Density Functional Theory Study on Subtriazaporphyrin Derivatives

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Density Functional Theory Study on Subtriazaporphyrin Derivatives: Dipolar/ Octupolar Contribution to the Second-Order Nonlinear Optical Activity Lijuan Zhang, Dongdong Qi, Luyang Zhao, Chao Chen, Yongzhong Bian, and Wenjun Li J. Phys. Chem. A, Just Accepted Manuscript • Publication Date (Web): 28 Sep 2012 Downloaded from http://pubs.acs.org on September 29, 2012

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The Journal of Physical Chemistry

Density Functional Theory Study on Subtriazaporphyrin Derivatives: Dipolar/Octupolar Contribution to the Second-Order Nonlinear Optical Activity

Lijuan Zhang, Dongdong Qi, Luyang Zhao, Chao Chen, Yongzhong Bian,* and Wenjun Li*

Beijing Key Laboratory for Science and Application of Functional Molecular and Crystalline Materials, Department of Chemistry, University of Science and Technology Beijing, Beijing 100083, China

* Corresponding author. Tel.: +86 10 6233 4509; Fax: +86 10 6233 2462. E-mail address: [email protected] (YB), [email protected] (WL)

ACS Paragon Plus Environment


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Abstract: Density functional theory calculations have been carried out on the subtriazaporphyrin

skeletons,

an

excellent

prototype

for

investigating

the

dipolar/octupolar contribution to the second-order nonlinear optical (2nd-NLO) activity, revealing the size effect and clarifying the nature of the limit when expanding the conjugated system is employed to improve the hyper-Rayleigh scattering response coefficient (βHRS). The octupolar and dipolar contributions are theoretically separated, rendering it possible to control the dipolar/octupolar 2nd-NLO contribution ratio by changing the number and orientation of the peripheral fused benzene moieties. In addition, both the dispersion and solvent effect were also revealed to lead to the enhancement of βHRS.

Keywords: Second-order nonlinear optical properties; Subtriazaporphyrin; Size dependence; Dispersion effect; Solvent effect; Dipolar/octupolar contribution.


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1. Introduction

In the past two decades, there has been an increasing interest to searching for new organic nonlinear materials, in particular the second-order optical (2nd-NLO) materials with potential applications in ultra-fast modulators and switches, laser frequency conversion devices, surface and interface characterization tools, and biological and chemical sensors.1-5 The most intensively studied 2nd-NLO chromophores are donor-acceptor-substituted dipolar molecules.6-11 However, these dipolar molecules tend to align in an anti-parallel fashion and thus more easily form centrosymmetric bulk materials, leading to no or very weak 2nd-NLO response.12,13 More recently, multipolar, especially octupolar molecules have been developed as alternative NLO chromophores since these molecules do not possess a permanent dipole moment and therefore can easily form noncentrosymmetric bulk materials as required to obtain a large macroscopic 2nd-NLO response.12-18 Subtriazaporphyrin (SubTAP) and subphthalocyanine (SubPc) are cone-shaped macrocyclic compounds consisting of three pyrrole or isoindole units. Due to their distinct structural, optical, and electronic properties, the SubPc derivatives have attracted much research interests.19-31 In 2010, the structure, electronic distribution, molecular orbitals, infrared (IR) spectra, and electronic absorption spectra of a full series of low-symmetrical fluoroboron-subtriazaporphyrin (FB-SubTAP) derivatives were systematically investigated based on density functional theory (DFT) and time-dependent density functional theory (TDDFT) calculation.27a In addition, as a



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typical octupolar molecule with 14-π electron aromatic structure, the 2nd-NLO activities of SubPc and its analogues have been experimentally and theoretically investigated.20,28-31 For example, Torres et al. studied the NLO response of SubPcs with electron-donating or -accepting substituents at the peripheral positions.29 Theoretical studies over SubPcs and subnaphthalocyanines30 based on semiempirical calculations and trinitrosubphthalocyanine isomers by sum over states (SOS) and finite field methods were also carried out.31 However, these studies just focus on the radially symmetric SubPc derivatives and the effect of different peripheral push-pull moieties on the hyperpolarizabilities. Systematic investigation for evaluating the NLO properties of a full series of SubTAP and SubPc derivatives, especially the benzo-fused low-symmetrical analogues, appears not yet conducted thus far. Actually, such a series of low-symmetrical SubPc derivatives, whose size and symmetry can be successfully tuned through fusing different number of benzene moieties, are expected to be one of the excellent prototype systems for assessing the dipolar/octupolar contribution to the first hyperpolarizabilities. As part of our continuous efforts towards theoretical studies over the benzo-fused low-symmetrical SubTAP derivatives,27 in the present paper, the DFT and TDDFT calculations were conducted on

both

the

static

and

dynamic

hyperpolarizabilities

of

a

series

of

chloroboron-subthriazaporphrin derivatives (ClB-SubTAP) in vacuum and chloroform (Chart 1). Choosing chloro-substituted derivatives instead of FB-SubTAPs is due to the fact that boron trichloride has been usually employed for preparing subphthalocyanines.20


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2. Methodology and Computational Details.

2.1 Density functional theory for hyper-Rayleigh scattering response coefficient calculation. Champagne and co-workers32-39 developed an effective method to evaluate the hyper-Rayleigh scattering (HRS) response β HRS ( −2ω ; ω , ω ) , which is described as:

(

2 2 β HRS (−2ω ; ω , ω ) = β ZZZ + β ZXX

where

2 β ZZZ

and

2 β ZXX

12

)

(1)

are the orientational average of the molecular β tensor

components, which can be calculated using the following equations: 2 β ZZZ =

1 x,y ,z 2 6 x,y ,z 9 x,y ,z 2 3 x,y ,z 2 x,y,z 2 β + β β + β + β β + ∑ ζζζ 35 ζ∑≠η ζζζ ζηη 35 ζ∑≠η ηζζ 35 ζ ∑ ∑ βζηξ (2a) ηζζ ηξξ 7 ζ 35 ζ ≠η ≠ξ ≠η ≠ξ

2 βZXX =

1 x,y ,z 2 2 x,y ,z 11 x,y ,z 2 1 x,y,z 4 x,y ,z 2 β − β β β − β β + + ∑ ζζζ 105 ζ∑≠η ζζζ ζηη 105 ζ∑≠η ηζζ 105 ζ ∑ ∑ βζηξ ηζζ ηξξ 35 ζ 105 ζ ≠η ≠ξ ≠η ≠ξ (2b)

In addition, the molecular geometric information is given by the depolarization ratio 2 (DR), which is expressed by DR = β ZZZ

2 β ZXX .

To further clarify the nature of the symmetric Rank-3 β tensor, can be decomposed as the sum of the dipolar (βJ=1) and octupolar (βJ=3) tensorial components,12a,38 which are expressed as:

β HRS = 2

(β )=

β J =1 =

2 HRS

10 10 2 β J =1 + β J =3 45 105

2

3 x ,y ,z 2 6 x ,y ,z 3 x ,y ,z 2 3 x ,y ,z βζζζ + ∑ β ζζζ β ζηη + ∑ βηζζ + ∑ βηζζ βηξξ ∑ 5 ζ 5 ζ ≠η 5 ζ ≠η 5 ζ ≠η ≠ξ ,


(3) (4a)


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2

β J =3 =

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x ,y ,z 2 x ,y ,z 2 6 x ,y ,z 12 x ,y ,z 2 3 x ,y ,z 2 . (4b) β ζζζ − ∑ βζζζ β ζηη + ∑ βηζζ − ∑ βηζζ βηξξ + ∑ β ζηξ ∑ 5 ζ 5 ζ ≠η 5 ζ ≠η 5 ζ ≠η ≠ξ ζ ≠η ≠ξ

And then the nonlinear anisotropy parameter ρ=|βJ=3|/|βJ=1| is employed to evaluate the ratio of the octupolar [ΦJ=3 = ρ/(1+ρ)] and dipolar [ΦJ=1 = 1/(1+ρ)] contribution to the hyperpolarizability tensor. Furthermore, assuming a general elliptically polarized incident light propagating along the X direction, the intensity of the harmonic light scattered at 90° along the Y direction and vertically (V) polarized along the Z axis are given by the Bersohn’s expression:38,40 2

2ω 2 2 IΨV ∝ β ZXX cos 4 ψ+ β ZZZ sin 4 ψ+sin 2 ψcos 2 ψ× ( β ZXZ +β ZZX ) -2β ZZZ β ZXX

where the orientational averages

( β ZXZ +β ZZX )

2

( β ZXZ +β ZZX )

2

− 2β ZZZ β ZXX

(5)

is expressed as:

− 2β ZZZ β ZXX

2 2 =7 β ZXX − β ZZZ

=

2 x ,y ,z 2 32 x ,y ,z 10 x ,y ,z 2 16 x ,y ,z 22 x ,y ,z 2 β − β β + β − β β + ∑ ζζζ 105 ζ∑≠η ζζζ ζηη 21 ζ∑≠η ηζζ 105 ζ ∑ ∑ βζηξ ηζζ ηξξ 35 ζ 105 ζ ≠η ≠ξ ≠η ≠ξ

(6)

Moreover, the general theory for second-order nonlinear optical phenomena has been summarized simply in the Supporting Information.

2.2 Computational Details. Density functional theory (DFT) and time dependent density functional theory (TD-DFT), owing to their excellent performance-to-cost ratio, have been widely used to predict various molecular physico-chemical properties.41-46 However, as early as in 2000, Champagne and co-workers pointed out that conventional DFT methods present serious drawbacks in evaluating the linear and nonlinear electric field responses of the


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push-pull π-conjugated systems.47 Fortunately, the range separated hybrid functional CAM-B3LYP, which combines the hybrid qualities of B3LYP and the long-rang correction,48 has been proposed specifically to overcome the limitations of the conventional density functional according to Yanai49 and therefore become a good candidate for the evaluation of the NLO properties of molecular materials.50-56 In addition, it has been proved that CAM-B3LYP significantly improves the agreement between the calculated and experimental structural results in comparison with the most popular functional B3LYP. For details, please see the section of Validity of the

Functional CAM-B3LYP for Geometry Optimization in Supporting Information. In the present work, the optimized molecular structures with all real frequencies were obtained in vacuum at the DFT level of approximation using the CAM-B3LYP functional. A mixed basis set, including 6-31+G(d) for Cl and 6-31G(d) for all other atoms, was used for geometry optimization. On the basis of the above optimized geometries, the static (λ=∞) and dynamic (λ=1064, 1340, 1460, and 1907 nm) first hyperpolarizabilities were evaluated at the CAM-B3LYP/6-31+G(d) theory level. Using solvent chloroform20,29 with the polarizable continuum model within the integral equation formalism (IEF-PCM), solvent effect combined with dispersion effect at λ=1340 nm20,29 was calculated at the same level to simulate the real HRS system. All the calculations were carried out using the Gaussian 09 program housed at Shandong University High Performance Computing Center.57 In addition, these calculation results were analyzed and treated using NLO Calculator program (version 0.2).58



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3. Results and Discussion

3.1. Geometrical and Electronic Structure. The molecular structures of a full series of FB-SubTAP derivatives have been carefully described in our previous work based on the level of B3LYP/6-31G(d).27 As can be found in Table S2 (Supporting Information), although the longer B-Cl and B-C bond owing to the lowered electronegativity of Cl compared with F, the ClB-SubTAP derivatives (Chart 1) show similar geometrical structures to their FB-SubTAP counterparts. As a result, detailed structural analysis of ClB-SubTAP seems not necessary in the present manuscript. According to the frontier molecular orbital analysis in our previous paper,27 the SubTAP macrocycle is a uniform conjugated system while the peripheral fused benzene rings further expand the π electron motion space. It is also worth noting that the absorption spectra of the FB-SubTAP series reported previously27a will be used as the linear optical description in the following discussions.

3.2. Ideal Situation with Vacuum Static Hyperpolarizability: Molecular Size Dependence. In this section, the size dependence of βHRS of the full series of ClB-SubTAP derivatives based on their vacuum static hyperpolarizabilities will be explored (Figure 1). In general, the static βHRS has an uptrend with increasing number of the fused


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benzene moieties. In particular, increasing the number (N) of benzene moieties at one direction while keeping those unchanged at the two other directions (M) also reveals an uptrend of βHRS. For the series of M = 0, the βHRS increases with increasing the number of N in the order of 000 (630 au) < 001 (783 au) ≈ 002 (811 au) < 003 (1552 au), revealing an accelerated trend upward. In contrast, for the series of M = 1, 2, and 3, βHRS first increases and then decreases along with increasing the number of benzene moieties, revealing the limit when expanding the conjugated system is employed to improve the hyper-Rayleigh scattering response coefficient. On the other hand, as depicted by Figure 1b, βHRS value by no means increases endlessly along with Ntot. For the series of N = 0 and 1, the βHRS saturates around 110 and 221. The limits as mentioned above come from the same source as follows. According to the previously-revealed results,4,51,59 the NLO response is to a large extent caused by the π-electron delocalization and transfer. Therefore, expansion of π-conjugated systems could increase the number of the mobile electrons and enhance the NLO response. While in the case where the conjugated part is large enough with enough mobile electrons, further expanding the conjugated systems will over-lengthen the electron-transfer pathway, which holds off further improvement of the β value. In addition, excessive conjugation will limit electrons to achieve non-stationary state due to the increased binding energy. Consequently, excessive conjugation will do harm for enhancing the NLO response.

3.3. Vacuum Dynamic Hyperpolarizability: Dispersion Correction.



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The dynamic perturbations were added in order to explore the effect of frequency dispersion. For comparison, four fundamental optical wavelengths with λ = 1907, 1460, 1340, and 1064 nm used in NLO measurements were employed to reveal the dispersion correction contribution to the NLO response in these molecules (see Table S3 in Supporting Information). The vacuum dynamic hyperpolarizabilities of each molecule versus its static value at these wavelengths (except 1064 nm) are plotted in Figure 2a. As can be seen, a good linear relationship is obtained at fundamental wavelength of λ = 1907 nm, with the slope of 1.78, revealing that the frequency dispersion have consistent influence to this class of molecules. In addition, this slope also indicates the correcting factor of the frequency dispersion at λ = 1907 nm for the present species. However, the curves of λ = 1460 and 1340 nm display an accelerating trend rather than linear relationship, revealing a weak resonance effect. Pronounced resonance encountered at λ = 1064 nm leads to numerical instabilities, for which the linear relationship was destroyed completely (Figure 2b). From Equations (S1) and (S2) in Supporting Information, there are two resonance frequencies at ω0 and ω0/2 in the case of SHG. According to the previous result,27a the electronic absorption bands of the present ClB-SubTAP systems should appear at the range of 400-700 nm. As a consequence, one of the resonance regions is expected at the range of 800-1400 nm. It is clear that the closer the foundational wavelength to this region, the larger value β owes. As shown in Figure S1 (Supporting Information), the βHRS increases along with increasing the optical frequency, ie,

βHRS(∞) < βHRS(1907 nm) < βHRS(1460 nm) < βHRS(1340 nm) < βHRS(1064 nm).


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In particular, the predicted resonance region of 000 is around 800 nm, resulting in no resonant value found at the above-mentioned optical frequencies including 1907, 1460, 1340, and 1064 nm. However, due to the systematic red-shift of the lowest-energy band of SubTAP derivatives along with increasing Ntot,27a the resonance region also red-shifts along with increasing the number of benzene moieties. At the functional wavelength of λ = 1064 nm, the obvious resonance effect starts emerging from Ntot = 4. Therefore, the frequency dispersion factor at a definite functional wavelength λ, β HRS (λ ) / β HRS (λ∞ ) , obtained for Ntot ≤ 4 at 1064 nm is somewhat larger than that at 1460 and 1340 nm. However, for Ntot > 4, the value

β HRS (1064nm) / β HRS (λ∞ ) increases considerably, which is significantly larger than β HRS (1460nm) / β HRS (λ∞ ) and β HRS (1340nm) / β HRS (λ∞ ) . It is worth noting that at the functional wavelength of λ = 1907 nm, even increasing the fused benzene number Ntot to 9, the β HRS (1907 nm) / β HRS (λ∞ ) also remains unchanged since the λ = 1907 nm is far from the resonance region, i.e. off-resonance.

3.4. Approximation to Real Hyper-Rayleigh Scattering System: Dipole/Octupole Contribution Analysis. In order to simulate the real HRS system, dispersion effect with λ = 1340 nm and solvent effect (chloroform) are taken into account. As shown in Figure 3 and Table S4 (Supporting Information), a comparison of the dynamic βHRS (λ = 1340 nm) obtained in vacuum and in chloroform reveals that the solvent effect significantly enhances the HRS hyperpolarizabilities of the SubTAP derivatives quantified by a solvent effect



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Sol Vac factor ( β HRS / β HRS ) ranging from 1.54 for 220 to 4.54 for 333, which is in agreement

with the previous investgations.33,60-62 The dynamic βHRS (λ = 1340 nm) in chloroform increases even more rapidly than in vacuum with increasing number Ntot (Figure 3a). In order to clarify this increasing degree, the βHRS in chloroform of each molecule versus its value in vacuum at λ = 1340 nm is plotted in Figure 3b. As visualized, the Sol Vac slope of β HRS (1340nm) / β HRS (1340nm) is positively correlated to βHRS in vacuum,

indicating the significant solvent effect on the molecules with large vacuum βHRS value (or Ntot). In addition, since the DRsol / DRvac ratio ranges from 0.75 to 1.36 for dynamic DR (λ = 1340), the solvent chloroform has little effect on DR (see Table S4 in Supporting Information). In order to compare the relative magnitudes of the octupolar and dipolar components of the 2nd-NLO response for molecular materials, the β tensor is decomposed into the βJ=1 (dipolar) and βJ=3 (octupolar) components. The DR (Figure 4a) as well as the octupolar [Φ (βJ=3)] and dipolar [Φ (βJ=1)] contributions (Figure 4b) to the 2nd-NLO response with respect to ρ is displayed to provide a quantitative classification of the systems studied in term of their more or less pronounced octupolar versus dipolar character.63 As can be seen, most of these selected molecules fall in the area of right of ρ = 1 axis except 300, indicating that most of them correspond to more pronounced octupolar character. As shown in Figure 4, the DR value decreases along with increasing ρ from 7.64 for 300 to 1.50 for 111, covering the wide anisotropy factor range from 0.36 to 34.6. In particular, 111 displays almost pure octupolar character. In all the cases, the octupolar contribution gradually


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increases in the order: 300 < 330 < 220 < 333 < 311 < 200 < 332 < 331 < 322 < 110

Density Functional Theory Study on Subtriazaporphyrin Derivatives

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