Theoretical Study of Effect of the Number of N,N-dimethyl-4-nitroaniline Units in Novel “Parallel Connection” Chromophores on Its Nonlinear Optical Properties

Design of “parallel connection” chromophores could give a way of acquiring effective chromophores. The semiempirical method ZINDO was employed to study relationship between static first hyperpolarizabilities of “parallel connection” chromophores and the number of parallel nonconjugated N,N-dimethyl-4-nitroaniline (DMNA) units in the chromophore. The results show that the chromophore containing three parallel non-conjugated DMNA units exhibits the highest static first hyperpolarizability, which is 1.8 times that of chromophore DMNA. However, static first hyperpolarizabilities of the chromophores containing four or five DMNA units are very small. The absorption maximum wavelength (λmax) of “parallel connection” chromophores is remarkably shorter (34.9 nm–38.1 nm) than that of 1DMNA. Therefore, the “parallel connection” chromophore containing three DMNA units would be an effective chromophore with a large first hyperpolarizability and a good optical transparency. It could give a useful suggestion for designing effective chromophores containing parallel non-conjugated D-π-A units.


Introduction
Organic and polymeric second-order nonlinear optical (NLO) materials have attracted much attention due to their potential applications in the fields of telecommunication, optical data storage, and optical information processing [1][2][3][4][5][6][7][8].Chromophores always play a key role in design of effective NLO materials.The first hyperpolarizability β of a chromophore increases with increasing length of the conjugated π system and increasing strength of the donor and/or acceptor [9][10][11][12][13].Generally, an increase in the β value is accompanied by a bathochromic shift due to a larger π-conjugated length and/or stronger donor and acceptor ability [9][10][11][12][13].Therefore, there is always a tradeoff between nonlinearity and transparency [14][15][16][17][18][19][20][21][22][23].To resolve this problem, we had designed and synthesized a series of H-typed chromophores with two parallel and nonconjugated D-π-A units [24][25][26][27].The results of hyper-Rayleigh scattering (HRS) and UV-vis spectra show that the first hyperpolarizability (β) values of H-typed chromophores are remarkably increased compared with the corresponding mono-D-π-A unit reference compounds without causing a large shift of the absorption band to longer wavelength [24][25][26][27].It suggests an available way of solving the tradeoff between nonlinearity and transparency in designing NLO chromophores, that is, design of chromophore with parallel and non-conjugated multi-D-π-A units.
Relationship between NLO properties and a π-conjugated length in a "series connection" chromophore is an interesting subject and has been investigated comprehensively in theoretical and experimental areas [9,[28][29][30][31][32].Similarly, it would be very interesting that relationship between the β 0 Scheme 1: Structures of "parallel connection" chromophores containing DMNA units.
of chromophores and the number of parallel non-conjugated D-π-A units in a "parallel connection" chromophore would be investigated.N,N-dimethyl-4-nitroaniline (DMNA) is an effective chromophore and usually is used as a reference chromophore for study of NLO properties of chromophores [33,34].Therefore, a series of chromophores with two or multiple parallel and non-conjugated DMNA units were designed, and their static first hyperpolarizabilities (β 0 ) were given from quantum chemistry calculations for investigating relationship between static first hyperpolarizabilities of "parallel connection" chromophores and the number of parallel non-conjugated DMNA units in the chromophore (Scheme 1).

NLO Properties of "Parallel Connection" Chromophores.
We have reported that the Semi-Empirical method ZINDO would be a suitable method for calculating the first hyperpolarizabilities of "parallel connection" chromophores when electronic acceptors are strong electron-withdrawing group NO 2 [44].The reason could be that interactions between parallel non-conjugated D-π-A units are taken into account when the ZINDO method is used for calculating the first hyperpolarizabilities.Therefore, the semi-empirical method ZINDO was employed to study the effect of the number of DMNA units in a "parallel connection" chromophore on its NLO properties.
The NLO properties of chromophores containing two or multiple parallel and non-conjugated DMNA units were given based on theoretical calculations.The calculated values of these chromophores are shown in Table 1.
Table 1 shows that static first hyperpolarizability of 3DMNA acquired from the methods ZINDO is the highest.Enhancement of β 0 value of 3DMNA is 1.8 times as β 0 value of DMNA.Enhancement of β 0 value of 2DMNA is 0.8 times as β 0 value of DMNA.However, static first hyperpolarizabilities of 4DMNA and 5DMNA are quite small due to interactions between DMNA units.

Relationship between Static First Hyperpolarizabilities of "Parallel Connection" Chromophores and the Number of Paral-
lel Nonconjugated DMNA Units in the Chromophore.Figure 1 shows clearly that β 0 value of chromophore decreases from 24.1 × 10 −30 esu to 19.0 × 10 −30 esu with increasing the number of parallel and non-conjugated DMNA units in the chromophore from 1 to 2. Then β 0 value of the chromophore increases from 19.0 × 10 −30 esu to 44.1 × 10 −30 esu with increasing the number of parallel and non-conjugated DMNA units in the chromophore from 2 to 3. The β 0 value decreases rapidly from 44.1 × 10 −30 esu to −0.1 × 10 −30 esu with increasing the number of DMNA units in the The absorption maximum wavelength.c Blue shift of the absorption maximum wavelength (the values were calculated according to following method: Δλ = λ max of 1DMNA-λ max of "parallel connection" chromophores.).d Enhancement of β 0 of "parallel connection" chromophores compared with that of 1DMNA (the values were calculated according to following method: β 0 of chromophores containing DMNA units/β 0 of 1DMNA).chromophore from 3 to 4. At last, β 0 value of the chromophore increases slightly from −0.1 × 10 −30 esu to 1.1 × 10 −30 esu with increasing the number of parallel and nonconjugated DMNA units in the chromophore from 4 to 5. It shows that β 0 value of the chromophore would decrease when the number of parallel non-conjugated DMNA units in the chromophore increases (a DMNA unit) from an odd to an even.However, β 0 value of the chromophore would increases when the number of parallel non-conjugated DMNA units in the chromophore increases (a DMNA unit) from an even to an odd.
The two-state model ( 1) is usually employed to estimate the first hyperpolarizability of chromophore [37][38][39][40][41][42][43]: where μ eg is the transition dipole moment between the ground state |g and the charge-transfer excited state |e , Δμ eg is the difference in dipole moment, and E eg is the transition energy.ω eg is angular frequency corresponding to the transition between the ground and the first excited state; ω is the angular frequency of incident light.
According to the two-state model, β 0 values depend on the differences of energy between the ground and the first excited states (E eg ), the transition dipole moment between the ground state |g and the charge-transfer excited state |e (μ eg ) and the difference in dipole moment (Δμ eg ).
Figure 2 shows clearly that nitro group and benzene ring in DMNA are coplanar.Two benzene rings and their respective substituted nitro group are noncoplanar in a 2DMNA molecule compared with the structure of 1DMNA due to steric repulsion between two dimethylamino groups and electrostatic repulsion between O25, and O28 atoms in a 2DMNA.
Generally, a HOMO energy level and a LUMO energy level depend on the electron-donating strength of donor and the electron-withdrawing strength of acceptor, respectively [45].From the structure of 2DMNA, the probability of transition from ground to excited state in a DMNA unit containing atom N30 would be the biggest, because the difference between the charge of nitro group containing atoms N26, O27, and O28 and the charge of dimethylamino group containing atom N30 is the biggest.As we know, if π electrons could be delocalized well in a DMNA unit, the difference of energy levels between HOMO of amino group and LUMO of nitro group should be small, and electron distribution should be uneven and further results in a large difference between the charge of nitro group and the charge of dimethylamino group.The transition from ground to excited state would result in increasing the charge of a nitro group containing atoms N26, O27, and O28.The charge of another nitro group containing atoms N23, O24, and O25 would decrease due to electrostatic repulsion between O25 and O28 atoms when π electron is excited.The electrostatic repulsion would result in the benzene ring and their respective substituted nitro group containing atoms N23, O24, and O25 being non-coplanar in a DMNA unit and further reducing dipole moment of the unit at the excited state.Therefore, increase of an excited dipole moment of DMNA unit and decrease of another excited dipole of DMNA unit would slightly decrease Δμ eg and μ eg value of 2DMNA compared with 1DMNA.According to the two-state model [37][38][39][40][41][42][43], the first hyperpolarizability of 2DMNA could be smaller than that of DMNA.
Based on a two-state model, Di Bella et al. [46,47] estimated that the NLO response of hypothetical PNA trimer would have a sharp increase, when three PNA molecules were arranged in the same direction and distance between two adjacent PNA molecules was shorter than 3.0 Å.In the present case, the three DMNA units in a single molecule are nearly arranged in the same direction and the limited distances between two adjacent DMNA units are 2.520 Å (C3-C10) and 2.513 Å (C12-C19), respectively from computational results of 3DMNA.Therefore, it implies that the 3DMNA can exhibit large second-order NLO responses because close contact among three DMNA units in a molecule induces the strong dipole-dipole interaction among three DMNA units.
From the structure of 3DMNA, the probability of transition from ground to excited state in the DMNA unit containing atom N41 would be the biggest, because the difference between the charge of nitro group containing atoms N41, O42, and O43 and the charge of dimethylamino group containing atoms N46 is the biggest.The electrostatic repulsion would further result in the benzene ring and their respective substituted nitro group containing atoms N38, O39, and O40 being non-coplanar in a DMNA unit and further reducing dipole moment at the excited state.However, the charge of a nitro group containing atoms N35, O36, and O37 would increase due to decreasing electrostatic repulsion between O37 and O40 atoms when π electron was excited.The decreasing electrostatic repulsion would enhance coplanarity of the DMNA unit containing atom N35.Therefore, increases of excited dipoles of two DMNA units and decrease of an excited dipole of DMNA unit would increase of Δμ eg and μ eg values of 3DMNA.According to the two-state model [37][38][39][40][41][42][43], 2DMNAcould exhibit a large the first hyperpolarizability.
Similarly, Figure 4 shows clearly that four benzene rings and their respective substituted nitro groups are non-coplanar in a 4DMNA molecule due to steric repulsion between dimethylamino groups and electrostatic repulsion between two adjacent O atoms, such as O57 and O55, O54 and O52, and O51 and O48 atoms.
From the structure of 4DMNA, the probability of transition from ground to excited state in the DMNA unit containing atom N56 would be the biggest.Similarly, increases of excited dipole moments of two DMNA units and decreases of excited dipole moments of two DMNA units would decrease μ eg and Δμ eg values of 4DMNA.According to two-state model, the first hyperpolarizability of 4DMNA would be smaller than that of 1DMNA.Moreover, the first hyperpolarizability values of 4DMNA would depend on interactions among DMNA units in a chromophore.Here the local field corrections due to interactions among DMNA units begin to play an important role in determining the first molecular hyperpolarizability [48][49][50].The interactions among four DMNA units in 4DMNA could result in a small Δμ eg and μ eg value of 4DMNA.
Similarly, Figure 5 shows clearly that five benzene rings and their respective substituted nitro groups are non-coplanar in a 5DMNA molecule due to steric repulsion between dimethylamino groups and electrostatic repulsion between two adjacent O atoms, such as O61 and O63, O64 and O67, O66 and O70, and O69 and O73 atoms.
From the structure of 5DMNA, the probability of transition from ground to excited state in the DMNA unit containing atom N71 would be the biggest.Similarly, increases of excited dipole moments of three DMNA units and decreases of excited dipole moments of two DMNA units would induce a small β 0 value of 5DMNA.Moreover, the first hyperpolarizability values of 5DMNA would depend on interactions among DMNA units in a chromophore.Here the local field corrections due to interactions among DMNA units begin to play an important role in determining the first molecular hyperpolarizability [48][49][50].The interactions among five DMNA units in 5DMNA could result in a small Δμ eg and μ eg value of 5DMNA.

Optical Transparency of "Parallel
Connection" Chromophores.Table 1 shows clearly that the absorption maximum wavelength (λ max ) of "parallel connection" chromophores is remarkably shorter than that of 1DMNA.Blue shift of the absorption maximum wavelength of "parallel connection" chromophores is at the range from 34.9 nm to 38.1 nm compared with 1DMNA.The main reason is that π electrons would be better delocalized in the 1DMNA than those in "parallel connection" chromophores containing two or multi-DMNA units, because nitro group and benzene ring in 1DMNA are coplanar and benzene rings and their respective substituted nitro group are non-coplanar in the "parallel connection" chromophores due to steric repulsion between dimethylamino groups and electrostatic repulsion between two adjacent O atoms.Therefore, the "parallel connection" chromophores containing two or multi DMNA units have shorter λ max than 1DMNA.It implies that these "parallel connection" chromophores would exhibit good optical transparency.It suggests that design of chromophores containing three parallel non-conjugated DMNA units would be an effective strategy for designing NLO chromophores with a large β 0 value and good optical transparency.

Conclusion
The structure geometries of five chromophores were optimized by the density functional theory (DFT) calculations using Gaussian03 software at the B3LYP/6-31G(d) level.Then, the Semi-Empirical method ZINDO was employed to study relationship between static first hyperpolarizabilities of "parallel connection" chromophores and the number of parallel non-conjugated N,N-dimethyl-4-nitroaniline (DMNA) units in the chromophore.The results show that the chromophore containing three parallel non-conjugated DMNA units exhibits the highest static first hyperpolarizability, which is 1.8 times that of chromophore 1DMNA.However, static first hyperpolarizabilities of the chromophores containing four or five DMNA units are very small.The β 0 value of the chromophore would decrease when the number of parallel non-conjugated DMNA units in the chromophore increases (a DMNA unit) from an odd to an even.However, β 0 value of the chromophore would increase when the number of parallel non-conjugated DMNA units in the chromophore increases (a DMNA unit) from an even to an odd.The absorption maximum wavelength (λ max ) of "parallel connection" chromophores is remarkably shorter (34.9 nm-38.1 nm) than that of 1DMNA.It implies that these "parallel connection" chromophores would exhibit good optical transparency.Therefore, the "parallel connection" chromophore containing three DMNA units would be an effective chromophore with a large first hyperpolarizability and a good optical transparency.It could give a useful suggestion for designing effective chromophores containing parallel non-conjugated D-π-A units.
The number of DMNA units in a chromophore

Figure 1 :
Figure 1: Relationship between static first hyperpolarizabilities of "parallel connection" chromophores and the number of DMNA units in the chromophore.

HFigure 2 :
Figure 2: The structures of 1DMNA and 2DMNA optimized by DFT and atomic charges (unit: atomic unit) of N and O atoms (the numbers in brackets are charges of nitro and dimethylamino groups).

Figure 3 :
Figure 3: The structures of 3DMNA optimized by DFT and atomic charges (unit: atomic unit) of N and O atoms (the numbers in brackets are charges of nitro and dimethylamino groups).

Figure 4 :
Figure 4: The structures of 4DMNA optimized by DFT and atomic charges (unit: atomic unit) of N and O atoms (the numbers in brackets are charges of nitro and dimethylamino groups).

Figure 5 :
Figure 5: The structures of 5DMNA optimized by DFT and atomic charges (unit: atomic unit) of N and O atoms (the numbers in brackets are charges of nitro and dimethylamino groups).

Table 1 :
Linear and nonlinear properties of the designed "parallel connection" chromophores are calculated by ZINDO.
a Dipole moment at ground state.b