TDDFT-SOS Studies on the Polarizabilities and Second-order Hyperpolarizabilities of Zn_3O_3 II-VI Semiconductor Clusters

1 INTRODUCTION II-VI semiconductor materials with ZnO as the representative possess wide forbidden gaps and high exciton binding energy, which have paved the way for the study of exciton characters and short wave photo-conducting devices. They present wide appli- cations, such as ultraviolet laser transmitting device, piezoelectric device, optical waveguild and high efficient quantum dot luminous apparatus[1～8]. Re- cently, II-VI semiconductor cluster materials with nano-structure ha…     

TDDFT-SOS Studies on the Polarizabilities and Second-order Hyperpolarizabilities of Zn3O3 Ⅱ-Ⅵ Semiconductor Clusters

The geometrical structure of semiconductor clusters including Zn3O3 was optimized by the DFT B3LYP method. With the same basis sets, dipole moments, polarizabilities and second- order hyperpolarizabilities have been calculated and compared with the results obtained by TDDFT B3LYP method combined with sum-over-state (SOS) formula. The calculation results indicate that the dipole moments of the ground state depend on the atom radius and electronegative differences between elements and are their balance point as well. The polarizabilities of the clusters accord with the rule of the corresponding energy transformation from ground to excited state. The results predict an increase of second-order hyperpolarizabilities with increasing the distances between atoms in the clusters as well as a decrease of the polarizabilities and second-order hyperpolarizabilities in the same serial of semiconductor clusters with increasing the dipole moments of the ground states. The changes of dipole moments in ground states are inconsistent with transition moments. Spatial structure, charge transfer and other factors play an important role in composing the transition moments.     

Theoretical Studies on the First Hyperpolarizabilities of One-dimensional Donor-bridge-acceptor Chromophores

The ground-state dipole moments and second-order nonlinear optical （NLO） properties of a series of one-dimensional （1D） chromophores with donor-bridge-acceptor （D-B-A） structures have been investigated by using the second-order MФller-Plesset （MP2） and density functional theory （DFT） methods with the basis set of 6-31＋G（d）. According to the calculated results, the relationship between the molecular static first hyperpolarizability （βμ） and the directions of electron transition has been summarized. In terms of the sign of βμ, these 1D organic chromophores were classified into two categories： type Ⅰ with negative βμ and type Ⅱ bearing positive βμ. The analyses show that the remarkable difference of the first hyperpolarizabilities between Ⅰ and Ⅱ chromophores is associated mainly with the electrostatic interaction between terminal groups and the transport electrons in excited states. Moreover, different from the popular viewpoint, the obtained results also show that most of this series of 1D D-B-A molecules are more charge-separated in the ground states than in the excited states. As a whole, this theoretical investigation, to some extent, can be considered as a useful reference in designing the NLO chromophores with large first hyperpolarizabilities.     

新型双重电荷转移分子的二阶非线性光学性质的 理论研究

以INDO/SCI方法为基础,按完全态求和(SOS)公式编制了计算分子二阶非线性光学系数β~i~j~k和β~μ的程序。研究了1,2-二氨基-4,5-二硝基苯1和其异构体1,3-二氨基-4,6-二硝基苯2的电子光谱和二阶非线性光学性质。计算表明分子1具有与分子2几乎相等的二阶非线性极化率。但由于分子1的偶极矩明显大于分子2的,故分子1的μβ值比分子2的μβ值大的多。在此基础上,研究了2,3-二(β-苯乙烯基)-5,6-二氰基吡嗪和2,3-二(β-噻吩乙烯基)-5,6-二氰基吡嗪和2,3-二(β-噻吩乙烯基)-5,6二氰基吡嗪衍生物的电子光谱和二阶非线性光学性质。结果表明,这些化合物均具有两个相距很近的强吸收峰,它们对β值的呈加和模式。由于这类化合物特征吸收峰均位于413nm以下且具有大的μβ值,所以,它们是一类很有前途的二阶非线性光学候选材料。     

Electronic structure and hyperpolarizability of some conjugated molecules in excited states

For the examples of aromatic and antiaromatic five-membered heterocycles, the static electronic polarizabilities and hyperpolarizabilities are determined in the ground and first singlet- and triplet-excited electronic states. The theoretical calculations are carried out in the SOS formalism and the correlation effects are taken into account using all mono- and biexcited configuration in the PPP approximation. It is shown that the singlet excitation of the molecules for the antiaromatic case is connected to an significant decrease of both polarizabilities and hyperpolarizabilities. Their values are discussed in terms of the index of average bond-order alternation for the ground and excited states and the localization of the electronic transitions in the molecules. © 1993 John Wiley & Sons, Inc.     

手性联萘桥联双卟啉的电子光谱与二阶非线性光学性质

在6-31G(d,p)水平上用B3LYP方法对手性联萘桥联双卟啉系列分子进行几何构型优化. 用半经验ZINDO/S方法计算了这些分子的电子光谱, 结果表明手性联萘桥联双卟啉中两个卟啉生色团之间存在强的激子耦合作用, B带的Davydov分裂大小与两个卟啉环的相对取向以及卟啉环中心之间距离有关. 用ZINDO/SOS方法计算了分子的一阶超极化率. 卟啉环上引入推/拉电子基团可以有效地提高手性联萘桥联双卟啉的二阶非线性光学系数. 一阶超极化率的大小与双卟啉中推/拉电子基团的空间排列方式有关. 一阶超极化率的提高不仅与分子激发态与基态偶极矩差增大有关, 还和基态偶极矩与激子耦合激发态跃迁矩矢量的相对取向密切相关.     

有限场方法研究环丁烯-1,2-二酮衍生物的非线性光学性质

本文利用有限场/PM3方法计算了环丁烯-1,2-二酮衍生物的偶极矩、极化率、一阶超极化率和二阶超极化率, 说明这类化合物是很好的非线性光学材料。     

有机染料敏化剂JK16和JK17的几何结构、电子结构及相关性质

运用密度泛函理论中的杂化泛函B3LYP研究了高效太阳能电池新型染料敏化剂JK16和JK17的几何结构、电子结构、极化率和超极化率, 并用含时密度泛函理论(TDDFT)研究了电子吸收谱. 基于含时密度泛函理论计算结果和实验结果的定性符合, 指认了在可见和近紫外区的吸收属于π→π*跃迁. 计算结果还表明JK16和JK17激发能最低的三个跃迁都与光诱导电荷转移过程有关, 而且二-二甲基芴氨基苯并噻吩基团对光电转换过程的敏化起主要作用, 发生于染料敏化剂JK16、JK17和TiO2界面之间的电荷转移是由染料分子激发态向半导体导带的电子注入过程. 此外, 通过对JK16和JK17的比较, 分析了亚乙烯基对几何结构、电子结构和谱学特性的影响.     

Theoretical Studies on the First Hyperpolarizabilities of One-dimensional Donor-bridge-acceptor Chromophores and New Applications of BLA in Determining Molecular First Hyperpolarizabilities

We present a quantum-chemical analysis of the relationship between the bond length alteration （BLA） and the static first hyperpolarizability of a series of one-dimensional （1D） chromophores with donor-bridge-acceptor （D-B-A） structures. The calculated results show that the parameter BLA can be considered as an indicator to evaluate the molecular first hyper- polarizability. Along the direction of molecular ground-state dipole moments, the evolutions of BLA can be classified into three categories： the first is a non-monotonic line, which represents most chromophores; the second is monotonic increasing; and the third, contrarily, is monotonic decreasing. On the whole, the first hyperpolarizabilities of these studied chromophores are the monotonic functions of BLA along the direction of dipole moments. Therefore, the first hyperpolarizability of these 1D chromophores can be preliminarily evaluated in terms of the development of BLA without a rigorous computation. In other words, one can roughly estimate the relative magnitude of the first hyperpolarizability according to the optimized geometry.     

Automatic generation of force fields and property surfaces for use in variational vibrational calculations of anharmonic vibrational energies and zero-point vibrational averaged properties

An automatic and general procedure for the calculation of geometrical derivatives of the energy and general property surfaces for molecular systems is developed and implemented. General expressions for an n-mode representation are derived, where the n-mode representation includes only the couplings between n or less degrees of freedom. The general expressions are specialized to derivative force fields and property surfaces, and a scheme for calculation of the numerical derivatives is implemented. The implementation is interfaced to electronic structure programs and may be used for both ground and excited electronic states. The implementation is done in the context of a vibrational structure program and can be used in combination with vibrational self-consistent field (VSCF), vibrational configuration interaction (VCI), vibrational Moller-Plesset, and vibrational coupled cluster calculations of anharmonic wave functions and calculation of vibrational averaged properties at the VSCF and VCI levels. Sample calculations are presented for fundamental vibrational energies and vibrationally averaged dipole moments and frequency dependent polarizabilities and hyperpolarizabilities of water and formaldehyde.     

Localized emitting state and energy transfer properties of quadrupolar chromophores and (multi)branched derivatives

In order to better understand the nature of intramolecular charge and energy transfer in multibranched molecules, we have synthesized and studied the photophysical properties of a monomer quadrupolar chromophore with donor-acceptor-donor (D-A-D) electronic push-pull structure, together with its V-shaped dimer and star-shaped trimers. The comparison of steady-state absorption spectra and fluorescence excitation anisotropy spectra of these chromophores show evidence of weak interaction (such as charge and energy transfer) among the branches. Moreover, similar fluorescence and solvation behavior of monomer and branched chromophores (dimer and trimer) implies that the interaction among the branches is not strong enough to make a significant distinction between these molecules, due to the weak interaction and intrinsic structural disorder in branched molecules. Furthermore, the interaction between the branches can be enhanced by inserting π bridge spacers (-C═C- or -C≡C-) between the core donor and the acceptor. This improvement leads to a remarkable enhancement of two-photon cross-sections, indicating that the interbranch interaction results in the amplification of transition dipole moments between ground states and excited states. The interpretations of the observed photophysical properties are further supported by theoretical investigation, which reveal that the changes of the transition dipole moments of the branched quadrupolar chromophores play a critical role in observed the two-photon absorption (2PA) cross-section for an intramolecular charge transfer (ICT) state interaction in the multibranched quadrupolar chromophores.     

Intermediate state representation approach to physical properties of electronically excited molecules

Propagator methods provide a direct approach to energies and transition moments for (generalized) electronic excitations from the ground state, but they do not usually allow one to determine excited state wave functions and properties. Using a specific intermediate state representation (ISR) concept, we here show how this restriction can be overcome in the case of the algebraic-diagrammatic construction (ADC) propagator approach. In the ISR reformulation of the theory the basic ADC secular matrix is written as a representation of the Hamiltonian (or the shifted Hamiltonian) in terms of explicitly constructable states, referred to as intermediate (or ADC) states. Similar intermediate state representations can be derived for operators other than the Hamiltonian. Together with the ADC eigenvectors, the intermediate states give rise to an explicit formulation of the excited wave functions and allow one to calculate physical properties of excited states as well as transition moments for transitions between different excited states. As for the ground-state excitation energies and transition moments, the ADC excited state properties are size consistent so that the theory is suitable for applications to large systems. The established hierarchy of higher-order [ADC(n)] approximations, corresponding to systematic truncations of the IS configuration space and the perturbation-theoretical expansions of the ISR matrix elements, can readily be extended to the excited state properties. Explicit ISR matrix elements for arbitrary one-particle operators have been derived and coded at the second-order [ADC(2)] level of theory. As a first computational test of the method we have carried out ADC(2) calculations for singlet and triplet excited state dipole moments in H(2)O and HF, where comparison to full CI results can be made. The potential of the ADC(2) method is further demonstrated in an exploratory study of the excitation energies and dipole moments of the low-lying excited states of paranitroaniline. We find that four triplet states, T1-T4, and two singlet states, S1 and S2, lie (vertically) below the prominent charge transfer (CT) excitation, S3. The dipole moment of the S3 state (17.0D) is distinctly larger than that of the corresponding T3 triplet state (11.7D).     

Revisiting the photophysical properties and excited singlet-state dipole moments of several coumarin derivatives

The solvent effects on the electronic absorption and fluorescence emission spectra of several coumarins derivatives, containing amino, N,N-dimethyl-amino, N,N-diethyl-amino, hydroxyl, methyl, carboxyl, or halogen substituents at the positions 7, 4, or 3, were investigated in eight solvents with various polarities. The first excited singlet-state dipole moments of these coumarins were determined by various solvatochromic methods, using the theoretical ground-state dipole moments which were calculated by the AM1 method. The first excited singlet-state dipole moment values were obtained by the Bakhshiev, Kawski-Chamma-Viallet, Lippert-Mataga, and Reichardt-Dimroth equations, and were compared to the ground-state dipole moments. In all cases, the dipole moments were found to be higher in the excited singlet-state than in the ground state because of the different electron densities in both states. The red-shifts of the absorption and fluorescence emission bands, observed for most compounds upon increasing the solvent polarity, indicated that the electronic transitions were of π-π* nature.     

Role of electron-driven proton-transfer processes in the excited-state deactivation of the adenine-thymine base pair

Exploratory electronic structure calculations have been performed with the CC2 (simplified singles and doubles coupled-cluster) method for two conformers of the adenine (A)-thymine (T) base pair, with emphasis on excited-state proton-transfer reactions. The Watson-Crick conformer and the most stable (in the gas-phase) conformer of the A-T base pair have been considered. The equilibrium geometries of the ground state and of the lowest excited electronic states have been determined with the MP2 (second-order M?ller-Plesset) and CC2 methods, respectively. Vertical and adiabatic excitation energies, oscillator strengths, and dipole moments of the excited states are reported. Of particular relevance for the photochemistry of the A-T base pair are optically dark (1)pipi* states of charge-transfer character. Although rather high in energy at the ground-state equilibrium geometry, these states are substantially lowered in energy by the transfer of a proton, which thus neutralizes the charge separation. A remarkable difference of the energetics of the proton-transfer reaction is predicted for the two tautomers of A-T: in the Watson-Crick conformer, but not in the most stable conformer, a sequence of conical intersections connects the UV-absorbing (1)pipi* state in a barrierless manner with the electronic ground state. These conical intersections allow a very fast deactivation of the potentially reactive excited states in the Watson-Crick conformer. The results provide evidence that the specific hydrogen-bonding pattern of the Watson-Crick conformer endows this structure with a greatly enhanced photostability. This property of the Watson-Crick conformer of A-T may have been essential for the selection of this species as carrier of genetic information in early stages of the biological evolution.     

On the accuracy of computed excited-state dipole moments

The dipole moments of furan and pyrrole in many electronically excited singlet states have been determined using coupled cluster theory including large one-electron basis sets. The inclusion of connected triple excitations is shown to uniformly decrease the equation-of-motion coupled-cluster singles and doubles (EOM-CCSD) excitation energies by 0.04-0.24 eV, with an average reduction of 0.08 eV. Using a basis set larger than DZP (++)D (double-zeta plus polarization augmented with atom- and molecule-centered diffuse functions) uniformly increases the computed EOM-CCSD excitation energies by 0.03-0.29 eV, with an average increase of 0.20 eV. The corresponding shifts in excited-state dipole moments are more erratic. Including connected triple excitations changes the computed dipole moments by an rms amount of 0.17 au. More importantly, using a larger basis set shifts the dipole moments by an rms amount of 0.52 au, with an increase or a decrease being equally likely. The CC dipole moments are compared to those from time-dependent density functional theory (TD-DFT) computed by Burcl, Amos, and Handy [ Chem. Phys. Lett. 2002, 355, 8]. For 29 excited states of furan and pyrrole, the predicted TD-DFT dipole moments differ from the CC results by rms amounts of 1.6 au (HCTH functional) and 1.5 au (B97-1 functional). Including the asymptotic correction to TD-DFT developed by Tozer and Handy [ J. Chem. Phys. 1998, 109, 10180; J. Comput. Chem. 1999, 20, 106] reduces the rms differences for both functionals to 1.2 au. If those Rydberg excited states with very large polarizabilities are excluded, the rms differences from the CC results for the remaining 17 excited states become 1.31 au (HCTH) and 0.88 au (B97-1). For asymptotically corrected functionals and this subset of states, the rms differences from the CC results are only 0.54 au (HCTHc) and 0.34 au (B97-1c). Thus, the Tozer-Handy asymptotic correction for TD-DFT significantly improves the predictions of excited-state dipole moments. For excited states without very large polarizabilities, good agreement is achieved between excited-state dipole moments computed by coupled cluster theory and by the asymptotically corrected B97-1c density functional.     

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.     

Stark effect,polarizabilities and the electric dipole moment of heteronuclear diatomic molecules in 1Σ states

The theory of second-order Stark effect in ¹Σ states of heteronuclear diatomic molecules is thoroughly reviewed. The rigorous treatment given demonstrates that by introducing rotational, vibrational and electronic branch polarizabilities, the intrinsic character of the second-order Stark effect in diatomic molecules can be shown to be related more closely to polarizabilities than to dipole moments. The well-known expression for the Stark shift in ¹Σ levels which is dominated by the square of the dipole moment is only a crude, though sufficient approximation whenever large dipole moments are involved. For small dipole moments, however, this approximation is likely to fail, leading to an erroneous determination of such dipole moments. In the limiting case of negligible influence of the molecular rotation on the vibronic matrix elements, the arithmetic mean of the electronic branch polarizabilities turns out to be equal to the well-known static electronic polarizabilities α_∥ and α_⊥. The results are applied to the interpretation of the Stark splitting in the A¹Σ⁺, υ′ = 5, J′ = 1 level of ⁷LiH, recently determined by Stark quantum-beat spectroscopy.     

含碱金属分子簇体系的结构和NLO性质

采用MP2方法优化得到Li(HF)n(n=2~4)体系的三个环型结构. 使用高水平的从头算方法MP2/6-311++G(3df,3pd)计算了它们的偶极矩μ0、极化率α0和一阶超极化率β0. 得出了大的一阶超极化率的变化规律, 并揭示出额外电子是引起大一阶超极化率的主要原因.     

Theoretical description of the electronic structure of the alkali hydride cation NaH+

A theoretical determination of the electronic structure of NaH+ is presented. Potential energy curves and dipole moments have been computed for 48(2)Lambda(+) electronic states (i.e., correlated adiabatically up to Na(6s) + H+) through a model-potential-type method over a wide range of R. Equilibrium distances, transition energies, depths of wells, and/or heights of humps predicted at short and large interatomic separations are reported and compared with available experimental and theoretical values. Variations of the static dipole polarizabilities versus internuclear distance have been determined for the two lowest states.