Introduction

Owing to their excellent properties, nonlinear optical (NLO) materials are playing a crucial role in modern day hi-tech applications. The field of NLO material designing has got further momentum since the use of a photon as a carrier of information [1]. Over the past few decades a huge variety of NLO materials have been proposed, synthesized, and characterized using different experimental and theoretical techniques [2–6]. Among these explored materials, some main classes are organic, inorganic, and organic–inorganic hybrid materials [7, 8]. Every class has its own intrinsic advantages and disadvantages during their potential use in NLO applications. Nevertheless, the organic class remains as the front-runner for designing efficient NLO materials because of their huge structural diversity, larger NLO coefficients as well as their ease of fabrication, etc. [9–11]. Different structural modification strategies have been used to modulate their NLO response of several organic compounds including donor-π-conjugated-acceptor configuration [12–14], bond length alternation theory [15, 16], interaction of lithium atoms [17–19], proton-trasfer/deprotonation [20], twisted-π-conjugated structures [21, 22], and many similar others [23, 24].

The family of chalcone derivatives has been significantly studied over recent years for their potential NLO applications [25, 26]. Several chalcone derivatives have attracted significant attention due to their efficient NLO properties and good transparency through blue and yellow transmittance, etc. [27, 28]. Shettigar et al. [29], have synthesized and grown yellow color crystals of chalcone derivatives with methoxy phenyl terminal groups and found their second harmonic generation (SHG) efficiency ~15 times that of urea molecule. Menezes et al. [30], also reported single crystals of pyridine based chalcone derivatives that have found transparent in entire visible and infrared range with efficient NLO properties. The importance of charge transfer has been discussed for NLO properties. Several other freshly spotted chalcone derivatives for NLO applications include chalcone derivatives linked by triazole rings [31], bis-chalcones [32], pyrene based chalcones [33] as well as amino derivatives of chalcones [34], etc.

Recently, we synthesized and reported the crystal structures of simple chalcogen derivatives including (2E)-1-(2,5-dimethylthiophen-3-yl)-3-(2-methoxyphenyl)prop-2-en-1-one) [35] with terminal o-methoxy phenyl group and (E)-1-(2,5-Dimethyl-3-thienyl)-3-(2,4,5-trimethoxyphenyl)prop-2-en-1-one [36] with o, m, p-trimethoxy phenyl groups. Considering these methoxy phenyl groups as terminal donors, these derivatives with push-pull configuration are expected as good candidates for potential NLO materials. In the present investigation, we aim to perform a systematic probe for NLO properties, primarily based on the exploitation of number and position effects of methoxy groups with a subsequent substitution to tune the push-pull effects for possible future syntheses (Fig. 1).

Computational details

All the calculations have been performed using Gaussian suite of programs [37]. The molecular geometries of all the systems were optimized by density functional theory (DFT) using LC-wPBE/6-311G** level of theory. A preliminary investigation has been performed with a variety of different methods to simulate the molecular geometry of experimentally synthesized system 1 [35]. These different methods include MP2, B3LYP, M06, PBE0, and LC-wPBE. Figure 2 shows the relative tendency of each method to simulate different bond lengths of system 1 as compared to their experimentally reported data. A careful analysis of the graph in Fig. 2, shows that all the methods have reasonably reproduced the experimental bonding parameters where LC-wPBE method has shows a relatively good agreement with experimentally reported values (see Fig. 2). Further discussion about the selection of methodology has been given in the Supplementary information. The time dependent density functional theory (TD-DFT) has been used to calculate excitation energies. The static first hyperpolarizability (β tot ) and its components for all systems were calculated by the finite field (FF) approach. The FF method, which was originally developed by Kurtz et al. [3] has been broadly applied to investigate the NLO properties of organic materials because this approach can be used in concert with the electronic structure method to calculate β values. Recently, several β tot amplitudes calculated by this method were found to be in reasonable agreement with the experimental structure property relationship [38, 39]. In the FF method, a molecule is subjected to a static electric field (F), the energy (E) of the molecule is expressed by the following equation:

Fig. 1
figure 1

Optimized structure of parent system 1 at LC-wPBE/6-311G** level of theory where green label indicates the important geometrical parameters included in Fig. 2 and Table 1

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Fig. 2
figure 2

A comparison of different bond lengths of parent system 1 at various methods as well as with its experimental values

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$$ E={E}^{(0)}-{\mu}_1{F}_1-\frac{1}{2}{\alpha}_{ij}{F}_i{F}_j-\frac{1}{6}{\beta}_{ijk}{F}_i{F}_j{F}_k-\frac{1}{24}{\gamma}_{ijkl}{F}_i{F}_j{F}_k{F}_l-\dots $$
(1)

Here, E (0) represents the total energy of molecule in the absence of an electronic field, μ is the vector component of the dipole moment, α is the linear polarizability, β and γ are the second and third-order polarizabilities respectively, while x, γ, and z label the i, j ,and k components, respectively. It can be seen from Eq. 1 that differentiating E with respect to F obtains the μ, α, β, and γ values. The molecular first polarizability β is a measure of how easily a dipole is induced in a molecule in the presence of an electric field.

In our present investigation, we have calculated the electronic dipole moment, molecular polarizability, polarizability anisotropy, and molecular first hyperpolarizability. For a molecule, its dipole moment (μ) is defined as follows:

$$ \mu =\left({\mu}_x^2+{\mu}_y^2+{\mu}_z^2\right) $$
(2)

The average polarizability (α 0)can be calculated by following equations:

$$ {\alpha}_0=\frac{1}{3}\left({\alpha}_{xx}+{\alpha}_{yy}+{\alpha}_{zz}\right) $$
(3)

Similarly, the magnitude of the total first static hyperpolarizability (β tot) can also be calculated using the following Eq.

$$ {\beta}_{tot}={\left({\beta}_x^2+{\beta}_y^2+{\beta}_z^2\right)}^{\frac{1}{2}} $$
(4)

where,

$$ {\beta}_x = {\beta}_{xxx}+{\beta}_{xyy}+{\beta}_{xzz} $$
(5)
$$ {\beta}_x = {\beta}_{yyy}+{\beta}_{xxy}+{\beta}_{yzz} $$
(6)
$$ {\beta}_x = {\beta}_{zzz}+{\beta}_{xxz}+{\beta}_{yyz} $$
(7)

while the static first hyperpolarizability (β0) is also calculated using the following Eq.

$$ {\beta}_0 = \raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$5$}\right.\left({\beta}_{tot}\right) $$
(8)

The second-order polarizability (β) that is a third rank tensor that can be described by a 3×3×3 matrix. According to Kleinman symmetry (βxyy = βyxy = βyyx, βyyz = βyzy = βzyy,… likewise other permutations also take the same value), the 27 components of the 3D matrix can be reduced to ten components.

Results and discussion

Molecular geometries

All the molecular geometries for experimental parent system 1 (2E)-1-(2,5-dimethylthiophen-3-yl)-3-(2-methoxyphenyl)prop-2-en-1-one) [35] and system 4 (E)-1-(2,5-dimethylthiophen-3-yl)-3-(2,4,5-trimethoxyphenyl)prop-2-en-1-one [40] along with their derivatives are shown in Fig. 3. Systems 1, 2, and 3 are (E)-1-(2,5-dimethylthiophen-3-yl)-3-phenylprop-2-en-1-one with methoxy group at ortho, meta, and para positions, respectively. Similarly, system 4 has three simultaneous methoxy groups at ortho, meta, and para positions. The systems 3a and 4a are same the as systems 3 and 4 except for the additional 2-5-(cyano(isocyano)methylene) groups at thiophen rings as shown in Fig. 3. It is important to mention that systems 1–4 are selected to check a systematic effect of number and position of methoxy groups while systems 3A and 4A are designed to further robust NLO properties of systems 3 and 4.

Fig. 3
figure 3

The chemical structures of all adopted systems in the present investigation

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A comparison of different bond lengths at our best-selected method LC-wPBE with experimental values has been made in Table 1 for system 1 (see Fig. 1). From Table 1, it can be seen that the maximum difference between experimental and calculated bond length is 0.012 Å for C13-O3 bond length, 2.75° for C13-C12-C11 triangle, and 5.18° for C4-C9-O2-C10 torsion angle, which indicates the reliability of our selected methodology and gives us confidence for further calculations with the above selected methodology.

Table 1 Some important geometrical parameters of parent system 1 according to Fig.1 as calculated at LC-wPBE/6-311G** level of theory
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Ground state dipole moments

The total dipole moments along with their individual components for all the systems have been collected in Table 2. It can be seen from Table 2 that systems 1–4 have y-components as dominant dipole moment components among others. Furthermore, system 2 with m-OCH3 group at phenyl ring has larger dipole moment ~4.58 D as compared with those of systems 1, 3, and 4 having o-OCH3, p-OCH3, and o,m,p-(OCH3)3 groups on terminal phenyl rings, respectively. It is important to mention here that the electronic dipole moment is dependent on the amount of partial positive and negative charges as well as their distances between these charges in a molecule. To get more molecular level intuitive on the trend in change in dipole moments, we have used the results from Milliken population analysis as shown in Fig. 4. It is clear from Fig. 4 that in system 2 the phenyl ring with m-OCH3 carries more negative charge (with two black and four brown atoms) as compared with systems 1, 3, and 4, which subsequently leads to its larger dipole moment. For qualitative analysis among ortho, meta, and para methoxy substitutions, the Milliken atomic charges of systems 1–3 are shown in Fig. S1 of the Supplementary information. While on the other hand, for systems 3a and 4a, there are strong push-pull configurations that lead to their significantly larger dipole amplitudes. Additionally, a comparison among dipole moments calculated with LC-wPBE and PBE0 methods shows that there are no significant effects of long-range correction on dipole amplitudes as the relative trend is the same at both levels of theories (see the parenthesis values in Table 2).

Table 2 The calculated ground state dipole moments (μg) and excited state (μee) dipole moments (Debye) in parenthesis for all adopted systems calculated at LC-wPBE/6-311G** level of theory
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Fig. 4
figure 4

The representation of relative orientation of electronic dipole moment vector (blue arrow) based on Milliken population analysis with color scheme for partial charges of all atoms in molecule

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Polarizability and first hyperpolarizability

The calculated average (α0) and anisotropic (Δα0) polarizability amplitudes are shown in Table 3. From Table 3, it can be seen that the anisotropic polarizability that depends on the direction of electric field is significantly larger than the average polarizability. The average polarizability does not show a significant effect of position and number of methoxy groups on the terminal phenyl ring but it does indicate the influence of push-pull configuration in systems 3a and 4a with a significant increase in their polarizability amplitudes. The amplitude of average polarizability for systems 3a and 4a are 342 and 375 a.u., which are about ~138 and 136 a.u. larger than those of systems 3 and 4, respectively. In addition to polarizability, we also calculated first static hyperpolarizability (β 0 and β tot) as collected along with their individual components in Table 4. The static first hyperpolarizability has a non-zero value for all the systems. The trend of increasing first static hyperpolarizability (β 0 and β tot) amplitudes is sys. 2 < sys. 1 < sys. 3 < sys. 4 < sys. 3a < sys. 4a.

Table 3 The calculated polarizability (α, a.u.a) and its individual components for all adopted systems at LC-wPBE/6-311G** level of theory
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Table 4 The calculated values of first hyperpolarizability β 0 and β tot (a.u. and × 10−30 esu)a along their individual tensor components for all systems at LC-wPBE/6-311G** level of theory
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For all systems in the present investigation, their longitudinal components β xxx are dominant among all other individual components of β 0 and β tot because the x-axis is the major charge transfer axis in all our adopted systems. From Table 4, it can be seen that β 0 and β tot amplitudes for systems 1, 2, and 3 show a significant methoxy substitution position effect where system 3 with p-OCH3 shows larger β 0 and β tot amplitudes as compared with those of systems 1 and 2 that contains o-OCH3 and m-OCH3 groups at the terminal phenyl ring, respectively. Unlike its corresponding ortho and meta substitutions, the para OCH3 substitution is aligned with the x-axis, which is perhaps the reason for its β xxx component being ~3 times larger than those of systems 1 and 2. A further comparison shows that the β tot amplitude of system 1 (779 a.u.) decreases by 7 % and increases by 128 % for meta- and para-methoxy substitutions, respectively. For system 4 with simultaneous substitution of three-methoxy groups at ortho, meta, and para positions, it shows an increment of about 159 % from the β tot amplitudes of its parent system 1 indicating an important effect of position and number of methoxy group(s) on their NLO properties. While on the other hand, the tuning of push-pull configurations of systems 3 and 4 by substituting cyanide groups at thiaophene rings results in systems 3a and 4a with their robust β 0 and β tot amplitudes. For instance, the β tot values of systems 3a and 4a are about two times larger than their corresponding systems 3 and 4, respectively. Similarly, these β tot values of systems 3a and 4a are about four and six times larger than those of their parent systems 1. Additionally, as a PNA molecule with typical donor acceptor configuration is often taken as the standard reference molecule to calculate the first hyperpolarizability amplitudes of organic systems, we have made a comparison among first hyperpolarizability of PNA with our designed systems. For example, a comparison with this well-known prototype NLO molecule of PNA shows that some systems in the present investigation possess larger amplitudes of their β tot values compared to that of PNA molecule (β tot = 1025 a.u. as calculated in the present study) as calculated at the same level of theory. The last row of Table 4 shows relative ratios (δ = β tot/β tot PNA) indicating the increase/decrease in β tot values of all the systems as compared with that of the PNA molecule.

Origin of first hyperpolarizability

To trace the origin of static first hyperpolarizability, we have performed TD-DFT calculations using TD-LC-wPBE/6-311G** level of theory. How do the β values of derivative molecules enhanced by changing the number and position of methoxy groups? For the static case (ω = 0.0), a simple two-level expression [41] is often employed in the literature for quantitative approximations of β values. In two-level approximation, the nonlinear optical response is calculated including the ground and one excited state in sum-over-state expression. However, care should be taken while applying the two-level model to the molecules with significantly populated excited states [42].

Despite the fact that the general validity of the two-level model has also been questioned for extrapolating β value to zero frequency, it is widely used in experimental studies of nonlinear optical properties of organic molecules. Unlike the sum-over-state approximation, the two-level model is a simple representation of molecular response including wavelength dependence. This model is also the origin of the most widely applied push-pull technique for designing efficient NLO chromophore. Oudar and Chemla first used the two-level model to study the static first hyperpolarizability of nitroanilines [41]. In two-level expression the β 0 value is expressed as:

$$ {\beta}_0\cong \left(3/2\right)\varDelta \mu \times \raisebox{1ex}{${f}_0$}\!\left/ \!\raisebox{-1ex}{$\varDelta {E}^3$}\right. $$
(9)

Here, Δμ is the dipole moment difference between the ground and crucial excited states, f 0 is the oscillator strength and ΔE is the transition energy as given in Table 5. We have performed TD-DFT calculations to approximate the relative contributions of the three parameters above to tuning the NLO properties of our designed systems. From the two-level model, it can be seen that the β 0 value is directly proportional to the oscillator strength f 0 and change in dipole moment between ground and first excited state Δμ, while it is inversely proportional to cube of transition energy ΔE. From Table 5, it can be seen that all the parameters have constructive contributions to optimize the β 0 amplitudes. For instance, to better understand, we have drawn a graph among transition energies of two crucial (with larger oscillator strengths) transitions as well as the amplitudes of their oscillator strengths for all adopted systems as shown in Fig. 5. From Fig. 5, it can be seen that among the systems 1 through 4, the system 4 has a lower value of transition energies. Similarly, the cyano substituted systems 3a and 4a show a further reduction in their transition energies that have ultimately resulted in their robust β amplitudes. Somewhat similar trends but with lesser extent are also present in the case of their oscillator strengths for both the transitions which provides a semi-quantitative agreement with β amplitudes calculated using FF method.

Table 5 The change in dipole moment between ground and excited states (Δμ), oscillator strength (f o), transition energies (ΔE), and % configuration interaction of crucial transitions at TD-LC-wPBE/6311G** level of theory
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Fig. 5
figure 5

A plot of TD-DFT parameters including transition energies and oscillator strengths for two crucial transitions

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To roughly approximate the contribution of dipole moment change between ground and the first excited state, we have also calculated the change in dipole moment between ground and the first excited state Δμ at TD-PBE0/6311G** level of theory as shown in Table 5. It is important to mention here that we used TD-PBE0 instead of TD-LC-wPBE because of the lack of analytic excited-state gradient for TD-LC-wPBE method in G09 suites of program. The change in dipole moment between ground and the first excited state indicates a constructive contribution (Δμ ≥ 1 a.u.) to tune the β amplitudes. For example, the change in dipole moments for systems 3 and 4 are 2.026 and 2.155 a.u. that mounts to 5.743 and 10.701 a.u. in their respective cyano substituted systems of 3a and 4a. Thus, the above results indicate that an optimal combination of optical parameters involved in two-level approximation plays a crucial role to tune the NLO properties of our designed derivatives.

The frontier molecular orbitals (FMOs) analysis

The knowledge of frontier molecular orbitals (FMOs) plays a very crucial role to judge the nature of intramolecular charge transfer in a molecule as well as its reactivity. Among FMOs, the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) are more important. We have also drawn the frontier molecular orbitals involved in the crucial transitions (with the highest oscillator strengths) as given in Fig. 6. From Fig. 6, it can be seen that there is significant intramolecular charge transfer in our designed systems where dimethylthiophen groups are acting as electron acceptors while terminal methoxy phenyl groups as electron donor during transition. The HOMOs of system 1, 3, and 4 are somewhat similar except in system 2 that has significant weight of its HOMO on the dimethylthiophen group. This perhaps leads to less extend of charge transfer, higher transition energy, and the lowest β amplitude in system 2 as compared with other systems. Unlike the others, systems 3a and 4a show more charge transfer like nature due to the involvement of cyano groups where significant weights of their LUMO orbitals are present. The stronger withdrawing effect of cyano groups significantly reduced the transition energy leading to larger β amplitudes in systems 3a and 4a.

Fig. 6
figure 6

Three-dimensional representations of the frontier orbitals (HOMO, LUMO, and LUMO+1) of all adopted systems based on ground-state DFT calculations

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Conclusions

In the present investigation by signifying the importance of position and the number of methoxy substitutions, we have designed different chalcones derivatives. The rotation of methoxy group substitutions at three different possible ortho, meta, and para positions on the phenyl ring show significant changes in NLO properties of these chalcones derivatives. System 3 with terminal 4-methoxyphenyl group (para-methoxy substitution) has shown β tot amplitude of 1776 a.u. which is ~2.2 and 2.4 times larger than that of ortho- and meta-methoxyphenyl in systems 1 and 2, respectively. For system 4 simultaneous substitution of three-methoxy groups at ortho, meta, and para positions cause an increment of ~159 % in the β tot amplitude of its parent system 1. Additionally, systems 3a and 4a, which are cyano derivatives of systems 3 and 4 with stronger push-pull configurations, show reasonably large β tot amplitudes of 3280 and 4388 a.u., respectively, which are due to their lower transition energy and higher oscillator strengths. Most importantly, among all the derivatives, the cyano derivatives have shown superior NLO properties as compared with those of systems 1–4. Milliken population analysis is used to highlight the changes in their ground state dipole moments. Thus, the present investigation has revealed the importance of methoxyphenyl and cyano groups in the above designed derivatives.