Frequency-dependent Hyperpolarizabilities Research Articles

Effect of spirocyclization of xanthene dyes on linear and nonlinear optical properties by considering D-π-A and D-A-D Systems: DFT and TD-DFT approach

Spirocyclization, a unique feature of xanthene dyes, makes it a promising candidate for developing fluorescent ratiometric probes for sensing, imaging, tracking, and labeling. How will this feature of xanthene dyes influence the linear and nonlinear optical properties? To examine the effect of spirocyclization of xanthene dyes, we have selected both the open-close form of rhodamine B and π-extended xanthene dyes substituted with thienyl and thieno[3,2-b]thienyl group at position 3 and 6. Here, rhodamine B will serve as the (Donor)D-π-A(Acceptor) system and thiophene-substituted xanthene dyes will serve as the D-A-D system. The geometry optimization of the close-open form of xanthene dyes at B3LYP/6–311++G(d,p) and CAM-B3LYP/6–311++G(d,p) revealed that the open form is energetically more stable in the S0 state than the closed form. The vertical excitation energy (ΔE), from Time-Dependent-Density Functional Theory (TD-DFT) calculation at B3LYP/6–311++G(d,p), CAM-B3LYP/6–311++G(d,p), ωB97XD/6–311++G(d,p) revealed that (ΔE)open < (ΔE)close. Further, the open form of xanthene dyes displays red-shifted absorption compared to the closed form. The λVt of xanthene dyes (open-close forms) is mainly assigned to HOMO → LUMO transition (S0 → S1) with % orbital contribution for open form ∼ 90 % and close form ∼ 60 %. The oscillator strength of xanthene dyes is obtained in the range of 0.01 – 1.74. The λVt of xanthene dyes is in agreement with experimental absorption. The static polarizability (α0), first-order hyperpolarizability (β0), second-order hyperpolarizability (γ), molecular hyperpolarizability (µβ0), and frequency-dependent hyperpolarizability (β1064), of the open form of xanthene dyes, were found to be higher than the close form. Thus, the open form of xanthene dyes will show superior linear and nonlinear optical properties than the closed form. The thienyl[3, 2-b] thieno substituted xanthene dye with red-shifted absorption shows higher α0, β0, γ, µβ0, β1064, and γ values, show better linear and NLO properties than thienyl and diethylamine substituted xanthene dyes.

Superalkali-alkaline earthide ion pairs of δ+(AM-HMHC)-AM'δ- (AM = Li, Na and K; AM' = Be, Mg and Ca) possessing large NLO responses and excellent electronic stabilities and alkalide characteristics: a DFT study.

To identify superalkali-alkaline earthide ion pairs, it's theoretically shown that, as a novel class of excess electron superalkali compounds, both chair and boat forms of (AM-HMHC)-AM' (AM = Li, Na, and K; AM' = Be, Mg, and Ca; HMHC = 1,4,7,10,13,16-hexamethyl-1,4,7,10,13,16-hexaazacyclooctadecane) are good candidates. An attractive superalkali-alkaline earthide ion pair in δ+(AM-HMHC)-AM'δ- is firstly exhibited, which possesses alkaline-earthide characteristics and nonlinear optical response superior to similar M+(calix[4]pyrrole)M'- (M = Li, Na, and K; M' = Be, Mg, and Ca) with high stability. The electronic and vibrational second order hyperpolarizabilities and the frequency-dependent first hyperpolarizabilities of δ+(AM-HMHC)-AM'δ- are presented. For each pair of (AM-HMHC)-AM', the boat conformation is preferred to its chair one in the case of Hyper-Rayleigh scattering response (βHRS). These alkaline earthides suggest prominently high βHRS up to 2.59 × 104 a.u. (boat forms of δ+(Na-HMHC)-Caδ-). We expect that this work will inspire the preparation and characterization of these new alkaline earthides as high-performance NLO materials.

Frequency-Dependent Quadratic Response Properties and Two-Photon Absorption from Relativistic Equation-of-Motion Coupled Cluster Theory.

We present the implementation of quadratic response theory based upon the relativistic equation-of-motion coupled cluster method. We showcase our implementation, whose generality allows us to consider both time-dependent and time-independent electric and magnetic perturbations, by considering the static and frequency-dependent hyperpolarizability of hydrogen halides (HX, X = F-At), providing comprehensive insights into their electronic response characteristics. Additionally, we evaluated the Verdet constant for noble gases Xe and Rn and discussed the relative importance of relativistic and electron correlation effects for these magneto-optical properties. Finally, we calculate the two-photon absorption cross sections of transition [ns1S0 → (n + 1)s1S0] of Ga+ and In+, which are suggested as candidates for new ion clocks. As our implementation allows for the use of nonrelativistic Hamiltonians as well, we have compared our EOM-QRCC results to the QR-CC implementation in the DALTON code and show that the differences between CC and EOMCC response are in general smaller than 5% for the properties considered. Collectively, the results underscore the versatility of our implementation and its potential as a benchmark tool for other approximated models, such as density functional theory for higher-order properties.

Modulation of the NLO properties of p-coumaric acid by the solvent effects and proton dissociation

Solute-solvent interactions and deprotonation effects have been related to second-order nonlinear optical response modulators. This work takes advantage of sequential Monte Carlo/Quantum mechanics together with Time-Dependent Density Functional Theory, Coupled Cluster methods, and the hyper-Rayleigh scattering formalism to investigate how these effects influence the stability and optical response of p-coumaric acid (pCA) and its anionic and diionic forms. The solvent influences the chromophores in different ways, inducing bathochromic and hypsochromic solvatochromism so for the neutral pCA molecule as for its deprotonated derivatives. The results indicate a high sensitivity of the nonlinear optics (NLO) parameters with relation to proton dissociation. Ionization of the carboxyl group produces the lowest values of the first frequency-dependent hyperpolarizability (βHRS), while phenolic deprotonation leads to the highest values. The results show that proton removal can be used as a switch that modulates the NLO response within a wide range of values (159.15≤βHRS≤4393.97 au) greater than those reported for reference NLO chromophores like urea (37.3 au) and p-nitroaniline (74.3 au). Thermochemical analysis of enthalpies and Gibbs free energies indicate that both monoionic forms of the pCA molecule are the most stable in gas or water solvents. Furthermore, these structures represent the limits of NLO modulation in the gas and solvent phases. Analysis of the projected density of states and mapping of the molecular electrostatic potential indicate that increased contributions from conduction electrons found in the aromatic ring are the mechanism by which deprotonation enhances the NLO response. All the results show that ionic pCA forms are promising in the functionalization of optoelectronic devices.

Alkali metals doped cycloparaphenylene nanohoops: Promising nonlinear optical materials with enhanced performance

In the ongoing pursuit of novel and efficient NLO materials, the potential of alkali metal-doped {6}cycloparaphenylene ({6}CPP) and methylene bridged {6} cycloparaphenylene (MB{6}CPP) nanohoops as excellent NLO candidates has been explored. The geometric, electronic, linear, and nonlinear optical properties of designed systems have been investigated theoretically. All the nanohoops demonstrated thermodynamic stability, with remarkable interaction energies reaching up to −1.39 eV (−0.0511 au). Notably, the introduction of alkali metals led to a significant reduction in the HOMO-LUMO energy gaps, with values as low as 2.92 eV, compared to 6.80 eV and 6.06 eV for undoped {6}CPP and MB{6}CPP, respectively. Moreover, the alkali metal-doped nanohoops exhibited exceptional NLO response, with the K@r6-{6}CPP complex achieving the highest first hyperpolarizability of 56,221.7 × 10−30 esu. Additionally, the frequency-dependent first hyperpolarizability values are also computed at two commonly used wavelengths of 1550 nm and 1907 nm, respectively. These findings highlight the potential of designed nanohoops as promising candidates for advanced NLO materials with high-tech applications.

Alkaline earth metal Atom-Doped Aza-Single-Strand pyridine Helix M@SP-Helix (M = Be, Mg, and Ca) as high-performance candidates for Single-Molecular redox SPDT NLO molecular switches

Redox molecular switch is undoubted to be a good choice for the requirement of terminal molecular device. By doping an alkaline earth metal atom into the aza-single-strand pyridine helical ligand to form M@SP-Helix (M = Be, Mg, and Ca), the alkaline earth metal atom not only act the role of providing two electrons but also the type of them can significantly affect the distribution region of every two electrons on SP-Helix in the in the redox process. Our results found that the electronic and vibrational static first hyperpolarizabilities as well as the frequency-dependent first hyperpolarizability exhibit high-performance single-pole double-throw (SPDT) nonlinear optics (NLO) switching effects from its oxidized state (off form) to neutral (on form) and to reduced states (on form) as obtaining four electrons by twice. Notably, the electronic first hyperpolarizability is increased approximately 1003- and 1.34 × 106-fold from 35 to 3.51 × 104 and 4.69 × 107 au for Ca@SP-Helix. Therefore, this work can provide a theoretical reference that the alkaline earth atom doping is an important method to design high-performance NLO molecular switch material.

Impact of π-Linkers Modifications on Tuning Nonlinear Optical Amplitudes of Pyridoquinazolinone-Based Aromatic Dyes: A Rational Entry to Novel D-π-A NLO Materials

Developing efficient nonlinear optical (NLO) materials is a cutting-edge field of study. The desirability of promising NLO materials for optoelectronic applications drove us to investigate the pyridoquinazolinone-based D-π-A architectured chromophores for predicting proficient NLO compounds. Pyridoquinazolinone-based dye (WL-O) is chosen as a reference and its nine derivatives (ASH1-ASH9) are quantum chemically modeled by inserting variously reported π-linkers into the D-π-A framework. Simulations using DFT and TD-DFT provide insight into how π-linker alteration affects the NLO properties. The potential use of investigated dyes for NLO response applications is confirmed by evaluating photophysical aspects, frontier molecular orbital (FMO), natural population analysis (NPA), molecular electrostatic potential (MEP), the density of state (DOS), transition density matrix (TDM) analysis, and static, frequency-dependent NLO response properties. FMO analysis shows that all dyes’ energy gaps are lower when compared to the reference, resulting in a strong NLO response. The highest absorption wavelength of the studied dyes was found to be in the visible spectrum, as determined by UV-Vis analysis. NPA-based findings demonstrated the movement of the electrons from D to A through π-linkers resulting in the formation of a charge separation state and active NLO sensitivity of the proposed dyes. Moreover, MEP, LOL, and ELF topological investigations are performed to appraise the charge transfer inside ASH1-ASH9 and high NLO characteristics. The robust NLO response revealed the eye-catching linear polarizability(α0 ), first-hyperpolarizability (β), particularly ASH3, with the highest α0 and β0 computed to be 520.44 a.u. and 26166.79 a.u., respectively. Additionally, frequency-dependent hyperpolarizability SHG β(−2ω,ω,ω) and EOPE β(−ω,ω,0) calculations for commonly used lasers were performed at 1907.21, 532, and 1064 nm. ASH3 with terthiophene linker exhibits a striking EOPE β(−ω,ω,0) and SHG β(−2ω,ω,ω) response of 2.94 × 104 a.u. and 3.80 × 104 a.u. respectively at 1907.21 nm. This theoretical framework confirmed that the investigated dyes have fine NLO potential and are recommended for future NLO applications.

Role of Delocalization, Asymmetric Distribution of π-Electrons and Elongated Conjugation System for Enhancement of NLO Response of Open Form of Spiropyran-Based Thermochromes.

Switchable nonlinear optical (NLO) materials have widespread applications in electronics and optoelectronics. Thermo-switches generate many times higher NLO responses as compared to photo-switches. Herein, we have investigated the geometric, electronic, and nonlinear optical properties of spiropyranes thermochromes via DFT methods. The stabilities of close and open isomers of selected spiropyranes are investigated through relative energies. Electronic properties are studied through frontier molecular orbitals (FMOs) analysis. The lower HOMO-LUMO energy gap and lower excitation energy are observed for open isomers of spiropyranes, which imparts the large first hyperpolarizability value. The delocalization of π-electrons, asymmetric distribution and elongated conjugation system are dominant factors for high hyperpolarizability values of open isomers. For deep understanding, we also analyzed the frequency-dependent hyperpolarizability and refractive index of considered thermochromes. The NLO response increased significantly with increasing frequency. Among all those compounds, the highest refractive index value is observed for the open isomer of the spiropyran 1 (1.99 × 10-17 cm2/W). Molecular absorption analysis confirmed the electronic excitation in the open isomers compared to closed isomers. The results show that reversible thermochromic compounds act as excellent NLO molecular switches and can be used to design advanced electronics.

Nonlinear optical response of [formula omitted]-terpinolene and [formula omitted]-phellandrene chromophores: An octupolar gas-to-solvent enhancement able to retain light conduction

The search for new materials with improved nonlinear optical (NLO) response is a field of growing interest in materials science. Typically, the dipole ΦJ=1 contributions exceed the octupolar ΦJ=3 ones and dominate the optical behavior. However, the latter is essential for NLO device engineering. Under this scenario, this work investigates the electronic-optical properties of the α-terpinolene and β-phellandrene molecules within the Hyper-Rayleigh scattering formalism (HRS). It includes solvent contributions using a sequential Monte Carlo/Quantum Mechanics procedure. According to Density Functional Theory analysis, molecular solvatochromism acts differently for the two chromophores. While α-terpinolene undergoes a hypsochromic effect, the β-phellandrene molecule shows moderate bathochromism, both with a strong absorption band in the ultraviolet region (λmax<240nm), making them attractive for potential UV filters. Regarding the NLO response, both compounds present similar values for the first frequency-dependent hyperpolarizability (βHRS) with values that vary from 62.46 to 138.73 au in aqueous environment, superating urea (β=42.82 au), a standard optical material. Furthermore, while one of these chromophores is best described by dipole contributions (ΦJ=1≈68%), the other is dominated by the octupolar term (ΦJ=3≈60%) even when the solvent moderates it. These characteristics allow the building of optical switches without losing the strength of the NLO response. In addition, the polarization of the solute due to the solvent conveniently reduces the refractive index (n), providing light conduction applications. Therefore, these chromophores can be used to promote a decoupling between dipolar and octupolar contributions in NLO.

The effect of the CPP size on the nonlinear optical properties of the new necklace-type molecules formed by carborane and [n]Cycloparaphenylenes(n = 8–11)

The new necklace-type molecules were formed by [8–13]CPP and carborane, which further manipulated the size of the macroring, revealing the effect of size on its luminescence behavior. In this work, the effects of ring size on the absorption spectrum, electron excitation and nonlinear optical properties of the compounds were investigated in detail, aiming to reveal an effective way to improve the optical properties of these necklace-type compounds. The absorption spectra of the compounds showed that the size of the CPP ring had little effect on the spectral shape and position, but the electron transition information showed that there were the significant charge transfer within the CPP ring and a gradual enhancement of interfragment charge transfer from the CPP ring to carborane. The increasing order of polarizability, first and second hyperpolarizability values of these compounds with the increase of CPP size indicated that increasing the size of the CPP ring was an effective way to increase the nonlinear optical properties of necklace-type molecules. Among the frequency dependent hyperpolarizability values, the γ(-ω;ω,0,0) value increased by a factor of 4 from complex 1 to 6 with the increase of CPP ring size, which indicated that increasing the size of the CPP ring was an effective way to increase the optical Kerr effect of necklace-type molecules. Therefore, these the new necklace-type nolecules formed by carborane and [n]Cycloparaphenylenes would be excellent nonlinear optical materials in the field of the all-optical switch.

Superalkalis fabricated Te-containing [8]circulenes as outstanding NLO materials; a DFT perspective

There is a growing demand for thermodynamically stable and highly polarizable materials with excess electrons in the fields of optics. In this study, a new class of theoretically designed materials (AxY@C16Te8 (A = K, Na, Li, and x = 2, 3 4)) are explored for optoelectronic and nonlinear (NLO) applications via DFT calculations. Various superalaklis (AxY (Y = O, N, F and x = 2, 3, 4)) are doped on C16Te8 nano-surface. The outcomes of DFT revealed high thermodynamic stability of these complexes. Natural bond orbital (NBO) charge analysis illustrated that charge transfer occurred from superalkali toward Te-containing [8]circulene (C16Te8). HOMO − LUMO energy gap is reduced after doping. Moreover, (AxY@C16Te8 (A = K, Na, Li, x= 2, 3 4, and Y = O, N, F) complexes exhibit remarkably large nonlinear optical (NLO) response. The static first hyperpolarizability (βo) of these complexes ranges between 3.28 × 103 – 2.60 × 105 au. The NLO response of the designed complexes is further explored by computing second hyperpolarizability (γtot), frequency-dependent hyperpolarizability, and nonlinear refractive index.

Transition metals based metalides TM-Janus-TM (where TM=Sc–Zn and Janus=F6C6H6); A theoretical study of nonconventional metalides with excellent static and dynamic nonlinear optical properties

Continuous progress is being made to bring forward the novel strategies for designing materials with excellent stability and exceptional nonlinear optical response. For the first time, 3d-transition series (Sc–Zn) is doped as source of excess electrons to design novel class of TM-JN-TM (TM = Sc–Zn) metalides based upon Janus-type all-cis1,2,3,4,5,6-hexafluorocyclohexane (JN) molecule. DFT calculations are performed at M06-2X/6-31+G(d,p) level of theory to explore the electronic and NLO properties of these complexes. The obtained novel metalides show excellent thermal stabilities than those of conventional alkalides and their interaction energies ranging from −3.50 to −88.33 kcal mol−1. Under the large facial polarization of JN, the valence electrons of transition metals (TM) on fluorine face serve as source of excess electron to TM metals on hydrogen face. With the excellent electronic stabilities, these complexes show significant decreased HOMO-LUMO gaps and, the performed NBO analysis also reveals their metalide character where the negative charge is observed at metal (TMH) on hydrogen face of complex C, D, G, H, and I. Among the designed metalides (TM-JN-TM), the significant first and second hyperpolarizability values of 2.43 × 106 au and 1.72 × 109 au are observed for Fe-JN-Fe complex. Simple excess electron complexes have better NLO response than that of true metalides. The observed dynamic first hyperpolarizabilities β(ω) values are much pronounced at smaller dispersion frequency (1064 nm). The frequency-dependent second hyperpolarizability γ(ω) value increased up to 5.75 × 1010 au for V-JN-V. At 1300 and 1900 nm, significant dynamic second hyperpolarizability γ(ω) values are observed. The scattering hyperpolarizability (βHRS) show significant value (2.0 × 107 au) for Fe-JN-Fe complex. We hope this work could open up new possibilities for NLO material design by using transition metals as source excess electron and, on the other hand, encourage greater experimental efforts in the laboratory to synthesize such stable compounds.

Design of A-D-A-Type Organic Third-Order Nonlinear Optical Materials Based on Benzodithiophene: A DFT Study.

The acceptor-donor-acceptor (A-D-A) type conjugated organic molecule has been widely applied in the organic optoelectronics field. A total of Nine compounds (1–9) were designed under the A-D-A framework, with the electron donor benzodithiophene as the core and dicyanomethylene as the acceptor moiety, modifying the benzodithiophene with the phenyl, naphthyl, and difluorinated phenyl groups. The conjugation length can be changed by introducing a thiophene π-conjugated bridge. The geometric structures, electronic structure, excited state properties, aromaticity, and the static- and frequency-dependent second hyperpolarizabilities were investigated by employing high-precision density functional theory (DFT) calculations with an aug-cc-pVDZ basis set. As a result, the three compounds with the longest conjugation length exhibit a smaller energy gap (Egap), larger UV-vis absorption coefficient, and response range, which are the three strongest third-order nonlinear optical (NLO) response properties in this work. This work systematically explored the connection between molecular structure and NLO response, which provides a rational design strategy for high-performance organic NLO materials.

Hyper-Raman spectroscopy of benzene and pyridine revisited.

Hyper-Raman (HR) spectra of benzene-h6, benzene-d6, and pyridine in the liquid phase excited at 1064nm were measured by a picosecond laser with a high repetition rate. Although benzene and pyridine are important aromatic molecules, the qualities of the HR spectra previously reported were not high enough to be compared with those of IR and Raman spectroscopy. Our HR spectroscopic system significantly improves sensitivity that enables the detection of HR bands of benzene and pyridine not observed before. In addition to band assignments, we interpret HR bands of benzene based on the vibronic coupling theory of (pre-) resonance hyper-Raman scattering. Depolarization ratios of HR bands of benzene and pyridine, obtained from polarized-HR measurements, are first examined from a theoretical point of view of HR spectroscopy. Moreover, we evaluate quantum chemical calculations for HR spectra by comparing experimental and computational spectra. We show that the frequency-dependent polarizability and hyperpolarizability calculations using time-dependent density functional theory well reproduce the HR experiments for bulk aromatic compounds.

Deciphering the Role of Alkali Metals (Li, Na, K) Doping for Triggering Nonlinear Optical (NLO) Properties of T-Graphene Quantum Dots: Toward the Development of Giant NLO Response Materials.

Nanoscale nonlinear optical (NLO) materials have received huge attention of the scientists in current decades because of their enormous applications in optics, electronics, and telecommunication. Different studies have been conducted to tune the nonlinear optical response of the nanomaterials. However, the role of alkali metal (Li, Na, K) doping on triggering the nonlinear optical response of nanomaterials by converting their centrosymmetric configuration into noncentrosymmetric configuration is rarely studied. Therefore, to find a novel of way of making NLO materials, we have employed density functional theory (DFT) calculations, which helped us to explore the effect of alkali metal (Li, Na, K) doping on the nonlinear optical response of tetragonal graphene quantum dots (TGQDs). Ten new complexes of alkali metal doped TGQDs are designed theoretically. The binding energy calculations revealed the stability of alkali metal doped TGQDs. The NLO responses of newly designed complexes are evaluated by their polarizability, first hyperpolarizability (βo), and frequency dependent hyperpolarizabilities. The Li@r8a exhibited the highest first hyperpolarizability (βo) value of 5.19 × 105 au. All these complexes exhibited complete transparency in the UV region. The exceptionally high values of βo of M@TGQDs are accredited to the generation of diffuse excess electrons, as indicated by NBO analysis and PDOS. NCI analysis is accomplished to examine the nature of bonding interactions among alkali metal atoms and TGQDs. Our results suggest alkali metal doped TGQD complexes as potential candidates for nanoscale NLO materials with sufficient stability and enhanced NLO response. This study will open new doors for making giant NLO response materials for modern hi-tech applications.

Lanthanum doped corannulenes with enhanced static and dynamic nonlinear optical properties: A first principle study

In this work, lanthanum doping on corannulene (C20H10) buckybowls has been explored for their geometrical, electronic and nonlinear optical (NLO) properties via DFT simulations. The interaction energies of −21.75 to −40.01 kcal/mol reflect that A-D complexes are thermodynamically stable. The HOMO-LUMO energy gaps of designed complexes are decreased significantly up to 48.92%. A maximum charge transfer of 1.452 |e| is observed for complex A as revealed by natural bond orbital analysis. Non-covalent interaction (NCI) and quantum theory of atoms in molecules (QTAIM) analyses have confirmed the presence of various interactions in the complexes. The complexes are transparent in UV–Visible region and absorption maxima fall near infrared region (1123–2032 nm). The highest nonlinear optical response in terms of first hyperpolarizability value of 5.08 × 104 au is observed for complex C. The hyper-Rayleigh scattering (βHRS) and frequency dependent hyperpolarizability coefficients including electro-optical Pockel's effect and second harmonic generation are also computed theoretically.

Insights into the nonlinear optical (NLO) response of pure Aum (2 ≥ m ≤ 7) and copper-doped Au m -xCu x clusters.

A series of small pure Aum (2 ≥ m ≤ 7) and copper-doped Aum−xCux clusters was evaluated by density functional theory (DFT) at the CAM-B3LYP/LANL2DZ level for their geometric, electronic, and nonlinear optical (NLO) properties. The charge transfer for the Au cluster significantly improved by reducing the HOMO–LUMO energy gap from 3.67 eV to 0.91 eV after doping with Cu atoms. The doping of Cu also showed noteworthy impacts on other optical and NLO properties, including a decrease in the excitation energy and increase in the dipole moment and oscillator strength. Furthermore, changes in the linear isotropic and anisotropic polarizabilities (αiso and αaniso) and first and second NLO hyperpolarizabilities (βstatic, γstatic) were also observed in the pure and Cu-doped clusters, which enhanced the NLO response. The nonlinear optical properties of the clusters were evaluated by calculating the static and frequency dependent second- and third-order NLO polarizabilities at 1064 nm wavelength. Among all the doped structures, the Au3Cu1 cluster showed the largest static first hyperpolarizability of β(total) = 4.73 × 103 au, while the Au1Cu6 cluster showed frequency dependent first hyperpolarizability of β(−2w;w,w) = 1.26 × 106 au. Besides this, large static and frequency-dependent second hyperpolarizability values of 6.30 × 105 au and 1.05 × 10 au were exhibited by Cu7 and Au1Cu6, respectively. This study offers an effective approach to design high-performance NLO materials utilizing mixed metal clusters which might have broad applications in the fields of optoelectronics and electronics.

Extremely large static and dynamic nonlinear optical response of small superalkali clusters NM3M’ (M, M’=Li, Na, K)

Exploring novel nonlinear optical (NLO) materials with excess electron properties is essential for advancing the use of excess electron compounds in optics. The studied superalkali clusters NM3M’ (M, M′ = Li, Na, K) are thermodynamically stable and their binding energies range from −27.10 to −53.84 kcal mol−1. The observed significant values for VIPs suggest their electronic stabilities. Being excess electron candidate these clusters show significant βo value (3.9 × 107 au), which nicely correlates the hyperpolarizability reported by a two-level model (βtl). Furthermore, these clusters exhibit a remarkable static second hyperpolarizability (γo) value of 1.1 × 1010 au for the NK4 superalkali cluster. The hyper Rayleigh scattering (βHRS) is also computed where the highest value of 2.9 × 107 is recorded for NNa3K superalkali. The obtained values of βvec values (projection of hyperpolarizability on dipole moment vector) also signify the excellent nonlinearity of clusters. Besides, the calculated electro-optica pockel's effect β(-ω; ω,0) and second harmonic generation β(-2ω; ω, ω) values are much pronounced at larger dispersion frequency ω = 1064 nm. Moreover, the frequency-dependent second hyperpolarizability γ(ω) with dc-Kerr effect γ(-ω; ω,0,0) and electric field induced second harmonic generation γ(-2ω; ω,ω,0) show larger values at ω = 1064 nm. Thus the highest value of the dc-Kerr constant increases up to 1.0 × 1011 au which also signifies the larger nonlinear refractive index of the studied cluster. We hope this work could open up new possibilities using superalkali clusters as NLO materials for optoelectronics, laser, second harmonic generation and as frequency doubler.

Turning diamondoids into nonlinear optical materials by alkali metal Substitution: A DFT investigation

Electronic properties, absorption spectra and nonlinear optical properties of alkali metal substituted diamantanes are presented. A significant reduction in HOMO-LUMO gap has been observed by alkali metal substitution. K@CHa has the lowest H-L gap of 1.64 eV as compared to 8.88 eV for pristine diamantane. A remarkable increase in the first hyperpolarizability (βo) has been observed due to the substitution of alkali metals. Among these structures, K substituted complexes show the largest first hyperpolarizability (25526–36328 a.u). This significant increase in the first hyperpolarizability (βo) is attributed to low crucial transition energy (ΔE). K@CHa has the lowest ΔE value (2.06 eV) which results in the highest βo value (36328 a.u.) for K@CHa. Furthermore, frequency-dependent hyperpolarizability calculations have been carried out using 1906 nm and 1340 nm frequencies for commonly used lasers. The values of dynamic hyperpolarizabilities are greater than those of static ones for the majority of the substituted systems. This suggests the application of the proposed complexes under different frequencies of incident radiations. The substitution of alkali metals leads to the shift in absorption from ultraviolet to the visible region. Bathochromic shifts in the absorption spectra are observed with an increase in the size of alkali metal atom (λmax = 600 nm for K@CHa). This study provides an efficient approach to design high-performance NLO materials having extensive applications in the field of electronics and optoelectronics.

Theoretical investigation of superalkali clusters M2OCN and M2NCO (where M=Li, Na, K) as excess electron system with significant static and dynamic nonlinear optical response

Confining excess electrons in a specific space is an effective strategy to design high-performance nonlinear optical (NLO) materials. Herein, with the aid of density functional theory (DFT) calculations, we investigated the nonlinear optical (NLO) properties of excess electron superalkali/supermetals M2OCN and M2NCO (where M = Li, Na, K) clusters. The electronic and optoelectronic properties of these superalkali clusters are studied at CAM-B3LYP/6−311+G(d,p) level of theory. The studied clusters possess significant thermal stability and their binding energies per atom are in the range of -120.98 to -128.04 kcal mol−1. Furthermore, the analyzed superalkali clusters show excellent electronic properties. Being excess electron candidate, these supermetals clusters show significant reduced HOMO-LUMO gaps (-4.40 ∼ 2.79 eV). The HOMO-LUMO gaps are further reduced for M2NCO configuration that reveals excellent conductive properties. The further comprehensive piture of electronic properties is obtained from the plotted density of states (DOS) analysis spectra. With the justified excess electron character, the static hyperpolarizability (βo) response increases up to 1.4 × 104 au. The strong resemblance of total hyperplarizability with βvec provides evidence for practical design of NLO materials. Moreover, the hyperpolarizability from the two-level βtl model nicely correlates with βo. Besides, static nonlinearity, frequency-dependent hyperpolarizability (β(ω)) shows remarkable values for electro-optical pockel’s effect β(-ω;ω,0) at dispersion frequency of 532 nm whereas, the second harmonic generation (SGH) phenomena is much pronounced at higher frequency (ω = 1064 nm). The obtained second hyperpolarizability (γ(ω)) response increase up to 2.1 × 108 au. The dc-Kerr effect (nonlinear refractive index) γ(-ω;ω,0,0) shows a remarkable response (2.1 × 1010 au) at ω = 532 nm.