecules with improved electronic properties, a complete understanding of the structure–property relationship is necessary. To the best of our knowledge, there has been no study on the charge transport property of TSAN molecules. Hence, in the present work, we analyzed the charge transport property of the TSANs through reorganization energy, charge transfer integral, site energy and charge carrier mobility, and the optical properties of the molecules through the orbital energies, absorption and emission spectra using a time-dependent density functional theory (TDDFT) method. In addition, the structure and conformational stability of the TSAN molecules were studied.

Fig. 1 The structural diagrams of tris(N-saclicylideneanilines).

Fig. 2 The optimized geometry of the TSAN2 tautomer at the B3LYP/6-311G(d,p) level of theory.

2. Theoretical methodology

The ground state geometry of tris(N-saclicylideneanilines) (TSANs) was optimized at the B3LYP^29–31/6-311G(d,p) level of theory using the Gaussian 09 program.³² The B3LYP functional uses the Becke's three parameter exchange functional (B3)²⁹ along with the non-local correlation function provided by Lee–Yang–Parr (LYP)³⁰ and the local correlation functional of Vosko–Wilk–Nusair (VWN).³¹ Previous studies^33–35 have reported that the B3LYP functional and the split valence polarized basis set, 6-311G(d,p), provide reliable structural parameters for molecules ranging from small to medium sizes. The frequency calculations performed at the B3LYP/6-311G(d,p) level of theory show that the optimized geometry of TSANs are at stationary points without any imaginary frequency. Using the ground state optimized geometry at B3LYP in the gas phase, a dimer was constructed with a fixed intermolecular distance of 3.29 Å, and the charge transport calculations were then performed using the fragment orbital approach as implemented in the Amsterdam density functional (ADF) theory program.³⁶ To calculate the charge transfer integral and site energy, the single point energy calculations for the stacked dimer with different stacking angles were performed with the generalized gradient approximation (GGA) using Becke³⁷ (exchange) and Perdew³⁸ (correlation) functional and an atomic basis set of Slater-type orbitals (STOs) of triple-ζ quality, including two sets of polarization functions on each atom (TZ2P), was used. To reduce the computational expense, the side chains in TSANs were replaced with OCH₃ groups in all the calculations. The rate of charge transfer between neighboring molecules (K_CT) can be calculated through the Marcus equation^39–41 using the reorganization energy (λ), effective charge transfer integral (J_eff), Boltzmann's constant (k_B) and temperature (T) as

Here, the rate of charge transport between the TSAN molecules was calculated for the dimer molecule constructed from the gas phase optimized structure with an intermolecular distance of 3.29 Å, as mentioned earlier. The effective charge transfer integral is defined as

where J_ij represents the charge transfer integral (or electronic coupling) corresponding to HOMO (or LUMO) of nearby molecules i and j, which measures the strength of the overlap between the orbitals of nearby molecules. ε_i and ε_j are the energy of a charge when it is localized at the i^th and j^th molecules, respectively, and S represents the spatial overlap integral. As reported in the previous studies,^42,43 J_ij and ε_i are directly calculated as the matrix elements of the Kohn–Sham Hamiltonian, H_KS = SCEC⁻¹. Here, C and E are the coefficient and energy, respectively, of the molecular orbitals involved in charge transport.

The reorganization energy, λ, is the change in energy of the molecule due to structural relaxation upon the presence of excess positive (λ⁺) or negative (λ⁻) charge. The reorganization energies, λ⁺ and λ⁻, are calculated by the total energies of the neutral and ionic states of the molecules,⁴⁴

λ^± = [E^±(g^o) − E^±(g^±)] + [E^o(g^±) − E^o(g^o)] (3)

In the abovementioned equation, E^±(g^o) is the total energy of a molecule with an excess positive or negative charge in the optimized neutral geometry, E^±(g^±) is the total energy in the optimized ionic geometry, E^o(g^±) is the total energy of a neutral molecule in the ionic geometry and E^o(g^o) is the total energy of the optimized neutral molecule.

Since the molecules exhibit stacking angle fluctuations from equilibrium values, the effective charge transfer integral differs from place to place, depending on the stacking angle. In this case, the mobility can be calculated numerically by performing a Monte Carlo simulation of the polaron hopping transport method.⁴⁵ In this model, it is assumed that the charge transport occurs along the sequence of π-stacked molecules. Here, the charge is allowed to move from one site to another by incoherent hopping with a hopping rate calculated from the Marcus charge transfer rate, as mentioned in eqn (1). In each step of the Monte-Carlo simulation, the most probable hopping pathway is found from the simulated trajectories based on the charge transfer rate at a particular conformation. During the Monte Carlo simulation, the mean squared displacement, 〈x²(t)〉, of the charge carrier along the π-stack is calculated as a function of time. For normal Gaussian diffusion, the mean squared displacement of the charge carrier increases linearly with time. The mean squared displacement and time are related by the diffusion constant, D as

〈x²(t)〉 = 2Dt (4)

The Monte Carlo simulations were performed up to 1 ns. The charge carrier mobility is related to the diffusion constant according to the Einstein relation,

where e is the electronic charge.

To gain qualitative insight into the charge transport properties of organic molecules, knowledge about the stacking angle and dynamics of the structural fluctuations is required. Hence, the molecular dynamics simulation was performed using the TINKER package,⁴⁶ implementing the standard molecular mechanics force field, MM3.⁴⁷ It has been shown in earlier studies that the MM3 force field adequately describes the crystals of normal alkanes and aromatics such as graphite, benzene and hexamethylbenzene.^48,49 Furthermore, the MM3 force field includes improved van der Waals potential compared to the MM2 force field.⁴⁸ The MD simulations were performed at a time step of 1 fs, and the atomic coordinates in the trajectories were saved at an interval of 0.1 ps. Therefore, for every 100 dynamic steps, the atomic coordinates and energy values were saved, and the dynamic calculations were carried out up to 10 ns.

The excited state geometry of TSANs was optimized by the time-dependent density functional theory method at the B3LYP/6-311G(d,p) level of theory. Based on the ground and excited state geometries, the absorption and emission spectra were calculated using the TD-DFT method at the B3LYP and PBE0 level of theories. To include the solvent effect on the optical properties, the self consistent reaction field (SCRF) calculation was performed using the Tomasi’s⁵⁰ polarizable continuum model (PCM). In the PCM, the solute molecule is present inside a cavity representing a solvent medium defined in terms of structureless material characterized by its dielectric constant, radius, density and molecular volume. In the present study, the dielectric constant of 7.43 was used to represent the tetrahydrofuran medium. The SWizard program^51,52 was used to simulate the absorption and emission spectra of the studied TSAN molecules. The spectra were generated using the Gaussian function with a half-bandwidth of 2000 cm⁻¹, as given in the following equation,

where ε(ω) is the molar extinction coefficient in M⁻¹ cm⁻¹, ω is the energy of the allowed transition in cm⁻¹, f_I is the oscillator strength and Δ_1/2 is the half-bandwidth and is fixed at 2000 cm⁻¹.

3. Results and discussion

3.1 Molecular structure and stability of tris(N-saclicylideneanilines) (TSANs)

The geometry of the enol and the keto forms of the tris(N-saclicylideneanilines) (TSANs) was optimized at the B3LYP/6-311G(d,p) level of theory. The TSAN1 molecule has an enol group, whereas TSAN2, TSAN3, TSAN4, TSAN5 and TSAN6 have a keto group. The optimized geometries of the enol and keto TSANs are shown in Fig. 2 and S1.† The selected structural parameters of TSANs calculated at the B3LYP/6-311G(d,p) level of theory are summarized in Table 2. The formation of the keto and enol tautomers is due to the reversible proton transfer between the two forms. The bond length R₁(N20–H25) of TSAN1 is 1.624 Å, and it is around 1.03 Å in the TSAN2, TSAN3, TSAN4, TSAN5 and TSAN6 tautomers. The bond length R₂(O24–H25) of TSAN1 and TSAN2 are 1.015 Å and 1.810 Å, respectively. From Table 2, it can be noted that the structural parameters of TSAN1 (enol form) and TSAN2 (keto form) are significantly different. The angles θ₁(C21–N20–H25) and θ₂(N20–H25–O24) corresponding to the TSAN1 and TSAN2 tautomers are 100° and 151° versus 113° and 135°, respectively. Except the angle θ₄(C1–O10–C11) and dihedral angles Φ₁(C3–C4–N20–H25) and Φ₂(C2–C1–O10–C11), the other structural parameters of the keto tautomers TSAN2, TSAN3, TSAN4, TSAN5 and TSAN6 are approximately similar. The differences in the angles θ₄, Φ₁ and Φ₂ among the keto tautomers are due to slight differences in the planarity of the structures. It was observed that the optimized structures of TSAN1, TSAN5 and TSAN6 are slightly out of plane, while the tautomers TSAN2, TSAN3 and TSAN4 exhibit a planar structure. It is confirmed from the dihedral angle Φ₁(C3–C4–N20–H25), which has a value of 29° in TSAN1, 5° in TSAN5, −15° in TSAN6 and 0° in the TSAN2, TSAN3 and TSAN4 tautomers.

The calculated relative energies of the TSANs at the B3LYP/6-311G(d,p) level of theory are summarized in Table 1. As discussed earlier, in the first set of tautomers, TSAN1, TSAN2, TSAN3 and TSAN4, the relative energy was calculated with respect to TSAN2. It can be observed from Table 1 that the keto form TSAN2 is more stable than the enol form TSAN1 by 13.99 kcal mol⁻¹, and the relative energies of the other keto forms TSAN3 and TSAN4 are 0.94 and 0.44 kcal mol⁻¹, respectively, with respect to TSAN2. The total energies calculated for the TSAN5 and TSAN6 tautomers show that the former is more stable than the latter by 0.82 kcal mol⁻¹. Previous quantum chemical studies on different TSANs showed that the keto form is more stable than the enol form by 10–18 kcal mol⁻¹.²⁸ The present results and those of the past studies show that the keto form is more stable than the enol form.

Table 1 The calculated relative energy ΔE (in kcal mol⁻¹) of tris(N-saclicylideneanilines) at the B3LYP/6-311G(d,p) level of theory in the gas phase

Molecule	Relative energy ΔE (kcal mol^−1)
a With respect to TSAN2.b With respect to TSAN5.
TSAN1^a	13.99
TSAN2	0.0
TSAN3^a	0.94
TSAN4^a	0.44
TSAN5	0.0
TSAN6^b	0.82

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Table 2 The selected geometrical parameters (bond length in Å, angle in degrees) of tris(N-saclicylideneanilines) at the B3LYP/6-311G(d,p) level of theory in the gas phase (for labeling of atoms see Fig. 2 and S1)

Parameters	TSAN1	TSAN2	TSAN3	TSAN4	TSAN5	TSAN6
R1(N20–H25)	1.624	1.028	1.025	1.028	1.027	1.025
R2(O24–H25)	1.015	1.810	1.833	1.807	1.810	1.836
R3(O24–C23)	1.328	1.252	1.267	1.252	1.251	1.266
R4(N20–C21)	1.294	1.333	1.335	1.333	1.334	1.335
R5(C21–C22)	1.442	1.385	1.384	1.386	1.385	1.384
R6(N20–C4)	1.407	1.407	1.407	1.407	1.407	1.408
R7(C30–C29)	1.418	1.458	1.475	1.458	1.459	1.476
R8(C22–C27)	1.416	1.465	1.469	1.464	1.466	1.470
R9(C21–H26)	1.091	1.084	1.084	1.084	1.084	1.084
R10(C1–O10)	1.359	1.360	1.360	1.360	1.367	1.368
θ1(C21–N20–H25)	99.7	112.6	113.0	112.6	112.6	113.2
θ2(N20–H25–O24)	150.5	135.4	134.3	135.4	135.3	134.0
θ3(C21–N20–C4)	122.4	128.2	128.1	128.2	128.0	127.4
θ4(C1–O10–C11)	118.1	118.0	118.0	118.0	114.8	114.9
θ5(C55–N56–H57)	99.7	112.6	112.9	112.4	112.6	113.2
Φ1(C3–C4–N20–H25)	28.9	0.0	0.0	0.0	5.2	−15.0
Φ2(C2–C1–O10–C11)	0.10	0.0	0.0	0.0	−91.6	90.2
Φ3(C30–C55–N56–H57)	−0.51	0.0	0.0	0.01	0.05	−1.11

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The stacking angle strongly influences the charge transport properties of the organic molecules. The results obtained from the present and past studies show that the J_eff strongly depends on the stacking distance and stacking angle.^42,53 Hence, the molecular dynamics (MD) simulation was performed to calculate the stacking angle and its fluctuations in the studied TSAN molecules. The optimized monomer geometry of tris(N-saclicylideneanilines) (TSANs) was used to construct the dimer with different initial configurations, i.e., with initial stacking angle values such as 30°, 45° and 60°. The MD simulation was performed for the dimer molecule. As reported in previous studies,^18,19 the side chain octyloxy (OC₈H₁₇) in TSAN2, TSAN3, TSAN5 and TSAN6 and 3,7-dimethyloctyloxy in TSAN4 was retained during the MD simulation. It has been reported in earlier studies⁵⁴ that the side chains play a significant role in the molecular packing of organic molecules. To achieve an ordered crystal packing, bulky side groups are substituted at the periphery of the molecules, which leads to improved π-orbital overlap between the molecules. The MD simulations were performed using the TINKER package, employing the standard molecular mechanics force field, MM3. Because the TSAN molecules exhibit the discotic liquid crystalline property at room temperature, the MD simulations were performed at 298 K. The barostat was described through the Berendsen algorithm. The stacking angle between the molecules in the saved 100 000 frames was calculated, and the total number of occurrences of each stacking angle was noted along with the calculated potential energy of the respective dimer. A graph was plotted between the stacking angles versus the number of occurrences of a particular conformation with that stacking angle.

The MD results of the selected tautomers are shown in Fig. 3. From the calculated results, it was noted that the stacking angle with the maximum number of occurrences has the minimum potential energy. It was observed that the maximum number of occurrences in the TSAN2 tautomer is observed around a stacking angle of 35°. It was observed that except for TSAN3, the favourable stacking angle of TSAN molecules lies between the stacking angles of 35° and 40° irrespective of the initial stacking angle. For the TSAN2 tautomer, the MD calculations were also performed with different side chain lengths, such as OC₄H₉ and OC₁₀H₁₉, and the results show that the stacking angle does not significantly vary depending on the side chain length. For the TSAN6 tautomer, the favourable stacking angle is observed at 40°. The TSAN6 molecule exhibits the same tautomerism as TSAN3 but the side chains are substituted at three positions over the end phenyl rings. Notably, as shown in Fig. 3b for the TSAN3 tautomer, the favourable stacking angle is observed around 70°. The number of occurrences of the stacking angle and the potential energy of the TSAN3 tautomer calculated from MD simulation for 50 ns and 100 ns also confirm that the favourable stacking angle for TSAN3 is 70°. In agreement with an earlier study,⁵⁴ the abovementioned results show that the substitution of side chains at an appropriate position is important when designing liquid crystalline molecules. It has been inferred from angle distribution that the stacking angle fluctuations up to 10–15° from the equilibrium value on both sides are expected in these molecules. To investigate the intermolecular distance between the stacked dimer, the MD simulations were also performed for the TSAN molecules with the same procedure as described above. It has been observed that the maximum number of occurrences of the molecule is noted at 3.33 Å, which is comparable with the experimental stacking distance of 3.29 Å.

Fig. 3 The results obtained from molecular dynamics simulation for the TSAN2 and TSAN3 molecules. Number of occurrences, N (left y-axis, solid line) and potential energy, PE (right y-axis, dotted line) at different stacking angles.

3.2 Molecular orbitals of tris(N-saclicylideneanilines) (TSANs)

The density plots of the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) of TSANs calculated at the B3LYP/6-311G(d,p) level of theory in gas phase are shown in Fig. 4 and 5. The orbital diagrams were plotted with a contour value of 0.03 a.u. The positive charge migrates through the highest occupied molecular orbitals (HOMOs) and the negative charge migrates through the lowest unoccupied molecular orbitals (LUMOs). The HOMOs of TSAN1, TSAN2 and TSAN5 are delocalized on the central cylohexanetrione ring and on the two sides of the end phenyl group attached to the core, whereas the HOMOs of TSAN3 and TSAN6 are delocalized over the entire molecule. The HOMO of TSAN4 is delocalized over the entire molecule but with a lower density on the side of the end phenyl ring attached to the nitrogen atom. From Fig. 5, it is observed that except for the TSAN1 molecule, the LUMOs of TSANs are delocalized over the entire molecule with a higher charge density on the core regions and a lower density on the end phenyl rings of the molecules. The energies of the HOMOs, LUMOs and energy gaps between them for the ground state TSANs calculated at the B3LYP/6-311G(d,p) level of theory are summarized in Table 3. The HOMO–LUMO energy gap (E_H–L) of the enol TSAN1 is 3.70 eV. Among the studied molecules, the E_H–L of TSAN3 is 3.27 eV, which is slightly lesser than those of the other keto TSANs. The E_H–L of TSAN2 and TSAN4 are approximately same at around 3.32 eV. The abovementioned results show that changing the position of side chain (OCH₃) on the end phenyl rings does not significantly alter the HOMO and LUMO energy levels, and it is expected that the charge transport and spectral properties of these molecules will be the same. With respect to TSAN2 and TSAN3, the E_H–L of TSAN5 and TSAN6 are slightly increased to 3.37 and 3.35 eV, respectively. This is because the LUMO energy levels of TSAN5 and TSAN6 have decreased significantly but the HOMO energy levels have increased, and thus there are slight increases in E_H–L.

Fig. 4 The ground state density plot of the HOMO of tris(N-saclicylideneanilines) calculated at the B3LYP/6-311G(d,p) level of theory in the gas phase.

Fig. 5 The ground state density plot of the LUMO of tris(N-saclicylideneanilines) calculated at the B3LYP/6-311G(d,p) level of theory in the gas phase.

Table 3 The ground state molecular orbital energies (E_HOMO, E_LUMO) and energy gap (E_H–L) (in eV) of tris(N-saclicylideneanilines) calculated at the B3LYP/6-311G(d,p) level of theory

Molecule	Gas phase
	EHOMO	ELUMO	EH–L
TSAN1	−5.29	−1.59	3.70
TSAN2	−5.14	−1.82	3.32
TSAN3	−5.12	−1.85	3.27
TSAN4	−5.15	−1.82	3.33
TSAN5	−5.41	−2.04	3.37
TSAN6	−5.39	−2.04	3.35

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3.3 Charge transport properties

3.3.1 Reorganization energy. The reorganization energies of the TSANs calculated at the B3LYP/6-311G(d,p) level of theory are summarized in Table 4. It is expected that the structure with small reorganization energy possesses high carrier mobility. Among the studied molecules, TSAN3 has the minimum reorganization energy of 0.16 eV in the presence of excess positive charge. When comparing the reorganization energies for excess positive and negative charges, it has been observed that the tautomers TSAN2, TSAN3 and TSAN4 have lower reorganization energies for excess positive charge, whereas TSAN5 and TSAN6 have lower reorganization energies for excess negative charge. From Table 4, it is noted that TSAN5 and TSAN6 have a maximum value of approximately 0.53 eV in the presence of an excess positive charge. The tautomers TSAN2 and TSAN4 possess similar reorganization energies in the presence of excess positive and negative charges, i.e., 0.20 and 0.26 eV, respectively, because the difference between TSAN2 and TSAN4 is the position of the substituted side chains in the end phenyl rings (see Fig. 1). Notably, the reorganization energy of the TSAN1 tautomer in the presence of excess negative charge is 0.87 eV, which shows that the presence of excess negative charge in the TSAN1 tautomer increased the structural relaxation of the molecule. Except for TSAN6, the reorganization energies for excess negative charge in the tautomers are around 0.27 eV. It has been noted that the structural parameters of cationic and anionic geometries vary slightly from that of the neutral geometry. Significantly, with respect to the neutral geometry, the bond length R₂(O24–H25) in the cationic geometry varies between 0.02–0.09 Å. In the anionic geometry, the bond length R₄(N20–C21) increased by 0.03 Å from that of the neutral geometry. However, with respect to neutral geometry, the change in the other bond length is within 0.02 Å in the cationic and anionic geometries. The changes in the bond angles θ₁(C21–N20–H25), θ₂(N20–H25–O24) and θ₃(C21–N20–C4) between the ionic and neutral geometries range from 1° to 4°. Significantly, the bond angle θ₄(C1–O10–C11) of TSAN5 in the cationic geometry varies by approximately 9° from that of the neutral geometry. It has been observed that the dihedral angles Φ₁(C3–C4–N20–H25) and Φ₂(C2–C1–O10–C11) of the TSAN2, TSAN3 and TSAN4 molecules do not vary significantly. However, the dihedral angle Φ₁(C3–C4–N20–H25) of the TSAN5 and TSAN6 tautomers varies by approximately 14° and 5°, respectively, between the ionic and neutral geometries. Significantly, the dihedral angle Φ₂(C2–C1–O10–C11) in the cationic geometries of TSAN5 and TSAN6 varies by approximately 64° and 20°, respectively. This notable difference in the dihedral angle is due to the out-of-plane alignment of the OCH₃ groups substituted at the end phenyl rings.

Table 4 The calculated values of the reorganization energy (λ in eV), vertical ionization potential (VIP), adiabatic ionization potential (AIP), vertical electron affinity (VEA), adiabatic electron affinity (AEA), hole extraction potential (HEP) and electron extraction potential (EEP) of tris(N-saclicylideneanilines) calculated at the B3LYP/6-311G(d,p) level of theory in the gas phase

Molecule	Reorganization energy		Ionization potential		Electron affinity		HEP	EEP
	Hole	Electron	VIP	AIP	VEA	AEA
TSAN1	0.26	0.87	6.28	6.16	0.47	1.19	6.02	1.34
TSAN2	0.20	0.26	6.14	6.05	0.76	0.89	5.95	1.02
TSAN3	0.16	0.27	6.11	6.04	0.77	0.91	5.95	1.05
TSAN4	0.20	0.26	6.15	6.07	0.76	0.89	5.96	1.02
TSAN5	0.52	0.27	6.39	6.18	0.99	1.12	5.87	1.25
TSAN6	0.54	0.30	6.36	6.17	0.98	1.14	5.82	1.28

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3.3.2 Effective charge transfer integral. The charge transfer integral or electronic coupling is one of the key parameters determining the rate of charge transport in organic molecules. The effective charge transfer integrals (J_eff) corresponding to hole and electron transport of TSANs calculated at various stacking angles from 15° to 90° are shown in Fig. 6, and their values are summarized in Table S1.† It has been shown in earlier studies^42,53 that J_eff strongly depends on the stacking distance and stacking angle. In the present work, the stacking distance between the TSAN molecules was fixed at 3.29 Å, as reported in past studies,^18,19 and J_eff was calculated at different stacking angles. From Fig. 6 and Table S1,† it has been observed that at a stacking angle of 15°, the molecules have a maximum J_eff for both the hole and electron transport. On increasing the stacking angle from 15° to 90° in steps of 15°, the effective charge transfer integral decreases gradually for all the TSANs up to a stacking angle of 45° or 75°, which is due to the unequal contribution of the monomer's HOMO (or LUMO) on the dimer's HOMO (or LUMO). For hole transport, the J_eff of TSAN3 decreases gradually up to 90°, whereas the J_eff of TSAN2 increases as the stacking angle increases from 45°. For other tautomers, J_eff slightly increases at 90°. From Fig. 6 and Table S1,† it is observed that the changes in J_eff of TSAN3 and TSAN6 are similar for electron transport because the LUMO delocalization on the TSAN3 and TSAN6 tautomers is nearly similar. In addition, the J_eff of TSAN2, TSAN4 and TSAN6 corresponding to electron transport are approximately the same. It has been observed that beyond a stacking angle of 45°, the J_eff corresponding to electron transport of the TSAN1 tautomer is less than those of the other tautomers. The results obtained from MD simulations show that except for TSAN3, the favorable stacking angle of the TSAN tautomers lies between 35° and 40°, and stacking angle fluctuations up to 10–15° from the equilibrium angle may occur in these molecules. As shown in Fig. 6, near the equilibrium stacking angle, i.e., around 20° to 50°, the calculated J_eff values for all the tautomers are higher for electron transport than those for hole transport.

Fig. 6 The effective charge transfer integral for hole and electron transport of tris(N-saclicylideneanilines) at various stacking angles.

At a stacking angle of 30°, except for that of the TSAN5 tautomer, the J_eff values corresponding to hole transport in the investigated tautomers are around 0.10 eV. At a stacking angle of 45°, except for that of the TSAN2, the J_eff values corresponding to hole transport of all the tautomers are around 0.06 eV. However, at stacking angles of 30° and 45°, the J_eff values corresponding to electron transport in all the tautomers are around 0.12 and 0.09 eV, respectively. Because the J_eff values corresponding to electron transport are higher than those for hole transport, the electron mobility is expected to be higher than the hole mobility. The abovementioned results show that depending on the tautomerism, the J_eff values of the studied TSAN molecules do not vary significantly. However, the effective charge transfer integrals corresponding to hole and electron transport depend on the stacking angle, and this is in agreement with the previous charge transport studies on organic molecules.^42,55

3.3.3 Site energy. The calculated site energies for the hole and electron transport of TSANs are summarized in Table S2.† In Table S2,† ε₁ and ε₂ represent the site energy of monomer 1 and monomer 2, respectively. The difference between ε₁ and ε₂ acts as a barrier or driving force for the charge transport between the adjacent molecules.⁵⁶ It has been observed that the difference between ε₁ and ε₂ is higher for hole transport than that for electron transport. At a stacking angle of 15°, the site energy difference corresponding to hole transport in TSAN2 is 0.03 eV. On increasing the stacking angle from 15° to 90°, the difference between ε₁ and ε₂ is increased and a difference of 0.08 eV is observed at a stacking angle of 90°, corresponding to hole transport in the TSAN2 tautomer. A similar trend is observed in the TSAN3 and TSAN4 tautomers. Notably, in TSAN2, TSAN3 and TSAN4, at a stacking angle of 60°, the difference between ε₁ and ε₂ corresponding to hole or electron transport is approximately the same. At this stacking angle, the atoms of each monomer experience a similar environment due to the presence of phenyl rings on three sides of the central cyclohexanetrione group. Among the studied molecules, the maximum site energy differences of approximately 0.27 eV for TSAN1 and 0.22 eV for TSAN5 and TSAN6 are observed. This is due to the slightly out-of-plane arrangement of the end phenyl rings and one OCH₃ group substituted on the phenyl ring. It is expected that the tautomers with a lower site energy difference near the equilibrium stacking angle will have a high rate of charge transport between the nearby molecules. In TSAN2, TSAN3 and TSAN4, the site energy differences at 30° and 45° vary between 0.01 and 0.07 eV, whereas the differences between ε₁ and ε₂ in TSAN1, TSAN5 and TSAN6 are slightly higher than those of the other tautomers. Notably, for TSAN3 tautomer, the site energy differences at stacking angles of 60° and 75° are around 0.01 eV only.

3.3.4 Charge carrier mobility. The charge carrier mobility of organic molecules is an important parameter for determining the performance of electronic devices.⁵⁶ The calculated charge carrier mobilities using the polaron-hopping method are summarized in Table 5. In reality, the molecules exhibit significant deviation from the ordered stack, and the deviations can be both of static and dynamic nature. Hence, it is necessary to include the effect of structural fluctuations in the calculation of charge carrier mobility. In the present work, the structural fluctuations in the form of stacking angle have been taken into account, and the charge carrier mobility has been calculated using a Monte Carlo simulation technique as described in Section 2. The structural fluctuation leads to variation in the hopping rate between the neighbouring molecules along the stack. Except for the TSAN3 tautomer, the stacking angle between the molecules was sampled between 20° and 50° at a symmetrical interval of angles around the equilibrium angle of 35°, which was obtained from molecular dynamics simulation. For the TSAN3 tautomer, the stacking angle was sampled between 55° and 80°. The MC simulation was performed up to 1 ns. A graph was plotted for the mean-squared displacement over time and is shown in Fig. 7, S2 and S3.† From Fig. 7, S2 and S3,† it has been observed that in all the TSAN tautomers the mean-squared displacement increased linearly with time. The diffusion constant, D, was calculated by taking half of the slope, and was substituted in the Einstein relation (eqn (5)) to calculate the charge carrier mobility.

Table 5 The calculated charge carrier mobility (μ in cm² V⁻¹ s⁻¹) for the hole and electron transport of tris(N-saclicylideneanilines) using Monte Carlo simulation

Molecule	Hole	Electron
a Stacking angles were sampled between 55° and 85°.b Stacking angles were sampled between 20° and 50°.
TSAN1	0.26	0.0003
TSAN2	0.21	0.83
TSAN3	0.09^a	1.89^a
	0.88^b	0.78^b
TSAN4	0.18	0.79
TSAN5	0.01	0.99
TSAN6	0.01	0.58

---

Fig. 7 The plots of mean squared displacement of (a) hole and (b) electron transport in TSAN3 as a function of time.

From Table 5, it has been observed that except for the TSAN1 tautomer, the electron mobility of the studied tautomers is higher than the hole mobility because in all the tautomers the effective charge transfer integral corresponding to electron transport is higher than the hole transport. The electron mobility of TSAN3 is 1.89 cm² V⁻¹ s⁻¹, and those of the TSAN2 and TSAN4 tautomers are 0.83 and 0.79 cm² V⁻¹ s⁻¹, respectively. Note that the reorganization energy for hole transport in TSAN3 is less than that of electron transport (by 0.11 eV), and the electron mobility is higher than the hole mobility if the stacking angle was sampled around 70°. However, if the stacking angle was sampled around 35°, as done for the other tautomers, the mobility values calculated for hole and electron transport are approximately the same (0.88 cm² V⁻¹ s⁻¹ and 0.78 cm² V⁻¹ s⁻¹ for hole and electron transport, respectively). Notably, the electron mobility of the enol tautomer TSAN1 is much lower (0.0003 cm² V⁻¹ s⁻¹), which is due to the high reorganization energy of 0.87 eV in the presence of excess electron. The electron mobility of the studied keto TSAN molecules does not vary significantly depending on the tautomerism because the J_eff corresponding to electron transport and the reorganization energy in the presence of excess negative charge are similar for the keto tautomers. The hole mobility of the enol tautomer TSAN1 is 0.26 cm² V⁻¹ s⁻¹, and those of the keto tautomers TSAN2 and TSAN4 are 0.21 and 0.18 cm² V⁻¹ s⁻¹, respectively. It has been observed that the high reorganization energy causes lower hole mobility in the TSAN5 and TSAN6 tautomers. The abovementioned results show that the studied TSAN molecules are n-type organic semiconductors. The calculated electron mobility of TSAN tautomers is comparable to the electron mobility of perylene diimide discotic molecules, which ranges between 0.1 and 1.3 cm² V⁻¹ s⁻¹.^7,57,58

Note that it is possible to calculate the charge carrier mobility without performing the Monte-Carlo simulation.^14,15,59 It is expected that a molecule with a minimum reorganization energy and maximum effective charge transfer integral at an equilibrium angle will exhibit high charge carrier mobility. From Table S1,† it is noted that for both hole and electron transport the effective charge transfer integral of the studied molecules is similar at a stacking angle of 30°. Thus, in these TSAN molecules, depending on the reorganization energy, the mobility value will change. For hole transport, TSAN3 exhibits a high charge carrier mobility due to its low reorganization energy. For electron transport, because the J_eff and reorganization energy values of the keto TSAN molecules corresponding to electron transport are similar, it is expected that the mobilities of TSAN2, TSAN3, TSAN4 and TSAN5 are similar and will be higher than those of the TSAN1 and TSAN6 molecules. From Table S2,† it is observed that the average site energy differences of the molecules at a stacking angle of 30° are around 0.08 and 0.03 eV, corresponding to the hole and electron transport, respectively.

3.4 Ionic state properties

Ionization potential (IP) and electron affinity (EA) are important properties of organic molecules because they are related to the stability, injection barrier and polarity of the charge carrier. The IP and EA are well-defined properties that can be calculated by electronic structure calculations to estimate the energy barriers for the injection of holes and electrons into the molecules. These parameters are calculated using the neutral and ionic state geometries and energies calculated at the B3LYP/6-311G(d,p) level of theory. The vertical ionization potential (VIP), adiabatic ionization potential (AIP), vertical electron affinity (VEA), adiabatic electron affinity (AEA), hole extraction potential (HEP) and electron extraction potential (EEP) were calculated based on the equations reported in a previous study,⁶⁰ and the results are summarized in Table 4. A molecule with a relatively small IP allows effective hole injection from the source electrode. From Table 4, it is observed that TSAN3 possesses a slightly lower IP compared to those of TSAN2, TSAN4 and TSAN5. The vertical and adiabatic ionization potentials of TSAN3 are 6.11 and 6.04 eV, respectively. A molecule with higher EA will exhibit good electron accepting ability. Among the studied molecules, TSAN1 possesses a high adiabatic electron affinity of 1.19 eV. Among the keto tautomers, TSAN5 and TSAN6 possess higher EA and their LUMO energy levels decrease with respect to TSAN2 and TSAN3. The vertical and adiabatic electron affinities of TSAN5 and TSAN6 are around 0.98 and 1.13 eV, respectively. The abovementioned results show that the substitution of an additional OCH₃ group in the end phenyl rings enhanced the electron accepting nature of TSAN molecules. This is in agreement with the results of a previous study by Su et al.,⁶¹ which reported that a molecule with a lower LUMO energy level will exhibit a high EA. It has been noted that the HEP of TSAN6 is smallest at 5.82 eV, that is, the energy required to inject an electron in the cationic geometry of TSAN6 is smaller than that for the other tautomers. The extraction of electrons from the anionic geometry of TSAN1 requires 1.34 eV, while that of TSAN6 requires 1.28 eV, which is higher than those of TSAN2 and TSAN4 by 0.26 eV and that of TSAN3 by 0.23 eV.

3.5 Absorption spectra of tris(N-saclicylideneanilines) (TSANs)

The ground state geometries of TSANs have been optimized at the B3LYP/6-311G(d,p) level of theory in the gas phase and tetrahydrofuran medium. The absorption spectra of TSANs were calculated using time-dependent DFT at the B3LYP/6-311G(d,p) and PBE0/6-311G(d,p) levels of theories in the gas phase and tetrahydrofuran medium. The calculated absorption energies and the corresponding oscillator strengths of TSAN molecules are summarized in Tables 6 and S3.† To study the nature and the energy of the singlet–singlet electronic transition, the first 10 low lying electronic transition energies were calculated. Absorption energies with an oscillator strength greater than 0.01 are considered throughout the discussion. Absorption intensity is directly related to the dimensionless oscillator strength value, and the dominant absorption bands are the transitions with a higher oscillator strength. The experimental absorption wavelength is available only for the TSAN4 tautomer, and two absorption bands are reported, the first band is at 416 nm and the second band is at 329 nm. It has been reported in a previous study¹⁹ that a molecule with the same core as TSAN6 exhibits two absorption bands at 416 and 329 nm, similar to TSAN4. From Table 6, it is observed that the absorption spectra calculated at the TD-PBE0/6-311G(d,p) level of theory in tetrahydrofuran medium are in agreement with the experimental results described above.¹⁹ With respect to the experimentally observed absorption bands, the deviations in the calculated absorption wavelength for TSAN4 are around 6 nm (0.05 eV) and 13 nm (0.15 eV) for the first and second bands, respectively, and those of TSAN6 are around 10 nm (0.08 eV) and 23 nm (0.24 eV), respectively, with the PBE0 method. In the B3LYP method, the differences between the experimental and calculated results are around 15 nm (0.1 eV) to 30 nm (0.33 eV) for TSAN4, and for TSAN6, the difference is 5 nm (0.06 eV) to 20 nm (0.23 eV). From Table 6, it is observed that the orbital transitions calculated at the B3LYP and PBE0 levels are similar. It is observed that the average difference between the calculated absorption wavelength corresponding to the HOMO → LUMO transition in the gas phase and in tetrahydrofuran medium is 10 nm (0.08 eV), that is, the effect of solvent on the absorption spectra is not significant. The absorption energies of the TSAN molecules calculated at the PBE0/6-311G(d,p) level of theory in dichloromethane medium were simulated using the SWizard program, and are shown in Fig. 8.

Table 6 Computed absorption wavelength (in nm), oscillator strength (in a.u.) and orbital transitions of tris(N-saclicylideneanilines) calculated at the B3LYP/6-311G(d,p) and PBE0/6-311G(d,p) levels of theory in tetrahydrofuran medium

Molecule	Orbital transitions^a	B3LYP/6-311G(d,p)			PBE0/6-311G(d,p)
		λabs		f	λabs		f
		nm	eV		nm	eV
a H and L represent HOMO and LUMO, respectively. The transitions with oscillator strength higher than 0.01 a.u. are given.
TSAN2	H → L	431	2.88	0.85	411	3.02	1.0
	H−1 → L	431	2.88	0.85	411	3.02	1.0
	H−1 → L+2	362	3.43	0.68	345	3.60	0.60
	H → L+1
	H−1 → L+1	362	3.43	0.68	345	3.60	0.60
	H → L+2
	H−2 → L+1	314	3.95	0.02	—	—	—
	H−2 → L+2	314	3.95	0.02	—	—	—
TSAN3	H → L	439	2.83	0.76	419	2.96	0.86
	H−1 → L	427	2.91	0.79	405	3.06	0.99
	H → L+1	381	3.25	0.19	361	3.43	0.17
	H−2 → L	373	3.32	0.06	352	3.52	0.07
	H−1 → L+1	361	3.42	0.59	344	3.60	0.50
	H−1 → L+2	352	3.52	0.48	335	3.70	0.43
	H → L+2	337	3.68	0.04	324	3.83	0.05
	H−3 → L	315	3.93	0.09	—	—	—
TSAN4	H → L	430	2.88	0.84	410	3.03	0.99
	H−1 → L	427	2.90	0.75	407	3.05	0.89
	H → L+1	360	3.44	0.65	342	3.62	0.57
	H−1 → L+1	359	3.46	0.62	341	3.63	0.57
	H−3 → L	316	3.93	0.10	—	—	—
	H−2 → L+1	315	3.94	0.01	—	—	—
TSAN5	H → L	418	2.96	0.81	399	3.11	0.96
	H−1 → L	417	2.97	0.80	398	3.11	0.94
	H−1 → L+1	351	3.53	0.67	334	3.71	0.60
	H → L+2
	H−1 → L+2	351	3.53	0.66	334	3.71	0.59
	H → L+1
	H−3 → L+1	331	3.74	0.02	314	3.95	0.03
	H−4 → L+1	331	3.74	0.02	314	3.95	0.03
TSAN6	H → L	424	2.92	0.71	406	3.06	0.81
	H−1 → L	414	3.0	0.80	394	3.15	1.0
	H → L+1	370	3.35	0.18	352	3.53	0.16
	H−2 → L	361	3.43	0.09	341	3.64	0.11
	H−1 → L+1	351	3.54	0.58	334	3.71	0.47
	H−1 → L+2	342	3.62	0.48	326	3.81	0.43
	H−3 → L	331	3.75	0.02	314	3.95	0.06

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Fig. 8 The absorption spectra of tris(N-saclicylideneanilines) computed at the PBE0/6-311G(d,p) level of theory in tetrahydrofuran medium.

From Table 6, it is observed that the calculated absorption wavelengths of TSAN2 and TSAN4 are approximately the same because in these molecules the difference is the position of the substituted OCH₃ groups at the end phenyl rings. The absorption spectra of TSAN2 have two features. The first band is observed at 411 nm and is associated with HOMO → LUMO and HOMO−1 → LUMO transitions. The second dominant band is observed at 345 nm, corresponding to HOMO−1 → LUMO+2, HOMO → LUMO+1, HOMO−1 → LUMO+1 and HOMO → LUMO+2 transitions. Similarly, TSAN4 exhibits two intense peaks. The first peak observed around 408 nm corresponds to the excitation of electrons from HOMO → LUMO and HOMO−1 → LUMO transitions. The second dominant band is observed around 342 nm and is associated with HOMO → LUMO+1 and HOMO−1 → LUMO+1 transitions. The molecular orbital analysis reveals that the absorption bands of TSAN4 observed around 408 and 342 nm are due to n → π* and π → π* transitions, which is in agreement with previously reported experimental results.¹⁹ Similar to those of TSAN4, the absorption bands of TSAN2 observed at 411 and 345 nm are due to n → π* and π → π* transitions. From Table 6, it is observed that the absorption wavelength of TSAN3 has slightly increased compared to those of TSAN2 and TSAN4. TSAN3 has four absorption features and the first and second dominant bands are observed at 419 and 405 nm, corresponding to HOMO → LUMO and HOMO−1 → LUMO transitions. Additional intense peaks are observed at 344 and 335 nm and are associated with HOMO−1 → LUMO+1 and HOMO−1 → LUMO+2 transitions, respectively. In TSAN3, the absorption bands observed around 400 and 340 nm are due to n → π* and π → π* transitions.

The absorption patterns of TSAN5 and TSAN6 are similar to those of TSAN2 and TSAN3 because both the tautomers have the same symmetry, differing only in the number of OCH₃ substitution in the end phenyl rings. The absorption bands for the TSAN5 tautomer are observed around 398 and 334 nm and correspond to HOMO → LUMO and HOMO−1 → LUMO versus HOMO−1 → LUMO+1 and HOMO−1 → LUMO+2 transitions, respectively. The dominant absorption bands of the TSAN6 tautomer are observed at 406 and 394 nm and are associated with HOMO → LUMO and HOMO−1 → LUMO transitions, respectively. The other absorption features of TSAN6 are observed at 334 and 326 nm. In TSAN6, the absorption bands observed around 400 and 330 nm are due to n → π* and π → π* transitions, which is in agreement with the previously reported experimental results.¹⁹ The abovementioned results show that the position of the OCH₃ group does not have a significant effect on the absorption spectra of the TSAN tautomers.

3.6 Emission spectra of tris(N-saclicylideneanilines) [TSANs]

The excited state geometries of TSANs were optimized at the TD-B3LYP/6-311G(d,p) level of theory. With respect to the ground state structures, the excited state structures of the TSAN molecules changed slightly. The selected bond lengths, bond angles and dihedral angles of the TSAN molecules in the excited state calculated at the TD-B3LYP/6-311G(d,p) level of theory in the gas phase are summarized in Table S4.† With respect to the ground state structures, in the excited state, the bond lengths and bond angles of all the TSAN molecules changed by 0.002 to 0.05 Å and 1° to 5°, respectively, and the dihedral angles of TSAN5 and TSAN6 changed by 5° to 15°. This is due to the change in the orientation of the OCH₃ group attached at the end phenyl rings. Based on the optimized geometry, the emission spectra were calculated using the time-dependent density functional theory method at the B3LYP/6-311G(d,p) and PBE0/6-311G(d,p) levels of theory. The calculated emission energies and the corresponding oscillator strengths of TSANs are summarized in Tables 7 and S5.† It has been reported in a previous study¹⁹ that the emission band of TSAN4 is observed at 482 nm, and as observed for absorption spectra, the emission spectra of TSAN4 and TSAN6 are comparable. With the PBE0 method, the deviation between the experimental and calculated emission wavelengths of the TSAN4 and TSAN6 tautomers corresponding to HOMO → LUMO transition are around 20 nm (0.11 eV). With the B3LYP method, the deviation between the experimental and calculated emission wavelengths of TSAN4 is only 7 nm (0.03 eV), whereas for TSAN6 the difference is around 50 nm (0.25 eV). The emission energies of the TSAN molecules calculated at the PBE0/6-311G(d,p) level of theory in dichloromethane medium are simulated using the SWizard program, and is shown in Fig. 9. From Fig. 9, it is observed that the calculated molar extinction coefficients of the studied TSAN molecules are around 130 × 10³ cm⁻¹ L mol⁻¹. Similar to the absorption spectra, the calculated emission spectra of TSAN2 and TSAN4 are nearly the same with bands observed around 462 nm. The emission band of TSAN3 was observed at 467 nm. The emission spectra of the TSAN5 and TSAN6 tautomers red shifted by about 40 nm compared with those of TSAN2 and TSAN3. Thus, the substitution of an additional OCH₃ group on the end phenyl rings of TSANs significantly increases the emission wavelength.

Table 7 Computed emission wavelength (in nm) and oscillator strength (in a.u.) corresponding to the electronic transition between HOMO and LUMO energy levels of tris(N-saclicylideneanilines) calculated at the B3LYP/6-311G(d,p) and PBE0/6-311G(d,p) levels of theory in tetrahydrofuran medium

Molecule	B3LYP/6-311G(d,p)			PBE0/6-311G(d,p)
	λemis		f	λemis		f
	nm	eV		nm	eV
TSAN2	487	2.54	0.74	462	2.68	0.88
TSAN3	496	2.50	0.58	467	2.65	0.73
TSAN4	489	2.54	0.71	463	2.68	0.85
TSAN5	540	2.29	0.51	505	2.45	0.62
TSAN6	534	2.32	0.57	503	2.46	0.66

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Fig. 9 The emission spectra of tris(N-saclicylideneanilines) computed at the PBE0/6-311G(d,p) level of theory in tetrahydrofuran medium.

4. Conclusions

Parameters involved in the charge transport and optical properties of tris(N-saclicylideneanilines) (TSAN) existing in different tautomeric forms were studied using density functional theory (DFT) methods. The calculated relative energies of TSANs show that the keto form is more stable than the enol form. The effective charge transfer integral strongly depends on the stacking angle. Except for TSAN3, MD studies on stacking angle fluctuations in the investigated molecules show that the favourable stacking angle is around 35°, and for the TSAN3 molecule, the favourable stacking angle is 70°. The charge carrier mobility values calculated through a polaron hopping transport method show that the studied TSAN molecules are n-type organic semiconductors. TSAN3 has the maximum electron mobility of 1.89 cm² V⁻¹ s⁻¹. The absorption and emission spectra of the TSANs were calculated using the TD-DFT method at the B3LYP and PBE0 levels of theory, and were compared with the available experimental results. It was found that the position of the OCH₃ group has a significant effect on the emission spectra. The calculated absorption and emission spectra confirm that the studied TSAN molecules can be used for OLED applications.

Acknowledgements

One of the authors (K.S.) is thankful to the Department of Science and Technology (DST), India for funding the research project under the DST-Fast track scheme. The authors thank the reviewers for giving valuable suggestions to improve the manuscript.

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Footnote

† Electronic supplementary information (ESI) available: The ground state optimized structures of tris(N-saclicylideneanilines) molecules at the B3LYP/6-311G(d,p) level of theory in the gas phase are shown in Fig. S1. The effective charge transfer integral (J_eff) values corresponding to hole and electron transport in tris(N-saclicylideneanilines) molecules calculated at various stacking angles are summarized in Table S1. The calculated site energies for hole and electron transport in tris(N-saclicylideneanilines) molecules are summarized in Table S2. Plots of the mean squared displacement of charge carrier in the studied molecules as a function of time are shown in Fig. S2 and S3. The selected geometrical parameters of tris(N-saclicylideneanilines) molecules in the excited state calculated at the TD-B3LYP/6-311G(d,p) level of theory in the gas phase are summarized in Table S4. The absorption and emission energies of tris(N-saclicylideneanilines) molecules calculated at the B3LYP/6-311G(d,p) and PBE0/6-311G(d,p) levels of theory in the gas phase are summarized in Tables S3 and S5, respectively. See DOI: 10.1039/c4ra01372g

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