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

Jun 4, 2019 - Find my institution ..... For the QS part, we employed the range-separated hybrid of the .... Line Width (Γ in cm–1) for the DANS Mol...
0 downloads 0 Views 661KB Size
Download PDF
Article Cite This: J. Phys. Chem. A 2019, 123, 5334−5340

pubs.acs.org/JPCA

Discrete Solvent Reaction Field Calculations for One- and TwoPhoton Absorptions of Solution-Phase Dimethylaminonitrostilbene Molecule Shih-I Lu* Department of Chemistry Soochow University No. 70 Lin-Shih Road, Taipei City, 111, Taiwan

Downloaded via NOTTINGHAM TRENT UNIV on August 14, 2019 at 11:47:42 (UTC). See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.

S Supporting Information *

ABSTRACT: Based on the configurations generated by molecular dynamics (MD) simulations using the on-the-fly 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. Dimethylaminonitrostilbene (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 are in good agreement with available experimental data. For the two-photon absorption cross section, even though our approach overshot the experimental data by 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.

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. In particular, explicit representation of solvent molecules gains reliable modeling when one is 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 This is 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 © 2019 American Chemical Society

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. The 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 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 nonlinear 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 dimethylaminonitrostilbene (DANS, Figure 1) solvated in chloroform (CHCl3), dichloromethane (DCM), and dimethyl sulfoxide (DMSO) molecules. Solvent configurations were generated by molecular dynamics Received: April 30, 2019 Revised: June 4, 2019 Published: June 4, 2019 5334

DOI: 10.1021/acs.jpca.9b04041 J. Phys. Chem. A 2019, 123, 5334−5340

Article

The Journal of Physical Chemistry A

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 Thole’s effective atomic polarizabilities.65,66 The used atomic polarizabilities are independent from the chemical environment of atoms: αC = 8.6959 au, αH = 2.7927 au, αN = 6.5565 au, αO = 5.7494 au, and αS = 16.6984 au. For the QS part, we employed the range-separated hybrid of the CAMYB3LYP exchange-correlation functional67 with the TZ2P basis set. The CAMY-B3LYP uses the Slater-type functions with α = 0.19 and β = 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 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 σTPA (σGM in GM) with the microscopic transition probability (δau, in atomic unit) for the absorption of two identical photons via the following equation:70

Figure 1. Molecular structure of dimethylaminonitrostilbene.

(MD) simulations using on-the-fly density-functional tightbonding (DFTB)55,56 force fields. DANS molecule is archetype of the dipolar and positive solvatochromic molecule containing donor and acceptor groups connected via a π-electronic bridge. It can be categorized as quasilinear push−pull π-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 quantities in the description of the OPA and TPA are the excitation energy (λmax) and TPA cross section (σTPA), 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.

σGM =

2. COMPUTATIONS The MD/DFTB simulations57,58 were performed using the CP2K program59 and the TD-DFT/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 were 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 the 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. Use of DRF calculations requires atomic point charges and atomic polarizabilities for each atom in the MM part. We

Nπ 3 αa0 5ω2 δaug(2ω , ω0 , Γ) c

(1)

where N is an integer value (chosen as 4 here, referring to the work of Beerepoot et al.71), α is the fine-structure constant, a0 is the Bohr radius, c is the speed of light, Γ is an empirical damping parameter describing the spectral broadening of an excitation, ω is the energy of the incoming photons, and g(2ω,ω0,Γ) is the line shape function describing spectral broadening effects. For the line shape function, the Lorentzian and Gaussian functions are most commonly used.72 The corresponding maxima at ω = ω0/2 are 1/(πΓ) and ln 2 /(Γ π ) with Γ the half width at half-maximum (HWHM). When these maxima are inserted for g(2ω,ω0,Γ) in eq 1, one obtains σGM =

Nπ 2 αa0 5(ω0 /2)2 δau cΓ

(2)

and ln 2 N π5/2αa 0 5(ω0 /2)2 δau cΓ

σGM =

(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 π ln(2) ≈ 1.48.71 In this work, we employed the Lorentzian line shape function. We performed OPA calculations for the 92 snapshots taken from MD simulations. Γ was estimated from the standard deviation, s, of the spread of these transition energies, i.e., Γ = 2 2 ln 2 s . At last, to calculate the δau for the quasilinear molecule, we adopted the semiquantitative two-state model (TSM): TSM

δau ∼ ⟨δ

2 16 (μgeΔμge) ⟩= 5 ω0 2

(4)

in which the excitation energy (ω0), excess dipole moment (Δμge), and transition dipole moment (μge) are calculated through the TD-DFT/DRF directly. For the Δμge, the four5335

DOI: 10.1021/acs.jpca.9b04041 J. Phys. Chem. A 2019, 123, 5334−5340

Article

The Journal of Physical Chemistry A 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 fourpoint formula for finite difference derivative was given in the Supporting Information.

Table 4. Average Two-Photon Absorption Cross Section (σGM in GM) for the DANS Molecule in Different Organic Solvents Method DRF-0 DRF-1 DRF-2 DRF-3 QM/MMa Expt.79 Expt.76

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 a 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 λmax of the DANS as a function of dielectric constant of the solvent is nonmonotonic.73,75 For visualization, Figure S2 gave the variation of the λmax vs the dielectric constant using data taken from the work of Shin and Whitten.75 Calculated results from using different solvent models for the λmax, Δμge, Γ, and σGM of DANS molecule surrounded by different solvents are collected in Tables 1−4, respectively. The

method

DANS in CHCl3

DANS in DCM

DANS in DMSO

389 416 413 443 420 − 437

397 424 421 452 − 440 438

410 439 435 467 451 454 451

Table 2. Average Excess Dipole Moments (Δμge in Debye) for the DANS Molecule in Different Organic Solvents DANS in CHCl3

DANS in DCM

DANS in DMSO

11.24 12.14 13.21 14.13

11.84 12.89 14.01 15.03

12.52 13.64 14.84 15.84

Table 3. Line Width (Γ in cm−1) for the DANS Molecule in Different Organic Solvents method

DANS in CHCl3

DANS in DCM

DANS in DMSO

DRF-0 DRF-1 DRF-2 DRF-3

2011 3458 2285 3531

1990 3414 2207 3369

1932 3320 2145 3318

80 55 112 131 −

116 ± 18

108 ± 13

126 88 183 137 149 190 114 ± 14

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) ExptII presented a subtle difference (1 nm) between the λmax of DANS molecule in CHCl3 and in DCM; (iii) both gave very close values of the λmax 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 chargeonly 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 the MAE to around 12 nm. Apparently, the DRF-3 performs the best. However, the DRF-3 predicted 9 nm of the difference between the λmax 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 Γ values diminish with the increasing solvent polarity in agreement with the observed experimental trend.76 Continuing to the Δμge, 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 Δμge. Also, the more polar the solvent is, the larger the Δμge is. Our calculations are consistent with this rationale. The solute molecule exhibits a higher dipole moment value in the excited state than in the ground state by Δμge = 12.52 and 15.84 D 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 Δμge 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 λmax due to solvent-induced geometrical distortions of the solute is −15 nm in CHCl3 and rises to −11 nm in DCM and 6 nm in DMSO. The corresponding contribution to the Δμge is −0.86, −0.26, and 0.42 D. The solvent-induced geometrical changes resulted in appreciable solvatochromic shifts of the λmax and Δμge. 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 Δμge. By contrast, a medium of high polarity effects in the opposite direction from that of a medium of low polarity. A different observation was found in

TD-DFT calculations with the CAM-B3LYP/Turbomole-TZVP for the QS part, using the response theoretical framework.27

DRF-0 DRF-1 DRF-2 DRF-3

70 48 101 142 231

DANS in DMSO

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

a

method

DANS in DCM

a

Table 1. Average Absorption Maxima (λmax in nm) for the DANS Molecule in Different Organic Solvents DRF-0 DRF-1 DRF-2 DRF-3 QM/MMa Expt-I75 Expt-II76

DANS in CHCl3

CAMY-B3LYP/TZ2P//DFTB-calculated λmax of DANS molecule in the vacuum is 404 nm. The corresponding Δμge is 12.10 D. Experimental data for the λmax and σGM are also given in Tables 1 and 4, respectively, for a comparison. For the λmax of the solvated DANS, two sets of available experimental data were given, designated as Expt-I and Expt-II. 5336

DOI: 10.1021/acs.jpca.9b04041 J. Phys. Chem. A 2019, 123, 5334−5340

Article

The Journal of Physical Chemistry A the theoretical work of Muguran et al.,27 where a red shift appeared in CHCl3, DMSO, and water solvents. The difference could be partly attributed to different force fields employed in their MD simulations and ours. Another property of interest is the σGM. In experiment, a nonmonotonic behavior of the σGM with increasing solvent polarity was observed.73,76 The changes in the σGM 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 were used as a reference. We note that the DRF-0, DRF-1, and DRF-2 models predict a monotonic increase in the σGM 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 σGM values are found to agree qualitatively with the experimental trend with R2 of 0.95 though the DRF-3 gives estimates of the σGM (142, 131, and 137 GM for CHCl3, DCM and DMSO, respectively) higher than experimental results by around 20%. Regardless, in the present work, more important than absolute ones are the relative σGM values calculated for DANS molecule in different solvents. Finally, to examine the effects of atomic charges and polarizabilities of solvent molecules to the λmax, Δμge, and σGM, 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 ΔC, ΔD, and ΔCD. Figure 2 illustrated these model shifts. For the λmax, we observe from Figure 2a 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 Δμge, Figure 2b shows more than twice as the contributions from the atomic polarizabilities than that from the atomic charges. The ratios of the ΔDΔμge to ΔCΔμge are 2.19, 2.07, and 2.07 for those in CHCl3, DCM and DMSO, respectively. For the model shifts concerning the λmax and Δμge, the calculations show that effect in the λmax in the transgression from solvent of low polarity to that of high polarity is on average not great, the effect in the Δμge being substantially larger. For the σGM, shown in Figure 2c, while the induced dipoleonly DRF-2 model gave positive contribution to the σGM (ΔDσGM = 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 σGM, i.e., ΔCσGM = −22 GM in CHCl3, −25 GM in DCM, and −38 GM in DMSO. Unlike the case for the λmax that showed good additivity of the model shifts (ΔCDλmax ≈ ΔCλmax + ΔDλmax), there is no pronounced pattern for the σGM. 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 Γ and then results in a high estimate of the σGM, but on the other hand, the low estimate of the σGM 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.

Figure 2. Contributions to the TD-CAMY-B3LYP/TZ2P/DRF solvent-induced shifts of (a) the λmax, (b) Δμge, and (c) σGM for solvated dimethylaminonitrostilbene.

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 the DANS molecule surrounded by CHCl3, DCM, and DMSO molecules. Using snapshots extracted from the MD simulations, we examined the calculated spectroscopic properties of interest. The TDCAMY-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 5337

DOI: 10.1021/acs.jpca.9b04041 J. Phys. Chem. A 2019, 123, 5334−5340

Article

The Journal of Physical Chemistry A

(13) Olsen, J. M.; Aidas, K.; Kongsted, J. Excited States in Solution through Polarizable Embedding. J. Chem. Theory Comput. 2010, 6, 3721−3734. (14) Olsen, J. M. H.; Kongsted, J. Chapter 3 - Molecular Properties through Polarizable Embedding. Adv. Quantum Chem. 2011, 61, 107− 143. (15) Sneskov, K.; Schwabe, T.; Christiansen, O.; Kongsted, J. Scrutinizing the effects of polarization in QM/MM excited state calculations. Phys. Chem. Chem. Phys. 2011, 13, 18551−60. (16) Sneskov, K.; Schwabe, T.; Kongsted, J.; Christiansen, O. The polarizable embedding coupled cluster method. J. Chem. Phys. 2011, 134, 104108. (17) Olsen, J. M. H.; Steinmann, C.; Ruud, K.; Kongsted, J. Polarizable Density Embedding: A New QM/QM/MM-Based Computational Strategy. J. Phys. Chem. A 2015, 119, 5344−5355. (18) Gordon, M. S.; Freitag, M. A.; Bandyopadhyay, P.; Jensen, J. H.; Kairys, V.; Stevens, W. J. The Effective Fragment Potential Method: A QM-Based MM Approach to Modeling Environmental Effects in Chemistry. J. Phys. Chem. A 2001, 105, 293−307. (19) Gordon, M. S.; Slipchenko, L.; Li, H.; Jensen, J. H. Chapter 10 The Effective Fragment Potential: A General Method for Predicting Intermolecular Interactions. Annu. Rep. Comput. Chem. 2007, 3, 177− 193. (20) Gordon, M. S. Fragmentation: Toward Accurate Calculations on Complex Molecular Systems. John Wiley & Sons: 2017. (21) Slipchenko, L. V.; Gordon, M. S. Electrostatic energy in the effective fragment potential method: Theory and application to benzene dimer. J. Comput. Chem. 2007, 28, 276−291. (22) Ghosh, D.; Kosenkov, D.; Vanovschi, V.; Williams, C. F.; Herbert, J. M.; Gordon, M. S.; Schmidt, M. W.; Slipchenko, L. V.; Krylov, A. I. Noncovalent Interactions in Extended Systems Described by the Effective Fragment Potential Method: Theory and Application to Nucleobase Oligomers. J. Phys. Chem. A 2010, 114, 12739−12754. (23) Ghosh, D.; Kosenkov, D.; Vanovschi, V.; Flick, J.; Kaliman, I.; Shao, Y.; Gilbert, A. T. B.; Krylov, A. I.; Slipchenko, L. V. Effective fragment potential method in Q-CHEM: A guide for users and developers. J. Comput. Chem. 2013, 34, 1060−1070. (24) Kaliman, I. A.; Slipchenko, L. V. LIBEFP: A new parallel implementation of the effective fragment potential method as a portable software library. J. Comput. Chem. 2013, 34, 2284−2292. (25) Schwabe, T.; Olsen, J. M. H.; Sneskov, K.; Kongsted, J.; Christiansen, O. Solvation Effects on Electronic Transitions: Exploring the Performance of Advanced Solvent Potentials in Polarizable Embedding Calculations. J. Chem. Theory Comput. 2011, 7, 2209−2217. (26) Murugan, N. A.; Kongsted, J.; Rinkevicius, Z.; Ågren, H. Demystifying the solvatochromic reversal in Brooker’s merocyanine dye. Phys. Chem. Chem. Phys. 2011, 13, 1290−1292. (27) Arul Murugan, N.; Kongsted, J.; Rinkevicius, Z.; Aidas, K.; Mikkelsen, K. V.; Ågren, H. Hybrid density functional theory/ molecular mechanics calculations of two-photon absorption of dimethylamino nitro stilbene in solution. Phys. Chem. Chem. Phys. 2011, 13, 12506−12516. (28) Silva, D. L.; Murugan, N. A.; Kongsted, J.; Rinkevicius, Z.; Canuto, S.; Ågren, H. The Role of Molecular Conformation and Polarizable Embedding for One- and Two-Photon Absorption of Disperse Orange 3 in Solution. J. Phys. Chem. B 2012, 116, 8169− 8181. (29) Olesiak-Banska, J.; Matczyszyn, K.; Zaleśny, R.; Murugan, N. A.; Kongsted, J.; Ågren, H.; Bartkowiak, W.; Samoc, M. Revealing Spectral Features in Two-Photon Absorption Spectrum of Hoechst 33342: A Combined Experimental and Quantum-Chemical Study. J. Phys. Chem. B 2013, 117, 12013−12019. (30) Wielgus, M.; Zaleśny, R.; Murugan, N. A.; Kongsted, J.; Ågren, H.; Samoc, M.; Bartkowiak, W. Two-Photon Solvatochromism II: Experimental and Theoretical Study of Solvent Effects on the TwoPhoton Absorption Spectrum of Reichardt’s Dye. ChemPhysChem 2013, 14, 3731−3739.

of the TD-DFT methods for modeling TPA processes within the DRF context.

■

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.9b04041.

■

Molecular orbitals involved in the charge transfer excitation of dimethylamino nitro stilbene in a vacuum, variation of the λmax vs the dielectric constant, and details on how the excess dipole moment is being calculated (PDF)

AUTHOR INFORMATION

Corresponding Author

*(S.-I.L.) E-mail address: [email protected]. Telephone: 886-2-28819471 ext 6825. Fax: 886-2-28811053. ORCID

Shih-I Lu: 0000-0001-7508-2088 Notes

The author declares no competing financial interest.

■

ACKNOWLEDGMENTS 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 1072113-M-031-003), for financial support.

■

REFERENCES

(1) Reichardt, C.; Welton, T. Solvents and Solvent Effects in Organic Chemistry; Wiley-VCH: 2010. (2) Papadopoulos, M. G.; Sadlej, A. J.; Leszczynski, J. Non-Linear Optical Properties of Matter; Springer: The Netherlands, 2010. (3) Mennucci, B.; Cammi, R. Continuum Solvation Models in Chemical Physics: From Theory to Applications; Wiley, VCH: 2008. (4) Santoro, F.; Barone, V.; Gustavsson, T.; Improta, R. Solvent Effect on the Singlet Excited-State Lifetimes of Nucleic Acid Bases: A Computational Study of 5-Fluorouracil and Uracil in Acetonitrile and Water. J. Am. Chem. Soc. 2006, 128, 16312−16322. (5) Improta, R.; Barone, V. PCM/TD-DFT study of the two lowest excited states of uracil derivatives in solution: The effect of the functional and of the cavity model. J. Mol. Struct.: THEOCHEM 2009, 914, 87−93. (6) Warshel, A.; Levitt, M. Theoretical studies of enzymic reactions: Dielectric, electrostatic and steric stabilization of the carbonium ion in the reaction of lysozyme. J. Mol. Biol. 1976, 103, 227−249. (7) Gordon, M. S.; Smith, Q. A.; Xu, P.; Slipchenko, L. V. Accurate First Principles Model Potentials for Intermolecular Interactions. Annu. Rev. Phys. Chem. 2013, 64, 553−578. (8) Warshel, A.; Kato, M.; Pisliakov, A. V. Polarizable Force Fields: History, Test Cases, and Prospects. J. Chem. Theory Comput. 2007, 3, 2034−2045. (9) Severo Pereira Gomes, A.; Jacob, C. R. Quantum-chemical embedding methods for treating local electronic excitations in complex chemical systems. Annu. Rep. Prog. Chem., Sect. C: Phys. Chem. 2012, 108, 222−277. (10) Vesely, F. J. N-particle dynamics of polarizable Stockmayer-type molecules. J. Comput. Phys. 1977, 24, 361−371. (11) Halgren, T. A.; Damm, W. Polarizable force fields. Curr. Opin. Struct. Biol. 2001, 11, 236−242. (12) Baker, C. M. Polarizable force fields for molecular dynamics simulations of biomolecules. Wiley Interdiscip. Rev. Comput. Mol. Sci. 2015, 5, 241−254. 5338

DOI: 10.1021/acs.jpca.9b04041 J. Phys. Chem. A 2019, 123, 5334−5340

Article

The Journal of Physical Chemistry A (31) Steindal, A. H.; Olsen, J. M. H.; Ruud, K.; Frediani, L.; Kongsted, J. A combined quantum mechanics/molecular mechanics study of the one- and two-photon absorption in the green fluorescent protein. Phys. Chem. Chem. Phys. 2012, 14, 5440−5451. (32) Sneskov, K.; Olsen, J. M.; Schwabe, T.; Hattig, C.; Christiansen, O.; Kongsted, J. Computational screening of one- and two-photon spectrally tuned channelrhodopsin mutants. Phys. Chem. Chem. Phys. 2013, 15, 7567−7576. (33) List, N. H.; Pimenta, F. M.; Holmegaard, L.; Jensen, R. L.; Etzerodt, M.; Schwabe, T.; Kongsted, J.; Ogilby, P. R.; Christiansen, O. Effect of chromophore encapsulation on linear and nonlinear optical properties: the case of ″miniSOG″, a protein-encased flavin. Phys. Chem. Chem. Phys. 2014, 16, 9950−9959. (34) Beerepoot, M. T.; Steindal, A. H.; Kongsted, J.; Brandsdal, B. O.; Frediani, L.; Ruud, K.; Olsen, J. M. A polarizable embedding DFT study of one-photon absorption in fluorescent proteins. Phys. Chem. Chem. Phys. 2013, 15, 4735−4743. (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.; Erra-Balsells, 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 PolarizableEmbedding 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. Solventinduced 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, 6028−6038. (44) Kosenkov, D.; Slipchenko, L. V. Solvent Effects on the Electronic Transitions of p-Nitroaniline: 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-4methylcoumarin. 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, 164109−14.

(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. (52) Jensen, L.; Swart, M.; van Duijnen, P. T. Microscopic and macroscopic polarization within a combined quantum mechanics and molecular mechanics model. J. Chem. Phys. 2005, 122, 034103. (53) Lu, S.-I. Application of discrete solvent reaction field to secondorder susceptibility of organic molecular crystal. Theor. Chem. Acc. 2016, 135 (180), 1−6. (54) Lu, S.-I. Application of discrete solvent reaction field model with self-consistent atomic charges and atomic polarizabilities to calculate the χ(1) and χ(2) of organic molecular crystals. Chem. Phys. Lett. 2018, 691, 8−13. (55) Elstner, M.; Porezag, D.; Jungnickel, G.; Elsner, J.; Haugk, M.; Frauenheim, T.; Suhai, S.; Seifert, G. Self-consistent-charge densityfunctional tight-binding method for simulations of complex materials properties. Phys. Rev. B: Condens. Matter Mater. Phys. 1998, 58, 7260− 7268. (56) Gaus, M.; Cui, Q.; Elstner, M. DFTB3: Extension of the SelfConsistent-Charge Density-Functional Tight-Binding Method (SCCDFTB). J. Chem. Theory Comput. 2011, 7, 931−948. (57) Irle, S.; Zheng, G.; Wang, Z.; Morokuma, K. The C60 Formation Puzzle “Solved”: QM/MD Simulations Reveal the Shrinking Hot Giant Road of the Dynamic Fullerene Self-Assembly Mechanism. J. Phys. Chem. B 2006, 110, 14531−14545. (58) Goyal, P.; Qian, H.-J.; Irle, S.; Lu, X.; Roston, D.; Mori, T.; Elstner, M.; Cui, Q. Molecular Simulation of Water and Hydration Effects in Different Environments: Challenges and Developments for DFTB Based Models. J. Phys. Chem. B 2014, 118, 11007−11027. (59) VandeVondele, J.; Krack, M.; Mohamed, F.; Parrinello, M.; Chassaing, T.; Hutter, J. Quickstep: Fast and accurate density functional calculations using a mixed Gaussian and plane waves approach. Comput. Phys. Commun. 2005, 167, 103−128. (60) Fonseca Guerra, C.; Snijders, J. G.; te Velde, G.; Baerends, E. J. Towards an order-N DFT method. Theor. Chem. Acc. 1998, 99, 391− 403. (61) te Velde, G.; Bickelhaupt, F. M.; Baerends, E. J.; Fonseca Guerra, C.; van Gisbergen, S. J. A.; Snijders, J. G.; Ziegler, T. Chemistry with ADF. J. Comput. Chem. 2001, 22, 931−967. (62) ADF2018, SCM, Theoretical Chemistry; Vrije Universiteit: Amsterdam, The Netherlands. (63) Bussi, G.; Donadio, D.; Parrinello, M. Canonical sampling through velocity rescaling. J. Chem. Phys. 2007, 126, 014101. (64) Swart, M.; van Duijnen, P. T.; Snijders, J. G. A charge analysis derived from an atomic multipole expansion. J. Comput. Chem. 2001, 22, 79−88. (65) van Duijnen, P. T.; Swart, M. Molecular and Atomic Polarizabilities: Thole’s Model Revisited. J. Phys. Chem. A 1998, 102, 2399−2407. (66) Jensen, L.; Åstrand, P.-O.; Osted, A.; Kongsted, J.; Mikkelsen, K. V. Polarizability of molecular clusters as calculated by a dipole interaction model. J. Chem. Phys. 2002, 116, 4001−4010. (67) Seth, M.; Ziegler, T. Range-Separated Exchange Functionals with Slater-Type Functions. J. Chem. Theory Comput. 2012, 8, 901− 907. (68) Yanai, T.; Tew, D. P.; Handy, N. C. A new hybrid exchange− correlation functional using the Coulomb-attenuating method (CAMB3LYP). Chem. Phys. Lett. 2004, 393, 51−57. (69) Akinaga, Y.; Ten-no, S. Range-separation by the Yukawa potential in long-range corrected density functional theory with Gaussian-type basis functions. Chem. Phys. Lett. 2008, 462, 348−351. 5339

DOI: 10.1021/acs.jpca.9b04041 J. Phys. Chem. A 2019, 123, 5334−5340

Article

The Journal of Physical Chemistry A (70) Peticolas, W. L. Multiphoton Spectroscopy. Annu. Rev. Phys. Chem. 1967, 18, 233−260. (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 twophoton absorption of a spiropyran-merocyanine system: experimental and theoretical studies. J. Phys. Chem. B 2015, 119, 1515−1522. (73) Wicks, G.; Rebane, A.; Drobizhev, M. Two-photon solvatochromism of 4-dimethylamino-4’-nitrostilbene (DANS). Proc. SPIE 2014, 89830R. (74) Reichardt, C. Solvatochromic Dyes as Solvent Polarity Indicators. Chem. Rev. 1994, 94, 2319−2358. (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.

5340

DOI: 10.1021/acs.jpca.9b04041 J. Phys. Chem. A 2019, 123, 5334−5340