螺旋双芴体系二阶非线性光学性质的ZINDO-SOS理论研究

用密度泛函B3LYP/631G*方法优化螺旋双芴的几何构型,在获得稳定构型的基础上,用半经验ZINDO方法计算体系的激发能和跃迁偶极矩,然后代入完全态求和公式得到体系的二阶极化率.结果表明,螺旋双芴具有较大的二阶极化率、较小的色散行为以及在可见光范围内透明等优点,是具有很好应用前景的非线性光学材料.     

Brueckner doubles coupled cluster method with the polarizable continuum model of solvation

We present the theory and implementation for computing the (free) energy and its analytical gradients with the Brueckner doubles (BD) coupled cluster method in solution, in combination with the polarizable continuum model of solvation (PCM). The complete model, called PTED, and an efficient approximation, called PTE, are introduced and tested with numerical examples. Implementation details are also discussed. A comparison with the coupled-cluster singles and doubles CCSD-PCM-PTED and CCSD-PCM-PTE schemes, which use Hartree-Fock (HF) orbitals, is presented. The results show that the two PTED approaches are mostly equivalent, while BD-PCM-PTE is shown to be superior to the corresponding CCSD scheme when the HF reference wave function is unstable. The BD-PCM-PTE scheme, whose computational cost is equivalent to gas phase BD, is therefore a promising approach to study molecular systems with complicated electronic structure in solution.     

Analytic gradient for the multireference Brillouin-Wigner coupled cluster method and for the state-universal multireference coupled cluster method

We present the analytic gradient theory and its pilot implementation for the multireference Brillouin-Wigner coupled cluster (BWCC) method and for the state-universal multireference coupled cluster method. The analytic gradient has been derived for three cases: (i) BWCC method without a size-extensivity correction, (ii) BWCC method with the iterative size-extensivity correction, and (iii) for the rigorously size-extensive state-universal method. The pilot implementation is based on full-configuration interaction expansions and is presently limited to single and double excitation levels; however, the resulting equations are general. For BWCC methods, they also do not contain terms explicitly mixing amplitudes of different reference configurations and can thus be implemented in an efficient way. The analytic gradients have been verified with respect to numerically computed ones on the example of CH2 molecule, and geometry optimizations of CH2 and SiH2 have been carried out.     

An efficient local coupled cluster method for accurate thermochemistry of large systems

An efficient local coupled cluster method with single and double excitation operators and perturbative treatment of triple excitations [DF-LCCSD(T)] is described. All required two-electron integrals are evaluated using density fitting approximations. These have a negligible effect on the accuracy but reduce the computational effort by 1-2 orders of magnitude, as compared to standard integral-direct methods. Excitations are restricted to local subsets of non-orthogonal virtual orbitals (domain approximation). Depending on distance criteria, the correlated electron pairs are classified into strong, close, weak, and very distant pairs. Only strong pairs, which typically account for more than 90% of the correlation energy, are optimized in the LCCSD treatment. The remaining close and weak pairs are approximated by LMP2 (local second-order Mo?ller-Plesset perturbation theory); very distant pairs are neglected. It is demonstrated that the accuracy of this scheme can be significantly improved by including the close pair LMP2 amplitudes in the LCCSD equations, as well as in the perturbative treatment of the triples excitations. Using this ansatz for the wavefunction, the evaluation and transformation of the two-electron integrals scale cubically with molecular size. If local density fitting approximations are activated, this is reduced to linear scaling. The LCCSD iterations scale quadratically, but linear scaling can be achieved by neglecting some terms involving contractions of single excitations. The accuracy and efficiency of the method is systematically tested using various approximations, and calculations for molecules with up to 90 atoms and 2636 basis functions are presented.     

Application of double ionization state-specific equation of motion coupled cluster method to organic diradicals

The state-specific equation of motion coupled cluster method is applied to three systems of diradical character: automerization of cyclobutadiene, singlet-triplet gaps of trimethylmethylene, and Bergman reaction. The aim of the paper is to assess the performance of the method and test numerically the importance of orbital optimization, three-body terms in transformed Hamiltonian, and the choice of cluster equations.     

Application of the Bergson model to the optical properties of chiral disulfides

Bergson developed a simple model to explain the observed red shift of the long-wavelength transition of disulfides as the dihedral angle is reduced from 90° to smaller values. This model is extended here to a calculation of the oscillator strengths and rotational strengths of the n → σ^* transitions of chiral disulfides. Explicit expressions for the gradient and angular momentum matrix elements for the n → σ^* transitions as functions of the dihedral angle are presented. Transition monopoles suitable for the calculation of the coupling of disulfide n → σ^* transitions with other chromophoric groups in complex disulfides are also presented. It is shown that this extension of the Bergson model can account quite well for the observed intensities and rotational strengths of chiral disulfides. The quadrant behavior of the long-wavelength rotational strength derived by Linderberg and Michl and verified experimentally by Ludescher and Schwyzer is observed in our results as well. The observed transitions in the far ultraviolet spectrum of disulfides are assigned to an n → σ^* transition at 205 nm and a σ → σ^* transition at 190 nm.     

High-order excitations in state-universal and state-specific multireference coupled cluster theories: model systems

For the first time high-order excitations (n>2) have been studied in three multireference couple cluster (MRCC) theories built on the wave operator formalism: (1) the state-universal (SU) method of Jeziorski and Monkhorst (JM) (2) the state-specific Brillouin-Wigner (BW) coupled cluster method, and (3) the state-specific MRCC approach of Mukherjee (Mk). For the H4, P4, BeH(2), and H8 models, multireference coupled cluster wave functions, with complete excitations ranging from doubles to hextuples, have been computed with a new arbitrary-order string-based code. Comparison is then made to corresponding single-reference coupled cluster and full configuration interaction (FCI) results. For the ground states the BW and Mk methods are found, in general, to provide more accurate results than the SU approach at all levels of truncation of the cluster operator. The inclusion of connected triple excitations reduces the nonparallelism error in singles and doubles MRCC energies by a factor of 2-10. In the BeH(2) and H8 models, the inclusion of all quadruple excitations yields absolute energies within 1 kcal mol(-1) of the FCI limit. While the MRCC methods are very effective in multireference regions of the potential energy surfaces, they are outperformed by single-reference CC when one electronic configuration dominates.     

Basis set dependence of coupled cluster optical rotation computations

Specific rotations for five notoriously difficult molecules, (S)-methyloxirane, (S)-methythiirane, (S)-2-chloropropionitrile, (1S,4S)-norbornenone, and (1R,5R)-β-pinene, have been computed using coupled cluster (CC) and density functional theory (DFT). The performance of the recently developed LPol basis sets compared to the correlation-consistent sets of Dunning and co-workers has been examined at four wavelengths: 355, 436, 589, and 633 nm. We find that the LPol basis sets are an efficient choice, often outperforming the more commonly used correlation-consistent basis sets of comparable size. The smallest of the four, LPol-ds, performs nearly as well as the rest of the series and often yields results closer to the basis set limit than appreciably larger basis sets. While the performance of the LPol bases is admirable, they still do not alleviate the need for high levels of electron correlation, vibrational corrections, and the inclusion of solvent effects to accurately reproduce experimental rotations. In particular in the case of β-pinene we find that they do not produce agreement between DFT and experiment as was previously suggested.     

Synthesis,crystal structure and nonlinear optical properties of a cluster compound containing the bipy ligand

The [MoO_0.75S_3.25Cu₃Cl(bipy)₂] complex was synthesized for nonlinear optical studies by the reaction of (NH₄)₂[MoOS₃], CuCl and bipy in CH₂Cl₂ solution. A single crystal X-ray analysis revealed that the complex consists of a nest-shaped core. The Mo atom is tetrahedrally coordinated by four S atoms, or three S atoms and one terminal O atom. There are two types of copper atom in the MoO_0.75S_3.25Cu₃ aggregate: two copper atoms are tetrahedrally coordinated and another copper atom is trigonally coordinated. The third-order nonlinear optical properties were investigated by the Z-scan technique with 8 ns laser pulses at 532 nm. The cluster exhibits both optical self-focusing and optical nonlinear absorption (effectively n ₂ = 1.3 × 10^–11 e.s.u., ₂ = 1.2 × 10^–10 m W^–1 in a 2.68 × 10^–4 mol dm^–3 CH₂Cl₂ solution).     

Analysis of the nuclear-electronic orbital method for model hydrogen transfer systems

Fundamental issues associated with the application of the nuclear-electronic orbital (NEO) approach to hydrogen transfer systems are addressed. In the NEO approach, specified nuclei are treated quantum mechanically on the same level as the electrons, and mixed nuclear-electronic wavefunctions are calculated with molecular orbital methods. The positions of the nuclear basis function centers are optimized variationally. In the application of the NEO approach to hydrogen transfer systems, the hydrogen nuclei and all electrons are treated quantum mechanically. Within the NEO framework, the transferring hydrogen atom can be represented by two basis function centers to allow delocalization of the proton vibrational wavefunction. In this paper, the NEO approach is applied to the [He-H-He]+ and [He-H-He]++ model systems. Analyses of technical issues pertaining to flexibility of the basis set to describe both single and double well proton potential energy surfaces, linear dependency of the hydrogen basis functions, multiple minima in the basis function center optimization, convergence of the number of hydrogen basis function centers, and basis set superposition error are presented. The accuracy of the NEO approach is tested by comparison to grid calculations for these model systems.     

Theoretical study on nonlinear optical properties of metalloporphyrin using elongation method

A quantum-chemical analysis of the central metal effect on the (hyper)polarizabilities of meso-meso-linked metalloporphyrin (MP) oligomers was carried out using elongation finite-field (ELG-FF) method. It is found that meso-meso-linked MPs exhibit evident evolution of the third-order nonlinear optical (NLO) response (γ) along with an increasing number of porphyrin units N. The order of γ values is as following: γ_Mg > γ_Zn > γ_Ni. In contrast to the polarizability, the γ values of meso-meso-linked MPs are sensitive to the metals, that is, the nature of the metal can influence the third-order NLO response of MPs. However, the band structures for three MPs are similar to each other, and the differences on the band gaps of three MPs are very small. The local density of states (LDOSs) shows that the central metal gives the significant contributions for unoccupied bands in meso-meso-linked MPs.     

Impurity levels and nonlinear optical properties of doped BaTiO3 from extended cluster LDA calculations

The electronic structures of some transition-metal ions doping the ferroelectric oxide BaTiO₃ are calculated through the density functional theory framework (LCAO-LSD ADF method) on extended clusters [XO₆Ba₈Ti₆] embedded in a punctual charge set depicting the crystalline environment. The transition ions X are Feⁿ⁺(n = 2, 3, 4, 5), Ti³⁺, Nb⁴⁺, and Nb⁵⁺. Some related defects like Fe(SINGLE BOND)V_o, where V_o stands for a lacunar oxygen site, are also investigated through a similar process. The positions of impurity levels insides the O_2p(SINGLE BOND)Ti_3d band gap are obtained from eigenvalues and related optical transition or ionization energies are calculated using excited states. This allows us to discuss the photorefractive effect present in such doped materials. The EPR fine-structure parameters a and D are also derived for Fe³⁺ in cubic and tetragonal symmetries from crystal field calculations using parameters drawn from molecular orbital results. © 1997 John Wiley & Sons, Inc.     

A sequential transformation approach to the internally contracted multireference coupled cluster method

The internally contracted multireference coupled cluster (ic-MRCC) approach is formulated using a new wave function ansatz based on a sequential transformation of the reference function (sqic-MRCC). This alternative wave function simplifies the formulation of computationally viable methods while preserving the accuracy of the ic-MRCC approach. The structure of the sqic-MRCC wave function allows folding the effect of the single excitations into a similarity-transformed Hamiltonian whose particle rank is equal to the one of the Hamiltonian. Consequently, we formulate an approximation to the sqic-MRCC method with singles and doubles (included respectively up to fourfold and twofold commutators, sqic-MRCCSD[2]) that contains all terms present in the corresponding single-reference coupled cluster scheme. Computations of the potential energy curves for the dissociation of BeH(2) show that the untruncated sqic-MRCCSD scheme yields results that are almost indistinguishable from the ordinary ic-MRCCSD method. The energy obtained from the computationally less expensive sqic-MRCCSD[2] approximation is found to deviate from the full ic-MRCCSD method by less than 0.2 mE(h) for BeH(2), while, in the case of water, the harmonic vibrational frequencies of ozone, the singlet-triplet splitting of p-benzyne, and the dissociation curve of N(2), sqic-MRCCSD[2] faithfully reproduces the results obtained via the ic-MRCCSD scheme truncated to two commutators. A formal proof is given of the equivalence of the ic-MRCC and sqic-MRCC methods with the internally contracted and full configuration interaction approaches.     

Application of open-shell coupled cluster theory to the ground state of GaAs

Summary Theoretical calculations at the coupled cluster level of theory including all single, double and perturbative triple excitations, CCSD(T), are carried out for the^3– ground state of GaAs. Employing a (7s5p3d1f) basis set, the theoretical predictions forr _e (2.560 Å), _e (217 cm^–1),D _e (1.84 eV), and IP (7.80 eV), are in good agreement with recent experimental results. The importance of includingf-type polarization functions in the basis set and the effect of correlating 3d electrons are discussed in detail.     

Two-dimensional nonlinear optical activity spectroscopy of coupled multi-chromophore system

Most biomolecules are chiral. A variety of optical activity measurement techniques have been extensively used to study chiral natures of complicated biological molecules such as proteins and nucleic acids. Recently, coherent two-dimensional (2D) spectroscopic techniques have been developed and widely used to study structures and dynamics of biomolecules via measuring couplings between chromophores. However, such 2D optical spectroscopic methods utilizing linearly polarized beams do not provide information on the molecular chirality. Thus, we have theoretically shown that novel 2D optical activity measurement techniques based on three- and four-wave-mixing schemes are of use to obtain the 2D spectrum of a chiral molecule. Particularly, we carried out numerical simulations of 2D optical activity spectra of polypeptides and a light-harvesting complex. These methods utilizing circularly polarized beams and related spectroscopic techniques will be of great use in understanding and elucidating the underlying mechanisms of ultrafast chemical and conformational changes of chiral biomolecules in the future.     

Triple excitations in state-specific multireference coupled cluster theory: application of Mk-MRCCSDT and Mk-MRCCSDT-n methods to model systems

We report the first implementation with correct scaling of the Mukherjee multireference coupled cluster method with singles, doubles, and approximate iterative triples (Mk-MRCCSDT-n, n=1a,1b,2,3) as well as full triples (Mk-MRCCSDT). These methods were applied to the classic H4, P4, BeH(2), and H8 model systems to assess the ability of the Mk-MRCCSDT-n schemes to accurately account for triple excitations. In all model systems the inclusion of triples via the various Mk-MRCCSDT-n approaches greatly reduces the nonparallelism error (NPE) and the mean nonparallelism derivative diagnostics for the potential energy curves, recovering between 59% and 73% of the full triples effect on average. The most complete triples approximation, Mk-MRCCSDT-3, exhibits the best average performance, reducing the mean NPE to below 0.6 mE(h), compared to 1.4 mE(h) for Mk-MRCCSD. Both linear and quadratic truncations of the Mk-MRCC triples coupling terms are viable simplifications producing no significant errors. If the off-diagonal parts of the occupied-occupied and virtual-virtual blocks of the Fock matrices are ignored, the storage of the triples amplitudes is no longer required for the Mk-MRCCSDT-n methods introduced here. This proves to be an effective approximation that gives results almost indistinguishable from those derived from full consideration of the Fock matrices.     

Calculation of the nonlinear optical properties of molecules

A finite-field method for the calculation of polarizabilities and hyperpolarizabilities is developed based on both an energy expansion and a dipole moment expansion. This procedure is implemented in the MOPAC semiempirical program. Values and components of the dipole moment (μ), polarizability (α), first hyperpolarizability (β), and second hyperpolarizability (γ) are calculated as an extension of the usual MOPAC run. Applications to benzene and substituted benzenes are shown as test cases utilizing both MNDO and AM1 Hamiltonians.     

Syntheses, structures, and nonlinear optical properties of heteroselenometallic W-Se-Ag cluster compounds containing phosphine ligands

Treatment of [Et4N]2[WSe4] with a 1:1 mixture of AgNO3 and PCy3 (Cy = cyclohexyl) in the absence of iodide afforded a linear trinuclear compound [(mu-WSe4)(AgPCy3)2] (1). A similar reaction in the presence of iodide gave rise to the isolation of the cubanelike compound [(mu3-WSe4)Ag3(PCy3)3(mu3-I)] (2). Treatment of [Et4N]2[WSe4] with AgI in the presence of bidentate phosphine ligands bis(diphenylphosphino)amine (dppa) and bis(diphenylphosphino)methane (dppm) afforded the tetranuclear compounds [(mu3-WSe4)Ag3(mu-I)(mu-dppa)2] (3) and [(mu3-WSe4)Ag3(mu3-I)(mu-dppm)2] (4), respectively, which exhibit an open butterfly configuration. A novel hexanuclear cluster compound [(mu3-WSe4)2Ag4(mu-dppm)3] (5) was obtained from interaction of [Et4N]2[WSe4] with AgNO3 and dppm in the absence of iodide source. The above cluster compounds are electrically neutral and air-stable in both solution and the solid state and have been characterized by electronic, infrared, mass, and NMR spectroscopies. The solid-state structures of five cluster compounds have been established by X-ray crystallography. The nonlinear optical properties of compounds 4 and 5 were examined by z-scan techniques with 7 ns pulses at 532 nm. The optical limiting effects of compounds 1, 2, 4, and 5 were determined and compared with related argentoselenometallic compounds.     

Direct evaluation of one-electron properties in coupled cluster methods

Summary An analysis of a method for approximate calculations of expectation values for one-electron operators from available coupled cluster amplitudes is presented and illustrated numerically for the polarizability of the Be atom. The one-particle density matrix resulting from the present approach is accurate through the fourth order in the electron correlation perturbation. It has been found that, in order to obtain quantitative agreement between the energy derivative results and the approximate expectation value formalism, the third orderT ₁ T ₂⁽⁰⁾ wave function term must be included into the calculation of the one-particle density matrix. The present method is also considered as a promising tool for calculations of higher-order atomic and molecular properties from high level correlated wave functions.     

Third-order nonlinear optical properties of open-shell supermolecular systems composed of acetylene linked phenalenyl radicals

The third-order nonlinear optical (NLO) properties, at the molecular level, the static second hyperpolarizabilities, γ, of supermolecular systems composed of phenalenyl and pyrene rings linked by acetylene units are investigated by employing the long-range corrected spin-unrestricted density functional theory, LC-UBLYP, method. The phenalenyl based superethylene, superallyl, and superbutadiene in their lowest spin states have intermediate diradical characters and exhibit larger γ values than the closed-shell pyrene based superpolyene systems. The introduction of a positive charge into the phenalenyl based superallyl radical changes the sign of γ and enhances its amplitude by a factor of 35. Although such sign inversion is also observed in the allyl radical and cation systems in their ground state equilibrium geometries, the relative amplitude of γ is much different, that is, |γ(regular allyl cation)/γ(regular allyl radical)| = 0.61 versus |γ(phenalenyl based superallyl cation)/γ(phenalenyl based superallyl radical)| = 35. In contrast, the model ethylene, allyl radical/cation, and butadiene systems with stretched carbon-carbon bond lengths (2.0 ?), having intermediate diradical characters, exhibit similar γ features to those of the phenalenyl based superpolyene systems. This exemplifies that the size dependence of γ as well as its sign change by introducing a positive charge on the phenalenyl based superpolyene systems originate from their intermediate diradical characters. In addition, the change from the lowest to the highest π-electron spin states significantly reduces the γ amplitudes of the neutral phenalenyl based superpolyene systems. For phenalenyl based superallyl cation, the sign inversion of γ (from negative to positive) is observed upon switching between the singlet and triplet states, which is predicted to be associated with a modification of the balance between the positive and negative contributions to γ. The present study paves the way toward designing a variety of open-shell NLO supermolecular systems composed of phenalenyl radical building blocks.