3.1Estimation of ground and excited-state dipole moments
The absorption and fluorescence spectra of synthesized bromomethyl coumarin fluorescent dyes in different solvents were recorded multiple numbers times in order to check the reproducibility of readings, to avoid any procedural mistakes and the verified spectra are shown in Figs. 1–2. The absorption maxima, emission maxima, Stoke's shift and arithmetic mean of Stoke's shift values in different solvents for all molecules are tabulated in Tables 1–2. The value of the Stokes shift undergoes redshift with an increase in solvent polarity for all the molecules, which indicates π−π∗ transition and also suggests that, the dipole moments for all the molecules in the excited state may be higher than the ground state.
When a molecule is excited, the solvent dipoles can reorient or relax around the excited probe molecule and lowers the energy of the excited state. Further, as the solvent polarity increases, this effect becomes larger, which in turn, may result in the emission at lower energies or longer wavelengths. When the molecule is in the excited state, there will be a redistribution of the charges, which may lead to the change in dipole moment [18]. In the excited state, no more the fluorophore remains in equilibrium with its environment. As the molecule relaxes and attains equilibrium with the surrounding environment, some amount of energy is dissipated in the form of non-radiative energy and as a result the fluorescence emission wavelength gets shifted. In addition to this, there may be specific interactions between the probe molecule and solvent like hydrogen-bonding, formation of charge transfer states, complex formation, etc., which may lead to large spectral shifts [18]. Therefore, a systematic analysis of solvent effect is useful in order to understand the effect of the environment and the various mechanisms of deexcitation and relaxation of an excited molecule in solution.
In this regard, the theories developed by various researchers in the field of estimation of ground and excited state dipole moments through solvatochromic methods are used in the present study. The Lippert [19] derived equations based on Onsager's reaction field theory for the determination of dipole moments considering fluorophore as a point dipole in a continuous medium of uniform dielectric constant.
The excited state dipole moments can also be estimated using Bakhshiev [20]and Kawskiet al. [21] have developed a simple quantum mechanical second order perturbation theory to explain absorption and fluorescence band shifts in different solvents of refractive index (\(\text{N}\)) and varying permittivity (ε0) corresponding to the band position of a solute molecule.
According to Lippert [19], the expression for Stoke’s shift is
$${\text{ῡ}}_{\text{a}}-{\text{ῡ}}_{\text{f}}=\text{S}\text{F}\left({\epsilon },\text{n}\right)+\text{c}\text{o}\text{n}\text{s}\text{t}$$
1
Where \(\text{F}\left({\epsilon },\text{n}\right) \text{t} \text{t}\)is Lippert’s polarity function and is given by,
$$\text{F}\left({\epsilon },\text{n}\right)=\left[\frac{{\epsilon }-1}{2{\epsilon }+1}-\frac{{\text{n}}^{2}-1}{2{\text{n}}^{2}+1}\right]$$
2
The expression for Stoke’s shift according to Bakhshiev [20] is given by,
$${ \text{ῡ}}_{\text{a}}-{\text{ῡ}}_{\text{f}}={\text{S}}_{1}{\text{F}}_{1}\left({\epsilon },\text{n}\right)+\text{c}\text{o}\text{n}\text{s}\text{t}$$
3
Where \({\text{F}}_{1}\left({\epsilon },\text{n}\right) \text{t}\) is Bakhshiev’s polarity function and is given by,
$${ \text{F}}_{1}\left({\epsilon },\text{n}\right)=\frac{2{\text{n}}^{2}+1}{{\text{n}}^{2}+2}\left[\frac{{\epsilon }-1}{{\epsilon }+2}-\frac{{\text{n}}^{2}-1}{{\text{n}}^{2}+2}\right]$$
4
According to Kawski-Chamma-Viallet’s [21] equation,
$$\frac{1}{2}\left({\text{ῡ}}_{\text{a}}+{\text{ῡ}}_{\text{f}}\right)={\text{S}}_{2}{\text{F}}_{2}\left({\epsilon },\text{n}\right)+\text{c}\text{o}\text{n}\text{s}\text{t}$$
5
Where \({\text{F}}_{2}\left({\epsilon },\text{n}\right)\) is Kawski-Chamma-Viallet’s polarity function and is given by
$${\text{F}}_{2}\left({\epsilon },\text{n}\right)=\frac{2{\text{n}}^{2}+1}{2({\text{n}}^{2}+2)}\left[\frac{{\epsilon }-1}{{\epsilon }+2}-\frac{{\text{n}}^{2}-1}{{\text{n}}^{2}+2}\right]+\frac{3}{2}\left[\frac{{\text{n}}^{4}-1}{{({\text{n}}^{2}+2)}^{2}}\right]$$
6
Here ῡa and ῡf are absorption and fluorescence maxima in wave numbers respectively and other terms have their usual meaning.
The dielectric constants, refractive indices, solvent polarity parameter and the calculated values of various polarity functions like F(ε, n), F1(ε, n) and F2(ε, n) are given in Table-3.
Dielectric constant (ε), refractiveindex (N), microscopic solvent polarity function (\({\text{E}}_{\text{T}}^{ \text{t}\text{N}}\)) values tare taken from literature [22].
From Eq. 1, .3 and 5, it follows that (ῡa - ῡf) versus F(ɛ, n), (ῡa - ῡf) versus F1(ɛ, n) and (ῡa + ῡf)/2 versus F2(ɛ, n) plots should be linear with slopes S, S1 and S2 respectively and are given as,
$$\text{S}=\frac{2({{{\mu }}_{\text{e}}-{{\mu }}_{\text{g}})}^{2}}{\text{h}\text{c}{\text{a}}_{0}^{3}}$$
7
$${\text{S}}_{1}=\frac{{2({{\mu }}_{\text{e}}-{{\mu }}_{\text{g}})}^{2}}{\text{h}\text{c}{\text{a}}_{0}^{3}}$$
8
$${\text{S}}_{2}=\frac{2({{\mu }}_{\text{e} \text{t} \text{t}}^{2}-{{\mu }}_{\text{g} \text{t}}^{2})}{\text{h}\text{c}{\text{a}}_{0}^{3}}$$
9
Where µe and µg are excited and ground state dipole moments respectively. Here the term ‘h’ is Planck’s constant, ‘c’ is velocity of light in vacuum and ‘a0’ is the Onsager cavity radius of the probe molecule and is calculated using Edward’s [23] atomic increment method.
The Stoke’s shift vs. F(ε, n), Stoke’s shift vs. F1(ε, n) and arithmetic mean of Stoke’s shift vs. F2(ε, n) plots for fluorescent dyes are shown in Fig. 3a-b. The statistical data like slopes, intercepts and correlation coefficients for all molecules are reported in Tables 4. It is observed that, the correlation coefficient values are greater than 0.8, which indicates a good linearity for the slopes S, S1, and S2.
Assuming that the symmetry of the probe molecule remains unchanged upon electronic transition and considering the ground and excited state dipole moments to be parallel, the expression for ground state dipole moment (µg), excited state dipole moment (µe) and ratio of µe and µg are given by
$${ {\mu }}_{\text{g}}=\frac{{\text{S}}_{2}-{\text{S}}_{1}}{2}{\left[\frac{\text{h}\text{c}{\text{a}}_{0}^{3}}{2{\text{S}}_{1}}\right]}^{1/2}$$
10
$${{\mu }}_{\text{e}}=\frac{{\text{S}}_{1}+{\text{S}}_{2}}{2}{\left[\frac{\text{h}\text{c}{\text{a}}_{0}^{3}}{2{\text{S}}_{1}}\right]}^{1/2}$$
11
\(\frac{{{\mu }}_{\text{e}}}{{{\mu }}_{\text{g}}}=\frac{{\text{S}}_{1}+{\text{S}}_{2}}{{\text{S}}_{2}-{\text{S}}_{1}} ;({\text{S}}_{2}>{\text{S}}_{1}\) ) (12)
Using the slopes S1 and S2, the values of µg, µe and their ratio µe/µg were calculated according to Eqs. 10, 11 & 12 and the results are given in Tables 5 and6. Further, by substituting the value of µg calculated from Eq. 10, the excited state dipole moment (µe)is calculated according to Lippert’s, Bakhshiev’s and Kawski-Chamma-Viallet’s method i.e. from Eqs. 7, 8 & 9 respectively and the results are presented in Table 4.
If the angle between ground and excited state dipole moments are not parallel, then the angle θ between the two dipole moments is determined from the following equation.
$$\text{c}\text{o}\text{s}{\theta }= \frac{1}{2{{\mu }}_{\text{g}}{{\mu }}_{\text{e}}}\left[\left({{\mu }}_{\text{g}}^{2}+{{\mu }}_{\text{e}}^{2}\right)-\frac{{\text{S}}_{2}}{{\text{S}}_{3}}\left({{\mu }}_{\text{e}}^{2}-{{\mu }}_{\text{g}}^{2}\right)\right]$$
13
The angle between ground and excited state dipole moments is calculated according to Eq. 13 and the results are presented in Table 5.
3.2 Change in dipole moment (Δµ) and excited state dipole moment (µ e ) by solvent polarity parameter \({(\mathbf{E}}_{\mathbf{T}}^{ \mathbf{N}})\) :
This method is based on solvent polarity parameter \(\left({\text{E}}_{\text{T}}^{ \text{N}}\right)\) to estimate change in dipole moment (Δµ)proposed by Reichardt [24]and developed by Ravi et. al.[25]. In this method, the problem associated with the estimation of Onsager cavity radius has been minimized.
The expression for Stoke’s shift according to Reichardt and Ravi et a. is,
$${\text{ῡ}}_{\text{a}}-{\text{ῡ}}_{\text{f}}=11307.6\left[{\left(\frac{\varDelta {\mu }}{\varDelta {{\mu }}_{\text{B}}}\right)}^{2}{\left(\frac{{\text{a}}_{\text{B}}}{\text{a}}\right)}^{3}\right]{\text{E}}_{\text{T}}^{\text{N}}+ \text{c}\text{o}\text{n}\text{s}\text{t}$$
14
where ΔµB (= 9D) and aB (= 6.2 Å) are the change in dipole moment on excitation and Onsager cavity radius of reference betaine dye molecule and Δµ and ‘a’ are the change in dipole moment and molecular radius of the molecule under investigation.
The change in dipole moment (Δµ) is determined from the following equation.
$$\varDelta {\mu }={{\mu }}_{\text{e}}-{{\mu }}_{\text{g}}=\sqrt{\frac{\text{m} \times 81}{{\left(\frac{6.2}{{\text{a}}_{\text{o}}}\right)}^{3}11307.6}}$$
15
Where m is the slope obtained from the linear plot of Stoke’s shift versus\({(\text{E}}_{\text{T}}^{\text{N}})\).
Then by using Eq. 15 and knowing the value of µg (From Eq. 10), the excited state dipole moment is determined from the following equation.
$${{\mu }}_{\text{e}}={\Delta }{\mu }+{{\mu }}_{\text{g}}$$
16
The relevant plots of Stoke’s shift vs.\({(\text{E}}_{\text{T}}^{\text{N} })\) required for the determination of change in dipole moment (Δµ) for all the probe molecules are shown in Fig. 3a-b. Using the slopes calculated from Stoke's shift versus \({\text{E}}_{\text{T}}^{\text{N}}\), the excited state dipole moment (µe) and change in dipole moment (Δµ) for both the molecules were calculated using Eq. 16 and the results are presented in Table 5–6.
The ground state dipole moment of 4BDYMBCis higher as compared to 1BDYMBCand it may be due to the substitution of benzene in coumarin moiety due to more electro negativitywhich create decreases the bond length and increases polarizability, which may lead to the increase in the dipole moment [26]. It is also observed from Table-5 that, the excited state dipole moment (µe) for the molecule 1BDYMBC is less than the 4BDYMBC. The decrease of excited state dipole moment (µe) for the molecule 1BDYMBC may suggest different geometry for the singlet excited state than remaining molecules, indicating a significant difference in the charge distribution.
The excited state dipole moment (µe) determined by using Bakhshiev's, KawskiChamma-Viallet's, and solvatochromic eqns. (Table-5) were found to be in good agreement with each other. The higher values of excited state dipole moment (µe) observed in case of Lippert's method compared to other methods may be due to the non-accountability of polarizability. However, µe calculated by using solvent polarity parameter \({\text{E}}_{\text{T}}^{\text{N}}\) (Eq. 6) is found to be smaller than µe determined from Bakhshiev's, Kawski-Chamma-Viallet's and solvatochromic methods. This may be due to the reason that these methods do not consider specific solute-solvent interactions like hydrogen bonding, complex formation and molecular aspects of solvation, whereas they are incorporated in the solvent polarity parameter [27].
The µe values are found to be higher than µg values for all the molecules (Table 5). The higher values of µe indicate that the probe molecules are more polar in the excited state than the ground state. The angle between ground and excited state dipole moment for both the molecules are found to be zero degree which suggest that, µg and µeare parallel to each other and the molecular symmetry remains same upon electronic transition [27]. Further, it is observed that the change in dipole moment (Δµ) value is found to be higher. The higher values of Δµ may indicate the existence of more relaxed excited state and which may be due to ICT. The possible intramolecular charge transfer may be attributed to the resonance structures of synthesized molecule and are shown in Fig. 4a-b.
3.3. Computational analysis
The absorption and emission spectra of all molecules in different solvents were computed by using Gaussian 09W in order to compare with the experimental results. For this purpose, the molecule is optimized for the ground and excited state using DFT and TD-DFT with the basis sets B3LYP/3-211G combined with integral equation formalism variant-Polarizable Continuum Model (IEFPCM) solvation model.
The ground-state dipole moment of the probe molecule in the gaseous state is also estimated theoretically by using DFT with basis sets B3LYP/3-11G and the result is presented in Table 7. The optimized molecular geometry of all molecules along with the direction of dipole moment is shown in Fig. 5.
It is observed from Tables6-7 that the theoretically computed µg value is higher than the experimental µg value. It is to be noted that the experimental methods take solvent and environmental effects like solute-solvent interactions into account, whereas the ab initio computations are based on gaseous phase [28–30]. Further, in order to analyze the solute-solvent interactions, the ground dipole moments are estimated theoretically for all the studied solvents by using IEF-PCM solvation model and the results are given in Table 8 and it is noticed that the ground-state dipole moment values for each of the solvents are found to be higher than the ground-state dipole moment value of the probe molecule in the gaseous phase. The increase in the dipole moment value is due to the consideration of environmental effects like solute-solvent interactions in the IEF-PCM solvation model. Further, the excited-state dipole moment values were found to be higher than the corresponding ground-state dipole moment values for all the solvents and this suggests that the probe molecule is more polar in the excited state than the ground state. It is interesting to note that the computational studies also reproduce the similar trend as observed experimentally. However, the theoretically computed ground- and excited-state dipole moments were found to be higher than the experimental dipole moments.
The 3D plots of HOMO and LUMO of synthesized fluorescent dye are shown in Fig. 6. The HOMO, LUMO energies and HOMO-LUMO energy band gap (ΔE) value for the probe molecule are presented in Table 7.
The optical band gap Eoptg is determined from absorption threshold wavelength for both molecules and the results are tabulated in Table 8. It is observed that the HOMO-LUMO energy band gap is in order with the experimental optical energy band gap. The lower values of energy gap for the probe molecule also support the observed higher values of excited-state dipole moments. The determination of HOMO-LUMO energies also helps in understanding the chemical stability of a molecule in terms of a parameter known as chemical hardness (η). The molecules possessing large HOMO-LUMO energy gap are considered as hard, whereas moleculespossessing small HOMOLUMO energy gaps are considered as soft molecules [31–32]. The chemical hardness (η) of a molecule is determined from Eq. 17.
$${\eta }=\frac{{\text{E}}_{\text{L}}-{\text{E}}_{\text{H}}}{2}$$
17
where EH and EL are the HOMO and LUMO energies
The chemical hardness (η) estimated for all fluorescent dyes and are given in Table 8. The small values of chemical hardness (η) and HOMO-LUMO energy gaps suggest that the molecule may be considered as soft molecule. These results also support the observed higher values of µe.
The molecular electrostatic potential (MESP) plots provide the information for determining a suitable position for nucleophilic and electrophilic attack along with the hydrogen bonding interactions of solvent. The MESP 3D plot shown in Fig. 7.
In this plot, different colors correspond to different values of electrostatic potential at the surface. The red color represents negative phase, which can be related to the electrophilic site, and blue color represents positive phase, which corresponds to nucleophilic site. From Fig. 7, it is observed that the MESP plot of all molecule shows negative phases around 3H-benzo[f]chromen-3-onewhereas positive phases around all hydrogen atoms.