Extended First Hyperpolarizability of Quasi-Octupolar Molecules by

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Extended First Hyperpolarizability of Quasi-Octupolar Molecules by Halogenated Methylation: Whether the Iodine Atom is the Best Choice Zeyu Liu, Shugui Hua, and Guohua Wu J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b04167 • Publication Date (Web): 28 Aug 2018 Downloaded from http://pubs.acs.org on August 28, 2018

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The Journal of Physical Chemistry

Extended First Hyperpolarizability of Quasi-Octupolar Molecules by Halogenated Methylation: Whether the Iodine Atom is the Best Choice Zeyu Liu†, Shugui Hua§, and Guohua Wu∗,† †

College of Biotechnology and Sericultural Research Institute, Jiangsu University of Science and Technology, Zhenjiang 212018, People’s Republic of China §

College of Life Science and Chemistry, Jiangsu Key Laboratory of Biological Functional

Molecules, Jiangsu Second Normal University, Nanjing 210013, People’s Republic of China

∗

Corresponding author. Tel: +86 511 85616840. E-mail: [email protected]. 1

ACS Paragon Plus Environment

The Journal of Physical Chemistry 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

Abstract Inspired by a previous report, in which the quasi-octupolar molecules DPATSB, DPATSP, and (DPATSP-Me)+I- were synthesized and the iodized salt was proposed as a suitable optical limiting chromophore, we performed the linear and nonlinear optical analyses on the synthesis molecules and several extension halogenated dyes ((DPATSP-Me)+X- (X = F, Cl, and Br)) by using density functional theory (DFT) and time-dependent DFT (TD-DFT) methods. The energy gap of frontier molecular orbitals (FMOs) was diminished by introducing the pyridinium ion into the system, and a charge-separated state was formed in halogenated salts. The N-methylation of the dye leads to a sharp increase in response characteristics, accompanied by a red-shift of the absorption spectrum from the ultraviolet region to the visible light region. Importantly, our studies show that there exists a significant halogen atomic-species dependence of the nonlinearity of the salts. Fluorination and bromination of the molecule seem to be more potential in improving the nonlinearity in zero-frequency and frequency-dependent incident light, respectively, without causing the undesirable red-shift of the absorption band relative to their halogenated analogues. The nonlinear optical (NLO) response calculated by different DFT are identical in trend.

2


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1. Introduction For a long time, the nonlinearity of the molecule is one of the most important properties that people pay close attention to. The preparation of effective nonlinear optical (NLO) materials has always been a hot topics in the field of photoelectric functional materials design.1-9 So far, many kinds of NLO chromophores, such as organic dyes, inorganic molecules, or metal clusters have emerged endlessly.10-15 For purely organic dyes, it is a well-established rule that a molecule with a strong electron donor (D) connected to a powerful electron acceptor (A) through a π-bridging system, known as the D-π-A type dipolar compound, usually exhibits large molecular first hyperpolarizability, and then affect second-order (quadratic) NLO susceptibilities of the bulk material containing it.1,16-23 Based on this conception, a large number of extended conjugated systems, such as quadrupolar (D-π-A-π-D, A-π-D-π-A, …)24-27 and octupolar ((D-π)3-A, (A-π)3-D, …)28-32 organic molecules, were designed in theory and/or synthesized in experiment. Owing to the lack of static permanent dipole moment, octupolar molecules are not easy to form molecular aggregation in bulk material. So, they are considered as a potential alternative to the dipolar molecules in NLO applications.33-38 However, this advantage of octupolar molecules generally accompanied by a recognized drawback of poor poling capability. In this case, tremendous amount of research for octupolar compounds similar to those already devoted to the dipolar molecules have been made.38-41 An octupolar molecule DPATSB has been synthesized and the NLO properties of it were studied in detail by Zhang et al. in 2008.42 Subsequently, the preparation of DPATSP and its N-methyl iodized salt, denoted by (DPATSP-Me)+I-, were realized for studying their two-photon absorption (TPA) properties by Bisht and co-workers.43,44 It was found that the TPA cross section of (DPATSP-Me)+Isignificantly increases relative to that of the DPATSP, and the former can be serve as a better candidate for applications in nonlinearity. Although so much progress has been made in experimental study of synthesis and NLO properties of the DPATSB-based dyes, an in-depth theoretical investigation of the structure-nonlinearity relationship for this system has not been reported. A 3



natural question in allusion to these works is how does the ion pair affect the optical properties of the molecule and whether other kinds of halogens make a greater improvement than I atom in the first hyperpolarizability? This issue impelled us to perform a quantum chemical calculation to provide an explanation for the nonlinearity of existing dyes at the molecular level, and more important, it is possible to predict the optical properties of the molecules involved in the design by theoretical research and then to guide the relevant experimental investigations in future. 2. Computational details As calculations of large systems by using the methods containing electron correlation are costly, density functional theory (DFT) is usually employed to strike a balance between the accuracy and computational cost. B3LYP45,46 is generally considered suitable for the optimization of molecular structures and PBE38, which is a hybrid density functional based on PBE047 with the Fock exchange of ax = 3/8, is proved to be a reliable functional to calculate the response properties for charge-transfer chromophores. The ground-state molecular structures were fully optimized by using the B3LYP functional. Vibrational frequency analyses at the same level were carried out on all stationary points to determine the nature of them. Absorption spectra as well as the (hyper)polarizabilities were calculated with the time-dependent DFT (TD-DFT)48,49 and DFT method, respectively, by using the PBE38 functional for the optimized geometries. For comparison purposes, two other hybrid functionals PBE0 and BHandHLYP50 were employed in calculation of the NLO properties of the dyes. For halogen atoms, the def2-TZVP basis set51 was adopted for geometric optimizations and spectral calculations, and def2-TZVPD basis set52 was used for NLO analyses. While for other atoms (H, C, and N), the 6-311G(d) basis set53 was adopted in the whole process. The structures and properties of the studied chromphores in toluene solution (ε = 2.38) were calculated within the solvation model of density (SMD)54 approach. In calculating the average polarizability ( α ) of a molecule, only the contribution of its three diagonal elements is usually considered, and the formula is described as 4


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α = (α x x + α y y + α zz ) 3

total molecular hyperpolarizability (βtot) and its vectorial part (βvec) are determined by β tot = ( β x 2 + β y 2 + β z 2 )1/ 2

β vec = ∑ i

µi β i , i = x, y , z µ

where x, y, z

β i = (1 3 ) ∑ ( β ijj +β jji +β jij ), i = x, y , z j

All calculations in present work were performed with the Gaussian 16 package.55 The (hyper)polarizabilities were evaluated by analytical third energy derivatives and adopted T-convention of Willetts et al.56 The resulting data referring to the linear and nonlinear optical properties were analyzed by means of code Multiwfn 3.4.1.57,58 3. Results and discussion For the chromophores studied in Figure 1, DPATSB, DPATSP, and (DPATSP-Me)+I-

are

experimentally

synthesized

and

characterized,

while

(DPATSP-Me)+F-, (DPATSP-Me)+Cl-, and (DPATSP-Me)+Br- are theoretical designed for comparative analysis. All these dyes are quasi-octupolar molecules with (D-π)3-A configuration, in which three diphenylamino (DPA) units at periphery and benzene, pyridine, or N-methyl pyridinium group combined halogen atom in the center of the molecules act as, respectively, the electron donor and acceptor. DFT optimized Cartesian coordinates for ground- and excited-state molecules are displayed in Tables S1 and S2.

5



Figure 1. Geometric structure of the studied chromophores in present work. Hydrogen atoms are omitted for clarity. Skeleton color code: cyan, electron donor; pink, conjugated bridge; purple, electron acceptor.

3.1 Stabilities and Electronic Structures We start with the discussion of the stability of the studied salts, (DPATSP-Me)+X- (X = F, Cl, Br, and I), in the solution phase. The free energies of the ion pairs (E(DPATSP-Me)+X-), cations (E(DPATSP-Me)+), and anions (EX-) in toluene solution are reported in Table 1. The derived binding energies in N-methyl halogenated salts are found to be -122.1 to -63.8 kJ/mol, suggesting that they are very well-stabilized in solution in the form of cation-anion pair. The comparisons of theoretical absorption spectra of (DPATSP-Me)+I- and (DPATSP-Me)+ with the experimental one provide further support for our claim (see Section 3.2).

Table 1. Free energies obtained at the B3LYP/6-311G(d)/def2-TZVP level of theory in toluene solution for salts (E(DPATSP-Me)+X-), cations (E(DPATSP-Me)+), and anions (EX-) (in Hartree), as well as derived molecular binding energies (Eb, in kJ/mol) for (DPATSP-Me)+X- (X = F, Cl, Br, and I) X F Cl Br I a

E(DPATSP-Me)+X- E(DPATSP-Me)+ EXEba -2865.522773 -99.976455 -122.1 -3225.903312 -460.369609 -89.0 -2765.499799 -5339.863720 -2574.334446 -77.4 -3063.491681 -297.967587 -63.8

the binding energies for (DPATSP-Me)+X- (X = F, Cl, Br, and I), Eb =

E(DPATSP-Me)+X- - (E(DPATSP-Me)+ + EX-)

The frontier molecular orbital (FMO) theory is a simple but practical method to study the chemical stability and the properties related to the intramolecular charge transfer (ICT) of molecules. The highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) are undoubtedly the most important pair in FMOs. The HOMO-LUMO energy difference (∆EL-H) can be used to qualitatively predict the chemical reactivity, dynamic stability, and some optical 6


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properties of the compounds.4,59-61 DFT calculated energy levels of the FMOs for studied dyes are shown in Figure 2 and Table S3.

Figure

2.

FMO

levels

(isovalue

=

0.02

au)

obtained

at

the

B3LYP/6-311G(d)/def2-TZVP level of theory in toluene solution for studied molecules. The numbers on chart denote the ∆EL-H.

The ∆EL-H of DPATSB is calculated to be of 3.25 eV. By replacing C atom with N in the central ring, the increased electronegativity of electron acceptor makes the DPATSP molecule exhibit a relatively small energy gap (2.98 eV). Furthermore, with the increase in the atomic number of halogens, the ∆EL-H values of the series of halogenated molecules (DPATSP-Me)+X- (X = F, Cl, Br, and I) are observed to be decreased gradually from 2.31 to 2.12 eV, which are much smaller than those of the DPATSB and DPATSP. The reduction of ∆EL-H mainly originates from the diminution

of

the

LUMO

level

caused

by

the

introduction

of

strong

electron-accepting halogens. Accordingly, it can be predicted that the first hyperpolarizability of these dyes will improve by modification of the molecules with pyridinium ion, and (DPATSP-Me)+X- (X = F, Cl, Br, and I) may be excellent 7



candidates for photoelectric functional material. The electrostatic potential (ESP) charge is often used in the study of ICT by virtue of its high reliability. In this work, ESP charge analyses with increased point density realized by using IOp(6/42=10) keyword were implemented to inspect the charge transfer and charge density distribution in the molecules. The ESP charges for different units are gathered in Table 2. It should be noted that the sums of ESP charges for each dye given in Table 2 are not equal to zero due to a certain charge distribution on the conjugated bridges (phenyl vinyl groups). There is no obvious charge-separation in DPATSB and DPATSP molecules due to the weak electronegativity of the electron acceptor (benzene and pyridine ring, respectively) in them. The distribution of partial charge for (DPATSP-Me)+X- (X = F, Cl, Br, and I), in vivid contrast, presents significant separation characteristic with almost a negative charge located on halogen atom, indicating electrons are successfully transferred from molecular organic skeleton to halogen atom after introducing the pyridinium ion. The chromophores with effective electron polarization are expected to have large optical nonlinearity.

Table 2. ESP charges of electron donor and acceptor (in au) calculated at the B3LYP/6-311G(d)/def2-TZVP level of theory in toluene solution for studied dyes Dye DPATSB DPATSP (DPATSP-Me)+F(DPATSP-Me)+Cl(DPATSP-Me)+Br(DPATSP-Me)+Ia

Donor DPAs 0.29 0.33 0.51 0.56 0.55 0.57

Acceptor Central ringa Halogen atom 0.23 0.30 0.72 -0.88 0.71 -0.89 0.71 -0.89 0.70 -0.92

benzene, pyridine, or N-methyl pyridinium group combined halogen atom in the

center of the molecules

3.2 Linear optical properties: absorption and emission spectra Absorption spectrum The excitation energies and oscillator strengths in toluene 8


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solution for studied molecules are listed in Table S4 (due to limited space, only the first 30 states of 50 excited states calculated for each dye are presented). The simulated absorption spectra obtained by Gaussian-fitting algorithm upon TD-DFT calculation are plotted in Figure 3. Precursor dye DPATSB exhibits two absorption peaks in the ultraviolet region at 379 and 286 nm, respectively. In contrast, the maximum absorption wavelength (λabs) of DPATSP (397 nm) is red-shifted by 18 nm and the oscillator strength reduces obviously. Meanwhile, DPATSP shows almost the same high-energy absorption band as DPATSB at 286 nm. The theoretical spectrum of DPATSP correlates fairly well with the available experimental observation both in peak positions and in relative intensities. The deviation of the maximum absorption peak between theoretical and experimental values is only 3 nm for DPATSP, demonstrating the computational methodology we have chosen is suitable for the studied systems. Figure 3 shows that the (DPATSP-Me)+I- salt has three distinct absorptions, located at 500, 358, and 283 nm, which can be viewed as corresponding to the absorption peaks of 493, 363 (visual result of the inconspicuous shoulder peak), and 300 nm in experimental observation, respectively. In contrast, the absorption spectrum of (DPATSP-Me)+ cation with only two peaks lied at 521 and 364 nm is quite different from that of experimental result. The comparisons of theoretical absorption spectra of (DPATSP-Me)+I- and (DPATSP-Me)+ with the experimental one give another proof that the salt exists as a bound form (not independent cation and anion species) in solution. The λabs of (DPATSP-Me)+X- (X = F, Cl, Br, and I) concentrate in the visible region of 478-519 nm, and the absorption strengths increase with halogen atom change from F to I. Specifically, a new absorption peak with weak strength appears between high- and low-energy absorption bands at about 355-358 nm for halogenated species.

9



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Figure 3. Absorption spectra obtained at the TD-PBE38/6-311G(d)/def2-TZVP level of theory for studied chromophores. The numbers on chart refer to the value of approximate absorption wavelengths. A Gaussian function has been employed with a full width at half-maximum of 3000 cm-1.

The natural transition orbital (NTO)62 analyses for the maximum absorption of the molecules, which have been proved to be a very practical method for exploring the orbital topology involved in the excitation,30 are displayed in Figure 4. It can be seen that the spatial distributions of NTO hole/particle for chromophores are sometimes different from those of HOMO/LUMO, typically for DPATSB, (DPATSP-Me)+Br-, and (DPATSP-Me)+I-. The most fundamental reason for the distinction lies in that the maximum absorption peaks of these species are not contributed by (or only by) the HOMO→LUMO transition (see Table S4). For instance, the absorption band is described by multiple HOMO-n→LUMO+m transitions

in

precursor

dye

DPATSB,

such

as

HOMO-2→LUMO

and

HOMO→LUMO+2 besides HOMO→LUMO, while HOMO-3→LUMO transition is a dominant form in excitation for (DPATSP-Me)+Br- and (DPATSP-Me)+I-. The crucial FMOs associated with maximum absorption of the chromophores with their energy levels are shown in Figure S1 (only the major contributions of more than 10% are shown). Good correlation between NTO hole/particle in Figure 4 and HOMO-n/LUMO+m distribution in Figure S1 was observed for each dye. 10


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Figure 4. Dominant NTO pairs (isovalue = 0.02 au) involved in the maximum absorption obtained at the TD-PBE38/6-311G(d)/def2-TZVP level of theory for investigated systems. The numbers on chart denote the associated eigenvalue for each transition.

All the low-lying excitations for DPATSB and DPATSP are being characterized as a π→π* transition of ICT as shown in the results of the NTO analysis. However, for halogenated molecules (DPATSP-Me)+X- (X = F, Cl, Br, and I), the transitions seem to be the results of the coexcitation of the π-bonding orbital electrons in molecular skeleton and the lone pair electrons (n electrons) of halogen atoms, i.e., they are considered to possess the characteristics of n→π* transition rather than only a π→π* transition. Moreover, very clear atomic-species dependence was observed in their particle NTOs. The proportion of the n→π* transition increases with the increase of atomic number of halogen atom from X = F to X = I. Similar trend is also observed in the FMOs of chromophores in Figure 2. Although the stability of cation-anion pair in solution has been clearly identified, the internal interaction of anion and cation within ion pair is apparently not as strong as the covalent bonds between atoms on π-conjugated skeleton (see Table 1), which causes a relatively high energy of transition from lone-pair orbital n of halogen atom to π* orbitals of molecular skeleton. It inevitably leads to a blue-shift of the maximum absorption of the originally simple π→π* transition as rendered by (DPATSP-Me)+ cation after the involvement of n→π* transition in (DPATSP-Me)+X- (X = F, Cl, Br, and I) salts. Emission spectrum Calculated emission spectra for studied dyes are presented 11



in Figure 5. Although many attempts have been taken in the optimization, the excited-state geometry of (DPATSP-Me)+Br- is still not available, and so the fluorescence spectrum of (DPATSP-Me)+Br- is absent here. The emission peak of precursor DPATSB has the highest energy (at 436 nm) and the strongest strength among all chromophores. In contrast, DPATSP features a red-shifted fluorescence emission at 457 nm with the weakest intensity. A further red-shift in emission wavelength (λem) is observed as introducing the pyridinium ion to the system. The λem of the N-methyl halogenated salts (DPATSP-Me)+X- (X = F, Cl, and I) are located at the region of 566-577 nm, and the fluorescence shows medium strength.

Figure 5. Emission spectra obtained at the TD-PBE38/6-311G(d)/def2-TZVP level of theory for studied chromophores. The numbers on chart refer to the value of approximate emission wavelengths. A Gaussian function has been employed with a full width at half-maximum of 3000 cm-1.

From Figure 5, we can see that the calculated emission spectra (457 nm) of molecule DPATSP basically coincides with the experimental observation (469 nm). However, for (DPATSP-Me)+I- molecule, the λem of theoretical simulation is much smaller in wavelength than the experimental value (566 nm vs 612 nm). This is possibly due to the TD-DFT method does not account for the exact geometry of the excited state for charge-separated (DPATSP-Me)+I- salt. 12


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3.3

Nonlinear

optical

properties:

static

and

dynamic

molecular

(hyper)polarizabilities The effect of introducing the pyridinium ion on molecular (hyper)polarizabilities is the focus of this article. The polarizabilities as well as zero-frequency (static, λ = ∞ nm) and frequency-dependent (dynamic, λ = 1907, 1460, 1340, and 1064 nm) first hyperpolarizabilities were evaluated using three hybrid functionals with different content of Hartree-Fock (HF) exchange, namely PBE0 (25.0%), PBE38 (37.5%), and BHandHLYP (50.0%). For the sake of clarity, we report only the results from the PBE38 calculations in this section, and the comparisons of the performance of various functionals will be discussed in detail in the next section. Static molecular (hyper)polarizability The dipole moments (µ0), average polarizabilities ( α ), total hyperpolarizability (βtot) and its vectorial part (βvec) within the static field limit for studied dyes are demonstrated in Table S5. DPATSB has almost vanishing dipole moment with µ0 = 0.09 au due to its octupolar character with C3 symmetry. The introduction of N atom causes the separation of positive-negative charge centre, thus make the DPATSP present a certain dipole moment (0.98 au). As expected, the halogenated molecules (DPATSP-Me)+X- (X = F, Cl, Br, and I) show considerable dipole moment on account of significant intramolecular charge-separation as depicted by ESP charge analyses (see Table 2). Molecules DPATSB and DPATSP show almost equal average polarizability, and the α values of the (DPATSP-Me)+X- (X = F, Cl, Br, and I) are slightly promoted relative to those of the precursors. One of the most important variables that is often used in the discussion of molecular nonlinearity is the projection of the total hyperpolarizability along the direction of the dipole moment, i.e., the vectorial part of βtot, which was usually denoted by βvec. This parameter is being considered to be comparable with the measured value determined by the electric-field-induced second-harmonic (EFISH) experiment. From Table S5 and Figure 6(a), one can see that the βvec(∞) value of precursor DPATSB is almost zero as a result of its octupole characteristic, while the molecule DPATSP shows a certain size of βvec(∞) = 4962 au due to the 13



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electron-withdrawing property of N atom. Importantly, an abrupt promotion in βvec(∞) value (-13907 au) of the (DPATSP-Me)+F- is observed. The enhancement in molecular hyperpolarizability is evidently induced by the strong affinity of the F atom. The remaining halogenated salts (DPATSP-Me)+X- (X = Cl, Br, and I) possess obviously smaller first hyperpolarizability relative to the (DPATSP-Me)+F-, and the βvec(∞) of them decreases gradually with the increase of atomic number and the decrease of electron-withdrawing ability in halogen atom. This conforms to our general chemical intuition. Even better, no undesirable red-shift was found in their maximum absorption with the change of molecular hyperpolarizability. Given the facts above, it is reasonable to recommend (DPATSP-Me)+F- be a novel candidate for NLO material unit as an alternative to (DPATSP-Me)+I-, and the modulation of the first molecular hyperpolarizability of the system can be realized by selecting different halogen atoms.

Figure 6. Calculated dipole moments (µ0), average polarizabilities ( α ), and the vectorial

part

of

the

total

hyperpolarizabilities

(βvec)

at

the

PBE38/6-311G(d)/def2-TZVPD level of theory for studied dyes: (a) the responses in the zero-frequency limit (λ = ∞ nm) and (b) the responses to the frequency-dependent fields (λ = 1907, 1460, 1340, and 1064 nm).

We explored the spatial distributions of the hyperpolarizability density63 for the halogenated salts to understand the characteristic of the NLO response for different 14


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species. The studies have concentrated on the isosurface of β density in the presence of electric field along the molecular dipole, which is the most crucial component of βvec. Simultaneously, for ease of operation and disscussion, the direction of dipole moments were adjusted to coincide with the z-axis and the halogen atoms were set at the original points of the coordinate system. Thereby, the hyperpolarizability density r

(2) r we concerned corresponds to ρ zz (r ) . The visualized results of the − z ρ zz(2) (r )

function of halogenated molecules are illustrated in Figure 7. The remarkable positive contribution principally stems from the top DPA moiety and most of the negative contribution is located near the central ring for each species. Clearly, the value of r − z ρ zz(2) (r ) function becoming increasingly sparse with the increase of atomic number

of halogens in the dye from F to I. This is particularly evident for the negative spatial distributions in the closest branch to halogen (the left branch) of molecules. Although the complex electron density distribution hinders our visual quantitative analysis of the magnitude of the hyperpolarizability, we believe that the distinction of the spatial density is the most important reason for the difference in hyperpolarizability of halogenated salts.

15



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r

Figure 7. Contour surface (isovalue = 20 au) of − z ρ zz(2) (r ) function based on the r

static first hyperpolarizability density ρ zz(2) (r ) at the PBE38/6-311G(d)/def2-TZVPD level of theory for halogenated salts (DPATSP-Me)+X- (X = F, Cl, Br, and I). Surface color code: blue, positive spatial contributions; red, negative spatial contributions. As shown in Table S5, the change trend of the total hyperpolarizability βtot(∞) is consistent with that of its projection βvec(∞) but less obvious. Discussions of the similar situation will be ignored for the sake of brevity. It is generally known that the value of βvec(∞)/βtot(∞) is the cosine component of the angle between the total first hyperpolarizability and the dipole moment. This value reflects whether the total hyperpolarizability of the molecule is along the dipole direction, and then the complexity of the electric-induced ICT can be inferred. From Table S5 one can easily see that the value of βvec(∞)/βtot(∞) of the dyes seems to be a serious deviation from unity except for the case of DPATSP, implying the multi-directionality and complexity of the ICT process in them. This is consistent with the characteristics of octupolar molecule and is distinguishable from the D-π-A type dipolar molecules.5,35 Dynamic molecular (hyper)polarizability It is known that the measured values of hyperpolarizability are determined by dispersion effects on the chromophores. In practice, the wavelength-dependent experiments are usually performed to explore the optical resonance effects by the use of a 1064 nm (ħω = 1.17 eV) near infrared ray (NIR) laser. Here, the usual three wavelengths in experiments (λ = 1907, 1460, and 1340 nm), together with the most frequently used λ = 1064 nm, were applied in calculations to compare the dispersion effect on the first hyperpolarizability of the molecules. The frequency-dependent hyperpolarizabilities βvec(-2ω;ω,ω) (abbreviated to βvec(ω): βvec(1064), βvec(1340), βvec(1460), and βvec(1907)) of the studied dyes are depicted in Figure 6(b). We can see that the βvec(ω) values are significantly higher than the zero-frequency βvec(∞). Responses under low-frequency incident light fields 16


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(λ = 1907, 1460, and 1340 nm) make the nonlinearity of the molecule increase steadily, while the hyperpolarizability increase rapidly and reach the maximum on excitation at 1064 nm. It reveals that a strong resonance effect caused at the 1064 nm fundamental, which is almost two times the maximum absorption wavelength of the molecules. It is worth mentioning that although the chromophores show the maximum response properties at a wavelength of 1064 nm, second harmonic generation (SHG) is often measured in the off-resonant condition to reduce the effect of other processes like TPA. Further analysis indicates that at the low-frequency applied electric fields of λ = 1907, 1460, and 1340 nm, the (DPATSP-Me)+F- presents the largest first hyperpolarizability

among

its

analogues.

However,

the

βvec(ω)

value

of

(DPATSP-Me)+Br- obtained from resonance at a wavelength of 1064 nm is larger than those of other halogenated molecules. Invariably, the first hyperpolarizability of (DPATSP-Me)+I- is always the smallest among those of halogenated salts, irrespective of the frequency of incident light. The total first hyperpolarizability of the molecule and its projection in dipole direction

show

the

same

trend

as

the

above

discussion.

Again,

the

frequency-dependent βvec(ω) values indicate that it may not be the optimum strategy to employ I as a electron acceptor to improve the nonlinearity of the research system. The N-methyl salts with other halogens (F or Br) are expected to have a relatively better nonlinear response. 3.4 Comparisons of the performance of various functionals It is generally believed that the response properties of molecules depend on the calculation method selected. In particular, charge-transfer characters between the ground and excited states are closely dependent on the amount of HF exchange. Calculated response properties using three hybrid functionals for investigated molecules are listed in Figure 8 and Tables S5 and S6.

17



Page 18 of 38

Figure 8. Calculated response properties using three hybrid functionals at the 6-311G(d)/def2-TZVPD level of theory for studied dyes: (a) the responses in the zero-frequency limit (λ = ∞ nm) and (b) the responses to the frequency-dependent fields (λ = 1907, 1460, 1340, and 1064 nm). Line color code: cyan, PBE0; pink, PBE38; purple, BHandHLYP.

The result shows that functionals PBE0, PBE38, and BHandHLYP all provide similar results of dipole moments (µ0) for each dye, but the average polarizabilities ( α ) slightly decrease with the gradual increase of the HF component in hybrid functionals. The first hyperpolarizabilities (βtot and βvec) both for zero-frequency and frequency-dependent cases, by contrast, display an obvious functional dependence, i.e., the more HF exchange mixed in the functionals, the smaller the calculated hyperpolarizability of the chromophores. Recent theoretical study on the NLO responses of spirooxazine-fulgide biphotochromic molecular switches by Yuan et al. supports this conclusion.63 Although the response properties of the molecules show the above trend of change to different methods, it is not difficult to find that the values of the molecular hyperpolarizabilities are almost consistent in sequence for each functional. Generally speaking, (DPATSP-Me)+F- and (DPATSP-Me)+Br- can gain a greater first hyperpolarizability with the resonance excitation than those of their analogues in low(λ = ∞, 1907, 1460, and 1340 nm) and high-frequency (λ = 1064 nm) field, respectively. 4. Conclusions A

series

of

experimentally

synthesized

and

theoretically

designed

quasi-octupolar dyes have been investigated in electronic structure, linear and nonlinear optical properties by using (TD-)DFT method. The reduction of the energy 18


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gap in FMOs and the intramolecular charge-separation of the studied quasi-octupolar molecules are observed with the formation of cation-anion pair by introducing the pyridinium ion. The maximum absorption bands of halogenated chromophores are found to be located in the visible light region, and different halogen atoms have little impact on it. The halogenated salts (DPATSP-Me)+X- (X = F, Cl, Br, and I) were found to be good candidates for nonlinear performance, and F and Br atoms show a greater potential in improving the molecular NLO response within the static field limit and resonance excitation, respectively. Moreover, the modulation of the photoelectric performance by changing the species of halogen atoms is not accompanied by an unfavourable shift of absorption to longer wavelengths. It is our expectation that (DPATSP-Me)+F- and (DPATSP-Me)+Br- will be prepared and their optical analysis will be implemented in experiment soon.

Acknowledgments This work was supported by the financial supports from the Jiangsu Specially Appointed Professor Program (Grant No. Sujiaoshi [2015]17), the Natural Science Foundation of Jiangsu Province (Grant No. BK20130748), and Major Program for the Natural Science Research of the Higher Education Institutions of Jiangsu Province (Grant No. 18KJA180005).

Supporting Information for Publication: Optimized Cartesian coordinates; Energy levels of FMOs; Excitation energies and oscillator strengths; Crucial FMOs associated with maximum absorption; Calculated response properties; Full citation for references 15, 21, and 55. This material is available free of charge via the Internet at http://pubs.acs.org.

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Extended First Hyperpolarizability of Quasi-Octupolar Molecules by

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