Abstract
The possibility of tuning the chemical structures of oligothiophenes offers various applications in designing of optoelectronics and nonlinear optical (NLO) materials. In the current study, we report a computational study of quinoidal oligothiophenes to explore the influence of type of π-conjugation chains and nature of terminal acceptor groups to push their linear (α) and third-order nonlinear optical (γ) polarizability to a robust limit. The ground-state molecular geometries of designed compounds 1–8 are optimized using DFT at the M06/6-311G** level of theory. Among all the designed compounds, the largest linear isotropic (αiso) and anisotropic (αaniso) polarizability values of 342.7 × 10–36 and 765.6 × 10–36 esu are shown by compound 8 owing to its excellent electronic connection between central thiophene rings and terminal acceptor groups. Similarly, the highest average static third-order nonlinear optical (NLO) polarizability < γ > amplitude of 7448 × 10–36 esu is shown by compound 8 which is ~ 1319, ~ 103, ~ 21, ~ 77, ~ 40, ~ 28, and ~ 13 times greater as compared to compounds 1–7, respectively. Strikingly, comparative analysis of < γ > between compound 8 and p-NA (prototype NLO molecule) reveals that < γ > amplitude of compound 8 is 1021 times more than that of p-NA at the same M06/6-311G** methodology as calculated in current investigation. Remarkably, the large difference between < γ > values of compound 8 and p-NA designates significant potential of our designed compound for various NLO applications. Furthermore, TD-DFT computations indicate that the greater NLO response of compound 8 is because of its higher oscillator strength and lower transition energy in contrast to other designed molecular systems. Moreover, TD-DFT calculations are also used to investigate structure-NLO property relations in terms of frontier molecular orbitals (FMOs), the density of states (DOS), molecular electrostatic potential (MEP), and transition density matrix (TDM) parameters. We believe the current design will instigate the materials science community for such novel motifs with efficient optoelectronic and NLO properties.
Graphical abstract
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Data availability
The optimized coordinates required to produce these findings are given in supporting information.
References
Adeel M, Khalid M, Ullah MA, Muhammad S, Khan MU, Tahir MN, Khan I, Asghar M, Mughal KS (2021) Exploration of CH⋯ F & CF⋯ H mediated supramolecular arrangements into fluorinated terphenyls and theoretical prediction of their third-order nonlinear optical response. RSC Adv 11:7766–7778. https://doi.org/10.1039/D0RA08528F
Agostinelli T, Caironi M, Natali D, Sampietro M, Dassa G, Canesi EV, Bertarelli C, Zerbi G, Cabanillas-Gonzalez J, Silvestri D (2008) A planar organic near infrared light detector based on bulk heterojunction of a heteroquaterphenoquinone and poly [2-methoxy-5-(2′-ethyl-hexyloxy)-1, 4-phenylene vinylene]. J Appl Phys 104:114508. https://doi.org/10.1063/1.3033376
Albert ID, Marks TJ, Ratner MA (1998) Remarkable NLO response and infrared absorption in simple twisted molecular π-chromophores. J Am Chem Soc 120:11174–11181. https://doi.org/10.1021/ja982073c
Ambika VR, Jayalakshmi D, Narendran K, Athimoolam S, Valan M, Kamalarajan P, Ahamed JI (2021) Growth, structural, spectral, optical and thermal studies of a novel third-order nonlinear optical single crystal: Piperazine-1, 4-diium bis (2, 4-dichlorobenzoate). J Mol Struct 1225:129292. https://doi.org/10.1016/j.molstruc.2020.129292
Andrews DL, Bradshaw DS, Coles MM (2011) Perturbation theory and the two-level approximation: a corollary and critique. Chem Phys Lett 503:153–156. https://doi.org/10.1016/j.cplett.2010.12.055
Avcı D, Tamer Ö, Atalay Y (2016) Solvatochromic effect on UV–vis absorption and fluorescence emission spectra, second-and third-order nonlinear optical properties of dicyanovinyl-substituted thienylpyrroles: DFT and TDDFT study. J Mol Liq 220:495–503. https://doi.org/10.1016/j.molliq.2016.05.023
Baroudi B, Argoub K, Hadji D, Benkouider A, Toubal K, Yahiaoui A, Djafri A (2020) Synthesis and DFT calculations of linear and nonlinear optical responses of novel 2-thioxo-3-N, (4-methylphenyl) thiazolidine-4 one. J Sulphur Chem 41:310–325. https://doi.org/10.1080/17415993.2020.1736073
Beytur M, Avinca I (2021) Molecular, electronic, nonlinear optical and spectroscopic analysis of heterocyclic 3-substituted-4-(3-methyl-2-thienylmethyleneamino)-4,5-dihydro-1H-1,2,4-triazol-5-ones: experiment and DFT calculations. Heterocycl Comm 27:1–16. https://doi.org/10.1515/hc-2020-0118
Bibi A, Muhammad S, UrRehman S, Bibi S, Bashir S, Ayub K, Adnan M, Khalid M (2021) Chemically modified quinoidal oligothiophenes for enhanced linear and third-order nonlinear optical properties. ACS Omega 6:24602
Bouzzin S, Salgado-Morán G, Hamidi M, Bouachrine M, Pacheco AG, Glossman-Mitnik D (2015) DFT study of polythiophene energy band gap and substitution effects. J Chem. https://doi.org/10.1155/2015/296386
Bredas JL, Adant C, Tackx P, Persoons A, Pierce BM (1994) Third-order nonlinear optical response in organic materials: theoretical and experimental aspects. Chem Rev 94:243–278. https://doi.org/10.1021/cr00025a008
Cheng X, Yao J, Zhang H, Wang X, Bai J (2021) The nonlinear optical properties of two-dimensional metal-organic framework. J Alloys Compd 855:157433. https://doi.org/10.1016/j.jallcom.2020.157433
Chopde HN, Pagadala R, Meshram JS, Jetti V (2010) An efficient synthesis and biological testing of novel 3-chloro-4-aryl-1-(4-(phenyldiazenyl) phenyl) azetidin-2-ones. J Heterocycl Chem 47:1361–1366. https://doi.org/10.1002/jhet.459
Duan YA, Geng Y, Li HB, Jin JL, Wu Y, Su ZM (2013) Theoretical characterization and design of small molecule donor material containing naphthodithiophene central unit for efficient organic solar cells. J Comput Chem 34:1611–1619. https://doi.org/10.1002/jcc.23298
Essid M, Muhammad S, Marouani H, Saeed A, Aloui Z, Al-Sehemi AG (2020) Synthesis, characterization, Hirshfeld surface analysis and computational studies of 1-methylpiperazine-1, 4-diium bis (hydrogen oxalate):[C5H14N2](HC2O4)2. J Mol Struct. https://doi.org/10.1016/j.molstruc.2020.128075
Etienne T (2015) Transition matrices and orbitals from reduced density matrix theory. J Chem Phys 142:244103. https://doi.org/10.1063/1.4922780
Frisch, M, Trucks G, Schlegel H, Scuseria G, Robb M, Cheeseman J, Scalmani G, Barone V, Mennucci B, Petersson GJ (2009) Gaussian Inc Revision d. 01, Gaussian. Inc., Wallingford CT, 201
Guo L, Guo Z, Li X (2018) Design and preparation of side chain electro-optic polymeric materials based on novel organic second order nonlinear optical chromophores with double carboxyl groups. J Mater Sci Mater 29:2577–2584. https://doi.org/10.1007/s10854-017-8181-y
He GS, Zhu J, Baev A, Samoc M, Frattarelli DL, Watanabe N, Facchetti A, Ågren H, Marks TJ, Prasad PN (2011) Twisted π-system chromophores for all-optical switching. J Am Chem Soc 133:6675–6680. https://doi.org/10.1021/ja1113112
Hickey AL, Rowley CN (2014) Benchmarking quantum chemical methods for the calculation of molecular dipole moments and polarizabilities. J Phys Chem A 118:3678–3687. https://doi.org/10.1021/jp502475e
Hussain A, Khan MU, Ibrahim M, Khalid M, Ali A, Hussain S, Saleem M, Ahmad N, Muhammad S, Al-Sehemi AG (2020) Structural parameters, electronic, linear and nonlinear optical exploration of thiopyrimidine derivatives: a comparison between DFT/TDDFT and experimental study. J Mol Struct 1201:127183. https://doi.org/10.1016/j.molstruc.2019.127183
Imoto N, Haus H, Yamamoto Y (1985) Quantum nondemolition measurement of the photon number via the optical Kerr effect. Phys Rev A 32:2287. https://doi.org/10.1103/PhysRevA.32.2287
Irfan A, Muhammad S, Chaudhry AR, Al-Sehemi AG, Jin R (2017) Tuning of optoelectronic and charge transport properties in star shaped anthracenothiophene-pyrimidine derivatives as multifunctional materials. Optik 149:321–331. https://doi.org/10.1016/j.ijleo.2017.09.065
Irfan A, Al-Sehemi AG, Chaudhry AR, Muhammad S (2018) The structural, electro-optical, charge transport and nonlinear optical properties of oxazole (4Z)-4-Benzylidene-2-(4-methylphenyl)-1, 3-oxazol-5 (4H)-one derivative. Optik 30:75–82. https://doi.org/10.1016/j.ijleo.2016.08.007
Khalid M, Ali M, Aslam M, Sumrra SH, Khan MU, Raza N, Kumar N, Imran M (2017) Frontier molecular, Natural bond orbital, UV-Vis spectral stduy, Solvent influence on geometric parameters, Vibrational frequencies and solvation energies of 8-Hydroxyquinoline. Int J Pharm Sci Res 8:13040. https://doi.org/10.13040/IJPSR.0975-8232.8(2).457-69
Khalid M, Khan MU, Shafiq I, Hussain R, Mahmood K, Hussain A, Jawaria R, Hussain A, Imran M, Assiri MA, Ali A (2021) NLO potential exploration for D–π–A heterocyclic organic compounds by incorporation of various π-linkers and acceptor units. Arab J Chem 14:103295. https://doi.org/10.1016/j.arabjc.2021.103295
Khan MU, Khalid M, Asim S, Hussain R, Mahmood K, Iqbal J, Akhtar MN, Hussain A, Imran M, Irfan M (2021) Exploration of nonlinear optical properties of triphenylamine-dicyanovinylene co-existing donor-π-acceptor architecture by the modification of π-conjugated linker. Front Mater 8:287
Kim P, Ham S, Oh J, Uoyama H, Watanabe H, Tagawa K, Uno H, Kim D (2013) Shape-dependent two-photon absorption in two-dimensionally extended benzoporphyrin arrays. Phys Chem Chem Phys 15:10612–10615. https://doi.org/10.1039/C3CP50166C
Kumar S, Muhammad S, Koh J, Khalid M, Ayub K (2019) A combined experimental and computational study of 2, 2’-(diazene-1, 2-diylbis (4, 1-phenylene)) bis (6-(butylamino)-1H-benzo [de] isoquinoline-1, 3 (2H)-dione): Synthesis, optical and nonlinear optical properties. Optik 192:162952. https://doi.org/10.1016/j.ijleo.2019.162952
Lanata M, Bertarelli C, Gallazzi MC, Bianco A, Del Zoppo M, Zerbi G (2003) Molecules with quinoid ground state: a new class of large molecular optical nonlinearities? Synth Met 138:357–362. https://doi.org/10.1016/S0379-6779(03)00036-5
Li Y, Ullrich CJCP (2011) Time-dependent transition density matrix. Chem Phys 391:157–163
Li ZJ, Wang FF, Li ZR, Xu HL, Huang XR, Wu D, Chen W, Yu GT, Gu FL, Aoki Y (2009) Large static first and second hyperpolarizabilities dominated by excess electron transition for radical ion pair salts M 2+ TCNQ−(M= Li, Na, K). Phys Chem Chem Phys 11:402–408. https://doi.org/10.1039/B809161G
Li Y, Li H, Zhao X, Chen M (2010) Electronic structure and optical properties of dianionic and dicationic π-Dimers. J Phys Chem A 114:6972–6977. https://doi.org/10.1021/jp103204q
Lukeš V, Breza M, Pálszegi T, Laurinc V, Vrábel I (2001) On the relation between conformational changes and optical properties in oligothiophenes, 2. Linear and nonlinear optical properties. Macromol Theory Simul 10:592–599. https://doi.org/10.1002/1521-3919(20010701)10:6%3c592::AID-MATS592%3e3.0.CO;2-4
Mahmood R, Janjua MRSA, Jamil S (2017) DFT molecular simulation for design and effect of core bridging acceptors (BA) on NLO response: first theoretical framework to enhance nonlinearity through BA. J Clust Sci 28:3175–3183. https://doi.org/10.1007/s10876-017-1287-9
Marder SR, Sohn JE, Stucky GD (1991) Materials for nonlinear optics chemical perspectives. American Chemical Society Washington DC.
Mehboob MY, Khan MU, Hussain R, Fatima R, Irshad Z, Adnan M (2020) Designing of near-infrared sensitive asymmetric small molecular donors for high-efficiency organic solar cells. J Theor Comput Chem 19:2050034. https://doi.org/10.1142/S0219633620500340
Mohan B, Choudhary M, Bharti S, Jana A, Das N, Muhammad S, Al-Sehemi AG, Kumar S (2019) Syntheses, characterizations, crystal structures and efficient NLO applications of new organic compounds bearing 2-methoxy-4-nitrobenzeneamine moiety and copper (II) complex of (E)-N’-(3, 5-dichloro-2-hydroxybenzylidene) benzohydrazide. J Mol Struct 1190:54–67. https://doi.org/10.1016/j.molstruc.2019.04.059
Mohan B, Choudhary M, Kumar G, Muhammad S, Das N, Singh K, Al-Sehemi AG, Kumar S (2020) An experimental and computational study of pyrimidine based bis-uracil derivatives as efficient candidates for optical, nonlinear optical, and drug discovery applications. Synth Commun 50:2199–2225. https://doi.org/10.1080/00397911.2020.1771369
Muhammad S, Minami T, Fukui H, Yoneda K, Kishi R, Shigeta Y, Nakano M (2012) Halide ion complexes of decaborane (B10H14) and their derivatives: noncovalent charge transfer effect on second-order nonlinear optical properties. J Phys Chem 116:1417–1424. https://doi.org/10.1021/jp209385b
Muhammad S, Xu HL, Zhong RL, Su ZM, Al-Sehemi AG, Irfan A (2013) Quantum chemical design of nonlinear optical materials by sp 2-hybridized carbon nanomaterials: issues and opportunities. J Mater Chem 1:5439–5449. https://doi.org/10.1039/C3TC31183J
Muhammad S, Irfan A, Shkir M, Chaudhry AR, Kalam A, AlFaify S, Al-Sehemi AG, Al-Salami AE, Yahia IS, Xu HL, Su ZM (2015) How does hybrid bridging core modification enhance the nonlinear optical properties in donor-p-acceptor configuration? A case study of dinitrophenol derivatives. J Comput Chem 36:118–128. https://doi.org/10.1002/jcc.23777
Muhammad S, Al-Sehemi AG, Irfan A, Chaudhry AR (2016) Tuning the push–pull configuration for efficient second-order nonlinear optical properties in some chalcone derivatives. J Mol Graph Model 68:95–105. https://doi.org/10.1016/j.jmgm.2016.06.012
Muhammad S, Al-Sehemi AG, Su Z, Xu H, Irfan A, Chaudhry AR (2017a) First principles study for the key electronic, optical and nonlinear optical properties of novel donor-acceptor chalcones. J Mol Graph Model 72:58–69. https://doi.org/10.1016/j.jmgm.2016.12.009
Muhammad S, Chaudhry AR, Al-Sehemi AG (2017b) A comparative analysis of the optical and nonlinear optical properties of cross-shaped chromophores: quantum chemical approach. Optik 147:439–445. https://doi.org/10.1016/j.ijleo.2017.08.104
Muhammad S, Al-Sehemi AG, Irfan A, Algarni H, Qiu Y, Xu H, Su Z, Iqbal J (2018) The substitution effect of heterocyclic rings to tune the optical and nonlinear optical properties of hybrid chalcones: a comparative study. J Mol Graph Model 81:25–31. https://doi.org/10.1016/j.jmgm.2018.02.005
Muhammad S, Hussain S, Chen X, Al-Sehemi AG, Li ZJ, Lai CH, Iqbal J (2019a) A dual approach to study the synthesis, crystal structure and nonlinear optical properties of binuclear Pd (II) complex of 3-methyl-5-(trifluoromethyl) pyrazole and its potential quantum chemical analogues. Inorg Chim Acta 494:160–167. https://doi.org/10.1016/j.ica.2019.05.023
Muhammad S, Shehzad RA, Iqbal J, Al-Sehemi AG, Saravanabhavan M, Khalid M (2019b) Benchmark study of the linear and nonlinear optical polarizabilities in proto-type NLO molecule of para-nitroaniline. J Theor Comput Chem 18:1950030. https://doi.org/10.1142/S0219633619500305
Muhammad S, Lai CH, Al-Sehemi AG, Alshahrani T, Iqbal J, Ayub K (2021) Exploring the twisted molecular configurations for tuning their optical and nonlinear optical response properties: a quantum chemical approach. J Mol Graph Model 102:107766. https://doi.org/10.1016/j.jmgm.2020.107766
Muhammad S, Sarwar F, Bibi S, Nadeem R, Mushtaq MW, Al-Sehemi AG, Alarfaji SS, Hussain S (2022) Insighting the functionally modified C60 fullerenes as an efficient nonlinear optical materials: a quantum chemical study. Mater Sci Semicond Process 141:106421. https://doi.org/10.1016/j.mssp.2021.106421
Nakano M, Okumura M, Yamaguchi K, Fueno T (1990) CNDO/S-CI calculations of hyperpolarizabilities. III. regular polyenes, charged polyenes, di-substituted polyenes, polydiacetylene and related species. Mol Cryst Liq Cryst 182:1–15. https://doi.org/10.1080/00268949008047783
Pandey AK, Baboo V, Mishra VN, Singh V, Dwivedi A (2020) Comparative study of molecular docking, structural, electronic, vibrational spectra and fukui function studies of thiadiazole containing schiff base: a complete density functional study. Polycyclic Aromat Compd. https://doi.org/10.1080/10406638.2020.1712440
Pinko C, Margosiak SA, Vanderpool D, Gutowski JC, Condon B, Kan CC (1995) Single-chain recombinant human cytomegalovirus protease: activity against its natural protein substrate and fluorogenic peptide substrates (∗). J Biol Chem 270:23634–23640
Ramesh K, Saravanabhavan M, Rajkumar M, Edison D, Sekar M, Muhammad S, Al-Sehemi AG (2019) Synthesis, growth, structural, thermal, third order nonlinear and computational studies of organic single crystal: 2-Amino-4-picolinium 2-chloro-4-nitrobenzoate. Opt Mater 96:109341. https://doi.org/10.1016/j.optmat.2019.109341
Saeed A, Muhammad S, Rehman Su, Bibi S, Al-Sehemi AG, Khalid M (2020) Exploring the impact of central core modifications among several push-pull configurations to enhance nonlinear optical response. J Mol Graph Model 100:107665. https://doi.org/10.1016/j.jmgm.2020.107665
Shehzad RA, Muhammad S, Iqbal J, Al-Sehemi AG, Yaseen M, Aloui Z, Khalid M (2021) Exploring the optoelectronic and third-order nonlinear optical susceptibility of cross-shaped molecules: insights from molecule to material level. J Mol Model 27:1–10. https://doi.org/10.1007/s00894-020-04619-7
Shinde SS, Sreenath MC, Chitrambalam S, Joe IH, Sekar N (2019) Non-linear optical properties of disperse blue 354 and disperse blue183 by DFT and Z-scan technique. Polycyclic Aromat Compd. https://doi.org/10.1080/10406638.2019.1686404
Shkir M, AlFaify S, Abbas H, Muhammad S (2015) First principal studies of spectroscopic (IR and Raman, UV–visible), molecular structure, linear and nonlinear optical properties of l-arginine p-nitrobenzoate monohydrate (LANB): a new non-centrosymmetric material. Spectrochim Acta A Mol Biomol Spectrosc 147:84–92. https://doi.org/10.1016/j.saa.2015.02.111
Shkir M, AlFaify S, Arora M, Ganesh V, Abbas H, Yahia, (2018) A first principles study of key electronic, optical, second and third order nonlinear optical properties of 3-(4-chlorophenyl)-1-(pyridin-3-yl) prop-2-en-1-one: a novel D-$$\pi $$ π-A type chalcone derivative. J Comput Electron 17:9–20. https://doi.org/10.1007/s10825-017-1050-3
Shkir M, Irfan A, AlFaify S, Patil PS, Al-Sehemi AG (2019) Linear, second and third order nonlinear optical properties of novel noncentrosymmetric donor-acceptor configure chalcone derivatives: a dual approach study. Optik 199:163354. https://doi.org/10.1016/j.ijleo.2019.163354
Song J, Ghosh S, Dhingra N et al (2019) Feasibility study of a Ge2Sb2Te5-clad silicon waveguide as a non-volatile optical on-off switch. OSA Contin 2:49–63. https://doi.org/10.1364/OSAC.2.000049
Srinivasan P, Kanagasekaran T, Gopalakrishnan R (2008) A highly efficient organic nonlinear optical donor: acceptor single crystal: l-valinium picrate. Cryst Growth Des 8:2340–2345. https://doi.org/10.1021/cg701143n
Sun ZN (2018) Electrically tuned nonlinearity. Nat Photon 12:383–385. https://doi.org/10.1038/s41566-018-0201-9
Suzuki Y, Miyazaki E, Takimiya K (2010) ((Alkyloxy) carbonyl) cyanomethylene-substituted thienoquinoidal compounds: a new class of soluble n-channel organic semiconductors for air-stable organic field-effect transistors. J Am Chem Soc 132:10453–10466. https://doi.org/10.1021/ja103171y
Suzuki Y, Shimawaki M, Miyazaki E, Osaka I, Takimiya K (2011) Quinoidal oligothiophenes with (acyl) cyanomethylene termini: synthesis, characterization, properties, and solution processed n-channel organic field-effect transistors. Chem Mater 23:795–804. https://doi.org/10.1021/cm102109p
Takahashi K, Suzuki T, Akiyama K, Ikegami Y, Fukazawa Y (1991) Synthesis and characterization of novel p-terphenoquinone analogs involving a central dihydrothiophenediylidene structure. J Am Chem Soc 113:4576–4583. https://doi.org/10.1021/ja00012a029
Takahashi K, Fujita S, Akiyama K, Miki M, Yanagi K (1998) The first heterotriquinone and dicyanoheterotriquinone methide that undergo a five-stage amphoteric redox reaction. Angew Chem Int Edn 37:2484–2487. https://doi.org/10.1002/(SICI)1521-3773(19981002)37:18%3c2484::AID-ANIE2484%3e3.0.CO;2-B
Van Keuren E, Möhwald H, Rozouvan S, Schrof W, Belov V, Matsuda H, Yamada S (1991) Linear and third order nonlinear optical properties of substituted oligothiophenes. J Chem Phys 110:3584–3590. https://doi.org/10.1063/1.478226
Vishnumurthy K, Sunitha M, Philip R, Adhikari AV (2011) New diphenylamine-based donor–acceptor-type conjugated polymers as potential photonic materials. React Funct Polym 71:1119–1128. https://doi.org/10.1016/j.reactfunctpolym.2011.08.011
Wang WY, Ma NN, Sun SL, Qiu YQ (2014) Redox control of ferrocene-based complexes with systematically extended π-conjugated connectors: switchable and tailorable second order nonlinear optics. Phys Chem Chem Phys 16:4900–4910. https://doi.org/10.1039/C3CP54468K
Willetts A, Rice JE et al (1992) Problems in the comparison of theoretical and experimental hyperpolarizabilities. J Chem Phys 97:7590–7599. https://doi.org/10.1063/1.463479
Xie X, Liu Z, Bai FQ, Zhang HX (2019) Study on the spectral complementary composite dye molecules designed for high performance dye-sensitized solar cells: a theoretical investigation. Comput Theor Chem 1154:44–49. https://doi.org/10.1016/j.comptc.2019.03.017
Zhang GL, Zhang H, Li DP, Chen D, Yu XY, Liu B, Li ZS (2008) End-substitution effect on the geometry and electronic structure of oligoheterocyclics. Theor Chem Acc 121:109–122. https://doi.org/10.1007/s00214-008-0454-3
Zhao Y, Truhlar DG (2008) The M06 suite of density functionals for main group thermochemistry, thermochemical kinetics, noncovalent interactions, excited states, and transition elements: two new functionals and systematic testing of four M06-class functionals and 12 other functionals. Theor Chem Account 120:215–241. https://doi.org/10.1007/s00214-007-0310-x
Zhao Y, Truhlar DG (2011) Applications and validations of the Minnesota density functionals. Chem Phys Lett 502:1–13. https://doi.org/10.1016/j.cplett.2010.11.060
Zhao MT, Samoc M, Singh BP, Prasad PN (1989) Study of third-order microscopic optical nonlinearities in sequentially built and systematically derivatized structures. J Chem Phys 93:7916–7920. https://doi.org/10.1021/j100360a036
Acknowledgements
The authors extend their appreciation to Deanship of Scientific Research at King Khalid University for funding the work through Research Project (R.G.P.2/156/42).
Author information
Authors and Affiliations
Contributions
Shabbir Muhammad has considered the idea and performed calculations Amina Bibi has written the methodology and discussion, visualization. Shafiq-urReheman has performed conceptualization and technical supervision Shamsa Bibi has done supervision and formal analysis of results Abdullah G. Al-Sehemi has done project administration and funding acquisition, H.Algarni and Fatima Sarwar have provided technical support and writing methodology and Supervision.
Corresponding authors
Ethics declarations
Conflict of 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.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Supplementary Information
Below is the link to the electronic supplementary material.
Rights and permissions
About this article
Cite this article
Muhammad, S., Bibi, A., Shafiq-urRehman et al. Exploring the quinoidal oligothiophenes to their robust limit for efficient linear and nonlinear optical response properties. Chem. Pap. 76, 4273–4288 (2022). https://doi.org/10.1007/s11696-022-02167-3
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11696-022-02167-3