Discrete Solvent Reaction Field Calculations for One-and Two-Photon

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Discrete Solvent Reaction Field Calculations for One-and Two-Photon Absorptions of Solution-Phase Dimethylamino Nitro Stilbene Molecule Shih-I Lu J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.9b04041 • Publication Date (Web): 04 Jun 2019 Downloaded from http://pubs.acs.org on June 6, 2019

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The Journal of Physical Chemistry

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Discrete Solvent Reaction Field Calculations for One- and Two-Photon Absorptions of SolutionPhase Dimethylamino Nitro Stilbene Molecule

Shih-I Lu* Department of Chemistry Soochow University No. 70 Lin-Shih Road, Taipei City, 111, Taiwan Email address: [email protected] Tel: 886-2-28819471 ext 6825 Fax: 886-2-28811053

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Abstract Based on the configurations generated by molecular dynamics (MD) simulations using the on-thefly density-functional tight-bonding (DFTB) force field, we investigated performance of the discrete solvent reaction field (DRF) model coupled to time-dependent density functional theory (TD-DFT) for solvatochromic effect of one- and two-photon absorption phenomena. Dimethylamino nitro stilbene (DANS) molecule solvated in chloroform, dichloromethane and dimethyl sulfoxide solvents was selected as a model system for our research purpose. For every selected MD/DFTB configuration, within the context of the DRF, solute molecule is represented by TD-DFT and solvent molecules are described by atomic charges and polarizabilities. The calculated one-photon absorption energies reproduce well the positive solvatochromic behavior of solvated DANS and in good agreement with available experimental data. For the two-photon absorption cross section, even though our approach overshot the experimental data about 20% in absolute magnitude, experimentally observed solvatochromic change was captured qualitatively in this work. At last, we examined the contributions of atomic charges and polarizabilities of solvent molecules to the solvatochromic shifts of properties of interest.


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1. INTRODUCTION Solvatochromism has been of constant interest for spectroscopic studies.1-2 It allows for the analysis of the interactions between solute and solvent molecules and reveals the character of an excited state of solute molecule. Many methodologies have been developed to theoretically study solvent effects. Especially, explicit representation of solvent molecules gains reliable modeling when examining solidly interacting systems.3-5 One of the schemes extensively used to model molecules in condensed phase is the quantum mechanics/molecular mechanics (QM/MM) approach.6-7 The basic QM/MM strategy, in which the interaction between the QM and MM parts is described by electrostatic embedding. An improvement can be obtained by using the polarizable force fields8 in which the charge distributions in the MM part can respond to the changes in the electronic distribution in the QM part.9 Use of the polarizable force fields in the QM/MM framework enables an advanced and flexible modeling of condensed phases.10-12 The polarizable embedding (PE) approach13-17 and the quantum mechanics/effective fragment potential (QM/EFP) method18-24 are popularly utilized approaches using the polarizable force fields in the literature for solvatochromic shifts. Both have been shown to be able to model the effects of the environment on various spectroscopic properties in different types of systems and in general achieve good agreement with experiments.13-14, 16, 25-48 Besides the PE and QM/EFP approaches cited above, we identified the discrete solvent reaction field (DRF) model with standard time-dependent density functional theory (TD-DFT) as a potential computational candidate to estimate solvatochromic properties. The DRF also utilizes the polarizable force fields. Electronic polarization effect resulting from the surrounding molecules is modeled through atomic point charges, while the distributed atomic polarizabilities are included in order to model the polarization of surrounding molecules stemming from many-body



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interactions. Originally, the DRF was used to analyze solvation effects on molecular properties such as dipole moments, excitation energies and (hyper)polarizabilities with the density functional theory (DFT).49-52 In addition, we have applied the DFT/DRF to calculate non-linear optical properties of organic molecular crystals and obtained results in agreement with experiments in our recent works.53-54 To illustrate the combined TD-DFT/DRF method within the context of explicit representation of solvent molecules for the one-photon absorption (OPA) and two-photon absorption (TPA) phenomena, we consider dimethylamino nitro stilbene (DANS, Figure 1) solvated in chloroform (CHCl3), dichloromethane (DCM) and dimethyl sulfoxide (DMSO) molecules. Solvent configurations were generated by molecular dynamics (MD) simulations using on-the-fly densityfunctional tight-bonding (DFTB)55-56 force fields. DANS molecule is archetype of the dipolar and positive solvatochromic molecule containing donor and acceptor groups connected via a -electronic bridge. It can be categorized as quasilinear push-pull -conjugation molecule possessing an intense electron transition (usually π  π*, Figure S1) in the UV–Vis region which is assigned to the intramolecular charge-transfer occurring along the molecular axis. The most often used quantity in the description of the OPA and TPA are the excitation energy (max) and TPA cross section (TPA), respectively. The electronic excitation energies, transition dipole moments and excess dipole moments between the ground and excited states of the selected configurations of solute in solvent are calculated within the TD-DFT/DRF context.

2. COMPUTATIONS


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The MD/DFTB simulations57-58 were performed using the CP2K program59 and the TDDFT/DRF calculations using the ADF suite of programs.60-62 For explicit representation of solvent molecules, we used three different solvent models in the present study: (i) a charge-only model denoted as the DRF-1 in which no atomic polarizabilities are included and then all induced dipoles are zero; (ii) an induced dipole-only model denoted as the DRF-2 in which atomic charges are set to zero and only atomic polarizabilities are considered; (iii) an atomic charge plus induced dipole model denoted as the DRF-3 in which the atoms interact via induced dipoles and atomic static charges. In addition, we calculated the absorption spectra of DANS molecule for the configurations obtained from MD/DFTB simulations but without including the solvent molecules explicitly. The results from this set of calculations was referred to as the DRF-0. The DRF-0 results include the contributions from solvent-induced geometrical changes. Solvents used in this work are not involved in significant hydrogen bonding interactions with solute, and so the popular microsolvation scheme are not considered here. The DFTB method is the central method employed to compute on-the-fly potential energy surfaces and energy gradients for direct trajectory calculations in the presented study. Periodic boundary conditions were applied for all MD simulations and were based on a cubic box of 29.18 Å edge length. In each box, one target molecule was placed, and the box was filled with 128 solvent molecules. An NVT ensemble was used in conjunction with the canonical sampling velocity rescale thermostat (CSVR)63 and a constant temperature set to 298 K with a 0.5 fs time step for a total simulation time of 50 ps. Using the optimized configuration as starting geometries, the system of study was equilibrated for 25 ps. Next, 92 configurations from the trajectory of the last 25 ps were chosen at equal intervals. During the MD simulations, the geometrical structure of each solvent molecule was not frozen.



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Use of DRF calculations requires atomic point charges and atomic polarizabilities for each type of atom in the MM part. We followed a procedure proposed in the ADF manual to obtain these required parameters. Accordingly, we employed the multipole derived charges up to quadrupole (MDC-q) atomic charges64 and the Thole’s effective atomic polarizabilities.65-66 The used atomic polarizabilities are independent from the chemical environment of atoms: αC = 8.6959 a.u., αH = 2.7927 a.u., αN = 6.5565 a.u. and αO = 5.7494 a.u., and αS = 16.6984. For the QS part, we employed the range-separated hybrid of the CAMY-B3LYP exchange-correlation functional67 with the TZ2P basis set. The CAMY-B3LYP uses the Slater-type functions with  = 0.19 and  = 0.46 but with the Yukawa potential rather than the Coulomb potential used in the CAM-B3LYP68 attenuated by the complementary error function. For the attenuation parameters, we adopted 0.34 bohr-1, as recommended by Akinaga and Te-no.69 Also, the CAMY-B3LYP/TZ2P was employed to calculate the atomic MDC-q charges for each solvent molecule. To make a direct comparison between experiment and theory, we connect the macroscopic TPA (GM in GM) with the microscopic transition probability (au, in atomic unit) for the absorption of two identical photons via the following equation:70 σGM =

N𝜋3αa50ω2 c

(1)

δau𝑔(2𝜔,𝜔0,Γ)

where N is an integer value (chosen as 4 here, referring to the work of Beerepoot et al.71),  is the fine-structure constant, a0 is the Bohr radius, c is the speed of light,  is an empirical damping parameter describing the spectral broadening of an excitation,  is the energy of the incoming photons, and 𝑔(2𝜔,𝜔0,𝛤) is the lineshape function describing spectral broadening effects.


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For the lineshape function, the Lorentzian and Gaussian functions are most commonly used.72 The corresponding maxima at 𝜔 = 𝜔0/2 are 1 (𝜋𝛤) and ln2 (𝛤 𝜋) with  the half width at half maximum (HWHM). When these maxima are inserted for 𝑔(2𝜔,𝜔0,𝛤) in eqn (1), one obtains σGM =

)2

(

𝑁𝜋2αa50 𝜔0 2 c𝛤

𝛿𝑎𝑢,

(2)

and 5

σGM =

(

)2

ln2𝑁π2αa50 𝜔0 2 c𝛤

𝛿𝑎𝑢,

(3)

for the Lorentzian and Gaussian line shape functions, respectively. The Lorentzian function has a broader base and the Gaussian function has a higher maximum by a factor of 𝜋ln (2)  1.48.71 In this work, we employed the Lorentzian lineshape function. We performed OPA calculation for the 92 snapshots taken from MD simulations.  was estimated from the standard deviation, s, of the spread of these transition energies, i.e., 𝛤 = 2 2ln2𝑠. At last, to calculate the au for the quasilinear molecule, we adopted the semi-quantitative two-state model (TSM): 𝛿𝑎𝑢 ∼ 〈δTSM〉 =

2 16(μgeΔμge) , 5 𝜔20

(4)

in which the excitation energy (0), excess dipole moment (ge) and transition dipole moment (ge) are calculated through the TD-DFT/DRF directly. For the ge, the four-point formula for finite difference derivative with an error being approximately quadratic in step size (0.0002 au here) was employed to obtain its components. The four-point formula for finite difference derivative gives better accuracy and less sensitivity to step size at the cost of doing twice as many calculations. The detail about derivation of the four-point formula for finite difference derivative was given in the supplementary.



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3. RESULTS AND DISCUSSION The OPA spectra of DANS molecule have been reported in a number of solvents, both nonpolar and polar.73 Experimentally, it exhibits bathochromic shift,74 which can be explained by the more favorable stabilization of the charge-separated excited state in solution as compared to the neutral ground state, leading to a decrease in excitation energy. However, the behavior of the max of the DANS as a function of dielectric constant of the solvent is non-monotonic.73,

75

For

visualization, Figure S2 gave the variation of the max vs. the dielectric constant using data taken from the work of Shin and Whitten.75 Calculated results from using different solvent models for the max, ge,  and GM of DANS molecule surrounded by different solvents are collected in Tables 1-4, respectively. The CAMYB3LYP/TZ2P//DFTB-calculated max of DANS molecule in the vacuum is 404 nm. The corresponding ge is 12.10 Debye. Experimental data for the max and GM are also given in Table 1 and 4, respectively, for a comparison. For the max of the solvated DANS, two sets of available experimental data were given, designated as Expt-I and Expt-II. They were taken from the works of Shin and Whitten75 and Wielgus, Bartkowiak and Samoc,76 respectively. It is found that (i) Expt-I did not report data for that in CHCl3; (ii) Expt-II presented a subtle difference (1 nm) between the max of DANS molecule in CHCl3 and in DCM; (iii) both gave very close values of the max either in DCM or in DMSO. All models applied – DRF-0 to DRF-3 – correctly predict the positive solvatochromic effect for solvated DANS molecule. The mean absolute error (MAE) against the data of the Expt-II is evaluated to be around 43 nm using the DRF-0. The charge-only DRF-1 approach gives the MAE of around 16 nm, and the induced dipole-only DRF-2 model around 19 nm. The DRF-3 reduces



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the MAE to around 12 nm. Apparently, the DRF-3 performs the best. However, the DRF-3 predicting 9 nm of the difference between the max of DANS in CHCl3 and in DCM while experiment gave 1 nm. More elaborated description of the DRF-constructed polarization field should be necessary for improving the insufficiency of the models applied. At last, the calculated

 values diminish with the increasing solvent polarity in agreement with the observed experimental trend.76 Continuing to the ge, the ground state of DANS molecule is neutral while the excited state is charge-separated. When DANS molecule is surrounded by organic solvent molecules, we expect that a more increase in the dipole moment of the excited state than that of the ground state, eventually leading to an increase in ge. Also, the more polar the solvent is, the larger the ge is. Our calculations are consistent with the rationale. The solute molecule exhibits higher dipole moment value in the excited state than in the ground state by ge = 12.52 and 15.84 Debye in the gas phase and in DMSO solution, respectively. The same trend is observed in the cases of using CHCl3 and DCM as the solvent. The solvent-dependence of the calculated values of the ge is also in complete agreement with the positive solvatochromic behavior for which the excited state is supposed to be more polar. Passing from the gas phase to the DRF-0, indirect contribution of the medium to the max due to solvent-induced geometrical distortions of the solute is -15 nm in CHCl3, rises to -11 nm in DCM, and 6 nm in DMSO. The corresponding contribution to the ge is -0.86, -0.26, and 0.42 Debye. The solvent-induced geometrical changes resulted in appreciable solvatochromic shifts of the max and ge. Similar observations have been obtained in previous studies.26-27,

77-78

It is

interesting that molecular structure generated in a medium of low polarity delivered an increase of HOMO-LUMO gap and an accompanying decrease in ge. By contrast, a medium of high polarity



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effects in the opposite direction from that of a medium of low polarity. A different observation was found in the theoretical work of Muguran et al.27, a red shift appeared in CHCl3, DMSO and water solvents. The difference could be partly attributed different force fields employed in their MD simulations and ours. Another property of interest is the GM. In experiment, a non-monotonic behavior of the GM with increasing solvent polarity was observed.73, 76 The changes in the GM are minor, that is 116 GM in CHCl3, 108 GM in DCM and 114 GM in DMSO, along with the solvent polarity.76 The experimental data was used as a reference. We note that the DRF-0, DRF-1 and DRF-2 models predict a monotonic increase in the GM with increasing solvent polarity. This evidently is not consistent with experiment. When both atomic charges and polarizabilities of solvent molecules are included in the DRF-3 model, the predicted GM values are found to agree qualitatively with the experimental trend with R2 of 0.95 though the DRF-3 gives estimates of the GM (142, 131 and 137 GM for CHCl3, DCM and DMSO, respectively) higher than experimental results around 20%. Regardless, in the present work more important than absolute ones are the relative GM values calculated for DANS molecule in different solvents. Finally, to examine the effects of atomic charges and polarizabilities of solvent molecules to the max, ge and GM, we calculated the model shifts of the DRF-0 to DRF-1, DRF-0 to DRF-2 and DRF-0 to DRF-3, designated as the C, D, and CD. Figure 2 illustrated these model shifts. For the max, we observe from Figure 2(a) that contributions from atomic charges and polarizabilities are close regardless of the polarity of solvent, that is around 3~4 nm for DANS in a given solvent for all cases. For the ge, Figure 2(b) shows more than twice as the contributions from the atomic polarizabilities than that from the atomic charges. The ratios of the Dge to Cge are 2.19, 2.07 and 2.07 for those in CHCl3, DCM and DMSO, respectively. For the model


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shifts concerning the max and ge, the calculations show that effect in the max in the transgression from solvent of low polarity to that of high polarity is on average not great, the effect in the ge being substantially larger. For the GM, shown in Figure 2(c), while the induced dipole-only DRF-2 model gave positive contribution to the GM (DGM = 31, 32 and 57 GM for that in CHCl3, DCM and DMSO, respectively), the charge-only DRF-1 model results in a decrease of the GM, i.e., CGM = -22 GM in CHCl3, -25 GM in DCM and -38 GM in DMSO. Unlike the case for the max that showed good additivity of the model shifts (CDmax  Cmax+Dmax), there is no pronounced pattern for the GM. This indicates the interaction between the two terms employed in the context of the DRF has a more complicated influence on the TPA activity than on the OPA. Our results also reveal the effects of atomic charges and polarizabilities within the DRF settings on the TPA cross sections. On the one hand, a lack of atomic charges in the induced-dipole only DRF-2 model underestimates the  and then results in a high estimate of the GM, but on the other hand, the low estimate of the GM from the charge-only DRF-1 model is caused by underestimating the excess dipole moment owing to an absence of atomic polarizabilities. These provide us with new insights into the nature of atomic charges and polarizabilities in explicit treatment of solute-solvent interactions for properties of interest.

4. CONCLUSIONS We have employed an QM/MM-MD based approach to consider one- and two-photon absorption of DANS in solution. MD simulations based on the DFTB force fields were performed for DANS molecule surrounded by CHCl3, DCM and DMSO molecules. Using snapshots extracted from the MD simulations, we examined the calculated spectroscopic properties of



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interest. The TD-CAMY-B3LYP/TZ2P calculation for solute within the context of the DRF-based solvent molecules reproduces qualitative the positive solvatochromic behavior of DANS molecule in all considered solvents. Also, the quantitative estimates of the absorption maxima and solvent shifts are satisfactory. For the TPA strength, even though our best results (the DRF-3) estimated the absolute values higher by about 20%, the correct relative trend was obtained. The insight and promising results gained in this pilot study would warrant further development of the TD-DFT methods for modeling TPA processes within the DRF context.

ACKNOWLEDGEMENTS We are grateful to the National Center for High-performance Computing for computer time and facilities and to the Ministry of Science and Technology, Taiwan (MOST 107-2113-M-031003) for financial support.

Supporting Information Available: Molecular orbitals involved in the charge transfer excitation of dimethylamino nitro stilbene in a vacuum. Variation of the max vs. the dielectric constant. Details on how the excess dipole moment is being calculated.


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35. Beerepoot, M. T. P.; Steindal, A. H.; Ruud, K.; Olsen, J. M. H.; Kongsted, J., Convergence of environment polarization effects in multiscale modeling of excitation energies. Comput. Theor. Chem. 2014, 1040-1041, 304-311. 36. Schwabe, T.; Beerepoot, M. T. P.; Olsen, J. M. H.; Kongsted, J., Analysis of computational models for an accurate study of electronic excitations in GFP. Phys. Chem. Chem. Phys. 2015, 17, 2582-2588. 37. Hrsak, D.; Holmegaard, L.; Poulsen, A. S.; List, N. H.; Kongsted, J.; Denofrio, M. P.; ErraBalsells, R.; Cabrerizo, F. M.; Christiansen, O.; Ogilby, P. R., Experimental and computational study of solvent effects on one- and two-photon absorption spectra of chlorinated harmines. Phys. Chem. Chem. Phys. 2015, 17, 12090-12099. 38. Krause, K.; Bauer, M.; Klopper, W., Approaching Phosphorescence Lifetimes in Solution: The Two-Component Polarizable-Embedding Approximate Coupled-Cluster Method. J. Chem. Theory Comput. 2016, 12, 2853-2860. 39. Norby, M. S.; Steinmann, C.; Olsen, J. M.; Li, H.; Kongsted, J., Computational Approach for Studying Optical Properties of DNA Systems in Solution. J. Chem. Theory Comput. 2016, 12, 5050-5057. 40. Slipchenko, L. V., Solvation of the Excited States of Chromophores in Polarizable Environment: Orbital Relaxation versus Polarization. J. Phys. Chem. A 2010, 114, 8824-8830. 41. DeFusco, A.; Ivanic, J.; Schmidt, M. W.; Gordon, M. S., Solvent-induced shifts in electronic spectra of uracil. J. Phys. Chem. A 2011, 115, 4574-4582. 42. DeFusco, A.; Minezawa, N.; Slipchenko, L. V.; Zahariev, F.; Gordon, M. S., Modeling Solvent Effects on Electronic Excited States. J. Phys. Chem. Lett. 2011, 2, 2184-2192. 43. Ghosh, D.; Isayev, O.; Slipchenko, L. V.; Krylov, A. I., Effect of Solvation on the Vertical Ionization Energy of Thymine: From Microhydration to Bulk. J. Phys. Chem. A 2011, 115, 60286038. 44. Kosenkov, D.; Slipchenko, L. V., Solvent Effects on the Electronic Transitions of pNitroaniline: A QM/EFP Study. J. Phys. Chem. A 2011, 115, 392-401. 45. Ghosh, D.; Roy, A.; Seidel, R.; Winter, B.; Bradforth, S.; Krylov, A. I., First-Principle Protocol for Calculating Ionization Energies and Redox Potentials of Solvated Molecules and Ions: Theory and Application to Aqueous Phenol and Phenolate. J. Phys. Chem. B 2012, 116, 7269-7280. 46. De Silva, N.; Minezawa, N.; Gordon, M. S., Excited-State Hydrogen Atom Transfer Reaction in Solvated 7-Hydroxy-4-methylcoumarin. J. Phys. Chem. B 2013, 117, 15386-15394. 47. Bose, S.; Chakrabarty, S.; Ghosh, D., Effect of Solvation on Electron Detachment and Excitation Energies of a Green Fluorescent Protein Chromophore Variant. J. Phys. Chem. B 2016, 120, 4410-4420. 48. Nanda, K. D.; Krylov, A. I., The effect of polarizable environment on two-photon absorption cross sections characterized by the equation-of-motion coupled-cluster singles and doubles method combined with the effective fragment potential approach. J. Chem. Phys. 2018, 149, 164109: 114. 49. Jensen, L.; van Duijnen, P. T.; Snijders, J. G., A discrete solvent reaction field model within density functional theory. J. Chem. Phys. 2003, 118, 514-521. 50. Jensen, L.; van Duijnen, P. T.; Snijders, J. G., A discrete solvent reaction field model for calculating molecular linear response properties in solution. J. Chem. Phys. 2003, 119, 3800-3809. 51. Jensen, L.; van Duijnen, P. T.; Snijders, J. G., A discrete solvent reaction field model for calculating frequency-dependent hyperpolarizabilities of molecules in solution. J. Chem. Phys. 2003, 119, 12998-13006.



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71. Beerepoot, M. T.; Friese, D. H.; List, N. H.; Kongsted, J.; Ruud, K., Benchmarking two-photon absorption cross sections: performance of CC2 and CAM-B3LYP. Phys. Chem. Chem. Phys. 2015, 17, 19306-19314. 72. Matczyszyn, K.; Olesiak-Banska, J.; Nakatani, K.; Yu, P.; Murugan, N. A.; Zalesny, R.; Roztoczynska, A.; Bednarska, J.; Bartkowiak, W.; Kongsted, J.; Ågren, H.; Samoc, M., One- and two-photon absorption of a spiropyran-merocyanine system: experimental and theoretical studies. J. Phys. Chem. B 2015, 119, 1515-1522. 73. Tabor, C. E.; Kajzar, F.; Kaino, T.; Koike, Y.; Wicks, G.; Rebane, A.; Drobizhev, M., Twophoton solvatochromism of 4-dimethylamino-4'-nitrostilbene (DANS). In Organic Photonic Materials and Devices XVI, 2014. 74. Reichardt, C., Solvatochromic Dyes as Solvent Polarity Indicators. Chem. Rev. 1994, 94, 23192358. 75. Shin, D. M.; Whitten, D. G., Solvatochromic behavior of intramolecular charge-transfer diphenylpolyenes in homogeneous solution and microheterogeneous media. J. Phys. Chem. 1988, 92, 2945-2956. 76. Wielgus, M.; Bartkowiak, W.; Samoc, M., Two-photon solvatochromism. I. Solvent effects on two-photon absorption cross section of 4-dimethylamino-4′-nitrostilbene (DANS). Chem. Phys. Lett. 2012, 554, 113-116. 77. Arul Murugan, N.; Kongsted, J.; Rinkevicius, Z.; Aidas, K.; Ågren, H., Modeling the Structure and Absorption Spectra of Stilbazolium Merocyanine in Polar and Nonpolar Solvents Using Hybrid QM/MM Techniques. J. Phys. Chem. B 2010, 114, 13349-13357. 78. Murugan, N. A., Solvatochromism in a pyridinium cyclopentadienylide: insights from a sequential Car-Parrinello QM/MM and TD-DFT/semicontinuum approach. J. Phys. Chem. B 2014, 118, 7358-66. 79. Antonov, L.; Kamada, K.; Ohta, K.; Kamounah, F. S., A systematic femtosecond study on the two-photon absorbing D-π-A molecules–π-bridge nitrogen insertion and strength of the donor and acceptor groups. Phys. Chem. Chem. Phys. 2003, 5, 1193-1197.



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Table 1. Average absorption maxima (max in nm) for DANS molecule in different organic solvents Method

DANS in CHCl3

DANS in DCM

DANS in DMSO

DRF-0

389

397

410

DRF-1

416

424

439

DRF-2

413

421

435

DRF-3

443

452

467

QM/MMa

420

---

451

Expt-I75

---

440

454

Expt-II76

437

438

451

a: TD-DFT calculations with the CAM-B3LYP/Turbomole-TZVP for the QS part. Using response theoretical framework.27


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Table 2. Average excess dipole moments (ge in Debye) for DANS molecule in different organic solvents Method

DANS in CHCl3

DANS in DCM

DANS in DMSO

DRF-0

11.24

11.84

12.52

DRF-1

12.14

12.89

13.64

DRF-2

13.21

14.01

14.84

DRF-3

14.13

15.03

15.84



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20

Table 3. Linewidth ( in cm-1) for DANS molecule in different organic solvents Method

DANS in CHCl3

DANS in DCM

DANS in DMSO

DRF-0

2011

1990

1932

DRF-1

3458

3414

3320

DRF-2

2285

2207

2145

DRF-3

3531

3369

3318


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Table 4. Average two-photon absorption cross section (GM in GM) for DANS molecule in different organic solvents Method

DANS in CHCl3

DANS in DCM

DANS in DMSO

DRF-0

70

80

126

DRF-1

48

55

88

DRF-2

101

112

183

DRF-3

142

131

137

QM/MMa

231

---

149

Expt.79 Expt.76

190 11618

10813

11414

a: Response theoretical framework employing the TD-CAM-B3LYP/Turbomole-TZVP for the QS part.27



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22

Figure 1. The molecular structure of dimethylamino nitro stilbene.

O2N NMe2

O2N

N NMe2

O2N

O2N

O2N

N

NMe2

N

NMe2

N

N N

NC

NH2

N N

NMe2


Page 23 of 25

23

Figure 2. Contributions to the TD-CAMY-B3LYP/TZ2P/DRF solvent-induced shifts of (a) the max (b) ge and (c) GM for solvated dimethylamino nitro stilbene. (a)

70 Model shift of λmax (nm)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


60

57

55

54

50 40 30

27

24

27

24

29

25

20 10 0 in CHCl3 DRF-0 to DRF-1

in DCM DRF-0 to DRF-2

in DMSO DRF-0 to DRF-3

(b)



Page 24 of 25

24

(c)


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Table of Contents Graphic


Discrete Solvent Reaction Field Calculations for One-and Two-Photon

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