Beryllium-cyclobutadiene multidecker inverse sandwiches: electronic structure and second-hyperpolarizability

Polaron Formation in Conducting Polymers: A Novel Approach to Designing Materials with a Larger NLO Response

Substantial efforts have been made to design and investigate new approaches for high-performance nonlinear optical (NLO) materials. Herein, we report polaron formation in conducting polymers as a new approach to designing materials with a large NLO response. A comparative study of polypyrrole and polypyrrole-based polaron (nPy+ where n = 1, 3, 5, 7, and 9) is carried out for optoelectronic and NLO properties. The studied polarons (PPy+) show excellent electronic properties and have reduced ionization potential (IP) as compared to neutral PPy, and a monotonic decrease is observed with increased chain lengths (1Py to 9Py). Interesting trends of global reactivity descriptors can be seen; the softness (S) increases with an increase in the chain length of PPy, while the hardness (η) decreases in the same fashion. The EH-L gaps for the PPy+ polaronic state are significantly lower than their corresponding neutral PPy. In the polaronic model (PPy+), radicals decisively reduce the crucial excitation energy, reminiscent of excess electrons (alkali metals). The performed TDOS spectral analysis further justifies the better conductive and electronic properties of polarons (PPy+) with increased chain lengths (conjugation). The static hyperpolarizability response (βo) is recorded up to 1.3 × 102 au for 9Py, while for polaron 9Py+, it has increased up to 3.2 × 104 au. The static hyperpolarizability of the 9Py+ polaronic state is 246 times higher than that of the corresponding neutral analogue, 9Py. It is observed that the values of βo obtained at the CAM-B3LYP/6-311+G(d,p) level of theory are comparable to those obtained at the LC-BLYP and ωB97XD functionals. The βvec values show a strong correlation with the total hyperpolarizability (βo). Furthermore, the calculated second harmonic generation (SHG) values are up to 4.0 × 106 au at 532 nm, whereas electro-optic Pockel's effect (EOPE) is much more pronounced at the smaller dispersion frequency (1064 nm). The TD-DFT study reveal the red-shifted absorption maxima (λmax) with an increased length of PPy+. A significant reduction in excitation energy (ΔE) is observed with increased length of PPy and PPy+, which also favors the improved NLO response. Hence, the studied thermally conducting polypyrrole-based polarons (PPy+) are new entries into NLO materials with better electrical and optical features.

Geometric, Electronic, and Optoelectronic Properties of Carbon-Based Polynuclear C3O[C(CN)2]2M3 (where M = Li, Na, and K) Clusters: A DFT Study

Carbon-based polynuclear clusters are designed and investigated for geometric, electronic, and nonlinear optical (NLO) properties at the CAM-B3LYP/6-311++G(d,p) level of theory. Significant binding energies per atom (ranging from -162.4 to -160.0 kcal mol^-1) indicate excellent thermodynamic stabilities of these polynuclear clusters. The frontier molecular orbital (FMOs) analysis indicates excess electron nature of the clusters with low ionization potential, suggesting that they are alkali-like. The decreased energy gaps (E_H-L) with increased alkali metals size revael the improved electrical conductivity (σ). The total density of state (TDOS) study reveals the alkali metals' size-dependent electronic and conductive properties. The significant first and second hyperpolarizabilities are observed up to 5.78 × 10³ and 5.55 × 10⁶ au, respectively. The β_o response shows dependence on the size of alkali metals. Furthermore, the absorption study shows transparency of these clusters in the deep-UV, and absorptions are observed at longer wavelengths (redshifted). The optical gaps from TD-DFT are considerably smaller than those of HOMO-LUMO gaps. The significant scattering hyperpolarizability (β_HRS) value (1.62 × 10⁴) is calculated for the C3 cluster, where octupolar contribution to β_HRS is 92%. The dynamic first hyperpolarizability β(ω) is more pronounced for the EOPE effect at 532 nm, whereas SHG has notable values for second hyperpolarizability γ(ω).

New kind of electride sandwich complexes based on the cyclooctatetraene ligand M12(η8-C8H8)2M22 (M1 = Na, K and M2 = Ca, Mg): a theoretical study

In the present study, the electronic structures of a series of binuclear sandwich complexes based on the cyclooctatetraene ligand M¹₂(η⁸-C₈H₈)₂M²₂ (M¹ = Na, K and M² = Ca, Mg) are studied theoretically. Each cyclooctatetraene ligand binds with the metal in the η⁸ binding mode. The M²-M² bond length agrees well with the reported bimetallic covalent Ca₂ and Mg₂ bond lengths. The Wiberg bond index (WBI) also indicates the presence of covalent M²-M² bonds, which gives additional stability to the complex. A non-nuclear attractor (NNA) is found in-between the M²-M² bond and the negative Laplacian of the electron density is found at the NNA. Noncovalent interaction (NCI) plot shows that electron density is localized at the M²-M² bond. Based on the performed analysis, we have concluded that the designed sandwich complexes are electrides. We herein report, for the first time, the electride sandwich complexes of the cyclooctatetraene ligand. Due to the presence of a diffuse electron system, the electride complexes exhibit higher values of the static second hyperpolarizability within the range of 2.6 × 10⁵ to 1.4 × 10⁶ a.u. Among the studied complexes, M¹₂(η⁸-C₈H₈)₂Ca₂ exhibit a higher value of static second hyperpolarizability.

Shedding light on the optical and nonlinear optical properties of superalkali-doped borophene

The present investigation highlights the two-dimensional design of several interesting superalkali-doped borophene derivatives for efficient nonlinear optics (NLO). The combination effects and resulting NLO responses of borophene (B₃₆) and superalkali units (Li₃O) were evaluated by orienting superalkali clusters at various sites, such as the hub, rim, and bridge, around an B₃₆ molecule. The charge analysis was characterized by frontier and natural bond orbital analyses, a narrowed HOMO-LUMO bandgap and greater intramolecular charge transfers. Molecular electrostatic potential surfaces demonstrated enhanced optoelectronic features of these complexes that are viable due to Li₃O adsorption. Singly doped and doubly doped complexes were considered, and their NLO properties were calculated. Bandgap energy was reduced approximately threefold when doped with two Li₃O. As a considerably high figure of merit, first hyperpolarizability (β_o) values of up to five digits (including 10,611 au for complex A) prove that these systems can be utilized as promising candidates in various NLO applications.

Oxacarbon superalkali C3X3Y3 (X = O, S and Y = Li, Na, K) clusters as excess electron compounds for remarkable static and dynamic NLO response

An intriguing class of excess electron oxacarbon superalkali clusters is explored for nonlinear optical response through density functional theory (DFT) methods at CAM-B3LYP/6-311++G(d,p). These superalkali clusters shows noticeable binding energies per atom (E_b) which reveals their thermodynamic stabilities (-86.45 ∼ -119.44 kcal mol^-1). The obtained significant VIPs values also suggest the electronic stability of these clusters. The VIP values range from 2.06 eV to 3.42 eV. These clusters show remarkable electronic properties and their HOMO-LUMO gaps (E_H-L) are significantly reduced. The lowest H-L gap of 0.96 eV is obtained for C₃O₃K₃ while the highest H-L gap of 2.07 eV is calculated for C₃S₃Li₃. The obtained PDOS spectra further provide evidence for the superior electronic properties of these clusters. The clusters show excellent nonlinear optical properties as revealed from remarkable values (1.6 × 10⁶ au) of static first hyperpolarizability. The controlling factors for hyperpolarizability are also explored by using conventional two-level model. The calculated values of β_o are correlated nicely with β_tl. The crucial excitation energy is the key factor in controlling the first hyperpolarizability. In these excess electron clusters, the second hyperpolarizability (γ_o) response increases up to 4.3 × 10⁹ au. Moreover, the calculated scattering hyperpolarizability (β_HRS) values are quite significant in these clusters and the highest value of 1.3 × 10⁶ au is calculated for C₃S₃K₃. Additionally, these clusters also possess larger dynamic nonlinearities. The dynamic second hyperpolarizability with dc-Kerr effect increases up to 1.0 × 10¹¹ au. The remarkable values for refractive index (n₂) also suggest the excellent nonlinearity of these superalkali clusters.

The shape selectivity of corannulene dimers based on concave-convex and convex-convex shape complementarity as hosts for C60 and C70

In the formation of noncovalent complexes, the stacking arrangements of corannulene and fullerene are diverse, most of which are combinations of multiple corannulenes and fullerene. Here, a composition ratio of 2 : 1 was selected for the complex between corannulene and fullerene (C60 and C70) to investigate the effects of different superposition modes, including concave-convex and convex-convex interactions, on the stability and third-order nonlinear optical (NLO) properties of the composite materials. It was found that the concave-convex interaction was stronger and it was reported to stabilize the charge-transfer (CT) complex more effectively than the convex-convex interaction. The dispersion range of the concave-convex interaction was larger than that of the convex-convex interaction, which is consistent with the interaction energy results. The packing design with the double convex-convex interactions exhibited the largest linear optical response and third-order NLO response, which showed that the convex-convex interaction was more likely to be excited and cause intermolecular CT as compared to the concave-convex interaction. This work confirmed that the packing arrangement significantly affected the NLO response and will advance the development of NLO crystals.

Electronic structure and large second-order non-linear optical property of COT derivatives - a theoretical exploration

A new strategy to design new molecules based on a fused hydrocarbon ring system comprising a COT ring and two 5-membered rings has been proposed for the study of second order NLO properties. The four charge transferring groups -NR2 (R = H, Li, Na and K) in conjunction with a sufficient number of electron withdrawing groups lead to significant variation of structural parameters and polarity. The charge transfer characteristics can be strongly modulated by introducing calcium metal atoms at suitable sites. Ca metal atoms end-capping the nitrogen ends of two adjacent -CN groups lead to electride character while a Ca metal atom bonded directly to the COT ring leads to greater charge transfer. The size of the alkali metal atom has been found to have a dramatic effect on the enhancement of first hyperpolarizability. The most significant electronic asymmetry induced by the larger potassium metal atom strongly enhances the magnitude of first hyperpolarizability. The variation of first hyperpolarizability has been satisfactorily explained in terms of TD-CAMB3LYP calculated spectroscopic parameters in light of the two-state model.

Crystal growth and characterization of second- and third-order nonlinear optical chalcone derivative: (2E)-3-(5-bromo-2-thienyl)-1-(4-nitrophenyl)prop-2-en-1-one

Experimental and computational studies of linear and nonlinear optical (NLO) properties of (2E)-3-(5-bromo-2-thienyl)-1-(4-nitrophenyl)prop-2-en-1-one (5B2SNC) single crystals are reported. Good-quality and large-sized single crystals of 5B2SNC were successfully grown and characterized by powder X-ray diffraction and high-resolution X-ray diffractometry techniques. 5B2SNC was found to crystallize in the monoclinic noncentrosymmetric space group Cc and possesses moderately good crystalline perfection. The linear optical properties were investigated using the absorption spectrum, which reveals a direct optical band gap of 3.1 eV. The thermal stability was studied with thermogravimetric analysis/differential thermal analysis. The powder second harmonic generation efficiency was evaluated by the Kurtz and Perry method, and 5B2SNC was found to be 26 times more efficient than urea standard. Third-order NLO properties were studied by the z-scan technique with a femtosecond laser. The second hyperpolarizability was obtained to be ∼1.45 × 10−31 e.s.u. The molecule reveals a strong reverse saturation absorption and negative nonlinear refraction. The molecule exhibited good optical limiting properties, and its limiting threshold was measured to be ∼3.2 mJ cm−2. In addition, static electric dipole moments, linear polarizabilities, and first- and second-order hyperpolarizabilities were calculated by density functional theory (DFT). Highest occupied molecular orbital/lowest unoccupied molecular orbital band gaps were also evaluated by DFT calculations. The experimental and theoretical results showed that 5B2SNC exhibits excellent second- and third-order nonlinear optical properties.

Successive lithiation of acetylene, ethylene and benzene: a comprehensive computational study of large static second hyperpolarizability

This work is a revisit of the study of the electron correlation effect of lithium substitution on the second hyperpolarizability (10⁶ a.u.) of acetylene, ethylene and benzene. The large quenching of mean second hyperpolarizability has been addressed by CCSD calculations. The inclusion of triple excitation in the MP4 method generally overestimates second hyperpolarizability in comparison to the MP4SDQ method. The present CCSD γ_av value of C₆Li₆: 405 × 10⁴ a.u. obtained with a relatively larger basis set established the earlier prediction of Sadlej et al. [Phys. Chem. Phys. Chem., 2000, 2, 3393-3399] where degenerate non-dipolar transitions in low lying excited states play the crucial role. The successive lithiation results in gradual red shifting of transition energy leading to significant enhancement of second hyperpolarizability. Most of the chosen DFT functionals predict the correct qualitative trend of second hyperpolarizability. The quantitatively different results may be attributed to the case when the ground state wave function cannot be approximated by a single SD.

The novel link between planar möbius aromatic and third order nonlinear optical properties of metal-bridged polycyclic complexes

Metal–bridged polcyclic aromatic complexes, exhibiting unusual optical effects such as near-infrared photoluminescence with particularly large Stokes shifts, long lifetimes and aggregation enhancement, have been established as unique “carbonloong chemistry”. Herein, the electronic structures, aromaticities, absorption spectra and third order nonlinear optical (NLO) responses of metal–bridged polcyclic aromatic complexes (M = Fe, Re, Os and Ir) are investigated using the density functional theory computations. It is found that the bridge–head metal can stabilize and influence rings, thus creating π–, σ– and metalla–aromaticity in an extended, π–conjugated framework. Interestingly, metal radius greatly influence the bond, aromaticity, liner and third order NLO properties, which reveals useful information to develop new applications of metal regulatory mechanism in NLO materials field. Significantly, the novel relationship between the aromaticity and third order NLO response has firstly been proposed, that the metal-bridged polycyclic complex with larger aromaticity will exhibit larger third order nonlinear optical response. It is our expectation that the novel link between aromaticity and NLO response could provide valuable information for scientists to develop the potential NLO materials on the basis of metal–bridged polycyclic complexes.

First hyperpolarizability of cyclooctatetraene modulated by alkali and alkaline earth metals

In the present investigation, the first hyperpolarizability of alkali and alkaline earth metal derivatives of cyclooctatetraene (COT) has been calculated using BHHLYP and CAM-B3LYP functional for 6-311++G(d,p), 6-311++G(3df,3pd), and aug-pc 2 basis sets. Introduction of Na/K atoms at the axial position of COT and Li, Na, K/Be, Mg, Ca metal atoms and cyanide groups at the equatorial sites leads to lager enhancement of first hyperpolarizability. The ring charge density can account for the variation of first hyperpolarizability. The two state model has been invoked to explain the variation of first hyperpolarizability.

The influence of Sc doping on structural, electronic and optical properties of Be12O12, Mg12O12 and Ca12O12 nanocages: a DFT study

Density functional theory (DFT) calculations were used to study the effect of scandium doping on the structural, energetic, electronic, linear and nonlinear optical (NLO) properties of Be₁₂O₁₂, Mg₁₂O₁₂ and Ca₁₂O₁₂ nanoclusters. Scandium (Sc) doping on nanoclusters leads to narrowing of their E _g, which enhances their conductance greatly. Also, the polarizability (α) and first hyperpolarizability (β₀) of nanoclusters were dramatically increased as Be, Mg or Ca atoms are substituted with a Sc atom. Among all clusters, α and β₀ values for Sc-doped Ca₁₂O₁₂ were the largest. Consequently, the effect of the doping atom, as well as of cluster size, on electronic and optical properties was explored. Time dependent (TD)-DFT calculations were also carried out to confirm the β₀ values; the results show that the higher value of first hyperpolarizability belongs to Sc-doped Ca₁₂O₁₂, which has the smallest transition energy (ΔEgn). The results obtained show that these clusters can be candidates for using in electronic devices and NLO materials in industry.

Effect of alkaline earth metal at the single wall CNT mouth on the electronic structure and second hyperpolarizability

In the present work, electronic structure and second hyperpolarizability of a number of alkaline earth metals (M [Formula: see text] Be, Mg and Ca) complexes with carbon nanotube (CNT) has been studied by using different DFT functional. The complexes have sufficient thermal stability. Significant amount of charge transfer from metal to CNT results in stronger ground state polarization. The second hyperpolarizability obtained at different DFT functional (BHHLYP, CAM-B3LYP, B2PLYP, [Formula: see text]B97XD) showed a consistent trend. The magnitude of second hyperpolarizability of M@CNT[3,0] complexes enhances rather appreciably when a second metal atom is introduced into other mouth position. The longitudinal component of second hyperpolarizability of M@CNT[3,0]@M complexes increases with increasing size of metal atom. The magnitude of second hyperpolarizability of Ca@CNT[3,0]@Ca complex is comparable with Fe([Formula: see text]-C[Formula: see text]B[Formula: see text]. However, widening/lengthening of CNT markedly reduces the cubic responses. The two state model can qualitatively explain the variation of second hyperpolarizability.

Electronic structures and second hyperpolarizabilities of alkaline earth metal complexes end-capped with NA2 (A = H, Li, Na)

The ground state structures and NLO properties of a number of alkaline earth metal complexes end-capped with NA₂ groups (A = H, Li, Na) are calculated by employing the CAM-B3LYP, wB97XD and B2PLYP functionals along with MP2 and CCSD(T) for 6-311++G(d,p), 6-311++G(3df,3pd), aug-cc-pVTZ, aug-pc-2 and Hypol basis sets.

Second hyperpolarizability of delta shaped disubstituted acetylene complexes of beryllium, magnesium, and calcium

Present theoretical study involves the delta shape complexes of beryllium, magnesium, and calcium where the metal atom interacts perpendicularly with disubstituted acetylene. Most of the complexes are found to be fairly stable. The dependence of second-hyperpolarizability on the basis set with increasing polarization and diffuse functions has been examined which showed the importance of 'f-type' type polarization function for heavy metal (Mg, Ca) and 'd-type' polarization function for beryllium. Larger second hyperpolarizability has been predicted for complexes having significant ground state polarization and low lying excited states favoring strong electronic coupling. Transition energy plays the most significant role in modulating the second hyperpolarizability.

Second hyperpolarizability of multimetallocenes [Cp–Mn–Cp] of Be, Mg and Ca

Multimetallocene complexes ( Cp – M n– Cp ) of Be , Mg and Ca have been considered for the theoretical study of static second hyperpolarizability using a number of DFT functionals. Owing to the cooperative effect in bonding, beryllium forms multiberyllocene complexes ( Cp – Be n– Cp ) which have sufficient thermal stability with respect to dissociation into neutral fragments up to n = 10. On the other hand, multimetallocene complexes of Mg and Ca are found to be stable for n ≤ 5 which may be due to the weaker covalent bonding interaction between the larger metal atoms. The rather small variation of linear and cubic polarizabilities of Cp – Be n– Cp complexes beyond n = 5 arises from the rather weaker charge transfer transitions. The difference in NLO property among the investigated metal complexes arises from the extent of charge transfer from the terminal metal atoms and the distance between them. The charge transfer at longer distances in the ground state of Mg and Ca complexes leads to more intense electronic transition — the spectroscopic parameters of which strongly favors the enhancement of second hyperpolarizability.

Exploring bridging effect on first hyperpolarizability

Modulation of first hyperpolarizability on varying structure of the bridge.

Third order NLO properties of corannulene and its Li-doped dimers: effect of concave–convex and convex–convex structures

The convex–convex stacking motif of corannulene dimers enhances the third-order NLO response due to obvious interlayer charge transfer.

Static second hyperpolarizability of Λ shaped alkaline earth metal complexes

A number of Λ shaped complexes of alkaline earth metals Be , Mg and Ca with varying terminal groups have been considered for the theoretical study of their second hyperpolarizability. The chosen complexes are found to be sufficiently stable and for a chosen ligand the stability decreases in the order: Be -complex > Ca -complex > Mg -complex. The calculated results of second hyperpolarizability obtained at different DFT functionals for the 6-311++G(d,p) basis set are found to be fairly consistent. The Λ shaped ligands upon complex formation with metals lead to strong enhancement of second hyperpolarizability. The highest magnitude of cubic polarizability has been predicted for the metal complex having > C ( C 2 H 5)2 group. For a chosen ligand, the magnitude of second hyperpolarizability increases in the order Be -complex < Mg -complex < Ca -complex which is the order of increasing size and electropositive character of the metal. The variation of second hyperpolarizability among the investigated metal complexes has been explained in terms of the transition energy and transition moment associated with the most intense electronic transition.