Structure-emission relationship of some coumarin laser dyes and related molecules: Prediction of radiative energy dissipation and the intersystem crossing rate constants

Dye lasers are commonly used in optical investigation because their solutions in organic solvents deliver tunable, coherent emissions. They exhibit intense fluorescence owing to some specific spectroscopic characteristics. One drawback of the laser dyes is that it shows excessive triplet-state losses (TSLs.) The lack of theoretical predictions of fluorescence rates, intersystem crossing (ISC), and phosphorescence in laser dyes prompted us to report on the predicted rates of radiative and nonradiative transitions of some laser dyes. Structural engineering by some substituents influencing the simulated rates of coumarin laser dye derivatives for an efficient operation was investigated. The NH2 functional group renders the coumarin 120 more fluorescents with reduced TLS than the other investigated materials. Tailoring new efficient laser dyes can be achieved guided by the calculated rates of emission and nonradiative processes.


Computational method
All calculations were carried out using the ORCA 4.2 (parallel) software package [34].Structures were optimized using the B3LYP functional and the def2-TZVP(-F) basis, as recommended [35,36].The rates and spectra were calculated using the same methods recommended and detailed in the literature [34][35][36] and summarized here.Ground state calculations were performed for triplet states by setting the multiplicity to three rather than computing the triplet excited states from TD-DFT.To accelerate the computation of two-electron integrals, the resolution of identity approximation was used for the Coulomb part (RIJ) and the chain of spheres algorithm for the exchange part (COSX), with the corresponding auxiliary basis and grid settings [36].The DFT grid was set to GRID5, and the COSX grid was GRIDX5.ORCA allows vibronic coupling or the so-called Herzberg-Teller (HT) effect by setting the DOHT keyword to true (See the supplementary file).The spin-orbit (SO) coupling integrals were calculated using the RI-SOMF(1X) approximation [36].For the excited states, TD-DFT no optimized structure presented negative frequencies.The individual rates were calculated using the ORCA_ ESD module impeded in the ORCA package.The temperature was set to 77 K. Further details are defined explicitly in the Supplementary material file.
We considered the triplet spin-sublevels (1, 0, or -1).For the molecules under investigation, we predicted the k ISC as the mean of the sum of the individual k ISC (T1), k ISC (T2), and k ISC (T3).A detailed example illustrating the methodology we followed is given in the supplementary file.We employed the well-known conductor-like polarizable continuum (C-PCM) solvation model as treated in ORCA [34] using ethanol (dielectric constant of 24.3 value impeded in ORCA) as a solvent.The supplementary material file gives more details and several examples of calculating the spectra and rates for a molecule.

Results and discussion
The effect of substituents on the dipole moment is summarized in Table 2.The theoretically simulated photophysical parameters are summarized in Table 3. Figure 2 represents the ground state potential energy surfaces (PES) mapped with the electron density.The electrostatic potential limits in kJ are given in Table 2 for comparison.
Referring to Figure 1, Table 1, and Table 2, architecturally, three important modified positions are observed in the coumarin skeleton for controlling the photophysical properties.One is the 1-position (X in Figure 1), the second is 7-position (Y in Figure 1), and the third is the 4-position (Z in Figure 1).In this framework, the molecular engineering of  1).3D designs are shown in Figure 2.
these three positions by sensible substituent effect to understand the dominant deactivation channel and the laser efficiency of coumarin derivatives is addressable.Herein, two members of coumarin derivatives with O and N atoms substituted at the X-position were selected.For now, the rates of deactivation channels were successfully tuned by introducing substituents with various electronic properties at the Y-position (OH and NH 2 , Figure 1) and two-electron donor (CH 3 ) and electron acceptor (CF 3 ) functional groups at the Z-position.The effect of substituents can be quantitatively measured by the calculated dipole moment of the molecules given in Table 2 and depicted in Figure 3.The predicted spectra of dye 3 (coumarin 120) are depicted in Figure 4 as an example; all other compounds showed similar spectra.
A glance at Figure 5, showing the predicted ISC and fluorescence rates for various molecules at 77 K, reveals the effect of substituents on the nonradiative transition rate k ISC and the radiative k flu .Interestingly, a structural change in Y significantly influenced the molecules' fluorescence, ICS, and phosphorescence rates (see Table 3).One can notice that substituting the OH group in dye 5 (of dipole moment 4.35 Debye) with the more electron-donating NH 2 group (dye 3, of dipole moment 6.57Debye) enhances k flu, and k pho slightly depresses k ICS .Based on the energies of the fluorescence and the phosphorescence (Table 3), the change in Y by a more powerful electron-donating group could be explained due to lowering the energy gaps between the excited singlet state and the triplet state and the ground state in the case of NH 2 substituent relative to the OH, resulting in the changes as mentioned above in the rates calculated.Most importantly, the triplet state lifetime is significantly shortened, decreasing light loss by T à T absorption.In other words, the shortening of a triplet-state lifetime due to the replacement of the OH group by the more electron-donating NH 2 group prevents or limits excessive triplet-state losses (TSLs.)and enhances laser dye efficiency.Moreover, replacing the CH 3 group in 3 (of 6.57Debye) with the more electron-withdrawing CF 3 group in 4 (of 6.33 Debye) further decreases the k ICS value and renders dye 4 less efficient phosphorescent.Consequently, considerable TLS is diminished.Table 3.Some predicted radiative (S 1 à S 0 and T 1 à S 0 ) and nonradiative (ISC) transitions of the dyes 1-5.Phosphorescence lifetime (τ) in ms is given between parentheses.The percent of the Hertzberg-Teller coupling (HT%) due to vibronic coupling is also provided.Wavelength is shown in the linear wavenumber units.Astonishingly, the N heteroatom in the X position, as in the carbostyryl 7 (dye 1), significantly depresses both k flu and k pho, noticeably enhancing the k ISC value relative to that of dye 3. Consequently, dye 1 should be a less efficient laser dye than dye 3. Molecule 2 behaves similarly to dye 1, indicating that its CF 3 group is of minor influence, in this case, showing the dominant role the N heteroatom plays in increasing the ISC and decreasing the fluorescence rate.Molecules 1 and 2 are structurally related molecules to the investigated laser dyes.However, the N heteroatom acts as an electron sink (with values of -0.609 and -0.601 natural charges for molecules 1 and 2, respectively) relative to the O heteroatom in coumarins 3, 4, and 5 (having natural charges of -0.521, -0.512, and -0.518, respectively) (See Figure 3).

Dye
Noteworthy mentioning is that the experimentally available photophysical data in the literature [4,[38][39][40] match our theoretically predicted parameters (see Table 3).To the best of our knowledge, the triplet state characteristics of all the molecules studied are not reported in the literature [39,40].Previous experimental research [39,40] rolled out the possibility of ISC based on the absence of empirical proof.However, it was generally assumed that the ISC process is partially responsible for the fast nonradiative deexcitation channel for the fluorescent state of many dyes in nonpolar solvents [39,40].

Conclusions
For the first time, the research simulates the missing excited-state dynamic parameters such as fluorescence, ISC, and phosphorescence rates of some extensively reported coumarin laser dyes induced by different substituents.Structural substituents that influence the simulated spectroscopic rates of coumarin laser dye derivatives for an efficient operation have been highlighted.
The results showed that all the NH 2 -based dyes (3 and 4) exhibit a much higher fluorescence rate with short-lived triplet-state than those of OH-(dye 5) or -N-heteroatom and NH 2 -based molecules (1 and 2).The results obtained based on the mentioned findings pave the way for designing new efficient laser dyes.

Conflicts of interest
There is no conflict of interest.

Supplementary materials
ORCA can compute dynamic properties involving excited states such as absorption spectra, fluorescence, and phosphorescence rates and spectra using the ORCA Excited State Dynamic module.Optimization and frequency calculations should be performed for the ground singlet and triplet states and the excited singlet and triplet states.Hessians are automatically generated, which will be used for generating the spectra and the rates.As an example, full details are given in the supplementary file for the case of dye 4. ORCA manual (https://orcaforum.kofo.mpg.de/)describes the procedure stepwise.However, we added below some explanations to enable interested researchers to perform their own research using ORCA software. #

Figure 2 .
Figure 2. 3D structure and PES in the S 0 state.Color code: blue is the electron-deficient site (positive kJ value), and the red region is the electron-rich region (negative kJ value).

Figure 3 .
Figure 3.The calculated dipole moment vector directions and the natural charges on the heteroatoms (N and O).

Figure 4 .
Figure 4.The simulated absorption, fluorescence, and phosphorescence spectra of the laser dye 3 (coumarin 120) in ethanol.Similar spectra were obtained for the other molecules studied.

Figure 5 .
Figure 5. Predicted ISC and fluorescence rates for various molecules at 77 K.

Table 2 .
Structure-properties correlation of the coumarins which are listed in Table1.