Dynamic Hyperpolarizabilities Research Articles

Relativistic full-configuration-interaction calculations of magic wavelengths for the 2 3S1→2 1S0 transition of helium isotopes

A large-scale full-configuration-interaction calculation based on Dirac-Coulomb-Breit (DCB) Hamiltonian is performed for the $2\,^1S_0$ and $2\,^3S_1$ states of helium. The operators of the normal and specific mass shifts are directly included in the DCB framework to take the finite nuclear mass correction into account. High-accuracy energies and matrix elements involved n (the main quantum number) up to 13 are obtained from one diagonalization of Hamiltonian. The dynamic dipole polarizabilities are calculated by using the sum rule of intermediate states. And a series of magic wavelengths with QED and hyperfine effects included for the $2\,^3S_1\rightarrow2\,^1S_0$ transition of helium are identified. In addition, the high-order Ac Stark shift determined by the dynamic hyperpolarizabilities at the magic wavelengths are also evaluated. Since the most promising magic wavelength for application in experiment is 319.8 nm, the high-accuracy magic wavelength of 319.815 3(6) nm of $^4$He is in good agreement with recent measurement value of 319.815 92(15) nm [Nature Physics (2018)/arXiv:1804.06693], and present magic wavelength of 319.830 2(7) nm for $^3$He would provide theoretical support for experimental designing an optical dipole trap to precisely determine the nuclear charge radius of helium in future.

Dynamic first hyperpolarizability of trans- and cis-isomers of azobenzene chromophore DO3 calculated at DFT and MP2 levels

Both static and dynamic molecular quadratic nonlinear-optical characteristics of trans- and cis-isomers of azochromophore Disperse Orange, DO3, are studied by correlated MP2 technique and TD-DFT with two density functionals: meta-GGA M06-2X and range-separated ωB97X ones. The effect of solvent and radiation frequency on the first hyperpolarizability values is considered.All the tendencies obtained at the MP2 level are found to be valid at DFT level, the first hyperpolarizability values estimated with M06-2X being quite close to those calculated at MP2 level. The solvent (chloroform) effect results in 3 times growth of the static first hyperpolarizability values for trans-isomer, and ca 2.5 times – for cis-DO3.The effect of radiation frequency on the first hyperpolarizability values reveals the systematic decrease of the βtot values with the decrease of frequency. The comparison of the first hyperpolarizability values for trans- and cis-isomers demonstrates the dominating value for trans-DO3, MP2 providing systematically larger ratio βtot[trans]/βtot[cis] than DFT; the estimations obtained by TD-DFT being in a very good agreement with the values presented in literature.

Linear and Nonlinear Optical Properties of Triphenylamine-Indandione Chromophores: Theoretical Study of the Structure-Function Relationship under the Combined Action of Substituent and Symmetry Change.

Linear and nonlinear optical properties of experimentally synthesized triphenylamine-indandione chromophores were investigated by time-dependent density functional theory calculations. The absorption and emission spectra, as well as the static and dynamic first hyperpolarizabilities related to the combined effect of substituent introduction and symmetry breaking, were discussed in detail. Theoretical analysis indicated the uniting of indandione acceptor group(s) with a precursor (triphenylamine, TriPhA), with the molecular symmetry destroyed simultaneously, leads to an obvious change in both the peak position and intensity of the linear spectra. The same process can also substantially magnify the molecular first hyperpolarizabilities. The triphenylamine-indandione molecules exhibit efficiencies in static first hyperpolarizability relative to that of the electron-donating TriPhA component and the electron-accepting indandione moiety. The optical nonlinearity would be further expanded under the influence of a resonance effect induced by appropriate excitation. Incident light with a wavelength nearly two times the one-photon absorption is likely to cause a greater frequency dispersion response. In particular, the first hyperpolarizabilities of the title compounds can be enlarged by about 3.2 times on average by resonance enhancement at a fundamental wavelength of 1064 nm.

First-Order Hyperpolarizability of Triphenylamine Derivatives Containing Cyanopyridine: Molecular Branching Effect

In the present work, we report the multibranching effect on the dynamic first-order hyperpolarizability (β(−2ω; ω, ω)) of triphenylamine derivatives containing cyanopyridine one-branch (dipolar structure), two-branch (V-shaped structure), and three-branch (octupolar structure) structures. For this study, we used the hyper-Rayleigh scattering (HRS) technique involving picosecond pulse trains at 1064 nm. Our results show that βHRS increases from 2.02 × 10–28 to 9.24 × 10–28 cm5/esu when an extra branch is added to the molecule, configuring a change from a dipolar to a V-shaped (quadrupolar) molecular structure. When a third branch is added, leading to an octupolar structure, a decrease to 3.21 × 10–28 cm5/esu is observed. Such a significant decrease in βHRS is attributed to a negative contribution presented in the βHRS description by using a three-level energy approach due to their electronic structure and considering a specific combination of the angle between the dipole moments. On the other hand, the enh...

Static second hyperpolarizability of inverse sandwich compounds (M1-C5H5-M2) of alkali (M1 = Li, Na, K) and alkaline earth metals (M2 = Be, Mg, Ca).

In the investigated inverse sandwich complexes, charge transfer from alkali metal (M1) led to aromatically stabilized Cp ring, which prevented further charge transfer from the alkaline earth metal (M2). This electron push effect resulted in diffusion of electron density from the outermost "ns" subshell of alkaline earth metal. The alkaline earth metal is weakly bound to the alkali metal-C5H5 complex. The vertical ionization energy of the chosen M1-Cp-M2 complexes was smaller than that of the corresponding alkaline earth metals. Large second hyperpolarizability (106-108 a.u.) was obtained for the studied molecules. The correction due to the basis set superposition error (BSSE) in the calculated second hyperpolarizability was found to be small for larger systems, while it was rather significant for small systems. The MP4SDQ and CCSD results were in fair agreement, which indicates the necessity of higher order electron correlation treatment in the accurate description of second hyperpolarizability. Calculated dynamic second hyperpolarizabilities at 1064 nm were found to increase considerably for most of the chosen metal complexes.

Quadratic Response Properties from TDDFT: Trials and Tribulations.

We report on the efficient turbomole implementation of quadratic response properties within the time-dependent density functional theory (TDDFT) context that includes the static and dynamic dipole hyperpolarizability, ground-to-excited-state two-photon absorption amplitudes (through a single residue) and state-to-state one-photon absorption amplitudes (through a double residue). Our implementation makes full use of arbitrary (including non-Abelian) point-group symmetry as well as permutational symmetry and enables the calculation of nonlinear properties with hybrid density functionals for molecules with hundreds of atoms and thousands of basis functions at a cost that is a fixed multiple of the cost of the corresponding linear properties. Using the PBE0 hybrid density functional, we show that excited-state absorption spectra computed within the pseudowavefunction approach contain the qualitative features of transient absorption spectra tracking excimer formation in perylene diimide dimers, two-photon absorption cross sections for a series of highly twisted fused porphyrin chains are semiquantitatively reproduced, and the computed dynamic hyperpolarizability of several calix[4]arene stereoisomers yield simulated hyper-Raleigh scattering signals consistent with experiment. In addition, we show that the incorrect pole structure of adiabatic TDDFT properties can cause incorrect excited-state absorption spectra and overly resonant hyperpolarizabilities, and discuss possible remedies.

Experimental and computational studies on second-and third-order nonlinear optical properties of a novel D-π-A type chalcone derivative: 3-(4-methoxyphenyl)-1-(4-nitrophenyl) prop-2-en-1-one

The present study reports the theoretical and experimental investigations of linear and nonlinear optical (static and dynamic) properties of 3-(4-methoxyphenyl)-1-(4-nitrophenyl)prop-2-en-1-one (MNC). The crystal structure was confirmed from powder X-ray diffraction (PXRD) analysis and evaluated the crystalline quality using high-resolution X-ray diffraction (HRXRD). Linear absorption and fluorescence spectra were recorded and the optical band gap was determined by Tauc’s relation. Third-order nonlinear optical (NLO) characteristics along with optical limiting behavior were explored using the femtosecond (fs) Z-scan technique at 800 and 900nm wavelengths (Ti: sapphire laser, 150fs, 80MHz). The experimental results are supported by theoretical calculations obtained from the density functional theory (DFT). The optimized geometry, linear optical absorption, HOMO-LUMO energy gap, molecular electrostatic potential (MEP), dipole moments and global chemical reactivity descriptors (GCRD) were computed by employing B3LYP/6-311+G(d) level of theory. The static and dynamic linear polarizability (α), first hyperpolarizability (β) and second hyperpolarizability (γ) components were calculated using time-dependent Hartree–Fock (TDHF) method. The computed first hyperpolarizability β(−2ω;ω,ω) at 1064nm wavelength was found to be 55 times greater than that of urea standard. The experimental and calculated dynamic molecular second hyperpolarizabilities γ(−3ω;ω,ω,ω) are in good accordance at 800 and 900nm wavelengths.

Molecular structure, second- and third-order nonlinear optical properties and DFT studies of a novel non-centrosymmetric chalcone derivative: (2E)-3-(4-fluorophenyl)-1-(4-{[(1E)-(4-fluorophenyl)methylene]amino}phenyl)prop-2-en-1-one

In the present work, the title chalcone, (2E)-3-(4-fluorophenyl)-1-(4-{[(1E)-(4-fluorophenyl) methylene]amino}phenyl)prop-2-en-1-one (abbreviated as FAMFC), was synthesized and structurally characterized by single-crystal X-ray diffraction. The compound is crystallized in the monoclinic system with non-centrosymmetric space group P21 and hence it satisfies the essential condition for materials to exhibit second-order nonlinear optical properties. The molecular structure was further confirmed by using FT-IR and 1H NMR spectroscopic techniques. The title crystal is transparent in the Vis-NIR region and has a direct band gap. The third-order nonlinear optical properties were investigated in solution (0.01M) by Z-scan technique using a continuous wave (CW) DPSS laser at the wavelength of 532nm. The title chalcone exhibited significant two-photon absorption (β=35.8×10−5cmW−1), negative nonlinear refraction (n2=−0.18×10−8cm2W−1) and optical limiting (OL threshold=2.73kJcm−2) under the CW regime. In support of the experimental results, a comprehensive theoretical study was carried out on the molecule of FAMFC using density functional theory (DFT). The optimized geometries and frontier molecular orbitals were calculated by employing B3LYP/6-31+G level of theory. The optimized molecular structure was confirmed computationally by IR vibrational and 1H NMR spectral analysis. The experimental UV–Vis-NIR spectrum was interpreted using computational chemistry under time-dependent DFT. The static and dynamic NLO properties such as dipole moments (μ), polarizability (α), and first hyperpolarizabilities (β) were computed by using finite field method. The obtained dynamic first hyperpolarizability β(−2ω;ω,ω) at input frequency ω=0.04282a.u. is predicted to be 161 times higher than urea standard. The electronic excitation energies and HOMO–LUMO band gap for FAMFC were also evaluated by DFT. The experimental and theoretical results are in good agreement, and the NLO study suggests that FAMFC molecule can be a potential candidate in the nonlinear optical applications.

Large Hyperpolarizabilities at Telecommunication-Relevant Wavelengths in Donor-Acceptor-Donor Nonlinear Optical Chromophores.

Octopolar D2-symmetric chromophores, based on the MPZnM supermolecular motif in which (porphinato)zinc(II) (PZn) and ruthenium(II) polypyridyl (M) structural units are connected via ethyne linkages, were synthesized. These structures take advantage of electron-rich meso-arylporphyrin or electron-poor meso-(perfluoroalkyl)porphyrin macrocycles, unsubstituted terpyridyl and 4′-pyrrolidinyl-2,2′;6′,2″-terpyridyl ligands, and modulation of metal(II) polypyridyl-to-(porphinato)zinc connectivity, to probe how electronic and geometric factors impact the measured hyperpolarizability. Transient absorption spectra obtained at early time delays (tdelay < 400 fs) demonstrate fast excited-state relaxation, and formation of a highly polarized T1 excited state; the T1 states of these chromophores display expansive, intense T1 → Tn absorption manifolds that dominate the 800–1200 nm region of the NIR, long (μs) triplet-state lifetimes, and unusually large NIR excited absorptive extinction coefficients [ε(T1 → Tn) ∼ 105 M–1 cm–1]. Dynamic hyperpolarizability (βλ) values were determined from hyper-Rayleigh light scattering (HRS) measurements, carried out at multiple incident irradiation wavelengths spanning the 800–1500 nm spectral domain. The measured βHRS value (4600 ± 1200 × 10–30 esu) for one of these complexes, RuPZnRu, is the largest yet reported for any chromophore at a 1500 nm irradiation wavelength, highlighting that appropriate engineering of strong electronic coupling between multiple charge-transfer oscillators provides a critical design strategy to realize octopolar NLO chromophores exhibiting large βHRS values at telecom-relevant wavelengths. Generalized Thomas–Kuhn sum (TKS) rules were utilized to compute the effective excited-state-to-excited-state transition dipole moments from experimental linear-absorption spectra; these data were then utilized to compute hyperpolarizabilities as a function of frequency, that include two- and three-state contributions for both βzzz and βxzx tensor components to the RuPZnRu hyperpolarizability spectrum. This analysis predicts that the βzzz and βxzx tensor contributions to the RuPZnRu hyperpolarizability spectrum maximize near 1550 nm, in agreement with experimental data. The TKS analysis suggests that relative to analogous dipolar chromophores, octopolar supermolecules will be likely characterized by more intricate dependences of the measured hyperpolarizability upon irradiation wavelength due to the interactions among multiple different β tensor components.

Physico-chemical studies of the experimental and theoretical properties of organic nonlinear optical material 4-chloro-4'methoxy benzylideneaniline

The FT-IR, FT-Raman and UV–visible spectral analysis of 4-chloro 4’-methoxy benzylidene aniline were done experimentally and interpreted with the aid of normal coordinate analysis based on density functional theory (DFT) at the B3LYP/6–311++G (d, p) level of theory. Natural Bond orbital analysis was performed to understand the charge transfer interactions and reactive sites within the system. HOMO-LUMO analysis and first static and dynamic hyperpolarizability calculations were carried out in order to confirm the NLO activity of CMOBA. Photophysical characterization was done to understand the fluorescence emission and lifetime of CMOBA leading to application in blue OLEDs. The Molecular Electrostatic Potential Map was simulated to identify the active sites for electrophilic and nucleophilic attack or the active sites of the molecule which can bind to proteins. Molecular docking analysis revealed its potential as an inhibitor for different proteins which are responsible for cancer and many inflammatory diseases such as rheumatoid arthritis, inflammatory bowel disease, Crohn's disease and psoriasis. Experimental studies of invitro antiproliferative effect by MTT assay verified the anticancer properties of CMOBA.

Theoretical insight into the substituent effects on linear and nonlinear optical properties of azobenzene-based chromophores

The linear and nonlinear optical properties of 4 kinds of experimental synthesized azobenzene-based chromophores were investigated by different density functional theories (DFTs) upon the electronic structures. The structure-property relationship was studied on each single molecule either in the gas phase or in diethylether and tetrahydrofuran (THF) solutions. The substituent effect on optical properties was revealed by checking the positions of substituent groups, and the influence of dynamic perturbation to the optical nonlinearity was investigated by simulating the experimental excitation. The results revealed that the substituent in the meta-position of the azobenzene group affects the optical properties more significantly than that in the ortho-position, which is in agreement with the experimental finding. The modulation of molecular hyperpolarizability of bridge-substituted azobenzene derived by dynamic perturbation is not recommended because of the reduced dynamic hyperpolarizability relative to the static one. The different functions of the DFT method hardly affect the calculated results, while solvent effects of diethylether and THF solutions are significant on the optical properties, especially for optical nonlinearity. The information derived from the single chromophore may be helpful in the design and preparation of high-performance nonlinear optical materials in further.

Shedding light on molecular structure, spectroscopic, nonlinear optical and dielectric properties of bis(thiourea) silver(I) nitrate single crystal: A dual approach

The current work is to spotlight the key structure-property features of a novel thiourea complex bis(thiourea) silver(I) nitrate (BTSN) for future applications in nonlinear optical devices through dual approach involving experimental and theoretical techniques. The synthesis and growth of good quality single crystals of a relatively new material BTSN have been done. The crystal structure, quantitative and qualitative, vibrational, optical and dielectric analysis of the grown single crystals was carried out. The optical transparency of the grown crystals is found to be more than 80% confirms its colorless nature and applications in optoelectronic devices. Further, the state-of-art computational methods have been applied to obtain the ground state molecular geometry at B3LYP/6-31G∗, MP2/6-31G∗ and M06/6-31G∗ levels of theory. Various key electro-optical properties (complementary to experimental results) such as IR, Raman, and polarizabilities have been determined at the same levels of theory. The static and dynamic polarizability and first hyperpolarizability both were calculated to comprehend the potential applications of BTSN in nonlinear optics. In addition to the above, numerous novel molecular level insights have been achieved in the form of total and partial density of states, HOMO-LUMO gap and molecular electrostatic potential map. The calculated values of static and frequency dependent dynamic first hyperpolarizability are found to be 8.46×10−30 and 2.30×10−30esu which are about 23 times and 13 times greater than those of prototype urea molecule, respectively, calculated at the same B3LYP/6-31G∗ level of theory. From the analyzed results it is clear that the titled compound possesses excellent electro-optic properties that make it a decent contestant for photonic devices.

Tuning the push–pull configuration for efficient second-order nonlinear optical properties in some chalcone derivatives

Using the density functional theory methods, we effectively tune the second-order nonlinear optical (NLO) properties in some chalcone derivatives. Various unique push–pull configurations are used to efficiently enhance the intramolecular charge transfer process over the designed derivatives, which result in significantly larger amplitudes of the first hyperpolarizability as compared to their parent molecule. The ground state molecular geometries have been optimized using B3LYP/6-311G** level of theory. A variety of methods including B3LYP, CAM-B3LYP, PBE0, M06, BHandHLYP and MP2 are tested with 6-311G** basis set to calculate the first hyperpolarizability of parent system 1. The results of M06 are found closer to highly correlated MP2 method, which has been selected to calculate static and frequency dependent first hyperpolarizability amplitudes of all selected systems. At M06/6-311G** level of theory, the permanent electronic dipole moment (μtot), polarizability (α0) and static first hyperpolarizability (βtot) amplitudes for parent system 1 are found to be 5.139 Debye, 274a. u. and 24.22×10−30esu, respectively. These amplitudes have been significantly enhanced in designed derivatives 2 and 3. More importantly, the (βtot) amplitudes of systems 2 and 3 mount to 75.78×10−30 and 128.51×10−30esu, respectively, which are about 3 times and 5 times larger than that of their parent system 1. Additionally, we have extended the structure-NLO property relationship to several newly synthesized chalcone derivatives. Interestingly, the amplitudes of dynamic frequency dependent hyperpolarizability μβω (SHG) are also significantly larger having values of 366.72×10−48, 856.32×10−48 and 1913.46×10−48esu for systems 1–3, respectively, at 1400nm of incident laser wavelength. The dispersion behavior over a wide range of change in wavelength has also been studied adopting a range of wavelength from 1907 to 544nm. Thus, the present work realizes the potential of designed derivatives as efficient NLO-phores for modern NLO applications.

Efficient polarized basis sets for evaluation of static and dynamic molecular electric properties

New medium size Gaussian-type basis set R-ORP for evaluation of static and dynamic electric properties in molecular systems is presented. It is obtained in a close resemblance to the original ORP basis set, from the source basis set through addition of two first-order polarization functions whose exponent values are optimized with respect to the finite field restricted open-shell Hartree–Fock (ROHF) atomic polarizabilities. As the source set the VTZ basis set of Ahlrichs and coworkers, augmented with additional diffuse functions and contracted to the form [6s/3s] for hydrogen and [11s7p/4s3p] for carbon through fluorine, is chosen. The resulting basis set is of the form [6s2p/3s2p] for hydrogen and [11s7p2d/4s3p2d] for other atoms. Presented basis set is next tested in the CCSD static and dynamic molecular polarizability and hyperpolarizability calculations for a set of ten and four test molecules, respectively, for which very accurate reference data exist. Additionally, the recently developed ORP basis set is employed in the calculations to examine the limits of its applicability. Results are compared to the literature data obtained in both, large and diffuse, as well as reduced-size basis sets. In the case of polarizability calculations, the aug-pc-1 and R-ORP are the optimal choices among the investigated smaller basis sets, with the overall performance of the aug-pc-1 set being better. Among the larger sets, the ORP performs better in the case of average polarizability, while the RMSE values for polarizability anisotropy are practically identical for d-aug-cc-pVDZ and ORP sets. Finally, the R-ORP and ORP basis sets compete other small bases in the evaluation of the first hyperpolarizability in investigated systems. © 2016 Wiley Periodicals, Inc.

Calculation of the dynamic first electronic hyperpolarizability β(-ω(σ); ω(1), ω(2)) of periodic systems. Theory, validation, and application to multi-layer MoS2.

We describe our implementation of a fully analytical scheme, based on the 2n + 1 rule, for computing the coupled perturbed Hartree Fock and Kohn-Sham dynamic first hyperpolarizability tensor β(-ωσ; ω1, ω2) of periodic 1D (polymer), 2D (slab), and 3D (crystal) systems in the CRYSTAL code [R. Dovesi et al., Int. J. Quantum Chem. 114, 1287 (2014)], which utilizes local Gaussian type basis sets. The dc-Pockels (dc-P) and second harmonic generation (SHG) tensors are included as special cases. It is verified that (i) symmetry requirements are satisfied; (ii) using LiF as an example, the infinite periodic polymer result agrees with extrapolated finite oligomer calculations and, likewise, for the build-up to a 2D slab and a 3D crystal; (iii) the values converge to the static case for low frequencies; and (iv) the Bishop-deKee dispersion formulas relating dc-P, SHG, and general processes are reproduced through quartic terms. Preliminary SHG calculations on multi-layer MoS2 satisfactorily reproduce experimental data.

Study on Pyrrole 4-Pyrazoline Derivatives: Experimental and Quantum Chemical Approaches

As part of a study on pyrrole derivatives we report here a combined experimental and quantum chemical study of pyrrole 4-pyrazoline biheterocyclic derivatives. The structure of the synthesised compounds have been studied using experimental IR, UV, 1H and 13C NMR spectroscopic analyses along with density functional theory (DFT) calculations using the B3LYP functional with 6–311+G (d,p) basis set. The global, local reactivity, and thermodynamic parameters support the analysis. All the experimental vibrational bands have been discussed and assigned to normal modes on the basis of our calculations. In addition, the computed 1H and 13C NMR data, obtained by DFT calculations, are found to be in good agreement with the experimental data and serve as valuable tools in identifying the products. The vibrational analysis shows red shifts in vN–H and vC=O stretching vibrations as a result of dimer formation. The theoretical electronic absorption spectra have been calculated by using time dependent-DFT methods. The static first hyperpolarizability (β0) values for the synthesized pyrrole–pyrazoline derivatives 4A–D are calculated as 16.97 × 10–30, 47.64 × 10–30, 65.40 × 10–30, 65.39 × 10–30 esu, respectively, and increase from 4A to 4C as a result of the addition of an –NO2 acceptor in 4B and two –NO2 group acceptors in 4C. However, an additional –Cl group in 4D on the phenyl ring attached to the pyrazoline moiety does not result in a clear change from 4C. The calculated static and dynamic hyperpolarizability results show that the investigated molecules might be used as non-linear optical materials.

Second hyperpolarizabilities of the lithium salt of pyridazine Li–H3C4N2 and lithium salt electride Li–H3C4N2⋯Na2

This Letter reports static and dynamic second hyperpolarizabilities of the lithium salt of pyridazine Li–H3C4N2 and lithium salt electride Li–H3C4N2⋯Na2. The results show strong dependence of the computed values with respect to the electron correlation treatment. The static value obtained at the CCSD level with the aug-cc-pVDZ basis set for the Li–H3C4N2⋯Na2 is 1.1×109au. This extremely large value of the second hyperpolarizability reinforces the potential of this system for application in nonlinear optics.

Interpreting the First-Order Electronic Hyperpolarizability for a Series of Octupolar Push–Pull Triarylamine Molecules Containing Trifluoromethyl

In this present paper, we investigate the relationship between the dynamic first-order hyperpolarizability (DFH, or βHRS) of a triarylamine core bearing two 3,3′-bis(trifluoromethyl)phenyl arms and the nature of a third group containing distinct electron-withdrawing strength (H < CN < CHO < NO2 < Cyet < Vin). For that, we have combined hyper-Rayleigh scattering (HRS) experiments with picosecond pulse train at 1064 nm and quantum chemical calculations at the density functional theory (DFT) level. The βHRS values exhibited pronounced enhancement from 56 × 10–30 cm5/esu (EWG = CN) up to ∼400 × 10–30 cm5/esu (EWG = Vin) due to the increase in the degree of donor–acceptor charge transfer concomitant with the intensification of the resonance enhancement effect observed when the scattered photon (2ω = 532 nm) approaches, in energy, the lowest energy band of chromophores. Furthermore, our experimental results suggest that the CF3 group has a significant effect on the βHRS, since we observed a considerable increas...

Theoretical study of second-order hyperpolarizability for nitrogen radical cation

We report calculations of the static and dynamic hyperpolarizabilities of the nitrogen radical cation in doublet state. The electronic contributions were computed analytically using density functional theory and multi-configurational self-consistent field method with extended basis sets for non-resonant excitation. The open-shell electronic system of nitrogen radical cation provides negative second-order optical nonlinearity, suggesting that the hyperpolarizability coefficient, in the non-resonant regime is mainly composed of combinations of virtual one-photon transitions rather than two-photon transitions. The second-order optical properties of nitrogen radical cation have been calculated as a function of bond length starting with the neutral molecular geometry (S0 minimum) and stretching the N–N triple bond, reaching the ionic D0 relaxed geometry all the way toward dissociation limit, to investigate the effect of internuclear bond distance on second-order hyperpolarizability.

Second-order nonlinear optical properties of dithienophenazine and TTF derivatives: A butterfly effect of dimalononitrile substitutions

Using density functional theory (DFT) methods, the nonlinear optical (NLO) properties have been calculated with strong donor-π-conjugation-acceptor configurations. The static first hyperpolarizability (β0) and dynamic (frequency dependent) electric field induced second harmonic generation (EFISHG) first hyperpolarizability (μβ) are calculated for all designed systems. Our DFT calculations show dithienophenazine merged TTF (2) holds larger β0 amplitudes (β0=21.04×103a.u.) as compared to its corresponding compounds of TTF merged-difurophenazine (1), dicyclopentaphenazine (3) and dipyrrolophenazine (4) derivatives having β0 amplitudes of 16.25×103, 12.69×103, and 18.38×103a.u., respectively. Furthermore, substitution of dimalononitrile [C(CN)2]2 groups at acceptor end of these compounds results in new derivatives 1a–4a, respectively. Interestingly, a butterfly effect on first hyperpolarizability of all systems 1a–4a has been spotted, which not only results in their robustly larger β0 amplitudes but also changes the increasing order of β0 amplitudes from systems 3<1<4<2 to 1a<2a<3a<4a at both PBE0/6-31G* and CAM-B3LYP/6-31+G* levels of theory. For example, the increase in β0 amplitudes of systems 1a, 2a, 3a and 4a are 3, 3, 5, and 19 times as compared with their corresponding non dimalononitrile derivatives at PBE0/6-31G* level of theory, respectively. Remarkably, unlike the static first hyperpolarizability, the dynamic EFISHG hyperpolarizability (μβω) has the largest value for system 4a with its amplitudes of 1378.59×10−46 and 1349.40×10−46esu, at PBE0/6-31G* and CAM-B3LYP/6-31+G* levels of theory, respectively. TD-DFT calculations have been performed to trace the origin of first hyperpolarizability. It has been found that the lower transition energy and higher oscillator strengths cause robustly large amplitudes especially in systems 3a and 4a, which consequently stems in strong donor-π-conjugation-acceptor configuration of these systems. Thus the present results intrigue the butterfly effect of a two-step substitution on NLO properties of TTF merged dithienophenazine compounds that can be used as an efficient NLO material.