Home Fluorescent styryl chromophores with rigid (pyrazole) donor and rigid (benzothiophenedioxide) acceptor – complete density functional theory (DFT), TDDFT and nonlinear optical study
Article
Licensed
Unlicensed Requires Authentication

Fluorescent styryl chromophores with rigid (pyrazole) donor and rigid (benzothiophenedioxide) acceptor – complete density functional theory (DFT), TDDFT and nonlinear optical study

  • Sulochana Bhalekar , Archana Bhagwat and Nagaiyan Sekar ORCID logo EMAIL logo
Published/Copyright: March 4, 2021
Become an author with De Gruyter Brill
Submit Manuscript Author Information
Physical Sciences Reviews
From the journal Physical Sciences Reviews Volume 8 Issue 4

Abstract

Density functional theory (DFT) and time-dependent DFT computations were employed to examine linear and nonlinear optical (NLO) characteristics of (E)-4-((1,1-dioxido-3-oxobenzo[b]thiophen-2(3H)-ylidene) ethyl)-1-phenyl-1H-pyrazol-5(4H)-one derived styryl dyes. NLO properties were computed using the two different global hybrid functionals B3LYP, BHandHLYP and three range separated hybrid functionals CAM B3LYP, wB97, wB97X and wB97XD with the basis sets 6–311++G(d,p), cc-pVDZ and cc-pVTZ. The compounds shows higher values of dipole moment around 8–9 Debye than the other compounds. They show higher values of α 0, ß 0 and γ 0 values. The values of γ 0 are around 204–544 × 10−36 e.s.u. with the method, B3LYP/6–311++G(d, p). We have calculated the mean absolute error (MAE) for dipole moment, α 0, ß 0 and γ 0 values. It is observed that MAE is less (0.89) for wB97/6–311++G(d,p) which indicates that wB97 is the most suited functional for all three compounds. Chemical stability and reactivity of these dyes were studied using electrophilicity index and chemical hardness and hyperhardness.

Keywords: electrophilicity index; MAE; NLO; pyrazole
Corresponding author: Nagaiyan Sekar, Department of Dyestuff Technology, Institute of Chemical Technology, Matunga, Mumbai 400 019, India, E-mail:

Funding source: University Grants Commission (UGC)

Award Identifier / Grant number: 501100001501

Acknowledgment

Author SBB and AAB are thankful for University Grants Commission (UGC) New Delhi, India for financial support as a junior and senior research fellowship.

  1. Author contributions: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.

  2. Research funding: None declared.

  3. Conflict of interest statement: The authors declare no conflicts of interest regarding this article.

References

1. Körzdörfer, T, Brédas, J-L. Organic electronic materials: recent advances in the DFT description of the ground and excited states using tuned range-separated hybrid functionals. [Internet]. Acc Chem Res 2014;47:3284–91. Available from: http://pubs.acs.org/doi/10.1021/ar500021t.10.1021/ar500021tSearch in Google Scholar PubMed

2. Barone, V. Structure, magnetic properties and reactivities of open-shell species from density functional and self-consistent hybrid methods. [Internet]; 1995:287–334. Available from: http://www.worldscientific.com/doi/abs/10.1142/9789812830586_0008.10.1142/9789812830586_0008Search in Google Scholar

3. Verma, D. Density Functional Theory (DFT) as a powerful tool for designing corrosion inhibitors in aqueous phase[Internet] 2018:87–104. Available from: https://www.intechopen.com/doi.org10.5772intechopen.78333.10.5772/intechopen.78333Search in Google Scholar

4. Boyd, RJ, Wang, J, Eriksson, LA. The electron density as calculated from density functional theory. [Internet]; 1995:369–401. Available from: http://www.worldscientific.com/doi/abs/10.1142/9789812830586_0010.10.1142/9789812830586_0010Search in Google Scholar

5. Zara, Z, Iqbal, J, Ayub, K, Irfan, M, Mahmood, A, Khera, RA, et al.. A comparative study of DFT calculated and experimental UV–vis spectra for thirty carboline and carbazole based compounds. [Internet]. J Mol Struct 2017;1149:282–98. https://doi.org/10.1016/j.molstruc.2017.07.093.Search in Google Scholar

6. Casida, ME. Time-dependent density functional response theory for molecules. [Internet]; 1995:155–92. Available from: http://www.worldscientific.com/doi/abs/10.1142/9789812830586_0005.10.1142/9789812830586_0005Search in Google Scholar

7. Chermette, H. Chemical reactivity indexes in density functional theory. [Internet]. J Comput Chem 1999;20:129–54. Available from: http://doi.wiley.com/10.1002/%28SICI%291096-987X%2819990115%2920%3A1%3C129%3A%3AAID-JCC13%3E3.0.CO%3B2-A.Search in Google Scholar

8. Chai, J-D, Head-Gordon, M. Systematic optimization of long-range corrected hybrid density functionals. [Internet]. J Chem Phys 2008;128:84106. Available from: http://aip.scitation.org/doi/10.1063/1.2834918.10.1063/1.2834918Search in Google Scholar PubMed

9. Kohn, W, Becke, AD, Parr, RG. Density functional theory of electronic structure. [Internet]. J Phys Chem 1996;100:12974–80. Available from: https://pubs.acs.org/doi/10.1021/jp960669l.10.1021/jp960669lSearch in Google Scholar

10. Tsang, TY, Osbrn, TA. The Spectral Prerties of Time Delay Department of Physics. Brooklyn college of the city University of New York, NY 11210. Nucl Phys 1975;247:43–50. https://doi.org/10.1016/0375-9474(75)90275-4.Search in Google Scholar

11. Mohbiya, DR, Sekar, N. Electronic structure and spectral properties of indole based fluorescent styryl dyes: comprehensive study on linear and non-linear optical properties by DFT/TDDFT method. [Internet]. Comput Theor Chem 2018;1139:90–101. https://doi.org/10.1016/j.comptc.2018.07.015.Search in Google Scholar

12. Geerlings, P, De Proft, F, Langenaeker, W. Conceptual density functional theory. [Internet]. Chem Rev 2003;103:1793–874. Available from: https://pubs.acs.org/doi/10.1021/cr990029p.10.1021/cr990029pSearch in Google Scholar PubMed

13. Parr, RG, Szentpály, LV, Liu, S. Electrophilicity index. [Internet]. J Am Chem Soc 1999;121:1922–4. Available from: https://pubs.acs.org/doi/10.1021/ja983494x.10.1021/ja983494xSearch in Google Scholar

14. Rao, VP, Jen, AKY, Wong, KY, Drost, KJ. Dramatically enhanced second-order nonlinear optical susceptibilities in tricyanovinylthiophene derivatives. J Chem Soc Chem Commun 1993;14:1118–20. https://doi.org/10.1039/C39930001118.Search in Google Scholar

15. Miniewicz, A, Palewska, K, Sznitko, L, Lipinski, J. Single- and two-photon excited fluorescence in organic nonlinear optical single crystal 3-(1,1-Dicyanoethenyl)-1-phenyl-4,5-dihydro-1 H -pyrazole. [Internet]. J Phys Chem 2011;115:10689–97. Available from: http://pubs.acs.org/doi/abs/10.1021/jp204435s.10.1021/jp204435sSearch in Google Scholar PubMed

16. Jen, AK, Rao, P, Drost, KJ, Michael, YW. Functionalized fused thiophenes: a new class of thermally stable and efficient second-order nonlinear optical chromophores. Chem Mater 1994;6:2210–12. https://doi.org/10.1021/cm00048a004.Search in Google Scholar

17. Drost, KJ, Rao, VP, Jen, AKY. Theoretical and experimental studies of the molecular second order nonlinear optical responses of heteroaromatic compounds. J Chem Phys 1994;100:6818. https://doi.org/10.1063/1.467041.Search in Google Scholar

18. Steybe, F, Effenberger, F, Gubler, U, Bosshard, C, Günter, P. Highly polarizable chromophores for nonlinear optics: syntheses, structures and properties of donor-acceptor substituted thiophenes and oligothiophenes. Tetrahedron 1998;54:8469–80. https://doi.org/10.1016/S0040-4020(98)00450-5.Search in Google Scholar

19. Jen, AK, Rao, VP, Wong, KY, Drost, KJ. Functionalized thiophenes : second-order nonlinear optical materials 2000;90:90–2. https://doi.org/10.1039/C39930000090.Search in Google Scholar

20. Wong, KY, Drost, KJ. Novel push-pull thiophenes for second order nonlinear optical applications 2000;34:1747–50. https://doi.org/10.1016/S0040-4039(00)60768-2.Search in Google Scholar

21. Wong, KY, Jen, AKY, Pushkara Rao, V, Drost, KJ. Theoretical and experimental studies of the molecular second order nonlinear optical responses of heteroaromatic compounds. J Chem Phys 1994;100:6818–25. https://doi.org/10.1063/1.467041.Search in Google Scholar

22. Cidália, MR, Castroa, R, Maurício, AA, Fonsecaa, C, Belsleyb, M, Manuela, M, et al.. Highly efficient and thermally stable NLO organic materials based on pyrrole and thiophene heterocycles. Available from: https://www.researchgate.net/journal/0277-786X_Proceedings_of_SPIE-The_International_Society_for_Optical_Engineering 26 July 2011; https://doi.org/10.1117/12.892205.Search in Google Scholar

23. Chandrakantha, B, Isloor, AM, Sridharan, K, Philip, R, Shetty, P, Padaki, M. Novel N-substituted-5-phenyl-1H-pyrazole-4-ethyl carboxylates as potential NLO materials. Arab J Chem 2013;6:97–102. https://doi.org/10.1016/j.arabjc.2010.09.024.Search in Google Scholar

24. Makowska-Janusik, M, Kajzar, F, Miniewicz, A, Mydlova, L, Rau, I. First principle calculations of the electronic and vibrational properties of the 3-(1,1-Dicyanoethenyl)-1-phenyl-4,5-dihydro-1H-pyrazole molecule. [Internet]. J Phys Chem 2015;119:1347–58. Available from: https://pubs.acs.org/doi/10.1021/jp510102q.10.1021/jp510102qSearch in Google Scholar PubMed

25. Bureš, F. Fundamental aspects of property tuning in push–pull molecules. [Internet]. RSC Adv 2014;4:58826–51. Available from: http://xlink.rsc.org/?DOI=C4RA11264D.10.1039/C4RA11264DSearch in Google Scholar

26. Chen, S, Li, Y, Yang, W, Chen, N, Liu, H, Li, Y. Synthesis and tuning optical nonlinear properties of molecular crystals of benzothiadiazole. [Internet]. J Phys Chem C 2010;114:15109–15. Available from: https://pubs.acs.org/doi/10.1021/jp103159b.10.1021/jp103159bSearch in Google Scholar

27. Liyanage, PS, de Silva, RM, de Silva, KMN. Nonlinear optical (NLO) properties of novel organometallic complexes: high accuracy density functional theory (DFT) calculations. [Internet]. J Mol Struct THEOCHEM 2003;639:195–201. Available from: http://linkinghub.elsevier.com/retrieve/pii/S0166128003006377.10.1016/j.theochem.2003.08.009Search in Google Scholar

28. Facchetti, A, Abbotto, A, Beverina, L, van der Boom, ME, Dutta, P, Evmenenko, G, et al.. Azinium−(π-Bridge)−pyrrole NLO-phores: influence of heterocycle acceptors on chromophoric and self-assembled thin-film properties #. [Internet]. Chem Mater 2002;14:4996–5005. Available from: https://pubs.acs.org/doi/10.1021/cm0205635.10.1021/cm0205635Search in Google Scholar

29. Kwon, O-P, Ruiz, B, Choubey, A, Mutter, L, Schneider, A, Jazbinsek, M, et al.. Organic nonlinear optical crystals based on configurationally locked polyene for melt growth. [Internet]. Chem Mater 2006;18:4049–54. Available from: https://pubs.acs.org/doi/10.1021/cm0610130.10.1021/cm0610130Search in Google Scholar

30. Oudar, JL. Optical nonlinearities of conjugated molecules. Stilbene derivatives and highly polar aromatic compounds. [Internet]. J Chem Phys 1977;67:446–57. Available from: http://aip.scitation.org/doi/10.1063/1.434888.10.1063/1.434888Search in Google Scholar

31. Shao, J, Ji, S, Li, X, Zhao, J, Zhou, F, Guo, H. Thiophene-inserted aryl-dicyanovinyl compounds: the second generation of fluorescent molecular rotors with significantly redshifted emission and large stokes shift. [Internet]. Eur J Org Chem 2011;2011:6100–9. Available from: http://doi.wiley.com/10.1002/ejoc.201100891.10.1002/ejoc.201100891Search in Google Scholar

32. Scholz, N, Jadhav, A, Shreykar, M, Behnke, T, Nirmalananthan, N, Resch-Genger, U, et al.. Coumarin-rhodamine hybrids—novel probes for the optical measurement of viscosity and polarity. [Internet]. J Fluoresc 2017;27:1949–56. Available from: http://link.springer.com/10.1007/s10895-017-2165-4.10.1007/s10895-017-2165-4Search in Google Scholar PubMed

33. Haidekker, MA, Brady, TP, Lichlyter, D, Theodorakis, EA. Effects of solvent polarity and solvent viscosity on the fluorescent properties of molecular rotors and related probes. [Internet]. Bioorg Chem 2005;33:415–25. Available from: http://linkinghub.elsevier.com/retrieve/pii/S0045206805000763.10.1016/j.bioorg.2005.07.005Search in Google Scholar PubMed

34. Paul, A, Samanta, A. Free volume dependence of the internal rotation of a molecular rotor probe in room temperature ionic liquids. [Internet]. J Phys Chem B 2008;112:16626–32. Available from: https://pubs.acs.org/doi/10.1021/jp8060575.10.1021/jp8060575Search in Google Scholar PubMed

35. Shreykar, MR, Sekar, N. NLOphoric donor-rigidified ESIPT dyes – synthesis, pH study, solvatochromism and DFT insights. [Internet]. J Lumin 2017;192:343–58. https://doi.org/10.1016/j.jlumin.2017.06.061.Search in Google Scholar

36. Haidekker, MA, Theodorakis, EA. Environment-sensitive behavior of fluorescent molecular rotors. [Internet]. J Biol Eng 2010;4:11. Available from: http://jbioleng.biomedcentral.com/articles/10.1186/1754-1611-4-11.10.1186/1754-1611-4-11Search in Google Scholar PubMed PubMed Central

37. Jin, Y-J, Park, H, Ohk, Y-J, Kwak, G. Hydrodynamic fluorescence emission behavior of molecular rotor-based vinyl polymers used as viscosity sensors. [Internet]. Polymer 2017;132:79–87. https://doi.org/10.1016/j.polymer.2017.10.054.Search in Google Scholar

38. Gao, Z, Wang, Z, Shan, T, Liu, Y, Shen, F, Pan, Y, et al.. High-efficiency deep blue fluorescent emitters based on phenanthro[9,10-d] imidazole substituted carbazole and their applications in organic light emitting diodes. [Internet]. Org Electron 2014;15:2667–76. https://doi.org/10.1016/j.orgel.2014.07.019.Search in Google Scholar

39. Pander, P, Motyka, R, Zassowskic, P, Etherington, MK, Varsano, D, da Silva, TJ, et al.. Thermally activated delayed fluorescence mediated through the upper triplet state manifold in non-charge-transfer star-shaped triphenylamine–carbazole molecules. [Internet]. J Phys Chem C 2018;122:23934–42. Available from: http://pubs.acs.org/doi/10.1021/acs.jpcc.8b07610.10.1021/acs.jpcc.8b07610Search in Google Scholar

40. Uoyama, H, Goushi, K, Shizu, K, Nomura, H, Adachi, C. Highly efficient organic light-emitting diodes from delayed fluorescence. [Internet]. Nature 2012;492:234–8. https://doi.org/10.1038/nature11687.Search in Google Scholar PubMed

41. Seniutinas, G, Tomašiūnas, R, Czaplicki, R, Sahraoui, B, Daškevičienė, M, Getautis, V, et al.. Arylmethylene-1,3-indandione based molecular glasses: third order optical non-linearity. [Internet]. Dye Pigment 2012;95:33–40. Available from: https://linkinghub.elsevier.com/retrieve/pii/S0143720812000678.10.1016/j.dyepig.2012.03.011Search in Google Scholar

42. Hauck, M, Stolte, M, Schönhaber, J, Kuball, H, Müller, TJJ. Synthesis, electronic, and electro-optical properties of emissive solvatochromic phenothiazinyl merocyanine dyes. [Internet]. Chem Eur J 2011;17:9984–98. Available from: http://doi.wiley.com/10.1002/chem.201100592.10.1002/chem.201100592Search in Google Scholar PubMed

43. Haenle, JC, Bruchlos, K, Ludwigs, S, Köhn, A, Laschat, S. Rigidified push-pull dyes: using chromophore size, donor, and acceptor units to tune the ground state between neutral and the cyanine limit. [Internet]. Chempluschem 2017;82:1197–210. Available from: http://doi.wiley.com/10.1002/cplu.201700347.10.1002/cplu.201700347Search in Google Scholar PubMed

44. Ruiz Delgado, MC, Casado, J, Hernández, V, Lopez Navarrete, JT, Orduna, J, Villacampa, B, et al.. Electronic, optical, and vibrational properties of bridged dithienylethylene-based NLO chromophores. [Internet]. J Phys Chem C 2008;112:3109–20. Available from: https://pubs.acs.org/doi/10.1021/jp710459c.10.1021/jp710459cSearch in Google Scholar

45. Lawrentz, U, Grahn, W, Lukaszuk, K, Klein, C, Wortmann, R, Feldner, A, et al.. Donor-acceptor oligoenes with a locked all-trans conformation: synthesis and linear and nonlinear optical properties. [Internet]. Chem Eur J 2002;8:1573–90. Available from: http://doi.wiley.com/10.1002/1521-3765%2820020402%298%3A7%3C1573%3A%3AAID-CHEM1573%3E3.0.CO%3B2-T.10.1002/1521-3765(20020402)8:7<1573::AID-CHEM1573>3.0.CO;2-TSearch in Google Scholar

46. Kumari, R, Varghese, A, George, L, KBA. Photophysical study of 6-amino-3-methyl-4-(4-nitrophenyl)-1,4-dihydropyrano[2,3-c]pyrazole-5-carbonitrile and estimation of ground-state and singlet excited-state dipole moments by solvatochromic approaches. [Internet]. J Mol Liq 2016;222:828–35. https://doi.org/10.1016/j.molliq.2016.07.133.Search in Google Scholar

47. Xia, J Bin, Li, FY, Yang, H, Li, XH, Huang, CH. A novel quasi-solid-state dye-sensitized solar cell based on monolayer capped nanoparticles framework materials. J Mater Sci 2007;42:6412–6. https://doi.org/10.1007/s10853-006-1184-3.Search in Google Scholar

48. Chen, X-L, Yu, R, Zhang, Q-K, Zhou, LJ, Wu, XY, Zhang, Q, et al.. Rational design of strongly blue-emitting cuprous complexes with thermally activated delayed fluorescence and application in solution-processed OLEDs. Chem Mater [Internet] 2013 [cited 2018];25:3910–20. Available from: https://pubs.acs.org/doi/pdf/10.1021/cm4024309.10.1021/cm4024309Search in Google Scholar

49. Lanke, SK, Sekar, N. Pyrazole based solid state emissive NLOphores with TICT characteristics: synthesis, DFT and TDDFT studies. [Internet]. Dye Pigment 2016;126:62–75. https://doi.org/10.1016/j.dyepig.2015.11.014.Search in Google Scholar

50. Szukalski, A, Sznitko, L, Cyprych, K, Miniewicz, A, Mysliwiec, J. Light amplification in derivatives of pyrazoline-based systems. [Internet]. J Phys Chem C 2014;118:8102–10. Available from: http://pubs.acs.org/doi/10.1021/jp411031b.10.1021/jp411031bSearch in Google Scholar

51. Barberá, J, Clays, K, Giménez, R, Houbrechts, S, Persoons, A, Serrano, JL. Versatile optical materials: fluorescence, non-linear optical and mesogenic properties of selected 2-pyrazoline derivatives. [Internet]. J Mater Chem 1998;8:1725–30. https://doi.org/10.1039/A802070A.Search in Google Scholar

52. Moylan, CR, Twieg, RJ, Lee, VY, Swanson, SA, Betterton, KM, Miller, RD. Nonlinear optical chromophores with large hyperpolarizabilities and enhanced thermal stabilities. [Internet]. J Am Chem Soc 1993;115:12599–600. Available from: http://pubs.acs.org/doi/abs/10.1021/ja00079a055.10.1021/ja00079a055Search in Google Scholar

53. Fang, W, Shao, C-S, Cheng, W-D, Tang, H-Y, Zheng, W-C. Theoretical investigation of optical and paramagnetic resonance spectra of [NiF6]4− clusters with orthorhombic symmetry. [Internet]. Spectrochim Acta Part A Mol Biomol Spectrosc 2013;115:483–7. https://doi.org/10.1016/j.saa.2013.06.074.Search in Google Scholar PubMed

54. Hu, ZY, Fort, A, Barzoukas, M, Jen, AKY, Barlow, S, Marder, SR. Trends in optical nonlinearity and thermal stability in electrooptic chromophores based upon the 3-(dicyanomethylene)-2,3-dihydrobenzothiophene-1, 1-dioxide acceptor. J Phys Chem B 2004;108:8626–30. https://doi.org/10.1021/jp036728u.Search in Google Scholar

55. Singh Bhatti, H, Seshadri, S. Novel disperse dyes from benzo[b]thiophene-3(2H)-one-1,1-dioxide and ethyl benzo[b]thien-3(2H)-ylidenecyanoacetate,S,S-dioxide: synthesis and properties. [Internet]. Dye Pigment 2004;62:83–92. Available from: http://linkinghub.elsevier.com/retrieve/pii/S0143720803002365.10.1016/j.dyepig.2003.11.010Search in Google Scholar

56. Shenoy, VU, Patel, VP, Seshadri, S. Disperse dyes derived from 3-Oxo-2,3-dihydrobenzo[b]thiophene-1,1-dioxide and 3[dicyanomethylene-2,3-dihydrobenzo[b]thiophene-1,1-dioxide. Dye Pigment 1989;11:37–46.10.1016/0143-7208(89)85024-7Search in Google Scholar

57. Yanai, T, Tew, DP, Handy, NC. A new hybrid exchange-correlation functional using the Coulomb-attenuating method (CAM-B3LYP). Chem Phys Lett 2004;393:51–7. https://doi.org/10.1016/j.cplett.2004.06.011.Search in Google Scholar

58. Li, R, Zheng, J, Truhlar, DG. Density functional approximations for charge transfer excitations with intermediate spatial overlap. Phys Chem Chem Phys 2010;12:12697–701. https://doi.org/10.1039/c0cp00549e.Search in Google Scholar PubMed

59. Chai, J-D, Head-Gordon, M. Long-range corrected hybrid density functionals with damped atom–atom dispersion corrections. [Internet]. Phys Chem Chem Phys 2008;10:6615. Available from: http://xlink.rsc.org/?DOI=b810189b.10.1039/b810189bSearch in Google Scholar PubMed

60. Lanke, SK, Sekar, N. Coumarin push-pull NLOphores with red emission: solvatochromic and theoretical approach. J Fluoresc 2016;26:949–62. https://doi.org/10.1007/s10895-016-1783-6.Search in Google Scholar PubMed

61. Carthigayan, K, Xavier, S, Periandy, S. HOMO-LUMO, UV, NLO, NMR and vibrational analysis of 3-methyl-1-phenylpyrazole using FT-IR, FT-Raman FT-NMR spectra and HF-DFT computational methods. [Internet]. Spectrochim Acta Part A Mol Biomol Spectrosc 2015;142:350–63. https://doi.org/10.1016/j.saa.2014.11.011.Search in Google Scholar PubMed

62. Islam, N, Ghosh, DC. On the electrophilic character of molecules through its relation with electronegativity and chemical hardness. [Internet]. Int J Mol Sci 2012;13:2160–75. Available from: http://www.mdpi.com/1422-0067/13/2/2160.10.3390/ijms13022160Search in Google Scholar PubMed PubMed Central

63. Figueredo, S, Páez, M, Torres, F. The electrophilic descriptor. [Internet]. Comput Theor Chem 2019;1157:34–9. https://doi.org/10.1016/j.comptc.2019.04.011.Search in Google Scholar

64. Gutiérrez-Oliva, S, Jaque, P, Toro-Labbé, A. Using Sanderson’s principle to estimate global electronic properties and bond energies of hydrogen-bonded complexes. [Internet]. J Phys Chem 2000;104:8955–64. Available from: https://pubs.acs.org/doi/10.1021/jp000777e.10.1021/jp000777eSearch in Google Scholar

65. Fuentealba, P, Parr, RG. Higher‐order derivatives in density‐functional theory, especially the hardness derivative ∂η/∂ N. [Internet]. J Chem Phys 1991;94:5559–64. Available from: http://aip.scitation.org/doi/10.1063/1.460491.10.1063/1.460491Search in Google Scholar

66. Morell, C, Grand, A, Toro-Labbé, A, Chermette, H. Is hyper-hardness more chemically relevant than expected?. [Internet]. J Mol Model 2013;19:2893–900. Available from: http://link.springer.com/10.1007/s00894-013-1778-z.10.1007/s00894-013-1778-zSearch in Google Scholar PubMed

67. Sharma, R, Joshi, S, Bhattacharjee, R, Pant, DD. Solvent effect on absorption and fluorescence spectra of cinchonine and cinchonidine dications: estimation of ground and excited state dipole moments by experimental and numerical studies. [Internet]. J Mol Liq 2015;206:159–64. https://doi.org/10.1016/j.molliq.2015.02.002.Search in Google Scholar

68. Ghanavatkar, CW, Mishra, VR, Sekar, N, Methew, E, Thomas, E, Joe, I. Benzothiazole pyrazole containing emissive azo dyes decorated with ESIPT core: linear and non linear optical properties, Z scan, optical limiting, laser damage threshold with comparative DFT studies. J Mol Str 2019;1203:127401. https://doi.org/10.1016/j.saa.2014.08.111.Search in Google Scholar PubMed

69. Lytel, R, Mossman, S, Crowell, E, Kuzyk, MG. Exact fundamental limits of the first and second hyperpolarizabilities. [Internet]. Phys Rev Lett 2017;119:73902. Available from: https://link.aps.org/doi/10.1103/PhysRevLett.119.073902.10.1103/PhysRevLett.119.073902Search in Google Scholar PubMed

70. Kuzyk, MG. Fundamental limits of all nonlinear-optical phenomena that are representable by a second-order nonlinear susceptibility. [Internet]. J Chem Phys 2006;125:154108. Available from: http://aip.scitation.org/doi/10.1063/1.2358973.10.1063/1.2358973Search in Google Scholar PubMed

71. Kuzyk, MG, Watkins, DS. The effects of geometry on the hyperpolarizability. [Internet]. J Chem Phys 2006;124:244104. Available from: http://aip.scitation.org/doi/10.1063/1.2205859.10.1063/1.2205859Search in Google Scholar PubMed

72. Pérez-Moreno, J, Zhao, Y, Clays, K, Kuzyk, MG. Modulated conjugation as a means for attaining a record high intrinsic hyperpolarizability. [Internet]. Opt Lett 2007;32:59. Available from: https://www.osapublishing.org/abstract.cfm?URI=ol-32-1-59.10.1364/OL.32.000059Search in Google Scholar

73. Kuzyk, MG, Pérez-Moreno, J, Shafei, S. Sum rules and scaling in nonlinear optics. [Internet]. Phys Rep 2013;529:297–398. https://doi.org/10.1016/j.physrep.2013.04.002.Search in Google Scholar

Supplementary Material

The online version of this article offers supplementary material (https://doi.org/10.1515/psr-2019-0129).

Published Online: 2021-03-04

© 2020 Walter de Gruyter GmbH, Berlin/Boston

Articles in the same Issue

  1. Frontmatter
  2. Reviews
  3. Non-collinear magnetism & multiferroicity: the perovskite case
  4. Fluorescent styryl chromophores with rigid (pyrazole) donor and rigid (benzothiophenedioxide) acceptor – complete density functional theory (DFT), TDDFT and nonlinear optical study
  5. Investigating the biological actions of some Schiff bases using density functional theory study
  6. Traditional uses, biological activities, and phytochemicals of Lecaniodiscus cupanioides: a review
  7. Protein modeling
  8. Advancements in cancer chemotherapy
  9. Synthesis of magnetic ferrogels: a tool-box approach for finely tuned magnetic- and temperature-dependent properties
https://doi.org/10.1515/psr-2019-0129
Keywords for this article
electrophilicity index; MAE; NLO; pyrazole

Articles in the same Issue

  1. Frontmatter
  2. Reviews
  3. Non-collinear magnetism & multiferroicity: the perovskite case
  4. Fluorescent styryl chromophores with rigid (pyrazole) donor and rigid (benzothiophenedioxide) acceptor – complete density functional theory (DFT), TDDFT and nonlinear optical study
  5. Investigating the biological actions of some Schiff bases using density functional theory study
  6. Traditional uses, biological activities, and phytochemicals of Lecaniodiscus cupanioides: a review
  7. Protein modeling
  8. Advancements in cancer chemotherapy
  9. Synthesis of magnetic ferrogels: a tool-box approach for finely tuned magnetic- and temperature-dependent properties
Sign up now to receive a 20% welcome discount
Institutional Access
How does access work?
Have an idea on how to improve our website?
Please write us.
© 2025 De Gruyter Brill
Downloaded on 11.9.2025 from https://www.degruyterbrill.com/document/doi/10.1515/psr-2019-0129/pdf
Scroll to top button