Influence of acceptor tethering on the performance of nonlinear optical properties for pyrene-based materials with A-π-D-π-D architecture

Muhammad Usman Khan; Muhammad Khalid; Rasheed Ahmad Khera; Muhammad Nadeem Akhtar; Amna Abbas; Muhammad Fayyaz ur Rehman; Ataualpa Albert Carmo Braga; Mohammed Mujahid Alam; Muhammad Imran; Yao Wang; Changrui Lu

doi:10.1016/j.arabjc.2021.103673

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Original article

03 2022

:15;

103673

doi:

10.1016/j.arabjc.2021.103673

Influence of acceptor tethering on the performance of nonlinear optical properties for pyrene-based materials with A-π-D-π-D architecture

Muhammad Usman Khan^{^a,^b}, Muhammad Khalid^{^c,⁎}, Rasheed Ahmad Khera^{^d}, Muhammad Nadeem Akhtar^{^e}, Amna Abbas^{^c}, Muhammad Fayyaz ur Rehman^{^f}, Ataualpa Albert Carmo Braga^{^g}, Mohammed Mujahid Alam^{^h}, Muhammad Imran^{^h}, Yao Wang^ⁱ,⁎, Changrui Lu^{^a,⁎}

a Department of Chemistry, Chemical Engineering and Biotechnology, Donghua University, Shanghai 201620, China

b Department of Chemistry, University of Okara, Okara 56300, Pakistan

c Department of Chemistry, Khwaja Fareed University of Engineering & Information Technology, Rahim Yar Khan 64200, Pakistan

d Department of Chemistry, University of Agriculture, 38000 Faisalabad, Pakistan

e Division of Inorganic Chemistry, Institute of Chemistry, Baghdad-ul-Jadeed Campus, The Islamia University of Bahawalpur, Bahawalpur 63100, Pakistan

f Institute of Chemistry, University of Sargodha, Sargodha 40100, Pakistan

g Departamento de Química Fundamental, Instituto de Química, Universidade de São Paulo, Av. Prof. Lineu Prestes, 748, São Paulo 05508-000, Brazil

h Department of Chemistry, Faculty of Science, King Khalid University, P.O. Box 9004, Abha 61413, Saudi Arabia

i Department of Assisted Reproduction, Shanghai Ninth People’s Hospital, Shanghai Jiao Tong University, School of Medicine, Shanghai, China

⁎Corresponding authors. muhammad.khalid@kfueit.edu.pk (Muhammad Khalid), alid@iq.usp.br (Muhammad Khalid), Wangyao9h@aliyun.com (Yao Wang), crlu@dhu.edu.cn (Changrui Lu)

Received: 2021-11-12, Accepted: 2021-12-26,

Disclaimer:
This article was originally published by Elsevier and was migrated to Scientific Scholar after the change of Publisher.

Peer review under responsibility of King Saud University.

Abstract

Abstract

In this study, we designed a series of pyrene-based donor-π-donor-π-acceptor compounds (HPTC1-HPTC7) by structural tailoring the reference compound (HPTC) using acceptor units. Nonlinear optical (NLO) properties, frontier molecular orbitals (FMOs), natural bonding orbital (NBO), transition density matric (TDM) analysis, and absorption spectra of reference and proposed derivatives were calculated at M06/6-31G(d,p) functional. All the designed compounds have smaller energy bandgaps than the HPTC compound. Moreover, the designed compounds exhibited larger global softness values than the reference. The absorption maxima of HPTC2, HPTC3, and HPTC7 are blue shifted with respect to HPTC. NBO analysis revealed that prolonged hyper conjugative associations and strong interactions between the donor (π) and acceptor (π*) moieties play a crucial part in their stabilization. The FMO and NBO findings supported the NLO responses of entitled compounds, and consequently, the linear and nonlinear properties of designed derivatives elevate compared to the reference molecule. Promisingly, the NLO response for HPTC7 comprises of highest values of <α>, β_total and < γ > as 1.92 × 10⁻²² esu, 1.95 × 10⁻²⁷ esu, and 4.69 × 10⁷ (a.u). This NLO behavior shows push–pull NLO chromophores for HPTC7 predicting its role in pursuing NLO materials for optoelectronic applications.

Keywords

Pyrene

FMO

DFT

NBO

NLO

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1 Introduction

The promising nonlinear optical (NLO) materials have gained immense attention in ongoing explorations (Christodoulides et al., 2010) due to their utilization in the area of solid-state physics, surface interfaces, biophysics, medicine, atomic, molecular, materials science, chemical dynamics (Eaton, 1991), applications in telecommunication sector (Tsutsumi et al., 1998), optoelectronic devices and optics (Breitung et al., 2000). Many studies have focused on manufacturing various effective synthetic materials and natural nanomaterials (Ivanov et al., 2013), polymer systems (Yamashita, 2011), and organic and inorganic semiconductor frameworks for NLO responses. Among different materials, organic-based NLO materials show significant signal processing, optical modulation, optical switching, and frequency conversion. Further, organic-based materials have many advantages: low cost, facile synthesis, tunable absorption wavelengths, facile fabrication, and structural modulation using suitable substituents (Issa et al., 2021; Abdel-Kader et al., 2021; Abdel-Kader et al., 2019; Abdel-Latif and Mohamed, 2018; Abdel-Latif and Moustafa, 2018 ). Therefore, researchers have turned to them for promising NLO response. To enhance the NLO properties, studies show that the π-electronic polarization can further improve the NLO response of chromophores (Yamashita, 2011; Guo et al., 2018).

Organic NLO compounds with donor (D) and acceptor (A) moieties coupled via π-spacers delocalize the electronic charge distribution along with the π-bond skeleton (Prasad and Williams, 1991). NLO response properties are reinforced by increasing intramolecular charge transfer (ICT) (Zyss and DĖ chemla., 1987) while charges delocalize from electron-D constituent to an electron-A constituent via π-spacers (Janjua, 2017). This mechanism of organic compounds manifests as a push–pull mechanism, significant for NLO response (Chemla, 2012). Many studies have focused on developing efficient models for organic NLO compounds by using the criteria mentioned above (Nagarajan et al., 2017; Siddiqui et al., 2012). The modeling of organic NLO compounds involves joining appropriate substituents at a suitable position through π-spacers (Janjua et al., 2012) which impart increased NLO response by improving the asymmetric electronic distribution (Janjua et al., 2012).

Literature reveals that organic compounds possess D − A, D − A − π − A, D − π − A, D − π − D − π − A, D − π − A − π − D, D − π − π–A and D–D–π–A, etc. architectures (Wielopolski et al., 2013; Katono et al., 2014; Panneerselvam et al., 2017; Namuangruk et al., 2012 ). Among these, the D-π-A construction is most frequently used to increase CT transitions (Haid et al., 2012; Srinivasan et al., 2017). Further, literature discloses that moieties such as donors and acceptors cause crucial charge asymmetry in ground-state; whereas, π-spacers provide a pathway for charge transfer (Janjua et al., 2014; Janjua et al., 2015; Janjua et al., 2016; Janjua, 2012; Janjua et al., 2014 ). NLO properties of organic compounds result from donor and acceptor moieties with π-spacers (Dalton, 2002; Dalton, 2001). Experimental and theoretical studies show that the enormous NLO response of second-order (β_total) comes from robust donor and acceptor units at contrary ends of a suitable π-conjugated system. This structure–property relationship shows that the optimal length of π-conjugated system also increases the NLO response (Dulcic et al., 1981). Therefore, an attempt is made for originating push–pull mechanism (A-π-D-π-A) for synthesized molecule dihexyl 3,3′-(pyrene-1,6-diylbis(thiophene-5,2-diyl))(2E,2′E)-bis(2-cyanoacrylate)) (HPTC) containing hexyl 2-cyanoacrylate (HCA) as an acceptor moiety, thiophene as π-spacer and pyrene as a donor moiety (Scheme 1) using different acceptors (Nan et al., 2020). We report novel NLO properties of the reference and designed compounds since they show NLO responses from D-π-A-type molecules.

The sketch map for studied structures and series of acceptors used for the modification of HPTC compound.

The present study named the synthesized compound (A-π-D-π-A) HPTC (Nan et al., 2020). Compound HPTC1 is designed by replacing one terminal A unit (HCA) of HPTC with pyrene, while keeping the D unit (pyrene), π-spacers (thiophene), and 2nd terminal A unit (HCA) of HPTC unchanged. Further series of organic compounds HPTC2-HPTC7 are designed by modification of 2nd terminal A unit (HCA) of HPTC1 with reported acceptors: 2-(2-methylene-3-oxo-2,3-dihydro-1H-inden-1-ylidene)malononitrile(MOI), 2-(5,6-difluoro-2-methylene-3-oxo-2,3-dihydro-1H-inden-1-ylidene)malononitrile(DMM), 2-(4,5,6-trifluoro-2-methylene-3-oxo-2,3-dihydro-1H-inden-1-ylidene)malononitrile(TOM), 2-(5,6-dichloro-2-methylene-3-oxo-2,3-dihydro-1H-inden-1-ylidene)malononitrile(MDI), 2-(4,5,6-trichloro-2-methylene-3-oxo-2,3-dihydro-1H-inden-1-ylidene)malononitrile(TIM) and 1-(dicyanomethylene)-2-methylene-3-oxo-2,3-dihydro-1H-indene-5,6-dicarbonitrile (CMD), respectively. This design results in seven new organic compounds (Scheme 1) for the calculation of NLO characteristics to govern the outcome of diverse A units on NLO activity. The electronic characteristics, such as FMO, NBO, GRP, absorption spectra, and NLO responses, were calculated by density functional theory (DFT) computations. This computational work will deliver a guideline for the design and synthesis of NLO compounds.

2 Computational procedure

The absorption spectra, NBO, FMO and NLO response of pyrene-based compound abbreviated as HPTC with A–π–D–π–A conformation and proposed compounds abbreviated as HPTC1-HPTC7 coexisting A–π–D–π–D conformation are determined by DFT calculations with the Gaussian 09 program (Frisch et al., 2009). Entire analysis analyses of the current study were completed by using the M06/6-31G (d,p) functional (Muhammad et al., 2016; Muhammad et al., 2018; Bibi et al., 2021; Khalid et al., 2021 ). Natural bond orbital (NBO) and transition density matrix (TDM) analysis determined the interaction during charge transfer. Moreover, electronic transitions were determined by UV/Vis. absorption spectra and HOMO-LUMO energies by the same level of theory with the TD-DFT approach. Avogadro (Hanwell et al., 2012) and Chemcraft software (Andrienko, 2010) were used to develop input files and determine results from output files. The dipole moment (µ), linear response polarizability < a>, nonlinear responses such as hyperpolarizability of first order (β), and second-order < γ > were computed with the following Equations (Islam and Chimni, 2016).

(1)

u = {(μ_{x}^{2} + μ_{y}^{2} + μ_{z}^{2})}^{1 / 2}

Average polarizability < a > is computed with Equation (2).

(2)

< a > = 1 / 3 (a_{x}^{2} + a_{y}^{2} + a_{z}^{2})

Hyperpolarizability tensors were collected by Gaussian output file.

(3)

β t_{otal} = {[(β_{xxx} + β_{xyy} + β_{xzz}) + (β_{xxy} + β_{yzz} + β_{zzz}) + (β_{xxz} + β_{yyz} + β_{xyz})]}^{1 / 2}

Second-order hyperpolarizability is calculated by Equation (4).

(4)

< γ > = 1 / 5 [γ_{xxx} + γ_{yyy} + γ_{zzz} + 2 (γ_{xxx} + γ_{yyy} + γ_{zzz)}]

3 Results and discussion

We conducted this quantum chemical study for computational designing of pyrene based NLO organic compounds. Therefore, an organic synthesized A-π-D-π-A type compound, HPTC was employed as a reference. Structurally, the HPTC compound consists of (i) hexyl 2-cyanoacrylate (HCA) as an acceptor moiety, (ii) thiophene as π-spacer and (iii) pyrene as a donor moiety as shown in Scheme 1. Experimentally and theoretically studies disclose that the large NLO response results from placing strong D/A moieties at opposite sides of suitable π-spacers (Dulcic et al., 1981). Based on this principle, we designed HPTC1 by replacing one terminal acceptor hexyl 2-cyanoacrylate (HCA) acceptor unit with pyrene donor moiety. Furthermore, new series of NLO species (HPTC2-HPTC7) comes from structural tailoring of HPTC1 by introducing various end caped acceptor units (see Scheme 1). The IUPAC names with abbreviations of these compounds are reported: (dihexyl 3,3′-(pyrene-1,6-diylbis(thiophene-5,2-diyl))(2E,2′E)-bis(2-cyanoacrylate)) (HPTC), (hexyl (E)-2-cyano-3-(5-(6-(5-(pyren-1-yl)thiophen-2-yl)pyren-1-yl)thiophen-2-yl)acrylate) (HPTC1), ((Z)-2-(3-oxo-2-((5-(6-(5-(pyren-1-yl)thiophen-2-yl)pyren-1-yl)thiophen-2-yl)methylene)-2,3-dihydro-1H-inden-1-ylidene)malononitrile) (HPTC2), ((Z)-2-(5,6-difluoro-3-oxo-2-((5-(6-(5-(pyren-1-yl)thiophen-2-yl)pyren-1-yl)thiophen-2-yl)methylene)-2,3-dihydro-1H-inden-1-ylidene)malononitrile) (HPTC3), ((Z)-2-(4,5,6-trifluoro-3-oxo-2-((5-(6-(5-(pyren-1-yl)thiophen-2-yl)pyren-1-yl) thiophen-2-yl) methylene)-2,3-dihydro-1H-inden-1-ylidene)malononitrile) (HPTC4), ((Z)-2-(5,6-dichloro-3-oxo-2-((5-(6-(5-(pyren-1-yl)thiophen-2-yl)pyren-1-yl)thiophen-2-yl)methylene)-2,3-dihydro-1H-inden-1-ylidene)malononitrile) (HPTC5), ((Z)-2-(4,5,6-trichloro-3-oxo-2-((5-(6-(5-(pyren-1-yl)thiophen-2-yl)pyren-1-yl)thiophen-2-yl)methylene)-2,3-dihydro-1H-inden-1-ylidene)malononitrile) (HPTC6), and ((Z)-1-(dicyanomethylene)-3-oxo-2-((5-(6-(5-(pyren-1-yl)thiophen-2-yl)pyren-1-yl)thiophen-2-yl)methylene)-2,3-dihydro-1H-indene-5,6-dicarbonitrile) (HPTC7). The pictographs of these compounds are shown in Figure S1 (Supplementary Information). DFT/TD-DFT study was carried out for HPTC and HPTC1-HPTC7 to evaluate how different acceptor and donor units influence the NLO properties i.e. α, β, light harvesting efficiency (LHE) and absorption wave length. The optimized geometries of entitled compounds are demonstrated in Fig. 1. The Cartesian co-ordinates of investigated systems are shown in Tables S1-S8 (Supplementary Information) while optimized bond angles and lengths data of studied systems are presented in Tables S9-S16 (Supplementary Information).

The optimized structures of reference (HPTC) as well as designed compounds (HPTC1-HPTC7).

3.1

3.1 Frontier molecular orbital (FMO) analysis

The FMO theory explains the optical characteristics, chemical stability and electronic features of compounds (Khan et al., 2019). In a conjugated system, the highest occupied molecular orbitals (HOMO) and the lowest unoccupied molecular orbitals (LUMO) determine the numerous interactions and reactions among molecules (Adeel et al., 2017; Arshad et al., 2017; Tahir et al., 2017 ). The E_LUMO-E_HOMO results show chemical reactivity, stability, chemical hardness and softness of investigated systems. Compounds with a larger energy gap comprises chemically hard species having more kinetic stability with low chemical reactivity. On the contrary, molecules containing small E_LUMO-E_HOMO are considered softer compounds with higher reactivity and low stability (Amiri et al., 2016). These soft molecules with a narrow energy gap are exceedingly polarizable with admirable NLO response (Parr and L.v. Szentpaly, S. Liu, 1999; Chattaraj and Roy, 2007). The calculations of E_HOMO, E_LUMO, and E_LUMO-E_HOMO for the HPTC and HPTC1-HPTC7 are tabulated in Table 1.

Table 1 The E_HOMO, E_LUMO, and energy gap (E_LUMO-E_HOMO) in eV of studied compounds.

Compounds	LUMO	HOMO	ΔE
HPTC	−2.73	−5.79	3.05
HPTC1	−2.59	−5.46	2.87
HPTC2	−3.08	−5.46	2.39
HPTC3	−3.15	−5.49	2.34
HPTC4	−3.21	−5.49	2.28
HPTC5	−3.22	−5.49	2.27
HPTC6	−3.28	−5.48	2.20
HPTC7	−3.49	−5.51	2.02

The calculated HOMO-LUMO energy gap (3.05 eV) of HPTC matches the experimentally determined value of 2.99 eV (Nan et al., 2020). This coherence showed that the implemented computational methodology could investigate the NLO properties of HPTC1-HPTC7. Table 1 reveals that HPTC and HPTC1-HPTC7 have a clear difference in energy gaps. This difference in energy disclosed that donor and acceptor units implicated in these compounds have a remarkable influence on HOMO and LUMO.

The energy gap of HPTC (3.054 eV) is narrowed to 2.87 eV for HPTC1 owing to the substitution of HCA acceptor with the pyrene donor unit and ultimately changed the architecture from A-π-D- π-A to A-π-D- π-D, having more strong and good push–pull mechanism. The bandgap of HPTC1 is reduced to 2.39 eV in HPTC2 due to the replacement of the HCA acceptor unit of HPTC1 with the MOI acceptor unit having two additional electron-withdrawing cyano-groups, which enhance its push–pull mechanism. Furthermore, the HPTC3 has a reduced bandgap of 2.34 eV than HPTC2 due to the replacement of MOI with the DMM acceptor unit having two electron-withdrawing fluoro-groups. Similarly, HPTC4 has a narrower value of ΔE (2.28 eV) than HPTC3 due to the replacement of DMM with TOM having three fluoro-groups. The effect for reducing the energy gap is found more in disubstituted chloro-groups present in MDI of HPTC5 than disubstituted and trisubstituted fluoro-groups present in DMM and TOM of HPTC3 and HPTC4, respectively. The bandgap of HPTC5 is reduced to 2.20 eV in HPTC6 due to the replacement of MDI with TIM with three highly resonating chloro-groups. Moreover, HPTC7 has the smallest bandgap of 2.02 eV because TIM of HPTC6 was replaced by CMD, having four cyano-groups which make its push–pull mechanism stronger among all compounds. The computed energy bandgap (E_LUMO-E_HOMO) of HPTC-HPTC7 compounds increases at the subsequent order: HPTC7 < HPTC6 < HPTC5 < HPTC4 < HPTC3 < HPTC2 < HPTC1 < HPTC.

Overall, all modulated compounds (HPTC1-HPTC7) exhibited narrow energy gaps. The molecules’ structural modulation by alteration of acceptor unit proves to enhance and influence the NLO activity. The LUMO and HOMO distribution patterns with the pictographic display are painted in Fig. 2. The attained electronic density allocations provide proficient transfer of charge from D to A. From Fig. 2, a major portion of charge density for HOMO/LUMO in HPTC exists over the central donor group and π-spacers.

HOMO and LUMO of entitled compounds (HPTC and HPTC1- HPTC7).

Meanwhile, in HOMOs of HPTC1-HPTC7, the major charge density exists predominantly over donor units and a small portion of charge density on their π-spacers. Whereas, in LUMOs of HPTC1-HPTC7, the charge density predominantly positions on acceptor unit and 1st π-spacers while minimally located over middle donor unit. This shows that charge transfer is directed from pyrene donors towards acceptors unit through π-spacers. This proficient transfer of charge confirmed that all modulated systems (HPTC1-HPTC7) would be desirable NLO materials.

3.2

3.2 Global reactivity parameters

The global reactivity parameters (GRP) such as global softness (σ), electron affinity (EA), ionization potential (IP), (Fukui, 1982), electronegativity (X), electrophilicity index (ω), chemical potential (μ), and global hardness (η) come from E_gap = E_LUMO-E_HOMO (Koopmans, 1934). Global reactivity parameters are estimated employing Koopman’s theorem. The Hartree-Fock approach is used in Koopmans' theorem to approximate the orbital energy which is calculated from the wave function of the spin orbital as well as the kinetic and nuclear attraction energies. A molecule's first ionization energy is equal to the negative of the HOMO's energy, according to Koopmans' theorem (HOMO). Koopman’s theorem was initially designed to compute ionization energies in closed-shell systems, but it has since been expanded to include energy changes when electrons are supplied or deleted (Sandoval-Yañez and Martínez-Araya, 2019). All these parameters can be measured using the subsequent Equations:

(5)

IP = - E_{H O M O}

(6)

EA = - E_{L U M O}

(7)

X = \frac{[I P + E A]}{2} = - \frac{[E_{L U M O} + E_{H O M O}]}{2}

(8)

η = \frac{[I P - E A]}{2} = - \frac{[E_{L U M O} - E_{H O M O}]}{2}

(9)

μ = \frac{E_{H O M O} {+ E}_{L U M O}}{2}

(10)

σ = \frac{1}{2 η}

(11)

ω = \frac{μ^{2}}{2 η}

The GRP results are measured using Equation (5–11) and tabulated in Table 2. The IP values of designed compounds HPTC1-HPTC7) are found less than reference HPTC. This implies that releasing electrons in the designed compounds is easier and requires less energy to make them polarizable than HPTC. Greater electron affinity (EA) values of designed compounds (HPTC2-HPTC7) as compared to the reference compound (HPTC) show greater electron accepting capability of designed compounds because of the existence of robust electron-acceptor segments MOI, DMM, TOM, MDI, TIM, CMD in HPTC2-HPTC7 respectively. The global hardness values (η) of designed compounds (HPTC1-HPTC7) are lower in the range of 1.01–1.43 eV than reference compound HPTC7 hardness value 1.53 eV. The effect of the acceptor unit in making the chemical potential values more negative, which in turn makes the molecules more reactive, more polarizable, and less stable, as evident in designed compounds (up to −4.50 eV) compared to reference (-4.26 eV). Similarly, ω and X values are also higher in designed compounds HPTC2-HPTC7 than reference. The global softness (σ) order is; HPTC7 > HPTC6 > HPTC5 > HPTC4 > HPTC3 > HPTC2 > HPTC1 > HPTC. This order is exactly opposite to the increasing HOMO-LUMO order of energy gap HPTC7 < HPTC6 < HPTC5 < HPTC4 < HPTC3 < HPTC2 < HPTC1 < HPTC. From this order, it can be seen that terminal acceptor unit CMD containing two CN groups in HPTC7 pulled more electrons toward itself, which results in more ICT between D and A units.

Table 2 Global reactivity parameters of HPTC and HPTC1- HPTC7.

Compounds	IP	EA	X	μ	η	S	ω
HPTC	5.79	2.73	4.26	−4.26	1.53	0.32	5.93
HPTC1	5.46	2.59	4.02	−4.02	1.43	0.34	5.64
HPTC2	5.46	3.08	4.27	−4.27	1.19	0.42	7.66
HPTC3	5.49	3.15	4.32	−4.32	1.17	0.42	7.97
HPTC4	5.49	3.21	4.35	−4.35	1.14	0.43	8.29
HPTC5	5.49	3.22	4.35	−4.35	1.13	0.44	8.35
HPTC6	5.48	3.28	4.38	−4.38	1.10	0.45	8.72
HPTC7	5.51	3.49	4.50	−4.50	1.01	0.49	10.02

IP = ionization potential, EA = electron affinity, X = electro negativity, μ = chemical potential, η = global hardness, σ = global softness and ω = global electrophilicity. Units in eV.

In the same way, the efficiency of three Cl groups present in the TIM acceptor unit of HPTC6 is found better than the remaining compounds acceptor units except for HPTC7. Among HPTC3-HPTC5, pulling of electrons from D moiety and ICT performance of 2Cl groups present in MDI acceptor unit of HPTC5 is found even better than three F groups present in TOM of HPTC4 and two F in DMM of HPTC3. The HPTC2 was also found with a lower energy gap and higher softness values than HPTC1 and reference HPTC compound owing to MOI acceptor unit. Overall, this order specifies added charge transfer ability of compounds amongst their HOMO and LUMO orbitals, which results in more polarizability and desirable NLO properties.

3.3

3.3 Natural bonding orbital (NBO) analysis

NBO investigation is an effective procedure for observing bonding nature, interaction among bonds, electron-transfer pathway, hyper conjugative associations and charge distribution (Weinhold, 2012). Moreover, NBO study offers a defined framework of intermolecular delocalization, providing a suitable and appropriate origin for examining electron charge transfer from packed to vacant orbitals (Sadlej-Sosnowska, 2001). NBO based analysis for HPTC and HPTC1-HPTC7 have been done by DFT/M06/6-31G (d,p) level, and major transitions are tabulated in Table 3, while further transitions are displayed in Tables S10-S17. The numbering of atoms used in Table 3 and Tables S18-S25 for NBO explanation is mentioned in Figure S9 (Supplementary Information)

Table 3 NBO results of studied compounds (HPTC and HPTC1-HPTC7).

Compounds	Donor (i)	Type	Acceptor(j)	Type	E (2)	E(J)E(i)^b	F(I,j)^e
HPTC	C52-C53	π	C25-C27	π*	26.39	0.31	0.082
	C59-C60	π	C59-C60	π*	0.52	0.3	0.012
	C25-H26	σ	C52-S54	σ*	7.65	0.74	0.067
	C84-C87	σ	C87-H91	σ*	0.5	1.04	0.02
	C6	LP(1)	C4-C5	π*	72.9	0.15	0.108
	O32	LP(1)	C34-C37	σ*	0.59	1.01	0.022
HPTC1	C52-C53	π	C25-C27	π*	26.7	0.31	0.082
	C55-C57	π	C55-C57	π*	0.65	0.3	0.013
	C25-H26	σ	C52-S54	σ*	7.65	0.74	0.067
	S54-C57	σ	C6-C57	σ*	0.51	1.17	0.022
	C11	LP(1)	C8-C9	π*	72.95	0.15	0.107
	O32	LP(1)	C34-C37	σ*	0.59	1.01	0.022
HPTC2	C27-C28	π	C25-C73	π*	29.25	0.31	0.086
	C81-N82	π	C83-N84	π*	0.69	0.46	0.016
	C25-H26	σ	C27-S29	σ*	9.01	0.73	0.073
	C28-H31	σ	C25-H26	σ*	0.5	0.97	0.02
	C11	LP(1)	C8-C9	π*	72.62	0.15	0.107
	S29	LP(1)	C16-H17	σ*	0.63	1.12	0.024
HPTC3	C27-C28	π	C25-C73	π*	30.01	0.31	0.087
	C81-N82	π	C79-N80	π*	0.7	0.46	0.016
	C25-H26	σ	C27-S29	σ*	9.06	0.73	0.073
	C30-C32	σ	C27-S29	σ*	0.51	0.93	0.02
	S29	LP(2)	C30-C32	π*	26.62	0.27	0.077
	S29	LP(1)	C16-H17	σ*	0.57	1.13	0.023
HPTC4	C27-C28	Π	C25-C73	π*	30.64	0.31	0.087
	C80-N81	π	C78-N79	π*	0.72	0.46	0.016
	C25-H26	σ	C27-S29	σ*	9.15	0.73	0.073
	C30-C32	σ	C27-S29	σ*	0.52	0.93	0.02
	S29	LP(2)	C30-C32	π*	26.78	0.27	0.077
	F82	LP(2)	C68-C69	σ*	0.52	0.98	0.02
HPTC5	C27-C28	π	C25-C73	π*	30.52	0.31	0.087
	C78-N79	π	C80-N81	π*	0.69	0.46	0.016
	C25-H26	σ	C27-S29	σ*	9.09	0.73	0.073
	C30-C32	σ	C27-S29	σ*	0.51	0.93	0.02
	C11	LP(1)	C34-C35	π*	26.88	0.14	0.067
	Cl83	LP(2)	C67-C68	σ*	0.52	0.93	0.02
HPTC6	C27-C28	π	C25-C73	π*	31.10	0.30	0.088
	C78-N79	π	C80-N81	π*	0.71	0.46	0.016
	C25-H26	σ	C27-S29	σ*	9.19	0.73	0.073
	C69-Cl82	σ	C68-C69	σ*	0.52	1.28	0.023
	C11	LP(1)	C34-C35	π*	29.82	0.14	0.071
	Cl83	LP(2)	C66-C71	σ*	0.56	0.92	0.02
HPTC7	C25-C73	π	C72-C78	π*	27.47	0.29	0.08
	C79-N80	π	C81-N82	π*	0.68	0.46	0.016
	C25-H26	σ	C27-S29	σ*	9.24	0.73	0.073
	C28-H31	σ	C25-H26	σ*	0.51	0.97	0.02
	C11	LP(1)	C8-C9	π*	73.04	0.15	0.107
	S29	LP(1)	C16-H17	σ*	0.65	1.13	0.024

In the reference molecule (HPTC), the most reliable transition π(C52–C53) → π*(C25–C27) with 26.39 kcal/mol is witnessed, which designated the chief stabilization energy. The other π → π* transition is from π(C59-C60) to π*(C59-C60) with 0.52 kcal/mol is obtained with minimum stabilization energy. In σ → σ* transitions, σ(C25-H26) → σ*(C52-S54) showed higher energy value of 7.65 kcal/mol while σ(C84-C87) → σ*(C87-H91) showed smallest energy of 0.5 kcal/mol. This smallest stabilization energy results from less interface amongst σ and σ* moieties. For lone pair resonance, (C6) LP(1) → π*(C4-C5) transition with larger stabilization energy 72.9 kcal/mol is found. In comparison, transition (O32) LP(1) → σ*(C34-C37) with lower stabilization energy of 0.59 kcal/mol is examined in the reference molecule. In the designed compound HPTC1, the transition π(C52–C53) → π*(C25–C27) with the maximum stabilization energy value (26.7 kcal/mol) is noticed. The other π → π* transition, from π(C55-C57) to π*(C55-C57) with 0.65 kcal/mol is detected as lower energy. Whereas, tiniest dominant transitions are σ → σ* that resulted owing to the weaker interaction amongst σ and σ* of HPTC1. Therefore, σ(C25-H26) → σ*(C25-H26) transition in HPTC1 offers huge stabilization energy of 7.65 kcal/mol. Similarly, σ(S54-C57) → σ*(C6-C57) transitions showed the smallest energy of 0.51 kcal/mol. The LP1(C11) → π*(C8-C9) transition is due to resonance and exhibits a higher 72.95 kcal/mol stabilization energy, while LP1(O32) → σ*(C34-C37) with a stabilization energy of 0.59 kcal/mol is observed as least value of energy in HPTC1. In HPTC2, π(C27-C28) → π*(C25-C73) transition with 29.25 kcal/mol stabilization energy value is present as a larger stabilization value. Besides, a transition from π(C81-N82) to π*(C83-N84) with 0.46 kcal/mol expressed a lower stability value. Additionally, the energy value of 9.01 kcal/mol is obtained in σ(C25-H26) → σ*(C27-S29) transition because of weaker interaction between σ and σ* in HPTC2 which is the largest value of stabilization energy for σ → σ* transitions. The other transition, σ(C28-H31) → σ*(C25-H26), showed the smallest energy value of 0.5 kcal/mol. Due to resonance, the other electronic transitions: the highest probable transition LP1(C11) → π*(C8-C9) and the transition LP1(S29) → σ* (C16-H17) are noticed with 72.62 and 0.63 kcal/mol stabilization energy values, respectively. In HPTC3, the energy transition π(C27-C28) → π*(C25-C73) holding highest 30.01 kcal/mol energy is noticed as a greater stabilization energy value. In comparison, the transition from π(C81-N82) → π*(C79-N80) with 0.7 kcal/mol is obtained as a lower value. In HPTC3, σ(C25-H26) → σ*(C27-S29) transition showed the largest stabilization energy of 9.06 kcal/mol. Along with the other transitions, the σ(C30-C32) → σ*(C27-S29) showed the smallest energy value of 0.51 kcal/mol. The greater stabilization value because of resonance is 26.62 kcal/mol in LP2(S29) → π*(C30-C32) transition. LP1(S29) → σ*(C16-H17) transition with 0.57 kcal/mol value is witnessed as the lowest energy. In HPTC4, the π → π* transition with uppermost stabilization energy is found π(C27-C28) → π*(C25-C73) with 30.64 kcal/mol, and the transition from π(C80-N81) → π*(C78-N79) with 0.72 kcal/mol is examined as a lower value of stability. Besides these, for σ → σ* transition, the stabilization energy (9.15 kcal/mol) is marked as a larger value in HPTC4 due to σ(C25-H26) → σ*(C27-S29) transition. On the other hand, transition σ(C30-C32) → σ*(C27-S29) showed smallest energy value of 0.52 kcal/mol. The values 26.78 and 0.52 kcal/mol are noticed as larger and smaller values of stability due to LP2 (S29) → π*(C30-C32) and LP2(F82) → π*(C68-C69) transitions, respectively. The chromophore (HPTC5) showed the transition as π(C27-C28) → π*(C25-C73) with the utmost energy value (30.52 kcal/mol). The other π → π* transition from π(C78-N79) to π*(C80-N81) with 0.69 kcal/mol is noticed as the minimum stability value. The stabilization energy value (9.09 kcal/mol) due to weaker interaction between σ and σ* is observed as a greater value in HPTC5 for σ(C25-H26) → σ*(C27-S29) transition while the transition from σ(C30-C32) to σ*(C27-S29) showed smallest energy 0.51 kcal/mol. The transition LP1(C11) → π*(C34-C35) is observed as the highest stability transition with 26.88 kcal/mol and LP2(Cl83) → π*(C67-C68) with 0.52 kcal/mol expressed the least stability value. In HPTC6, the transition π(C27-N28) → π*(C25-N73) exhibited the uppermost energy of stabilization (31.10 kcal/mol), while π(C78-N79) → π*(C80-N81) transition showed the lowest stabilization energy (0.71 kcal/mol). The greater stabilization energy, 9.19 kcal/mol, is perceived in HPTC6 because of σ(C25-H26) → σ*(C27-S29) transition. Similarly, σ(C69-Cl82) → σ*(C68-C69) showed the slightest energy of 0.52 kcal/mol. The transition LP1(C11) → π*(C34-C35) has been observed due to resonance with 29.82 kcal/mol stabilization energy value showed the greater stability. The 0.56 kcal/mol is the least stabilization energy due to LP2(Cl83) → π*(C66-C71). In HPTC7, the energy transition as π(C25-C73) → π*(C72-C78) with 27.47 kcal/mol is examined as maximum stabilization value while the transition from π(C79-N80) to π*(C81-N82) with 0.68 kcal/mol is considered as minimum energy value. Additionally, for σ → σ* transitions,9.24 kcal/mol is observed as the highest stability value in σ(C25-H26) → σ*(C27-S29) but σ(C28-H31) → σ*(C25-H26) showed smallest energy value of 0.51 kcal/mol. The highest stabilization energy value (73.04 kcal/mol) is perceived for LP1(C11) → π*(C8-C9) because of resonance. LP1(S29) → π*(C16-H17) transition expressed the least stability value, 0.65 kcal/mol. Moreover, obtained results showed that delocalized π-electrons of C-C bonding orbitals play a major role in stabilization and overall structural design. Consequently, prolonged hyper conjugations in entitled chromophores play a significant part in stabilizing these compounds and support tremendous NLO response.

3.4

3.4 UV–Vis analysis

This analysis gives important evidence about the nature of electronic transitions, probability of charge transfers, and absorption in HPTC and its derivatives (HPTC1-HPTC7). Therefore, the results of computed transition energy (eV), maximum absorption wavelengths (λ_max/nm), oscillator strengths (f_os), and molecules transition nature were computed at TD-DFT/M06/6-31G(d,p) level of theory, and attained data is tabulated in Table 4 while other transitions are displayed in Tables S26-S33.

Table 4 Computed transition energy (eV), maximum absorption wavelengths (λ_max/nm), oscillator strengths (f_os), transition moment (Δμ_gm) and transition natures of compounds (HPTC and HPTC1-HPTC7).

Compounds	**E_ge(eV)**	λ_max(nm)	ƒ_os	LHE	Δμ_gm	MO transition
HPTC	2.42	511.36	1.48	0.97	0.84	H $\to$ L (97%), H-1 $\to$ L + 1 (2%)
HPTC1	2.36	524.42	1.02	0.90	7.75	H-1 $\to$ L (13%), H $\to$ L (84%)
HPTC2	2.82	438.99	1.03	0.91	6.15	H-3 $\to$ L (15%), H $\to$ L + 2 (48%)
HPTC3	2.81	441.54	0.99	0.89	7.31	H-3 $\to$ L (29%), H-2 $\to$ L (30%)
HPTC4	2.78	445.53	0.88	0.87	8.21	H-3 $\to$ L (37%), H-2 $\to$ L (34%)
HPTC5	2.79	447.75	0.97	0.89	7.84	H-3 $\to$ L (36%), H-2 $\to$ L (31%)
HPTC6	2.73	454.42	0.88	0.86	7.99	H-3 $\to$ L (35%), H-2 $\to$ L (34%)
HPTC7	2.63	471.31	0.63	0.76	9.19	H-3 $\to$ L(54%), H-2 $\to$ L (32%)

MO = Molecular orbital (HOMO & LUMO); H = HOMO ; L = LUMO.

Usually, energy (E) and maximum absorption wavelengths (λ_max) have an inverse relationship (Khan et al., 2019). According to this inversely relationship, Table 4 shows the value of λ_max for entitled compounds decreases with increasing E values. Two peaks, namely primary and secondary absorption peaks, are observed in all investigated molecules. Table 4 is equipped with a primary peak observed with maximum oscillation strength, while all excitations found in studied molecules are mentioned in Tables S26-S33. The secondary peak is found with larger λ_max and lesser oscillation strength values. All designed species are observed with red-shifted behaviors. The λ_max values of HPTC-HPTC7 are found as 511.36, 524.42, 438.99, 441.54, 445.53, 647.75, 454.42, and 471.31 nm, respectively. The decreasing order of λ_max for HPTC-HPTC7 is: HPTC1 > HPTC > HPTC7 > HPTC6 > HPTC5 > HPTC4 > HPTC3 > HPTC2. Among all the designed compounds, HPTC1 showed the lowest E_ge value, 2.36 eV, and the largest λ_max value, 524.42 nm, with an oscillator strength of 1.02. Table 4 shows that the proposed derivative’s absorption spectrum is observed in the visible region (438 to 524 nm).

The HPTC and HPTC1-HPTC7 absorption spectra are displayed in Fig. 3, which indicate two distinct absorption bands for each compound. The primary and secondary bands may attribute to π → π* and n → π*transitions, correspondingly. The λ_max of HPTC2, HPTC3, and HPTC7 are blue-shifted with respect to HPTC.

Simulated absorption spectra of compounds (HPTC and HPTC1-HPTC7).

The designed compounds (HPTC1, HPTC4-HPTC7) have larger absorption maximum values with lower oscillator strength (f_os) as compared to the reference molecule (HPTC) (Mahmood et al., 2015). The presence of negative inductive (-I effect) electron-withdrawing groups on acceptor moieties may reduce the energy gap between the ground and excited states, exhibiting better optical properties (Chen et al., 2021).

Light-harvesting efficiency (LHE) determines the optical efficiency of compounds. Literature has shown that structures having a large value of LHE exhibited maximum photocurrent response (Islam and Chimni, 2016) LHE values are estimated using Equation (12) (Nalwa, 2000):

(12)

LHE = 1 - 10^{- f}

In the above equation, oscillator strength is represented by f. The values of LHE for HPTC and HPTC1-HPTC7 are given in Table 4. The noticed LHE results of HPTC exhibited higher among the computed compounds. The justification for second-order NLO properties is well explained through more clarification of the structure–property relationship. The two-state model for the complex sum-over-states (SOS) demonstration was formulated by Oudar and Chemla (Oudar and Chemla, 1977) which made a assembly amongst hyperpolarizability and transitions involving charge transfer. It is symbolized with Equation (13):

(13)

β_{CT} = \frac{Δ μ_{gm} f_{gm}}{E_{gm}^{3}}

In this Equation, Δμ_gm shows dipole moment variations between excited and ground state directly proportional to the β_CT. The oscillator strength among ground state (g) and excited state (m) is represented by f_gm, which is precisely associated with β_CT. The $E_{g m}^{3}$ value represents the cube of transition energy, and second-order polarizability value or β_CT is inversely proportional to it. In Eq (13), it is obvious that the transition moment and oscillator strength product is the conclusive aspect for the estimation of β_CT. The NLO material with a big transition moment magnitude, by f_gm, and lower energy CT excited state is an ideal model having significant β_CT values. The values of by f_gm, Δμ_gm, and are given in Table 4. Consequently, for HPTC and HPTC1-HPTC7, Δμ_gm, $E_{g m}^{3}$ and f_gm are strongly related with each other. The relation among the first hyperpolarizability and the subsequent two-level model values for HPTC and HPTC1-HPTC7 are shown in Fig. 4. β_CT values are proportional to the corresponding Δµ_gmf_gm/ΔE³gm values as shown in Fig. 4.

Relationship between the βtotal (blue line) values and the corresponding βCT (red line) values for compounds (HPTC and HPTC1-HPTC7).

Our results conclude that for designing novel, interesting D-π-D-π-A assemblies with excellent NLO responses, adjusting the A-type unit proves to be a viable method. Therefore, with this approach, we can design novel optical and photoelectric devices with improved switching, modulation and optical data processing.

3.5

3.5 Transition density matrix (TDMs) analysis

The TDM analysis mainly measures the nature and degree of transitions present in charge transfer molecules (Khan et al., 2021; Khalid et al., 2021; Khalid et al., 2021 ). This method also explains the performance of optoelectronic molecules. TDM analysis is performed at DFT/M06/6-31G(d,p) level to have insight into the transitions of charge density among different parts, including donor (D), bridge (B), and acceptor (A) of investigated molecules. Charge transitions from ground to excited state in TDM analysis are represented as a heat map consisting of a band of colors (Fig. 5). In HPTC, higher charge density is observed on donor pyrene moiety atoms 1–16, shifting to the atoms 29–40 of bridge unit. Further charge transfers from the bridge to terminal acceptor atoms 46–51 is found in dark blue colour, which describes the zero value of charges at the acceptor. This indicates that terminal acceptors are weak to pull electron density in HPTC. The replacement of one terminal acceptor with donor pyrene changes the nature of transitions in HPTC1, where more significant charge density is found on central donor pyrene, which is transferred to thiophene bridge atoms 29–40 and toward 17–29 atom numbers of acceptor unit. On the other hand, replacing the acceptor unit of HPTC1 with strong electron-withdrawing end-capped acceptor units results in diagonal charge transfer in HPTC2 to HPTC7 molecules. Small charge density is seen on atom numbers 27–43 of HPTC2 to HPTC7 that belong to the terminal donor pyrene unit, which indicates that this terminal donor unit pushes the charges toward the bridge unit that is found with the significant charge density. The bridge units further shift the charges to the end-capped acceptor units with atom numbers > 43. Hence, TDM analysis provides vital evidence for successful intramolecular charge transfer among D, B, and A units in studied molecules.

3.6

3.6 Nonlinear optical (NLO) properties

A reasonable comprehension of the NLO field contributes greatly towards designing NLO materials (Khan et al., 2021; 2021; 2021). The strength of the linear response (α) and nonlinear responses: hyperpolarizabilities of first and second order as β and γ, respectively, heavily depends on the electronic properties of used materials. Literature shows that the narrow energy gap between HOMO and LUMO influences the linear polarizability of a molecule (Bibi et al., 2021; Khalid et al., 2021). Moreover, the molecules having small energy gaps show larger α and β and γ values. Furthermore, NLO properties relate to the ICT phenomenon where the stronger the ICT value leads to larger NLO values (Khan et al., 2019). To understand the effect of different acceptor “A” units over chemical structures of HPTC-HPTC7 for linear and nonlinear properties and their results: average polarizability values (<a > ), first hyperpolarizability (β_total) and second-order hyperpolarizability (γ_total) are tabulated in Table 6. The reduction in energy band gaps leads to an increase in the values of < a>, γ_total β_total. Moreover, the $μ$ _total values of all studied compounds are diminishing with following order: HPTC7 > HPTC > HPTC5 > HPTC3 > HPTC6 > HPTC4 > HPTC2 > HPTC1. HPTC7 is found one of the significant molecules, consisting of the highest value of dipole moment $μ$ _tot_al (6.405 D), including with the smallest bandgap because of the existence of CMD A unit having four electron-withdrawing groups. The average polarizability value < a > of all examined compounds decreases in the following tendency: HPTC7 > HPTC6 > HPTC5 > HPTC4 > HPTC2 > HPTC3 > HPTC1 > HPTC. Modification of different A units influenced the polarizability values in HPTC1-HPTC7. This indicates that the < a > value of more electron-withdrawing substitution-based A units (MOI, DOM, TOM, MDI, CMD) was higher than the reference HTPC compound. The uppermost < a > value was found in the HPTC7 designed compound having four highly electron-withdrawing cyano-groups.

Table 6 The

μ

_total, <α>_, β_total and γ_total of the entitled compounds (HPTC and HPTC1- HPTC7).

Compounds	$μ$ *_total* (D)	<a> (esu)	*β_total* (esu)	*γ_total* × 10⁷
HPTC	4.96	1.35 × 10⁻²²	1.22 × 10⁻²⁸	0.76
HPTC1	3.43	1.50 × 10⁻²²	3.88 × 10⁻²⁸	0.99
HPTC2	3.54	1.76 × 10⁻²²	1.13 × 10⁻²⁷	2.59
HPTC3	3.93	1.76 × 10⁻²²	1.15 × 10⁻²⁷	2.61
HPTC4	3.59	1.77 × 10⁻²²	1.28 × 10⁻²⁷	2.90
HPTC5	4.15	1.84 × 10⁻²²	1.31 × 10⁻²⁷	3.06
HPTC6	3.92	1.91 × 10⁻²²	1.59 × 10⁻²⁷	3.78
HPTC7	6.41	1.92 × 10⁻²²	1.95 × 10⁻²⁷	4.69

The results of β_total values for all studied compounds HPTC-HPTC7 are tabulated in Table 6. β_total results of all examined (HPTC-HPTC7) systems decreases in the following order: HPTC7 > HPTC6 > HPTC5 > HPTC4 > HPTC3 > HPTC2 > HPTC1 > HPTC. Among all derivatives, HPTC7 has the largest β_total value (1.95 × 10⁻²⁷ esu), and HPTC1 has the smallest β_total value (3.88 × 10⁻²⁸ esu). The γ_total values of all examined compounds (HPTC-HPTC7) decreases in the following order: HPTC7 > HPTC6 > HPTC5 > HPTC4 > HPTC3 > HPTC2 > HPTC1 > HPTC. Likewise, attaining the largest $μ$ _total, <a>_, and β_total values, HPTC7 has the largest γ_total value (4.69 × 10⁷ a.u) among all studied compounds. The main reason behind that was the presence of CMD “A” unit having four strongly electron-withdrawing cyano-groups that induced the strong negative inductive effect in HPTC7. The urea is repeatedly utilized as reference in nonlinear optical comparisons (Prasad and Williams, 1991; Donaldson and Tang, 1984; Halbout et al., 1979). As a result, we compared our computed values to urea levels. All proposed compounds HPTC1-HPTC7 have 9.03 × 10⁻³⁰ esu, 2.62 × 10⁻²⁹ esu, 2.67 × 10⁻²⁹ esu, 2.97 × 10⁻²⁹ esu, 3.05 × 10⁻²⁹ esu, 3.69 × 10⁻²⁹ esu and 4.54 × 10⁻²⁹ esu times higher first-order hyperpolarizability value than urea (β = 0.372 × 10⁻³⁰ esu) respectively. In a nutshell, the NLO response is found highest for HPTC7 because of the existence of four stronger electron-withdrawing cyano-units on A moiety (CMD) that may diminish the LUMO-HOMO energy gap by creating a strong push–pull mechanism, leading to an increase in the ICT between both poles of the molecule. Subsequently, HPTC7 might be considered as an excellent NLO molecule among all studied molecules.

4 Conclusion

This work designed pyrene-based organic compounds having D-π-D-π-A architecture by HPTC and explored the potential effect of acceptor moieties on their NLO properties. All designed compounds showed maximum wavelengths λ_max in the visible region with small transition energy values. Our FMO analysis of HPTC and HPTC1-HPTC7 indicated that energy band gaps of the entitled compounds were reduced from 3.05 eV to 2.02 eV. The global softness values of HPTC-HPTC7 were increased from 8.910 to 13.451 E_h. The global softness values revealed that all compounds have the ability to polarize promptly. Their NBO results showed that electrons could effectively migrate from D to A units through π-spacer. TDM analysis provides vital evidence for successful intramolecular charge transfer among D, B, and A unit in studied molecules. The entitled compounds (HPTC1-HPTC7) exhibited a promising NLO response than the HPTC compound due to the stronger acceptor moieties. NLO responses leading to favorable < α> , β_total and < γ > values with following order: HPTC7 > HPTC6 > HPTC5 > HPTC4 > HPTC3 > HPTC2 > HPTC1 > HPTC. The favorable structural relationship of HPTC7 significantly amplifies the electron transportability, accordingly boosting NLO responses to < α>, β_total and < γ > of 1.92 × 10⁻²² esu, 1.95 × 10⁻²⁷ esu, and 4.69 x10⁷ (a.u.), respectively. Eventually, it was concluded that entitled compounds behave in the aspect of a classical push–pull NLO chromophore. The current data ascertains that entitled compounds have fascinating NLO properties for up-to-the-minute NLO applications. Furthermore, HPTC1-HPTC7 can also be synthesized due to its high efficacy in the NLO field.

Acknowledgements

Funding in the Lu lab was provided by the Fundamental Research Funds for the Central Universities (2232021G-04), Shanghai Science and Technology Committee (19ZR1471100). A.A.C.B. (grants 2015/01491-3 and 2014/25770-6) is thankful to Fundacão de Amparo à Pesquisa do Estado de Sao Paulo for financial support. A.A.C.B. (grant 312550/2020-0) also thanks the Brazilian National Research Council (CNPq) for financial support and fellowships. This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nivel Superior do Brasil (CAPES) Finance Code 001. M. M. A and M. I. express appreciation to the Deanship of Scientific Research at King Khalid University Saudi Arabia through a research groups program under grant number R. G. P. 2/109/1442.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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Appendix A

Supplementary material

Supplementary data to this article can be found online at https://doi.org/10.1016/j.arabjc.2021.103673.

Appendix A

Supplementary material

The following are the Supplementary data to this article:

Supplementary data 1

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Introduction

Computational procedure

Results and discussion

Frontier molecular orbital (FMO) analysis
Global reactivity parameters
Natural bonding orbital (NBO) analysis
UV–Vis analysis
Transition density matrix (TDMs) analysis
Nonlinear optical (NLO) properties

Conclusion

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Influence of acceptor tethering on the performance of nonlinear optical properties for pyrene-based materials with A-π-D-π-D architecture

Abstract

Abstract

Keywords

Pyrene

FMO

DFT

NBO

NLO

1 Introduction

2 Computational procedure

3 Results and discussion

3.1 Frontier molecular orbital (FMO) analysis

3.2 Global reactivity parameters

3.3 Natural bonding orbital (NBO) analysis

3.4 UV–Vis analysis

3.5 Transition density matrix (TDMs) analysis

3.6 Nonlinear optical (NLO) properties

4 Conclusion

Acknowledgements

Declaration of Competing Interest

References

Appendix A

Supplementary material

Appendix A

Supplementary material

Supplementary data 1

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