Fused ring effect on optical nonlinearity and structure property relationship of anthracenyl chalcone based push-pull chromophores

The Ultraviolet-visible (UV-Vis) spectra indicate that anthracenyl chalcones (ACs) have high maximum wavelengths and good transparency windows for optical applications and are suitable for optoelectronic applications owing to their HOMO–LUMO energy gaps (2.93 and 2.76 eV). Different donor substituents on the AC affect their dipole moments and nonlinear optical (NLO) responses. The positive, negative, and neutral electrostatic potential regions of the molecules were identified using molecular electrostatic potential (MEP). The stability of the molecule on account of hyperconjugative interactions and accompanying charge delocalization was analyzed using natural bond orbital (NBO) analysis. Open and closed aperture Z-scans were performed using a continuous-wave frequency-doubled diode-pumped solid-state (DPSS) laser to measure the nonlinear absorption and nonlinear refractive index coefficients, respectively. The valley-to-peak profile of AC indicated a negative nonlinear refractive index coefficient. The obtained single crystals possess reverse saturation absorption due to excited-state absorption. The structural and nonlinear optical properties of the molecules have been discussed, along with the role of anthracene substitution for enhancing the nonlinear optical properties. The calculated third-order susceptibility value was 1.10 x10-4 esu at an intensity of 4.1 kW/cm2, higher than the reported values for related chalcone derivatives. The NLO response for both ACs offers excellent potential in optical switching and limiting applications.


Introduction
Nonlinear optics is a key area in science and technology for modern hi-tech applications. Organic materials have delocalized electrons in the n!π � or π!π � orbitals resulting in better nonlinear optical (NLO) properties than inorganic materials [1][2][3][4]; further, they have attracted the continued interest of researchers to develop better organic nonlinear optical materials [5]. Chalcones are donor-acceptor-conjugated organic materials with electron donor (D) and The crystal structure was solved directly using SHELXTL [20] and refined using the full-matrix least-squares technique on F 2 . Absorption correction of the final crystal data was performed using SADABS [19]. All geometrical calculations were performed using PLATON [21], and the molecular graphics were drawn using SHELXTL [20]. Anisotropic thermal factors were assigned to all the non-hydrogen atoms. The hydrogen atoms bound to carbon were positioned geometrically (C-H = 0.93 Å) with U iso (H) = 1.2 U eq (C). Details of the data collection conditions and parameters of the refinement process are given in Table 1.

Spectroscopy analyses
Fourier transform infrared spectroscopy (FTIR) spectra were recorded using a Fourier transform infrared attenuated total reflectance spectroscope (FTIR-ATR) (Perkin Elmer Spotlight 2000) equipped with a diamond crystal accessory. 1 H and 13 C nuclear magnetic resonance (NMR) spectra were recorded at 500 MHz in DMSO-d6 using a Bruker 500 MHz Avance III spectrometer. The chemical shifts (δ) are reported in parts per million (ppm) downfield from tetramethylsilane (TMS) internal reference. The UV-Vis absorption spectrum of the sample was recorded in Dimethylsulfoxide (DMSO) solution using a Shimadzu UV-1800 spectrophotometer in the spectral region of 200-800 nm.

Third order nonlinearity
The refractive index, n, of the samples was measured using a digital refractometer (DR201-95, KRUSS). UV-Vis absorbance spectra of both samples were obtained to calculate the linear absorption coefficient, α, with DMSO solvent. The NLO properties of the structure were investigated using the Z-scan technique, which computes the intensity-dependent transmission used to detect nonlinear refractions and nonlinear absorption simultaneously. The Z-scan setup is illustrated in Fig 3. A continuous-wave frequency-doubled diode-pumped solid-state (DPSS) laser was used as the excitation laser, and a silicon-amplified photodetector with an adjustable gain was used as the detector. The radius of the Gaussian beam spot at the focal point was found to be 23 μm using a laser beam profiler (Beam Master, Coherent) with a converging lens of f = 20 cm. The sample was kept in a quartz cuvette of 1 mm path length and mounted on a precision motorized stage. Although the NLO coefficient of organic solvents, such as DMSO, is low (10 −14 -10 −16 esu) [22], Z-scan measurements were performed using DMSO at several laser intensities to remove the NLO contribution of the solvent in the results. These scans did not reveal nonlinear signals, indicating that the nonlinear optical properties of the samples originate from the AC compounds.
The peak followed by a valley-normalized transmittance, obtained from the closed-aperture Z-scan, is defined as ΔT P-V = T P −T v [23]. The variation in this quantity as a function of |Δφ 0 | is given by where, |Δφ 0 | = on-axis phase shift at the focus where, r 0 = Aperture radius ω 0 = beam radius at the aperture in the linear regime. Then nonlinear refractive index, n 2 [23] is given by where, λ = wavelength of the laser I 0 = intensity of the laser beam at focus z = 0 [23] where, L eff = effective thickness of sample α = linear absorption coefficient. L = Thickness of the sample.

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Fused ring effect on optical nonlinearity of anthracenyl chalcone The nonlinear absorption coefficient, β, can be estimated using the open-aperture Z-scan data. The normalized transmittance for the open-aperture condition [24] is given by or q 0 (z) < 1 [24], where, = diffraction length of the beam ω 0 = beam waist radius at the focal point k = 2π/λ = Wave vector. Then, the nonlinear absorption coefficient, β, is given by [25] b ¼ 2 ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi The real and imaginary parts of the third-order NLO susceptibility, χ (3) , were evaluated using the n 2 and β, respectively. The relationships [26] are defined as follows: and lm w ð3Þ ðesuÞ ¼ 10 À 2 ε 0 c 2 n 0 2 l where, ε 0 = Vacuum permittivity, c = Light velocity in vacuum.
The following relation gives the absolute value of the third-order NLO susceptibility [26]:

Theoretical DFT calculation
The starting geometries of the compounds were obtained using X-ray refinement data. The optimization of the molecular geometries, leading to energy minima, was achieved using DFT [with Becke's non-local three-parameter exchange and the Lee-Yang-Parr correlation functional (B3LYP)] with the 6-311++G(d,p) basis set, as implemented in GAUSSIAN 09 program package [27]. The potential energy surface (PES) of Anth-1 and Anth-2 was scanned using B3LYP/6-311G++ (d,p) of the selected dihedral angle with an increment of 10˚to localize the structure corresponding to the energy minima. The vibrational wavenumber and isotropic chemical shifts were calculated using the optimized structural parameters. The calculated vibrational frequencies were uniformly scaled-down with a scaling factor of 1.0065 (Anth-1) and 0.9971 (Anth-2) for frequencies less than 1700 cm -1 , and 0.9948 (Anth-1) and 0.996 (Anth-2) for higher frequencies [28]. The 1 H and 13 C NMR chemical shifts in ppm were calculated relative to TMS as an internal standard using the gauge-invariant atomic orbital (GIAO) method, which computes the absolute chemical shielding owing to the electronic environment of the individual nuclei and is more accurate than other approaches for the same basis set [29].
The HOMO-LUMO energies, oscillator strengths, and absorption wavelengths, λ max , were calculated using time-dependent density functional theory (TD-DFT) at 6-311++G (d, p) and compared with the experimental UV absorption spectra. Furthermore, the molecular electrostatic potential (MEP) and Mulliken and ground-state dipole moments were computed using the same level of theory (B3LYP/6-311++G(d,p) basis set). Natural bond orbital (NBO) analysis was performed using the NBO 3.1 program implemented in the Gaussian 09 package.

Hirshfeld surface analysis
The Hirshfeld surface and the related 2-D fingerprint plots for the Anth-1 and Anth-2 crystal structures were obtained using Crystal Explorer 3.1 [30]. The Hirshfeld surface, used to study the close interactions in the crystals, is shown as a 3-D image and a 2-D fingerprint plot; the surface enables a graphical understanding of the intermolecular interactions. The distances between the surface and the nearest atom inside and outside the surface are represented as d i and d e , respectively [31,32]. The normalized contact distance (d norm ), calculated using Eq 10 based on the d i , d e , and van der Waals radii of the corresponding atom, provides a color-coded system for identifying intermolecular interactions. The blue color refers to the low frequency of the (d i , d e ) pair, and the gray color corresponds to the full fingerprint [33].
Where d i is distance to the nearest nucleus internal to the surface and d e is distance from the point to the nearest nucleus external to the surface. r i vdw and r e vdw are the van der Waals (vdW) radii of the internal and external to the surface, respectively.

Molecular and optimized structural analyses
X-ray crystallographic analysis is effective for correlating molecular structures with their molecular properties. Anth-1 and Anth-2 were synthesized with different scaffolding positions of donor anthracene groups of 9-anthracenecarboxaldehyde and 9-acetylanthracene systems, respectively. These anthracene systems were attached to different substituents of 1,4-benzodioxan-6-yl methyl ketone and 2,2-bithiophene-5-carboxaldehyde, which act as electrondonating moieties. The ORTEP and optimized structures of both compounds are shown in Fig  4, and the crystal structures of Anth-1 and Anth-2 belong to the monoclinic and orthorhombic systems with space groups P2 1 and Pbca, respectively. Additionally, the optimization process using DFT at the B3LYP/6-311G++(d,p) basis set without any constraints indicated a similarity between the selected geometrical parameters and the crystallographic data, as presented in S1 Table in S1 File. The bond distances and angles of both compounds were mutually consistent and within the normal ranges.  [1,4]dioxine plane (Anth-1) and 76.14 (5)˚with the 2,2'-bithiophene plane (Anth-2), as shown in Fig 5A and 5B, respectively. The large dihedral angle observed in Anth-2 suppresses the conjugation effect reducing the electronic effect between the two plane systems [35,36]. The planarity of the molecule contributes to NLO behavior owing to the ease of charge transfer within the molecules, and the twisted molecules help to consolidate the crystal structure via intermolecular interactions.
The molecules in the Anth-1 and Anth-2 were packed into one-and two-dimension due to the intermolecular C-H . . . π and π . . . π interactions. The molecules are packed in a side-by-side or head-to-tail fashion, enhancing the intermolecular charge transfer between the donor and acceptor groups of the molecules [18]. These positions improve the charge-transfer process between the molecules and increase the nonlinear susceptibility (χ3).

Potential energy surface
PES determines the most stable conformation of a molecule through energy minimization. Energy-minimization calculations of the Anth-1 and Anth-2 structures were performed using DFT at the B3LYP/6-3111G++(d,p) implemented in the Gaussian program [27]. Fig 7 shows the PES of Anth-1 and Anth-2 for the O1-C17-C16-C15 (Anth-1) and O1-C15-C16-C17 (Anth-2) dihedral angle with an increment of 10˚, which corresponds to the localized structure with minimum energy.
In Anth-1, conformation B has a maximum energy of 2.4434 eV, representing the s-trans configuration. The rest of the configurations exhibit minimum energies of 0.0175 (A) and 0.0179 (C) eV, representing the s-cis conformation. Contrastingly, Anth-2 has three minimum energies representing the s-trans conformation with values of 0.0053 (D), 0.04582 (F), and 0.00591 (H) eV. The conformational energy profile has two maxima at 90˚and 280˚dihedral angles with energies of 0.5731 (E) and 0.5713 (G) eV, and indicates s-cis conformation with the inner hydrogens on C-14 and C-16 close to each other. This proximity leads to van der Waals repulsion making the s-cis conformation less stable than the s-trans conformation of  Anth-2 [37]. The most stable molecular structure of Anth-1 and Anth-2, derived from PES, was comparable to the X-ray analysis, where Anth-1 was stable in the s-cis conformer, and Anth-2 was stable in the s-trans state.

Hirshfeld surface analysis
The nature of the intermolecular contacts inside the unit cell packing was analyzed using Hirshfeld surface analysis, and the shape index [38], surface, and curvature are shown in Fig  8. The pale orange and bright red spots present on the shape index surface of Anth-1 and  Anth-2 (identified with black arrows) confirm the presence of C-H� � � π interactions ( Fig  8A and 8D). The large, flat green curvature of the shape index surface of Anth-2 ( Fig 8B  and 8C) confirms the presence of π � � � π interactions. The results of the Hirshfeld surface analysis were analyzed using the two-dimensional fingerprint plots (Fig 9), indicating a difference between the intermolecular interaction patterns and the primary intermolecular contacts associated with both compounds. The H� � �H contact, as shown in Fig 9, is the major contributor, with a contact of 40.1% (Anth-1) and 42.0% (Anth-2), to the Hirshfeld surface, and is shown as a distinct spike with the minimum d e +d i value less than the sum of the van der Waals radii (2.4 Å). The intermolecular C-H� � �π interactions for Anth-1 and Anth-2 have small interatomic C� � �H/H� � �C contact percentage of 39.7% (Anth-1) and 30.2% (Anth-2), showing two distinct spikes with d e +d i~2 .8 Å (Anth-1) and 3.0 Å (Anth-2). The π� � �π (C� � �C) interactions have a contribution of 1.4% and 5.0% to the total Hirshfeld surface of Anth-1 and Anth-2, respectively, and appear as a significant spike in the middle of the 2-D fingerprint plot.

Fourier transform infrared spectroscopy analysis
The chemical bonding and molecular structure of the compounds were studied using infrared spectral analysis. The experimental and predicted infrared spectra are given in S1 and S2 Figs in S1 File, respectively. S2 Table in S1 File contains few theoretical and experimental vibrational frequencies, along with their assignments. A correlation graph between the calculated The C-H stretching mode is observed above 3000 cm −1 as a multiple of weak to moderate bands compared to the aliphatic C-H stretch [39]. The absorption bands for Anth-1 and Anth-2 at 3051 and 3049 cm −1 , respectively correspond to the C-H aromatic stretching vibrations. The theoretical DFT also aligns well with the experimental results, and the wavenumbers for C-H stretching frequencies are in the range of 3000-3125 cm −1 [40].
Carbonyl stretching C = O vibration is expected in the region of 1600-1700 cm −1 [41]. The experimental C = O stretching vibrations for Anth-1 and Anth-2, observed at 1655 and 1625 cm −1 , respectively, align well with the theoretically reported values of 1645 and 1606 cm −1 for Anth-1 and Anth-2, respectively. Additionally, a strong band was observed because of the significant dipole moment owing to the large partial positive and negative charge of the carbonyl carbon and oxygen, respectively.
Owing to the aromatic ring vibrations, a strong C = C band of the compounds was observed between 1572 (Anth-1) and 1592 (Anth-2) cm −1 , comparable to the theoretical values of 1581 (Anth-1) and 1588 (Anth-2) cm −1 . The vibrations are sensitive to the amount of charge transfer between the donor and acceptor groups, leading to the formation of a heavy doublet, and these results compare well with earlier reports [42,43]. According to Socrates (1981), the C = C stretching mode is expected around 1600 cm −1 when conjugated with the C = O group. The anthracene ring C = C stretching modes are expected between 1156-1615 cm -1 [44]. We observed the experimental and theoretical anthracene stretching between 1082-1665 cm -1 and 727-1655 cm -1 , respectively. The activation of the C = C anthracene stretching mode confirms the charge transfer between the C = O group and the anthracene fused ring via the ethylenic bridge.

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Fused ring effect on optical nonlinearity of anthracenyl chalcone proton chemical shifts, integrating for 9 protons, of the anthracene ring for Anth-1 and Anth-2 are observed in the de-shielded area between δ = 6.86-9.04 and 7.12-8.77 ppm, respectively, while the theoretical DFT values range between 7.73-8.92 (Anth-1) and 7.76-8.58 (Anth-2) ppm. The anthracene moiety of both compounds can be confirmed from the increased downfield chemical shifts between 7-9 ppm. The aromatic substituent protons were in the normal range. The δ values of the 1 H NMR depend on the type of aromatic ring and vary with the electronic effects of the substituent on the ring.

UV-vis absorption analysis
The linear optical properties were analyzed using the UV-NIR spectrum. The TD-DFT at 6-311++G(d,p) was used to calculate the absorption wavelength (λ max ) and HOMO-LUMO energies of the electronic transitions, which was compared with the experimental UV absorption spectra. The experimental and theoretical studies used the same solvent, DMSO. The influence of highly conjugated substituents at ring A and ring B (Scheme 1) on the absorption band is discussed further, and Table 4 summarizes the experimental and theoretical effect of the substituent in DMSO on the λ max of Anth-1 and Anth-2 using unsubstituted chalcone as the reference. The substitution of the electron-donating group increases the λ max values compared to the unsubstituted chalcone (Fig 11), while the substitution of phenyl in Ring A causes a bathochromic shift of λ max in increasing order of conjugating power [46].
The results in Table 4 summarize that Anth-2 has the highest absorption maximum wavelength. In the experimental spectra, the strong absorption maximum (λ max ) at 387 (Anth-1) and 392 (Anth-2) nm, corresponding to the π-π � transition, can be attributed to the excitation of the aromatic ring and C = O group [47]. The theoretical data of the electronic transition energies and the measured UV-vis data are presented in Table 4. The theoretical calculations are confined to the gaseous equivalent state, whereas the experimental data correspond to the solution state, resulting in a variation of the theoretical λ max from the experimental results.
Comparing the AC derivatives with the unsubstituted chalcone, a shift is observed in the peak wavelength towards the long-wavelength region, and the height of absorption peaks increases with an increase in the conjugated system at Ring A. There is a two-fold increase in the bathochromic effect when the larger conjugated substituent is located on the phenyl ring A than on ring B. This may be attributed to the charge transfer in Anth-2 [48] when the anthracene (strong donor and highly conjugated) ring is located near the carbonyl group (strong electron-withdrawing). Weakly positive groups, such as dioxine (Anth-1) and biothiophene (Anth-2), exhibit minor bathochromic effects when present on ring B and are absent on Ring A [48]. Substituting the electron-donating groups reduces the energy gap [49]. The energy band of Anth-1 and Anth-2 were calculated as 2.93 and 2.76 eV, respectively, by extrapolating the linear trend in the optical spectra. The low bandgap, on account of fused rings within the structures [50], makes these compounds suitable for optoelectronic applications [51].

Frontier molecular orbitals and global chemical reactivity
The bonding scheme of the compounds can be explained using the surface of the frontier orbital, shown in Fig 12. The HOMO-LUMO energy gaps for Anth-1 and Anth-2 chalcones were estimated using the B3LYP/6-311++G (d, p) level of theory ( Table 5). The positive and negative phases are represented using red and green colors, respectively. The frontier molecular orbital (FMO) results indicated that the HOMO electrons are distributed on the ethylenic bridge and the anthracene ring (strong donor). However, at the LUMO level, the charge densities are spread over the entire molecule (including the ethylenic bridge, aromatic rings, and  carbonyl functional group). The energy gap for Anth-1 and Anth-2 were calculated as 3.09 and 2.26 eV, respectively. The DFT method exaggerates the delocalization of the frontier orbital HOMO-LUMO due to the self-interaction error, resulting in significant deviation of the bandgap values from the experimental results. The low HOMO-LUMO energy gap in these compounds indicates stronger chemical reactivity and lower kinetic stability, increasing the polarizability and NLO activity [52]. Substituting the electron-donating group with fused rings within the structures reduces the energy gap [49,50], rendering these compounds suitable for optoelectronic applications [51]. The ionization potential (I), electron affinity (A), chemical potential (μ), Global hardness (η), Global Electrophilicity (ω), Softness (S), and Electronegativity (χ) were defined based on DFT. The I and A can be expressed using the HOMO and LUMO orbital energies as I = -E HOMO and A = -E LUMO , respectively. The HOMO-LUMO energy gap reflects the chemical activity of the molecule, and a small energy gap is associated with specific intramolecular charge transfer from the donor to the acceptor via a π-conjugated path [53]. The energy gap determines the chemical reactivity, optical polarizability, and chemical hardness [54]. Soft molecules have small excitation energies enabling easy modification of electron densities, while it is difficult to change in hard molecules with large excitation energies [55]. The global hardness is given as η = 1/2(ELUMO-EHOMO) � ½ (I-A). The softness of a compound measures the extent of chemical reactivity, and it is the reciprocal of hardness, S = 1/η [56]. Anth-2 exhibits higher softness when it has lower energy gap than Anth-1 ( Table 5).
The escaping tendency of electrons in the molecules is given by electronic chemical potential (μ), which can be obtained using electron affinity and ionization energy [57], μ = 1/2 (E LUMO + E HOMO ) �-½ (I+A). The electrophilicity index (ω) is a quantitative value intrinsic to a molecule used for predicting reactivity which was defined by Maynard [58] and Parr [59] defined ω as the tendency of an electrophile to acquire more electron density (chemical potential) divided by the resistance to exchange electron density with the environment (chemical hardness). The electrophilicity value is vital due to the enone moiety's susceptibility to nucleophilic attack. While Anth-2 was the softest, it contained the most electrophilic chalcones.
Absolute electronegativity, χ = (I + A/2), is related to the average value of the HOMO and LUMO energies defined by Mulliken [60]. Table 5 lists the reactivity indices of the compounds calculated using the TD-DFT method with the B3LYP/6-311++G(d,p) basis set in the ground state. Global reactivity descriptors establish Anth-2 as a soft molecule (very high chemical reactivity and low kinetic stability) having higher intermolecular charge transfer.

Mulliken and ground-state dipole moment
The chemical bonds in the molecule depend on the Mulliken charges and regulate the dipole moment [61]. The total dipole moment and their components with charge-based colors of atoms are tabulated in Table 6 and shown in Fig 13. The analysis revealed a positive acceptor (electrophilic) and a negative donor (nucleophilic) atomic charge [62]. The magnitude of the carbon Mulliken charges range from -0.111 to 1.427 a.u. and -0.188 to 0.756 a.u. for Anth-1 and Anth-2, respectively. Electrophilic charges are localized at all hydrogen atoms in the compound [62]. The dipole vectors (Table 6) are indicated using arrows pointing along the bond towards the less electronegative atom, and the length of the arrow is proportional to the magnitude of the electronegativity difference between the atoms in each molecule. The dipole moment increased with an increase in the length of the conjugated system. Anth-2 (6.77 D) exhibits a greater dipole moment than Anth-1 (5.24 D) due to the higher net charge of the dipole moment and the difference in electronegativity between atoms. The increase in the dipole moment in Anth-2 can also be attributed to the resonance effect of an electron-donating bithiophene substituent. Therefore, Anth-2 has a better response towards NLO properties as it has a higher dipole moment than Anth-1.

Molecular electrostatic potential
MEP corresponds to the distribution of electronic charges on the molecules and the shape of the molecules. MEP provides a visual method to understand the relative polarity of the molecules as it correlates with dipole moment, electronegativity, and partial charges. The electrostatic potential plot and contour map for the positive and negative potentials are shown in Fig  14. MEP indicates the regions susceptible to interaction with the environment and the preferred electrophilic or nucleophilic attack regions as well as the MEP map.
The color grading indicates molecular size, shape, and electrostatic potential value, helpful in studying the molecular structure and its physiochemical property [38]. The color scheme for the MEP surface includes red (electron-rich or partially negative charge), blue (electron- https://doi.org/10.1371/journal.pone.0257808.g014 deficient or partially positive charge), light blue (slightly electron-deficient region), yellow (slightly electron-rich region), and green (zero potential region) [63].
The areas of low potential (red) contain abundant electrons and are localized over the oxygen atom, O, of the carbonyl group, which is the site for electrophilic attack. Contrastingly, the region with the maximum positive charge is the preferred site for the nucleophilic attack and is indicated by the blue color. The proton-rich region exhibits a positive potential and repulsion energy between the protons, which corresponds to the white region, and the carbon and hydrogen of green benzene correspond to an intermediate potential system.
The MEP contour plot is a two-dimensional map representing the charge distribution and displays the regions where the relative electron density falls within a specific range at (0010) for Anth-1 and Anth-2. The electrostatic potential contour maps for the positive and negative potentials are shown in Fig 14C and 14D, respectively. The negative region was observed around the carbon atoms and oxygen, while the positive regions were near the hydrogen atoms.

Natural bond orbital analysis
NBO analysis was performed by examining all possible interactions (hydrogen bond, intraand intermolecular charge transfer) between the donor (Lewis-type) NBOs and acceptor (non-Lewis-type) NBOs, and estimating their second-order perturbation theory. The larger the energy of hyperconjugative interactions (E (2) ), the more intensive the interaction between electron donors and electron acceptors; that is, the extent of conjugation of the system increases with an increase in the donating tendency from electron donors to electron acceptors. The energy of delocalization, ΔE ij , is calculated as where E (2) is the energy of hyperconjugative interactions, q i is the occupancy of the donating (Lewis type) orbital, ε i and ε j are the energies of the donating and accepting orbitals, respectively, and Fij is the off-diagonal element of the Fock matrix in the NBO basis [64]. The high hyperconjugative interaction energies (Tables 7 and 8) indicate the ICT in Anth-1 and Anth-2, respectively, which induces NLO properties of molecular systems. In Anth-1, the charge transfer interactions between π � (C13-C14) and σ � (C15-H15) indicate C15-H15A� � � π1 hydrogen bonding with 277.62 kcal/mol energy. The interaction between LP O1 to σ � (C18-C19), LP O2 to σ � (C21-C22), and LP O3 to σ � (C21-C22) yields large E (2) energy values of 221.10, 553.18, and 269.32 kcal/mol, respectively, owing to the presence of an electrondonating oxygen atom attached to Anth-1 [65].
The results indicate that the ICT between the anthracene system and the substituent through an ethylenic bridge and the carbonyl group stabilizes the system, enhancing the NLO properties of Anth-1 and Anth-2.  Optical absorption causes heat transfer to the irradiated material during the light-matter interaction, potentially changing the properties of the material [66]. In this study, the absorption peaks were in the UV region, and the absence of linear absorption in the visible region indicates negligible thermal effects. The materials with reverse saturation absorption become opaque upon exposure to high photon fluxes due to the high absorption from the excited state [67]. Anth-2 exhibited superior nonlinear absorption compared to Anth-1 under continuous waves, enabling their optical limiting applications.

Third order nonlinear optics
Both samples exhibited a self-defocusing effect with a negative nonlinear refractive index, tabulated against the focal intensities in Table 9. The transmission between the peak and valley (ΔT P-V ) was calculated from the closed aperture Z-scan curves (Fig 16). The self-defocusing effect, on account of local variation in the refractive index with temperature, is essential for optical sensor applications, such as night vision devices [68], and increases the laser damage threshold [69]. Although the n 2 should be independent of the intensity for pure third-order nonlinearity, the value of n 2 in Fig 16 is marginally dependent on the intensity, indicating the presence of thermally induced nonlinearity. Therefore, the samples exhibit strong temperature-dependent nonlinearity.
Anth-2 exhibited a superior third-order NLO response than Anth-1, and the higher imaginary χ 3 compared to the real counterpart in Anth-2 indicates the dominance of nonlinear absorption over nonlinear refraction. Therefore, Anth-2 has significant potential for optical limiting applications. The absolute value of χ 3 for Anth-2 was calculated using the relation |χ 3 | = [(Re(χ3)) 2 +(Im(χ3)) 2 ] 1/2 at intensity of 4.1 kW/cm 2 , and was found to be 1.10 x10 -4 esu. The value of χ 3 cannot be calculated for Anth-1 because different intensities are used for open and closed apertures. However, the values of n 2 and β indicate that a lower third-order susceptibility than Anth-2. The χ 3 of Anth-2 is larger than some third-order NLO materials, such as organic polymers, organic metals, organic dyes, and Rh:BaTiO 3 thin films, which yielded the values for χ 3 in the order of 10 −7 and 10 −8 esu [70,71].

Anth-1
Anth-2 Laser intensity (kW/cm 2 ) β (x10 -5 ) (cm/W) Im χ 3 (x10 -6 ) (esu) Laser intensity (kW/cm 2 ) β (x10 -5 ) (cm/W) Im χ 3 (x10 -6 ) (esu) 41 enone bridge with respect to the C = O and C = C bonds, respectively. The s-trans conformation of Anth-2 is thermodynamically stable because the s-cis conformation has a steric repulsion between the two hydrogens inside the anthracene ring and the other substituent ring. The molecules in the crystal are packed in two dimensions by intermolecular C-H� � �π and π� � �π interactions, and are positioned in a head-to-tail fashion side by side, enhancing the ICT between the donor and acceptor groups of the molecules. The higher maximum absorption of Anth-2 (392 nm) is due to the significant charge transfer when the anthracene (strong donor and highly conjugated) ring is near the carbonyl group (strong electron-withdrawing). The absorption peak wavelengths shift toward longer wavelengths, resulting in a lower energy gap. The UV-Vis spectra revealed that the ICT of the two different structures influence the absorption peak shifts and the HOMO-LUMO energy levels.
Both UV-Vis and FMO indicate a lower energy bandgap for Anth-2. Global reactivity descriptors indicate that Anth-2 is soft (very high chemical reactivity and low kinetic stability) and has higher ICT. The dipole moment calculation shows that the electronegativity difference between the atoms leads to a strong push-pull effect and an increase in the dipole moment, resulting in an enhanced nonlinear response of organic molecules. The resonance effect of an electron-donating bithiophene substituent contributes to the higher dipole moment of Anth-2.
In MEP, the carbonyl group acts as a reactive site for electrophilic attack and the binding site for intermolecular C-H� � �O interactions, while the anthracene ring provides sites for nucleophilic attack. NBO analysis indicates that ICT in Anth-1 and Anth-2 induces the NLO properties of the molecules. The fast charge transfer between the strong donor (anthracene) and strong acceptor (carbonyl) group through the π-conjugation increases the nonlinearity of Anth-2 because anthracene is located near the carbonyl group. The superior third-order NLO response of Anth-2 is due to the molecular structure and the conjugated substituent factors. The higher magnitude of the imaginary χ 3 in Anth-2 indicates its potential use as an optical limiter.
The NLO properties of the materials can be attributed to the arrangement of the molecules in the crystal, strong conjugated electron donor substituents, small energy gap, and push-pull effect of the dipole moments. The enhanced electron affinities, extended conjugation lengths of molecular backbones, strong electron-donating substituents, and different positioning of the substituents within the molecule of D-π-A-D or D-A-π-D structure affect the structureproperty relationship and, subsequently, the nonlinear properties of the compounds.