Nonlinear optical (NLO) materials are the smartest materials of the era, and have the ability to generate new electromagnetic fields with changed frequencies, phases, and other physical properties. Recently, many cutting edge research reports have been focused on NLO materials especially on those which are composed of sp² hybridized carbon nanostructures. As the carbon nanostructures are composed of abundant π-electrons and have significant delocalization, these are potential candidates for modern NLO materials. Generally, sp² hybridized carbon nanostructures can be divided into zero-dimensional fullerenes, one-dimensional nanotubes and two-dimensional graphene nanoribbons and quantum dots etc. These dimensionally different carbon nanomaterials are promising candidates for a wide range of applications in next-generation nanotechnologies. In present feature article, we first briefly explain a theoretical structure–NLO property relationship based on perturbation theory and then elucidate the crucial factors to control the NLO responses. We put together the different random investigations of sp² hybridized carbon nanostructures for NLO application by highlighting the importance of their several structural designs to tune NLO amplitudes. Furthermore, we make a comparative and updated analysis of the NLO properties of dimensionally different sp² hybridized carbon nanomaterials i.e. fullerenes, carbon nanotubes, and graphene nanoribbons and quantum dots. Finally, we make a brief discussion about different aspects and opportunities to use the sp² hybridized carbon nanomaterials as high performance NLO materials of the future. This review is a focused perspective based on different updated quantum chemical investigations about fullerenes, nanotubes and graphene nanoribbons and quantum dots for their possible use in nonlinear optical applications.

To address the increasing demand of efficient photovoltaic compounds for modern hi-tech applications, efforts have been made herein to design and explore triazatruxene-based novel donor materials with greater efficiencies. Five new molecules, namely M1–M5, were designed by structural modification of acceptor moiety (rhodanine-3-acetic acid) of well known experimentally synthesized JY05 dye (reference R), and their optoelectronic properties are evaluated to be used as donor molecules in organic solar cells. In these molecules M1–M5, triazatruxene acts as a donor unit and benzene spaced different end-capped moieties including 2-(4-(dicyanomethylene)-2-thioxothiazolidin-3-yl)acetic acid (A1), (E)-2-(4-(1-cyano-2-methoxy-2-oxoethylidene)-2-thioxothiazolidin-3-yl)acetic acid (A2), (Z)-2-(3′-ethyl-4′-oxo-2,2′-dithioxo-3′,4′-dihydro-2′H,5H-[4,5′-bithiazolylidene]-3(2H)-yl)acetic acid (A3), (Z)-2-(4′-(dicyano-methylene)-3′-ethyl-2,2′-dithioxo-3′,4′-dihydro-2′H,5H-[4,5′-bithiazol-ylidene]-3(2H)-yl)acetic acid (A4) and 2-((4Z,4′E)-4′-(1-cyano-2-methoxy-2-oxoethylidene)-3′-ethyl-2,2′-dithioxo-3′,4′-dihydro-2′H,5H-[4,5′-bithiazolylidene]-3(2H)-yl)acetic acid (A5) respectively, as acceptor units. The electronic, photophysical and photovoltaic properties of the designed molecules M1–M5 have been compared with reference molecule R. All designed molecules exhibit reduced energy gap in the region of 1.464–2.008 eV as compared to reference molecule (2.509 eV). Frontier molecular orbital (FMO) surfaces confirm the transfer of charge from donor to acceptor units. All designed molecules M1–M5 exhibited an absorption spectrum in the visible region and they were broader as compared to that of reference R. Especially, M5 with highest λ_max value 649.26 nm and lowest transition energy value 1.90 eV was accredited to the strong electron withdrawing end-capped acceptor moiety A5. The highest value of open circuit voltage (V_oc) 1.02 eV with respect to HOMO_donor–LUMO_BTP-4Cl was shown by M5 among all investigated molecules which was 0.15 V larger than reference molecule R. The designed molecule M5 is proven to be the best candidate for both electron and hole transport mobilities due to its smallest λ_e (0.0212 eV) and λ_h (0.0062 eV) values among all studied molecules.

We are considering a new COVID-19 model with an optimal control analysis when vaccination is present. Firstly, we formulate the vaccine-free model and present the associated mathematical results involved. Stability results for ${\mathcal{R}}_0<1$ are shown. In addition, we frame the model with the vaccination class. We look at the mathematical results with the details of the vaccine model. Additionally, we are considering setting controls to minimize infection spread and control. We consider four different controls, such as prevention, vaccination control, rapid screening of people in the exposed category, and people who are identified as infected without screening. Using the suggested controls, we develop an optimal control model and derive mathematical results from it. In addition, the mathematical model with control and without control is resolved by the forward–backward Runge–Kutta method and presents the results graphically. The results obtained through optimal control suggest that controls can be useful for minimizing infected individuals and improving population health.

We report a novel type of organic–inorganic hybrid material with rare two-dimensional nonlinear optical (NLO) properties. The density functional theory (DFT) calculations combined with the finite-field (FF) method show that the designed molecules (6,9 organo-derivatives of B₁₀H₁₄) could carry the characteristic NLO properties of both organic and inorganic materials. Interestingly, due to their unique V-shaped structures, they have large off-diagonal first hyperpolarizability tensors or nonlinear anisotropy, which is an advantage in their practical applications over conventional donor–π-acceptor (D–π-A) NLO-phores. The systematic substitutions of terminal donor/acceptor groups as well as the extension of π-conjugation along the V-shape in these derivatives have been evaluated to guide a purpose-oriented synthesis of NLO material. All the systems in the present study have been categorized into Set-I and Set-II with D–π-A–π-D and A–π-D–π-A configurations, respectively. These designed derivatives show large amplitudes of β_z values. For example, systems 3N (6,9-[(NCPh–NO₂)₂]-B₁₀H₁₂) and 4N (6,9-[((NCPh)₂-NO₂)₂]-B₁₀H₁₂) have β_z amplitudes as large as 34.16 and 276.91 × 10³ a.u. which are 380 and 3000 times larger than those of a typical NLO molecule of urea, respectively. Remarkably, the substitution of nitrogen atoms with 6,9 hydrogen atoms in decaborane is shown to cause a lone pair back donation to vacant p orbitals of 6,9 boron atoms of the decaborane basket. This p orbital overlapping verticalizes the V-arms of the decaborane derivatives and boosts their nonlinear anisotropies due to their larger off-diagonal tensor components. The nonlinear anisotropy values are significantly larger, ranging from 1 (minimum in system 1) to 31.90 (maximum in system 3A) due to their unique V-shape. Comparison of their efficiencies with standard molecules demonstrates that our designed organic–inorganic hybrid molecules have significant potential as excellent candidates for NLO applications.