Modeling nonlinear optics of nanosystems with sum-over-states model

Three-stage strategies (ladder rule, few state model (FSM), and parallelization) were proposed to improve the computational efficiency of the sum-over-states (SOS) model in nonlinear optics (NLO) modeling. Ladder rule decomposes NLO coefficients of the nth state into the (n-1)th term and the contribution from the (n-1)th to the nth state without loss of rigor in theory. FSM singles out the states with substantial contribution to NLO. Those strategies are universal to all (including revised and simplified) SOS models. The computing cost reduces roughly to C/(n(i-1)) (C is a constant and i is the rank (order) of the NLO coefficients).     

Theoretical study on the second-order nonlinear optical properties of asymmetric spirosilabifluorene derivatives

The equilibrium geometries of four asymmetric spirosilabifluorene derivatives are optimized by means of the DFT/B3LYP method with the 6-31G* basis sets in this paper. On the basis of the optimized structures, the electronic structure and second-order nonlinear optical properties are calculated by using time-dependent density-functional theory (TDDFT) based on the 6-31G* level combined with the sum-over-states (SOS) method. The results show that these compounds possess remarkably larger molecular second-order polarizabilities than typical organometallic and organic compounds, and replacement of a carbon atom with nitrogen within the conjugated substituent has a great influence on the second-order nonlinear optical properties. Analysis of the main contributions to the second-order polarizability suggests that charge transfer from the z-axis directions plays a key role in the nonlinear optical response. These compounds have a possibility to be excellent second-order nonlinear optical (NLO) materials from the standpoint of large beta values, small dipole moment, high transparency, and small dispersion behaviors.     

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.     

呋喃同系物C4H4X(X=O,S,Se,Te)非线性光学性质的TDDFT-SOS理论研究

用含时密度泛函理论(TD-DFT)组合态求和(SOS)方法计算了呋喃同系物[呋喃(C4H4O)、噻吩(C4H4S)、硒吩(C4H4Se)、碲吩(C4H4Te)]的非线性光学性质.计算结果表明,体系的三阶NLO系数(γ)随着杂原子被重原子的取代而逐步增大,B3LYP等4种势函数计算的NLO系数基本一致.计算的色散关系曲线表明,标题化合物在宽频区存在小的色散作用,是一类具有应用前景的NLO材料.     

Theoretical Study on Structural Stability and Nonlinear Optical Properties of Non-conjugated Carbon and Nitrogen Diradical Molecules

The geometrical structures and stability of non-conjugated C5H10 and C3H8N2 singlet and triplet diradical molecules have been investigated at the UCCSD/6-311g** level. The effects of molecular structure, radical position, amount of Hartree Hork (HF) exchange and spin multiplicity on the nonlinear optical (NLO) coefficients have been also investigated. The reliable UCCSD results show that the triplets of all diradical molecules are more stable compared to their singlet analogues. In addition, the α s and β tot values of C5H10 and C3H8N2 triplet diradical mo-lecules have been investigated by the UBHandHLYP, UB3LYP, UBLYP, UHF and UCCSD methods. The investigation shows that the variations in α s and β tot values are closely connected to the amount of HF exchange. The increasing amount of HF exchange results in monotonic decreases in α s and β tot values, while the α s and β totvalues of singlet diradical molecules and the γ s of C5H10 and C3H8N2 singlet and triplet diradical molecules have been studied by the UBHandHLYP method. The results illustrate that the NLO coefficients for our studied non-conjugated carbon and nitrogen diradical species can be tuned by molecular structure, radical position and spin multiplicity, which are very significant for designing NLO materials.     

Theoretical Studies on the Electronic Structure of Nano-graphenes for Applications in Nonlinear Optics

In this work, azulene is introduced into nano-graphene with coronene center to enhance the second-order nonlinear optical (NLO) properties. The sum-over-states(SOS) model based calculations demonstrate that dipolar contributions are larger than octupolar contributions to the static first hyperpolarizability(〈β₀〉) in most nano-graphenes except those with high symmetry(e.g., a C_2v nano-graphene has octupolar contributions Φ^J=3 up to 59.0% of the 〈β₀〉). Nano-graphenes containing two parallel orientating azulenes (i.e., Out-P and Out-P_s) have large dipole moments, while their ground state is triplet. Introducing B/N/BN atoms into the positions with a high spin density transfers the ground state of Out-P and Out-P_s to closed-shell singlet, and the Out-P_s-2N has a large 〈β₀〉 of 1621.67×10⁻³⁰ esu. Further addition of an electron donor(NH₂) at the pentagon end enhances the 〈β₀〉 to 1906.22×10⁻³⁰ esu. The two-dimensional second-order NLO spectra predicted by using the SOS model find strong sum frequency generations and difference frequency generations, especially in the near-infrared and visible regions. The strategies to stabilize the electronic structure and improve the NLO properties of azulene-defect carbon nanomaterials are proposed, and those strategies to engineer nano-graphenes to be semiconducting while maintaining the π-framework are exten-dable to other similar systems.     

Quantum chemical study of redox-switchable second-order optical nonlinearity in Keggin-type organoimido derivative [PW11O39(ReNC6H5)] n− (n = 2–4)

To analyze the effect of redox state changes on the second-order nonlinear optical (NLO) responses of organoimido-functionalized Keggin-type heteropolyanions, the excitation properties and static second-order polarizabilities of fully oxidized state, the first and second reduced states were calculated by means of the time-dependent density functional theory (TDDFT) method combined with the sum-over-states (SOS) formalism. The incorporation of extra electrons causes significant enhancement in the second-order NLO activity. The reduced complexes show more than three times the efficiency of fully oxidized state. Moreover, the NLO activities for PW₁₁Re^VNPh system can also be modified by controlling the spin multiplicity. The high spin state (³ 3) has twice larger β _vec value than the low spin state (¹ 3). The characteristic of the charge-transfer transition corresponding to the dominant contributions to the β _vec values indicates that metal-centered redox processes influence the intramolecular donor or acceptor character, which accordingly leads to the variations in the computed β values. Owing to the reversible and manipulable redox processes, these kinds of the POM-based hybrid complexes could comprise a promising family of three-state redox-switchable molecular device combining chromic, magnetic, and NLO output.     

Theoretical studies of third-order nonlinear optical response for B12N12, B24N24 and B36N36 clusters

In this paper, we have calculated the third-order nonlinear optical polarizabilities corresponding to three optical processes: third-harmonic generation (THG), electric-field-induced second-harmonic generation (EFISHG) and degenerate four-wave mixing (DFWM) for B₁₂N₁₂, B₂₄N₂₄ and B₃₆N₃₆ clusters. The calculations have been performed by employing ab initio time-dependent density functional theory combined with sum-over-states method (SOS//TDDFT). We obtained the similar dynamic behavior of third-order NLO polarizabilities for three BN clusters. At input photon energy below 1.25 eV, the resonance enhancements of response haven't occurred. This is due to the fact that the calculated BN clusters have the large transition energy. B₂₄N₂₄ cluster has the larger transition dipole moments and the third-order polarizabilities of B₂₄N₂₄ are much larger than those of B₁₂N₁₂ and B₃₆N₃₆. We also estimate the static third-order optical susceptibility χ⁽³⁾ for BN fullerene materials from the average static third-order polarizability <γ>. The static χ⁽³⁾ of B₂₄N₂₄ fullerene materials are 1.36×10⁻¹⁴ esu for three NLO processes.     

Dipolar donor-acceptor-substituted schiff base complexes with large off-diagonal second-order nonlinear optical tensor components

The synthesis, characterization, and two-dimensional second-order nonlinear optical (NLO) response of a dipolar NiII donor- acceptor Schiff base complex and the related ligand are reported. Electric-field-induced second-harmonic generation and harmonic light (hyper-Rayleigh) scattering techniques, in combination with INDO/SCI-SOS theoretical calculations, were used to investigate the vector part of the hyperpolarizability tensor and the two-dimensional character of the molecular nonlinearity, respectively. Off-diagonal hyperpolarizability tensors can be related to charge-transfer transitions that are polarized perpendicular to the molecular dipolar axis, while parallel transitions account for the diagonal hyperpolarizability tensor. The role of the metal center in enhancing the two-dimensional NLO response of such molecules is twofold since it acts both as the donor and the bridging moiety of the planar donor-(pi-conjugate-bridge)-acceptor system. These dipolar two-dimensional molecules are interesting candidates from the perspective of polarization-independent NLO materials.     

Tailoring the donor moieties in TPA-based organic dyes for efficient photovoltaic,optical and nonlinear optical response properties

The current study reports tailoring the electronic donor structures of organic dyes to modify their optical and nonlinear optical (NLO) response properties. Five (5) tri-phenyl amine (TPA) based Donor-π-Acceptor (D-π-A) organic dyes with the codes ICAA1 , ICAA2 , ICAA3 , ICAA4 , and ICAA5 were designed and investigated for their optical and NLO properties using quantum chemical methods. Optical and NLO properties of these dyes were studied by CAM-B3LYP method and 6-311G* basis set. The focus has been on the impact of adding secondary donors and shifting their substitutions at ortho (o), meta (m) and para (p) positions. Among all designed compounds, ICAA4 showed the highest amplitude of average third-order NLO polarizability <γ>, which is calculated to be 1316 × 10⁻³⁶ esu. Time-dependent Density Functional Theory (TD-DFT) method was used to determine how a change in the position of the donor affected the excitation energy (E_g) and NLO response properties. The findings showed that changing the position of the secondary donor results in a red shift among absorption spectra as well as the increase in their NLO responses. Complete process of intramolecular charge transfer (ICT) has been investigated in terms of different optical parameters such as frontier molecular orbitals (FMOs), molecular electrostatic potentials (MEPs), transition density matrix (TDMs), density of states (DOS), electron density difference (EDD), and natural bond orbital (NBO) analysis. Our calculations for study of ICT process indicate that p-position of methoxy group performs better among all other positions and even it has better NLO response properties than the compound with three collective methoxy groups. The calculated V_oc values of all designed molecules range from 1.09 to 1.30, all of them are positive while their ΔG_inject is found to be in the range of −0.87 to −1.79 eV indicating their decent potential for photovoltaic applications. The studied optical, NLO and photovoltaic parameters illustrated that ICAA1 to ICAA5 are appropriate molecules not only for NLO applications but also for efficient photovoltaic purposes.     

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.     

Theoretical investigation on redox-switchable second-order nonlinear optical responses of push-pull Cp*CoEt2C2B4H3-expanded (metallo)porphyrins

The second-order nonlinear optical (NLO) properties of the Cp*Co(C(2)H(5))(2)C(2)B(4)H(3)-expanded (metallo)porphyrins (Cp* = C(5)Me(5)) have been investigated by using ab inito RHF and density functional theory (DFT) methods. The investigation shows that the compound with expand porphyrin possesses remarkable large molecular hyperpolarizability β(tot) value, ~414.1 × 10(-30) esu (at LC-ωPBE level), and might be an excellent second-order NLO material. From the character of charge transfer (CT) transition, it indicates that the -Cp*Co(C(2)H(5))(2)C(2)B(4)H(3) acts as an electron donor in this kind of systems. As a result of the redox behavior on expanded (metallo)porphyrin, the redox switching character of the NLO responses for the systems 2a-4a has also been studied. The results show that the β(tot) values of reduced forms are larger than that of neutral ones. Furthermore, the time-dependent DFT calculation illustrates that reduced forms have a significant difference on the CT patterns versus neutral ones. The present investigation provides insight into the comparison with DFT results on estimating first hyperpolarizability and the NLO properties of the series of push-pull compounds.     

Reversible redox-switchable second-order optical nonlinearity in polyoxometalate: a quantum chemical study of [PW11O39(ReN)]n- (n = 3-7)

In this paper, the relationship between the reversible redox properties and the second-order nonlinear optical (NLO) responses for the title series of complexes has been systematically investigated by using the time-dependent density functional theory (TDDFT) method combined with the sum-over-states (SOS) formalism. The results reveal that the successive reduction processes of five PW11ReN redox states should be PW11ReVII (1) --> PW11ReVI (2) --> PW11ReV (3) --> PW11ReV1e ( 4) --> PW 11ReV2e (5). Furthermore, their electrochemical properties have been reproduced successfully. It is noteworthy that the second-order NLO behaviors can be switched by reversible redox for the present studied complexes. Full oxidation constitutes a convenient way to switch off the second-order polarizability (system 1). The incorporation of extra electrons causes significant enhancement in the second-order NLO activity, especially for the third reduced state (system 4), whose static second-order polarizability (betavec) is about 144 times larger than that of fully oxidized 1. The characteristic of the charge-transfer transition corresponding to the dominant contributions to the betavec values indicates that metal-centered redox processes influence the intramolecular donor or acceptor character. Therefore, these kinds of complexes with the facile and reversible redox states could become excellent switchable NLO materials.     

三聚咔唑为中心的准八极矩分子二阶NLO性质

采用密度泛函理论B3LYP/6-31G*方法,对一系列以三聚咔唑为中心核的准八极矩分子的几何结构进行优化,在所得优化结构的基础上,结合有限场方法(FF)和含时密度泛函理论(TD-DFT)探讨了体系的二阶非线性光学(NLO)性质和电子光谱。结果表明,研究分子的极化率(α)及二阶NLO系数(β)随着取代基吸电子能力的增强而增大。当研究分子以三氰基苯乙烯为受体,碳-碳双键为共轭桥时,显示了较大的二阶NLO系数和良好透光性的优化,说明准八极矩分子内多重电荷转移可以有效地解决"非线性-透光性"矛盾。该系列分子在非线性材料领域中有望成为具有良好应用价值的候选分子。     

双环金属铱(Ⅲ)异腈配合物的二阶非线性光学性质

采用密度泛函理论(DFT)方法对双环金属Ir(III)异腈配合物的非线性光学(NLO)性质进行计算研究。用B3PW91(UB3PW91)(金属原子采用LANL2DZ基组,非金属原子采用6-31G*基组)方法对配合物进行几何结构优化。在优化构型基础上,采用B3PW91(UB3PW91)和B3LYP(UB3LYP)方法计算了配合物的第一超极化率(βtot),并用CAM-B3LYP(UCAM-B3LYP)(金属原子采用LANL2DZ基组,非金属原子采用6-31G**基组)方法模拟配合物的吸收光谱。结果表明,主配体的取代基(R1)和副配体的取代基(R2)对第一超极化率值贡献不大。配合物发生氧化还原反应,电荷转移方式增多,电荷转移程度增大,使βtot值显著增加,其中1a+([(C∧N)2Ir(CNR)2]+(R=CH3))发生氧化反应和还原反应的βtot值分别增大了75倍和144倍。因此,这类双环金属铱(III)异腈配合物的氧化还原反应可以有效地调节其二阶NLO性质。     

An investigation on the role of the nature of sulfonate ancillary ligands on the strength and concentration dependence of the second-order NLO responses in CHCl3 of Zn(II) complexes with 4,4'-trans-NC5H4CH=CHC6H4NMe2 and 4,4'-trans,trans-NC5H4CH=CH)2C6H4NMe2

To evidentiate the role of the nature of sulfonate ancillary ligands on the value of the quadratic hyperpolarizability of Zn(II) complexes with stilbazole-like ligands, the second-order nonlinear optical (NLO) properties of [ZnY(2)(4,4'-trans-NC5H4CH=CHC6H4NMe2)2] complexes (Y = CF3SO3, CH3SO3, or p-CH3C6H4SO3) are investigated. By working at relatively high concentrations (>3 x 10(-4) M), the positive effect of the triflate ligand remains unique while, with nonfluorinated sulfonate ligands, the second-order NLO response is comparable to that of the related complexes with acetate or trifluoroacetate as ancillary ligands. However, at dilutions higher than 10(-4) M, all of the sulfonate complexes reach huge quadratic hyperpolarizabilities because of solvolysis with the formation of cationic species such as [ZnY(4,4'-trans-NC5H4CH=CHC6H4NMe2)2]+, characterized by a large second-order NLO response. This view is supported by careful conductivity measurements. The same behavior occurs if 4,4'-trans-NC5H4CH=CHC6H4NMe2 is substituted by 4,4'-trans,trans-NC5H4(CH=CH)2C6H4NMe2.     

Development of calculation and analysis methods for the dynamic first hyperpolarizability based on the ab initio molecular orbital-quantum master equation method

We develop novel calculation and analysis methods for the dynamic first hyperpolarizabilities β [the second-order nonlinear optical (NLO) properties at the molecular level] in the second-harmonic generation based on the quantum master equation method combined with the ab initio molecular orbital (MO) configuration interaction method. As examples, we have evaluated off-resonant dynamic β values of donor (NH(2))- and/or acceptor (NO(2))-substituted benzenes using these methods, which are shown to reproduce those by the conventional summation-over-states method well. The spatial contributions of electrons to the dynamic β of these systems are also analyzed using the dynamic β density and its partition into the MO contributions. The present results demonstrate the advantage of these methods in unraveling the mechanism of dynamic NLO properties and in building the structure-dynamic NLO property relationships of real molecules.     

N－甲基-吡咯烷并[3,4]C60衍生物的结构、电子光谱 和二阶非线性光学性质的 理论研究

利用半经验AM1量子化学方法研究了N－甲基－吡咯烷并[3,4]C60(MPC)及其噻吩取代衍生物(TMPC)的几何结构。电子结构研究表明,MPC及TMPC衍生物的前沿轨道主要由C60部分决定,C60母体与成基团之间存在较强的分子内电荷转移,C60部分是电子受体,而噻吩环部分和吡咯环部分为电子给体。在AM1优化几何构型的基础上,用INDO/SCI方法计算了MPC及TMPC的电子光谱,用完全态求和(SOS)公式计算了其二阶非线性光学性质。结果表明,MPC与TMPC在400nm以上均存在吸收峰,TMPC的这些吸收峰(400nm以上)比MPC的吸收峰强得多,与实验所得结果一致。对于TMPC来说,其二阶非线性光学系数β0值随分子构型不同而有较大的变化,β0值最大可达60×10^-30esu。     

系列金化合物[X-{Au(PMe_3)}_2]的结构、电子光谱和非线性光学性质

采用密度泛函理论(DFT)B3LYP和BhandHLYP方法,对6个不同金化合物[X-{Au(PMe3)}2]的几何结构、电子光谱以及极化率和三阶非线性光学(NLO)效应进行了计算分析.本文采用的计算方法和基组适合所研究的对象,并发现用PMe3代替PPh3对分子整体结构影响不大.另外,分子桥连部分的空间效应对极化率有明显影响,对三阶极化率影响却不大.关于6个分子的三阶NLO性质,由于X部分的电子性质及共轭程度不同,分子1a的三阶极化率γ值最小,分子2a的γ值最大.通过分析电子光谱和对应的分子轨道组成可知,Au在分子1a中做电子给体,而在分子2a～6a中做电子受体,表明Au在此类化合物中对NLO性质的贡献不同.     

Prediction of second-order optical nonlinearity of trisorganotin-substituted beta-Keggin polyoxotungstate

The dipole polarizabilities, second-order polarizabilities, and origin of second-order nonlinear optical (NLO) properties of trisorganotin-substituted beta-Keggin polyoxotungstate [XW9O37(SnR)3](11-n)- (X = P, Si, Ge, R = Ph; X = Si, R = PhNO2, PhCCPh) have been investigated by using time-dependent density functional response theory. This class of organic-inorganic hybrid complexes possesses a remarkably large molecular second-order NLO response, especially for [SiW9O37(SnPhCCPh)3]7- (system 5) with the static second-order polarizability (beta(vec)) computed to be 1569.66 x 10(-30) esu. Thus, these complexes have the possibility to be excellent second-order nonlinear optical materials. Analysis of the major contributions to the beta(vec) value suggests that the charge transfer from the heteropolyanion to the organic segment along the z-axis plays the key role in the NLO response of [XW9O37(SnR)3](11-n)-. The computed beta(vec) values increase as a heavy central heteroatom changes in the order Ge > Si > P. Furthermore, nitro substitution on the aryl segment and the lengthening of organostannic pi-conjugation are more important in enhancing the optical nonlinearity, especially for the latter factor. The present investigation provides important insight into the origin of the NLO properties of trisorganotin-substituted heteropolyoxotungstate.