Tuning of Second-Order Nonlinear Optical Response Properties of

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Tuning of Second-Order Nonlinear Optical Response Properties of Aryl-Substituted Boron-Dipyrromethene Dyes: Unidirectional Charge Transfer Coupled with Structural Tailoring Ramprasad Misra J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b13035 • Publication Date (Web): 22 Feb 2017 Downloaded from http://pubs.acs.org on February 23, 2017

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The Journal of Physical Chemistry

Tuning of Second-Order Nonlinear Optical Response Properties of Aryl-Substituted Boron-Dipyrromethene Dyes: Unidirectional Charge Transfer Coupled with Structural Tailoring Ramprasad Misra1* Department of Physical Chemistry, Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700032, India Abstract Controlling the intramolecular charge transfer (ICT) process at the molecular level could be a key to develop strong nonlinear optical (NLO) active materials for technological applications. In this paper, we report quantum chemical investigation of NLO response properties of select aryl-substituted Boron-Dipyrromethene (BODIPY) dyes, a class of ICT molecules. Density functional theory (DFT) with long-range corrected CAM-B3LYP functional is employed to compute the electronic structures and NLO response properties of the aforesaid molecules. The effects of basis sets on the NLO response properties of these molecules are also considered. Calculations at the second order Møller-Plesset perturbation theory (MP2) are performed for comparison. The results suggest that the charge transfer process in these molecules is mostly unidirectional and the total first hyperpolarizability (βtotal) values of these molecules are dominantly shaped by the response in the direction of charge transfer. Donor/ acceptor substitution as well as twisting of the phenyl ring due to incorporation of methyl groups to BODIPY moiety affects charge transfer process of these molecules, ultimately altering their NLO response properties. The ratios of vector components of first hyperpolarizability (βvec) to βtotal of the probe molecules also support the unidirectional charge transfer process, except for some molecules with acceptor group substitutions alone or in conjunction with structural changes. The results presented here are expected to shed light on the origin of NLO response of several aryl-substituted BODIPY dyes and provide means to optimizing it for future technological applications.

___________________________________________________________________ 1

Present address: Department of Organic Chemistry, Weizmann Institute of Science, Rehovot 76100, Israel; *Corresponding author; E-mail: [email protected]

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Introduction Studies of materials with strong nonlinear optical (NLO) response have been primarily driven by their potential for technological applications, including, in the photochromic switches, in three dimensional optical data storage, in fluorescence imaging and in telecommunications, among several others1-7. In recent years, intramolecular charge transfer (ICT) based organic molecules become most popular for studies of NLO response, owing to high flexibility, durability as well as ease to syntheses8-13. Charge transfer from the electron donor to the electron acceptor of a molecule though a πelectron bridge in the excited state leads to a large difference in dipole moment between the ground and excited states14-15. So, from a simple two-state model one can expect a large NLO response from these so called ‘push-pull’ molecules16-17. Several studies are devoted to optimize the donor/ acceptor pair and ring-twisting to enhance the ICT process that finally could maximize the NLO response1,

18-19

. The ICT reaction of several

substituted Boron-Dipyrromethene (BODIPY) dyes has been studied widely20-21, but little seems to be known about their NLO response properties. BODIPY dyes are reported to be strongly absorbing and generally show relatively sharp fluorescence emission with high quantum yields22. The absorption and emission properties of these molecules can be tuned conveniently by changing the substitution pattern of the BODIPY framework that can ultimately push their fluorescence into the near-infrared (NIR) region22-24. These dyes are also reported to have excellent thermal and photochemical stability and the tripletstate formation is also negligible22. Very recently, some experimental studies on the NLO response of fluoroalkylated and dimethylaminostyryl substituted BODIPY dyes have been reported literature25-26. Lager et al27 have reported the synthetic methodologies of

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several aryl-substituted BODIPY dyes. Incorporation of donor/ acceptor group in the phenyl ring in conjugation with the BODIPY can be used to affect the ICT process, ultimately altering the NLO response28-30. The donor/ acceptor substitution also helps to tune the energy gap between the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO)28,31-32. Incorporation of the donor/ acceptor group is sometimes used to achieve non-centrosymmetry in several molecules33, a criterion for obtaining non-vanishing first hyperpolarizability. As the NLO response properties of a material is ultimately shaped by the properties of the individual chromophores, tuning of the NLO response at the molecular level using the aforesaid strategies could be a key develop novel NLO materials. It has been reported that the electron correlation plays a crucial role in the computation of NLO response properties of a molecule34-35. A number of studies have been devoted to understand the effect of theory/basis set on the NLO response properties of several organic molecules36-42. The coupled cluster singles and doubles calculations with perturbative estimates of triples [CCSD(T)] method is used in several studies for small molecules but calculation for relatively larger systems at the [CCSD(T)] level is costly3637

. MP2 theory and DFT with long-range corrected methods have become a viable

alternative for studying the NLO response properties of relatively large molecules38-41. Recently, Champagne et al42 have reported that CCSD approach provided a rare improvement over the MP2 method in predicting the values of first hyperpolarizability (β) of push-pull π-conjugated molecules, making the MP2 method a reliable choice to predict the values of β. The Coulomb-attenuated hybrid exchange-correlation DFT functional, CAM-B3LYP is reported to be useful for computing properties of several

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charge transfer based molecules, including, their NLO response43-45. To keep a balance between the computational cost and accuracy, CAM-B3LYP is used for optimization of the structures of the molecules studied. Calculations at the MP2 level of theory are performed to compute the electronic structures and NLO response of the selected probe molecules

for

comparison.

The

total

first

hyperpolarizability

or

intrinsic

hyperpolarizability (βtotal) is used widely to estimate the charge transfer from the donor to acceptor9,13. The values of βtotal are always positive, irrespective of the sign of the individual tensorial components and it cannot be measured experimentally. On the other hand, the vector component of first hyperpolarizability (βvec) could be positive or negative, it is expected to carry more information about the hyperpolarization process in the molecule than that of βtotal. The ratio of βvec and βtotal also provides important information about the direction of charge transfer in the molecules as13

=

(i)

where, θ is the angle between the vector formed by βvec components and the dipole moment vector. In this paper, our aim is to understand the origin of NLO response of some novel arylsubstituted BODIPY dyes (Scheme - 1). The effect of change in structure through incorporation of methyl groups that restricts the motion of the phenyl ring and modulation of π-conjugation strength through wax and wane in the donor/ acceptor strength on the NLO response properties of these molecules are investigated. The methodologies adopted for this work are described in Section 2. Sections 3(a-b) deal with the ground state electronic structures and the absorption spectra of the molecules studied. The effect of change in electronic structures of the polarizability and first

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hyperpolarizability of the BODIPY dyes are discussed in Section 3c. A detailed analysis of βvec and βtotal values of the molecules studied is done to understand the directions of charge transfer in these molecules. How change in HOMO – LUMO energy gap affect the NLO response of the aforesaid molecules are also discussed in this section.

2. Methods The ground state equilibrium geometries of the molecules (1-6) of Scheme - 1 have been optimized fully using density functional theory (DFT) employing CAM-B3LYP functional. The values of first hyperpolarizability (β) have been reported to be quite sensitive on the basis set used3-4. We have used Pople’s split-valence 6-31G(d,p), 631+G(d,p) basis sets and Dunning’s correlation-consistent cc-pVTZ basis set to study the effect of basis sets in these calculations. The geometry optimizations are followed by calculations of components of polarizability (α) and the first hyperpolarizability (β) at the respective optimized structures at the same level of theory. The effect of electroncorrelation, which is reported to be an important parameter in polarizability calculations, has been taken care of using second order Møller - Plesset perturbation theory (MP2) calculations28-29. In every case, the lack of imaginary frequencies in the optimized structures confirmed the optimization of the geometries of the molecules by reaching at least one local minimum. Time-dependent density functional theory (TDDFT) calculations were performed using CAM-B3LYP functional and cc-pVTZ basis set to get first ten vertical excited states of the molecules. All these calculations have been carried out with Gaussian09 quantum chemistry software46, while the visualizations of the structures have been carried out by Chemcraft47 and GausView 5.048 softwares.

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The dipole moment (µ) of the molecules under investigation has been calculated using the following equation –

µ = ( µ x2 + µ y2 + µ z2 )1/ 2

(ii)

where, µx, µy and µz are components of the dipole moments in the x, y and z directions, respectively. The average polarizabilities (αav) of the molecules are obtained from the components of polarizability using the following equation2, 49: 1 3

α av = (α xx + α yy + α zz )

(iii)

The first hyperpolarizability (β) is a tensor of rank 3 with twenty seven components that are reduced to ten by the virtue of Kleinman symmetry of the (3 × 3 × 3) matrix representing the β tensor49. The values of total first hyperpolarizability (βtotal) of the molecules (1-6) are calculated using the x, y and z components of first hyperpolarizability using the equation5,49 (iv). /

= + +

(iv)

where, = + ∑! + +

(# = $, &, ')

(v)

Using Kleinman symmetry12, we get = + +

(vi)

Similarly, = + + and = + + . The values of βvec at the static limit can be calculated from the tensorial components of first hyperpolarizability using equation (vii)12,13. *+, =

- .- /0 .0 /1 .1 .

(vii)

3. Results and Discussion 3a. Electronic structure of the aryl-substituted BODIPY dyes 6


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The electronic structure of a molecule plays a crucial role in determining its properties. The structure, therefore, the NLO response property of a molecule is very sensitive to the theory and basis set used. We have used DFT (CAM-B3LYP functional) and MP2 level of theories to optimize the ground state structures of the aryl-substituted BODIPY dyes used for our studies. The front and side views optimized structures of molecules (1-2) using DFT (CAM-B3LYP functional) and cc-pVTZ basis set are displayed in figure 1. The structures of molecules (3-6) obtained using same level of theory are shown in figure 2. The important geometrical parameters are reported in Table - 1 and in Table - S1 in supporting information. The ground state optimized structures obtained using DFT (CAM-B3LYP functional) employing cc-pVTZ and 6-31G(d,p) basis sets along with those obtained through MP2/6-31G(d,p) calculations are shown in figures (S1-S26) in the Supporting Information. The results show that the 3-4-5-6 dihedral angle (Scheme - 1) gets twisted due to incorporation of the methyl groups. For example, CAM-B3LYP/ 631+G(d,p) calculations predict the aforesaid dihedral angle to be 90o for molecules 1, 5 and 6 vis-à-vis 57o, 51o and 59o, for molecules 2, 3 and 4, respectively. The predicted values of 3-4-5-6 dihedral angle are comparable in all other theory and basis set combinations. The changes in predicted bond lengths of the molecules due to substitution of methyl groups and also due to donor/ acceptor substitution are rather small (Table - 1). The changes in structures of aryl-substituted BODIPY dyes affect several properties of the molecules. For example, Tang and co-workers20 have reported that attaching an unsubstituted phenyl ring to the BODIDY decreases the quantum yield of fluorescence (φf) compared to BODIPY alone, incorporation of two methyl groups in the BODIPY moiety restricts the motion of the phenyl ring, ultimately increasing the φf of the

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molecule. Effect of the change in the ground state electronic structures on the absorption spectra, polarizabilities and first hyperpolarizabilities of the aryl-substituted BODIPY dyes are discussed in the following sections.

3b. Molecular orbital pictures and absorption spectra of the aryl-substituted BODIPY dyes Time dependent density functional theory (TDDFT) calculations were performed on the ground state optimized geometries of the molecules (1-6) obtained using CAM-B3LYP functional and cc-pVTZ basis set to get the energy and oscillator strength of the first ten vertical excitation of these molecules. The vertical transition maxima, oscillator strength first two excited states and contribution from the dominant transitions have been reported in Table - 2. TDDFT method is used widely by several groups to calculate the vertical excitation energy of molecules, although its limitation in predicting the excitation energies of charge transfer based molecules are known50. Jacquemin and co-workers have studied the photophysics of several BODIPY and aza-BODIPY dyes using TDDFT51-52. Brown et al53 have pointed out the disadvantage of TDDFT method for a series of BODIPY dyes that do not show charge transfer behavior. As several molecules of this class show intramolecular charge transfer, cautions must be taken while selecting the correct functional as TDDFT in many cases overestimate the excitation energies of charge transfer based molecules. Long-range corrected functionals like CAM-B3LYP are used to overcome this problem54-55. This functional is reported to be quite useful for studying electronic structure and properties of several charge transfer based molecules. The TDDFT results show that S0→S1 transitions dominantly shape the electronic

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absorption profiles of the molecules studied, except for molecule 3 where both S0→S1 and S0→S2 transitions are expected to occur. The computed energy (∆Egs) and oscillator strength (f) of S0 → S1 transition in molecule 1 are 410.35 nm and 0.535, respectively. The ∆Egs and f values for molecule 2 are 397.69 nm and 0.441, respectively. The ∆Egs value gets slightly blue shifted due to substitution of –N(CH3)2 group, while substitution of –NO2 group leads to slight red shift from their unsubstituted counterparts (Table - 2). The oscillator strength values of higher excited states of these molecules are too low to contribute to their absorption spectra. The highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) pictures of molecules (1-6) obtained using CAM-B3LYP functional and cc-pVTZ basis set are shown in figure 3. TDDFT results (Table - 2) indicate that HOMO to LUMO transitions dominantly dictate the absorption spectra of the molecules studied, except for molecule 3, where (HOMO-1) to LUMO transition also plays an important role in shaping its absorption profile.

3c. Linear and nonlinear optical response properties of the molecules The components of polarizability and first hyperpolarizability of the molecules (1-6) are computed using their respective optimized geometries. The average polarizability (αav) and total first hyperpolarizability (βtotal) are obtained using equation (iii) and (iv), respectively from their components at the CAM-B3LYP/6-31+G(d,p) level of calculations are reported in Table - 3. The dipole moment (µ) values of these molecules are also reported in the same table. The values of µ, αav and βtotal of molecules (1-6) obtained using cc-pVTZ and 6-31G(d,p) basis sets are shown in Table - S2 in the supporting information. Among these molecules, the dipole moment is highest in

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molecule 3 while that is lowest in molecule 4. The change (in percentage) in the values of αav are rather less than that of µ. The values of µ, αav and βtotal of molecules (1-6) obtained using DFT and MP2 level of theory with different basis sets are shown in figure 4(a-c) for comparison. The figures show that the trend in values of µ, αav as well as βtotal of molecules (1-6) seems to be unchanged due to the alteration of theory/ basis sets in the calculations. The values of µ, αav and βtotal of molecules studied are seen to increase due to use of 6-31+G(d,p) basis set, compared to that obtained using 6-31G(d,p) basis set (Table - 3). The changes in structure affect the NLO response of the BODIPY dyes. An increase in values in βtotal is observed in molecule 1 (1130.48 a.u. vis-à-vis 483.07 a.u. in molecule 2) due to incorporation of two methyl groups in the BODIPY moiety. The change in conjugation strength due to incorporation of donor/ acceptor group affects the βtotal values. The computed value of βtotal of molecule 2 is 483.07 a.u. that is increased to 3942.95 a.u. and 1135.57 a.u. due to substitution of the –N(CH3)2 (molecule 3) and -NO2 (molecule 4) groups, respectively. Incorporation of -NO2 (molecule 6) group in molecule 1 shows an increase in the βtotal values while addition of –N(CH3)2 group in the same molecule seems to be detrimental. The HOMO – LUMO band gap (∆EH-L) of these molecules are calculated and reported in the Table - S3 in Supporting Information. Generally, the values of first hyperpolarizability increases with decrease in ∆EH-L32. The values of βtotal increase with the decrease of ∆EH-L, except for molecule 3. This deviation is expected as HOMO to LUMO as well as (HOMO-1) to LUMO transitions shape the absorption profile of molecule 3 (Table - 2), unlike other molecules studied, where HOMO to LUMO transition dominantly shape their absorption behavior. To understand the direction of polarization in these molecules, we have reported the components of

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dipole moment in Table – 4 and Table – S4 in the supporting information. The results show that the dipole moment in the x-direction (µx) dominantly dictate the µ values of the molecules, except for molecules 4 and 6 (Table - 4). Yu and co-workers56 have reported that βy dominantly shape the values of the βtotal of some metal cationic complex of 2,3naphtho-15-crown-5 ether derivatives, leading them to conclude that during polarization process the charge is expected to transfer in the y-direction. The βx, βy and βz values are calculated from the tensorial components of hyperpolarizability are reported in Table – 4 and Table – S4 in supporting information. The results show that the βx dominantly contributes to the values of βtotal for molecules (1-6), while the contribution of βy and βz to βtotal are quite small. This suggests that during polarization process of molecules (1-6) the charge is expected to transfer in the x-direction. In strong donor – acceptor system, where charge transfer is favored, the ICT is unidirectional and parallel to the molecular dipole moment, so that one of the components accounts for almost all of the NLO response13,57. So, one can expect maximum charge delocalization when the ratio of βvec and βtotal is unity57. The values of βvec as obtained using equation (vii) from the tensorial components of hyperpolarizability are reported in Table – 3 and Table - S2 in supporting information. The absolute values of βvec of molecules (1-6) of obtained using DFT and MP2 level of theory with different basis sets are shown in figure 4d for comparison. The ratio of βvec to βtotal is almost unity in most of the cases, except for molecules 4 and 6 that have –NO2 substitution. This ratio of βvec to βtotal implies the unidirectional and parallel charge transfer in the aryl-substituted BODIPY dyes. Wax and wane of either βtotal or βvec values due to substitution of –N(CH3)2/ –NO2 group also implies that the charge transfer processes influence the NLO responses of these molecules. Hyper-Rayleigh scattering

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(HRS) is one of the popular ways to study the NLO response properties. One needs to calculate the frequency dispersion to reach the static first hyperpolarizability (β0) from the hyperpolararizability values obtained from the HRS experiment (βHRS). We have used the two-state approximation (TPA) to study the frequency dispersion of these molecules58. This theory considers that only one excited state contributes to the first hyperpolarizability and it also dictates the frequency dispersion. 234 = 5 69

8 67

7 :;6

9

(viii)

9 :6 9 67

In equation viii, ωge is the excitation energy while ω is the energy of the incident laser radiation. We have used the energy of transition maxima of lowest excited state with highest oscillator strength obtained from TDDFT calculations as ωge to check the frequency dispersion at 1064 nm, wavelength of a commonly used laser. It is found that the frequency dispersion ranges between 2.57 to 2.93 among molecules (1-6). To understand the effect of donor/acceptor substitution as well as structural tuning on the NLO response properties of aryl – substituted BODIPY dyes in more detail, we have studied the effect –NH2, -CN, -CH3 and –CHO substitution (molecules 7–14, Scheme - 1) in conjunction with structural tailoring on the electronic structure and NLO response properties of these molecules. As the theory and basis set combinations used in our studies gave similar trend in the values of µ, αav and βtotal of molecules (1-6), we have optimized the molecules (7-14) at the CAM-B3LYP/6-31+G(d,p) level of theory, followed by calculation of polarizabilities and first hyperpolarizabilities. The important structural parameters are reported in Table - 1 and the values of µ, αav and βtotal are presented in Table - 3. The x, y and z components of µ along with the values of βx, βy and βz are reported in Table – 4. The 3-4-5-6 dihedral angle (Figure S7-S20 in supporting

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information) of molecules (7-14) ranges between 52 to 58 degrees for R= -H while the same is about 90 degree with methyl substitutions in the BODIPY moiety (R = -CH3). This indicates the changes in 3-4-5-6 dihedral angle are quite similar in all the donor/acceptor substitutions. The results suggest the dipole moment component in the direction of charge transfer dominantly dictate the values of dipole moments of these molecules. Like molecules (1-6), the βx dominates values of first hyperpolarizability in molecules (7-14), except for molecule 9, where z direction is equivalent to x direction in other molecules (Figure S15 in supporting information). The ratios of values of βvec to βtotal of these molecules are close to unity, except for molecule 10 and molecule 14. Therefore, the results obtained for molecules (7-14) strongly suggest the unidirectional charge transfer process in aryl-substituted BODIPY dyes. It can be noted that the ratios of values of βvec to βtotal are not unity in case of molecules with –NO2 substitution (molecules 4 and 6). The same observation is made in molecule 10 and molecule 14 that have –CN and –CHO substitution, respectively and also contain the methyl groups in the BODIPY moiety. From the HOMO and LUMO pictures (Figure 3) of these molecules, we can observe that the substitution of methyl groups in the BODIPY moiety changes the position of LUMO in these molecules. This led us to surmise that the substitution of an acceptor group (-NO2) alone or acceptor groups in conjunction with structural changes can open up another charge transfer pathway in these molecules. The changes in the position of HOMO and LUMO due to substitution of methyl groups in the BODIPY moiety also suggest the possibility of altering the direction of charge transfer in these molecules. To the best of our knowledge, this is the first report on unidirectional charge transfer in aryl-substituted BODIPY dyes. As controlling the change transfer in the

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molecular scale is a key to design molecular devices for nanooptoelectronics59, these results are expected to draw attention to scientific community for further studies of molecular electronics.

Conclusion Quantum chemical calculations at DFT (CAM-B3LYP functional) and MP2 level of theories are performed to study the electronic structure and NLO response of some novel aryl-substituted BODIPY dyes. The trends in values of dipole moments, average polarizabilities and first hyperpolarizabilities of the molecules studied are consistent at the level of theory and basis set combinations used for our calculations. The dipole moment (µ) and first hyporpolarizability (βtotal) of these molecules are dominantly shaped by their response in one direction, indicating strong unidirectional charge transfer in the molecules studied. The ratio of vector components of first hyperpolarizability (βvec) to that of βtotal is close to unity, except for some molecules with acceptor substitutions, also supports this behavior. The unidirectional charge transfer and the structural changes affect the NLO response of the molecules studied. As controlling the change transfer in the molecular scale is a key to design molecular devices for technological applications, the insight obtained from these studies are expected to be useful in designing novel BODIPY dyes for nonlinear optical applications.

Supporting Information The ground state optimized structures obtained using DFT (CAM-B3LYP functional) employing 6-31G(d,p) and cc-pVTZ basis sets and that obtained from MP2/6-31G(d,p)

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calculations.; The values of µ, αav and βtotal obtained using DFT (CAM-B3LYP functional) employing 6-31G(d,p) and cc-pVTZ basis sets and that obtained from MP2/631G(d,p) calculations.; The x, y and z components of µ along with the values of βx, βy and βz obtained using DFT (CAM-B3LYP functional) employing 6-31G(d,p) and cc-pVTZ basis sets and same parameters obtained from MP2/6-31G(d,p) calculations.; Coordinates of optimized geometries of molecules (1-6) at the CAM-B3LYP/ cc-pVTZ level of theory.

Note The author declares no competing financial interest.

Acknowledgements The author is grateful to Prof. S.P. Bhattacharyya and Prof. D.S. Ray (IACS) for encouraging him in taking up this work. The Computer Centre of IACS (IBM P7 cluster) acknowledged for providing with the computational facilities and Mr. Abhra Paul for technical helps. The author would like to thank Dr. Pralok K. Samanta and Dr. Debashree Manna (WIS, Israel) for several fruitful discussions.

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20. Hu, R.; Lager, E.; Anguilar-Anguilar, A.; Liu, J.; Lam, J.W.Y.; Sung, H.H.Y.; Williams, I.D.; Zhong, Y.; Wong, K.S.; Pena-Cabrera, E.; Tang, B.Z. Twisted Intramolecular Charge Transfer and Aggregation-Induced Emission of BODIPY Derivatives. J. Phys. Chem. C 2009, 113, 15845-15853. 21. Whited, M.T.; Patel, N.M.; Roberts, S.T.; Allen, K.; Djurovich, P.I.; Bradforth, S.E.; Thompson, M.E. Symmetry-breaking Intramolecular Charge Transfer in the Excited State of meso-linked BODIPY Dyads. Chem. Comm. 2012, 48, 284-286. 22. Loudet, A.; Burgess, K. BODIPY Dyes and Their Derivatives: Syntheses and Spectroscopic Properties. Chem. Rev. 2007, 107, 4891-4932. 23. Umezawa, K.; Matsui, A.; Nakamura, Y.; Citterio, D.; Suzuki, K. Bright, Colortunable Fluorescent Dyes in the Vis/NIR Region: Establishment of New "tailor-made" Multicolor Fluorophores Based on Borondipyrromethene. Chem. - Eur. J. 2009, 15, 1096-1106. 24. Umezawa, K.; Nakamura, Y.; Makino, H.; Citterio, D.; Suzuki, K. Bright, ColorTunable Fluorescent Dyes in the Visible−Near-Infrared Region. J. Am. Chem. Soc. 2008, 130, 1550-1551. 25. Kolmel, D.K.; Horner, A.; Castaneda, J.A.; Ferencz, J.A.P.; Bihlmeier, A.; Nieger, M.; Brase, S.; Padilha, L.A. Linear and Nonlinear Optical Spectroscopy of Fluoroalkylated BODIPY Dyes. J. Phys. Chem. C 2016, 120, 4538-4545. 26. Kulyk, B.; Taboukhat, S.; Akdas-Kilig, A.; Fillaut, J.-L.; Boughaleb, Y.; Sahraoui, B. Nonlinear Refraction and Absorption Activity of Dimethylaminostyryl Substituted BODIPY Dyes. RSC Advances 2016, 6, 84854-84859. 27. Lager, E.; Liu, J.; Anguilar-Anguilar, A.; Tang, B.Z.; Pena-Cabrera, E. Novel mesoPolyarylamine-BODIPY Hybrids: Synthesis and Study of Their Optical Properties. J. Org. Chem. 2009, 74, 2053-2058. 28. Misra, R.; Chakraborty, P.; Roy, S.C.; Maity, D.K.; Bhattacharyya, S.P. Tailoring of Spectral Response and Intramolecular Charge Transfer in β-enaminones Through Band Gap Tuning: Synthesis, Spectroscopy and Quantum Chemical Studies. RSC Adv. 2016, 6, 36811-36822. 29. Zhu, Y.; Champion, R.D.; Jenekhe, S.A. Conjugated Donor-Acceptor Copolymer Semiconductors with Large Intramolecular Charge Transfer: Synthesis, Optical

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Properties, Electrochemistry, and Field Effect Carrier Mobility of Thienopyrazine-Based Copolymers. Macromolecules 2006, 39, 8712-8719. 30. Ravikumar, C.; Joe, I.H.; Jayakumar, V.S. Charge Transfer Interactions and Nonlinear Optical Properties of Push-Pull Chromophore Benzaldehyde Phenylhydrazone: A Vibrational Approach. Chem. Phys. Lett. 2008, 460, 552-558. 31. Thanthiriwatte, K.S.; de Silva, K.M.N. Non-linear Optical Properties of Novel Fluorenyl Derivatives - ab initio Quantum Chemical Calculations. J. Mol. Struc.: THEOCHEM 2002, 617, 169-175. 32. Zhang, T.; Yan, L.-K.; Cong, C.; Guan, W.; Su, Z.-M. Prediction of Second-order Nonlinear Optical Properties of Wells–Dawson Polyoxometalate Derivatives [X– C(CH2O)3P2M′3M15O59]6− (X = NO2, NH2, and CH3, M′ = V and Nb, M = W and Mo). Inor. Chem. Front. 2014, 1, 65-70. 33. Benkova, Z.; Cernusak, I.; Zahradnik, P. Theoretical Study of Static Electric Properties of Benzothiazole Containing Push-Pull Systems as Potential Pandidates for NLO Materials. Struct. Chem. 2006, 17, 287-300. 34. Cardenuto, M.H.; Champagne, B. The First Hyperpolarizability of Nitrobenzene in Benzene Solutions: Investigation of the Effects of Electron Correlation within the Sequential QM/MM Approach. Phys. Chem. Chem. Phys. 2015, 17, 23634-23642. 35. Harczuk, I.; Vahtras, O.; Argen, H. First Hyperpolarizability of Collagen Using the Point Dipole Approximation. J. Phys. Chem. Lett. 2016, 7, 2132-2138. 36. Karamanis, P.; Maroulis, G. Single (C–C) and Triple (C≡C) Bond-length Dependence of the Static Electric Polarizability and Hyperpolarizability of H–C≡C–C≡C–H. Chem. Phys. Lett. 2003, 376, 403-410. 37. Maroulis, G. Electric (Hyper)polarizability Derivatives for the Symmetric Stretching of Carbon Dioxide. Chem. Phys. 2003, 291, 81-95. 38. Zhang, L.; Qi, D.; Zhao, L.; Chem. C.; Bian, Y.; Li, W. Density Functional Theory Study on Subtriazaporphyrin Derivatives: Dipolar/Octupolar Contribution to the SecondOrder Nonlinear Optical Activity. J. Phys. Chem. A 2012, 116, 10249-10256. 39. Karamanis, P.; Maroulis, G. An ab initio Study of CX3-substitution (X = H, F, Cl, Br, I) Effects on the Static Electric Polarizability and Hyperpolarizability of Diacetylene. J. Phys. Org. Chem. 2011, 24, 588-599.

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40. Castet, F.; Bogdan, E,; Plaquet, A.; Ducasse, L.; Champagne, B.; Rodriguez, V. Reference Molecules for Nonlinear Optics: A Joint Experimental and Theoretical Investigation. J. Chem. Phys. 2012, 136, 024506(1)-024506(15). 41. Garett, K.; Vazquez, X.A.S.; Egri, S.B.; Wilmer, J.; Johnson, L.E.; Robinson, B.H.; Isborn, C.M. Optimum Exchange for Calculation of Excitation Energies and Hyperpolarizabilities of Organic Electro-optic Chromophores. J. Chem. Theory Comput. 2014, 10, 3821-3831. 42. de Wergifosse, M.; Champagne, B. Electron Correlation Effects on the First Hyperpolarizability of Push–Pull π-Conjugated Systems. J. Chem. Phys. 2011, 134, 074113(1)-074113(13). 43. Limacher, P.A.; Mikkelsen, K.V.; Luthi, H.P. On the Accurate Calculation of Polarizabilities and Second Hyperpolarizabilities of Polyacetylene Oligomer Chains using the CAM-B3LYP Density Functional. J. Chem. Phys. 2009, 130, 194114(1)194114(7). 44. Bai, Y.; Zhou, Z.J.; Wang, J.J.; Li, Y.; Wu, D.; Chen, W.; Li, Z.R.; Sun, C.C. New Acceptor–Bridge–Donor Strategy for Enhancing NLO Response with Long-Range Excess Electron Transfer from the NH2...M/M3O Donor (M = Li, Na, K) to Inside the Electron Hole Cage C20F19 Acceptor through the Unusual σ Chain Bridge (CH2)4. J. Phys. Chem. A 2013, 117, 2835-2843. 45. Alparone, A. Response Electric Properties of α-helix Polyglycines: A CAM-B3LYP DFT Investigation. Chem. Phys. Lett. 2013, 563, 88-92. 46. Gaussian 09, Revision C.01, Frisch, M.J.; Trucks, G.W.; Schlegel, H.B.; Scuseria, G.E.; Robb, M.A.; Cheeseman, J.R.; Scalmani, G.; Barone, V.; Petersson, G.A.; Nakatsuji, H. et al. Gaussian, Inc., Wallingford CT, 2010. 47. Chemcraft; http://www.chemcraftprog.com (accessed on 11.29.2016) 48. GaussView, Version 5, Dennington, R.; Keith, T.; Millam, J. Semichem Inc., Shawnee Mission KS, 2009. 49. Jeewandara, A.K.; de Silva, K.M.N. Are Donor-Acceptor Self Organised Aromatic Systems NLO (Non-linear Optical) Active? J. Mol. Struc.: THEOCHEM 2004, 686, 131136.

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50. Drew, A.; Weisman, J.L.; Head-Gordon, M. Long-range Charge-transfer Excited States in Time-dependent Density Functional Theory Require Non-local Exchange. J. Chem. Phys. 2003, 119, 2943-2946. 51. Le Guennic, B; Maury, O.; Jacquemin, D. Aza-boron-dipyrromethene Dyes: TDDFT Benchmarks, Spectral Analysis and Design of Original Near-IR Structures. Phys. Chem. Chem. Phys. 2012, 14, 157-164. 52. Le Guennic, B; Chibani, S.; Charaf-Eddin, A.; Massue, J.; Ziessel, R.; Ulrich, G.; Jacquemin, D. The NBO Pattern in Luminescent Chromophores: Unravelling ExcitedState Features Using TD-DFT. Phys. Chem. Chem. Phys. 2013, 15, 7534-7540. 53. Momeni, M.R.; Brown, A. Why Do TD-DFT Excitation Energies of BODIPY/AzaBODIPY Families Largely Deviate from Experiment? Answers from Electron Correlated and Multireference Methods. J. Chem. Theory Comput. 2015, 11, 2619-2632. 54. Cai, Z.L.; Crossley, M.J.; Reimers, J.R.; Kobayashi, R.; Amos, R.D. Density Functional Theory for Charge Transfer: The Nature of the N-Bands of Porphyrins and Chlorophylls Revealed through CAM-B3LYP, CASPT2, and SAC-CI Calculations. J. Phys. Chem. B 2006, 110, 15624-15632. 55. Kobayashi, R.; Amos, R.D. The Application of CAM-B3LYP to the Charge-Transfer Band Problem of the Zincbacteriochlorin–Bacteriochlorin complex. Chem. Phys. Lett. 2006, 420, 106-109. 56. Yu, H.-L.; Wang, W.-Y.; Hong, B.; Zong, Y.; Si, Y.-L.; Hu, Z.-Q. Variational First Hyperpolarizabilities of 2,3-naphtho-15-crown-5 Ether Derivatives with CationComplexing: A Potential and Selective Cation Detector. Phys. Chem. Chem. Phys. 2016, 18, 26487-26494. 57. Gunter, P. Nonlinear Optical Effects and Materials, 4th ed.; Gunter, P., Ed.; 2000, Springer: Berlin. 58. de Wergifosse, M.; Liegeois, V.; Champagne, B. Evaluation of the Molecular Static and Dynamic First Hyperpolarizabilities. Int. J. Quant. Chem. 2014, 114, 900-910. 59. Felouat, A.; D’Aleo, A.; Charaf-Addin, A; Jacquemin, D.; Guennic, B.L.; Kim, E.; Lee, K.J.; Woo, J.H.; Ribierre, J.-C.; Wu, J.W.; Fages, F. Tuning the Direction of Intramolecular Charge Transfer and the Nature of the Fluorescent State in a T-Shaped Molecular Dyad. J. Phys. Chem. A, 2015, 119, 6283-6295.

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Figure Captions Figure 1: The front and side views of ground state optimized geometries of molecule 1 (panel a - b) and molecule 2 (panel c - d), obtained using DFT (CAM-B3LYP functional) calculations with cc-pVTZ basis set. The x, y and z directions are shown for reference. The dihedral angle is 900 in molecule 1 vis-à-vis 57o in molecule 2 due to the presence of methyl groups in the BODIPY moiety of the former.

Figure 2: The ground state optimized geometries of molecules (3 - 6) as obtained using DFT, employing CAM-B3LYP functional and cc-pVTZ basis set. The dihedral angle is changed due to incorporation of methyl groups in molecules 5 and 6, compared to molecules 3 and 4, respectively. The x, y and z directions are shown for reference.

Figure 3: The highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital LUMO pictures of molecules (a) 1, 5 and 6 (i to iii) and (b) molecules 2, 3 and 4 (i to iii), obtained using DFT, employing CAM-B3LYP functional and ccpVTZ basis set.

Figure 4: Comparison of (a) dipole moment (µ), (b) average polarizability (αav), (c) total first hyperpolarizability (βtotal) and (d) absolute values of vector component of first hyperpolarizability (/βvec/) of molecules (1 - 6) as obtained using DFT (CAM-B3LYP functional) employing cc-pVTZ, 6-31G(d,p) and 6-31+G(d,p) basis sets. The µ, αav, βtotal and /βvec/ values of molecules (2 - 4) using MP2 employing 6-31G(d,p) and 6-31+G(d,p) basis sets ate also presented for comparison.

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X 1 2 3 4

R 5

R 6 7

N R

B F 8 F

N R

Scheme - 1: The structure of the BODIPY dyes under investigation. Numbering of some of the heavy atoms is done for reference.

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Page 24 of 34

Table - 1: The bond lengths (Å) and dihedral angle (in degree) of the molecule (1 14) as obtained using DFT (CAM-B3LYP functional) employing 6-31+G(d,p) basis set. The same structural parameters obtained for molecules (2-4) using MP2 theory and 6-31+G(d,p) basis set are also reported. Theory/ Molecule DFT/6-31+G(d,p) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 MP2/6-31+G(d,p) 2 3 4

1-2

2-3

3-4

4-5

5-6

6-7

7-8

3-4-5-6

1.392 1.392 1.412 1.387 1.409 1.388 1.402 1.400 1.398 1.398 1.396 1.396 1.397 1.394

1.391 1.390 1.384 1.388 1.388 1.388 1.385 1.388 1.387 1.387 1.390 1.390 1.385 1.390

1.395 1.399 1.400 1.399 1.393 1.396 1.401 1.395 1.398 1.395 1.398 1.394 1.402 1.395

1.491 1.481 1.471 1.484 1.489 1.491 1.474 1.490 1.483 1.491 1.480 1.490 1.483 1.491

1.398 1.400 1.405 1.398 1.398 1.398 1.404 1.399 1.398 1.397 1.401 1.399 1.398 1.398

1.398 1.390 1.389 1.390 1.398 1.398 1.389 1.398 1.389 1.398 1.390 1.398 1.390 1.397

1.546 1.555 1.553 1.558 1.546 1.548 1.554 1.546 1.557 1.548 1.555 1.546 1.557 1.547

90 57 51 59 90 90 52 90 58 90 55 90 58 90

1.399 1.415 1.395

1.397 1.392 1.395

1.406 1.406 1.406

1.473 1.464 1.473

1.403 1.406 1.403

1.386 1.386 1.386

1.562 1.559 1.563

57 52 58

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Table - 2: The vertical transition maxima (in nm) and their corresponding oscillator strengths of molecules (1-6), as predicted from TDDFT calculations employing CAM-B3LYP functional and cc-pVTZ basis set. H and L stand for HOMO and LUMO respectively.

a

Molecule/ Excited Transition

Oscillator

Dominant

state

maxima (nm)

strength

transitionsa

1 S1

410.35

0.535

H – L (0.70)

S2

315.48

0.047

(H-2) – L (0.70)

2 S1

397.69

0.441

H – L (0.69)

S2

309.71

0.075

(H-1) – L (0.69)

3 S1

394.47

0.4238

H – L (0.69)

S2

382.42

0.3393

(H-1) – L (0.69)

4 S1

403.69

0.430

H – L (0.68)

S2

314.16

0.067

(H-1) – L (0.67)

5 S1

409.83

0.526

H – L (0.70)

S2

351.29

0.00

(H-1) – L (0.69)

6 S1

412.29

0.536

H – L (0.70)

S2

333.15

0.00

H – (L+1) (0.69)

The coefficient of corresponding transitions are mentioned in the parenthesis.

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Page 26 of 34

Table - 3: The values of dipole moments (µ µ, Debye), αav (a.u.) and βtotal (a.u.) of Molecules (1-14) as obtained by using density functional theory (DFT) with CAMB3LYP functional employing 6-31+G(d,p) basis set. The same parameters for molecules (2-4) obtained from MP2 calculations, employing 6-31+G(d,p) basis set are reported. The values of βvec and βvec/βtotal are also presented in the table. Molecule

CAM-B3LYP/ 6-31+G(d,p) µ

αav

βtotal

βvec

βvec/βtotal

1

5.12

272.06

1415.31

-1387.52

-0.980

2

6.01

220.73

534.86

530.96

0.993

3

9.68

271.59

4570.96

-4547.57

-0.995

4

0.88

240.87

1359.28

496.28

0.365

5

7.75

312.71

690.28

689.04

0.998

6

1.18

292.78

1973.91

-1019.83

-0.517

7

8.48

239.53

2269.61

-2237.57

-0.986

8

6.96

285.0

859.76

831.0

0.97

9

1.43

241.67

569.12

560.74

0.985

10

1.07

292.98

1667.42

888.89

0.53

11

6.71

235.93

51.68

50.44

0.978

12

5.70

286.03

1289.80

1266.57

0.98

13

3.20

240.62

1116.67

950.57

0.85

14

2.96

291.94

2227.76

1316.07

0.59

Molecule

MP2/ 6-31+G(d,p) µ

αav

βtotal

βvec

βvec/βtotal

2

5.57

226.11

155.84

150.51

0.966

3

8.44

275.55

4335.06

-4261.01

-0.983

4

1.24

246.47

920.06

246.94

0.268

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Table - 4: The x, y and z components of dipole moments (Debye) of molecules (1 14) along with the values of βx, βy and βz (equation vi) as obtained from DFT (CAMB3LYP functional), employing 6-31+G(d,p) basis set. The same parameters for molecules (2-4) obtained from MP2 calculations, employing 6-31+G(d,p) basis set are reported. Molecule

CAM-B3LYP/ 6-31+G(d,p) µx

µy

µz

βx

βy

βz

1

-5.02

0.89

0.42

1415.31

0.84

0.07

2

5.95

0.73

0.30

534.84

4.65

0.24

3

9.64

0.82

0.42

-4570.73

36.30

27.64

4

0.32

0.75

0.34

1359.28

2.25

0.21

5

-7.66

1.10

0.49

-680.61

115.14

-0.2

6

0.61

0.90

0.45

-1973.91

0.12

1.27

7

8.34

1.32

0.81

-2268.88

-53.15

22.26

8

-6.73

1.73

0.43

-859.76

-1.30

-0.46

9

0

0.33

1.40

18.14

17.85

568.55

10

0.0

0.90

0.58

-17.78

-17.64

1667.23

11

-6.66

0.77

0.32

51.24

0.89

6.69

12

-5.60

0.94

0.44

-1289.79

-3.74

0.21

13

2.55

-0.34

1.90

1111.1

-46.21

101.48

14

1.61

0.90

2.33

2223.63

-0.4

135.58

Molecule

MP2/ 6-31+G(d,p) µx

µy

µz

βx

βy

βz

2

5.48

0.83

-0.64

140.52

47.26

-48.04

3

8.35

1.16

-0.29

-4331.45

176.95

-0.27

4

0.305

0.91

-0.79

919.44

-1.07

-33.86

27



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

Figure 1

28


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Figure 2

29



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

Figure 3a

30


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Figure 3b

31



CAM-B3LYP/ cc-pVTZ CAM-B3LYP/ 6-31G(d,p) CAM-B3LYP/ 6-31+G(d,p) MP2/ 6-31G(d,p) MP2/ 6-31+G(d,p)

10

µ (Debye)

8

6

4

2

0 1

2

3

4

5

6

5

6

Molecules

Figure 4a


350 300

αav (atomic unit)

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

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250 200 150 100 50 0 1

2

3

4

Molecules

Figure 4b

32


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4500

βtotal (atomic unit)

4000 3500 3000 2500 2000 1500 1000 500 0 1

2

3

4

5

6

Molecules

Figure 4c


4500 4000

/βvec/ (atomic unit)

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


3500 3000 2500 2000 1500 1000 500 0 1

2

3

4

5

Molecules

Figure 4d

33


6


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

TOC Graphic


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Tuning of Second-Order Nonlinear Optical Response Properties of

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