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1.
The antisymmetrized geminal power (AGP) and sequential product of geminals(SPG) functions, the basis functions with symplectic symmetry, are linearly combined to calculate the ground state of the LiH molecule. The calculation results show that the AGP or SPG function gives the same ground state results as the linear combination. 相似文献
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. Molecular matrix elements of a physical operator are expanded in terms of polycentric matrix elements in the atomic basis
by multiplying each by a geometrical factor. The number of terms in the expansion can be minimized by using molecular symmetry.
We have shown that irreducible tensor operators can be used to imitate the actual physical operators. The matrix elements
of irreducible tensor operators are easily computed by choosing rational irreducible tensor operators and irreducible bases.
A set of geometrical factors generated from the expansion of the matrix elements of irreducible tensor operator can be transferred
to the expansion of the matrix elements of the physical operator to compute the molecular matrix elements of the physical
operator. Two scalar product operators are employed to simulate molecular two-particle operators. Thus two equivalent approaches
to generating the geometrical factors are provided, where real irreducible tensor sets with real bases are used.
Received: 3 September 1996 / Accepted: 19 December 1996 相似文献
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利用准自旋-辛群对称性基函数及Kummer提出的构造暴露算子法研究了量子化学中密度矩阵N表示理论的端点问题,找出了更多的二阶约化密度矩阵凸集的端点. 相似文献
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The symmetry of achiral single-walled (n,0) and (n,n) carbon nanotubes (CNTs) was examined and the frequencies and types of vibrations allowed in the Raman spectra were calculated. The vibrational spectrum was evaluated as the eigenvalues of the dynamical matrix at the -point of the Brillouin zone. The selection rules for the Raman active vibrations were estimated by the values of the matrix elements responsible for the intensities of corresponding vibrational transitions. The (n,n)-CNTs with even and odd n values are characterized by five and six allowed Raman active vibrations, respectively. The number of Raman active vibrations for (n,0)-CNTs is five if n is even and eight if n is odd. Detailed analysis of the results obtained is presented for the (10,10)-CNT as an example. 相似文献
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The fuzzy symmetry characteristics for the internal-rotation of propadine were analyzed using the fuzzy symmetry theory for molecule and molecular orbital (MO). In the process of rotation, three different symmetry point groups D2h, D2d, and D2 were considered. Using the D4h point group, which is the minimal point group including all symmetry elements of D2h, D2d, and D2, we can analyze the fuzzy symmetry for this process. The elements included in D4h point group can be classified to four subsets: (i) G0—it includes all the elements in D2 point group, also belongs to all the above three point groups of D2h, D2d, and D2; (ii) G1—it includes the elements in D2h point group, but not in D2d point group; (iii) G2—it includes the elements in D2d point group, but not in D2h point group; (iv) G3—it includes the elements in D4h point group, but not in D2h or D2d point group. On the basis of the above four subsets, we analyzed the membership functions and the regularity of variation in MOs for the internal-rotation of propadine. 相似文献
6.
过渡金属络合物荷移光谱的研究 总被引:1,自引:0,他引:1
在配位场近似下,用不可约张量方法对具有O_4对称性的FeCl_6~(3-)及与其结构相似的过渡金属络合物的Hamilton矩阵进行了矩阵分割,得到了一种计算荷移光谱的简单方法.在计算中采用方案,考虑了纯组态内部的Coulomb作用和旋轨作用,忽略了不同组态间的Coulomb作用.并采取冻结轨道近似.计算结果与实验光谱数据符合较好. 相似文献
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The conventional symmetry numbers σ_≠~' of activated complexes may lead to error in the rate constant expression of transition state theory, whereas the statistical factor ι~≠ or ι may violate the principle of detailed balance. A mathematically precise definition of the symmetry number σ_≠ of activated complex is given, i.e. σ_≠=_iN_4(?)/m, m is the number of physically distinct configurations of labelled transition state and N_i is the identical atoms in the activated complex. The identical atoms must belong to the same molecule of reactants and products. The present symmetry numbers σ_≠ of activated complexes assure not only obtaining correct rate constant expressions but also obeying the principle of detailed balance. It can be used with the statistical factor ι to construct the structures of transition states for unimolecular and bimolecular exchange reactions. 相似文献
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Orbital Correspondence Analysis in Maximum Symmetry (OCAMS) is applied to the decomposition pathways of formaldehyde to H2 + CO and to H + HCO. The symmetry adapted nuclear motions, which are preferentially incorporated in the energetically favoured fragmentation pathways on both the ground and excited state surfaces are singled out. The results of this analysis are in full agreement with those of published potential energy surfaces and consistent with the results of experimental investigations reported in the literature. The nuclear motions favouring the various processes thus appear to be deducible from considerations of orbital symmetry.This work was carried out during tenure of a Minerva Foundation grant to one of us. (E.A.H.) 相似文献
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Prof. Dr. Long‐Li Lai Sheng‐Wei Wang Dr. Kung‐Lung Cheng Dr. Jey‐Jau Lee Tsai‐Hui Wang Prof. Dr. Hsiu‐Fu Hsu 《Chemistry (Weinheim an der Bergstrasse, Germany)》2012,18(48):15361-15367
Two triazine‐based unconventional dendrimers were prepared and characterized by 1H and 13C NMR spectroscopy, mass spectrometry, and elemental analysis. Differential scanning calorimetry, polarizing microscopy, and powder XRD studies showed that these dendrimers display columnar liquid‐crystalline phases during thermal treatment. This is ascribable to breaking of their C2 symmetry. The molecular conformations of prepared dendrimers were obtained by computer simulation with the MM3 model of the CaChe program in the gas phase. The simulation showed that the conformations of the prepared dendrimers are rather flat and disfavor formation of the LC phase. However, due to C2‐symmetry breaking, the prepared dendrimers have structural isomers in the solid state and thus show the desired columnar phases. This new strategy should be applicable to other types of unconventional dendrimers with rigid frameworks. 相似文献
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The molecule with T_h symmetry is rare. A novel C60-like molecule C48O12 with rare Th symmetry has been studied at the B3LYP/6-31G(d) level of theory. Its structural, electronic, vibrational, NMR, and thermodynamic properties have been calculated at the B3LYP/6-31G(d) level of theory. Vibrational modes have been assigned according to their symmetry. There are 73 independent vibrational modes: 22 IR-active modes with T u symmetry and 37 Raman-active modes with Ag , Eg and Tg symmetry, respectively. The heat of formation has been calculated by using isodesmic reactions, 765.7 kJ mol-1 . According to the heat of formation and the HOMO-LUMO gap, C48O12 with rare Th symmetry is more stable than C60 . 相似文献
12.
Summary A novel approach of space symmetry adaptation is developed for multiconfigurational (MC) functions in fully optimized reaction space and complete active space SCF calculations. The bonded tableau and two box symmetric tableau are basic representations (rep) of configuration functions; the group symmetric localized orbitals are used as one-electron orbitals. The method is proposed for generating a complete and orthonormal set of MC single excited functions. The redundant variable in MCSCF can be eliminated by symmetry adaptation. 相似文献
13.
Dr. Adi Salomon Shaojun Wang Dr. James A. Hutchison Dr. Cyriaque Genet Prof. Thomas W. Ebbesen 《Chemphyschem》2013,14(9):1882-1886
The strong coupling of porphyrin J‐aggregates to plasmonic nanostructures of different symmetry is investigated. The nanostructures of higher symmetry show the strongest interaction with the molecular layer, suggesting that surface plasmon mode degeneracy plays an important role in the coupling efficiency. At high coupling strengths a new, weakly dispersive mode appears which has recently been predicted theoretically to be due to long‐range energy transfer between molecules mediated by surface plasmons. These findings point to new ways for optimizing strong coupling and thereby realize its full potential for molecular and material science. 相似文献
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A computer adapted vector method and Euler angle transformation procedures are used to generate the relationship between the atomic orbitals of icosahedral C60 Buckminsterfullerene cluster and to produce symmetry adapted molecular orbitals and vibrational species. The atomic overlaps based on the orientational relationship of the orbitals are used to compute the approximate molecular orbital energies and normalization constants. One of the vibrations of Au, symmetry is used to interpret the isomeric (dyotropic) rearrangement that breaks and forms two bonds to change two pentagons to two hexagons and vice versa. 相似文献
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1 INTRODUCTIONWith the invention of lasers[1] and the observation of second-harmonic generation in quartz[2], nonlinear optics(NLO), as a cornerstone of photonics, has been booming since 1960's. And intense interest has been aroused to search materials exhibiting appropriate nonlinear optical properties suitable for the construction of practical optical devices for the important techniques such as frequency converting, signal processing and optical computing[3~6]. In order to determine … 相似文献
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一般来说,点群理论认为M(o)bius带环分子最高的对称性只能是C2.本文讨论了由18个苯环组成的环并苯的异构体分子,包括柱面的Hückel型分子(HC-[18])和扭转180°的M(o)bius带环分子(MC-[18]).结果表明除了点对称性外,M(o)bius带环分子还存在一种可称为环面螺旋旋转(TSR)变换的对称性,为此还引用了环面正交曲线坐标系.此外,还讨论了这些分子关于TSR对称性匹配的原子集和原子轨道(AO)集.根据TSR对称性的循环群特征,可以建立此类群的不可约表示及有关特征标.这类分子的分子轨道(MO)关于TSR群的不可约表示是纯的,然而所含的相应的原子轨道对称性匹配的线性组合(SALC-AO)成分可以是多种的. 相似文献
17.
Mirror Symmetry Breaking by Chirality Synchronisation in Liquids and Liquid Crystals of Achiral Molecules
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Spontaneous mirror symmetry breaking is an efficient way to obtain homogeneously chiral agents, pharmaceutical ingredients and materials. It is also in the focus of the discussion around the emergence of uniform chirality in biological systems. Tremendous progress has been made by symmetry breaking during crystallisation from supercooled melts or supersaturates solutions and by self‐assembly on solid surfaces and in other highly ordered structures. However, recent observations of spontaneous mirror symmetry breaking in liquids and liquid crystals indicate that it is not limited to the well‐ordered solid state. Herein, progress in the understanding of a new dynamic mode of symmetry breaking, based on chirality synchronisation of transiently chiral molecules in isotropic liquids and in bicontinuous cubic, columnar, smectic and nematic liquid crystalline phases is discussed. This process leads to spontaneous deracemisation in the liquid state under thermodynamic control, giving rise to long‐term stable symmetry‐broken fluids, even at high temperatures. These fluids form conglomerates that are capable of extraordinary strong chirality amplification, eventually leading to homochirality and providing a new view on the discussion of emergence of uniform chirality in prebiotic systems. 相似文献
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RuXIA YuChuanZHANG YouMinYI ShiWeiSHI QunYANG QiangYU 《中国化学快报》2004,15(5):555-558
In this paper, a polymer spherical symmetry GRIN sphere lens were prepared by the suspension-diffusion-copolymerization(SDC) technique, selecting methyl methacrylate(MMA) as monomer M1 and acrylic 2,2,2-trifluoroethyl ester(3FEA) as M2. The radial distribution of refractive index of the lens was measured by the shearing interference method, which demonstrated that the quadratic refractive-index distribution was formed in the sphere lens, and its △ n=0.019. 相似文献
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