A sum-over-state scheme of analysis of hyperpolarizabilities and its application to spiroconjugated molecular system

The static first and second hyperpolarizabilities of a number of spiromolecules with varying degree of polarity have been calculated at the HF and MP2 level using the 6-31+G* basis set and the B3LYP/6-31+G* optimized geometry. The variation of mean second hyperpolarizability in these molecular systems has been explained in terms of the ground state dipole moment, mean linear polarizability and second-order polarizability. A number of relationships among these quantities have been derived in the framework of the sum-over-state scheme and the generalized Thomas–Kuhn sum rule. The spiroconjugation results in the significant increase of the mean polarizability. The appreciable enhancement of first hyperpolarizability due to the spiroconjugation between two dipolar monomer units has been accounted for the rather significant increase of the mean polarizability tensor and the ground state dipole moment. The relatively larger value of the average second hyperpolarizability of the spiroconjugated molecules compared to that of the corresponding monomers arises from the rather significant increase of the nonaxial component γ _xxyy . The replacement of spirocarbon by spirosilicon results in the enhancement of the cubic polarizability manifold. The donor–acceptor substituted spirocompounds are predicted to be the superior third-order nonlinear optical (NLO) phores. The nature of π-conjugation in the monomer units around the spirocenter shows a strong modulation of the NLO properties of spirocompounds. The influence of electron correlation on the NLO properties at the MP2 level has been found to be rather significant.     

Energetic of molecular interface at metal-organic heterojunction: the case of thiophenethiolate chemisorbed on Au(111)

To probe the cooperativity of charge transfer between organoimido and hexamolybdate, and enhance the second-order nonlinear optical (NLO) response of organoimido derivatives of hexamolybdates, electronic structures and second-order NLO properties of a series of charge-transfer covalently bonded organoimido derived hexamolybdate complexes with donor-(π conjugated bridge)-acceptor-(π conjugated bridge)-donor or acceptor-(π conjugated bridge)-donor-(π conjugated bridge)-acceptor structures were studied by density functional theory. Studies show that different combinations of the donor, acceptor, heterocycle, –C≡C– and –N=N– moieties, and orientation of heterocycle remarkably affect the second-order NLO responses. The complexes containing electronic acceptor matched with the direction of charge transfer possess remarkable large molecular second-order polarizabilities. Electronic transitions to crucial excited states show that x-polarized transition, contributed to the off-diagonal second-order polarizabiliy tensor (β_zxx), possesses lower excited energy compared with z-polarized transition which accounted for the diagonal second-order polarizabiliy tensor (β_zzz) and thus led to the large in-plane nonlinear anisotropy (u = β_zxx/β_zzz) value, as well as good two-dimensional (2-D) second-order NLO properties. These complexes can be used as excellent 2-D second-order NLO materials from the standpoint of both large β and u values.     

Physicochemical studies of bioactive heterocycles of some novel imidazole derivatives as sensitive NLO materials

Some novel imidazole derivatives were developed as highly sensitive chemisensors for transition metal ions. A prominent fluorescence enhancement was found in the presence of transition metal ions such as Hg(2+), Pb(2+), Cu(2+), Zn(2+), Co(2+) and Fe(2+) and this was suggested to result from the suppression of radiationless transitions from the n-π* state in the chemisensors. By DFT calculation HOMO-LUMO energies were calculated, the electric dipole moment (μ) and the hyperpolarizability (β) of the investigated molecules have been studied experimentally and also theoretically. These synthesized molecules were found to have microscopic non-linear optical (NLO) behaviour with non-zero tensor components.     

Direct metal-metal interaction contributions to quadratic hyperpolarizability: a study on dirhenium complexes

We present a comparative study of the metal-metal interaction effect on the static quadratic hyperpolarizabilities of two typical dinuclear rhenium clusters. The electronic structures, excitation spectra, dipolar moments, static polarizabilities, and quadratic hyperpolarizabilities of the two complexes with direct metal-metal interactions have been computed and analyzed with the use of high-level DFT/TDDFT methods. The geometries and the first intense excitations agree with the relevant reported measurements. The orbital decomposition scheme ( J. Phys. Chem. A 2006, 110, 1014-1021) has been applied to analyze the relationship between the electronic structures and nonlinear optical (NLO) properties of these two complexes. We propose an unprecedented NLO response mechanism featuring the contribution of the direct metal-metal interaction transition process in these dinuclear rhenium complexes. This contribution positively enhances the quadratic hyperpolarizability and relates to the intensity of the metal-metal interactions of the complexes. The results are helpful to the development of NLO chromophores in polynuclear metal clusters through the molecular design technique.     

Modulation of the Second Order Nonlinear Optical Properties of Helical Graphene Nanoribbons Through Introducing Azulene Defects or/and BN Units

The current study has obtained excellent potential nonlinear optical(NLO) materials by combining density functional theory methods with sum-over-states model to predict the second order NLO properties of helical graphene nanoribbons(HGNs) through introducing azulene defects or/and BN units. The introduction of these functional groups deforms the pristine HGN (compression or tension) and enhances obviously the static first hyperpolarizability(<b₀>) of system by up to two orders of magnitude. The tensor components along the helical axis of HGNs play a dominant role in the total <b₀>. The azulene defects and the BN units polarize the pristine HGN to different degrees, and the azulenes and contiguous benzenes are involved in the major electron excitations with significant contributions to <b₀> but the BN units are not. The BN-doped chiral HGNs have good kinetic stability and strong second order NLO properties(6.84×10⁵×10^-30 esu), and can be a potential candidate of high-performance second order NLO materials. The predicted two-dimensional second order NLO spectra provide useful information for further exploration of those helicenes for electro-optic applications.     

Role of spatial distortions on the quadratic nonlinear optical properties of octupolar organic and metallo-organic molecules

Following on the recent experimental demonstration of a discrepancy between the nonlinear optical (NLO) behavior of several pi-conjugated chromophores and their assumed octupolar symmetry, the authors investigate how geometrical distortions influence the NLO response of multipolar push-pull molecules. Their analytical model is set on a basis of valence-bond and charge-transfer states to estimate the hyperpolarizability of organic and metallo-organic chromophores using the lowest possible number of variables. Since symmetry breakdown changes the definition of the molecular Cartesian framework, tensorial spherical coordinates are implemented. The evolution of the nonlinear molecular anisotropy with possible rotational deviations is then evaluated for two recently studied chromophores. Zero-frequency calculations show that, outside optical resonance, weak geometrical distortions lead to strong anisotropy variations in agreement with experimental data. Their goal is to underscore which molecular engineering strategies should be applied when designing a photoisomerizable nonlinear octupole.     

Influence of isomerization on nonlinear optical properties of molecules

The influence of rotational and geometrical isomerism on the nonlinear optical (NLO) properties, specifically the first-order hyperpolarizability beta, of chromophores of current interest has been investigated with density functional theory (DFT). In the first of this two-part study, the rotational isomerism of a linear chromophore was explored. Calculation of the torsion potentials about two of the rotatable and conformation-changing single bonds in a chromophore demonstrated the near equality of the molecular energies at 0 degrees and 180 degrees rotational angles. To explore the consequences of this near conformational energy degeneracy to NLO behavior, the eight low energy rotational isomers of FTC [Robinson, B. H.; et al. Chem. Phys. 1999, 245, 35] were investigated. This study provides the first-reported DFT-based calculation of the statistical mechanical average of beta over the conformational space of a molecule having substantial nonlinear optical behavior. The influence of the solvent reaction field on rotameric populations and on the beta tensor is reported. In the second part, two molecules having two donors and two acceptors bonded respectively in ortho and meta positions on a central benzene ring are shown to have substantially different beta tensors. These two so-called molecular Xs have different highest occupied molecular orbital to lowest unoccupied molecular orbital (HOMO-LUMO) distributions, and consistent with expectations, it is found that the larger beta(zzz) is associated with a large spatial asymmetry between the HOMOs and LUMOs. Large hyperpolarizability correlates with the HOMO concentrated on the donor groups and the LUMO on the acceptor groups.     

Interplay among aromaticity, magnetism, and nonlinear optical response in all-metal aromatic systems

All-metal aromatic molecules are the latest inclusion in the family of aromatic systems. Two different classes of all-metal aromatic clusters are primarily identified: one is aromatic only in the low spin state, and the other shows aromaticity even in high-spin situations. This observation prompts us to investigate the effect of spin multiplicity on aromaticity, taking Al(4)(2-), Te(2)As(2)(2-), and their copper complexes as reference systems. Among these clusters, it has been found that the molecules that are aromatic only in their singlet state manifest antiaromaticity in their triplet state. The aromaticity in the singlet state is characterized by the diatropic ring current circulated through the bonds, which are cleaved to generate excess spin density on the atoms in the antiaromatic triplet state. Hence, in such systems, an antagonistic relationship between aromaticity and high-spin situations emerges. On the other hand, in the case of triplet aromatic molecules, the magnetic orbitals and the orbitals maintaining aromaticity are different; hence, aromaticity is not depleted in the high-spin state. The nonlinear optical (NLO) behavior of the same set of clusters in different spin states has also been addressed. We correlate the second hyperpolarizability and spin density in order to judge the effect of spin multiplicity on third-order NLO response. This correlation reveals a high degree of NLO behavior in systems with excess spin density. The variance of aromaticity and NLO response with spin multiplicity is found to stem from a single aspect, the energy gap between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO), and eventually the interplay among aromaticity, magnetism, and NLO response in such materials is established. Hence, the HOMO-LUMO energy gap becomes the cornerstone for tuning the interplay. This correlation among the said properties is not system-specific and thus can be envisaged even beyond the periphery of all-metal aromatic clusters. Such interplay is of crucial importance in tailoring novel paradigm of multifunctional materials.     

Molecular dynamics simulations applied to electric field induced second harmonic generation in dipolar chromophore solutions

Electric field induced second harmonic generation (EFISH) is an important experimental technique in extracting the first hyperpolarizability of an organic chromophore molecule. Such experiments are carried out in solutions with chromophore molecules dissolved in some common solvents. A known fact is that the first hyperpolarizabilities extracted from EFISH experiments are subject to the use of local field factors. In this work, we apply simulations to study the EFISH properties of chromophore solutions. By combining quantum chemistry calculations with the results derived from molecular dynamics simulations, we show how macroscopic EFISH properties can be modeled, using 4-(dimethylamino)-4'-nitroazobenzene dissolved in chloroform as a demonstration case. The focus of the study is on deriving accurate local field factors. We find that the local field approach applies very well to dipolar solutions, such as the one studied here, but that the local field factors derived are much smaller than the commonly used Onsager or Lorentz local field factors. Our study indicates that many of the reported first hyperpolarizabilities for dipolar molecules from EFISH experiments are most probably underestimated because the Onsager/Lorentz approach, commonly used in extracting the molecular first hyperpolarizability, neglects the effects of the shapes of dipolar chromophore molecules on the local field factors.     

Verbenone-based push–pull chromophores with giant first hyperpolarizabilities: A new structure–property correlation study

Novel chromophores Ch1–8 based verbenone bridge with various strong donors and acceptors were designed for applications in nonlinear optics, and the nonlinear optical (NLO) properties of those verbenone-type chromophores were systematically investigated using the bond length alteration (BLA) theory, two states model (TSM) and sum-over-states (SOS) model. The results show that several verbenone-based chromophores possess remarkably large molecular second-order hyperpolarizabilities, which is due to its electron distribution close to the cyanine limit, the appropriate strength of acceptor, rather large change in dipole moment and low excitation energy. Computed hyperpolarizability (β_tot) of Ch6 also approach an outstanding 2922 × 10⁻³⁰ esu in TFE. The hyperpolarizability density analyses and two states model (TSM) were carried out to make a further insight into the origination of molecular nonlinearity of this unique system, suggesting that tuning structure of acceptor and polarity of the medium have great influence on the second-order nonlinear optical properties. More importantly, chromophores Ch1–Ch8 exhibited distinct features in two-dimensional second order NLO responses, and the strong electro-optical Pockels effect and optical rectification responses. The excellent electronic sum frequency generations (SFG) and difference frequency generations (DFG) effect are observed in these verbenone-type chromophores. These chromophores have a possibility to be appealing second-order nonlinear optical (NLO) materials, data storage materials and DSSCs materials from the standpoint of large β values, high LHE, and excellent two-dimensional second order NLO responses.     

吡啶盐二维电荷转移分子的设计、合成和超级化氯的测定

设计、合成了以吡啶阳离子为吸电子基团的二维电荷转移非线性光学生色团分子－双四苯鹏(反式)-4,4'-二{p-[(N-乙基-N-羟乙基)氨基]苯亚乙烯基}-N,N'-(1,2-乙基)-2,2'-联吡啶盐和双四苯硼(反式)-N-己基-咔唑-3,6-二(p-亚乙烯基-N-羟乙基-吡啶盐),利用超瑞利散射技术(HRS)测定了这两种分子的第一超级化率β,在1064nm分别为786x10^-^3^0esu和1770x10^-^3^0esu。双能级模型计算得到的β0的值分别为215x10^-^3^0esu和119x10^-^3^0esu。从分子结构的角度定性地分析了该类分子具有大β值的原因。     

A time-dependent density functional theory investigation on the nature of the electronic transitions involved in the nonlinear optical response of [Ru(CF3CO2)3T] (T = 4'-(C6H4-p-NBu2)-2,2':6',2'-terpyridine)

We report a theoretical study based on density functional theory (DFT) and time-dependent DFT (TDDFT) calculations on the nature and role of the absorption bands involved in the nonlinear optical response of the complexes [Ru(CF3CO2)3T] (T = T1, T2; T1 = 4'-(C6H4-p-NBu2)-2,2':6',2'-terpyridine, T2 = 4'-(C6H4-p-NMe2)-2,2':6',2'-terpyridine). Geometry optimizations, performed without any symmetry constraints, confirm a twisting of the -C6H4-p-NBu2 moiety with respect to the plane of the chelated terpyridine. Despite this lack of strong pi interaction, TDDFT excited states calculations of the electronic spectrum in solution provide evidence of a relevant role of the NBu2 donor group in the low-energy LMCT band at 911 nm. Calculations also show that the two bands at higher energy (508 and 455 nm) are not attributable only to LMCT and ILCT transitions but to a mixing of ILCT/MLCT and ILCT/pi-pi* transitions, respectively. The 911 nm LMCT band, appearing at lower wavelength of the second harmonic (670 nm) of the EFISH experiment, controls the negative value of the second-order NLO response. This is confirmed by our calculations of the static component beta0(zzz) of the quadratic hyperpolarizability tensor, showing a large positive value. In addition we have found that the increase of the dipole moment upon excitation occurs, in all the characterized transitions, along the dipole moment axis, thus explaining why the EFISH and solvatochromic experimental values of the quadratic hyperpolarizability agree as sign and value.     

Polarizability and first-order hyperpolarizability of cyclic imides

Dipole moment, polarizability, and first-order hyperpolarizability of cyclic imides (maleimide, succinimide, phthalimide and some of their derivatives) have been investigated using ab initio and density functional theory calculations. It is found that 4,5-dichloro-, and 3,4,5,6-tetrachlorophthalimide have highest mean polarizabilities and total hyperpolarizabilities among the studied molecules. Furthermore, polarized continuum model has been employed to investigate solvent effects on the nonlinear optical (NLO) properties of succinimide; results indicate that solvent polarity has considerable influence on the NLO response of the molecules.     

An unprecedented switching of the second-order nonlinear optical response in aggregate bis(salicylaldiminato)zinc(II) Schiff-base complexes

A luminescent bis(salicylaldiminato)zinc(II) Schiff-base complex, 1, is characterized by a concentration dependent second-order nonlinear optical response, related to the degree of aggregation of the complex in a dichloromethane solution. The formation of the monomeric adduct, by addition of a Lewis base, such as pyridine, to concentrated solutions of 1, leads to a switch-on of the quadratic hyperpolarizability. This represents an unprecedented mode of NLO switching in molecular materials.     

The Solute Polarization and Structural Effects on the Nonlinear Optical Response of Based Chromone Molecules

The solute polarization due to solvent is a an electrostatic quantum effect that impacts diverse molecular properties, including the nonlinear optical response of a material. An iterative procedure that allows updating the solute charge distribution in the presence of the solvent is combined with a sequential Monte Carlo/Quantum Mechanics methodology and Density Functional Theory methods to evaluate the nonlinear optical (NLO) response using the hyper Rayleigh scattering (HRS) of a series of chromones recently identified in Chamaecrista diphylla, an herbaceous plant abundant throughout the Americas and used in folk medicine. From this study, it is determined that from gas to solvent environment, the systems acquire low refractive index (n) and an improvement of the first hyperpolarizability (β_HRS), signaling potential NLO uses. It is shown that the octupolar contributions (β^J=3) superate the dipolar ones (β^J=1) and dominate the second-order optical response in both gas and liquid phases, which indicate nontrivial optical materials. Moreover, the solvent environment and structural changes in the periphery can tune significantly the dipolar/octupolar balance, showing a key to control the decoupling between these contributions.     

Three-dimensional nonlinear optical chromophores based on metal-to-ligand charge-transfer from ruthenium(II) or iron(II) centers

In this article, we describe a series of new complex salts in which electron-rich transition-metal centers are coordinated to three electron-accepting N-methyl/aryl-2,2':4,4' ':4',4' '-quaterpyridinium ligands. These complexes contain either Ru(II) or Fe(II) ions and have been characterized by using various techniques, including electronic absorption spectroscopy and cyclic voltammetry. Molecular quadratic nonlinear optical (NLO) responses beta have been determined by using hyper-Rayleigh scattering at 800 nm and also via Stark (electroabsorption) spectroscopic studies on the intense, visible d --> pi* metal-to-ligand charge-transfer bands. The latter experiments reveal that these putatively octupolar D(3) chromophores exhibit two substantial components of the beta tensor which are associated with transitions to dipolar excited states. Computations involving time-dependent density-functional theory and the finite field method serve to further illuminate the electronic structures and associated linear and NLO properties of the new chromophoric salts.     

Heterocycle-based isomeric chromophores with substantially varying NLO properties: a new structure-property correlation study

A number of heterocycle-based aromatic and quinonoid molecular systems have been considered for the theoretical study of their electric response properties. The nonlinear optical (NLO) parameters have been calculated by using the ab initio MO and DFT methods. An approximate scheme for calculating the first hyperpolarizability (beta) and second hyperpolarizability (gamma) in the framework of the sum-over-state (SOS) method have been proposed by exploiting the generalized Thomas-Kuhn sum rule (TK-SR). The NLO properties in the present scheme can be evaluated solely from the ground-state dipole moment (mu) and linear polarizability (alpha) and have been found to correlate fairly with the ab initio calculated values. The approximate scheme can be reasonably used to explain the wider range of variation of higher-order polarizabilities in terms of the above quantities. The position of the N atom in the thiazole ring at the ortho position (versus meta position) to the acceptor increases beta and decreases gamma for aromatic compounds, while the reverse trend is found with quinonoid compounds. In the case of the pyridine ring, the shifting of the N atom toward the acceptor enhances gamma, with insignificant variation of beta predicted for both the aromatic and quinonoid molecules. The negative contribution of the cubic polarizability of the quinonoid species increases linearly with alpha(2)/mean transition energy (Delta E).     

First hyperpolarizability of a sesquifulvalene transition metal complex by time-dependent density-functional theory

The first hyperpolarizability and electronic excitation spectrum of sesquifulvalene and a sesquifulvalene ruthenium complex have been computed and analyzed with use of time-dependent density-functional theory. A new orbital decomposition scheme is introduced that allows the computed first hyperpolarizability to be related to the electronic structure of complex molecules. The analysis shows that the first hyperpolarizability of sesquifulvalene is not associated with the first intense absorption, with HOMO-1 --> LUMO+1 character, but is dominated by the lowest energy transition, with HOMO --> LUMO character, despite its very low intensity. In the ruthenium complex, the analysis reveals that the strong enhancement of the nonlinear optical response compared to free sesquifulvalene should not be attributed to the effect of complexation on the hyperpolarizability of sesquifulvalene. The strong hyperpolarizability originates from MLCT transitions from ruthenium d-orbitals to an empty orbital located at the seven ring of sesquifulvalene, transitions that have no analogue in free sequifulvalene.     

咪唑氧自由基分子NLO性质的密度泛函理论研究

采用密度泛函理论(DFT) UB3LYP方法, 在6-31g(d)水平上对2,2’-(1,2-乙炔基-4,1-亚苯基)双[4,4’,5,5’-四氢]咪唑氧自由基分子及其异构体的自旋耦合性质进行分析, 并结合有限场(FF)方法计算它们的非线性光学(NLO)系数, 以探讨咪唑氧环在共轭链不同位置时体系的自旋耦合规律和NLO系数. 结果表明, 所有体系基态自旋符合自旋极化规则, 它们的极化率随自旋多重度的增加而减小; 一阶超极化率因受分子对称性影响, 对称性不同其一阶超极化率的变化也不同; 二阶超极化率呈现随着自旋多重度的增加而增加的趋势. 从理论上探讨这些自由基分子自旋耦合规律与NLO活性的关系, 为有机自由基NLO材料的分子设计与实验研究提供一定的理论依据.     

Structural modulation of the dipolar-octupolar contributions to the NLO response in subphthalocyanines

Second order nonlinear optical properties of a series of trinitrosubphthalocyanine (SubPc) isomers were studied experimentally by electric field induced second harmonic (EFISH) generation and hyper Rayleigh scattering (HRS). These experimental values were compared to the ones obtained theoretically employing both sum over states (SOS) and finite field (FF) methods. From these studies, it was shown that the dipolar contributions to the beta tensor are very much dependent on the substitution pattern at the periphery of the subphthalocyanine macrocycle, whereas the octupolar contributions remain mostly unchanged. Consequently, it was deduced that SubPc is extremely well suited for the decoupling of octupolar and dipolar contribution to the NLO response.