The solvent effects on the absorption and emission analysis provide useful results on physical properties such as dipole moment changes, polarizability of the molecule in the ground, and excited state. The excitation of an electron is raised to a new electronic level and is excited in much less time than it takes the whole molecule to rearrange itself with the solvent environment. In excited states, the molecule is in the same structural environment in the excited state as in the ground state. The absorption and emission spectra of the solute show variation in their chemical properties. The solvatochromism of fluorophores is usually analysed using the linear correlations of Lippert-Mataga, Bakhshiev, Kawski-Chamma-Viallet, and Reichardt [1, 2, 4, 6, 7, 27, 35]. According to Lippert-Mataga,Stokes shift (\(\varDelta \stackrel{-}{v}={\overline{\nu }}_{A}-{\overline{\nu }}_{F}\)) of solute molecule is related to the permittivity (\({\epsilon }\)) and refractive index (\(n\)) of solvent as,

$${\overline{\nu }}_{A}-{\overline{\nu }}_{F}={m}_{1}{F}_{1}\left(\epsilon , n\right)+\text{c}\text{o}\text{n}\text{s}\text{t}\text{a}\text{n}\text{t}$$

1

Where, \({\overline{\nu }}_{A}\) and \({\overline{\nu }}_{F}\) are the absorption and fluorescence emission maxima wave numbers (cm−1), \({F}_{1}\left(\epsilon ,n\right)\)is the Lippert solvent polarity function (Eq. 2), and standard equation is given by

$$F\left(\epsilon ,n\right)=\frac{\epsilon -1}{2\epsilon +1}-\frac{{n}^{2}-1}{2{n}^{2}+1}$$

$${ F}_{1}\left(\epsilon ,n\right)=\frac{2{n}^{2}+1}{{n}^{2}+2}\left[\frac{\epsilon -1}{\epsilon +2}-\frac{{n}^{2}-1}{{n}^{2}+2}\right]$$

2

\({m}_{1}={2\left({\mu }_{e}-{\mu }_{g}\right)}^{2}/hc{a}^{3}\) , \({\mu }_{e}\) and \({\mu }_{g}\) are the dipole moments of ground and excited state \(a\) is the Onsager cavity radius of solute molecule, respectively that can be calculated using Eq. (3).

$$a= {\left(\frac{3M}{4\pi \delta {N}_{A}}\right)}^{1/3}$$

3

Here, \(M\) and \(\delta\) are the molecular weight and density, respectively.

Bakhshiev equation (Eq. 4) gives the dependency of the Stokes shift of solute on \(\epsilon\) and \(n\) of solvent as,

$${\overline{\nu }}_{A}-{\overline{\nu }}_{F}={m}_{2}{F}_{2}\left(\epsilon , n\right)+\text{c}\text{o}\text{n}\text{s}\text{t}\text{a}\text{n}\text{t}$$

4

Where, \({m}_{2}={2\left({\mu }_{e}-{\mu }_{g}\right)}^{2}/hc{a}^{3}\) and \({ F}_{2}\left(\epsilon ,n\right)\)is the Bakhshiev solvent polarity function (Eq. 5),

$${ F}_{2}\left(\epsilon ,n\right)=\frac{2{n}^{2}+1}{{2(n}^{2}+2)}\left(\frac{\epsilon -1}{\epsilon +2}-\frac{{n}^{2}-1}{{n}^{2}+2}\right)+\frac{{3(n}^{4}-1)}{{2\left({n}^{2}-1\right)}^{2}}$$

5

The equation Kawski-Chamma-Viallet gives the average of absorption and emission maximum of solute with \(\epsilon\) and \(n\) of solvent as,

$$\frac{{\overline{\nu }}_{A} + {\overline{\nu }}_{F}}{2}=-{{m}_{3}F}_{3}\left(\epsilon , n\right)+\text{c}\text{o}\text{n}\text{s}\text{t}\text{a}\text{n}\text{t}$$

6

Where, \({m}_{3}=2\left({{\mu }_{e}}^{2}-{{\mu }_{g}}^{2}\right)/hc{a}^{3}\)and\({ F}_{3}\left(\epsilon ,n\right)\) is the Kawski-Chamma-Viallet solvent polarity function as given in Eq. (7),

$${ F}_{3}\left(\epsilon ,n\right)=\frac{2(\epsilon -1)}{\epsilon +2}$$

7

\({ F}_{4}\left(\epsilon \right)\) is the Suppan’s polarity parameter and given in Eq. (8)

$${ F}_{4}\left(\epsilon ,n\right)=\frac{2(\epsilon -1)}{2\epsilon +2}$$

8

The computed values of\({ F}_{1}\left(\epsilon ,n\right)\),\({ F}_{2}\left(\epsilon ,n\right)\),\({ F}_{3}\left(\epsilon ,n\right)\)and \({F}_{4}\left(\epsilon ,n\right)\) along with the values of \({E}_{T}^{N}\)are given in **Table.1**.

Considering stable symmetry of molecule upon excitation and parallel orientation of the dipole moments, \({\mu }_{g}\),\({\mu }_{e}\), and \({\mu }_{e}\)*/*\({\mu }_{g}\) can be calculated from the slopes (m2 and m3) of the plots of \({\overline{\nu }}_{A}-{\overline{\nu }}_{F}\)versus \({ F}_{2}\left(\epsilon ,n\right)\)and \({(\overline{\nu }}_{A}+ {\overline{\nu }}_{F})/2\) versus\({ F}_{3}\left(\epsilon ,n\right)\)as,

$${\mu }_{g}=\frac{{m}_{3}-{m}_{2}}{2}{\left(\frac{hc{a}^{3}}{2{m}_{2}}\right)}^{1/2}$$

9

$${\mu }_{e}=\frac{{m}_{3}+{m}_{2}}{2}{\left(\frac{hc{a}^{3}}{2{m}_{2}}\right)}^{1/2}$$

10

$$\frac{{\mu }_{e}}{{\mu }_{g}}=\frac{{{m}_{2}+m}_{3}}{{m}_{3}-{m}_{2}}\text{F}\text{o}\text{r}{{m}_{3}>m}_{2}$$

11

If \({\mu }_{g}\) and \({\mu }_{e}\) subtend an angle,\(\varphi\)

$$cos\varphi =\frac{1}{2{\mu }_{g}{\mu }_{e}}\left[\left({\mu }_{g}^{2}+{\mu }_{e}^{2}\right)-\frac{{m}_{2}}{{m}_{3}}\left({\mu }_{e}^{2}-{\mu }_{g}^{2}\right)\right]$$

12

\({\mu }_{e}\) can also be determined using the empirical relation,

$${\overline{\nu }}_{A}-{\overline{\nu }}_{F}=11307.6 {\left(\frac{\varDelta \mu }{\varDelta {\mu }_{B}}\right)}^{2}{\left(\frac{{a}_{B}}{a}\right)}^{3}{E}_{T}^{N}+constant$$

13

Where, (\({E}_{T}^{N}\)) is themicroscopic solvent polarity function, \(\varDelta \mu\) and \(\varDelta {\mu }_{B}\) are the changes in the dipole moments of sample and reference (Betaine dye) molecules on excitation. \({a}_{B}\)mentiontheOnsager cavity radius of reference molecule. Where \(\varDelta \mu\)can be determined using the slope of \({\overline{\nu }}_{A}-{\overline{\nu }}_{F}\) versus \({E}_{T}^{N}\) plot and the reported values of \(\varDelta {\mu }_{B}\) and \({a}_{B}\) (9 D and 6.2 Å, respectively) for 5ABBM dye. Further, using \(\varDelta \mu\) and \({\mu }_{g}\) from Eq. (9), \({\mu }_{e}\) can be determined. Eq. (13), which accounts for more intermolecular interactions, better correlates the Stokes shift and solvent polarity function than the other relations.