具有辛群对称性的一类价激发n电子波函数的性质和应用

讨论了具有辛群对称性的一类价激发n电子波函数 ψ_(a,s_1,s_2)=N(multiply from t=s_1 to s_1+s_2-1)(a_1+(a_t))(multiply from k=s_1+s_2 to s_1+s_2+m-1)G+(ζ,k,V_(s+1))|0>的性质,它们对闭壳层和开壳层体系均适用.用此类函数计算了Li_2,LiH_2~-和CH_3~+,结果表明这类函数能较好地描述电子相关作用,并且变分得到的轨道都是自然轨道。     

The Wave Function with Symplectic Symmetry and Its Application

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.     

几种多步辛演化法的对比

提出了一种新的确定多步量子时间演化辛算法系数的方法，并比较了现有的三种确定系数的方法。发现对于三步辛算法，这里提出的方法在小时间隔下更精确，而文献中从对称性出发确定的数的稳定性区间更宽。     

Analogy between real irreducible tensor operator and molecular two-particle operator

. 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     

Symmetry measures of the electron density

In this communication we define electronic symmetry operation and symmetry group measures, eSOM and eSGM, respectively, develop the basic algorithms to obtain them, and give some examples of the possible applications of these new computational tools. These new symmetry measures based on the electron density have been tested in an analysis of (a) the inversion symmetry for heteronuclear diatomic molecules, for the eclipsed and staggered conformations of ethane and tetrafluoroethane, and for a series of octahedral sulfur halides; (b) the reflection symmetry of three different conformers of tetrafluoroethene; and (c) the loss of C₆ symmetry along the B_2u distortion mode of benzene and an analysis of rotational symmetry for different six‐member ring heterocycles. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010     

On the Role of Symmetry in Vibrational Strong Coupling: The Case of Charge-Transfer Complexation

It is well known that symmetry plays a key role in chemical reactivity. Here we explore its role in vibrational strong coupling (VSC) for a charge-transfer (CT) complexation reaction. By studying the trimethylated-benzene–I₂ CT complex, we find that VSC induces large changes in the equilibrium constant K_DA of the CT complex, reflecting modifications in the ΔG° value of the reaction. Furthermore, by tuning the microfluidic cavity modes to the different IR vibrations of the trimethylated benzene, ΔG° either increases or decreases depending only on the symmetry of the normal mode that is coupled. This result reveals the critical role of symmetry in VSC and, in turn, provides an explanation for why the magnitude of chemical changes induced by VSC are much greater than the Rabi splitting, that is, the energy perturbation caused by VSC. These findings further confirm that VSC is powerful and versatile tool for the molecular sciences.     

Symmetry and selection rules in the Raman spectra of carbon nanotubes

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.     

丙二烯分子的模糊对称性

利用作者提出的探讨分子及其轨道模糊对称性的方法分析了丙二烯在内旋转过程中模糊对称性特征. 考虑到此过程中经历不同状态所属的对称点群, 即D2h、D2d与D2. 利用包含这些点群中所有元素的最小点群D4h进行分析. 将D4h中的元素分为四组: (i) G0——包含在D2点群中的元素, 也是所有上述点群中都存在的元素; (ii) G1——包含在D2h点群中, 但不包含在D2d点群中的元素; (iii) G2——包含在D2d点群中, 但不包含在D2h点群中的元素; (iv) G3——包含在D4h点群中, 但不包含在D2h与D2d点群中的元素. 分别分析在内旋转过程中各个分子轨道(MO)相应每一组元素的隶属函数的共性变化规律性.     

约化密度矩阵中的N表示问题

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.     

Fuzzy Symmetry Characteristics of Propadine Molecule

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 D_2h, D_2d, and D₂ were considered. Using the D_4h point group, which is the minimal point group including all symmetry elements of D_2h, D_2d, and D₂, we can analyze the fuzzy symmetry for this process. The elements included in D_4h 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 D_2h, D_2d, and D₂; (ii) G1—it includes the elements in D_2h point group, but not in D_2d point group; (iii) G2—it includes the elements in D_2d point group, but not in D_2h point group; (iv) G3—it includes the elements in D_4h point group, but not in D_2h or D_2d 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.     

过渡金属络合物荷移光谱的研究

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.     

VRML在分子对称性教学中的应用

以椅式环己烷为例,介绍了如何应用分子模拟软件制作含有分子对称元素的VRML模型的过程。利用VRML的交互性可以帮助学生直观地掌握分子的三维结构以及对称元素的分布,切实提高了分子对称性的教学效果。     

POV-Ray软件在分子对称性中的应用

以交错式乙烷为例,详细地介绍了如何使用POV-Ray软件制作展示分子对称元素的精美视频动画,可以帮助学生直观形象地分析分子结构,很好地掌握分子对称性的相关教学内容,切实提高课程的教学效果。     

Symmetry Numbers of Activated Complexes

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.     

Symmetry analysis of the potential energy surfaces for the photochemical decomposition of formaldehyde

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.)     

f3组态离子在四角场中的基矢矩阵元

通过选用与群链[(O⊃D₄⊃C₄)×SU(2)]相匹配的单电子基矢,使其直积构成多电子fN体系的O⊃D₄⊃C₄旋量群的不可约表示的基矢,并讨论了有关的Coulomb矩阵元、Casimir矩阵元、旋-轨偶合矩阵元和晶体场作用矩阵元.     

Cr3+离子配合物电子结构和d-d 跃迁谱的研究

建议了一种采用考虑重叠修正项的多重散射Ｘα自治场方法，结合不可约张量方法求解过渡金属配合物价电子体系多电子Ｓｃｈｒｏｄｉｎｇｅｒ方程的方法，并将其应用到Ｃｒ＾３＋配合物光谱的计算，其计算结果与实验结果的方均根偏差仅１．５ｋｃｍ＾－１，同时分析了Ｘα方法中重叠修正项对配合物电子结构以及光谱计算结果的影响，以及选用的组态对计算结果的影响。