Second hyperpolarizability of ethynyl-linked azobenzene molecular wires

A series of oligomers consisting of ethynyl-linked azobenzene units was prepared using Pd-catalyzed cross coupling. The linear and nonlinear optical properties of the oligomers were investigated. The molecular second hyperpolarizability, gamma, followed the power law gamma proportional, variant n(2.12+/-0.05) (n is the number of repeat units) for unusually large molecular lengths exceeding 360 conjugated bonds (>49 nm). The exceptional exciton delocalization length is attributed to the rigidity of the conjugated backbone.     

Ab initio finite field (hyper)polarizability computations on stoichiometric gallium arsenide clusters GanAsn (n=2-9)

We report reliable ab initio finite field (hyper)polarizability values at Hartree-Fock and second order Moller-Plesset perturbation theory (MP2) levels of theory for different geometrical configurations of small gallium arsenide clusters Ga(n)As(n) with n=2-5. We relied on all-electron basis sets and pseudopotentials suitable for (hyper)polarizability calculations. In each case, we used structures that have been established in the literature after we optimized their geometries at B3LYP/cc-pVTZ-PP level of theory. Our results suggest that the first order hyperpolarizability (beta) is much more sensitive to the special geometric features than the second order hyperpolarizability (gamma). For the most stable configurations up to ten atoms the second order hyperpolarizability at MP2 level of theory varies between 15 x 10(4) and 32 x 10(4) e(4)a0 (4)Eh(-3). In addition, we examined the polarizability per atom evolution versus the cluster size for Ga(n)As(n) with n=2-9. Our work extends earlier theoretical studies which were limited to eight atoms and exposes that the polarizability/atom of the most stable stoichiometric configurations up to Ga(9)As(9) continues the monotonic downward trend with increasing size. Lastly, from the methodological point of view, our analysis shows that apart from polarizabilities, augmented pseudopotentials yield reliable first and second hyperpolarizability values as well.     

Nonlinear optical properties of polydiacetylene with donor-acceptor substitution block

The elongation finite-field (elongation-FF) method is applied to donor/acceptor substituted polydiacetylenes (PDAs) for the estimation of substituent effects on nonlinear optical (NLO) properties. The first hyperpolarizability (beta) and the second hyperpolarizability (gamma) of PDA with separated donor and acceptor substitution blocks have much larger values than those of the other substituted PDAs. For the PDAs with donor and acceptor substitution blocks, the relationship between the NLO properties and the block period is examined. It is shown, from the local density of states, that gamma of a system with a quantum well structure has a maximum value at a certain block size. This indicates that by tuning the size of proper block it is possible to achieve the largest gamma value in block polymers. Furthermore, the through-space/bond interaction analysis is performed to examine the pi-conjugation effects on the NLO properties for particular substituted PDA. It is demonstrated by our quantitative analysis that beta is affected by electron transfers in the molecule, and the quantum well structure is critical for gamma improvement.     

Static polarizability and second hyperpolarizability of closed- and open-shell pi-conjugated polymers

The static longitudinal linear polarizability (alpha) and second order hyperpolarizability (gamma) for neutral and charged, closed- and open-shell trans-polyacetylene (PA) chains C(2n)H(2n+2), C(2n-1)H(2n+1), C(2n-1)H(2n+1) (+), C(2n)H(2n+2) (+), and C(2n)H(2n+2) (2+) are systematically investigated and compared. The polarizabilities are calculated within the Pariser-Parr-Pople model, and the electron correlation effect is included through density matrix renormalization group. It turns out that for both alpha, and gamma, two neutral PA chains C(2n)H(2n+2) and C(2n-1)H(2n+1) give similar values, while both singly charged and doubly charged systems present significantly larger magnitude of alpha and gamma values than the two neutral chains. The two singly charged PA chains C(2n-1)H(2n+1) (+) and C(2n)H(2n+2) (+) give more apparent nonlinear optical responses than doubly charged case C(2n)H(2n+2) (2+) and both present negative second order hyperpolarizabilities for short to medium sized oligomers. The sign inversion of gamma values in singly charged PA molecules is anticipated to take place at the much longer length than ever observed due to the significant effects of electron correlation and geometry.     

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).     

含不同共轭桥的TCNQ开闭壳层体系NLO性质的DFT研究

采用密度泛函理论(DFT)结合有限场(FF)方法,对不同共轭桥连接的四氰代二甲基苯醌(TCNQ)开壳层和闭壳层电子态的非线性光学(NLO)系数进行计算,并以乙烯桥为例讨论共轭链长度与NLO性质的关系.结果表明:开壳层体系的极化率和二阶超极化率值都大于闭壳层体系,且共轭桥的共轭性越强,体系的极化率和二阶超极化率越大;在自由基体系中,单重态的二阶超极化率随双自由基成分y和自旋多重度的增加而增大.体系的共轭链增长,BLA(BondLength Alternation,共轭分子中相邻单、双键键长差的平均值)逐渐减小,双自由基成分y逐渐增大,体系的二阶超极化率也逐渐增大.     

Synthesis, molecular structure, spectroscopic studies and second-order nonlinear optical behaviour of N,N'-(2-hydroxy-propane-1,3-diyl)-bis(5-nitrosalicylaldiminato-N,O)-copper(II)

N,N'-(2-Hydroxy-propane-1,3-diyl)-bis(5-nitrosalicylaldiminato-N,O)-copper(II) has been synthesized. The crystal structure has been determined by X-ray diffraction analysis, and linear optical characterization has been determined by UV-vis spectroscopy. It was found that the molecule under investigation has solvatochromic behaviour in the UV region, implying non-zero microscopic first hyperpolarizability. To reveal the microscopic nonlinear optical (NLO) properties, the static first hyperpolarizabilities (beta) and the electric dipole moments (mu) were evaluated by using the ab initio finite field (FF) method. According to the results of the FF calculations, the synthesized compound exhibits non-zero beta values, and it might have microscopic NLO behaviour.     

6,6’-二氧-3,3’-二四联氮自由基及其衍生物不同构象 NLO性质的DFT研究

运用密度泛函理论(DFT) UB3LYP和有限场(FF)方法, 探讨了6,6’-二氧-3,3’-二四联氮自由基及其衍生物构象变化对非线性光学性质的影响, 分析了自由基分子极化率、二阶超极化率对构象、自旋多重度的依赖关系. 结果表明, 不同构象下各体系有效交换积分值都小于零, 自由基间表现为反铁磁性耦合. 各体系单三态不同构象时极化率α值的变化很小, 且不同构象时单重态的α值都大于三重态. 在构象变化过程中, 体系(a)和(b)单重态的二阶超极化率均为负值(体系(a)的45°和135°除外), 且绝对值都小于三重态的二阶超极化率值, 体系(c)的单三重态二阶超极化率值均为正值, 且在分子接近平面构型时, 三重态的γ值大于单重态. 不同的取代基R, 对体系的构型、极化率和二阶超极化率的影响也不同.     

双咪唑苯和双三唑苯及其衍生物非线性光学性质的密度泛函研究

采用密度泛函理论(DFT)的UB3LYP(B3LYP)/6-31+G**方法对双咪唑苯和双三咪唑苯双自由基及其衍生物几何结构进行优化,并结合有限场(FF)方法计算这些体系的非线性光学(NLO)系数.结果表明,引入给、受体取代基都能使体系的极化率α和二阶超极化率γ增大.在双自由基体系中,引入给体NH2的α和γ值大于引入受体NO2的值,与闭壳层体系中结果相反.分析自由基成分和电荷对体系的二阶超极化率γ影响的结果表明,处于中间双自由基成分的分子比相似共轭性的闭壳层分子有更大的二阶超极化率γ;带电荷的双自由基体系引入给、受体之后,与中性自由基体系相比具有更大的二阶超极化率γ.     

Frequency-dependent hyperpolarizabilities of the Ne, Ar, and Kr atoms using the approximate coupled cluster triples model CC3

The frequency-dependent electric field-induced second harmonic generation (ESHG) second hyperpolarizabilities gamma of neon, argon, and krypton are calculated using the approximate coupled cluster triples model CC3. Systematic basis set investigations are carried out to establish basis set limits, and scalar relativistic effects are accounted for by direct perturbation theory. To estimate higher-order correlation effects, full configuration-interaction results are used to benchmark the accuracy of CC3. The best theoretical estimates obtained thereby for the static second hyperpolarizabilities gamma(0) are 107.4, 1159, and 2589 a.u. for neon, argon, and krypton, respectively. These values as well as the results for the dispersion curve of the parallel component gamma( parallel) agree well with the latest experimental values from electric field-induced second harmonic generation. In addition, the dispersion of the perpendicular component gamma( perpendicular) and the hyperpolarizability ratios gamma( parallel)gamma( perpendicular) has been studied for the first time on a consistently correlated ab initio level. The analysis of the results indicates that, in particular for neon and krypton, the presently available experimental values are flawed.     

Theoretical study on the relationship between spin multiplicity effects and nonlinear optical properties of the pyrrole radical (C4H4N.)

The geometrical structure and stability of neutral pi-conjugated C4H4N. with three spin states were investigated by using ab initio and density functional theory (DFT) methods. In addition, the linear and nonlinear optical properties were studied at the same level combined with the finite field approach. The calculated results show that conjugation and stability decreased with increasing spin multiplicity. These reliable UCCSD results show that the polarizability (alpha) values of C4H4N. with the quartet state are maximal, while those of C4H4N. with the doublet state are minimal. The order of betatot values is betasextet > betadoublet > betaquartet. The second hyperpolarizability (gamma) values exhibit positive values. The variation trends of gamma are consistent with alpha.     

Origin of the enhancement of the second hyperpolarizability of singlet diradical systems with intermediate diradical character

The origin of the diradical character dependence of the second hyperpolarizability (gamma) of neutral singlet diradical systems is clarified based on the perturbation formula of gamma using the simplest diradical molecular model with different diradical characters, i.e., H2 under bond dissociation. The enhancement of gamma in the intermediate diradical character region turns out to originate from the increasing magnitude of the transition moment between the first and second excited states and the decrease of that between the ground and first excited states, respectively, with the increase in diradical character. This feature confirms that open-shell singlet conjugated molecules with intermediate diradical characters constitute a new class of third-order nonlinear optical systems, whose gamma values can be controlled by the diradical character in addition to the conjugation length.     

Second hyperpolarizabilities of singlet polycyclic diphenalenyl radicals: effects of the nature of the central heterocyclic ring and substitution to diphenalenyl rings

Adopting density functional theory and a hybrid exchange-correlation functional, the relationship between the second hyperpolarizability (gamma) and the diradical character has been investigated for diphenalenyl-based compounds containing different heterocyclic five-membered central rings (C(4)H(4)X, where X = NH, PH, O, S, CH(2), SiH(2), BH, GaH, C=O, C=S, and C=Se) or substituted by donor (NH(2))/acceptor(NO(2)) groups. It turns out that these structural modifications can tune the diradical character from 0.0 to 0.968 and lead to variations of gamma over more than 1 order of magnitude, demonstrating the controllability of gamma in this family of compounds. In particular, when the central ring is strongly aromatic, the diradical character is larger than 0.7, which is associated with pretty large gamma values except for almost the pure diradical case (y approximately 1). On the other hand, when the aromaticity decreases--or the antiaromaticity increases--the diradical character and the second hyperpolarizability get smaller. These relationships are correlated to structural (bond length alternation) and charge distribution (charge transfer between the phenalenyl rings and the central ring) properties, which account for the relative importance of the resonance diradical, zwitterionic, and quinoid forms. Therefore, the diradical character and the second hyperpolarizability can be controlled by the aromaticity of the ring while the paradigm of the enhancement of gamma for intermediate diradical character is globally verified. Then, upon introducing donor groups, the zwitterionic character increases, leading to closed-shell species and small second hyperpolarizabilities. In the case of substitution by acceptor groups, the charge transfer is reduced but the diradical character and the second hyperpolarizability hardly changes.     

TTF+1-π共轭桥-6-氧四联氮阳离子双自由基NLO性质的理论研究

采用量子化学UPBE1PBE结合有限场(FF)方法,对系列TTF+?-π共轭桥-6-氧四联氮阳离子双自由基体系的稳定性,极化率αs和第一超极化率βtot进行研究.结果表明,TTF+?-6-氧四联氮阳离子双自由基引入共轭桥后,随体系共轭性增强,αs和βtot值均增大(体系2S的βtot值除外).自旋多重度和构象对双自由基体系的极化率和第一超极化率都有影响,双自由基体系由单重态转变为三重态时,极化率减小,而第一超极化率明显增大.以体系2为例,在单重态时αs和βtot值随构象变化较小,而三重态时αs和βtot值随二面角θ1和θ2的增加而减小.     

Performance of density functional theory in computing nonresonant vibrational (hyper)polarizabilities

A set of exchange‐correlation functionals, including BLYP, PBE0, B3LYP, BHandHLYP, CAM‐B3LYP, LC‐BLYP, and HSE, has been used to determine static and dynamic nonresonant (nuclear relaxation) vibrational (hyper)polarizabilities for a series of all‐trans polymethineimine (PMI) oligomers containing up to eight monomer units. These functionals are assessed against reference values obtained using the Møller–Plesset second‐order perturbation theory (MP2) and CCSD methods. For the smallest oligomer, CCSD(T) calculations confirm the choice of MP2 and CCSD as appropriate for assessing the density functionals. By and large, CAM‐B3LYP is the most successful, because it is best for the nuclear relaxation contribution to the static linear polarizability, intensity‐dependent refractive index second hyperpolarizability, static second hyperpolarizability, and is close to the best for the electro‐optical Pockels effect first hyperpolarizability. However, none of the functionals perform satisfactorily for all the vibrational (hyper)polarizabilities studied. In fact, in the case of electric field‐induced second harmonic generation all of them, as well as the Hartree–Fock approximation, yield the wrong sign. We have also found that the Pople 6–31+G(d) basis set is unreliable for computing nuclear relaxation (hyper)polarizabilities of PMI oligomers due to the spurious prediction of a nonplanar equilibrium geometry. © 2013 Wiley Periodicals, Inc.     

Geometry, dipole moment, polarizability and first hyperpolarizability of polymethineimine: an assessment of electron correlation contributions

We have investigated the geometries as well as the longitudinal dipole moment (micro), polarizability (alpha), and first hyperpolarizability (beta) of polymethineimine oligomers using different approaches [Hartree-Fock (HF), second-order M?ller-Plesset (MP2), and hybrid density functional theory (DFT) methods (B3LYP and PBE0)] for evaluating the geometries and the nonlinear optical properties. It turns out that (i) HF and the selected DFT methods provide the incorrect sign for beta of short and medium size oligomers. (ii) The B3LYP and PBE0 electron correlation correction are too small for micro, too large for alpha, and for some oligomer lengths, they are in the wrong direction for beta. (iii) On the contrary to polyacetylene, the hybrid-DFT geometries are in poor agreement with MP2 geometries; the former showing much smaller bond length alternations.     

Structures and considerable static first hyperpolarizabilities: new organic alkalides (M+@n6adz)M'- (M, M'=Li, Na, K; n=2, 3) with cation inside and anion outside of the cage complexants

Eighteen structures of new organic alkalides (M+@n6adz)M'- (M, M'=Li, Na, K; n=2, 3) with the alkali-metal cation M+ lying near the center of the adz cage and the alkali-metal anion M'- located outside are obtained with all real frequencies. They exhibit very large static first hyperpolarizabilities (beta0) up to 3.2x10(5) au, which exceeds the record value of beta0=1.7x10(5) au for nonlinear optical compounds [Chem.-Eur. J. 1997, 3, 1091]. All potassides (M+@n6adz)K- (M=Li, Na, K; n=2, 3) have considerably large beta0 values (1.6x10(5)-3.2x10(5) au) much larger than the beta0 value (3.6x10(4) au) of the previously designed cuplike alkalide Li+(calix[4]pyrrole)K- [J. Am. Chem. Soc. 2006, 128, 1072]. This shows that the 26adz and 36adz cage complexants are preferable to cuplike calix[4]pyrrole complexant in enhancing the first hyperpolarizability. The effect of cage size of the complexant on the first hyperpolarizability is also presented here: in most cases, the smaller cage complexant corresponds to the larger beta0 value. Moreover, the crucial role by the alkali-metal anion in the large first hyperpolarizability of these alkalides is revealed. These results may provide new means for designing high-performance nonlinear optical materials.     

Nonlinear optical properties of ferrocene- and porphyrin-[60]fullerene dyads.

A series of novel [60]fullerene-ferrocene and [60]fullerene-porphyrin dyads, in which a fullerene and an electron donating moiety are attached through a flexible triethylene glycol linker are synthesized and their nonlinear optical (NLO) response studied. Specifically, the third-order susceptibility chi(3) of all fullerene derivatives are measured in toluene solutions by the optical Kerr effect (OKE) technique using 532 nm, 35 ps laser pulses and their second hyperpolarizability gamma are determined. All fullerene dyads studied exhibit enhancement of their NLO response compared to pristine fullerenes which has been attributed to the formation of a charge separated state. All experimentally measured hyperpolarizability gamma values are also calculated by the semiempirical methods AM1 and PM3. A good correlation is found between the theoretical and experimental values, suggesting that simple semiempirical methods can be employed for the designing and optimization of the fullerene-containing dyads displaying improved nonlinear responses.     

Theoretical investigation of the (hyper)polarizabilities of pyrrole homologues C4H4XH (X = N, P, As, Sb, Bi). A coupled-cluster and density functional theory study

Geometries, inversion barriers, static and dynamic electronic and vibrational dipole polarizability (alpha), and first (beta) and second (gamma) hyperpolarizability of the pyrrole homologues C(4)H(4)XH (X = N, P, As, Sb, Bi) have been calculated by Hartree-Fock, M?ller-Plesset second-order perturbation theory, coupled-cluster theory accounting for singles, doubles, and noniterative triple excitations methods, as well as density functional theory using B3LYP and PBE1PBE functionals and Sadlej's Pol and 6-311G basis sets. Relativistic effects on the heavier homologues stibole and bismole have been taken into account within effective core potential approximation. The results show that the electronic (hyper)polarizabilities monotonically increase with the atomic number of the heteroatom, consistent with the decrease in the molecular hardness. Ring planarization reduces the carbon-carbon bond length alternation of the cis-butadienic unit, enhancing the electronic polarizability values (alpha(e)) by 4-12% and the (hyper)polarizability values (and gamma(e)) by 30-90%. Pure vibrational and zero-point vibrational average contributions to the (hyper)polarizabilities have been determined within the clamped nucleus approach. In the static limit, the pure vibrational hyperpolarizabilities have a major contribution. Anharmonic corrections dominate the pure vibrational hyperpolarizabilities of pyrrole, while they are less important for the heavier homologues. Static and dynamic electronic response properties of the pyrrole homologues are comparable to or larger than the corresponding properties of the furan and cyclopentadiene homologue series.