A comparative analysis of the optical and nonlinear optical properties of cross-shaped chromophores: Quantum chemical approach

Accepted Manuscript Title: A Comparative Analysis of the Optical and Nonlinear Optical Properties of Cross-shaped Chromophores: Quantum Chemical Approach Authors: Shabbir Muhammad, Aijaz Rasool Chaudhry, Abdullah G. Al-Sehemi PII: DOI: Reference:

S0030-4026(17)31004-5 http://dx.doi.org/10.1016/j.ijleo.2017.08.104 IJLEO 59567

To appear in: Received date: Accepted date:

7-5-2017 18-8-2017

Please cite this article as: Shabbir Muhammad, Aijaz Rasool Chaudhry, Abdullah G.Al-Sehemi, A Comparative Analysis of the Optical and Nonlinear Optical Properties of Cross-shaped Chromophores: Quantum Chemical Approach, Optik - International Journal for Light and Electron Opticshttp://dx.doi.org/10.1016/j.ijleo.2017.08.104 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

A Comparative Analysis of the Optical and Nonlinear Optical Properties of Cross-shaped Chromophores: Quantum Chemical Approach Shabbir Muhammad*,a,b Aijaz Rasool Chaudhry, a,b Abdullah G. Al-Sehemi b,c a

Department of Physics, College of Science, King Khalid University, Abha 61413,

P.O. Box 9004, Saudi Arabia. b

Research Center for Advanced Materials Science (RCAMS), King Khalid

University, Abha 61413, P.O. Box 9004, Saudi Arabia dDepartment

of Chemistry College of Science, King Khalid University, Abha 61413,

P.O. Box 9004, Saudi Arabia Corresponding authors: [email protected] Abstract Using the first principles calculations, optical and nonlinear optical (NLO) properties are calculated for three crossed shaped chromophores having alike benzoic acid π-conjugated side chains but different central cores i.e. phenyl in 1-Ph, pyrazino[2,3-g]quinoxaline in 2-PyQ and tetrathiafulvalene in 3-TTF. Molecular geometries are effectively reproduced and compared to their experimental crystallographic structures. The third-order NLO polarizability is calculated with three different DFT functionals including M06, PBE0 and B3LYP and using 6-311G* basis set.

Our calculated third-order NLO polarizability amplitudes and their

comparison to those of standard and contemporary NLO chromophores indicate that all the three compounds have remarkably larger NLO response. The γ amplitudes of compounds 1-Ph, 2-PyQ and 3-TTF are 429.6×10-36, 1871.7×10-36 and 967.5×10-36 esu, respectively, at M06/6-311G* level of theory. Interestingly, in present investigation the γ amplitude of the best-studied NLO compound 2-PyQ is 257 times larger than that of para nitroaniline (7.279×10-36 esu) at the same M06/6-311G* level

of theory. The TD-DFT calculations are used to trace the origin of larger NLO response. Additionally, total and partial densities of states are calculated to compare the effect and contributions of central cores in all adopted compounds. Thus, the present investigation will not only highlight the NLO potential of entitled compounds but also provoke the interest of experimentalists to effectively modify the central cores for such other applications. Keywords:

Nonlinear

Optical;

Cross-shaped

chromophores;

Quinoxaline;

Tetrathiafulvalene; Third-order NLO polarizability 1. Introduction The progress of modern time hi-tech society profoundly depends on the discovery of novel optoelectronic materials. Over the last few decades, the optoelectronic materials got significant importance in field of materials science and chemistry. Many classes of materials are reported for optoelectronic for the past several years.[1] Every class of materials has some pros and cones to use it in optoelectronic applications. Nevertheless, organic class of materials emerged as one of the most prominent class of materials having potential for many advanced optical and nonlinear optical (NLO) applications.[2] Organic class of materials is being used to design efficient organic-light emitting diodes (OLEDs),[3] which is an important innovation in modern display technology. Similarly, organic materials are also frontrunner candidates for solar cell [4] applications, as thin film transistors[5] as well as for sensing and photoluminescence device applications.[6] Furthermore, many organic compounds have shown efficient NLO properties as compared to the other classes of materials.[7, 8] Several organic NLO materials are found not only cost effective but also easy for device fabrication with larger surface area deposition from solution to substrate at room temperature.[2] Another important

factor for the dominance of organic class of materials is their structural diversity having many functional groups with interesting electronic, optical and NLO properties. Over the past several years, many organic compounds have been studied for their efficiency as NLO materials. Among these studied materials, some famous classes are chalcones,[9-12] thiazoles,[13] pyridines[14, 15] and other similar heterocyclic ring containing compounds.[16] While on the other hand, among NLO response properties, the third-order polarizability is very important property.[17] The third-order polarizability is also considered as the signature of two-photon absorption (TPA) process.[18] In present investigation, we have selected three cross-shaped chromophores (see Figure 1) to explore their potential as efficient third-order NLO materials. In previous studies, these three compounds including 1-Ph, 2-PyQ and 3-TTF are explicitly synthesized and structurally investigated using single crystal techniques.[19, 20] To the best of our knowledge, there is no experimental and/or computational investigation focusing the nonlinear optical response (third-order polarizability) properties of the abovementioned compounds. Interestingly, in all three compounds, the central moiety is different while the rest of the skeleton is similar to each other, which results in the possibility of a comparative analysis and effect of central heteroatom rings. Thus, we plan to perform a comparative analysis of different optical and nonlinear optical properties to elucidate their structure-NLO property relationship, which might be strongly correlated to the central moiety of each compound.

Computational Details Gaussian 09 suit of programs is used for all calculations. In present study, we have guessed the performance of three different functionals including B3LYP, PBE0, and

more recently developed M06 for optimization of molecular geometries. All the methods show a reasonable agreement with experimental crystallographic data (see Table S1 - Table S3 in supporting information). For a molecule, it is not always true that a method reproducing geometrical parameters can also predict correctly its NLO properties. Similarly, the same three DFT functionals including B3LYP, PBE0, and M06 are also used to calculated third-order polarizability by 6-311G* basis set (see Table 1). From the Table 1, it can be seen that for all compounds 1-Ph, 2-PyQ and 3TTF, there is no catastrophic deviations among γ amplitudes as calculated with different DFT functionals including B3LYP, PBE0 and M06. As usual, the B3LYP has slightly over estimated the γ amplitudes as compared to those of PBE0 and M06 methods. For instance, the γ amplitudes of compound 1-Ph as calculated with PBE0 and M06 functionals are 13% and 16% lower as compared to that of B3LYP functional. The M06 is recently developed functional and it has given satisfactory performance in some recent theoretical investigations.[21] In present investigation, based on our test calculations (Table 1) as well as some previous quantum chemical reports, we preferred the M06 functional for other calculations (transition energy and DOS etc.) besides geometry and NLO response properties. For instance, the TD-M06 has been used to calculate the absorption spectra of compounds 1-Ph, 2-PyQ and 3TTF. A well-known finite field (FF) method is used to calculate the second hyperpolarizability. The FF method originally developed Kurtz et al.[22] is often used not only by theoreticians but also many experimentalists to assess the NLO properties of several organic of materials.[23, 24] The FF method has provided very consistent results with experiments as well as with other theoretical approaches i.e. Timedependent-sum over states (TD-SOS) and response methodologies[25] A static

electric field (F) is applied in FF approach and the energy (E) of the molecule is given by following Eq. 1

1

1

𝐸 = 𝐸 (0) − 𝜇1 𝐹1 − 2 𝛼𝑖𝑗 𝐹𝑖 𝐹𝑗 − 6 𝛽𝑖𝑗𝑘 𝐹𝑖 𝐹𝑗 𝐹𝑘 − 24 𝛾𝑖𝑗𝑘𝑙 𝐹𝑖 𝐹𝑗 𝐹𝑘 𝐹𝑙 − ⋯

(1)

In the absence of an electronic field, the total energy of molecule is represented by E(0),  is the dipole moment,  is the polarizability,



hyperpolarizabilities, respectively, while

label the

x, y and z

and  are the first and second i, j an d k

components,

respectively. It can be seen from above equation that differentiating E with respect to F obtains the μ, α, β, and γ values. Here β, and γ values represent the origin of secondorder (χ2) and third-order (χ3) nonlinear optical (NLO) susceptibilities, respectively. The third-order polarizability are calculated using following relations as defined under:

〈𝛾〉 =

1 15

∑𝑖𝑗=𝑥,𝑦,𝑧(𝛾𝑖𝑖𝑗𝑗 + 𝛾𝑖𝑗𝑖𝑗 + 𝛾𝑖𝑗𝑗𝑖 ).

(2)

Assuming Kleinmann symmetry, these are reduced to six components at least for static second hyperpolarizability. 〈𝛾〉 =

1 5

(𝛾𝑥𝑥𝑥𝑥 + 𝛾𝑦𝑦𝑦𝑦 + 𝛾𝑧𝑧𝑧𝑧 + 2(𝛾𝑥𝑥𝑦𝑦 + 𝛾𝑥𝑥𝑧𝑧 + 𝛾𝑦𝑦𝑧𝑧 )).

(3)

The components of γ amplitude in terms of Cartesian coordinates have been calculated using GAUSSIAN 09 and are collected in Table 1. 3. Results and Discussion 3.1. Molecular Geometries The optimized molecular geometries for compounds 1-Ph, 2-PyQ and 3-TTF are compared with their experimentally reported crystallographic data as provided in Tables S1-S3 according to Figures S1-S3, respectively. There is a reasonable agreement among the important optimized geometrical parameters and experimental crystallographic data as calculated with different DFT methods including B3LYP,

M06 and PBE0 (see Table S1-S3 of supporting information). The most important geometrical parameters are the planarity of benzoic acid groups as compared to their respective central core in all compounds. For instance, in compounds 1-Ph, 2-PyQ and 3-TTF the torsional angles among benzoic acid groups and their respective cores (as shown in red glow in Figure 1.) are -51.87o, -38.89o and -49.16o, respectively, at B3LYP/6-311G* level of theory. The planarity of structures for the entitled compounds increases as 2-PyQ > 3-TTF > 1-Ph based on the above reported torsion angles. It can be also seen that in each compound, its torsion angles among all four benzoic acid groups are somewhat similar having near C2 symmetry in optimized structures. A further detailed discussion about molecular geometries, variations among bond lengths and similar other trends in geometrical parameters of all compounds can be seen in supporting information. 3.2. Third-order Nonlinear Polarizability The third-order NLO polarizability (γ) along with its individual components are collected in Table 1 for compounds 1-Ph, 2-PyQ and 3-TTF. For every compound, there are three types of γ amplitudes as calculated with M06, PBE0 and B3LYP functionals. A comparative analysis about performance of each individual functional is seen from Figure 2 where all three methods give reasonable agreement with each other. Here in, we will choose γ amplitudes calculated with M06 method for all three compounds and compared them with each other as well as with similar type of other NLO compounds. The γ amplitudes of compounds 1-Ph, 2-PyQ and 3-TTF are 429.6×10-36, 1871.7×10-36 and 967.5×10-36 esu, respectively, at M06/6-311G* level of theory. The γ amplitudes of compounds 2-PyQ and 3-TTF, are 4 and 2 times larger than that of compounds 1-Ph at M06/6-311G* level of theory (see Figure 2). Similarly, a comparison of γ amplitudes of all compounds has been made with γ

amplitudes of para-nitroaniline (PNA), which is a prototype NLO molecule and used a reference in many previous investigations. To make a fair comparison among γ amplitudes of all compounds and PNA, we have calculated the γ amplitudes of PNA at the same three levels of theory as those for compounds 1-Ph, 2-PyQ and 3-TTF (see Table 1 for PNA<γ>). Interestingly, the γ amplitudes of compounds 1-Ph, 2-PyQ and 3-TT are 59 times, 257 times and 133 times larger than that of PNA (7.279×10-36 esu) at the same M06/6-311G* level of theory. Furthermore, it will be also fascinating to compare the γ amplitudes of compounds 1-Ph, 2-PyQ and 3-TTF with similar NLO molecules as reported in some recent investigation, which will highlight the merit of figure for above entitled molecules among contemporary realm of NLO field. A remarkably enhanced NLO response is achieved in present calculations as compared to those of contemporary NLO molecules. For instance, the best studied beryllium–hydrocarbon complex has 139.30×10−36 esu at PBE0/6-311++G** level of theory,[28] and conjugated TTF–quinones showed 4.13×10−36 and 4.66×10−36 esu at TDHF/6311+G** level of theory.[29] Similarly, 3-acetyl-6-bromocoumarin[30] and 6aminoquinoline (6AQ) [31] molecules showed 22.34×10−36 esu and 39.30×10−36 esu at CAM-B3LYP/6-311+G* and B3LYP/6-311++G** levels of theory, respectively. For third-order nonlinear polarizabilities, we have also calculated their average thirdorder nonlinear polarizabilities <γ> and frequency dependent dynamic third-order polarizabilities related with dc-Kerr effect γ(−ω;ω,0,0)[26] and EFISHG process γ(−2ω;ω,ω,0)[27]. The details about these processes at microscopic response level can be found from the given references. [26] A careful analysis of Table 1 shows that at 1907 nm the dynamic third-order nonlinear polarizabilities for γ(−ω;ω,0,0) process are 351.4×10−36, 1577.91×10−36 and 1012×10−36 esu for compounds 1-Ph, 2-PyQ and

3-TTF, respectively, at M06/6-311G* level of theory. Similarly, for EFISHG process γ(−2ω;ω,ω,0), the dynamic third-order nonlinear polarizabilities are 351.1×10−36, 1716.8×10−36 and 1285×10−36 esu for compounds 1-Ph, 2-PyQ and 3-TTF,

respectively, at M06/6-311G* level of theory. These dynamic third-order nonlinear polarizabilities are important parameters to check the real time application of NLO compounds and can be practically realized in experiments. 3.3. TD-DFT Study and Origin of NLO response A well-known perturbative formula for static longitudinal γL values is usually used to comprehend the origin of third-order NLO response. According to perturbation theory, the static electronic g expression of symmetric molecules only contains type-II (negative) and type-III-2 terms (positive), according to Equations (4–6)[32]

𝛾 = 𝛾 𝐼𝐼 + 𝛾 𝐼𝐼𝐼−2 𝛾 = −4 𝛾

𝐼𝐼𝐼−2

(𝜇𝑔,𝑒1 )

(4)

4

(5)

3 𝐸𝑒1,𝑔 2

=4

2

(𝜇𝑔,𝑒1 ) (𝜇𝑒1,𝑒2 )

(6)

2

(𝐸𝑒1,𝑔 ) 𝐸𝑒2,𝑔

where E is transition energy of crucial excited state, μg,e1 represents ground to excited state transition electric dipole moments. It is important to mention that above expression is a rough estimation to guess the quantitative role of spectroscopic parameters in tuning the γ amplitude. Nevertheless, this perturbative approximation is broadly applied in

theory and experiments

to

explain the changes

in

hyperpolarizabilities (β and γ) using spectroscopic parameters of several donoracceptor types of molecules.[33, 34] In our present investigation, we have used TD-

M06/6-311G* level of theory to calculate the spectroscopic parameters for compounds 1-Ph, 2-PyQ and 3-TTF. As seen from Equations (5) and (6), γII and γIII–2 are composed of the products of transition moments (μg,e1) in the numerator and those of excitation energies (Ee1,g) in the denominator, which signifies that any chemical system with lower transition energy and larger transition moments is expected to have larger γ amplitudes. The calculated values of μg,e1 and E are collected in Table 2. A careful analysis of Table 2 shows that the E for 2-PyQ is slightly lower and higher from compounds 1-Ph and 3-TTF, respectively. Interestingly, the ground to excited state transition electric dipole moments of μg,e1 of compound 2-PyQ is about ~2 times and ~17 times larger than those of compounds 1-Ph, and 3-TTF, respectively, which may have caused a remarkably larger γzzzz amplitude of 7141×10−36 esu for compound 2-PyQ as compared to those of 937.2×10−36 and 1844×10−36 esu for compounds 1-Ph and 3-TTF, respectively, at M06/6-311G* level of theory (see Table 1 for individual components). 3.4. Density of States The contributions of DOS have been calculated for the individual parts in the form of their total partial density of states (PDOS) as shown in Figure 3. We defined two fragments for each compound i.e. the fragment of central rings that contains the central cores and the fragment for side chain, which comprises of the benzoic acid side chains. Each specific fragment represents its contribution to the total density of states (TDOS) of the whole molecule as shown in the Figure 3 with different graphical lines. As shown in Figure 3, for compounds 2-PyQ and 3-TTF, their PDOS of central cores show relatively more contributions as compared to that of PDOS for compound 1-Ph. For 1-Ph at HOMO energy level between -7.0 and -6.0 eV, the major contribution is from the side chains, whereas the central ring shows minor

contribution in TDOS. Somewhat similar kinds of contributions are seen from both the fragments at LUMO energy level between -3.0 to -2.0 eV. On the other hand, the central rings in 2-PyQ taking maximum part in LUMO energies from -4.0 to -3.0 eV, while the side chains showing the minimum contribution for LUMO orbital. The side chains in 3-TTF have no contribution at HOMO between -6.0 to -5.0 eV, while has major contribution at LUMO from -3.0 to -2.0 eV. In conclusion, the PDOS of central cores indicates an acceptor trend in compound 2-PyQ, a donor trend in compound 3TTF while no significant donor/acceptor trend is observed in compound 1-Ph. These contributions from central ring and side chains to the TDOS/PDOS maps reports a good intramolecular charge transfer process especially for compounds 2-PyQ and 3TTF, which also inline with above reported good NLO responses as well as optical transition properties of these compounds. 4. Conclusions Thus, the present investigation represents three new compounds (1-Ph, 2-PyQ and 3TTF) to the realm of NLO materials by studying their third-order NLO polarizabilities with three different DFT functionals i.e. M06, PBE0 and B3LYP and 6-311G* basis set. The γ amplitudes of compounds 1-Ph, 2-PyQ and 3-TTF are 429.6×10-36, 1871.7×10-36 and 967.5×10-36 esu, respectively, at M06/6-311G* level of theory, which indicates their significant potential as efficient NLO materials. Additionally, the PDOS of central cores indicates an acceptor trend in compound 2PyQ, a donor trend in compound 3-TTF while no significant trend is observed in compound 1-Ph. Based on perturbative approximation, the larger NLO response of compound 2-PyQ is attributed to its lower energy transition with larger oscillator strength. Thus, the above several quantum chemical considerations including DOS, spectroscopic, optical and parameters are used to illustrate a structure-NLO property

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Figures

Figure 1. The optimized structures of all three studied systems at B3LYP/6-311G* level of theory

Figure 2. The graphical comparison of third-order NLO polarizability as calculated with three different DFT functional for compounds 1-Ph, 2-PyQ and 3-TTF.

Figure 3. Graphical representation of TDOS and PDOS for compounds 1-Ph, 2-PyQ and 3-TTF at the M06/6-311G* level of theory Table 1. The average and dynamic frequency dependent third-order nonlinear polarizabilities along with their individual components (Comp.) for compounds 1-Ph, 2-PyQ and 3-TTF using different functionals with 6-311G* basis set. 1-Ph

2-PyQ

3-TTF

Comp.

M06

PBE0

B3LYP

M06

PBE0

B3LYP

M06

PBE0

B3LYP

γxxxx

17.15

16.89

17.83

10.47

11.07

11.52

17.79

29.37

23.01

γyyyy

271.5

286.7

330.3

279.2

285.2

329.3

685.2

704.8

831.1

γzzzz

937.2

970.4

1126

7141

7214

8469

1844

1704

2213

γxxyy

5.165

5.312

5.870

21.07

21.31

23.72

46.65

72.12

63.45

γxxzz

1.021

2.278

2.671

41.02

43.53

50.08

64.22

103.8

92.33

γyyzz

455.1

469.2

542.5

902.3

911.5

1072

1034

958.9

1190

<γ>

429.6

445.4

515.3

1871.7

1892

2219

967.5

941.4

1151

PNA<γ>

7.279

7.474

7.416

7.279

7.474

7.416

7.279

7.474

7.416

γ(−ω;ω,0,0) a

351.4

364.9

423.2

1577.9

1596

1879

838.5

813.5

1012

γ(−2ω;ω,ω,0) a 351.1

364.0

426.9

1716.8

1728

2071

1016

969.7

1285

a

Frequency dependent dynamic third-order polarizabilities are calculated at 1900 nm

related with dc-Kerr effect γ(−ω;ω,0,0)[26] and EFISHG process γ(−2ω;ω,ω,0)[27]

Table 2. The oscillator strength (fo), ground to excited state transition electric dipole moments (μg,e1), transition energies (E), orbital contributions, and % configuration interaction (% C.I.) of crucial transitions at TD-M06/6-311G* level of theory

1-Ph 2-PyQ 3-TTF a S1 excitation

0.000)

Electronic Excitation

μg,e1

fo

E (eV)

Major Contribution

% C. I.

S0S1

2.154

0.445

3.917

HL

69

S0S3

3.722

1.494

4.402

HL+1

49

S0S2 a

3.421

0.859

2.995

H-1L

67

S0S8

3.551

1.172

3.792

HL+1

62

S0S1 S0S10

0.962

0.050 0.348

2.218 3.880

HL H-1L+1

51 67

1.9078

is not considered in 2-PyQ because of its zero oscillator strength (fo ≤